To find the product, we need to first factor the numerators and denominators of both fractions:
x^2 + 9x + 20 = (x + 5)(x + 4)
x^2 - x - 12 = (x - 4)(x + 3)
x^2 + 3x - 4 = (x + 4)(x - 1)
Substituting these into the expression, we get:
[(x + 5)(x + 4)/(x + 3)] * [(x - 4)(x + 3)/(x + 4)(x - 1)]
Now, we can simplify the product by cancelling out common factors:
[(x + 5) * 1/(x - 1)] * [(x - 4) * 1/1]
= (x + 5)(x - 4)/(x - 1)
So the product in simplest form is (x + 5)(x - 4)/(x - 1).
However, there is a restriction on the variable because the expression involves division by (x + 3), (x - 1), and (x - 4). Therefore, x cannot be equal to -3, 1, or 4, since these values would make the denominators zero and the expression undefined.
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According to the figure showing 2020 GDP for selected countries, how much larger (in percentage terms) is America's GDP than:
According to the figure showing 2020 GDP for selected countries, America’s GDP is 21.43% which is 7.19% larger than China’s GDP which is 14.24%.
A country's economic output is measured by its gross domestic product (GDP). GDP is estimated by totaling all the commodities and services produced in a nation within a predetermined time frame, typically a year. In 2020, America’s GDP was 21.43% of the total GDP of selected countries. This is 7.19% larger than China’s GDP which was 14.24% of the total GDP of selected countries.
We must use exchange rates to convert GDPs to a common currency in order to compare GDPs across nations. Once the GDPs are expressed in a similar currency, we can compare the GDP per capita of each nation by dividing the GDP by the population. Large GDPs are common in countries with big populations, although GDP is not always a reliable measure of a country's wealth. GDP per capita is a better metric.
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Complete question is:
According to the figure showing 2020 GDP for selected countries, how much larger (in percentage terms) is America's GDP than:
The G D Ps are as follow: United states, 21.43; China, 14.24; Japan, 5.08; Germany, 3.86; India, 3.87; Great Britain, 2.83; Russia, 1.70; Mexico, 1.27; Sweden, 0.53; Greece, 0.21; Haiti, 0.08.
Round your responses to the nearest whole number.
1. Russia?
______ % larger
2. Germany?
______ % larger
A young boy is growing at a rate of 3.5 centimeters per month. He is currently 90 cm tall. At that rate,
how many months will it take him to grow to a height of 132 cm?
Write an equation to represent this situation. Then, use algebra to solve. Show all steps.
Answer:
H = 3.5m + 90
m = 12 months
Step-by-step explanation:
We can use a linear equation (H = 3.5m + 90), where H is the height in centimeters and m is month.
We can let H = 132 to solve for m:
[tex]132=3.5m+90\\42=3.5m\\12=m[/tex]
Thus, it will take the boy 12 months to reach 132 cm.
in an examination, 90 % of the students passed out of 600 students. how many candidates passed the exam?
Answer:
Step-by-step explanation:
[tex]90 \% \text{ of }600=\frac{90}{100}\times600[/tex]
[tex]=90 \times 6[/tex]
[tex]=540[/tex]
So 540 students passed the exam.
Describe the shape of the dot plot. Are the dots evenly distributed or grouped on one
side?
The dot plot has a bell shape. The dots are more heavily clustered around the central point, with fewer dots on the ends.
What is heavily clustered?Heavily clustered refers to a situation when a large number of items, such as data points, are grouped together in a dense area. This can be seen in many forms of data visualisation, such as scatterplots, where items are represented in a graph and appear close together in a particular area. In some cases, the items can be so densely packed that they appear to form a single unit. Heavily clustered data can be used to identify areas of high concentration, or to identify trends or correlations.
This indicates that the data is normally distributed and that there is a higher probability of the data points falling around the central point. The dots are not evenly distributed, but rather grouped on one side.
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Zach bought 200 shares of Goshen stock years ago for $21. 35 per share. He sold all 200 shares today for $43 per share. What was his gross capital gain?
B. $ 8,600
C. $ 4,000
A. $4,270
D. $4,330
The gross capital gain is option (D) $4330
Gross capital gain is the total amount of profit that an investor makes when they sell an asset, such as stocks, real estate, or other investments, for a higher price than the purchase price.
Zach's gross capital gain is the difference between the selling price and the purchase price of the shares.
Purchase price of 200 shares = 200 x $21.35 = $4,270
Selling price of 200 shares = 200 x $43 = $8,600
Therefore, the gross capital gain is
= $8,600 - $4,270
Subtract the numbers
= $4,330
Therefore, the correct option is (D) $4,330.
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Jessica kicks a football. Its height in feet is given by h(t) = -16t^2+80t where h is the height and t is the time, in seconds, after the football is kicked. Graph the equation from t=0 to t=5 seconds. Be sure to include the vertex in your graph and table.
State the coordinates of the vertex and explain its meaning in the context of the problem.
The point is where the vertex is situated [tex](2.5, 100)[/tex].
What in math is a vertex?A vertex, which is a unique point on a mathematical object, is often where 2 or more lines or edges come together. The shapes that include vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are sometimes called nodes.
Vertex and parabola definitions.A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola which equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.
To graph the equation [tex]h(t) = -16t^2 + 80t[/tex] from [tex]t=0[/tex] to [tex]t=5[/tex] seconds, we can create a table of values by plugging in values of t and calculating the corresponding values of [tex]h(t)[/tex]:
t h(t)
0 0
1 64
2 128
3 144
4 128
5 80
To find the vertex, we can use the formula [tex]t = -b/(2a)[/tex], where [tex]a = -16[/tex] and [tex]b = 80[/tex].
[tex]t = -b/(2a) = -80/(2(-16)) = 2.5[/tex]
So the vertex occurs at [tex]t = 2.5[/tex] seconds.
Now we can plot the points from the table and graph the equation,
Graph of [tex]h(t)=-16t^2+80t[/tex] from [tex]t=0[/tex] to [tex]t=5[/tex] seconds
The vertex is located at the point [tex](2.5, 100)[/tex].
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The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2
Using proportions, the real height of the telephone mast is estimated to be 9 meters.
What exactly is a proportion?A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.
The following proportional relationship is established as a result:
x / 1.5 cm = 10.8 cm / 1.8 cm.
The relationship's left side can be simplified as follows:
6 = x / 1.5 cm.
The estimate is then calculated using cross multiplication, as shown below:
6 x 1.5 cm = 9.5 cm².
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a cyclist rides her bike at a speed of 21 kilometers per hour. what is this speed in kilometers per minute? how many kilometers will the cyclist travel in 2 minutes? (do not round the answer)
Answer:
see the answer and explanation in the attached figure below
Step-by-step explanation:
The bus depart by 8:30 because they want to start by 9:30. What time will the bus arrive at the beach if the bus ride takes 35 minutes?
The bus will arrive at the beach by 9:05 am. To calculate the arrival time of the bus, we need to add the travel time to the departure time.
First, we need to convert the departure time of 8:30 am to minutes.
8:30 am = 8 x 60 + 30 = 510 minutesThen, we add the travel time of 35 minutes to the departure time:
510 + 35 = 545 minutesFinally, we convert the arrival time back to hours and minutes:
545 ÷ 60 = 9 with a remainder of 5So the bus will arrive at 9:05 am.
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For this problem, determine whether the following sets of vectors spanR3, and feel free to use Octave for your calculations. (a)⎩⎨⎧100,021,103⎭⎬⎫(b)⎩⎨⎧110,300⎭⎬⎫(c)⎩⎨⎧101,310,−100,215⎭⎬⎫
The vectors in set (c) span R3.Answer: (a) The vectors span R3, (b) The vectors do not span R3, (c) The vectors span R3.
To solve this problem, you need to determine if the given sets of vectors spanR3 or not. You may use Octave for your calculations.Here are the sets of vectors: (a) S1 = { [1; 0; 0], [0; 2; 1], [1; 0; 3] }(b) S2 = { [1; 1; 0], [3; 0; 0] }(c) S3 = { [1; 0; 1], [3; 1; 0], [-1; 0; 0], [2; 1; 5] }To determine whether the vectors in the given sets span R3, you can place the vectors in a matrix as column vectors and compute the rank of the matrix. If the rank is 3, then the vectors span R3. Otherwise, they do not.
(a) S1 = { [1; 0; 0], [0; 2; 1], [1; 0; 3] }R1 = [1 0 1; 0 2 0; 0 1 3]rank(R1) = 3The rank of R1 is 3, so the vectors in set (a) span R3.
(b) S2 = { [1; 1; 0], [3; 0; 0] }R2 = [1 3; 1 0; 0 0]rank(R2) = 2The rank of R2 is 2, so the vectors in set (b) do not span R3.
(c) S3 = { [1; 0; 1], [3; 1; 0], [-1; 0; 0], [2; 1; 5] }R3 = [1 3 -1 2; 0 1 0 1; 1 0 0 5]rank(R3) = 3The rank of R3 is 3, so the vectors in set (c) span R3.Answer: (a) The vectors span R3, (b) The vectors do not span R3, (c) The vectors span R3.
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F= (y + 2x, 2x + 5z, 7y + 8x), C is the circle with radius 5, cen- ter at (2,0,0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0,0,0).
The set of points that represent the intersection of the curve of vector function F and circle C is
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t ranges from 0 to 2π}.
We have,
Vector function F = (y + 2x, 2x + 5z, 7y + 8x)
C is the circle with radius 5, center at (2,0,0), in the plane x = 2
C is oriented counterclockwise as viewed from the origin (0,0,0)
The vector function F represents a three-dimensional curve in space.
The circle C is a two-dimensional object in space, lying in the plane x = 2 and centered at (2,0,0) with a radius of 5. It is also oriented counterclockwise as viewed from the origin (0,0,0).
To find the intersection of vector function curve F and circle C, we can substitute the equation of the circle into the equation of the curve and solve for the parameter(s) that satisfy the equation. However, since the equation of the circle is given in terms of x only, we can simplify the equation of the curve by substituting y = 0 and z = 0:
F = (2x, 2x, 8x)
Now, we can substitute x = 2 + 5cos(t) and y = 5sin(t) (the parameterization of the circle C in the plane x = 2) into the equation of the curve F:
F = (2(2+5cos(t)), 2(2+5cos(t)), 8(2+5cos(t)))
= (4+10cos(t), 4+10cos(t), 16+40cos(t))
Thus, the intersection of vector function curve F and circle C is given by the set of points:
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t in [0, 2π)}
Note- that the parameter t represents the angle of rotation around circle C, and ranges from 0 to 2π to cover the entire circle.
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In the past 5 years company A sold 7.5x10^4 reams of paper. Company B sold 9.5 x10^3 reams. How many total reams did they sell altogether and how many more did company a sell than B?
Giving 20 pts please help!
84500 reams of paper are the total amount the two companies sell in the past five years.
65500 is the amount that Company B performed better than company A.
What is a Company?A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.
The Amount that is made by company A is
[tex]7.5 \times 10000[/tex]
[tex]=75000[/tex]
The amount of paper manufactured by company B is
[tex]= 9.5 \times 1000[/tex]
[tex]= 9500[/tex]
A) The total that is made by both companies in 5 years will be
[tex]= \text{Company A + Company B}[/tex]
[tex]= 75000 + 95000[/tex]
[tex]= 84500[/tex]
B) Company B made better products as compared to Company A
[tex]= \text{Company B - Company A}[/tex]
[tex]=75000 - 9500[/tex]
[tex]=65500[/tex]
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Answer:
total: 84,500 or 8.45×10⁴difference: 65,500 or 6.55×10⁴Step-by-step explanation:
You want the sum and difference of 7.5×10^4 and 9.5×10^3.
Scientific notationNumbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...
9.5×10^3 = 0.95×10^4
total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500
difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500
__
Additional comment
You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.
Geometry Altitudes Questions
The value for the height h of the right triangle is equal to 4.8990.
How to evaluate for the value of h for the triangleThe height h of the right triangle divides the triangle in two triangles with the same proportions as the original triangle, which implies that if the adjacent for the smallest triangle is 4 and the adjacent of the other triangle is h, then:
h/6 = 4/h {considering the tangent ratio}
h² = 4 × 6 {cross multiplication}
h = √24
h = 4.8990
Therefore, value for the height h of the right triangle is equal to 4.8990.
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Solve for a. Round to the nearest tenth of a degree, if necessary..
Answer: x=
२०
83
92
M
L
Submit Answer
attempt 1 out of 2
The value of angle x rounded to the nearest tenth of a degree is 53.6°.
How can trigonometric ratios be used to find the angle in a right triangle?
Trigonometric ratios are used to relate the sides of a right triangle to its angles. In a right triangle, one of the angles is always 90 degrees, which is the right angle. The three primary trigonometric ratios are sine, cosine, and tangent, which are defined as follows:
Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
To find the value of an angle in a right triangle, we can use the inverse trigonometric functions, also known as arc functions or anti trigonometric functions. These functions are denoted as [tex]sin^{-1}[/tex], [tex]cos^{-1}[/tex] , and [tex]tan^{-1}[/tex] , and they are used to find the angle whose trigonometric ratio is known.
Finding the value of x :
We can use the trigonometric ratio of sine to solve for x.
sin(x) = opposite/hypotenuse = MN/LN
[tex]sin(x) = 83/92[/tex]
Taking the inverse sine of both sides:
[tex]x = sin^{-1}(83/92)[/tex]
Using a calculator, we get:
[tex]x \approx 53.6^{o}[/tex]
Therefore, the value of x rounded to the nearest tenth of a degree is 53.6°.
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determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39oc and a wet bulb temperature of 18oc.
The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.
To determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39°C and a wet bulb temperature of 18°C, you can use a psychometric chart or a specialized software program that calculates these properties based on the given dry bulb and wet bulb temperatures, as well as other relevant parameters such as pressure, altitude, and air composition.
First, plot 39°C (the dry bulk temperature) and 18°C (the wet bulb temperature) on the chart. Then mark The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.
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Deon needs to read novels each month.
Let N be the number of novels Deon needs to read in M months.
Write an equation relating N to M. Then graph your equation using the axes below.
Equation can also be used to calculate how many novels Deon needs to read in a certain amount of months. For example, if the number of months is 4, then Deon needs to read 8 novels.
What is equation?An equation is a statement that expresses the relationship between two or more mathematical expressions. It is typically written in the form of an equality, such as "2x + 3 = 7", where "2x + 3" is the left-hand side and "7" is the right-hand side. Equations are used to model real-world problems and can be solved to determine the value of the unknowns within the equation.
The equation above shows that the number of novels Deon needs to read in a certain amount of months is twice the number of months. This can be graphically represented by a straight line, with a slope of 2, that passes through the origin on the graph. The graph below illustrates this equation. The x-axis represents the number of months (M) and the y-axis represents the number of novels (N). As the number of months increases, the number of novels Deon needs to read also increases, at a rate of 2 novels per month.
This equation can also be used to calculate how many novels Deon needs to read in a certain amount of months. For example, if the number of months is 4, then Deon needs to read 8 novels.
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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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the height of a diver above the water, is given by , where is time measured in seconds and is measured in meters. select all statements that are true about the situation. a. the diver begins 5 meters above the water. b. the diver begins 3 meters above the water. c. the function has 1 zero that makes sense in this situation. d. the function has 2 zeros that make sense in this situation. e. the graph that represents starts at the origin and curves upward. f. the diver begins at the same height as the water level.
Statement (b) and (c) are true about the situation.
Define the term measurement ?Using standardized instruments or units, measurements are the process of figuring out the size, quantity, or degree of anything.
Using the given function, h(t) = -5t^2 + 10t + 3, we can determine the true statements about the situation:
a. False: The diver begins at h(0) = 3 meters above the water, not 5 meters.
b. True: The diver begins at h(0) = 3 meters above the water.
c. True: The function has one zero that makes sense.
To find it, we set h(t) = 0 and solve for t: -5t² + 10t + 3 = 0
Using the quadratic formula, we find that: t ≈ 2.161
This means that the diver reaches a height of zero after 2.161 seconds.
d. False: As we found in part (c), the function has only one zero.
e. False: The graph of the function does not start at the origin.
f. False: The diver begins at 3 meters above the water, not at the same height as the water level.
Therefore, statement (b) and (c) are true about the situation.
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Complete question-
The cat population in catonsville has been recorded since 2010. The population. p. can be represented by the equation p = 1600(2)t where is time in years since the begging of 2010. What was that cat population 2007
A. 4000
B. 200
C. 800
D. 100
The cat population in Catonsville in 2007 was 200. The answer is option B.
What is population?Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.
According to question:We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.
From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:
[tex]p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200[/tex]
Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.
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Suppose the point (3, 6) is on the graph of y = f(x) What point does it transform to y = - f * (x) - 3 ?
4. Find the solution of the following equations:
a) x + 5 = 15
b) 12 – y = 12
c) 3a = 27
d) y/4 = 20
e) 2 + y = 0
Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
20x8 =
The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.
What is the simplified form of the given expression?It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.
On this note, since the given expression is; √20x⁸.
We have that; = √ (4 × 5 × x⁸)
Therefore, since 4 and x⁸ are perfect squares; it follows that we have;
= 2x⁴ √5.
Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.
Complete question; The correct expression is; √20x⁸.
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dr carl is a mathematics and statistics lecturer. he is interested in studying a new approach at teaching mathematics and statistics in high school. recently this new approach has been adopted. it was previously the case that the mean score for all high school students doing their end of year exam was 71, however, the population standard deviation is unknown. the scores of all students are approximately normally distributed. he thinks that, with this new teaching approach, the mean score may have increased. a random sample of 39 scores is gathered and the sample mean and standard deviation calculated. dr carl will conduct a hypothesis test using a level of significance of 0.01. select the correct null and alternative hypotheses for this test:
The test is one-tailed to the right due to the Alternate hypothesis.
In a hypothesis test, a Null hypothesis (H0) is a statement of "no effect" or "no difference," whereas the Alternate hypothesis (HA) is a statement of "some effect" or "some difference." Here are the correct null and alternative hypotheses for the given scenario: Null hypothesis: H0: μ = 71, Alternative hypothesis: HA: μ > 71 (One-tailed test) we have a one-tailed hypothesis test since the research hypothesis is directed. In a one-tailed test, we're looking for a difference in one direction only. In this case, Dr Carl thinks that there has been an improvement, so the alternative hypothesis reflects this. Therefore, the test is one-tailed to the right.
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Determine the horizontal component of reaction at A Express your answer in pounds to three significant figures. Enter positive value if the force is exerted in the positive direction and negative value of the force is exerted in the negative direction.
We have that, finding the horizontal component of the reaction at A in pounds, it is 866.03 pounds, with zero horizontal component in the negative direction.
How to determine the horizontal component?To determine the horizontal component of the reaction at A, we first need to draw a free-body diagram of the given structure. So, we can use the equation of equilibrium for the horizontal direction to find the horizontal component of the reaction at A. The equation of equilibrium for the horizontal direction is as follows:
∑Fx=0∑Fx=0
Equilibrium equation for the horizontal direction, where ∑Fx is the sum of all forces acting horizontally in the positive direction and in the negative direction. Let's draw the free body diagram of the given structure: Here, RAY is the horizontal component of the reaction at A. We can see that there is no force acting horizontally in the negative direction.
Therefore,∑Fx=RAx∑Fx=RAx
Now, we need to find the force that acts horizontally in the positive direction. In the free body diagram, we can see that:
∑Fx=1000cos30°=866.03∑Fx=1000cos30°=866.03
Therefore
∑Fx=RAx=866.03RAx=866.03
So the horizontal component of the reaction at A is 866.03 pounds. Therefore, the answer is 866.03 (positive).
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Solve the following system of equations using the method of substitution: 3x+2x=11 y=x+3
The solution to the system of equations 3x+2x=11 , y=x+3 is (x, y) = (1, 4) using the method of substitution.
To solve the system of equations using the method of substitution, we first need to solve for one variable in terms of the other in one of the equations. In this case, we can solve for y in terms of x in the second equation:
y = x + 3
We can then substitute this expression for y in the first equation:
3x + 2(x + 3) = 11
Simplifying the equation by distributing the 2:
3x + 2x + 6 = 11
Combining like terms:
5x + 6 = 11
Subtracting 6 from both sides:
5x = 5
Dividing both sides by 5:
x = 1
Now that we know the value of x, we can substitute it back into the second equation to find the value of y:
y = x + 3 = 1 + 3 = 4
In conclusion, the method of substitution involves solving one equation for one variable and substituting the resulting expression into the other equation.
By doing this, we can eliminate one variable and solve for the other. In this case, we solved for y in terms of x, substituted this expression for y in the first equation, and solved for x. Then, we substituted the value of x back into the second equation to solve for y.
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(a) Factorise 25t²₋ 4
(b) Factorise x²₋6x₋3xy₊18y
Step-by-step explanation:
(a) To factorize 25t² - 4, we can use the difference of squares formula:
a² - b² = (a + b)(a - b)
In this case, a = 5t and b = 2. So we have:
25t² - 4 = (5t + 2)(5t - 2)
Therefore, 25t² - 4 can be factorized as (5t + 2)(5t - 2).
(b) To factorize x² - 6x - 3xy + 18y, we can group the terms:
(x² - 3xy) - (6x - 18y)
We can then factor out the common factors from each group:
x(x - 3y) - 6(x - 3y)
Notice that both terms have a factor of (x - 3y), so we can factor it out:
(x - 3y)(x - 6)
Therefore, x² - 6x - 3xy + 18y can be factorized as (x - 3y)(x - 6).
(a)
.
in this case, a= 25t and b= 4.
.
ans: (5t-4)(5t+4)
Rina is climbing a mountain. She has not
yet reached base camp. Write an inequality
to show the remaining distance, d, in feet
she must climb to reach the peak.
The distance she must climb to reach the peak is greater than 2,663 feet. An inequality to show the remaining distance, d, in feet she must climb to reach the peak is d > 2,663.
Inequlity represents a relationship between two values that is not equal. That is inequlity means no equal and the symbols which used for not equal is ≠ and for comparison are < , > , ≤ , ≥. For example, ax > b etc. We have, Rina is climbing a mountain and mountain height present in above figure. See the figure carefully, the main two points in figure are the following: height of mountain peak
= 12,358 feet
height of base camp = 9,695 feet
we have to write an inequality for the remaining distance, d, in feet. Also, it is specified that she has not reached base camp yet. So, his climbed distance is less than 9,695 feet. Let the remaining distance be 'd feet '. From the above figures, d + base camp height > 12,358
Substract 9695 from both sides
=> d > 12,358 - 9,695
=> d > 2,663
Hence, required inequalty is d > 2,663.
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Complete question:
Rina is climbing a mountain. She has not yet reached base camp. Write an inequality to show the remaining distance, d, in feet she must climb to reach the peak. See tha above figure.
When solving the equation 3(x-2)=-12, what is a possible first step?
A) Distributing the 3 into each term of the parenthesis.
B) She could either divide by 3 or distribute 3 into the parenthesis
C) Adding 2 to each side of the equation
D) Subtracting 2 on each side of the equation
E) Dividing each side of the equation by 3
F) none of the answer choices tell what the first step could be.
A landscaper needs to mix a 80% pesticide solution with 35 gal of a 30% pesticide solution to obtain a 55% pesticide solution. How many gallons of the 80%
solution must he use?
By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.
What is equation?In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
Let's say a landscaper needs to use x gallons of an 80% pesticide solution.
The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.
After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.
Since we need a 55% pesticide solution, we can set the following formula:
[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]
Therefore, landscapers should use 35 gallons of an 80% pesticide solution.
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i am a parallelogram with a longer sides 15 cm each and a shorter sides 8m each my perimeter is
Answer:
Step-by-step explanation:
= 2(15+8)
=2(23)
=46