The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.
What are real solutions of an equation?A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.
How many real solutions does the discriminant have?When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.
So that we can find real solution of quadratic equation by finding discriminant of given equation.
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Select the correct answer. Which graph represents the solutions to this equation? x2 + 8x = -20 A. Linear-quadratic system graph shows upward parabola with vertex at (minus 2, 4) and passing through x and y-axis (minus 8, 0), and (0, 0) B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8) C. Linear-quadratic system graph shows upward parabola with vertex at (4, 0) and passing through (1, 4), and (6, 4) D. Linear-quadratic system graph shows a downward parabola with vertex at (0, 8) which intercepts the x-axis at 3 and minus 3 units.
A graph which represents the solutions to this equation x² + 8x = -20 include the following: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).
What are quadratic functions?In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.
Next, we would re-write the given quadratic function in standard form by equating it to zero (0) as follows;
x² + 8x = -20
Adding 20 to both sides of the linear-quadratic equation, we have the following:
x² + 8x + 20 = -20 + 20
x² + 8x + 20 = 0
In this scenario, we would use an online graphing calculator to plot the graph of the given quadratic function and then determine the point of intersection and vertex.
y = x² + 8x + 20
By critically observing the graph of the given quadratic function, we can logically deduce that the solutions and vertex are as follows;
x = -6, y = 8.
x = -2, y = 8.
Vertex = (-4, 4).
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A certain map shows two roads. Road A is 1 1/5 miles long but is 1 4/5 inches on the map. What is the unit rate for inches per mile on the map. If road B is 2 miles long, how long is road B on the map ?
The length of the map would be 3 inches.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: length of the road as 6/5 miles and on the map 9/5 inches and thus 1 mile = 1.5 inches and therefore the length of the 2 mile road on the map is 2×1.5=3 inches
Hence, The length of the map would be 3 inches.
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What is a shape with 1 trillion sides called?
A shape with 1 trillion sides is called a teragon. A teragon is a polygon that has an infinite number of sides, the most famous example of teragon is the Koch snowflake.
Typically, a teragon will be bounded by one or more self-similar fractal curves, which are formed by replacing each line segment in an initial figure with multiple interconnected parts, then substituting each of those parts with the same pattern of segments, then repeating the process an infinite number of times for every line segment in the figure.
Another example of a teragon is the horned triangle which is formed by pitching a series of smaller triangles on one corner of an equilateral triangle. It is also an example of a reptile, or shape that can be completely examined into smaller copies of itself.
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When graphing the function on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function
The most appropriate viewing window for determining the domain and range of a function when graphing it on a graphing calculator would depend on the specific function and what information you are trying to gain from the graph.
DETERMINING THE DOMAIN AND RANGE OF THE FUNCTIONWhen graphing a function, it is important to set the viewing window correctly so that the full behavior of the function is visible. The domain of a function is the set of all input values for which the function is defined. The range of a function is the set of all output values that the function can produce. To determine the domain and range of a function from its graph, you need to be able to see all of the points where the function is defined, as well as any asymptotes or singularities.
To set the appropriate viewing window, you should start with a wide window that includes the x- and y-values where the function is defined. For example, if the function is defined for all real numbers, you would want to set the x-min and x-max to a large negative and positive number respectively, and y-min and y-max to a large negative and positive number respectively. This will ensure that all of the function's behavior is visible on the graph.
Once you have a general idea of the function's behavior, you can adjust the viewing window as needed.
Also, it is a good idea to check the graph for symmetry or periodicity, which can help to narrow down the domain or range. For example, if the graph is symmetric about the y-axis, you know that the domain includes all real numbers. If the graph is periodic, you know that the domain includes all real numbers and the range is limited.
By adjusting the viewing window and looking for symmetry or periodicity, you should be able to determine the domain and range of the function from its graph.
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Last week, the price of a gallon of gasoline was `g` dollars.
This week, the price of gasoline per gallon increased by `5\%`.
Select all of the expressions that represent this week's price of gasoline per gallon. Select all that apply
g+0.05
g+0.05g
1.05g
0.05g
(1+0.05) g
The expressions that represent this week's price of gasoline per gallon =g+0.05g.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, we have,
the price of a gallon of gasoline was `g` dollars.
the price of gasoline per gallon increased by `5%`.
So, the expressions that represent this week's price of gasoline per gallon
=g + g*5%
=g+0.05g
Hence, the expressions that represent this week's price of gasoline per gallon =g+0.05g.
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Cameron worked as a salesperson at an electronics store and sells phones and phone accessories. Cameron earns a $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells. On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold.
The number of phones sold is 26 and the number of accessories sold is 30.
What is a Linear equation:An equation is said to be linear if the maximum power of the variable is usually 1. A linear equation with one variable has the standard form Ax + B = 0. In this case, x is the variable and A is the coefficient of x, and B is a constant.
In mathematical problems, 'x' stands for unknown value or quantity. Here we use the Linear equation concept to solve the problem.
Given that
Cameron earns an $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells.
On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold.
Let x and y be the number of phones and accessories
Given that
Cameron made a total of $361 in commission
=> 11x + 2.5y = 361 ----- (1)
Total number of phones and accessories sold
=> x + y = 56
Multiply by 11
=> 11x + 11y = 616 ----- (2)
Do (2) - (1)
=> 11x + 11y - ( 11x + 2.5y) = 616 - 361
=> 11x + 11y - 11x - 2.5y = 255
=> 8.5y = 255
=> y = 255/8.5
=> y = 30
Substitute y = 30 in x + y = 56
=> x + 30 = 56
=> x = 26
Therefore,
The number of phones sold is 26 and the number of accessories sold is 30.
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Khalil buy 8 pound of apple for $12. 0. He want to know and ue the unit rate of cot per pound True or Fale: Uing the unit rate of the cot per pound, do 5 pound of apple cot $7. 50?
False. Using the unit rate of cost per pound, 5 pounds of apples cost $6.00.
Cost per pound = $12.00 / 8 pounds = $1.50
5 pounds of apples cost = 5 pounds x $1.50 = $7.50
The unit rate of cost per pound can be calculated by dividing the total cost of 8 pounds of apples by the total number of pounds. In this case, the unit rate of cost per pound is $1.50. This means that for every pound of apples, the cost is $1.50. To calculate the cost of 5 pounds of apples, we need to multiply the unit rate of cost per pound by the number of pounds. In this case, 5 pounds of apples cost $7.50, which is calculated by multiplying $1.50 by 5. Therefore, the statement that using the unit rate of cost per pound, 5 pounds of apples cost $7.50 is false.
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Need Help! How would I complete this table?
The number of feet is dependent on the number of yards. The table is completed as shown in the attachment.
Dependent variable.A variable whose value can be determined only if another variable's value is known is called a dependent variable. Thus the value of the variable depends on another variable.
In the given question, the number of feet can be known when that of yards is multiplied by a multiplicative factor. The value of the factor can be determined as;
multiplicative factor = 15/ 5
= 3
So that feet is related to that of yards by this expression;
feet = multiplicative factor * yards
Thus,
when yards is 2, then;
feet = 3 * 2
= 6
when feet = 12
12 = 3 * yards
yards = 12/ 3
= 4
Thus the complete table is herewith attached to this answer for more clarifications.
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4382 round 1 significant figure
Answer:
4382 contains 4 significant figures, 4382 round to 1 significant figure is 4000.
Can u please help? .
Answer:
y = -3x -27
Step-by-step explanation:
Parallel lines have the same slope. So the slope will be -3
We need to solve for the y-intercept. Us the x and y values from the point (-6,-9) to find the y-intercept
m = -3 given
y = -9 from the point( -6,-9)
x = -6 from the point (-6,-9)
y = mx + b substitute in what you know and solve for b
-9 = (-3) (-6) + b
-9 = 18 + b Subtract 18 from both sides
-9 -18 = 18 - 18 +b
-27 = b
The equation of the line is y = -3x -27
How do u solve this?
Answer: [tex]3x^4 / 2y^4[/tex]
Step-by-step explanation: [tex](3x7x^6y^5)divide(2x7x^2y^9)[/tex] then [tex]x^6 divided by x^2 = x(^6 ^- ^2) = x^4[/tex] then
[tex]y^5 divided by y^9 = y(^5 ^- ^9) = y(^-^4) = 1/y^4[/tex] then
Canceling out 7 as it appears on both sides of the fraction line.
Hope this is clear and is helpful
in macy's department store, every item has a 30% discount or markdown. If the original price of a pair of Adidas sneakers cost $140, how much would the final price of the sneaker be after the discount is taken off
$98 is the final price of the sneaker be after the discount is taken off
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that in macy's department store, every item has a 30% discount or markdown.
The original price of a pair of Adidas sneakers cost $140
We need to find the final price of the sneaker be after the discount is taken off
Let us find 30% of 140
Convert 30% to decimal value by dividing with 100
30/100×140
0.3×140=42
So 30% of 140 is 42.
After removing discount the amount will be 140-42=98
Hence, $98 is the final price of the sneaker be after the discount is taken off
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A boat heading out to sea starts out at Point AA, at a horizontal distance of 862 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 15^{\circ}
∘
. At some later time, the crew measures the angle of elevation from point BB to be 8^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary
The distance from point A to point B is 781.5 ft.
Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,
tan(15°) = x / 862
Solve for x.
x = 862 (tan(15°))
Similarly, let y be the distance from point B to the lighthouse,
tan(8°) = x / y
Solve for y.
tan(8°) = 862 (tan(15°)) / y
y = 862 (tan(15°)) / tan(8°)
y = 1643.45 feet
Subtract 862 from 1643.45 to get the distance from point A to point B.
distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft
Therefore, the distance from point A to point B is 781.5 ft.
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Pls help
(3 x 8 x 5)⁷
To evaluate (3 x 8 x 5)⁷, you need to first multiply 3, 8, and 5 together to get the base, then raise that result to the seventh power.
What does a math exponent mean?
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
So,
(3 x 8 x 5)⁷ = (120)⁷ = 120 x 120 x 120 x 120 x 120 x 120 x 120
= (1.2 x 10^2)^7 = 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2
=1.2^7 x 10^14 = 1.2^7 x 10^14
=4096 x 10^14
=4.096 x 10^17
Therefore (3 x 8 x 5)⁷ = 4.096 x 10^17
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Katie plans to paint four toy chests that have the given net. She will buy 10-oz cans of paint that cover 933 square inches each
Two cans of paint are needed to cover the toy chest of 1866 in²
Area:
The area is the amount of space occupied by a two-dimensional object or figure. Area (A) of the rectangle is:
A = length * breadth.
Area of A = 13 * 16 = 208 in²
Area of B = 13 * 25 = 325 in²
Area of C = 25 * 16 = 400 in²
Area of D = 13 * 25 = 325 in²
Area of E = 13 * 16 = 208 in²
Area of F = 25 * 16 = 400 in²
1) Combined Area = 208 + 208 = 416 in²
2) Combined Area = 325 + 325 = 650 in²
3) Combined Area = 400 + 400 = 800 in²
4) Combined Area = 416 + 650 + 800 = 1866 in²
5) Amount of paint = 1866 in² / 933 in² = 2
Therefore, Two cans of paint are needed to cover the toy chest of 1866 in²
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1. y=-1
y = 2x - 7
Hello, and I am confused on this question I was wondering if anyone could help!
Who created 4 steps in problem solving?
The 4 steps methods of problem solving is an approach that is agreed upon by many experts in different fields and developed over time, The answer is it is not attributed to any individual creator.
What is problem solving?Mathematical exercises with the potential to present intellectual challenges for advancing pupils' mathematical learning and growth are referred to as "problem solving." The three primary components of problem-solving are recognizing the issue, considering potential solutions, and selecting the best course of action.
What are four steps in problem solving?The 4 steps in problem solving, also known as the "scientific method" or the "4-step problem solving model" is a widely recognized method for solving problems that is used in many fields including science, engineering, and business. The four steps are: (1) Identifying the problem, (2) Gathering information, (3) Developing solutions, and (4) Implementing the solution.
It is not attributed to any individual creator, but an approach that is agreed upon by many experts in different fields and developed over time.
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20PTS 20PTS-Find the perpendicular line
Answer:
y = 3x - 2
Step-by-step explanation:
See the attached worksheet. Look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept. The slope of the line can be determined by taking two points on the line to calculate the Rise/Run. The points selected for this example are (0,-2) and (2,4). This makes the Rise/Run (6/2), or 3. The y-intercept, b, is -2 as per point (0,-2).
The equation for this (non)-prependicular line is thus y = 3x - 2.
What are angles 2 and 8 called?
The Angle 2 and angle 8 in the given figure are called as the alternate interior angle and they are equal .
What are Alternate Interior Angles ?
The alternate interior angles are defined as the angles that are formed when a transversal intersects the two coplanar lines.
The alternate interior angles lie on inner side of parallel lines but they are on the opposite sides of the transversal.
So , From the figure we can conclude that the angle 2 , angle 8 and angle 3 and angle 5 are the alternate interior angles .
Therefore , the angle 2 and 8 are alternate interior angles.
The given question is incomplete , the complete question is
What are the angles 2 and 8 called in the given figure ?
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I need help on this question. I dont understand it.
a. The system of equations is given as follows:
35x = 15 + 32x.
The solution is given as follows:
x = 5.
b. The meaning of the solution is that the cost to purchase 5 jackets in each company is the same.
c. Gabriela should choose Anastasia's Monogram, as the function has a lower numeric value when x = 10.
How to model the situation?The cost per jacket for each company is constant, hence a linear function is used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the cost paid per each jacket.b is the y-intercept, representing the design fee, which is a one-time payment.Hence the functions for each company are given as follows:
Anastasias's Monograms: y = 15 + 32x.Monograms Unlimited: y = 35x.The system of equations is used to find when both will have the same cost, as follows:
35x = 32x + 15
3x = 15
x = 5 jackets.
For 10 jackets, the costs are given as follows:
Anastasias's Monograms: y = 15 + 32(10) = $335 -> lower cost.Monograms Unlimited: y = 35(10) = $350.More can be learned about linear functions at https://brainly.com/question/24808124
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You can read 12 pages of a book in 15 minutes.
How many hours will it take you to read a 312-page book?
It will take you 6.5 hours to read a 312-page book
How many hours will it take you to read a 312-page book?From the question, we have the following parameters that can be used in our computation:
Rate = 12 pages of a book in 15 minutes
This means that
Rate = 12 pages/15 minutes
Convert to per hour
Rate = 12 pages/0.25 hour
Evaluate
Rate = 48 pages per hour
For a 312-page book, we have
Time = 312 pages/48 pages per hour
Evaluate
Time = 6.5 hours
Hence, the time is 6.5 hours
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Mia went shopping for a new pair of pants because of a sale. The price on the tag was $34, but Mia paid $27.20 before tax. Find the percent discount.
Answer:
There was a discount of 20% on the pair of pants.
Step-by-step explanation:
10% of $34 would be $3.40 meaning 20% would be double, which is $6.80.
If we subtract 20% or $6.80 from the original price $34, we get 34 - 6.80 = 27.20
75 Points!
A linear relationship is shown in the table.
Time (hours) 2 4 6 8
Distance (miles) 4 8 12 16
Is the linear relationship also proportional? Explain.
A. No, the constant of proportionality is 2.
B. Yes, the constant of proportionality is 2.
C. No, there is no constant of proportionality.
D. Yes, there is no constant of proportionality.
Answer:
B. Yes, the constant of proportionality is 2.
Step-by-step explanation:
Given:
A linear relationship is shown in the table.
Time (hours) 2 4 6 8
Distance (miles) 4 8 12 16
Is the linear relationship also proportional? Explain.
A. No, the constant of proportionality is 2.
B. Yes, the constant of proportionality is 2.
C. No, there is no constant of proportionality.
D. Yes, there is no constant of proportionality.
Solve:
To know if a linear relationship is proportional, all we have to find out is if after we divide distance by time and if all equal the same. Ex: 4/4=1,3/3=1. As we can see all are equal to 1.
Let's see the table:
Time (hours) Distance (miles)
2 4
4 8
6 12
8 16
The formula for it is 'k=y/x'
where;
k: constant of proportionality
y and x are two quantities that are directly proportional to each other.
Also means;
y = Distance
x = Time(Hours)
Time (hours) Distance (miles)
2 4 4/2=2
4 8 8/4=2
6 12 12/6=2
8 16 16/8=2
As you see all equal to 2. It a constant. Also means that;
Yes, the linear relationship is proportional and the constant of proportionality is 2.
Answer: B. Yes, the constant of proportionality is 2.
RevyBreeze
what is the quotient of 6x^3+2x-x/x where x≠0
Answer:
6[tex]x^{2}[/tex] + 1
Step-by-step explanation:
[tex]\frac{6x^{3}+ 2x-x }{x}[/tex] combine 2x -x = x
[tex]\frac{6x^{3} + x}{x}[/tex]
[tex]\frac{x(6x^{2} + 1) }{x}[/tex] the x's cancel out
6[tex]x^{2}[/tex] + 1
giving brainliest to the best answer
If two even integers are multiplied, then the product is also even. Hypothesis: Two even integers are multiplied. Hypothesis starts after the word "if". Conclusion starts after the word "then".
How do you identify a hypothesis and conclusion?The sentence that comes just after the word "if" in a conditional statement is known as the hypothesis. The sentence that comes after the word then in a conditional statement is the conclusion.
If you earn high grades, the portion that follows the "if" is referred to as a hypothesis, and if you get good grades, the part that follows the "then" is referred to as a conclusion.
An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.
p → q
Read this: if p, then q.
If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue.
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If two even integers are multiplied, then the product is also even. Hypothesis: Two even integers are multiplied. Hypothesis starts after the word "if". Conclusion starts after the word "then".
How do you identify a hypothesis and conclusion?The sentence that comes just after the word "if" in a conditional statement is known as the hypothesis. The sentence that comes after the word then in a conditional statement is the conclusion.
If you earn high grades, the portion that follows the "if" is referred to as a hypothesis, and if you get good grades, the part that follows the "then" is referred to as a conclusion.
An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.
p → q
Read this: if p, then q.
If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue.
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helppp me pleaseee i really need it
23310
Step-by-step explanation:
I actually calculated it aka 259000×9%
How would I do this?
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{28p^5-8p^4 + 40p^2}{4p^3}\implies \cfrac{28p^5}{4p^3}-\cfrac{8p^4 }{4p^3}+\cfrac{ 40p^2}{4p^3}\implies 7p^5 p^{-3}-2p^4 p^{-3}+10p^2p^{-3} \\\\\\ 7p^{5-3}-2p^{4-3}+10p^{2-3}\implies 7p^2-2p+10p^{-1}\implies 7p^2-2p+\cfrac{10}{p}[/tex]
Please help me with either 2 or 3, which ever one you would rather do.
Answer:
send the picture clearly i will help uou surely
Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for T.
2.5 cm
2 cm
cubic centimeters.
What is undecidable language?
Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
Describe an algorithm.Algorithms exist to identify, solve, and frequently automate a solution to a particular problem; regardless of the situation, they are essentially problem solvers of expression.
In area of beginning textbooks, algorithms are typically introduced as "a set of phases to solve a problem."
Here,
Alternatively, a Turing computer that halts for all inputs cannot recognize a language for whose membership cannot be determined by an algorithm.
It is known as undecidable language.
There is no Turing Machine for an undecidable language that accepts the language and decides on each input string (TM can make decision for some input string though).
When the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
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