Answer: To find the gradient of a curve at a given point, we need to find the derivative of the function with respect to x and then evaluate it at the desired x-coordinate.
Given the function y = 3x^4 - 2x^2 + 5x - 2, we can find its derivative dy/dx as follows:
dy/dx = d/dx(3x^4) - d/dx(2x^2) + d/dx(5x) - d/dx(2)
Taking the derivative of each term:
dy/dx = 12x^3 - 4x + 5
Now, let's evaluate the derivative at the given points:
Point (0, -2):
Substituting x = 0 into the derivative:
dy/dx = 12(0)^3 - 4(0) + 5
dy/dx = 0 - 0 + 5
dy/dx = 5
Therefore, the gradient at (0, -2) is 5.
Point (1, 4):
Substituting x = 1 into the derivative:
dy/dx = 12(1)^3 - 4(1) + 5
dy/dx = 12 - 4 + 5
dy/dx = 13
Therefore, the gradient at (1, 4) is 13.
Calculate the unknown length, x, in the shape below.
If your answer is a decimal, give it to 1 d.p.
8
8 cm
area = 55 cm²
area=178.2 cm²
15 cm
The triangles are similar triangles. Then the value of 'x' will be 27 cm.
The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
From the above theorem, the equation is given as,
(x/15)² = 178.2 / 55
Simplify the equation, then we have
(x/15)² = 3.24
x/15 = 1.8
x = 27 cm
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What number is equal to 13 ones and 62 hundredths
Answer:13.6
Step-by-step explanation:
Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points. Which of the following equations can be used to determine how many points Patrick earned?
5 + 6 = 14 + y
6y + 5 = 14
5y + 6 = 14
5 + 6 + y = 14
The equation can be used to determine how many points Patrick earned is ;5 + 6 + y = 14.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points.
We can determine the direct answer by taking Billy and Kip's points and subtracting it from the total combined points.
That will give us 11, which means Patrick earned 3 points.
The equation we can use to represent this is ;5 + 6 + y = 14.
Factor completely, then place the answer in the proper location on the grid.
9x4 -225y8
The factored expressions of 9x⁴ - 225y⁸ is (3x² + 15y⁴)(3x² - 15y⁴)
How to factor the expressions completelyFrom the question, we have the following parameters that can be used in our computation:
9x⁴ - 225y⁸
²⁴
For the expression, we can apply the difference of two squares
Where
9x⁴ = (3x²)²
225y⁸ = (15y⁴)²
Using the above as a guide, we have the following:
9x⁴ - 225y⁸ = (3x²)² - (15y⁴)²
So, we have
9x⁴ - 225y⁸ = (3x² + 15y⁴)(3x² - 15y⁴)
Hence, the factored expressions is 9x⁴ - 225y⁸ = (3x² + 15y⁴)(3x² - 15y⁴)
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For the matrix D shown below, determine the value of the element d12. If the element is not defined, click the undefined button. D = [-3 -8 6 -4] Answer:
The calculated value of the element d₁₂ is -8
How to determine the value of the element d₁₂From the question, we have the following parameters that can be used in our computation:
The matrix D given as
D = [-3 -8 6 -4]
The element d₁₂ represents the element located at the first row and the second column
In this case, the element located at the first row and the second column is -8
Using the above as a guide, we have the following:
d₁₂ = -8
Hence, the value of the element d₁₂ is -8
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Expand & simplify.
23p - 3( 2k + 14p ) + 5( 6k - p )
Answer:
23p -6k - 42p + 30k - 5p
23p - 42p - 5p + 30k - 6k
23p - 47p + 24k
-24p + 24k
24(- p + k)
24( k - p)
Answer:
The answer is
60p + 24k
Step-by-step explanation:
1: Expand
=23p - 6k + 42p + 30k - 5p
step2: collect like terms
=42p + 23p - 5p - 6k + 30k
step 3: add/subtract them to get your answer
=60p + 24k
your answer☝
What is the quotient of the expression
O7a³ + ab + 3
O7a³ + ab - 3
O7a³ + 4ab+
+8
O7a³+4ab-8
28a b+4a²b²-12ab?
4ab
The quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).
How to find the quotientBy dividing each term of the numerator by 4ab:
(7a³ + ab + 3) / (7a³ + ab - 3) ÷ 4ab
= (7a³ / 4ab) + (ab / 4ab) + (3 / 4ab)
Simplifying each term individually:
= (7/4a²) + (1/4b) + (3/4ab)
Thus, the quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).
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(2x^2-9x-5) \div(x-5)
Answer:2x+1
Step-by-step explanation:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
A. Because it would simplify this equation.
PLS HELP MARKING AS BRAINLIST
Answer:
108 sq ft
Step-by-step explanation:
The formulas are given in the bottom right.
For the triangles*, the base = 8 ft. The height = 6 feet.
Area = (bh)/2.
Area = (8*6)/2 = (48)/2 = 24 sq ft.
There are two of those identical triangles. 24+24 = 48.
(*Another way to look at this is to say that the base = 8+8 = 16. Area = (bh)/2 = (16*6)/2 = 96/2 = 48. It doesn't matter, mathematically. I can't tell if they have tried to show this as 2 triangles or one.)
For the bottom rectangle, area = length x width = 6*10 = 60 sq ft.
Add them up! 24 + 24 + 60 = 108 sq ft.
PLEASE HELP ME ITS DUE TODAY!!!
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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A paint machine dispenses dye into paint cans to create different shades of paint. The
amount of dye dispensed into a can is known to have a normal distribution with a mean of 5
milliliters and a standard deviation of 0.4 milliliters. Find the dye amount that represents the
99th percentile of the distribution.
Select one:
O a. 4.1 milliliters
O b. 5.9 milliliters.
O c. 4.9 milliliters
O d. 5.1 milliliters
Answer:
b. 5.9 mL
Step-by-step explanation:
You want the value that represents the 99th percentile of a normal distribution with a mean of 5 mL and a standard deviation of 0.4 mL.
Inverse normalThe inverse of the normal CDF function is used to find the X value for a given area. Here, we want X such that P(x < X) = 0.99 for μ = 5 and σ = 0.4.
The attached calculator output shows that is about X = 5.9305. Rounded to 1 decimal place, the volume is ...
5.9 mL
<95141404393>
A right circular cylinder has a surface area of 112 π. If the height of the cylinder is 10, find the diameter of the base.
If the height of the cylinder is 10, the diameter of the base of the cylinder is 8 units.
A right circular cylinder has two congruent circular bases and a curved surface area. To find the diameter of the base, we need to first find the radius of the base.
Let's begin by using the given information to write an equation. The surface area of a cylinder is given by the formula:
Surface Area = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
We are given that the surface area of the cylinder is 112π and the height is 10. Substituting these values, we get:
112π = 2πr² + 2πr(10)
Simplifying the equation by dividing both sides by 2π, we get:
56 = r² + 10r
Now we have a quadratic equation in terms of r. We can solve this equation by using factoring, completing the square, or the quadratic formula. Let's use factoring:
r² + 10r - 56 = 0
(r + 14)(r - 4) = 0
The solutions are r = -14 and r = 4. Since the radius cannot be negative, the radius of the base is 4.
The diameter of the base is twice the radius, so the diameter is 8.
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Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
14√2
14
45
14√2
14√3
45
7√2 7√3
The legs of the big triangle are 14 units and the legs of the small triangle are 7√2 units
How to determine the lengths of the missing segmentsFrom the question, we have the following parameters that can be used in our computation:
The right triangles
The right triangles are special triangles with acute angles of 45 degrees
This means that the relationship between the legs and the hypotenuse of the triangles is
Hypotenuse = Leg√2
Leg = Hypotenuse/√2
Using the above as a guide, we have the following:
Leg = 14√2/√2
Leg = 14
i.e. the legs of the big triangle are 14 units
Leg = 14/√2
Leg = 7√2
i.e. the legs of the small triangle are 7√2 units
See attachment for the triangles
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Answer:
Step-by-step explanation:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
It would take 21 weeks for the population to surpass 16,000.
The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.
For the population to surpass 16,000, we can set up the following equation:
15,000 + 2500 sin(πt/52) = 16,000
Subtracting 15,000 from both sides, we get:
2500 sin(πt/52) = 1000
Dividing both sides by 2500, we get:
sin(πt/52) = 0.4
We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:
πt/52 = sin⁻¹(0.4)
Multiplying both sides by 52/π, we get:
t = (52/π) sin⁻¹(0.4)
Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.
t = (52/π) (0.4115)
t = 21.02
Therefore, it would take 21 weeks for the population to surpass 16,000.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. All sides of a rhombus are congruent, so if DK = 8, then KL = 8.
B. The diagonals of a rhombus are perpendicular to each other, so if angle KAL = 2x - 8, then we have:
2x - 8 = 90
2x = 98, so x = 49.
C. All sides of a rhombus are congruent, so if DM = 5y + 2 and DK = 3y + 6, then we have:
5y + 2 = 3y + 6
2y = 4, so y = 2, and KL = 5(2) + 2 = 12.
Write and solve an equation to find the value of x.
The value of x for each item is given as follows:
28. x = 5.
29. x = 3.44.
How to obtain the value of x in each item?For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:
16x = 10 x 8
16x = 80
x = 5.
For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:
10(x + 10) = 12(12 + 25)
10x + 100 = 444
10x = 344
x = 3.44.
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Help me please! Thanks
The identification of the polygon that are given in the diagram above would be =
Polygon 1 = Isosceles trapezoid
polygon 2 = parallelogram
polygon 3 = Rectangle
polygon 4 = Rhombus
polygon 5 = Square
polygon 6 = trapezoid
What are the properties of the polynomials given above?Isosceles trapezoid : This is the type that of polygon in which the the top and base are not equal in length, but they are parallel to each other.
Parallelogram : This is defined as the type of polygon that has two pairs of parallel sides.
Rectangle : This has two pairs of sides that are equal and opposite.
Rhombus: All the sides are equal in length with its opposite angles equal .
Square: All sides are equal in length but and all angles are equal to 90°.
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1. The Roth Family took out a $215,000 with a 15-year mortgage at an APR of 5.4%. The
monthly payment was $1,850. What will be their total interest charges after 15 years?
The total interest charges to the Roth Family, after 15 years, given the monthly payment would be $ 118, 000
How to find the total interest charges ?First, find the total amount paid over the 15 years by the Roth Family to be :
= Number of years x Monthly payment x Number of months per year
= 15 x 1, 850 x 12
= $ 333, 000
The total interest charges that the Roth Family paid would be :
= Total amount paid after 15 years - Total amount borrowed as mortgage
= 333, 000 - 215, 000
= $ 118, 000
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The exponential model A=433.4e^0.032t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 796 million.
The population of the country will be 796 million in
(Round to the nearest year as needed.)
The population of the country will be 796 million approximately in the year 2022.
To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:
[tex]A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}[/tex]
Divide both sides by 433.4:
[tex]e^{(0.032t)} = 1.836[/tex]
Take the natural logarithm of both sides:
[tex]ln(e^{(0.032t)}) = ln(1.836)[/tex]
0.032t = 0.605
Divide both sides by 0.032:
t = 18.91
Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:
2003 + 19 = 2022
Therefore, the population of the country will be 796 million approximately in the year 2022.
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On Saturday, a local hamburger shop sold a combined total of 234 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
78
Step-by-step explanation:
Let the number of hamburgers sold = x.
Then, the number of cheeseburgers sold = 2x.
Total number of sales: x + 2x = 3x
Total number of sales: 234
3x = 234
x = 78
Answer: 78
Need Help ASAP. Thank you in advance :)
The value of x, considering the vertical angles in this problem, is given as follows:
x = 11.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles for this problem are given as follows:
(x + 7)º.(2x - 4)º.As the vertical angles are congruent, the value of x is obtained as follows:
2x - 4 = x + 7
x = 11.
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least common denominator of -3/a and 1/4a^2
Answer:
-12a-1/4a2
Step-by-step explanation:
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Lines y and z are parallel.
Parallel lines are cut by transversals s and t. The angles formed by lines s, t, and y, clockwise from top left, are blank, blank, (10 x + 5) degrees, blank, (4 x minus 7) degrees, blank; formed by s and z are 65 degrees, 1, blank, blank; formed by z and t are 2, blank, blank, blank.
What is the measure of angle 2?
6 degrees
11 degrees
28 degrees
37 degrees
The measure of Angle 2 is 17 degrees.
The measure of angle 2, the relationships between the given angles formed by the parallel lines and transversals.
1. The angles formed by lines s, t, and y, clockwise from top left, are:
- Blank
- Blank
- (10x + 5) degrees
- Blank
- (4x - 7) degrees
- Blank
2. The angles formed by s and z are:
- 65 degrees
- 1
- Blank
- Blank
3. The angles formed by z and t are:
- 2
- Blank
- Blank
- Blank
From the given information, we can deduce the following:
- Angle 1 is congruent to the angle formed by z and t (corresponding angles).
- Angle (10x + 5) degrees is congruent to angle 65 degrees (alternate interior angles).
- Angle (4x - 7) degrees is congruent to angle 2 (alternate interior angles).
Therefore, we can set up the following equations:
65 = 10x + 5 (Equation 1)
2 = 4x - 7 (Equation 2)
Solving Equation 1:
65 - 5 = 10x
60 = 10x
x = 6
Substituting x = 6 into Equation 2:
2 = 4(6) - 7
2 = 24 - 7
2 = 17
Hence, the measure of angle 2 is 17 degrees.
Therefore, the correct answer is:Angle 2 = 17 degrees.
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1/5 ( x - 10 ) = 4/5
The value of x is 14
What are fractions?Fractions are described as expression that shows the part of a whole number, a whole variable. a whole element.
The different types of fractions are listed as;
Improper fractionsProper fractionsMixed fractionsSimple fractionsComplex fractionsFrom the information given, we have that;
1/5 ( x - 10 ) = 4/5
This is written as;
(x -10)/5 = 4/5
cross multiply the values, we have;
5(x-10) = 20
expand the bracket
5x - 50 = 20
Collect like terms
5x = 70
Divide the values
x =14
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Currently it is estimated that 3 out of every 1000 Californians are infected with
coronavirus. The so-called rapid "antigen" test for coronavirus has a very low false
positive rate of just 0.05, but has a high false negative rate of 0.2. The so-called
PCR test is more reliable: it has an even lower false positive rate than the antigen
test, namely only 0.001, but even more importantly its false negative rate is much
lower at 0.01.
What is the probability that you have a coronavirus infection conditional on your
PCR test has coming back positive?
The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.
We have,
To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.
Now,
Prevalence of coronavirus in California: 3 out of 1000
False positive rate of the antigen test: 0.05 (5 out of 100)
Let's calculate the probability of a positive test result.
The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):
True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)
The probability of a positive test result can be calculated using Bayes' theorem:
P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)
P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)
P(Positive test) = 0.0024 + 0.04985
P(Positive test) = 0.05225
Therefore,
The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.
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please help me with this math question with solutions please
2×+4=4!
Answer: x= 10
Step-by-step explanation:
2x+4=24
2x=24-4
2x=20
x=10
Answer:
Step-by-step explanation:
2x+4=4
subtract 4 from both sides
2x=0
divide by 2 on both sides
x=0
Copy and complete the pattern in the table
The pattern in the table should be completed as follows;
Number of 1 3 9 27 81
students with pets
Total number 3 9 27 81 243
of students
A ratio that compares the number of blue squares to the total number of squares is 3 : 4.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would find the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/1 = 9/3
Constant of proportionality, k = 3.
y = 3x
81 = 3x
x = 27
x = 9/3
x = 3
y = 3(81)
y = 243
For the ratio of blue squares to total squares, we have:
18/24 = 3/4 = 3 : 4
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Solve the inequality for y.
-3>9-6y
Simplify your answer as much as possible.
Answer:
y > 2
Step-by-step explanation:
You want the solution to the inequality ...
-3 > 9 -6y
SolutionWe can add 6y+3 to both sides. This gives ...
6y > 12
Dividing by 6 tells us the solution for y:
y > 2
__
Additional comment
We could have solved by subtracting 9 to get ...
-12 > -6y
Then dividing by -6 reverses the inequality symbol:
2 < y
We avoid the issue with negative number multiplication or division by making the y-term positive in our solution process.
<95141404393>