10.
Evaluate the function rule for the given value. f(x) = 3^x for x = –5

A. 1/243
B. –15
C. 1/729
D. –125

Answer:

so ill tell you how to get the answer, okay?

Step-by-step explanation:

well, it's a right triangle so you use the formula for a rectangle and cut everything in half and what you have at the end is your answer. hope this helps somewhat. :-)

Answer:

the answer is 4√3

The length of the shortest side is 30 centimeters.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

Let the angles of the triangle be A, B, and C with side lengths a, b, and c, respectively. We know that the sum of the angles of a triangle is 180 degrees. So, we can find the third angle by subtracting the sum of the given angles from 180:

C = 180 - (59 + 63) = 58 degrees

Now, we can use the Law of Cosines to find the length of the shortest side, a:

a² = b² + c² - 2bc cos(A)

We know that A is the angle opposite the side with length 28 cm, so A = 58 degrees. We also know that B is the angle opposite the unknown side, so B = 180 - (A + C) = 63 degrees.

Substituting the given values into the Law of Cosines, we get:

a² = b² + c² - 2bc cos(A)

a² = b² + 28² - 2b(28) cos(58)

a² = b² + 784 - 56b cos(58)

The sum of the angles of a triangle is 180 degrees to find B in terms of A:

B = 180 - (A + C) = 180 - (58 + 59) = 63 degrees

Substituting B = 63 degrees into the Law of Cosines, we get:

b² = a² + c² - 2ac cos(B)

b² = a² + 28² - 2a(28) cos(63)

b² = a² + 784 - 56a cos(63)

a² = b² + 784 - 56b cos(58)      ....(i)

b² = a² + 784 - 56a cos(63)      ....(ii)  

Subtracting the second equation from the first, we get:

a² - b² = -56b cos(58) + 56a cos(63)

Rearranging and factoring, we get:

(a + b)(a - b) = 56(cos(63)a - cos(58)b)

We can solve for a - b by dividing both sides by a + b:

a - b = 56(cos(63)a - cos(58)b) / (a + b)

Substituting a = 28 (the length of the longest side) and cos(63) and cos(58), we get:

a - b = 3.864

Now, we can use the fact that a + b + c = 180 to solve for b:

a + b + c = 180

28 + b + 59 + 63 = 180

b = 30

Therefore, the length of the shortest side is b = 30 centimeters.

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Answer:

The single transformation that takes shape 'p' onto shape 'q' is a dilation by a scale factor of 3 with the center point (1, 0)

Step-by-step explanation:

The coordinates of the vertices of shape ΔP are;

A(2, 3), B(2, 1), C(3, 1)

The length AB = 3 - 1 = 2

The length CB = 3 - 2 = 1

∴ The length AC = √(2² + 1²) = √5

The coordinates of the vertices of shape ΔQ are;

A'(4, 9), B'(4, 3), C'(7, 3)

The length A'B' = 9 - 3 = 6

The length C'B' = 7 - 3 = 3

∴ The length A'C' = √(6² + 3²) = √(45) = 3·√5

∴ Figure Q ΔA'B'C' is a dilation of figure P ΔABC by a scale factor of A'B'/AB = 6/2 = 3

The distance of point B(2, 1) from the point (1, 0) = √((2 - 1)² + 1²) = √2

The distance of point B'(4, 3) from the point (1, 0) = √((4 - 1)² + 3²) = 3·√2

Therefore, the distances of points on figure Q from (1, 0) = 3 × the distances of points on figure from (1, 0)

Therefore, figure 'Q' can be obtained from figure 'P' by a dilation of figure 'P' by a scale factor of 3 with the center of dilation at point (1, 0).

Answer:

h  n ijnf j n2r4h njiw32

Step-by-step explanation:

The two possible locations of the point C are (1, 1) and (- 2, - 5).

According to the statement, we find the coordinates of the ends of a line segment and a partition ratio. There are two possible solutions concening the location of the point B:

Thus, we have the corresponding expressions for each case:

Case 1

C(x, y) = A(x, y) + (4 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 7) + (4 / 5) · [(2, 3) - (- 3, - 7)]

C(x, y) = (- 3, - 7) + (4 / 5) · (5, 10)

C(x, y) = (- 3, - 7) + (4, 8)

C(x, y) = (1, 1)

Case 2

C(x, y) = A(x, y) + (1 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 7) + (1 / 5) · [(2, 3) - (- 3, - 7)]

C(x, y) = (- 3, - 7) + (1 / 5) · (5, 10)

C(x, y) = (- 3, - 7) + (1, 2)

C(x, y) = (- 2, - 5)

The two possible locations of the point C are (1, 1) and (- 2, - 5).

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Answer:

Step-by-step explanation:

8 pounds.... 4hours

x pounds.... 3 hours

x=3 ×8 :4

x=24 :4

x=6 pounds of trash

The number of pounds of trash should the volunteers pick up this month is 6.

Since  Last month, the volunteers picked up 8 pounds of trash in 4 hours. This month, the same group of volunteers will spend 3 hours picking up trash.

So here we can do

x=3 ×8 :4

x=24 :4

x=6

Hence, The number of pounds of trash should the volunteers pick up this month is 6.

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In summary, the redesigned equation of the path from entrance a affects the coordinates of the fountain by changing the coefficients of x and y in the equation. This change in coefficients results in a different slope for the path.

The redesigned equation of the path from entrance a affects the coordinates of the fountain by changing the values of x and y in the equation of the path.


The original equation of the path from entrance a is 3x + y = 5. To redesign the equation, we need to analyze the changes mentioned in the question: "path a ---- = path b - 2x + 5y8 wao entrance bc".

From this information, we can deduce that the new equation of the path from entrance a is given by: 3x + y = -2x + 5y + 8.

To understand how this redesigned equation affects the coordinates of the fountain, we can compare it to the original equation.

By rearranging the terms in both equations, we can see that the coefficients of x and y have changed. In the original equation, the coefficient of x is 3 and the coefficient of y is 1. However, in the redesigned equation, the coefficient of x is now -2 and the coefficient of y is 5.

These changes in the coefficients affect the slope of the path. The slope of the original equation is -3 (the coefficient of x divided by the coefficient of y), while the slope of the redesigned equation is -2/5.

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Given :

Calculators cost $12.99 each, rulers cost $0.49 each, pencils cost $0.10 each, and erasers  cost $0.05 each.

To Find :

How much would Mrs. Algebra's single order be.

Solution :

Total price paid by Mrs. Algebra = Price of pencil + price of ruler + price of calculator + price of eraser.

T = $(0.10 + 0.49 + 12.99 + 0.05)

T = $13.63

Therefore, Mrs. Algebra's single order cost is $13.63 .

Hence, this is the required solution.

Using the standard z table, a 95% confidence interval for p is (0.5327,0.6173).

In the given question,

A poll is taken in which 302 out of 525 randomly selected voters indicated their preference for a certain candidate.

We have to find a 95% confidence interval for p.

From the question, x=302, n=525

So estimation point,

P=x/n

P=302/525

P=0.575

Now the z value of 95% confidence interval is 1.960 using the standard z table.

Margin of Error (E)=z×√{P(1−P)}/n

Now putting the value

E=1.960×√{0.575(1−0.575)}/525

E=1.960×√(0.575×0.425)/525

E=1.960×√0.244/525

E=1.960×√0.000465

E=1.960×0.0216

E=0.0423

At 95% confidence interval for p is

P−E ≤ p ≤ P+E

Now putting the value

0.575−0.0423≤ p ≤0.575+0.0423

0.5327≤ p ≤0.6173

Hence, a 95% confidence interval for p is (0.5327,0.6173).

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The regression equation for the given sample observations is Y = 12.071 - 1.087X.

By analyzing the given sample observations, we can determine the regression equation that represents the relationship between the variables X and Y.

The regression equation is derived through statistical analysis and allows us to estimate the value of Y based on the given values of X. In this case, the regression equation is Y = 12.071 - 1.087X.

This equation indicates that for every unit increase in X, the value of Y decreases by 1.087 units.

To determine the regression equation, statistical techniques such as linear regression are applied to find the best-fitting line that represents the relationship between the variables.

The coefficients in the equation, 12.071 and -1.087, represent the intercept and slope of the line, respectively.

They provide insights into the relationship and can be used to make predictions or analyze the impact of changes in X on the value of Y.

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Answer:

23

Step-by-step explanation:

f(x) = 2x² + 5\(\sqrt{(x-2)}\)    where x = 3

f(x) = 2(3)² + 5\(\sqrt{(3-2)}\)

f(x) = 2(9) + 5(1)

f(x) = 18 + 5

f(x) = 23

The value of x such that the point is on the unit circle is x = 1/5.

We know that the point (x, √24/5) lies on the unit circle.

That means that the distance between the origin and that point must be 1 unit, then we can use the distance formula to find the value of x, it is:

distance = √( (x - 0)² + (√24/5 - 0)²)

And that distance is 1 unit, then we need to solve:

1 = √( (x - 0)² + (√24/5 - 0)²)

1 = √( (x )² + (√24/5)²)

1 = √( x² + 24/25)

1 = x² + 24/25

1 - 24/25 = x²

1/25 = x²

√(1/25) = x

1/5 = x

That is the value of x.

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The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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Answer:

The answer is the second one

Step-by-step explanation:

First you go and you order each answer into the correct categories until every one of them are ordered. If they dont fit correctly then you just go onto brainly and report someone elses answer for no reason. i hope this helped :D

Answer:

When measuring the return on an investment, the real interest

rate accounts for inflation, while the normal interest rate does not.

Step-by-step explanation:

The original Length is, 6500 m.

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We calculate the volume of the cuboid :

60 x 100 x 40 = 240000 cm^3

If every bag has 8000 cm^3 of grit, he will need 240000 : 8000 = 30 bags

Every bag cost £2.50, so he will need £2.50 x 30 = £75

Since he only has £70, he doesn't have enough money to buy the grit.

This is an example of a correlation between the two variables, where they tend to change together in a predictable way, but it does not necessarily imply causation.

This is an example of a correlation between the two variables. When two variables are correlated, they tend to change together in a predictable way. In other words, when one variable goes up, the other tends to go up as well, or when one variable goes down, the other tends to go down as well.

It's important to note that correlation does not necessarily imply causation. Just because two variables are correlated, it does not mean that one causes the other. There may be other factors that influence both variables, or the correlation may be coincidental. To establish causation, a more rigorous study design and analysis is required.

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Answer:

the smallest dimension = 100 ft

the largest dimension = 150 ft

Maximum Area = 15000 ft²

Step-by-step explanation:

let x represent length of one side and L represent length of adjacent side

so from the question

3x + 2L = 600

2L = 600 - 3x

L = (600 - 3x)/2

L = (600/2) - (3x/2)

L  = 300 - (3x/2)

now Area of rectangle = L × x

Area = (300 - (3x/2)) × x

Area = 300x - 3x²/2

now we differentiate with respect to x  and equate to 0 in other to find critical point

dA/dx ⇒ 300x/x - 3x²/x = 0

300 - 3x = 0

3x = 300

x = 300/3

x = 100

so we input value of x into our previous equation

Area = 300x - 3x²/2

= 300(100) - (3(100)²)/2

= 30000 - 15000

Area = 15000

also we input value of x in L = 300 - (3x/2)

L  = 300 - (3(100))/2)

L = 300 - 150

L = 150

Therefore

the smallest dimension = 100 ft

the largest dimension = 150 ft

Maximum Area = 15000 ft²

At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.

We can use the chain rule to find the derivative of y = sin(f(x^2)) with respect to x:

dy/dx = cos(f(x^2)) * d/dx[f(x^2)]

To find d/dx[f(x^2)], we can use the chain rule again:

d/dx[f(x^2)] = f'(x^2) * d/dx[x^2] = 2xf'(x^2)

So, putting it all together:

dy/dx = cos(f(x^2)) * 2xf'(x^2)

At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.

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Answer: Shorts

Step-by-step explanation:

1:7 =  4: (6+8+4+10) = 4:28

4 is  number of shorts

So 1:7 is for shorts.

Answer:

3(2x + 5)

Step-by-step explanation:

What numbers go into both 6 and 15? What number is the largest of those numbers? The answer to both questions is 3, therefore we factor out the 3 using the distributive property

Answer:

It is 3(2x+5)

Step-by-step explanation:

Hope you get it right

The Angles that satisfy the equation 10cosB + 11 = 3cosB + 9, to the nearest tenth degree are  134.5° and 225.5°.

The all angles that satisfy the equation 10cosB + 11 = 3cosB + 9, we can start by simplifying the equation:

10cosB + 11 = 3cosB + 9

Subtract 3cosB from both sides:

10cosB - 3cosB + 11 = 9

Combine like terms:

7cosB + 11 = 9

Subtract 11 from both sides:

7cosB = 9 - 11

7cosB = -2

Divide both sides by 7:

cosB = -2/7

Now, to find the angles that satisfy this equation, we can use the inverse cosine function (cos⁻¹) to find the angle whose cosine is equal to -2/7. However, note that the inverse cosine function provides a principal value between 0° and 180°, so we need to consider both positive and negative angles.

Using a calculator, we can find the principal angle whose cosine is -2/7:

cos⁻¹(-2/7) ≈ 134.47°

To find the negative angle, we can subtract the principal angle from 360°:

360° - 134.47° ≈ 225.53°

Therefore, the angles that satisfy the equation 10cosB + 11 = 3cosB + 9, to the nearest tenth degree, are approximately 134.5° and 225.5°.

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The number of customers he would have in the seventh week is 37.

The customers of Felix grow at a linear rate. A linear growth rate is when a value increases a constant rate. The customers would increase by 2 each week.

The linear equation that represents the number of customers in the seventh week:

Initial number of customers + [ rate of increase x (number of weeks - 1)]

25 + [2 x (7 - 1)]

25 + (2 x 6)

25 + 12 = 37

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The value of integral of \(1/((x^2-1)^{(3/2)})\) with respect to x is \(-1/(2(x^2-1))\) + C.

We need to use the substitution method for solving this integral. Put \(x = sec (\theta)\) Then \(dx = sec(\theta)tan(\theta) d(\theta), x^2 - 1 = sec^2(\theta) - 1 = tan^2(\theta)\)

The integral becomes:integral of \(1/((x^2-1)^(3/2)) dx= integral of 1/(tan^3(\theta)\).

\(sec(\theta)tan(\theta) d(\theta)= integral of sec^2(\theta)/ tan^3(\theta) d(\theta)\) Again put \(tan(\theta) = t\) Then \(sec^2\theta d\theta = dt\) The integral becomes:integral of \(1/((x^2-1)^{(3/2))} dx= integral of 1/t^3 dt\) Now the integral of\(1/t^3 ,-1/2t^2 + C\) (where C is the constant of integration)

Therefore, integral of \(1/((x^2-1)^{(3/2))} dx= -1/(2t^2) + C\) Substituting\(t = tan(\theta)\) we get: integral of \(1/((x^2-1)^{(3/2)}) dx= -1/(2tan^2\theta) + C\) Substituting \(x = sec(\theta)\) we get:integral of \(1/((x^2-1)^{(3/2)}) dx= -1/(2(x^2-1)) + C\) Therefore, the value of integral of \(1/((x^2-1)^{(3/2)})\) with respect to x is \(-1/(2(x^2-1)) + C\).

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