7 X 12 x= [?] Round to the nearest tenth.​

Shift 4 units right, reflect over the y-axis, shift 2 units down is the transformation applied.

The parent function f(x) = 2x is transformed to g(x) = (2x-2)⁻²

To determine the transformations applied to f(x), we can work from the inside out, starting with the expression 2x-2:

Shift 2 units to the right: This can be achieved by replacing x with (x-2).

This gives us the expression 2(x-2) = 2x-4.

Reflect over the y-axis: This can be achieved by replacing x with (-x).

This gives us the expression 2(-x)-4 = -2x-4.

Square and take the reciprocal: This can be achieved by applying the transformation f(x) -> 1/f(x)².

This gives us the expression (-1/2x-4)².

Therefore, the transformations applied to f(x) are shift 2 units to the right, reflect over the y-axis, and square and take the reciprocal.

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The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).

We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.

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The complete factorization of the original expression is:

4x² (x + 1)²

We have,

First, we can factor out 4x².

4x² (x² + 2x + 1)

Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:

4x² (x + 1)²

Thus,

The complete factorization of the original expression is:

4x² (x + 1)²

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According to the given sample data, and assuming a sample standard deviation of 5 hours, the results of the hypothesis test suggest that there is substantial evidence to support the assertion that the average time spent using the internet by Canadians exceeds 12.5 hours.

To conduct the hypothesis test, we first set the null and alternative hypotheses. The null hypothesis (H0) states that the mean time spent by Canadians on the internet is equal to or less than 12.5 hours. The alternative hypothesis (Ha) states that the mean time spent by Canadians on the internet is greater than 12.5 hours.

Using the given sample data, and assuming a sample standard deviation of 5 hours, we calculate the test statistic and the p-value. To calculate the test statistic, we use the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

We find that the test statistic is 1.78 (rounded to two decimal places). If the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is strong evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.

If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean time spent using the internet by Canadians is greater than 12.5 hours.

In this case, assuming a significance level of 0.05, we calculate the p-value to be 0.0397 (rounded to four decimal places). Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is substantial evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.

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After considering the given options we come to the conclusion that the answer is 112 in² which is Option B.

The lateral surface area of a square pyramid is the summation of the areas of the side faces only, on the other hand

surface area = lateral area + area of the base.

The lateral area of a square pyramid = 2al (or) 2a√ [ (a 2 /4) + h² ].

Now, to get the surface area, we have to add the area of the base (which is a 2) to each of these formulas.

For the given case, we are given a square pyramid. Hence, all four sides are equivalent in length. We can apply Pythagoras theorem to evaluate the slant height (h) of the pyramid.

The slant height is given by h = √(a² + l²),

Here

a = length of one side

l = height of the pyramid.

Applying this information, we can evaluate the lateral surface area of the square pyramid

Lateral surface area = 2a * √((a²)/4 + l²)

                    = 2 * 8 * √((8²)/4 + 10²)

                    = 112 in²

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The complete question is

The net below shows a square pyramid. What is the lateral surface area?

A. 176 in^2

B. 112 in^2

C. 64 in^2

D. 210 in^2

Answer: (√2)(2) = 2√2

Step-by-step explanation:

To simplify the expression 3√2 - √2, you can factor out the common term √2:

3√2 - √2 = (√2)(3 - 1)

Now, subtract the numbers in parentheses:

(3 - 1) = 2

(√2)(2) = 2√2

The statement "Each additional serving will require 1 additional can of beans" is not correct.

It should be noted that to make more than 3 servings, Robert will need to increase the amount of both beans and ground turkey used in the recipe.

Assuming that the recipe calls for one 18-ounce can of beans for 3 servings, Robert will need to use 6 cans of beans for 12 servings.

This is because each serving requires 6 ounces of beans (18 ounces ÷ 3 servings), and 12 servings would require a total of 72 ounces of beans (12 servings × 6 ounces per serving).

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Answer:

∠x = 38°

Step-by-step explanation:

∠x + ∠y = 180°

∠x + 142° = 180°

∠x = 180° - 142

∠x = 38°

Answer: a and b

Step-by-step explanation:

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Using Pythagorean trigonometric identity, the value of cosθ is √2/2

To find the value of cosθ, we can use Pythagorean identity to do this. However, we are also told that θ terminates in the the first quadrant.

sinθ = √2/2

sin²θ + cos²θ = 1

Substituting the value of sin θ into the formula above

cos²θ + (√2/2)² = 1

cos²θ + 1/2 = 1

collect like terms

cos²θ = 1 - 1/2

cos²θ = 1/2

cosθ = √(1/2)

cosθ = √2/2

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Answer:

X = 20.25°

Step-by-step explanation:

Interior angle of the same side are suplementery which means their sum is equal to 180° .

So 38° +( 8x - 26°) = 180°

12° + 8x = 180° .... Simplify 38 and 26

8x = 180°- 12° .... taking 12 to the left side it

change the sighn to -ve

8x = 162° .... simplify

8x/8 = 162°/8 .... dividing both side 8

x = 20.25°

Answer:

Correct equation:

x + 22 + x + 22 + 10 = 48

The only valid value for t is approximately 1.53 seconds when the ball's height is 4 meters.

We are given the equation for the height of the ball h as a function of time t:

h(t) = 3 + 7t - 5t²

We want to find all values of t for which the height h is 4 meters. So, we set h(t) equal to 4 and solve for t:

4 = 3 + 7t - 5t²

Rearrange the equation to form a quadratic equation:

0 = 5t² - 7t - 1

Now, we can use the quadratic formula to solve for t:

t = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 5, b = -7, and c = -1. Plugging these values into the quadratic formula, we get:

t = (7 ± √((-7)² - 4 * 5 * (-1))) / (2 * 5)

t = (7 ± √(49 + 20)) / 10

t = (7 ± √69) / 10

We have two possible solutions for t:

t = (7 + √69) / 10 ≈ 1.53 (rounded to the nearest hundredth)

t = (7 - √69) / 10 ≈ -0.13(rounded to the nearest hundredth)

Since time cannot be negative, we discard the second solution.

So, the only valid value for t is approximately 1.39 seconds when the ball's height is 4 meters.

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The exact value of sin θ, given that cosθ = 1/2 and θ terminates in Quadrant IV, is -√(3)/2.

The Pythagorean Identity states that sin²θ + cos²θ = 1. This identity can be used to find the value of sinθ, given the value of cosθ, and vice versa.

In Quadrant IV, the cosine function is positive, and the sine function is negative. This is because in Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative.

Given that cosθ=1/2, we can use the Pythagorean Identity to find the value of sin²θ.

sin²θ + cos²θ = 1

sin²θ + (1/2)² = 1

sin²θ + 1/4 = 1

sin²θ = 1 - 1/4

sin²θ = 3/4

To find the value of sinθ, we take the square root of both sides of the equation:

sinθ = ±√(3/4)

However, since θ terminates in Quadrant IV, sinθ is negative. Therefore, we take the negative square root of 3/4:

sinθ = -√(3/4)

We can simplify this expression by writing 3/4 as a fraction in terms of its square roots:

sinθ = -√(3/4)

sinθ = -√(3)/√(4)

sinθ = -√(3)/2

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The water evaporated.

Option B is the correct answer.

We have,

When a liquid is left open in a container, it can undergo a phase change to become a gas or vapor, which is known as evaporation.

In this case,

The water in the beaker would have evaporated, leaving behind the salt. The water did not disappear forever but instead changed state to become a gas in the air.

Thus,

The water evaporated.

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The equation of the new line will be y = -9x + 4. Then the correct option is B.

Given that:

Linear equation, y = x + 2

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The y-value of the y-intercept will be raised by 2 units, and the slope will be multiplied by -9.

Then the slope of the equation will be given as,

m = -9 x 1

m = - 9

The y-intercept of the equation is given as,

c = 2 + 2

c = 4

The equation of the new line will be y = -9x + 4. Then the correct option is B.

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In the function y = x + 2, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function

Answer:

24

Step-by-step explanation:

Compare the known similar sides - - -

10 is to 30, and 14 is to 42. Triangle B is 3x Triangle A.

So the unknown side in Triangle B is 3x 8cm, so 24cm.

Answer:

quadratic

Step-by-step explanation:

linear is a straight line

exponential is a simple curved graph

Answer:

L = 9

Step-by-step explanation:

6x8=48

432÷48=9

Answer:

The answer is 24.1 unit²

Step-by-step explanation:

Volume of prisms=cross sectional area×h

cross sectional area=Volume of prisms/height

A=216.9/9

A=24.1 unit²

The bond's APR is 4.25%.

The formula for face value of the bond is given as following

F=P(1+rt) where F=face value, P= Purchase value, r=Annual rate & t=time of bond.

The given values are P=$5700, t=4 years & F=$6669

Substituting the above values we get

6669=5700(1+r*4)

0.17=4r

r=4.25%.

Hence, the APR for the given bond is 4.25%.

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The solution of the system of equations is (8, 2).

Given is a system of equations x-2y = 4 and x+3y = 14, we need to find the solution of the system of equations,

So, the equations are =

x-2y = 4

x = 2y + 4......(i)

x+3y = 14

x = -3y + 14..........(ii)

Equating the equations since their LHS is same,

2y + 4 = -3y + 14

5y = 10

y = 2

Put y = 2 in any equation to find the value of x,

So,

x = 2(2)+4

x = 8

Hence the solution of the system of equations is (8, 2).

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An equation to represent A, the area in square feet, as a function of w, the width in feet will be; A = 120W -2W²

Here, the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

We know that the area of a rectangle is l × w

When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000

When w = 20, length = 120 - 40 = 80,  area =  80 x 20  = 1600

When w = 40, length = 120 - 80 = 40.  area = 40 x 40 = 1600.

So, the completed table will be

Width            Length          Area

10                    100              1000

20                    80              1600

40                    40              1600  

w                  120 - 2w        (120 - 2w) w

To maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have,

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

A = 120W -2W²

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Answer:

0

Step-by-step explanation:

=1/2 × -5,6 × 0

=-8,4×0

=0

The  total surface area of this triangular prism is 976 square cm.

Here, we have,

Total surface area of a figure

The total surface area is the sum of the area of the faces of a figure.

The given shape is made up of three rectangles and 2 triangles.

Surface area = 2[25*10] + (14 * 10) + (24 * 14)

Surface area = 2(250) + 140 + 336

Surface area = 976 square cm

Hence the total surface area of this triangular prism is 976 square cm

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Answer:

The correct answer is: OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3).

To dilate a point using a scale factor of 4, we multiply each coordinate of the original point by 4.

Thus, the coordinates of A' are (-4 * 4, 6 * 4) = (-16, 24)

The coordinates of B' are (-2 * 4, 2 * 4) = (-8, 8)

The coordinates of C' are (4 * 4, -2 * 4) = (16, -8)

The coordinates of D' are (4 * 4, 4 * 4) = (16, 16)

To check our work, we can plot these points on a graph and compare with the original polygon:

Original Polygon:

A(-4, 6) B(-2, 2)

* *

\ /

\ /

\ /

\ /

\ /

* *

C(4,-2) D(4,4)

Dilated Polygon:

A'(-16, 24) B'(-8, 8)

* *

\ /

\ /

\ /

*

C'(16,-8) D'(16,16)

If we divide the coordinates of the dilated polygon by 4, we get the answer:

A'(-16/4, 24/4) = (-4, 6)

B'(-8/4, 8/4) = (-2, 2)

C'(16/4, -8/4) = (4, -2)

D'(16/4, 16/4) = (4, 4)

So the vertices of polygon A'B'C'D' are OA (3, -4.5), B(1.5, -1.5), C(-3, 1.5), and D'(-3,-3).

Answer:

251.327 km² (nearest thousandth)

Step-by-step explanation:

The formula for the surface area of a cylinder is:

[tex]\boxed{S.A. = 2\pi r^2 + 2\pi rh}[/tex]

where r is the radius and h is the height of the cylinder.

Substitute the given values of r = 4 km and h = 6 km into the formula and solve:

[tex]\begin{aligned}S.A. &= 2\pi (4)^2 + 2\pi (4)(6)\\&=2\pi (16)+2 \pi (24)\\&=32 \pi+ 48 \pi\\&=80 \pi\\&=251.327412...\\&=251.327\; \sf km^2 \end{aligned}[/tex]

Therefore, the surface area of the cylinder with height 6 km and radius 4 km is 251.327 square kilometers, rounded to the nearest thousandth.

Answer:

-------------------------

Curved surface area of a cylinder:

Substitute 6 for h and 4 for r:

Total surface area adds top and bottom faces: