Will give brainliest if correct.

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 tangent identity is: tan x = sin x / cos x. It relates the tangent, sine, and cosine of an angle in a right triangle.

The Pythagorean identity is: sin² x + cos² x = 1. .

The length of the hypotenuse of a right triangle with legs of equal length is √2 times the length of either leg.

The 30-60-90 triangle theorem states that the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b): c² = a² + b².

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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:

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.

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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Answer:

c is -3

Step-by-step explanation:

We are shifting the parabola 3 units to the right.

f(x+c) is a shift c units to the left so we need to shift -3 units

f(x-3) is a shift 3 units to the right 3 units

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:

quadratic

Step-by-step explanation:

linear is a straight line

exponential is a simple curved graph

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:

[tex]\displaystyle{(f+g)(x)=3x^2+8x+7}[/tex]

Step-by-step explanation:

Given both functions f(x) and g(x):

[tex]\displaystyle{f(x)=5x^2+8x}\\\\\displaystyle{g(x)=-2x^2+7}[/tex]

Finding (f+g)(x), is the same as finding the sum of both functions, f(x) + g(x). Therefore:

[tex]\displaystyle{(f+g)(x) = f(x)+g(x)}\\\\\displaystyle{(f+g)(x)=(5x^2+8x)+(-2x^2+7)}\\\\\displaystyle{(f+g)(x)=5x^2+8x-2x^2+7}\\\\\displaystyle{(f+g)(x)=3x^2+8x+7}[/tex]

Answer: $400

Step-by-step explanation:

Discount = 15%

The original price/value of an item is always 100%

So selling price (%) = original price - discount = 100%-15% = 85%

We got selling price as 85%

This implies that 85% = 340

Let's find 1% first, then 100%

1% = 340÷85 = 4

100% = 4 × 100 = $400

The usual (normal/original) price is $400

Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.

percentage, a relative value indicating hundredth parts of any quantity.

Let's represent the usual price of the bicycle by P.

Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).

We can express this relationship as an equation:

S = 0.85P

We also know that the selling price of the bicycle was $340.

Substituting S = $340 into the equation above, we get:

$340 = 0.85P

To find P, we can solve for it:

P = $340 / 0.85

P = $400

Therefore, the usual price of the bicycle was $400.

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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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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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Answer:

L = 9

Step-by-step explanation:

6x8=48

432÷48=9

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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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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Answer: a and b

Step-by-step explanation:

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°

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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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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Answer:

Correct equation:

x + 22 + x + 22 + 10 = 48

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

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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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

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:

Answer:

0

Step-by-step explanation:

=1/2 × -5,6 × 0

=-8,4×0

=0

The following are the values and correct description for the expressions:

(5/6) × (3/2) = 5/4 and is greater than 5/6

(5/6) × (7/8) = 35/48 and is less than 5/6

(5/6) × (9/9) = 5/6 and is equal to 5/6

(5/6) × (1¾) = 35/24 and is greater than 5/6

The given expressions can be simplified to get a value that can be used to describe them in comparison to the fraction 5/6 as follows:

(5/6) × (3/2) = (5 × 1)/(2 × 2)

(5/6) × (3/2) = 5/4 which is greater than 5/6

(5/6) × (7/8) = (5 × 7)/(6 × 8)

(5/6) × (7/8) = 35/48 which is less than 5/6

(5/6) × (9/9) = (5 × 1)/(6 × 1)

(5/6) × (9/9) = 5/6 and is equal to 5/6

(5/6) × (1¾) = (5/6) × (7/4)

(5/6) × (1¾) = (5 × 7)/(6 × 4)

(5/6) × (1¾) = 35/24 and is greater than 5/6

Therefore, the expressions (5/6) × (3/2) is greater than 5/6, (5/6) × (7/8) is less than 5/6, (5/6) × (9/9) is equal to 5/6, and (5/6) × (1¾) is greater than 5/6

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