Find the volume of the prism

Answer: Shift right 2 Units, Stretch by a factor of 3, then shift up 1 unit

Step-by-step explanation:

Just took the exam

The graph of function y = x² and transformed function  y = 3(x - 2)² + 1 are as shown below.

"A function that turns one function or graph into another."

"It is a set of points on the coordinate plane that follows given function."

For given question,

We have been given the graph of a function  y = x²

The graph of y = x² is transformed to y = 3(x - 2)² + 1

We need to describe the transformation.

The graph of a function  y = x² is a parabola having center at (0, 0)

y = (x - 2)² is a parabola with center at (2, 0)

We know that when function f(x) is transformed to kf(x), it means it the graph of function f(x) either compresses or expands.

If 0< k < 1, the graph of the function f(x) compress vertically by k units..

If k > 1, the graph of the function f(x) stretch vertically by k units.

So, y = 3(x - 2)²  is the graph of function y = (x - 2)² compresses vertically by 3 units.

We know that when function f(x) is transformed to f(x) + k, it means it the graph of function f(x) moves vertically up by 'k' units.

So, y = 3(x - 2)² + 1 is the graph of function y = 3(x - 2)² that moves vertically up by 1 unit.

So, the center of the parabola y = 3(x - 2)² + 1 is at (2, 1)

The graphs of function y = x² and transformed function  y = 3(x - 2)² + 1 are as shown below.

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Answer:

x=3

Step-by-step explanation:

with pemdas (x=3+2=5) because you do parenthesis first then you would do that x3 which would be 15.

For the system of equations, there are infinitely many solutions exist.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ - 2x + 2y = 10  .. (i)

⇒ y = x + 5  .. (ii)

Here, From (i) equation,

⇒ - 2x + 2y = 10

Take 2 as common,

⇒ 2 (- x + y) = 10

⇒ - x + y = 5

⇒ y = x + 5

Which is same as equation (ii).

Hence, There are infinitely many solutions exist.

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Answer:

238 B

Step-by-step explanation:

8.5*28    

Answer:

f(x)= 34x +56      34(12) +56=464

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

"Any particular event either (a) will happen or (b) won't happen."

That statement above is a certainty, probability = 100% = 1

This means the probability that event E will happen plus the probability that even E won't happen must add up to 100% = 1

So we can always say -->  prob(E) + prob (not E) = 1

The probability you will roll a 5 on a fair, six-sided die is 1/6.

So we use that to find the probability of not rolling the 5.

1/6 + prob(not E) = 1

   prob(not E) = 1 - 1/6  <---- This is answer G

    prob(not E) = 5/6

Hope this helps.

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

the answer is c

Step-by-step explanation:

Answer:

\(Probability = 0.00002619\)

Step-by-step explanation:

Given

Let d represents the event that a radar detects an aircraft.

So:

\(P(d) = 0.03\)

Required: Determine the probability that a radar detects three before it fails to detect 1.

This event is represented as: d d d d'

And the probability is calculated as thus:

\(Probability = P(d) * P(d) * P(d) * P(d')\)

Using complement rule:

\(Probability = P(d) * P(d) * P(d) * (1 - P(d))\)

So, we have:

\(Probability = 0.03 * 0.03 * 0.03 * (1 - 0.03)\)

\(Probability = 0.03 * 0.03 * 0.03 * 0.97\)

\(Probability = 0.00002619\)

Answer:

0.3

0.4

0.2

0.1

Step-by-step explanation:

look at the pic

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

(4x³- 4 + 7x) - (2x³ - x - 8) is equivalent to expression 2x³ + 8x + 4. Option B

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)  is equivalent to expression 3x⁴ - 3x² + 5x - 7. Option D

(x² - 2x) (2x + 3) is equivalent to expression 2x³ - x² - 6x. Option A

From the information given, we have that the expressions are;

(4x³- 4 + 7x) - (2x³ - x - 8)

expand the bracket, we have;

4x³ - 4 + 7x - 2x³ + x + 8

collect the like terms, we have;

2x³ + 8x + 4

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)

expand the bracket, we have;

-3x² + x⁴ + x + 2x⁴ - 7+ 4x

collect the like terms

3x⁴ - 3x² + 5x - 7

(x² - 2x) (2x + 3)

expand

2x³ + 3x² - 4x² - 6x

2x³ - x² - 6x

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AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.

In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

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Answer:

29

Step-by-step explanation:

f(8)=5(8)-11

=40-11

=29

The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

See explanation

Step-by-step explanation:

1) 5/10

2) 3/10

3) 2/10

4) 7/10

Answer:

1) \(\frac{5}{10} = \frac{1}{2}\)

2) \(\frac{3}{10}\)

3) \(\frac{2}{10} = \frac{1}{5}\)

4) \(\frac{7}{10}\)

Step-by-step explanation:

Probability = \(\frac{number of favourable outcomes}{total number of favourable outcomes}\)

gray marbles = 5

white marbles = 3

black marbles = 2

total number of marbles = 10

Answer:

2.2

Step-by-step explanation:

(1.85 x 2) - 1.50

...............

Answer:

17 seconds

Step-by-step explanation:

7.15 minus 6.58 is .17 or 17 seconds

Answer:

17 seconds

Step-by-step explanation:

7 minutes and 15 seconds minus 6 minutes and 58 seconds

You also have to remember that in a minute, there is 60 seconds, not 100

Answer:

∠ABC = 60°

Step-by-step explanation:

All angles in equilateral triangles are equal.

all angles in triangles added together = 180°

180°/3 = 60°

All angles in equilateral triangles are equal to 60°.

Answer:

g(t) = 22(1.09)t

Step-by-step explanation:

formula is y = a(1 + r)t

staticbigideasmathcom

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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Answer:

Option B) A and C

Step-by-step explanation:

Answer:

900π

Step-by-step explanation:

Hello!

The radius is represented by the function \(r(t) = 15\sqrt{t +2}\).

The radius of the ripple can be found when \(t=2\)

Solve:

The radius of the ripple is 30 inches

The area of a circle is calculated by the formula \(A = \pi r ^2\)

Given the radius is 30, we can find the area of the circle.

Solve:

Answer: -7, -0.75, -5, 0.5, 0.75, 9, 13

Step-by-step explanation:

Because negative numbers are always less

The deductible on a homeowner's earthquake insurance policy is typically between 10 and 25 percent of the total policy value. If your home is worth $250,000 and you have a 10% deductible on your insurance, you will be responsible for the first $25,000.

Insurance is a method for mitigating the effects of risk. When you acquire insurance, you are essentially purchasing protection against unforeseen monetary losses. If anything unfortunate occurs to you,

the insurance company will reimburse either you or another person of your choosing. If you do not have insurance and you are involved in an accident, you may be accountable for all of the expenses associated with the accident.

In conclusion, Deductibles for earthquake insurance are typically between 10 and 25 percent of the maximum amount covered by the policy for the residence.

For instance, if you had a housing coverage of $250,000 and a 10% deductible, you would need to pay $25,000 for repairs before the insurance company would begin to pay anything.

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