Click on the hot spot below to find the indicated values. If f(x)=7, then x=

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Step-by-step explanation:

The correct answer is 237

Answer:257

Step-by-step explanation:

Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.

We're given:

\(\dfrac{3240\hspace{4}feet}{hour}\)

We also know that:

\(\dfrac{hour}{60\hspace{4}minutes}\)

Multiply the two to cancel out the hour:

\(\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}\)

Simplify:

\(=\dfrac{54\hspace{4}feet}{minute}\)

\(\dfrac{54\hspace{4}feet}{minute}\)

Answer:

$7/lb

Step-by-step explanation:

$70 / 10 lb = $7/lb

Answer:

$7 per pound of letuce

Step-by-step explanation:

We know

10 pounds = $70

1 pounds = ?

We cross multiply and get:

$7 per pound of letuce

So, the answer is $7 per pound of letuce

Answer:

315 (C)

Step-by-step explanation:

If it takes 45 minutes to make 3 bracelets, (considering she spends equal time on each) she's making 1 bracelet every 15 minutes. There are two ways you can solve this.

45/3 = 15 times 21 (bracelets) = 315

Or,

21/3 is 7, so multiply 7 and 45 to get 315 as well.

(Second Question) If we're finding percentages you always want to find a number out of 100. We can get to 100 evenly by multiplying 25 by 4. Do the same for 15 so the ratio stays equal, and you get 60, or: 60%.

The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).

The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).

Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.

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Answer:

c .. I think that's right

Given:

Given that

Required: Convert to rectangular form.

Explanation:

The given equation in polar can be written as

Substitute

Then the equation becomes 3y - x = 5.

Solve for y.

Final Answer:

Answer:

\(\sqrt{41}\)  = x

Step-by-step explanation:

Basically, find the missing side lengths of each triangle so that you can solve for x:

1. right triangle w/ side lengths 48 and 52

2. right triangle w/ side lengths 12 and 20 (from previous triangle)

3. right triangle w/ side lengths 5 and 13

Take right triangle w/ side lengths 12, 20, and 16 (#2) and right triangle w/ side lengths 5, 13, and 12 (#3):

4. Solve for the final triangle that includes x:

Answer:

The required probability for the intersection of A & B = 0.25

Step-by-step explanation:

Given that:

Sample space S =  {E1, E2, E3, E4, E5, E6, E7} and the probability of each sample points are:

P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05.

Also;

A = {E1, E4, E6}

B = {E2, E4, E7}

C = {E2, E3, E5, E7}

Then

P(A) = 0.05 + 0.25 + 0.10 = 0.4

P(B) = 0.20 + 0.25 + 0.05 = 0.5

P(C) = 0.20 + 0.20 + 0.15 + 0.05 = 0.6

The intersection of A and B are:

P(A ∩ B) = E4

P(A ∩ B) = 0.25

The required probability for the intersection of A & B = 0.25

Answer:

126

Step-by-step explanation:

14 times 9

We can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.

What is the percent change?

Percentage change is a way to describe the difference between an old value and a new value, expressed as a ratio and then multiplied by 100.

To estimate the percent change in the number of club members, we can use the percent change formula:

percent change = (new value - old value) / old value x 100%

where the "old value" is the number of club members last year and the "new value" is the number of club members this year.

Plugging in the numbers we have:

percent change = (33 - 17) / 17 x 100%

percent change = 16 / 17 x 100%

percent change ≈ 94.1%

Therefore, we can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.

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Answer: $14.27 per CD before tax

Step-by-step explanation:

0.60 times 6= 3.60

88.20 subtracted by 3.60 = 85.60

85.60/6 = 14.2666667

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Given:

The area of the projection is

The width of the projection is w =(x-4) feet.

Let l be the height of the projection.

The shape of the projection is a rectangle.

Consider the formula for the area of the rectangle.

Cancel out the common factor.

Hence the height of the projection is (x-8).

b)

Given:

Height of the wall x=10 ft.

We know that the width of the projection w =(x-4) and height of the projection l=(x-8).

Substitute x=10 in the equation l and w, we get

Consider the perimeter of the rectangle.

Substitute l=2 and w=10 in the formula, we get

Hence the perimeter of the projection is 16 ft when the height of the wall is 10 ft.

Answer:

∠CDF = 48°

Step-by-step explanation:

∠CDE = ∠EDF + ∠CDF

Given that,

∠CDE = 114°

∠EDF = 66°

So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.

∠CDF = ∠CDE - ∠EDF

∠CDF = 114 - 66

∠CDF = 48°

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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The measure of the angle m∠ZYX of the trapezoid is equal to 139°

A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.

3x + 19 + x + 1 = 180°

4x + 20 = 180°

4x = 180 - 20 {collect like terms}

4x = 160

x = 160/4 {divide through by 4}

x = 40

m∠ZYX = 3(40) + 19 = 139°.

WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.

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Answer:

-5a + 3b

3a+2b−8a+b

=3a + 2b + (−8a) + b

Combine Like Terms:

=3a + 2b + (−8a) +b

=(3a+−8a)+(2b+b)

=−5a+3b

Step 1

State the expression for an exponential equation

Step 2

Test option 3 to see if it qualifies to be generated by an exponential equation

Answer:

1≠0.346485

Step-by-step explanation:

Answer:

mass divided by volume

Step-by-step explanation:

The density can be calculated as the mass divided by volume. So, the correct option is A.

Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.

Density = (Total amount available)/(total space which contains that amount)

Suppose that a finite amount of substance is there having its properties as:

The mass of substance = m kg

The density of substance = d kg/m³

The volume of that substance = v m³

Then, they are related as:

\(d = \dfrac{m}{v}\)

Therefore, the density can be calculated as the mass divided by volume. So, the correct option is A.

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Answer:

Step-by-step explanation:

Four quadrants:

Quadrant I (right side, above the x-axis to the right of the y-axis).

Quadrant II (left side, above the x-axis to the to the left of the y-axis).

Quadrant III ( left side , below the x-axis to the left of the y-axis).

Quadrant IV  (right side, below the x-axis to the right of the y-axis

                          Y

                            l                      

           II  (-x, y)    l           I      (x, y)      

    x                      l                        x

             III            l        IV    

         (-x, -y)         l        (x, -y)

                            l

                          Y      

 Now you can answer the questions by locating the point and explain.

Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Answer:

Step-by-step explanation:

Linearity condition is :  NOT MET

The equal variance condition is : NOT MET

The 10% condition : Does not need to be checked for multiple linear regression

The success failure condition : Does not need to be checked for multiple linear regression