. When f(x)=6x + 4 and g(x) = -6x + 3, find (g ◦ f)(6).

Answer:

Area of ΔEDF = 4.5 in²

Step-by-step explanation:

In the figure attached,

ΔBAC ~ ΔEDF

Property of similarity,

" If two triangles are similar then their corresponding angles will measure the same."

Scale factor for ΔBAC to ΔEDF = [tex]\frac{\text{Side EF}}{\text{Side BC}}[/tex]

                                                       = [tex]\frac{3}{4}[/tex]

"Ratio of the area of similar triangles = Square of the ratio of their corresponding sides"

[tex]\frac{\text{Area of triangle FDE}}{\text{Area of triangle CAB}}[/tex] = [tex](\frac{3}{4})^2[/tex]

[tex]\frac{\text{Area of triangle FDE}}{8}=\frac{9}{16}[/tex]

Area of ΔEDF = [tex]\frac{9\times 8}{16}[/tex]

                       = 4.5 square inches

Therefore, area of ΔEDF = 4.5 in²

Answer: C

Step-by-step explanation:

The slope stays the same but the y-intercept is moved up 7 units.

Answer: 79/4

Step-by-step explanation:

The kettle contains 20 3/8 cups of soup = 163/8 cups

A server scoops 5/8 cup from the kettle

So,

163/8 - 5/8 = 158/8 = 79/4

Answer:

The correct answer is A.

A) The IQR of Karla's data in 13.

Step-by-step explanation:

The interquartile range can be defined as the difference of upper quartile and lower quartile range. If we want to find the IQR from the box plot, we can simply see the length of the box from the box plot, as it represent the IQR.

We can clearly see that:

IQR of Steve's data is 45 - 31 = 14, hence the second statement is incorrect

IQR of Karla's data is 52 - 39 = 13, hence the first statement is CORRECT

The difference of medians is 43 - 36 = 7

Hence the difference of medians is not the half or twice of IQR ranges of both data sets

Answer:

A) The IQR of Karla’s data is 13

Step-by-step explanation:

Answer:

The solution is at (-0.5,0.5).

Step-by-step explanation:

I graphed both equations on the graph below to show you where the solution of the system is.

Answer:

Step-by-step explanation:

Given

T, T, F, F, S, S....

Required

Fill in the missing letters

To fill in the missing letters, one has to observe and study the pattern carefully;

Closely looking at the pattern, one would notice that the pattern is the first letter of number starting from Two;

The pattern is as follows:

Two, Three, Four, Five, Six, Seven

So, the next two on the list would be Eight and Nine;

Hence, the missing letters are E,N

And the complete pattern is T, T, F, F, S, S, E, N

Answer:

4 days

Step-by-step explanation:

8 people can do the job in 6 days, job is this case is picking apples.

1 person can do same job for 6*8= 48 days

12 people can do same for 48/12= 4 days

Answer:

The answer is option c

y = 9/5sin6x

Hope this helps.

Answer:

11*pi/36

Step-by-step explanation:

[tex]\displaystyle \frac{55 \pi}{180}[/tex]

[tex]=\displaystyle \frac{11\pi }{36}[/tex]

Answer:

x = -3 and x= 3

Step-by-step explanation:

Answer:

$ 432

Step-by-step explanation:

$ 8/h *9h/day * 6 day = $ 432

Answer:

$432

Step-by-step explanation:

9 hours x 6 days = 54 hours

54 x 8 = 432

Calculate Priscilla's tax.

Answer:

Priscilla will pay a tax of $18,623

Step-by-step explanation:

Priscilla's Income = $122,300.00

First, we determine the amount over $78,950.00

$122,300.00 - $78,950.00 =$43,350

Amount over $78,950.00= $43,350

Therefore:

Priscilla's Tax = $9086.00+ (22% of $43,350)

=$9086.00+9537

=$18,623

Priscilla will pay a tax of $18,623

Answer:

C

Step-by-step explanation:

It looks to me possibly C

hope it helps you

A graph is a way to represent a lot of data in a visual format. The graph which correctly displays the data from the list and table is graph c.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The bar graph that can represent the given situation will have the name of the color pattern on the x-axis, while the number of students who choose the pattern will be listed on the y-axis.

Since the last pattern is the yellow pattern, therefore, it should be on the leftmost side of the equation and must have the smallest candle. while the first candle should be the second-largest candle as it is selected by only four students. Since the second candle and the third candle has the value of 6 and 12. Therefore, the length of the third candle should be half of the length of the second candle.

Now, the only graph that fits these criteria is graph C.

Hence, the graph which correctly displays the data from the list and table is graph c.

Learn more about Graph:

https://brainly.com/question/14375099

Answer: 2x-5 / x+5

Step-by-step explanation:

(2x^2 - 3x - 5) / (x^2 + 6x + 5)

Write -3x as a difference

= (2x^2 +2x - 5x -5) / (x^2+5x+x+5)

Factor out 2x from the expression

= 2x *(x+1) -5 * (x+1) / x*(x+5)+x+5

Factor out x+1 from the expression

= (x+1) * (2x-5) / (x+5)* (x+1)

Reduce the fraction with x+1

= 2x-5 / x+5

Answer:

The answer is "340 units²"

Step-by-step explanation:

In the given question, an attachment file is missing, which can be defined as follows:

[tex]\therefore \tan \theta= \frac{height}{base}\\\\\to \tan 60^{\circ}=\frac{h}{3}\\\\\to \sqrt{3}=\frac{h}{3}\\\\\to 3\sqrt{3}=h\\\\\to h = 3\sqrt{3} units\\\\[/tex]

The area of trapezoid prism:

[tex](a)= (b_1+b_2)h+ph[/tex]

value:

[tex]b_1=6 \ units\\b_2=9 \units\\h=10 \ units\\\\\to P=6+9+3\sqrt{3}+\sqrt{3^2+(3\sqrt{3})^2}\\\\\to P=15+3\sqrt{3}+\sqrt{9+27}\\\\\to P=15+3\sqrt{3}+\sqrt{36}\\\\\to P=21+3\sqrt{3} \ unit\\\\\bold{ Area= (6+9) \times 3\sqrt{3}+(21+3\sqrt{3})\times 10}\\\\\to Area= (15) \times 3\sqrt{3}+(21+3\sqrt{3})\times 10\\\\\to Area= 45\sqrt{3}+210+30\sqrt{3}\\\\\to Area=339.9038\\\\\to Area=340 \ units^2[/tex]

Answer:

340 units² is right!

Step-by-step explanation:

I got it correct on my exercise!!

Answer:

(2,5)

Step-by-step explanation:

There you go.........

Answer:

[tex](2, 5)[/tex]

Step-by-step explanation:

[tex]y=2x+1[/tex]

[tex]x-y=-3[/tex]

[tex]x-(2x+1)=-3[/tex]

[tex]x-2x-1=-3[/tex]

[tex]-x-1=-3[/tex]

[tex]-x=-3+1[/tex]

[tex]-x=-2[/tex]

[tex]x=2[/tex]

[tex]y=2x+1[/tex]

[tex]y=2(2)+1[/tex]

[tex]y=4+1[/tex]

[tex]y=5[/tex]

Answer:

Extrapolate-estimate beyond data points

Correlation- a statistical measure to describe how two random variables are related

interpolate-estimate between data points

Let me know if you got it correct

Answer:

Since y varies inversely with x

y = k ×1/x

Where k is the constant of variation

k 1.4

When x is 5.6

y = 1.4 × 1/5.6

y = 1/4 or 0.25

Hope this helps

Answer:

y = 0.25

Step-by-step explanation:

given y varies inversely with x

this can be written:

[tex]y = \frac{k}{x}[/tex]

we are given that k = 1.4 and x = 5.6

simply substitute these values into the equation:

y = 1.4/5.6

y = 0.25

Answer:

[tex]\mathrm{C}[/tex]

Step-by-step explanation:

[tex]\frac{2}{9} \times \frac{3}{4}[/tex]

[tex]\mathrm{Reciprocal\:of\:\frac{3}{4} }[/tex]

[tex]\frac{2}{9} \div \frac{4}{3}[/tex]

Answer:

[tex]$\text{C) } \frac{2}{9} \div \frac{4}{3} = \frac{2}{9} \cdot\frac{3}{4} $[/tex]

Step-by-step explanation:

[tex]$\text{A) } \frac{2}{9} \div \frac{3}{4} = \frac{2}{9} \cdot\frac{4}{3} $[/tex]

[tex]$\text{B) } \frac{2}{9} \div \frac{2}{9} = \frac{2}{9} \cdot\frac{9}{2} $[/tex]

[tex]$\text{C) } \frac{2}{9} \div \frac{4}{3} = \frac{2}{9} \cdot\frac{3}{4} $[/tex]

[tex]$\text{D) } \frac{9}{2} \div \frac{4}{3} = \frac{9}{2} \cdot\frac{3}{4} $[/tex]

Note: See reciprocal of a fraction

Answer:

1.) F(x) = 3^(x+2) - 3

2.) F(x) = 1^x/2 - 2

3.) F(x) = 4^(1/3x)

4.) F(x) = 2^(x - 3) + 4

Step-by-step explanation:

 1.) The graph F(x)= 3^x, left 2 units, and down 3. This is a translation. The translated function will be

F(x) = 3^(x+2) - 3

Note: for x - axis, left is positive while right is negative

2.) The graph f(x)= 1^x/2 translated down 2 units. The translated function will be

F(x) = 1^x/2 - 2

3.) the graph of f(x)=4^x, stretched horizontally by a factor of 3.

That is, it is stretched along the x - axis.

X will be multiply by 1/3. The stretched function will therefore be

F(x) = 4^(1/3x)

4.) The graph of f(x)=2^x up 4 units and right 3 units. --

The translated function will be

F(x) = 2^(x - 3) + 4

Answer:

Divide each side by 2 to isolate x

Step-by-step explanation:

2x = 10

Divide each side by 2 to isolate x

2x/2 = 10/2

x = 5

Answer: x = 5

Step-by-step explanation: Since 2 is multiplied by x, divide both sides of the equation by 2 to get x by itself and show all your work.

Put both sides of the equation over 2 and cancel out

the 2's on the left side just like I have done below.

Don't just do this problem in your head.

It's extremely important to develop the habit of putting

all your steps down on paper or writing them digitally.

It will really pay off for you down the line.

You can always check your answer

by plugging it back into the equation.

Answer:

About 7500 cubic centimeters

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because the mouse goes through 8 segments, this becomes a series of 8

Answer:

x ≈ 31.3°

Step-by-step explanation:

We can use sin∅ to solve this:

sinx = 13/25

x = [tex]sin^{-1}(13/25)[/tex]

x = 32.3323

Answer:

The correct option is:

y = 4

Step-by-step explanation:

We can see in the graph the behavior of both the exponential function and linear function. The point (1,4) is considered to be the point where the graph of both the functions is getting separated. We can see in the graph that before point (1,4), initially the y value of exponential function is first greater than that of a linear function, then at y=2 it becomes equal, from y=2 to y=4 the value of linear function is slightly bigger than the value of exponential function. However, after point y=4, the value of exponential function corresponding to a particular value of x is always greater than the value of linear function for the same value of x

Answer:

y=4

Step-by-step explanation:

yes

Answer:

x=0

Step-by-step explanation:

solve with cross multiplying

Answer:

7.2222...

Step-by-step explanation:

Well first, to make it easier, remove the fractions by multiplying both sides by the LCM (or 65 in this case).

Thus, we will have:

[tex]65(\frac{4x}{5}+2)=65(\frac{5x}{13}+5)[/tex]

[tex]65(\frac{4x}{5})+65(2)=65(\frac{5x}{13})+65(5)[/tex]

[tex]52x+130=25x+325[/tex]

Now, simply isolate the [tex]x[/tex].

[tex]52x=25x+195[/tex]

[tex]27x=195[/tex]

[tex]x=7.2222...[/tex] or [tex]\frac{65}{9}[/tex]

Answer:

3x² - 9x - 30

Step-by-step explanation:

We use FOIL to multiply (First, Outside, Inside, Last)

Step 1: F

3x²

Step 2: O

6x

Step 3: I

-15x

Step 4: L

-30

Step 5: Rewrite

3x² + 6x - 15x - 30

Step 6: Combine like terms

3x² - 9x - 30

Answer:

[tex]3x^2-9x-30[/tex]

Step-by-step explanation:

Use the FOIL method to solve:

First: [tex]x*3x=3x^2[/tex]

Outer: [tex]x*6=6x[/tex]

Inner: [tex]-5*3x=-15x[/tex]

Last: [tex]-5*6=-30[/tex]

Combining them all, we get:

[tex]3x^2+6x-15x-30=\\3x^2-9x-30[/tex]

Answer:

Yes, the answer is your first option.

Step-by-step explanation:

i just took the test

The slope of a perpendicular line is going to be the opposite and reciprocal of the original slope.

Opposite: -1/2 -> 1/2

Reciprocal: 1/2 -> 2

Therefore, the answer is 2

Best of Luck!