Divide 405 in the ratio
4:11​

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[tex]4 \times {9}^{2x} = 42[/tex]

Divide sides by 4

[tex] \frac{4 \times {9}^{2x} }{4} = \frac{42}{4} \\ [/tex]

[tex] {9}^{2x} = \frac{2 \times 21}{2 \times 2} \\ [/tex]

[tex] {9}^{2x} = \frac{21}{2} \\ [/tex]

[tex]( { {9}^{2} })^{x} = \frac{21}{2} \\ [/tex]

[tex]x = log_{ {9}^{2} }( \frac{21}{2} ) \\ [/tex]

[tex]x = \frac{1}{2} log_{9}( \frac{21}{2} ) \\ [/tex]

[tex]x = \frac{1}{2} log_{ {3}^{2} }( \frac{21}{2} ) \\ [/tex]

[tex]x = \frac{1}{2 \times 2} log_{3}( \frac{21}{2} ) \\ [/tex]

[tex]x = \frac{1}{4} log_{3}( \frac{21}{2} ) \\ [/tex]

[tex]x = \frac{1}{4} ( \: \: log_{3}(21) - log_{3}(2) \: \: ) \\ [/tex]

[tex]x = \frac{1}{4} ( \: \: log_{3}(3 \times 7) - log_{3}(2) \: \: ) \\ [/tex]

[tex]x = \frac{1}{4} ( \: \: log_{3}(3) + log_{3}(7) - log_{3}(2) \: \: ) \\ [/tex]

[tex]x = \frac{1}{4} ( \: \: 1 + log_{3}(7) - log_{3}(2) \: \: ) \\ [/tex]

And we're done...

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Answer:

Width of rectangular piece = x = 8 inches

Step-by-step explanation:

Perimeter of rectangular piece = 62 inches

Let width of rectangular piece= x

and length of rectangular piece = x+15

We need to find width i.e value of x

The formula used for perimeter of rectangle is: [tex]Perimeter=2(Length+Width)\\[/tex]

Putting values in formula and finding Width:

[tex]Perimeter=2(Length+Width)\\\\62=2(x+x+15)\\62=2(2x+15)\\62=4x+30\\62-30=4x\\4x=32\\x=\frac{32}{4}\\x=8[/tex]

After solving we get value of x = 8

So, Width of rectangular piece = x = 8 inches

Answer:

B. [tex] y - 3 = \frac{2}{3}(x - 4) [/tex]

Step-by-step explanation:

We can create an equation to represent the graph in point-slope form, given as [tex] y - y_1 = m(x - x_1) [/tex], by using a point (x1, y1) on the line, (4, 3) and the slope (m) of the line.

Let's find slope using the two points (4, 3) and (-2, -1).

[tex] slope (m) = \frac{y_2 - y_1}{x_2 -x_1} = \frac{-1 - 3}{-2 - 4} = \frac{-4}{-6} = \frac{2}{3} [/tex]

Substitute m = ⅔, x1 = 4, and y1 = 3 in [tex] y - y_1 = m(x - x_1) [/tex].

The equation that represents the graph would be:

✅[tex] y - 3 = \frac{2}{3}(x - 4) [/tex],

Answer:

equation for slope:

y2-y1 / x2-x1

0- (-4) / 0 - (-5)

4/5 is your slope

Step-by-step explanation:

The measure of angle EDF from the given figure is 23°.

From the given figure, ∠EGF=23°.

The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

By using angles in the same segment theorem, we get

∠EGF = ∠EDF = 23°

Therefore, the measure of angle EDF from the given figure is 23°.

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Answer:

x = -3

Step-by-step explanation:

[tex]-54= 6(x-6)\\\\-9=x-6\\\\x=-3[/tex]

Answer:

x=-3

Step-by-step explanation:

-54= 6(x-6)

switch sides = 6(x-6)=-54

divide both sides by 6 =x-6=-9

add 6 to both sides = x=-3

x=-3

Answer:

Average rate of change from day 2 to day 5 is $43.33/day.

Step-by-step explanation:

Sales on day 2 = 200

Sales on day 5 = 330

Rate of change = [tex]\frac{330-200}{5-2} =\frac{130}{3}=43.33[/tex]

Answer:

6

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

srry. i meant to put 112 erlier

Answer:

It's C, g(x) = (1/2)^x

This is a horizontal reflection of y = 2^x

across the y axis.

Step-by-step explanation:

Using the process of elimination, you can spot this answer by applying what is logical about the transformations of an exponential function.

The transformations of a standard exponential function can be given by:

ab^(1/c(x-h))+k

First note that A must be incorrect because -2^x would be a reflection across the x axis which would not match the function g because a reflection across the x axis would cause the exponential growth or decay value b to become a reciprocal and -2 is not a reciprocal of 2.

Answer:

none of the answer choices are correct.

CORRECT ANSWER: 15,190

Answer:

The actual product is 15,190

Step-by-step explanation:

Answer: 69,960

Step-by-step explanation: all you have to do is divide 132,000 by 53%.

Answer: a

Step-by-step explanation:

82 is 122 degrees warmer than -40

Answer:

TriangleJXP = Triangle HCD

Side XJ = side HC

Side CD = side JP

Side PX = HD

Step-by-step explanation:

Looking at both of the triangles you use the lines on “top” of the side. These lines represent congruence meaning that they are similar to each other.

So looking at side JP u can see that there are two lines meaning that this is the second side that is congruent to another side, side CD.

Hope this helps.

Answer:

The two expressions are;

4(3x + 5)

and

(6x + 10) + (6x + 10)

Step-by-step explanation:

Here, we want to write two different expressions to represent the perimeter of the square

The perimeter is given as 12x + 20

Using factoring, we can have this as;

4(3x + 5)

Otherwise, we can have

(6x + 10) + (6x + 10)

Answer:

C. x=3

Step-by-step explanation:

Because the sides are proportionate to each other

Side 3 is 3x the length of Side 1

Therefore,

Side 9 is also 3x the length of side X

3x=9

Divide both by 3

and X will be 3.

Answer:

-1/2.

Change in y above change in x (don't mix that up)

The first coordinate is 3,-2 the second is 2,-4.

The change is x was -1 . (2-3)

The change in y was 2. (-4-(-2))

Answer:

5

Step-by-step explanation:

just do 12 minus 7 and you get 5

The value of p is 2.

The value of q is 14

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Two functions:

f(x) = 3x + p

g(x) = px + 4

Now,

f(g(x)) = 6x + 9

This means,

3(g(x)) + p = 6x + q

Substituting g(x) = px + 4.

3(px + 4) + p = 6x + q

3px + 12 + p = 6x + q

3px + (p - q) = 6x - 12

This means,

3p = 6

p = 2

p - q = -12

2 - q = -12

q = 2 + 12

q = 14

Thus,

p is 2 and q is 14.

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Answer:

Step-by-step explanation:

3/4a>-16=

a >- 64/3 or -21  1/3

The required sum of the measures of angles D and F is 260 degrees.

Let's represent the measures of angles D, E, and F as D, E, and F, respectively.

From the given information, we have the following equations:

D + E = 110 (The sum of the measures of angles D and E is 110)

E + F = 150 (The sum of the measures of angles E and F is 150)

Now, we want to find the sum of the measures of angles D and F, which is D + F.

To find D + F, we need to eliminate E from the equations. We can do this by adding equations (1) and (2):

(D + E) + (E + F) = 110 + 150

Now, the E terms cancel out:

D + F = 260

So, the sum of the measures of angles D and F is 260 degrees.

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Answer:

24

Step-by-step explanation:

well yea just trust me :)

Answer:

8 oz.

Step-by-step explanation:

there are 88 oz in 5.5 lbs.

the recipe calls for 80 oz.

subtract 88 from 80

answer - 8 ozs cut off.

Answer:

6/12 or 1/2

Step-by-step explanation:

there ya go i think its right

Answer:

Step-by-step explanation:

Given that :

Dimension of rail road toy trains :

Length = 15 inches

Width = 4 inches

Scale = 2/9

Dimension of car on the long Island rail road :

Let length = x

Length = 2/9 of x = 15 inches

= 0.22222x = 15 inches

LENGTH = 67.5 inches

WIDTH = 2/9 of x = 4 inches

0.22222x = 4 inches

Width = 18

Width = 6 inches

Answer: Y = 5

Step-by-step explanation:

Answer:

About 14 in the exact value is 14.38 smthn