For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.
35. f(x) = 3x + 2, g(x) = 5 − 6x

The domain of the function f(x) is: -6 < x ≤ 4, and the value that is in the domain of the function f(x) is 4

The function is given as:

f(x) = 2x + 5,   -6 < x ≤ 0

f(x) = 2x + 3,   0 < x ≤ 4

The above means that the domain of the function f(x) is:

-6 < x ≤ 0 and 0 < x ≤ 4

When combined, we have:

-6 < x ≤ 4

This means that x is greater than -6 but does not exceed 4

Hence, the value that is in the domain of the function f(x) is 4

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Answer:

4

Step-by-step explanation:

got it right on edge

The tenth term of the arithmetic sequence will be 15. Then the correct option is A.

Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as

[tex]\rm a_n = a_1 + (n - 1)d[/tex]

We have

a₇ = 6

d = 3

n = 7

Then the first term will be

a₇ = a₁ + (7 – 1)3

6 = a₁ + 18

a₁ = 6 – 18

a₁ = -12

Then the 10th term will be

a₁ = -12

d = 3

n =10

Then we have

a₁₀ = -12 + (10 – 1)3

a₁₀ = -12 + 27

a₁₀ = 15

Then the tenth term of the arithmetic sequence will be 15.

Then the correct option is A.

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Step-by-step explanation:

t = .25u        (given)

4 t = 4 (.25u)  = u

then u = 50% of 2 u

Answer:

  x = 1, 4

Step-by-step explanation:

We assume the graph is of the relation y = f(x). The desired values of x are those that correspond to points where the y-value is -2.

We are only interested in the x-coordinates of points that lie on the horizontal line where y = -2. Those points are (1, -2) and (4, -2).

The values of x such that f(x) = -2 are x=1 and x=4.

Answer:

135:147

Step-by-step explanation:

180/4=45

180-45=135

292-45=247

135:247

Answer:

its dependent varaible

Answer:

Step-by-step explanation:

NOW WATSH ME WIP WAHS E NYA NAY

The features of the function g(x) = 4log(x) + 4 are

The function is given as;

g(x) = 4log(x) + 4

The intercept

A logarithmic function has no y-intercept.

Set g(x) to 0, to determine the x-intercept

4log(x) + 4 = 0

Divide through by 4

log(x) + 1 = 0

This gives

log(x) = -1

Take the inverse of both sides

x = 10^-1

Evaluate

x = 0.1

The x-intercept is (0.1, 0)

The vertical asymptote

Recall that:

A logarithmic function has no y-intercept.

This is so because it is undefined at x = 0

So, the vertical asymptote is x = 0

The domain and the range

A logarithmic function cannot take a negative input or 0 input

So, the domain is x > 0

However, the range is all set of real numbers i.e (-∞, ∞)

Hence, the features of g(x) are (b), (d) and (e)

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Answer:

Step-by-step explanation:

2.5 miles = 12 fishes

Therefore,

8 miles = 12*8/2.5=96/2.5= 960/25=38.4 fishes

Answer:

school day

Step-by-step explanation:

When drawing a chart or a graph:

The two given variables are:

Therefore, in this scenario the independent variable is the school day and the dependent variable is the number of students since the former effects the latter.

So the data on the horizontal axis (x-axis) is:  school day

A table can be represented with a linear function equation as y = mx + b, where m is the slope and b is the y-intercept.

Assuming we have a table of values as shown in the image attached below, to write an equation of linear function for the table, do the following:

Pick two pairs of values, say, (1, 5) and (2, 25) and find the slope (m):

Slope (m) = change in y / change in x = (25 - 5)/(2 - 1)

Slope (m) = 20

Find the y-intercept (b) by substituting (x, y) = (1, 5) and m = 20 into y = mx + b:

5 = 20(1) + b

5 = 20 + b

5 - 20 = b

-15 = b

b = -15

Write the equation of the linear function by substituting m = 20 and b = -15 into y = mx + b:

y = 20x - 15

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The distribution where the mean is most likely to be less than the median is the third histogram.

It should be noted that when the histogram shows the day is left skewed, it means the mean is less than the median.

If it right skewed, the mean is greater than the median.

When they're equal, the data is symmetric.

In this case, based on the information, the distribution where the mean is most likely to be less than the median is the third histogram.

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Por lo tanto el número es p/q = 8/64.

Fracción es un número que se puede representar en forma de p/q, donde q no es igual a cero.

It is given that :

En su forma más simple, el número es 1/8

Sea el número p/q

p + q = 72 (dado)

p/q = 1/8

q = 8p

p+8p = 72

9p = 72

p = 8

q = 8p

q = 8 * 8 = 64

Por lo tanto el número es p/q = 8/64.

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Answer:

x = 6

Step-by-step explanation:

Line segment SU is a bisector of angle <TSV which means it divided the angle into two equal parts:

The measure of <TSV = 62 in this case the measure of <VSU = 62/2 = 31

we can write the following equation to find the value of x

5x + 1 = 31 subtract 1 from both sides

5x = 30 divide both sides by 5

x = 6

The geometry illustrates that the value of DB is 34°

AB = 87°

ED = 37°

BCD will be:

= (360° - 87° - 32°)/2

= 118°

FA will be:

= 118°/2

= 59°

DC = 118/2 = 59°

HB = GA = 17°

DB = 2 × 17° = 34°

EG = GA = 17°

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The correct option is (A). The factored form of a-b is (5-3p⁴)(25+15p⁴+9p⁸).

Given that A and B are monomials where a = 125 and b = 27p¹².

Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.

Firstly, substitute a=125 and b = 27p¹² into a-b, we get

a-b=125-27p¹²        ......(1)

As we know, 125=(5)³, 27p¹²=(3p⁴)

So, equation (1) can be rewritten as

a-b=(5)³-(3p⁴)

Now, apply a³-b³=(a-b)(a²+ab+b²).

a³-b³=(5-3p⁴)(5²+5(3p⁴)+(3p⁴)²)

Further, Simplify using exponent rule with the same exponent (ab)ⁿ=aⁿbⁿ.

a³-b³=(5-3p⁴)(5²+5×3p⁴+3²×(p⁴)²)

Furthermore, calculate the power, we get

a³-b³=(5-3p⁴)(5²+5×3p⁴+9(p⁴)²)

Then, Simplify using exponent power rule (aˣ)ⁿ=aˣⁿ, we get

a³-b³=(5-3p⁴)(5²+5×3p⁴+9p⁸)

Now, multiply the monomials, we get

a³-b³=(5-3p⁴)(5²+15p⁴+9p⁸)

Further, calculate the power, we get

a³-b³=(5-3p⁴)(25+15p⁴+9p⁸)

Finally, reorder the expressions, we get

a³-b³=(5-3p⁴)(9p⁸+15p⁴+25)

Hence, the factored form of a-b where a and b monomials and a = 125 and b = 27p¹² is (5-3p⁴)(9p⁸+15p⁴+25).

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Answer:a

Step-by-step explanation:

i just did it

Answer:

120 Phones

Step-by-step explanation:

3/5 of 200

Step 1: Divide 200 by 5

200 ÷ 5 = 40

Step 2: Multiply 40 by 3

40 · 3 = 120

Answer: 3/5 of 200 = 120

Tip: When finding a fraction of a whole, divided the whole by the denominator, then multiply the quotient you got by dividing the whole by the denominator by the numerator

Example: 1/2 of 80

80 ÷ 2 = 40

40 · 1 =40

1/2 of 80 = 40

The equation represented by the model is 3x²-4x+1=(3x-1)(x-1).

Given model represents a polynomial of the form ax²+bx and model is in figure.

Consider the given table.

The first row in the table represents first term of the polynomial.

In first row first three terms are variables and last term are constant.

Write all the terms of the first row in the form of sum.

+x+x+x-1=3x-1

The first column in the table represents second term of the polynomial.

In first column first term are variable and last term are constant.

Write all the terms of the first column in the form of sum.

+x-1=x-1

The product of first term of polynomial (3x-1) and second term of polynomial (x-1) is equal to the sum of all remaining terms in this table.

+x²+x²+x²-x-x-x-x+1=3x²-4x+1.

We can also check this by multiplying (3x-1) and (x-1) as

(3x-1)(x-1)=3x(x-1)-1(x-1)

(3x-1)(x-1)=3x(x)-3x(1)-1(x)+1(1)

(3x-1)(x-1)=3x²-3x-x+1

(3x-1)(x-1)=3x²-4x+1

Hence, the equation represented by the given model in the form of polynomial ax²+bx is (3x-1)(x-1)=3x²-4x+1.

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Answer: 70%

Step-by-step explanation:

A basket contains:

5 yellow balls

3 blue balls

2 white balls

What would be the probability of randomly picking a ball and the ball not being blue?

So, we can find the probability of picking up a blue ball. Let's do that first.

To calculate the probability of getting a blue ball, we need to divide the number of blue balls by the number of possible balls.

The number of blue balls = 3

The total number of balls = 2 + 3 + 5 = 10 balls

3 blue balls divided by 10 balls = 0.3.

If you multiply 0.3 by 100%, it will give you a probability of finding a blue ball equal to 30%

Now, we just need to find the probability of NOT finding a blue ball. Because we have 30% of finding a blue ball, we just need to subtract 30% from 100%.

100 - 30$ = 70%

The probability of not getting a blue ball is equal to 70%.

Hope I Helped!

[tex]|\Omega|=5+3+2=10\\|A|=5+2=7\\\\P(A)=\dfrac{7}{10}=70\%[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: ED = 5 \:\: units[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \:FE + ED = FD[/tex]

[tex]\qquad \tt \rightarrow \:5 + x = 10[/tex]

[tex]\qquad \tt \rightarrow \:x = 10 - 5[/tex]

[tex]\qquad \tt \rightarrow \:x = 5[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The value of ED is 5 units, which is determined by using the concept of midpoint.

The figure given below shows a line segment FD, where the length of line segment FD refers to the distance between its endpoints, F and D.

Given that E is the midpoint of FD.

FE = 5 units

FD = 10 units

Since M is the midpoint of FD, So FE = ED

⇒ FD = FE + ED

Substitute the values of FE = 5 and  FD = 10, in the above equation,

⇒10 = 5 +ED

⇒ ED = 10 - 5

⇒ ED = 5

Therefore, the value of ED is 5 units.

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Answer: 2y^2+6bny-8n^2b^2

Step-by-step explanation: I hope this helps!

Answer:

Hence the expression [tex]$$(5x-y)(x-4)=5x^2-xy-20x+4y$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 5x & - & y \\ \times & {} & {} & {} & x & - & 4 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 20x & + & 4y \\ 5{{x}^2} & - & xy & {} & {} & {} & {} \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}5{{x}^2} & - & xy & - & 20x & + & 4y \\ \end{matrix}$$[/tex]

The fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]

To find the fourth root of ⁴√(81x³y⁴z⁸) with rational exponents, we use the root rule of indices which states that [tex]\sqrt[n]{a} = a^{\frac{1}{n} }[/tex]

So, ⁴√(81x³y⁴z⁸) = ⁴√(81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸)

We now apply the

So, ⁴√(81x³y⁴z⁸) = ⁴√81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸

[tex]= 3 X x^{\frac{3}{4} } X y^{\frac{4}{4} } X z^{\frac{8}{4} } \\= 3 X x^{\frac{3}{4} } X y^{1} X z^{2} \\= 3x^{\frac{3}{4} }yz^{2}[/tex]

So, the fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]

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Using proportions, it is found that the value of x is of x = 5, hence option A is correct.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Since the triangles are similar, the lengths are proportional. Researching the problem on the internet, we have that the proportions are given as follows:

Hence:

[tex]\frac{x}{25} = \frac{5}{25}[/tex]

Simplifying the denominators:

x = 5.

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Answer:

4!

Step-by-step explanation:

using the slope formula and the points (-1, 0) and (-2, -4) on the line:

-4 - 0 / -2 - -1 = -4 - 0 / -2 + 1 = -4 / -1, and since both the top and bottom are negative, they make a positive, giving you a positive 4

the slope formula is rise/run, or y2 - y1 / x2 - x1!

Answer:

Hence, 0.026 can be expressed as [tex]$2.6 \times 10^{-2}$[/tex].

Step-by-step explanation:

- Given 0.026

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 0.026

[tex]$$\Rightarrow 2.6$$[/tex]

Decimal has moved 2 places to right.

The power will be negative as original no. is less than 1 .

[tex]$$\begin{aligned}&2.6 \times 10^{-2} \\&0.026=2.6 \times 10^{-2} .\end{aligned}$$[/tex]

The correct statement about the earthquake in the state is option c. State A had approximately 3,362 more earthquakes than State B.

we have x/y = 0.00299

y = 163696

To solve for x we have

163696 * 0.00299

= 4895 earthquakes

x = 0.1402 x 10931

= 1533

Next we have to find the difference

4895 - 1533 = 3362 earthquakes.

We have to conclude that state A has 3362 earthquakes more than B. Hence the answer is c.

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Complete question

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.

Which statement about the number of earthquakes the states had for the given time span is true?

State A had approximately 1,533 more earthquakes than State B.

State B had approximately 1,533 more earthquakes than State A.

State A had approximately 3,362 more earthquakes than State B.

State B had approximately 3,362 more earthquakes than State A.

The translation function is T(x,y) = (x + 3, y - 2) and the reflection function is (-x, y)

The point is given as:

(x, y)

The translation is given as:

3 units to the right and 2 units down.

This is represented as:

(x + 3, y - 2)

Hence, the translation function is T(x,y) = (x + 3, y - 2)

The point is given as:

(x, y)

The reflection is given as:

Reflection across the y-axis

This is represented as:

(-x, y)

Hence, the  reflection function is (-x, y)

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By applying the reflection rule across the x-axis to quadrilateral DEFG, we obtain the following true statements:

In Geometry, the x-axis would remain the same if a quadrilateral is reflected across the x-axis and the sign on the y-axis would change either from positive to negative and vice-versa.

By applying the reflection rule across the x-axis (x, y) → (x, -y), we obtain the following true statements:

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Answer:

A

B

C

Are the right answer

Step-by-step explanation:

The image of G when A IMG is rotated 180 around the origin is (-2,-4).

To rotate a figure 180 degrees around the origin, we reverse the signs of both the x-coordinate and the y-coordinate. In the image, the point G has coordinates (2,4). Reversing the signs of these coordinates gives us (-2,-4).

Rotate the figure 180 degrees around the origin. This means that we imagine the figure being flipped over the origin.

Reverse the signs of both the x-coordinate and the y-coordinate of the point G. This is because when we rotate a figure 180 degrees around the origin, the signs of both the x-coordinate and the y-coordinate are reversed.

The new coordinates of G are the coordinates of the point that is the result of rotating the figure 180 degrees around the origin and reversing the signs of the coordinates of point G. In this case, the new coordinates of G are (-2,-4).

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