(if f(x)=4x^2 and g(x)=x+1, find (f o g)(x)

Answer:

(x+2) (x+4)

Step-by-step explanation:

x^2+6x+8

What 2 numbers multiply together to give us 8 and add together to give us 6

(2*4) =8

(2+4) = 6

(x+2) (x+4)

Answer:

(x + 4)(x+2)

Step-by-step explanation:

We must multiply 8 and 1, and find two numbers which add to 6:

8 * x(suppose x is 1) = 8

Two numbers which add to 6, but also multiply to 8:

4 and 2

4 * 2 = 8

4 + 2 = 6

Hence, the answer would be (x + 4)(x+2)

The prism's base perimeter is 28 units, calculated by summing the lengths of its sides or using the rectangle perimeter formula.

Step 1: Identify the Prism and Its Base

Given a triangular prism, focus on the rectangular base formed by sides S1, S2, S3, and S4.

Step 2: Understand Perimeter Calculation

Recall that the perimeter of any shape is the sum of all its sides.

Step 3: Label the Sides of the Base

Define the sides of the rectangular base:

S1 = 4 + 5

S2 = 5

S3 = 4 + 5

S4 = 5

Step 4: Apply Perimeter Formula

Utilize the formula for the perimeter of a rectangle: P = 2 * (length + width).

For the rectangular base, length = S1 + S3 and width = S2.

Step 5: Calculate Perimeter

Substitute the values into the formula: P = 2 * (9 + 5) = 2 * 14 = 28 units.

Step 6: Verify Using Summation

Confirm the result by adding the individual sides: P = S1 + S2 + S3 + S4 = 9 + 5 + 9 + 5 = 28 units.

The question is missing the specific equation needed to estimate average annual snowfall for Columbia, South Carolina at 34 degrees north latitude. Factors like latitude and climate patterns influence snowfall levels, and based on Columbia's location, low snowfall would be expected.

The student is asking about an equation to estimate average annual snowfall for a specific location based on its latitude, in this case, Columbia, South Carolina, which is at 34 degrees north latitude. Unfortunately, the explicit equation needed to estimate the snowfall is not provided in the question or the contextual information. Generally, to estimate snowfall or precipitation levels using latitude, additional climatic data such as elevation, proximity to oceans or large bodies of water, and prevailing wind patterns are also necessary.

However, referring to the geographical regions mentioned, it's noted that certain latitudes often correspond with specific climate patterns. The comparison with other regions suggests that areas farther away from the equator, especially those close to either the Arctic Circle or the Antarctic Circle, experience more extreme temperatures and snowfall. Given the subtropical zone where Columbia, South Carolina, is located, the expected average snowfall would likely be relatively low compared to higher latitudes.

Answer:

C is your answer I did this test before.

Step-by-step explanation:

good luck.

C is your answer

We have given that,

when using the rational root theorem, which of the following is a possible root of the polynomial function below

F(x)=3x^3-x^2+4x+5

The rational root theorem says, a rational zeros of a polynomial is of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

p/q=±a0/a1

from the given polynomial a1=3 and a0=5

p/q=±3/5

+3/5 is not in the option so the correct option -3/2

So the root of the given polynomial is -3/5

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

-y=x+1

Find the y-intercept

For x=0

-y=0+1

y=-1

The y-intercept is the point (0,-1)

Find the x-intercept

For y=0

-0=x+1

x=-1

The x-intercept is the point (-1,0)

Find a third point

For x=1

-y=1+1

-y=2

y=-2

The third point is (1,-2)

Plot the three points to graph the linear equation

see the attached figure

Note Remember that to graph the linear equation is sufficient with two points

Answer:

(2,1) (0,-1) (-6,7)

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) = 2x² + 3x + x - 2 = 2x² + 4x - 2

To evaluate (f + g)(2) substitute x = 2 into (f + g)(x)

(f + g)(2) = 2(2)² + 4(2) - 2 = 8 + 8 - 2 = 14

Answer:

14

Step-by-step explanation:

First find an algebraic formula for (f + g)(x).  To do this, combine like terms from f and g:  (f + g)(x) = 2x^2 + 4x -2

Next, substitute 2 for x:  (f + g)(2) = 2(2)^2 + 4(2) - 2 = 8 + 8 - 2 = 14

Answer: 45.71 - 6x = y

Step-by-step explanation:

45.71 - 6x = y

x= the amount 1 pack of markers cost

y= how much money Heather has after the donation

Answer: The required expression for amount left in her bank after the donation is given by [tex]Amount\ left=45.71-6x[/tex]

Step-by-step explanation:

Since we have given that

Amount of her saving = $45.71

Number of packs of markers to donate to her school = 6

Let the cost of each pack of markers be 'x'.

So, Amount left in her bank account after the donation is given by

[tex]Amount\ left=45.71-6x[/tex]

Hence, the required expression for amount left in her bank after the donation is given by

[tex]45.71-6x[/tex]

Answer:

The answer in the procedure

Step-by-step explanation:

Remember that

[tex]1\ cm=10\ mm[/tex]

Elevated to the cube both sides

[tex](1\ cm)^{3}=(10\ mm)^{3}[/tex]

[tex](1)^{3}\ cm^{3}=(10)^{3}\ mm^{3}[/tex]

[tex]1\ cm^{3}=1,000\ mm^{3}[/tex]

[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]

[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]

The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;

x g(x)

1 0

2 3

3 6

f(x) = x − 1

We want to find; g(x) = 3⋅f(x)

This means that; g(x) = 3(x - 1)

Looking at the options, the input values to be used are x = 1, 2 3.

When x = 1; g(x) = 3(1 - 1 )

g(x) = 0

When x = 2; g(x) = 3(2 - 1)

g(x) = 3

When x = 3; g(x) = 3(3 - 1)

g(x) = 6

Looking at the options, only the table in option D is correct.

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Answer:

y= 4x + (-16)

Step-by-step explanation:

The slope of the given lime is m=4

x-intercept of the parallel line: (4,0)

plug that into the equation y= mx+b to find that b= -16

since the slope stays the same for parallel lines, and we just found b, we have the new line equation

The equation of parallel line with x intercept of 4 will be : y= 4x + (-16)

Given,

x intercept : 4

Slope = 4

Now,

x-intercept of the parallel line: (4,0)

As the equation of line to be obtained is parallel . Thus both lines will have same slope .

Slope of parallel line = 4

Substitute the value to find y intercept,

y = mx + b

0 = 4(4)  + b
b = -16

So,

Equation of parallel line: y = 4x + (-16)

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[tex]b=-1[/tex]

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

Answer:

X=2, X= -5/3

Step-by-step explanation:

let's solve your equation step-by-step

3x^2-x-10=0

step 1: factor left side of equation.

(3x+5)(x-2)=0

step 2: set factors equal to 0.

3x+5=0  or x-2=0

x= -5/3 or x=2

Answer:   [tex]\bold{a.\quad -\dfrac{2\sqrt{6}}{5}}[/tex]

Step-by-step explanation:

[tex]sin\theta=\dfrac{y}{h}\implies y=-1, h=5\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2 + y^2 = h^2\\x^2 + (-1)^2=5^2\\x^2+1=25\\x^2=24\\x=\sqrt{24}\\x=2\sqrt{6}[/tex]

[tex]\text{Since }\theta\text{ is between }\pi\text{ and }\dfrac{3\pi}{2} \text{ (Quadrant III)},\text{ then x and y are negative.}\\\implies x=-2\sqrt{6}\\\\\\cos\theta = \dfrac{x}{h}\quad =\boxed{-\dfrac{2\sqrt{6}}{5}}[/tex]

Answer:

The third term is [tex]24x^2y^2[/tex]

Step-by-step explanation:

The formula used to find the third term of the expansion (2x+y)^4 is called Binomial Theorem

The Binomial Theorem is:

[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]

In the given question x = 2x

a = y

n = 4

We have to find the third term, so value of k will be 2 as k starts from 0

Putting the values in the Binomial Theorem

[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex]

[tex]{n \choose k}==\frac{n!}{k!(n-k)!}[/tex]

Putting the values:

[tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]

So, the third term is [tex]24x^2y^2[/tex]

Which of the following lists the angles from smallest to largest?

Answer:

T, R, S

Answer:

B) -7m - 8 = m - 4

D) m - 4 = -7m - 8

E) -8 - 7m = -4 + m

Step-by-step explanation:

Solve all of the equations to see if they end up with the same result. Start with the original:

-2m - 5m - 8 = 3 + (-7) + m

-7m - 8 = -4 + m (now we know B and D and E are correct)

-7m - m - 8 = -4 + m - m

-8m - 8 = -4

-8m - 8 + 8= -4 + 8

-8m = 4

Answer:

-7m - 8 = m - 4

m - 4 = -7m - 8

-8 - 7m = -4 + m

Step-by-step explanation:

Given equation,

-2m - 5m - 8 = 3 + (-7) + m,

Combining like terms,

-7m - 8 =-4 + m

Subtract m from both sides,

-8m - 8 = -4

Add 8 on both sides,

-8m = 4

Divide both sides by -8,

m = [tex]-\frac{1}{2}[/tex]

(i)  -15m = -4m  ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0

(ii) -7m - 8 = m - 4  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(iii) -3m - 8 = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

(iv) m - 4 = -7m - 8  ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(v) -8 - 7m = -4 + m  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(vi) -8 - 3m = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

Answer:

x = 8

Step-by-step explanat

Answer:

6

Step-by-step explanation:

The answer you are looking for is 6y + 9.

In the equations (5y + 9) + y, you'd combine like terms to find the answer. You aren't distributing anything into the parenthesis, and 5y and 9 are not like terms (since the 9 doesn't have a "y" after it). That being said, you simply add "y" and 5y together to get 6y, and add the 9 to the end. Thus getting 6y + 9 as an answer.

I hope this helps!

Answer:

A. 6y+9

Step-by-step explanation:

Distributive property:

    ↓

[tex]A(B+C)=AB+AC[/tex]

First, you remove parenthesis.

5y+9+y

Group like terms:

   ↓

5y+y+9

Then,  you add by similar into elements.

5y+y=6y

6y+9 is the correct answer.

Answer:

x=a²+ab+b²/a+b , y=-ab/a+b

Step-by-step explanation:

The system of the given equation may b written as:

ax+by-a²=0

bx+ay-b²=0

Here,

a1=a,b1=b,c1= -a²

a2=b,b2=a and c2= -b²

By cross multiplication we get

x/b*(-b²)-(-a²)*a = -y/a*(-b²)-(-a²)*b = 1/a*a-b*b

x/-b³+a³ = -y/-ab²+a²b  = 1/a²-b²

Now

x/-b³+a³ = 1/a²-b²

x=a³-b³/a²-b²

x=(a-b)(a²+ab+b²)/(a-b)(a+b)

x=a²+ab+b²/a+b

And,

-y/-ab²+a²b = 1/a²-b²

-y=a²b -ab²/a²-b²

y=ab²-a²b/a²-b²

y=ab(b-a)/(a-b)(a+b)

y= -ab(a-b)/(a-b)(a+b)

y= -ab/a+b

Hence x=a²+ab+b²/a+b , y=-ab/a+b....

Answer:

y = 0.75x

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k substitute either of the 2 points into the equation

Using (12, 9 ), then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{9}{12}[/tex] = 0.75, so

y = 0.75x ← equation of variation

Answer:

67

Step-by-step explanation:

you have to divide

Answer

Step-by-step explanation:$149.50 is the answer

Answer:

D

Step-by-step explanation:

The system of equation will also have a solution of (2,0) are,

x + 4y = 2, 7x = 14.

Given that,

The solution to the system of equations shown is (2,0).

3x – 2y = 6 ,  x + 4y = 2

When the first equation is multiplied by 2, the sum of the two  equations is equivalent to 7x = 14.

We have to determine,

Which system of equations will also have a solution of (2,0).

According to the question,

To determine the system of the equation after applying all the given conditions in the steps, follow all the steps given below.

System of equations;  3x – 2y = 6 ,  x + 4y = 2.

                   [tex]2 \times (3x-2y) = 2 \times 6\\\\6x - 4y = 12[/tex]

                   [tex]6x - 4y + x + 4y = 12+ 2\\\\7x = 14\\\\x = \dfrac{14}{7}\\\\x = 2[/tex]

                      [tex]6(2) - 4y = 6\\\\12-4y = 6\\\\-4y = 6-12\\\\-4y == -6\\\\y = \dfrac{-6}{-4}\\\\y = \dfrac{3}{2}[/tex]

Hence, The required system of equation will also have a solution of (2,0) are, x + 4y = 2, 7x = 14.

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Answer:

Part 1) The exact value of the arc length is [tex]\frac{25}{6}\pi \ in[/tex]

Part 2) The approximate value of the arc length is [tex]13.1\ in[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi\ in[/tex]

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

[tex]\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in[/tex]

step 3

Find the approximate value of the arc length

To find the approximate value, assume

[tex]\pi =3.14[/tex]

substitute

[tex]\frac{25}{6}(3.14)=13.1\ in[/tex]

Answer:

13.1 (rounded to tenths)

Step-by-step explanation:

150 ° into radian is 5/6.

150°/1 (π/180) =5π/6.

Then multiply the radian angle by the radius.

5π/6 (5) = 25π/6

25π/6 = 13.1 (rounded to tenths)

Answer:

[tex]\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Step-by-step explanation:

we know that

Te volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=(r/2)\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (r/2)^{2}h[/tex]

[tex]V=\frac{1}{12}\pi r^{2}h[/tex]

Te volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we know that

To find the volume of the space remaining in the cylinder after the cone is placed inside it, subtract the volume of the cone from the volume of cylinder

so

[tex]\pi r^{2}h-\frac{1}{12}\pi r^{2}h=\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Answer:

AB = 4 cm

Step-by-step explanation:

The tangent and secant are drawn from an external point to the circle.

Then the square of the measure of the tangent is equal to the product of the external part of the secant and the entire secant.

let AB = x, then

x(x + 5) = 6²

x² + 5x = 36 ( subtract 36 from both sides )

x² + 5x - 36 = 0 ← in standard form

(x + 9)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 4 = 0 ⇒ x = 4

However x > 0 ⇒ x = 4 ⇒ b = 4 CM

Answer: 2X+5Y≥ 90

Step-by-step explanation:

since you get two points per/ each (key word of multiplication) true & false question, this will be represented by 2X

since you get five points per/ each multiple choice question, this will be represented by 5Y

he needs at least 90 points in total to get an A in his class

Answer : The correct answer is, [tex]29\frac{62}{7}[/tex]

Step-by-step explanation :

The given expression is:

[tex]10\frac{3}{7}+19\frac{5}{9}[/tex]

Step 1 : Convert mixed fraction into fraction.

[tex]\frac{73}{7}+\frac{176}{9}[/tex]

Step 2 : Taking L.C.M

[tex]\frac{(9\times 73)+(176\times 7)}{63}[/tex]

[tex]\frac{(657)+(1232)}{63}[/tex]

[tex]\frac{1889}{63}[/tex]

Step 3 : Convert fraction into mixed fraction.

[tex]=29\frac{62}{7}[/tex]

Thus, the correct answer is, [tex]29\frac{62}{7}[/tex]

Answer: 34.93 units

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=Bh[/tex]

Where "V" is the volume, "B" is the base area and "h" is the height.

Since we need to find the height, we must solve for "h":

[tex]h=\frac{V}{B}[/tex]

We know that the volume of that wooden chest (which is in the shape of a rectangular prism) is 524 cubic units and the base area is 15 square units. Then:

[tex]V=524units^3\\B=15units^2[/tex]

Subsitituting these values into [tex]h=\frac{B}{V}[/tex], we get that the height of the chest is:

 [tex]h=\frac{524units^3}{15units^2}=34.93units[/tex]

Answer:

the first one

Step-by-step explanation:

the number of mistakes went from 19 the first week of class to 0 the 20th week

Answer:

The answer is B

Step-by-step explanation:

happy cheating

Answer:

The answer is B

Step-by-step explanation:

And it's not cheating just trying to make it through high school.