Find f(g(x)) simplify completely f(x)= x^2+5x+2 g(x)=3x

Answer:

(2,0)

(-5,-4)

Step-by-step explanation:

you first have to determine where the two graphs intersect, then easily you should write the (x,y) of the point in which there is an intersection

Step-by-step explanation:

7. Since they are similar triangles we have:

[tex] \frac{10}{8} = \frac{x}{12} \\ \\ x = 15[/tex]

So DF is 15

8. They are also similar. So:

[tex] \frac{14}{7} = \frac{x}{5} \\ x = 10[/tex]

So PR is 10

The total annual fica tax for an annual salary of $38,480 is: d. $2,943.72.

FICA tax comprises of:

Social security= 6.2%

Medicare=1.45%

Hence:

Social Security=$38,480 x 0.062

Social security =$2,385.76

Medicare= $38,480 x 0.0145

Medicare=$557.96

FICA tax=$2,385.76+$557.96

FICA tax=$2,943.72

Therefore the total annual fica tax for an annual salary of $38,480 is: d. $2,943.72.

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Answer:

D

Step-by-step explanation:

Answer:

b ≤ 7

Step-by-step explanation:

Given that:

A red block and a blue block are on a scale.  The red block weights 9 ounces. The total weight of both blocks is 16 ounces.  

To Find:

Which inequality best represents b, the possible weight of the blue block in ounces?

Knowing that;

< ⇒ less than

> ⇒ Greater than

≤ ⇒ less than or equal to

≥ ⇒ greater than or equal to

Solve:

Since the total blocks is 16 ounces that means it can't be pass 16 also known as can't be greater than. As well as, it given us that the red block weight 9 ounces that means

16 - 9 = 7

which given us that it must be equal to 7 or less than 7 to make it true.

Thus,

b ≤ 7

Kavinsky

Answer:

D

Step-by-step explanation:

y=6x+2

2=12+2

NO
y=-x

2=-2

NO

y=2x+6

2=4+10

NO

y=x

2=2

6=6

Answer:

[tex]y=x[/tex]

Step-by-step explanation:

We will use slope-intercept form:

[tex]y=mx+b[/tex]

Where [tex]m=[/tex]slope and [tex]b =[/tex]y-intercept

To find the slope we use the slope formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We plug in the coordinates getting:

[tex]\frac{6-2}{6-2} =\frac{4}{4} = 1[/tex]

So we have a slope of 1:

[tex]y=(1)x+b[/tex]

If we look at the answer choice we see that only one of them has a slope of 1 so the equation is:

[tex]y =x[/tex]

Answer:

k = 13

Step-by-step explanation:

substitute x = x + 5 into f(x) , that is

f(x + 5) = (x + 5)² + 3(x + 5) - 10 ← expand squared factor using FOIL

          = x² + 10x + 25 + 3x + 15 - 10

         = x² + 13x + 30

compare this with f(x + 5) = x² + kx + 30

for the 2 expressions to be equal , then k = 13

Answer:

the answer of that question is 45

Answer:

(y + 3)² - 8

Step-by-step explanation:

y² + 6y +1

Step 1: Divide the co efficient of y by 2

6 ÷2 = 3

Step2: Now find the square of 3

3² = 9

Step3: Add and subtract 9

y² + 6y + 9 - 9 + 1  = y² +6y + 9 - 8  

                              = y² + 2*y*3 + 3² - 8    

Compare y² +2 * y*3 + 3² with a² +2ab + b²

                             = (y + 3)² - 8

Step-by-step explanation:

a. y-y1/y2-y1=x-x1/x2-x1

y+9/-5+9=x-9/10-9

y+9/4=x-9/1

y+9/4=x-9

b. y+9=4(x-9)

y+9=4x-45

y-4x=-45-9

y-4x=-54

Basically to find solutions of the equation. Find the x intercept points.

Equation: x² - 4x + 2

when solved using quadratic formula:

[tex]\dashrightarrow \sf x_{1,2}= \dfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \:2}}{2\cdot \:1}[/tex]

[tex]\dashrightarrow \sf x_1 \dfrac{-\left(-4\right)+2\sqrt{2}}{2\cdot \:1},\:x_2=\dfrac{-\left(-4\right)-2\sqrt{2}}{2\cdot \:1}[/tex]

[tex]\dashrightarrow \sf x=2+\sqrt{2}, \ 2-\sqrt{2}[/tex]

[tex]\dashrightarrow \sf x=3.414, \ 0.586[/tex]

These are the solutions to the quadratic equation.

Answer:

x ≈ 0.6 , x ≈ 3.4

Step-by-step explanation:

the solutions to the quadratic equation from the graph are where the graph crosses the x- axis.

these are at approximately x = 0.6 and x = 3.4

The answers will be:

a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).

b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).

c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:

 f(8) = 4·8 +3 = 35

 g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35

 g(8) > f(8)

d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).

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1.    (4,5)

2.    remain constant and increase

3.    g(x) exceeds the value of f(x)

4.     eventually

Step-by-step explanation:

Answer:

ok real answer 2,-3

Step-by-step explanation:

The distance between the diagonal and the the perimeter of the field is given by D = 229.2 m

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

Miranda is standing at the corner of a 70 m by 110 m soccer field.

Let the dimensions of the rectangle be 70m x 100m

Now , the length of the diagonal is D

And , from the Pythagoras theorem ,

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

D = √ ( 70 )² + ( 110 )²

D = 130.8 m

Now , the perimeter of the rectangle is P = 2 ( 70 + 110 ) = 360 m

And , walking around the perimeter of the field

Now , by cutting across the diagonal instead of walking around the perimeter of the field, Miranda can save approximately 360 m - 130.8 m ≈ 229.2 m.

Hence , the diagonal of the rectangle is 130.8 m

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Answer:

D. {(1,2) , (2,3) , (3,4) , (4,5)}

Step-by-step explanation:

Functions are relations with one output for any unique input. Relations that pass the vertical line test have one output for each input. In this case, D was the only set that met the criteria.

Answer:

4/19

Step-by-step explanation:

Both the numerator and denominator can be divided by 2, giving 4/19

Answer:

Given:

⇒ Weekly income = 38 × $19.50 = $741

⇒ Monthly income = ($741 × 52.14) ÷ 12 = $3219.65

28% of monthly income

= 0.28 × $3219.65 = $901.50

As $1700 > $901.50 Manuel should not rent the house for $1700 per month since it is more than 28% of his income.

The cost of rent at $1700 per month is actually 52.8% of his monthly income:

(1700 / 3219.65) x 100 = 52.8%

Another pair of coordinates that could be the missing ordered pair, (x,y) in this set is (1, 0)

Linear functions are functions that have a leading degree of one,

Given the coordinate points ((-2,-3), (0,-2), (2, -1), (x, y)}, we need to determine the missing coordinate points

Since the x-coordinates has a difference of 2, hence the missing x-coordinate is given as:

x = -1 + 2
x = 1

For the y-coordinate

y = -1 + 1
y = 0

Hence another pair of coordinates that could be the missing ordered pair, (x,y) in this set is (1, 0)

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The expression (2/7)x (1.4x² - 3.5y) can be written in the form of a polynomial as 0.4x³ - xy.

Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

The expression is given below

[tex]\rm \dfrac{2x}{7} \times (1.4x^2-3.5y)[/tex]

The expression can be written in the form of the polynomial

[tex]\rightarrow \rm \dfrac{2x}{7} \times (1.4x^2-3.5y)\\\\\\\rightarrow \rm \dfrac{2x \times 1.4x^2}{7} - \dfrac{3.5y\times 2x}{7 }\\\\\\\rightarrow \dfrac{2.8x^3}{7} - \dfrac{7xy}{7 }\\\\\\\rightarrow 0.4x^3 - xy[/tex]

The expression in the form of a polynomial is given as

[tex]\rm \rightarrow 0.4x^3 - xy[/tex]

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Answer:

68.3 miles per hour

Step-by-step explanation:

One kilometer is 0.62 miles.

110 times 0.62 is 68.3

Wendy's rate of 110 kilometers per hour is 68.3 miles per hour.

To convert kilometers per hour to miles per hour, we need to use the conversion factor of 1 kilometer = 0.621371 miles.

Given that Wendy drives at a rate of 110 kilometers per hour.

we can multiply this value by the conversion factor to obtain the equivalent rate in miles per hour.

110 kilometers per hour × 0.621371 miles per kilometer

= 68.34381 miles per hour

We get 68.3 miles per hour.

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Answer:

its answer a :)

Step-by-step explanation:

875/23 = 38.04, round down to get 38

Answer:

[tex]\Longrightarrow: \boxed{\sf{y=3-4x}}[/tex]

Step-by-step explanation:

To solve for y, you have to isolate it on one side of the equation.

First, you have to subtract by 12x from both sides.

[tex]\Longrightarrow:\sf{12x+3y-12x=9-12x}[/tex]

Solve.

[tex]\Longrightarrow:\sf{3y=9-12x}[/tex]

Then, you divide by 3 from both sides.

[tex]\Longrightarrow:\sf{\dfrac{3y}{3}=\dfrac{9}{3}-\dfrac{12x}{3}}[/tex]

Solve.

[tex]\sf{\dfrac{9}{3}-\dfrac{12x}{3}}[/tex]

[tex]\sf{\dfrac{9-12x}{3}}[/tex]

Use the distributive property.

[tex]\underline{\text{DISTRIBUTIVE PROPERTY:}}[/tex]

9-12x=3(3-4x)

[tex]\sf{\dfrac{3\left(3-4x\right)}{3}}[/tex]

Divide the numbers from left to right.

3/3=1

3-4x

Then, rewrite the problem down.

[tex]\Longrightarrow: \boxed{\sf{y=3-4x}}[/tex]

I hope this helps! Let me know if you have any questions.

Answer:

y = (3) - (4x)

Step-by-step explanation:

Note: Since there is only one equation given, the value of "y" will not be a fixed value.

Given equation:

Our main goal to solve for "y" is to have the y-variable on one side, and a specific value or variable on the other side (e.g., y = 3 or y = 4x) . Start out by subtracting both sides by 12x. This will isolate the y-variable and it's cooeficient (3).

Once the y-variable and the cooeificent of the variable have been isolated, we can divide both sides by the cooeficient to isolate the variable.

Therefore, the value of "y" is 3 - 4x.

Answer:

Step-by-step explanation:

1.

Center: (-2, 3)

Radius: 10/2 = 5

Standard form/ equation: (x + 2)² + (y - 3)² = 25

Standard form:

(x - (-2))² + (y - 3)² = 5²

(x + 2)² + (y - 3)² = 25

2.

Center: (1, 1)

Radius: 6/2 = 3

Standard form/ equation: (x - 1)² + (y - 1)² = 9

Standard form:

(x - 1)² + (y - 1)² = 3²

(x - 1)² + (y - 1)² = 9

Hope this helps!

#1

Equation:-

More simply.

#2

Equation

Answer:

11

Step-by-step explanation:

Perimeter is figured out by adding all 4 sides.

Width of 11 + width 11 + length 15 + length 15 = 52

And the length of 15 is 4 more than the width of 11

Answer:

Answer is B. Will he be able to stay under the 15,000 miles per year limit?

Step-by-step explanation:

Just took the tes

Answer:

B. Will he be able to stay under the 15,000 miles per year limit?

Step-by-step explanation:

Answer:

7^4 = 2401

Step-by-step explanation:

___, ___, ___, ___

all blank spaces can be filled with all 7 numbers each.. so 7*7*7*7 is total number of paterns you can get if repititions is allowed

Step-by-step explanation:

The area of the triangular base is: 19

square units

How to calculate the base area

The given parameters are:

Volume = 27.36 cubic units

Height = 2.88 unit

The volume of a triangular prism is:

V = 0.5 * B *h

Where B represents the base area.

So, we have:

27.36 = 0.5 * B * 2.88

27.36 B * 1.44 -

Solve for B

B = 19

Hence, the area of the triangular base is: 19 square units