given f(x) = x² + 5x +6 and g(x) = x +2, find (f ◦ g) (x)

Answer: Change = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

Answer: a set of quasilinear partial differential equations governing adiabatic and inviscid flow.

Step-by-step explanation:

that the definition of a Euler Equation.

The value of the variable x and y are 12 and 31 respectively.

Line a and b are parallel lines.

These parallel lines are cut by a transversal.

The traversal forms angle relationship as follows:

5x - 7 = 3x + 17 (alternate angles)

The variable x and y can be found as follows

5x - 7 = 3x + 17

5x - 3x = 17 + 7

2x = 24

x = 24 / 2

x = 12

Therefore,

4y + 3 + 3x + 17 = 180

4y + 3 + 3(12) + 17 = 180

4y + 3 + 36 + 17 = 180

4y = 124

y = 124 / 4

y = 31

Therefore, the value of the variable x and y are 12 and 31 respectively.

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The vertices that would minimize the objective function N = 7x + are (4, 0)

The objective function is given as

N = 7x + 2y

Next, we substitute the values in the options in the objective function

So, we have

A. (4,0)

N = 7(0) + 2(4)

N = 8

B. (6,3)

N = 7 x 6 + 2 x 3

N = 48

C. (3,9)

N = 7 x 3 + 2 x 9

N = 39

D. (0,12)

N = 7 x 0 + 2 x 12

N = 24

The smallest result in the above computations is 8

Hence, the vertices that would minimize the objective function N = 7x + are (4, 0)

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The answer should be parallel to each other

step by step

from plotting the graph line AB is parallel to Line DF

Answer: AB and DF are parallel.

Step-by-step explanation:

A=(-2,-11)

B=(6,5)

D=(-7,-10)

F=(2,0)

Slope (AB)=5-(-11) =

                    6-(-2)  =2

Slope (DF)=8-(-10)=

                    2-(-7) =2

Slope of AB=Slope of DF

AB and DF are parallel.

Answer:

So the answer would be 20 for 50-[20+[50-40]]

Step-by-step explanation:

50 - 40 =10 and 20 +10 = 30 so we 50 minus 30 which is 20

If its the other one it is 9 because 3 times 2 is 6 and 8 minus 6 is 2 and 7 plus 2 equals 9

The height of the rectangular pyramid will be 5 centimeters.

The volume of any solid body is defined as the space covered by the object in the three-dimensional space. For a rectangular pyramid, the volume will be the space covered by a pyramid in a three-dimensional space.

Given that the volume of 70 cubic centimeters, length of 7 centimeters, and width of 6 centimeters.

The height of the rectangular pyramid is calculated by using the formula:-

V = ( l w h ) / 3

70 = ( 7 x 6 x h ) / 3

h = 70 / 14

h = 5

Therefore, the height of the rectangular pyramid will be 5 centimeters.

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Answer:

19

Step-by-step explanation:

74+21=95       95/5=19

The zeros of the polynomial function are y = 4/5, y = -4/5 and y = ±4/5√i and the polynomial as a product of the linear factors is f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The polynomial equation is given as

f(y) = 625y^4 - 256

Express the terms as an exponent of 4

So, we have

f(y) = (5y)^4 - 4^4

Express the terms as an exponent of 2

So, we have

f(y) = (25y^2)^2 - 16^2

Apply the difference of two squares

So, we have

f(y) = (25y^2 - 16)(25y^2 + 16)

Apply the difference of two squares

So, we have

f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

Set the equation to 0

So, we have

(5y - 4)(5y + 4)(25y^2 + 16) = 0

Expand the equation

So, we have

5y - 4 = 0, 5y + 4 = 0 and 25y^2 + 16 = 0

This gives

5y = 4, 5y = -4 and 25y^2 = -16

Solve the factors of the equation

So, we have

y = 4/5, y = -4/5 and y = ±4/5√i

Hence, the zeros of the polynomial function are y = 4/5, y = -4/5 and y = ±4/5√i

How to write the polynomial as a product of the linear factors?

In (a), we have

The polynomial equation is given as

f(y) = 625y^4 - 256

Express the terms as an exponent of 4

So, we have

f(y) = (5y)^4 - 4^4

Express the terms as an exponent of 2

So, we have

f(y) = (25y^2)^2 - 16^2

Apply the difference of two squares

So, we have

f(y) = (25y^2 - 16)(25y^2 + 16)

Apply the difference of two squares

So, we have

f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

Hence, the polynomial as a product of the linear factors is f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

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The percentage loss is 25 %.

It is given that initial value of company stock is $28 and final value is $21 . Put these values in equation (1) , we get

     [tex]Percentage=\frac{21 - 28}{28} \times100\\\\Percentage=\frac{-7}{28} \times100\\\\Percentage=-25 \%[/tex]

Negative sign indicates loss in the percentage.

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Answer:

I think the length remains the same

Step-by-step explanation:

After expanding logarithm is [tex]\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa.

The basic form of the logarithm function can be written as  .

    [tex]log_ax =N[/tex]

where, a is the base of function or equation

          x define expression

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]log_b\frac{\sqrt{x} \sqrt{3} }{y^2 \sqrt{6z^2} } \\\\= log_b \sqrt{x} \sqrt{3} - log_b {y^2 \sqrt{6z^2} }\\\\= log_b\sqrt{x} + log_b\sqrt{3} - log_by^2 - log_b \sqrt{6z^2} \\\\= \frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - \frac{1}{2} log_b{(6z^2)} \\\\=\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]

Thus, after expanding logarithm is [tex]\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]

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Answer:

69

Step-by-step explanation:

The simple interest that Su Young paid for borrowing $2,900 for 15 months at 5.5% per year is $199.375.

Simple interest is interest that is not compounded.

Compounding involves adding earned interests to the principal when computing the next period's interest.

Principal = $2,900

Period = 15 months or 1.25 years

Interest Rate = 5.5%

Simple interest amount = Principal x Period x Rate

= $199.375 ($2,900 x 1.25 x 5.5%)

Thus, based on simple interest, Su Young paid $199.375.

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The expression as a single logarithm is log (2/3).

In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.

The general properties of logarithm for a fixed base are:

Now from the above properties of logarithms we can calculate:

log 8-2 log 6+log 3

=log 8 + log 3 - 2log6

We know that logₐx+logₐy=logₐxy and logₐxⁿ=n logₐx

∴log(8×3) -log(6²)

=log 24 - log 36

Again we know that logₐx-logₐy=logₐ(x/y)

=log(24/36)

=log(2/3)

Therefore the given expression written as a single logarithm is log(2/3).

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Answer:

It is Perpendicular

172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.

Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.

Here,
Original network address with a prefix  = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets =  172.16.0.0/20.

172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.

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If Sam says that 2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten as 2/21 to the power of 7 Sarah says it can be rewritten as 2/21 to the power of 10 Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.

2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten or express as [(2/7²)× (1/3^5)].

This implies that both Sam and Sarah are wrong, Only Steve is correct because  2/7 to the power of 2 times 1/3 to the power of 5 can either of the two expression that was mentioned by Sam and Sarah.

Therefore if Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.

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Area of base = 52

height = 5

Volume = 260

To find the volume of a rectangular prism all you need to do is multiply the length * width * height.

the area of base is the length * width = 13 * 4 = 52

then you multiply that by the height = 52 * 5 = 260

[tex]A(\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{k}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{k +1}{4} ~~ = ~~\stackrel{\stackrel{\textit{sllope of AB}}{\downarrow }}{5}\implies k+1=20\implies \boxed{k=19}[/tex]

Angles <6 and <12 are  alternate interior angle.

An interior angle is an angle that is inside a shape. It can also be described as an angle that lie in the area bounded between two parallel lines that are intersected by a transversal. In the given image, angles 6 and 11 are interior angles. The sum of interior angles is 180 degrees.

An alternate interior angle is an angle that is formed when two parallel lines are crossed by a transversal. The angle formed on the inner side of the parallel lines, and on the opposite sides of the transversal are called alternate interior angles. The alternate interior angles are angles 6 and 12.

A corresponding angle is an angle that is on  the same side of one of two lines cut by a transversal and on the same side of the transversal. Angle 4 and 12 are  corresponding angles.

An alternate exterior angle is the two angles that is formed  the outer side of the two parallel lines but on the opposite side of the transversal. Angles 4 and 14 are alternate exterior angle.

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The given exponential function  y = 3 eˣ is a exponential growth.

An exponential function is simply function that is used in a variety of real-world applications. It is primarily used to determine exponential decay as well as exponential growth, as well as to calculate investments, model populations, and so on.

Now, as per the given exponential functions;

y = 3 eˣ

The value of the exponent 'e' = 2.72.

This for any value of x > 0. this function will be of exponential Growth.

Therefore, the given function  y = 3 eˣ shows the exponential Growth.

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The question is testing on indices. Write 49 in its prime factors. By power rule (a^m)^(1/n)=a^(m/n). By factors, 49 = 7×7

49^(1/2)

(7^2)^(1/2) = 7^(2×1/2) = 7

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The measures of the angles are

1. Angle TLN, MZQ and NLM

The angles TLN and NLM are supplementary angles

So, we have

TLN + NLM = 180

This gives

3x - 18 + y = 180

Also, we have

TLN + MZQ = 180

So, we have

3x - 18 + 5x + 14 = 180

Evaluate the like terms

8x -4 = 180

This gives

8x = 184

Divide

x = 23

Substitute x = 23 in 3x - 18 + y = 180

3 x 23 - 18 + y = 180

Evaluate

51 + y = 180

So, we have

y = 129

The above computations imply that:

TLN = 3 x 23- 18 = 51

NLM = y = 129

MZQ = 5 x 23 + 14 = 129

2. Angle JZQ and TLN

The above means that

JZQ = TLN

So, we have

9x + 9 = 8x + 19

Evaluate

x = 10

So, we have

JZQ = TLN = 9 * 10 + 9

JZQ = TLN = 99

3. Angle ZMR, LMO and LMR

The angles ZMR and LMO are congruent angles

So, we have

ZMR = LMO

This gives

x + 14 = 2x - 6

Evaluate

x = 20

Also, we have

LMR + LMO = 180

So, we have

y + 2x - 6 = 180

y + 2 x 10 - 6 = 180

y + 14 = 180

So, we have

y = 166

The above computations imply that:

LMO= ZMR = 20 + 14 = 34

LMR = y = 166

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The radical expression ∛24  is between integers 2 and 3

The expression is given as

∛24

The above expression is a radical expression .

So, we have:

Express 24 as the product of 8 and 3

So, we have

∛24 = ∛(8 * 3)

Take the cube root of 8

So, we have

∛24 = 2∛3

Take the cube root of 3

So, we have

∛24 = 2 * 1.44

Evaluate the product

∛24 = 2.88

2.88 is between integers 2 and 3

Hence, the radical expression ∛24  is between integers 2 and 3

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The equation 3x - 1 = 1 - 3x has a solution x = 1/3

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

The expression is given as;

3x - 1 = 1 - 3x

Now, To check the solution is exist or not we can solve the equation as;

3x - 1 = 1 - 3x

Add '3x' both side,

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

6x - 1 = 1

Add '1' both side,

6x - 1 + 1 = 1 + 1

6x = 2

Divide '6' both side,

x = 1/3

Hence, The equation 3x - 1 = 1 - 3x has a solution x = 1/3.

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It should be noted that if your coefficient is a negative number, this indicates for a real life scenario that C. the starting amount is negative.

A negative coefficient indicates that the dependent variable tends to drop as the independent variable rises. The coefficient value is the amount that a one-unit change in the independent variable affects the mean of the dependent variable while keeping all other model variables constant.

If the correlation coefficient is negative, the two parameters you evaluated may have an inverse relationship.

Therefore, it should be noted that if your coefficient is a negative number, this indicates for a real life scenario that the starting amount is negative

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Answer:

$123.20

Step-by-step explanation:

Hey there!

To find the price for 308 bags of chips FOR 308 people, we need to first know what the price for 1 bag is

It says that it is 2 dollars for 5 bags

Now, we need to divide 2 by 5 to see how much money 1 bag is

2/5 is 0.4 and in this case 0.40 since we're dealing with money

Now that we know this, all we need to do is multiply 0.40 by 308 because we are buying for 308 people

0.40 x 308 is 123.2

This means that for 308 people, it would cost $123.20 to supply them all with a bag of chips!

The equations which could represent Relationship B which has a greater rate than Relationship A as described in the task content are; y = 2.2x and y = 3x.

It follows from the task content that the equation which could represent Relationship B given that it has a greater rate than Relationship A be determined.

It can be evaluated from the graph given that the slope of relationship A which is a measure of it's rate is;

Slope, m = (y2 - y1)/(x2 - x1)

m = (8 -4)/(4-2)

m = 4/2

m = 2.

Ultimately, since the rate of Relationship A is 2, and the rate of Relationship B has to be greater, it follows that the equations which are required are;

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