simplify. -2(7-n) +4

Functions and their domains of all the subparts are:

So,

(A) (fog)(x) and domain:

[tex](f \circ g)(x)=f(g(x))=(g(x))^2+g(x)=\left(x^2+14 x+2\right)^2+x^2+14 x+2\\=x^4+28 x^3+200 x^2+56 x+4+x^2+14 x+2=x^4+28 x^3+201 x^2+70 x+6[/tex]

The domain of (fog)(x) is the collection of domain values for g(x) with range values in the domain of f(x).

Because both functions are polynomials, the domain is [tex](-\infty, \infty)[/tex].

(b) (gof)(X) and domain:

[tex](g \circ f)(x)=g(f(x))=(f(x))^2+14(f(x))+2=\left(x^2+x\right)^2+14\left(x^2+x\right)+2\\=x^4+2 x^3+x^2+14 x^2+14 x+2=x^4+2 x^3+15 x^2+14 x+2[/tex]

The domain name is [tex](-\infty, \infty)[/tex] because this is a polynomial composition.

(c) (fof)(x) and domain:

[tex]\begin{aligned}&(f \circ f)(x)=f(f(x))=(f(x))^2+f(x)= \\&\left(x^2+x\right)^2+x^2+x=x^4+2 x^3+x^2+x^2+x=x^4+2 x^3+2 x^2+x\end{aligned}[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

(d) (gog)(x) and domain:

[tex](g \circ g)(x)=g(g(x))=(g(x))^2+14(g(x))+2=\left(x^2+14 x+2\right)^2+14\left(x^2+14 x+2\right)+2\\=x^4+28 x^3+200 x^2+56 x+4+14 x^2+196 x+28+2=x^4+28 x^3+214 x^2+252 x[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

Therefore, functions and their domains of all the subparts are:

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The complete question is given below:
Find the functions and their domains. (enter the domains in interval notation.)

[tex]f(x)=x^2+1 x, g(x)=x^2+14 x+2[/tex]

(a) (fog)(x) and domain

(b) (gof)(X) and domain

(c) (fof)(x) and domain

(d) (gog)(x) and domain

The numbers in terms of power of 10 is;

(i) [tex]10^{1}[/tex]

(ii) [tex]10^{6[/tex]

(iii) [tex]9 * 10^{4}[/tex]

Here,

Given numbers are;

i. 10

ii 1000000

iii 90000

We have to find in terms of power of 10.

What is Powers of a number?

The power of a number says how many times to use the number in a multiplication. Powers are also called Exponents or Indices.

Now,

Given numbers are;

i. 10

ii 1000000

iii 90000

We can write in terms of power of 10 as;

(i) 10 = [tex]10^{1}[/tex]

(ii) 1000000 = [tex]10^{6[/tex]

(iii) 90000 = [tex]9 * 10^{4}[/tex]

Hence, The numbers in terms of power of 10 is;

(i) [tex]10^{1}[/tex]

(ii) [tex]10^{6[/tex]

(iii) [tex]9 * 10^{4}[/tex]

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The values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1

The functions are given as:

f(x) = 2x^2 - 9x - 5

g(x) = x - 5

The composite function (f.g)(x) is calculated as

(f.g)(x) = f(x) * g(x)

This gives

(f.g)(x) = (2x^2 - 9x - 5) * (x - 5)

Evaluate the product

(f.g)(x) = 2x^3 - 9x^2 - 5x - 10x^2 + 45x + 25

Evaluate the like terms

(f.g)(x) = 2x^3 - 19x^2 + 40x + 25

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

This gives

(f/g)(x) = (2x^2 - 9x - 5)/(x - 5)

Factorize the numerator

(f/g)(x) = (2x + 1)(x - 5)/(x - 5)

Evaluate the quotient

(f/g)(x) = 2x + 1

Hence, the values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1

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If the quadratic is y = a*x^2 + b*x + c

the coordinates of the vertex are:

x = -b/2a

y = (1/2a)*( -0.5*b^2 + c)

For a quadratic equation in standard form:

y = a*x^2 + b*x + c

The x-value of the vertex is given as:

x = -b/2a

Once we get the x-value of the vertex, we can get the y-value by evaluating the quadratic equation in x = -b/2a, we will get:

y = a*(-b/2a)^2 + b*(-b/2a) + c

y = b^2/(4a) - b^2/2a + c = (1/2a)*(b^2/2  - b^2 + c)

y = (1/2a)*( -0.5*b^2 + c)

Then the coordinates of the vertex are:

x = -b/2a

y = (1/2a)*( -0.5*b^2 + c)

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Answer:

20%

Step-by-step explanation:

Every fifth car would be 1/5 or 20%

The  linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

Option (A) and (D) is correct.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

According to given question we have

a. y<-2x

To put the value of x any y (0,0) we get

=0<-2*0

=0<0

b. y<-3x+4

To put the value of x any y (0,0) we get

=0<-3*0+4

=0<0+4

=0<4

c. y>-2x+6

To put the value of x any y (0,0) we get

=0>-2*0+6

=0>0+6

=0>6

d. y>-3x

To put the value of x any y (0,0) we get

=0>-3*0

=0>0

Therefore, the  linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

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Answer:--------X=3/13---------

Step-by-step explanation:

Answer:

16cm

Step-by-step explanation:

The area of a 2d figure is w x h. We know the area, a, is 80cm^2, the height, h, is 5, and the width, w, is 2x + 8.

Since we are solving for x, we want to isolate the variable.

5 x 2x + 8 = 80
80/5 = 2x + 8

We can now solve for x.

80/5 = 2x + 8
16 = 2x + 8
16 - 8 = 2x + 8 - 8
8 = 2x
8/2 = 2x/2
4 = x

We aren't done, we still need to solve for w, where we now know x = 4

w = 2x + 8
w = 2(4) + 8
w = 8 + 8
w = 16

Answer:

Step-by-step explanation:

first let : x = 3 and y = 5

so x-3 means 3-3 = 0

and 2y means 2 * 3 = 6

therfore x-3 > 2y means 0 > 6, false

The surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

It is given that:

The triangular prism is given in the picture:

The surface area = 4x2 + 2x2.4 + 3.2x2 + 2(1/2)3.2x2.4

The surface area = 8 + 4.8 + 6.4 + 7.68

The surface area = 26.88 square cm

The volume = (1/2)x3.2x2x2.4

The volume 7.68 cubic cm

Thus, the surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.

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Each part of the question is plotted on the number line as an image with the solution.

How are rational numbers represented on the number line?

(1)      [tex]\frac{-3}{8} , 1\frac{1}{5} = \frac{6}{5} = 1.2 , \frac{-3}{4}[/tex]  are plotted on the number line as an image with the solution.

(2) -13+15+(-8) = -6 is plotted on the number line as an image with the solution.

(3) [tex]\frac{3-(-14)}{7} = \frac{17}{7} = 2.429, \frac{-36+58}{-11} = -2[/tex] are plotted on the number line as an image with the solution.

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The modified equation is expressed as g(x) = x^2 - 6

Translation is the process of changing the position on an x-plane.

Given the function of a graph expressed as y=x^2

If the function is shifted 6 units to the left, hence the resulting function is given as;

g(x) = x^2 - 6

Hence the modified equation is expressed as g(x) = x^2 - 6

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Answer: 125

Step-by-step explanation:

The total number of matches played is 552.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The given parameters are as;

Teams = 24

Matches against each other = 2

Therefore, the total number of matches played is;

Total = Teams * (Teams - 1)

This gives;

Total = 24 * (24 - 1)

Evaluate;

Total = 552

Hence, the total number of matches played is 552.

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Answer:

D. 491.52

Step-by-step explanation:

Quadratic equations are all those equations that can be reformulated in a standard format (αx² + bx + c(=0) where the value of x is unknown and the values of the coefficients (a, b and c) are unknown.

These equations can always be solved using the quadratic formula, although sometimes it is also possible to use factorization or isolation of variables.

Expand squared

It is distributed

Combine like terms.

Move terms to the left

Subtract the numbers

Use the quadratic formula.

                        [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} \end{gathered}$}[/tex]

In standard form we identify "a", "b" and "c" from the original equation and add to the quadratic formula.

                      [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-(-14)\pm\sqrt{(-14)^{2}-4\cdot1\cdot41 } }{2\cdot1} \end{gathered}$}[/tex]

Simplify

                                         [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14\pm4\sqrt{2} }{2} \end{gathered}$}[/tex]

Separate equations

To solve for the unknown variants, we split the equation into two: one with a plus sign and the other with a minus sign.

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14+4\sqrt{2} }{2} \end{gathered}$}[/tex]

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14-4\sqrt{2} }{2} \end{gathered}$}[/tex]

Solve

Order and isolate the variant to find each solution.

                                            [tex]\large\displaystyle\text{$\begin{gathered}\sf x=7+2\sqrt{2} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x=7-2\sqrt{2} \end{gathered}$}[/tex]

                            [tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\blue{Answer \ \ \longmapsto \ \ x=7\pm2\sqrt{2} }} \end{gathered}$}}}[/tex]

The automobile covers 224.48 km.

This problem can be solved by using the unitary method.

In this method we calculate the value for a unit quantity and then multiply it with the desired number for which we want to calculate.

Here it is given that a automobile covers 1122.4 km with 80 liters.

For 1 liter of gasoline distance covered = [tex]\frac{1122.4}{80}[/tex]

                                                              = 14.03 km

So, for 16 liters of gasoline distance covered will be = 16× 14.03

                                                                                  = 224.48 km

Therefore the automobile covers 224.48 km for 16 liters of gasoline.

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Step-by-step explanation:

photo please ......................

Answer:

Step-by-step explanation:

need to see the graph

Answer: -4 because 2(-6)2 = -24 and 5(2)2 = 20 so -24 + 20 is -4.

Answer:-4

Step-by-step explanation:

2(-6)2

2 x -6 x 2=-24

5 x 2 x 2=20

-24+20=-4

Answer:

Domain: [tex]x > -5[/tex] or [tex](-5,\infty)[/tex]

Range: [tex]y\geq -3[/tex] or [tex][-3,\infty)[/tex]

Step-by-step explanation:

The domain is essentially the set of x-values in a given graph. In this graph. we see that the lowest x-value is an unfilled dot when x=-5. The unfilled dot means that the function [tex]f(x)[/tex] doesn't include -5. We then see that the x-value goes to positive infinity. This means that [tex]x[/tex] must be greater than -5. It is not greater or equal to -5 because the dot is not filled.

Therefore, we have that [tex]x > -5[/tex]. To convert to interval notation we can take the lower value (-5) and put it on the left side and put the higher value ([tex]\infty[/tex]) and put it on the right side. Since the graph doesn't include -5, we can put parentheses around both values to get [tex](-5,\infty)[/tex].

Note: We always put parentheses around both [tex]\infty[/tex] and [tex]-\infty[/tex].

The range is basically the same as the domain but with the y-value. We can see that the lowest y-value is y=-3. This includes -3 since the line fills the point in. Then we see that the highest y-value is once again positive infinity. This means that [tex]y\geq-3[/tex].

Now when we convert to interval notation, we have -3 and [tex]\infty[/tex]. This time since y=-3 is included in the function, we put a hard bracket around -3. Thus, we get [tex][-3,\infty)[/tex].

Hope this helps!

Step-by-step explanation:

It's simple in the following diagram ( 13x + 45)° + (19x +3)° won't be equal to 180° as they are vertically opposite angle...... and are vertically opposite to each other...

So to find the value of x :

13x + 45° = 19x + 3°

13x - 19x = 3 - 45

-6x = - 42

x = -42 / -6

x = 7°

☘☘☘...

Answer: The total number of stamps is 132.

Step-by-step explanation:

We know that Erin has 36 stamps.

Given that information, we can calculate how many stamps Julia has which is 2/3 as many stamps as Erin.

2/3 * 36 = 24

Julia has 24 stamps.

Julia also has 1/3 as many stamps as Robert.

24 = 1/3 * Robert

Robert = 72 stamps

Add the three numbers together to get your final answer

24 + 72 + 36 = 132

Answer:

1013

Step-by-step explanation:

(6)(7)(8−0)(3)+5

=42(8−0)(3)+5

=(42)(8)(3)+5

=(336)(3)+5

=1008+5

=1013

Answer: To the right

Step-by-step explanation:

The negatives on a number line are on the left side and the positives on the right.

Step-by-step explanation: educated guess

Answer:

4/5

Step-by-step explanation:

8/10

=4/5

Answer:

8/9!!

all credit goes entirely to the person in comments for giving us all the right answer.

Answer: x=0.5, y=1

Step-by-step explanation:

-4x+3y=1

6x-y=2

6x-2=y

-4x+3(6x-2)=1

-4x+18x-6=1

-4x+18x=7

14x=7

x=0.5

6x-y=2

6(0.5)-y=2

3-y=2

y=1

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

¹/₄

Step-by-step explanation:

Given:

The dessert is the "whole", i.e. equal to 1.

To find how much of the dessert was left, subtract all the given portions from 1:

[tex]\begin{aligned}\textsf{Dessert left for Sara} & = 1-\dfrac{1}{8}-\dfrac{1}{4}-\dfrac{3}{8}\\\\& = \dfrac{8}{8}-\dfrac{1}{8}-\dfrac{2}{8}-\dfrac{3}{8}\\\\& = \dfrac{8-1-2-3}{8}\\\\& = \dfrac{2}{8}\\\\& = \dfrac{1}{4}\end{aligned}[/tex]

Therefore, ¹/₄ of the dessert was left for Sara.

Answer:

2/8 (or) 1/4

Step-by-step explanation:

The amount of desert she served is,

→ 1/8 + 1/4 + 3/8

→ (1 + 2 + 3)/8

→ 6/8

Then amount of desert left for Sara is,

→ 1/1 - 6/8

→ (8 - 6)/8

→ 2/8 (or) 1/4

Hence, she was left with 2/8 of desert.

Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

Let's define the variables:

We know that we want to make 200ml, then:

x  + y = 200

And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:

x*0.5 + y*0.8 = 200*0.68

(the concentrations are written in decimal form)

Then we have the system of equations:

x  + y = 200

x*0.5 + y*0.8 = 200*0.68

To solve it we start by isolating x in the first equation:

x = 200 - y

Replacing that in the other equation we get:

(200 - y)*0.5 + y*0.8 = 200*0.68

Now we can solve this for y, we will get:

100 - y*0.5 + y*0.8 = 136

y*0.3 = 136 - 100 = 36

y = 36/0.3 = 120

So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

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The population density of Singapore in residents per square kilometer is 8266.12 per square kilometer

What is Population Density ?

The given parameters are

Number of people = 21400 residents

Area = 1 mi²

Convert the square mile to square kilometer

1 x 1.609² = 2.588881 Km²

Population density = Number of residents ÷ area

Population density = 21400 ÷ 2.588881

Population density = 8266.12 per square kilometer

Therefore, the population density of Singapore in residents per square kilometer is 8266.12 per square kilometer

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