The **solution** to the **equation** g(x) = 6x - 9 whenx = -8b is g(-8b) = -48b - 9

From the question, the **equation **of the function is given as

g(x) = 6x - 9

Also, we have the value of the **variable **to be

x = -8b

So, we substitute -8b for x in the equation of the function

g(x) = 6x - 9

The above equation becomes

g(-8b) = 6(-8b) - 9

Open the brackets in the above expression

g(-8b) = -48b - 9

The above equation cannot be firther simplified

Hence, the solution is g(-8b) = -48b - 9

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What is the value of x? S *+559 W 2x–71° X-30

As shown in the figure :

The sum of the central angles = 360

so,

[tex](x+55)+(2x-71)+(x-3)+55=360[/tex]Solve the equation for x :

[tex]\begin{gathered} x+55+2x-71+x-3+55=360 \\ 4x+36=360 \\ 4x=360-36 \\ 4x=324 \\ \\ x=\frac{324}{4}=81 \end{gathered}[/tex]So, the answer is : x = 81

Using SSS, SAS, ASA, & AAS WITH CONGRUENT TRIANGLES For each problem below, state each of the following: a ) state the congruent parts b )state how the triangles are congruent c ) state the congruence

Given two triangles, ADB and CBD

So,

1. the measure of < D = the measure of angle < B

2. CB = AD

3. BD = DB

so, the triangle ADB is congruent to the triangle CBD by SAS [ side - angle - side ]

So, the corresponding parts are congruent :

So,

1. the measure of angle A = the measure of angle C

2. the measure of angle B = the measure of angle D

3. AB = CD

Find a polynomial function of degree 4 with - 1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.

The polynomial function in expanded form is f(x) = _

(Use 1 for the leading coefficient.)

**Answer: **[tex]f(x)=x^4 +3x^3 +3x^2 +x[/tex]

**Step-by-step explanation:**

[tex]f(x)=x(x+1)^3 \\\\=x(x^3 +3x^2 +3x+1)\\\\=x^4 +3x^3 +3x^2 +x[/tex]

Jessica is a software saleswoman. Her base salary is $1900, and she makes an additional $50 for every copy of History is Fun she sells.

Let P represent her total pay (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 28 copies of History is Fun.

Equation:

Total pay if Jessica sells 28 copies:

The **equation** which represents Jessica's income is 1900+50n.

Jessica's total income after selling 28 copies of **History** is **Fun** is $3300

Base **salary** of Jessica = $1900

The **additional** income per copy of History is Fun = $50

Let p represent her total pay (in dollars), and let n represent the number of **copies** of History is Fun she sells:

Formulating the equation we get the following:

Jessica's total pay = Base salary + Additional income per copy of History is Fun*Number of copies sold by Jessica

= 1900 + 50*n

Income, when she sells 28 copies of History, is Fun:

= 1900 + 50*28

= 1900 + 1400

= $3300

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What does the leading term of −5x^4+4x^3−6x^2+8 tell you?

**Step-by-step explanation:**

The leading term is -5x^4, which tells us the highest degree of the polynomial.

The leading term in the **equation** tells us about the** degree** and whether the curve opens outwards on inwards

**What is an equation in one variable?**

An **equation** is a polynomial in one **variable** with a finite **degree**

We are given an **equation**

[tex]-5x^4+4x^3-6x^2+8[/tex]

In this the leading term is -5x^4

Here the **coefficient** is negative this tells us that the curve opens downwards. if the **coefficient** has been positive then the curve would open outwards.

Also from the leading term we can find out the degree of the highest variable. the **degree** of highest variable in this case is 4

Hence, The leading term in the **equation** tells us about the degree of the variable and whether the curve opens outwards on inwards

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how do i graph the equation y=2000x+4000

**Answer:**

first draw the line edges and vertical

second put the dot every no.

And put the y=2000×+4000

An investment firm invested in two companies last year. They invested $12,000 in Company A and made a profit of 14%. They

invested $8000 in Company B and made a profit of 21%.

Answer the questions below. Do not do any rounding.

(a) What was the investment firm's total profit?

$0

(b) What was the percent profit for their total investment?

The **investment** firm's **total profit** is $ 3360 and the **percent profit** for their **total investment** is 16.8%.

How to calculate **percentage **of a situation?

A **value or ratio** that may be stated as a fraction of 100 is referred to as a **percentage** in mathematics. If we need to calculate a **percentage** of a number, we should divide it by its entirety and then multiply it by 100. The **proportion** therefore refers to a component per hundred. Per 100 is what the word **percent** means. The letter "**%**" stands for it. There is no dimension to **percentages**. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

Formula for **percentages**: **(Value/Total value) * 100**

Given, **amount invested** in **company A** = $ 12,000**Amount invested** in **company B** = $ 8000**Profit earned** by **company A** = 14%**Profit earned** by **company B** = 21%

Amount in profit earned from company A = (12000*14)/100 = $ 1680

Amount in profit earned from company B = (8000*21)/100 = $ 1680

Therefore total profit of the investment firm = $ (1680 + 1680) = $ 3360

Thus, the **investment** firm's **total profit** is $ 3360.

Now, percentage profit of total investment = (3360/20000)*100 = 16.8%, using available literature and formula.

Thus, the **percent profit** for their total** investment** is 16.8%

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I need help with Systems of 2 equations Word Problems. Could some one help?

Let x be the number of children and let y be the number of adults.

We know that the total number of attendants was 147, then:

[tex]x+y=147[/tex]We also know that each child ticket cost $4 and for each adult cost $12, and the total amount collected were $1156. Then we have:

[tex]4x+12y=1156[/tex]Hence we have the system:

[tex]\begin{gathered} x+y=147 \\ 4x+12y=1156 \end{gathered}[/tex]Now we have to solve the system. To do that we solve the first equation for y:

[tex]y=147-x[/tex]and we plug this value into the second equation and solve for x:

[tex]\begin{gathered} 4x+12(147-x)=1156 \\ 4x+1764-12x=1156 \\ -8x=1156-1764 \\ -8x=-608 \\ x=\frac{-608}{-8} \\ x=76 \end{gathered}[/tex]Now that we have the value we can find the value of y, then:

[tex]\begin{gathered} y=147-76 \\ y=71 \end{gathered}[/tex]**Therefore there were 76 children and 71 adults.**

n

4 Which expression is equivalent to 8.508 ÷ 70.9?

A 8.508 709

B 85.08 709

C 850.8 709

D 8,508 709

5 What is the value of 0.5 ÷ 0.8? Show your work.

**Answer:**

a because 8.508

**Step-by-step explanation:**

0.625 so it easy 0.5:0.8

The quotient of 134 and z is the same as 374

We will ahve the following:

[tex]\frac{134}{z}=374[/tex]which of the following equations would not contain the point (4,12)?

A. y=1/2x+8 B. y= -2x+20

**Answer:**

A is the answer :))))))))))))))))))

Triangle HIJ is similar to triangle KLM. Find the measure of side LM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.

Given the following question:

We know the two triangles are similar

We also have the bases of the two triangles which means we can find how bigger the second triangle is, compared to the first triangle.

[tex]\begin{gathered} 5\times3.6=18 \\ 7\times3.6=25.2 \\ 25.2\text{ is already rounded to the nearest tenth} \\ LM=25.2 \end{gathered}[/tex]4. Which number produces anirrational answer when multipliedby 0.79?A.B. 0.383838...C. 0.12D.קשותU

Recall that the product between two rational numbers is always a rational number, and the product between an irrational number and a rational number different from zero is always an irrational number.

Also, recall that a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Now, notice that:

[tex]\begin{gathered} 0.79=\frac{79}{100}, \\ 0.383838\ldots=\frac{38}{99}, \\ 0.12=\frac{12}{100}. \end{gathered}[/tex]Therefore, 0.79, 0.383838..., 0.12 are rational numbers.

Now, recall that:

[tex]\sqrt[]{7}[/tex]is an irrational number.

Therefore, the product between 0.79 and √7 is an irrational number.

**Answer:** Option A.

What does the fundamental theorem of algebra state about the equation 2x2−x+2 = 0?Question 5 options:The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots arex = 1±i15√4.The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1±i15√4.

**Given **

Equation

[tex]2x^2-x+2=0[/tex]**Procedure **

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are

[tex]x=\frac{1}{4}\pm\frac{\sqrt[]{15}}{4}[/tex]The discriminant b^2 - 4ac < 0

so, there are two complex roots.

If 8 - x = 17, then find the value

of 6x - 22

**Answer: -25**

**Step-by-step explanation: 8 - x = 17 ~ x=-9 6*(-9)-22=-25**

what is the base and coefficient of the exponential function:

[tex]y=10(\frac{1}{5})^x[/tex]

Given an exponential function

[tex]\begin{gathered} y=ab^x \\ \text{ wh}ere\text{ a and b are constants} \\ \text{then a is the coefficient} \\ \text{and b is the base} \end{gathered}[/tex]Therefore,

10 is the coefficient and 1/5 is the base

A cube has a surface area of 253 square inches.What is the area of one face of the cube in sqaure inches.

**Answer:**

42 1/6 square inches

**Step-by-step explanation:**

253=6x

x=42 1/6

42 1/6 square inches

:]

find 10-3. write the subtraction fact tow ways?

**Answer:**

10 - 3 = 7

10 - 7 = 3

**Step-by-step explanation:**

Name the transformations happening to the absolute value parent function, f(x) = |x|, in each of the following in the correct order.

**is one**

**the Answer:**

**Step-by-step explanation:**

1

A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.Enter the answer

Let's define,

X := Total **minutes** it takes to fill the plane (with fuel)

Then,

[tex]X\cdot0.20=12.40[/tex]Solving it for X, we get

[tex]X=\frac{12.40}{0.20}=62\text{ min}[/tex]This means that the vehicle takes **1 h 2 min **to fill the plane. If the fuelling finished at 10:35, it began at

**9:33**.

hello i have a upcoming test and want to know how to solve this

Expression given:

[tex]g>1[/tex]To know how to graph the given expression, it is easier if we determine what it means in words. In this case, this expression means all the values above one (without including one).

We know that one is not included as it has the sing ">", if the value were included, then it would have the sing "≥" or "≤".

This is important because when you are graphing, a discontinuous line is drawn for values not included, and a continuous one for included values.

Now, we would have to evaluate if it is the independent variable (generally called x), or the dependent variable (generally called y).

Assuming that *g *is the dependent variable, then the graph would be like this:

However, if the variable was de independent variable, then it would look like this:

We have to note that both graphs go from 1 to bigger values.

Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.

NEED FAST RESPONSE EQUATION AND SOLUTION

The **equation** is 6.75x = 5.875y

The price will be the same for 47 **Go Golf** games and 54 Golf **Games**

Go Golf charges for the **ball** and **club** rental = $2.50

Go Golf charges per game = $4.25

Total **charges** for Go Golf for one game = $6.75

Golf Games charges for the ball and club rental = $3.25

Golf Games charges for two games = $8.50

Total charges for Golf Game for two games = $11.75

Per game charges = $11.75/2 = $5.875

Let x be the number of games for Go Golf and y be the number of games for Golf Games

Formulating the equation we get:

6.75x = 5.875y

Converting into fractions we get:

675/100x = 5875/1000y

27/4x = 47/8y

After cross multiplication

x/y = 57/48

x = 57 and y = 48

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B= (s+z/2) m solve for s

please help i need to get my grade up

**Answer:**

See below

**Step-by-step explanation:**

1. Multiply m to get, m(s + z)/2 => (ms + mz)/2

2. Mutiply by 2 by both sides

2B = MS + MZ

3. Divide By M

2B = M(S+Z)

2B/M = S+Z

4. Minus Z

(2B/M - Z) = S

Could you provide a step by step resolution for this question?

Given:

Angle A = 120 degrees

Side opposite angle C = 150 meters

Side opposite angle B = 275 meters

Find:

Angle B

Solution:

Since we have two sides given and an included angle, we can use cosine law.

Let's look for the length of the side opposite Angle A first.

[tex]a^2=b^2+c^2-2bc\cos A[/tex]where a = length of the side opposite Angle A or side BC

b = side opposite Angle B or Side AC

c = side opposite Angle C or Side AB

A = Angle A

Since we already have the data above, let's plug it in to the formula we have.

[tex]a^2=275^2+150^2-2(275)(150)\cos 120[/tex]Then, solve a.

[tex]\begin{gathered} a^2=75,625+22,500-82,500(-0.5) \\ a^2=98,125+41,250 \\ a^2=139,375 \\ \sqrt[]{a^2}=\sqrt[]{139,375} \\ a\approx373.3296\approx373.33 \end{gathered}[/tex]Hence, the length of side opposite a or Side BC is approximately 373.33 meters.

Now, to solve for Angle B, we can use the sine law.

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]Let's plug in the value of Angle A, side BC or a, and side AC or b to the formula.

[tex]\frac{\sin120}{373.3296}=\frac{\sin B}{275}[/tex]Then, solve for Angle B.

[tex]\begin{gathered} \sin B=\frac{275\sin 120}{373.3296} \\ \sin B=0.6379268552 \\ B=\sin ^{-1}0.6379268552 \\ B\approx39.64 \end{gathered}[/tex]**Therefore, the bearing of ship C from ship B is approximately 40 degrees. (rounded off to the nearest degree)**

Determine whether the distribution represents a discrete probability distribution. Justify your answer

The probability distribution is given in the table.

The condition for the probability distribution is

1. The sum of the probability distribution is 1.

2. The probabilities value range between 0 and 1.

Condition to check the probability distribution

[tex]0.35+0.25+0.22+0.12=0.94[/tex]The sum of the probability is not equal to 1.

**Hence the distribution does not represents a discrete probability distribution.**

Which value makes the equation 5b + 15 = 30 true?

A b=3

B b=9

C b= 10

D b=75

**Answer:**

Hello! The answer is A) B=3

**Step-by-step explanation:**

Hope I helped! Please mark brainiest if get chance.

(Ps: Are you an army?)

5b+15=30

Then subtract 15 on both sides

5b=15

Divide 5 by 15

B=3

So , (5 x 3)+ 15= 30, would make this equation true.

I hope this helps :)

Then subtract 15 on both sides

5b=15

Divide 5 by 15

B=3

So , (5 x 3)+ 15= 30, would make this equation true.

I hope this helps :)

Write the correct expression for the following statement:

x six times

x^6

**Step-by-step explanation:**

I don't know how to explain but I think this is what you mean

Using Euler's formula, howmany edges does a polyhedronwith 7 faces and 10 verticeshave?[?] edgesEuler's Formula: F + V = E + 2

**Given: **The following

**To Determine:** The number of edges

**Solution:**

The Euler's formula is given as

F + V = E + 2,

where F is the number of faces,

V the number of vertices, and

E the number of edges.

Substitute the given into the formula

[tex]\begin{gathered} F=7 \\ V=10 \\ E=? \end{gathered}[/tex][tex]\begin{gathered} F+V=E+2 \\ E=F+V-2 \\ E=7+10-2 \\ E=17-2 \\ E=15 \end{gathered}[/tex]**Hence, the number of edges possessed by the polyhedron is ****15**

If L, M and N are the midpoints of the sides of the triangle PQR, PR= 46, PQ = 40, and LN = 17, find each measure.; LM, MN, QR and the perimeter of LMN

**LM = 23; MN = 20 ; QR = 34 ; Perimeter of LMN is 60**

Here, we want to find the measures

From what we have, triangle LMN is formed by joining the midpoints of the triangle PQR

From the midpoint theorem, the sides of PQR are parallel and exactly half the measure of the sides they face

For example, LM is half PR

a) LM

[tex]LM\text{ = }\frac{1}{2}\times PR\text{ = }\frac{1}{2}\times46\text{ = 23}[/tex]b) MN

[tex]MN\text{ = }\frac{1}{2}\times PQ\text{ = }\frac{1}{2}\times\text{ 40 = 20}[/tex]c) QR

Here, QR will be twice the measure of LN

[tex]QR\text{ = 2}\times LN\text{ = 2}\times17\text{ = 34}[/tex]d) To find the perimeter of LMN, we have to add up the measure of the side lengths

We have this as;

[tex]\text{LMN = LM + LN + MN = 23 + 17 + 20 = 60}[/tex](One-Step Inequalities MC) Write the inequality for the statement: the difference between a number and four sevenths is no more than negative nine elevenths f minus 4 over 7 is less than or equal to 9 over 11 f minus 4 over 7 is less than negative 9 over 11 f plus 4 over 7 is less than or equal to negative 9 over 11 f minus 4 over 7 is less than or equal to negative 9 over 11

The **inequality **for the given statement is [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .

By definition, any monotonically growing function can be applied to both sides of an **inequality **without destroying the relationship between the two (provided that both **expressions **are in the **domain **of that function).

The **inequality **for the given statement is [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .

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**Answer:**

**the answer is D.**

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