MATHEMATICS HIGH SCHOOL

Simplify the following algebraic expressions.

-6x + 5 + 12x -6

Answers

Answer 1
Answer: The answer is 6x-1.  

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A youth group has a yard sale to raise money for a charity. The group earns $800 but decides to put its money in thebank for a while. Calculate the amount of money the group will have given the following scenarios: c. If the youth group needs the money quickly, which is the better choice? Why?

Which of the following represents the factored form of f(x) = x3 − 81x?f(x) = x(x − 9)2
f(x) = (x + 9)(x − 9)
f(x) = x(x + 9)(x − 9)
f(x) = x(x2 − 9)

Answers

Factored form of f(x) = x^(3) -81x is equal to x(x+9)(x -9).

What is factored form?

" Factored form is defined as for the given polynomial product of the constant along with linear expressions."

Formula used

a^(2) -b^(2) =(a+ b)(a- b)

According to the question,

Given polynomial,

f(x) = x^(3) -81x

Simplify the given polynomial to get its factored form using formula,

x^(3) -81x\n\n= x(x^(2) -81)\n\n= x(x^(2) -9^(2) )\n\n= x(x+ 9)(x-9)

Hence, Option(C) is the correct answer.

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You're original equation has a -81, so the factored form will have to have a positive and negative multiplying one another to achieve that...

f(x) = x(x + 9)(x - 9)

Prove that cos 3 x =4 cos ^(3)x-3 cos x

Answers

cos3x=4cos^3x-3cosx\n\nL=cos(2x+x)=cos2xcosx-sin2xsinx\n\n=(cos^2x-sin^2x)cosx-2sinxcosxsinx\n\n=cos^3x-sin^2xcosx-2sin^2xcosx\n\n=cos^3x-3sin^2xcosx\n\n=cos^3x-3cosx(1-cos^2x)\n\n=cos^3x-3cosx+3cos^3x\n\n=4cos^3x-3cosx=R


cos(a+b)=cosa\ cosb-sina\ sinb\n\nsin^2a+cos^2b=1\to sin^2a=1-cos^2b\n\ncos2a=cos^2a-sin^2a\n\nsin2a=2sina\ cosa

Use the angle difference identity to sovle 5cos2(theta) =1 for 0 degrees is less than or equal to theta is less than 360 degrees

Answers

use cos (2∅)= 2cos² ∅ -1

5(2cos²∅ -1 )=1
10cos²∅ -5 = 1
10cos²∅ = 6
cos²∅ = 0.6
cos∅ = ± √(0.6)
∅=  39.2,180 - 39.2, 180 + 39.2 , 360 - 39.2
∅ = 39.2 , 140.8 , 219.2 , 320.8 

A newspaper carrier has $1.80 in change. He has two more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he have?

Answers

1\ quarter=\$0.25\n1\ dime=\$0.10\n1\ nickel=\$0.05\n\nq\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ quarters\nd\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ dimes\nn\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ nickels\n\nq=2d\ \ \ and\ \ \ n=3q\ \ \ \Rightarrow\ \ \ n=3\cdot 2d=6d\n\nq\cdot0.25+d\cdot0.10+n\cdot 0.03=1.80\n\n2d\cdot0.25+d\cdot0.1+6d\cdot0.05=1.8\n\n

0.5d+0.1d+0.3d=1.8\n\n0.9d=1.8\ \ \ \Rightarrow\ \ \ d=2\ \ \ \Rightarrow\ \ \ q=2\cdot2=4\ \ \ and\ \ \ n=6\cdot2=12\n\nAns.\ 4\ quarters,\ 2\ dimes,\ 12\ nickels

HELPPP 100 POINTS!Tyler belongs to a fitness club at a community centre. The graph below represents the relationship between the number of times he visited the club and his total monthly cost. What type of variation is this relationship, and what is the initial value? *

#1 Direct Variation, and initial value is 0
#2 Partial Variation, and initial value is 0
#3 Direct Variation, and initial value is 20
#4 Partial Variation, and initial value is 20

Answers

The type of variation in this relationship is direct variation, and the initial value is 20.

What is the linear relationship?

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The given graph represents the relationship between the number of times he visited the club and his total monthly cost.

As per the given graph, we can conclude as follows:

The type of variation in this relationship is a direct variation because the points are increasing, and the initial value is 20 because the coordinate of the initial point is (0, 20).

Hence, the correct answer would be option (C).

Learn about the linear relationship here :

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Answer:

#3

Step-by-step explanation:

Fatimah and four other women threw javelins in a competition.The distances, in metres, of the four other women are shown.
15.2
15.9
16.8
16.1
The mean distance for all five women was 16.04 metres.
Did Fatimah throw the javelin the furthest?
You must show your working.

Yes or no

Answers

Answer:

Hi,

NO

Step-by-step explanation:

sum of all distances=16.04*5=80.2

sum of the four distances=15.2+15.9+16.8+16.1=64

Fatimah 's distance=80.2-64=16.2

Fatimah throw the javelin not the furthest.
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