MATHEMATICS HIGH SCHOOL

Solve the equation, first for x and then for y.

Answers

Answer 1

Answer:

Answer:

x = 77 - 2y

y = -x/2 + 77/2

Step-by-step explanation:

2x + 4y - 31 = 123

add 31 both sides

2x + 4y - 31 + 31 = 123 + 31

2x +4y = 154

Solve for x

2x = 154 - 4y

divide both sides by 2

x = 77 - 2y

solve for y

2y = 77 - x

divide both sides by 2

y = 77/2 - x/2

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1. The perimeter of a rectangle is given by the expression below, where l is the length of the rectangle and w is the width.2(l + w)

Find the perimeter of a rectangular window frame with a length of 19 inches and a width of 3 inches.

Answers

2(l+w)
width=3
length=19
now the easiest thing you can do is this= 19+3+19+3= 44
or you can say 19+3*2=44

Put these in order of size smallest first , 0.3 , 75% 4/5

Answers

0.3, 75%, 4/5 Convert all to decimal

0.3, 0.75, 0.80 So we can now arrange it with smallest first.

It is already in that order from the smallest to biggest.

= 0.3, 75%, 4/5

convert them to decimal
0.3, 0.75, 0.8 so it is 0.3, 0.75, 0.8. answer is 0.3 , 75%, 4/5

5x^2-4x=6 solve for x

Answers

Let's solve your equation step-by-step.5x(2)−4x=6Step 1: Simplify both sides of the equation.5x(2)−4x=6Simplify: (Show steps)10x+−4x=6(10x+−4x)=6(Combine Like Terms)6x=66x=6Step 2: Divide both sides by 6.‌6x6‌=‌66‌x=1Answer:x=1

What is the inverse of the function f(x) = 2x – 10

Answers

f(x) is y given x
y=2x-10
inverse is switching x and y so
x=2y-10
solve for y
y=(x+10)/2

Joshua uses a rule to write the following sequence of numbers 1/6,1/2,5/6,----------,11/2 What rule did Joshua use? What is the missing number in the sequence?

Answers

Answer: The missing number in the sequence is $(7)/(6)$

Step-by-step explanation:

Since we have given that

$(1)/(6),(1)/(2),(5)/(6),----------,(11)/(2)$

First term = a= $(1)/(6)$

Common difference = d is given by

$d=a_2-a_1\n\n(1)/(2)-(1)/(6)\n\n=(6-2)/(12)\n\n=(4)/(12)=(1)/(3)\n\nSimilarly,\nd=a_3-a_2\n\n=(5)/(6)-(1)/(2)\n\n=(10-6)/(12)\n\n=(4)/(12)\n\n=(1)/(3)$

Therefore, it forms an arithmetic sequence.

Since, $a_4$ is missing,

So,

$a_4=a+3d\n\na_4=(1)/(6)+3* (1)/(3)\n\na_4=(1)/(6)+1\n\na_4=(1+6)/(6)\n\na_4=(7)/(6)$

Hence, the missing number in the sequence is $(7)/(6)$

This is an arithmetic progression at a rate of 2/6.

So 1/6 + 2/6 = 3/6 (1/2)
3/6 + 2/6 = 5/6
5/6 + 2/6 = 7/6
....
29/6 + 2/6 = 31/6
31/6 +2/6 = 33/6 (11/2)

The endpoints of on are located at O(1, 2) and N(3, 1). Using slope-intercept form, write the equation of line on.

Answers

y = -1/2x +2 1/2
General equation;
y = mx + c

Calculating the slope;
Change in y/ (change in x) = gradient m

(2-1)/(1-3) = - 1/2

Replacing m gives;
y= -1/2x + c

Calculating the value of c
take point (1,2) above and replace y with 2 and x with 1
2=-1/2 *1 +c
c = 2 1/2
Equation then is
y = -1/2x +2 1/2

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