Rewrite each expression by completing the square.
a. z^2 − 5z + 8
b. x^2 + 0.6x + 1

Answers

Answer 1
Answer:

Answer:

The answer to your question is below

Step-by-step explanation:

a)

                                                       z² - 5z + 8

Equal to zero                                 z² - 5z + 8 = 0

Subtract 8 in both sides                z² - 5z  + 8 - 8 = 0 - 8

Simplify                                           z² - 5z             = -8

Divide -5 by 2 write the result

in both sides of the equation       z² - 5z + (-5/2)² = -8 + (-5/2)²

to the power of 2

Simplify                                          z² - 5z + 25/4 = -8 + 25/4

                                                      z² - 5z + 25/4 = -32/4 + 25/4

                                                      z² - 5z + 25/4 = -7/4

Factor                                            (z - 5/2)² = -7/4

b)

                                                        x² - 0.6x + 1

Convert 0.6 to a fraction                0.6 = 6/10 = 3/5

                                                        x² - 3/5x + 1

Equal to zero                                 x² - 3/5x + 1 = 0

Subtract -1 in both sides                z² - 3/5z  + 1 - 1 = 0 - 1

Simplify                                           z² - 3/5z             = - 1

Divide -3/5 by 2 write the result

in both sides of the equation       z² - 3/5z + (-3/10)² = -1 + (-3/10)²

to the power of 2

Simplify                                          z² - 3/5z + 9/100 = -1 + 9/100

                                                      z² - 3/5z + 9/100 = -100/100 + 9/100

                                                      z² - 3/5z + 9/100 = -91/100

Factor                                            (z - 3/10)² = -91/100


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The average speed of a plane is 560 kilometers per hour. How long does it take the plane to travel 140 kilometers?

Answers

(140 km) x (1 hour / 560 km) = 0.25 hour = 15 minutes
560kph*x=140kilometers so x=.25 so .25*60 minutes is 15 minutes

Square root of 2(5 + square root of 8) is irrational and equal to what

Answers

Hello,
√2(5+√8)=5√2+√2*√8=4+5√2
===========================

While painting the interior of a large house, Gene is going to transfer some paint in a large 5 gallon container to a smaller bucket. Unfortunately he slips and spills 2 gallons of paint all over the floor. If each wall in the house takes 9/24 of a gallon to paint, how many walls can he paint with what he has left?

Answers

Answer:

8 walls

Step-by-step explanation:

While painting the interior of a large house, Gene is going to transfer some paint in a large 5 gallon container to a smaller bucket. Unfortunately he slips and spills 2 gallons of paint all over the floor.

The remaining amount of paint is

= 5 gallons - 2 gallons

= 3 gallons

If each wall in the house takes 9/24 of a gallon to paint, how many walls can he paint with what he has left?

Hence:

9/24 gallon = 1 Wall

3 gallons = x wall

Cross Multiply

9/24 × x = 3 × 1

x= 3 ÷ 9/24

x = 3 × 24/9

x = 8 walls

He can paint 8 walls with what is left.

In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?A. 90
B. 110
C. 130
D. 180​

Answers

Using matrices to solve, the number of calories that are in 1 serving of milk is; 110 Calories

How to solve Linear Programming problems?

Let the calories in one serving of milk be x

Let the calories in one serving of juice be y

Let the calories in one serving of soda be z

Thus, for Joe, equation to show amount of calories is;;

2x + y + z = 530    -----(1)

For Darius, equation to show amount of calories is; ;

x + 2y = 370     ------(2)

For Marian, equation to show amount of calories is;

3x + z = 510    ------(3)

Using matrix calculator online to calculate this 3 equations, we have;

x = 110 calories.

Read more about Linear Programming at; brainly.com/question/23414950

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Answer:

the answer is B on ed2020

Step-by-step explanation:

for answer b, if you subtract 330 from 510 you get soda = 180 cal. then if you subtract 110 from 370 you get 260, and 260 divided by two (he consumed 2 juice) equals 130.

so you have soda = 180 cal and juice = 130 cal

if you plug it into joe's calorie intake you do 130 (1 serving of juice) + 180 (1 serving of soda) and + 220 (two servings of milk) you get 530 which is joe's total calorie intake in liquids, so B (110) is correct

Divide £132 in the ratio 3:8

Answers

£132 in the ratio 3:8 as 36 and 96.

What is Ratio?

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Ratio= 3:8

Now, total = 3+ 8 = 11

So, First

£132 x 8/ 11

= 12 x 8

= 96

and, second

132 / 3/11

= 12 x 3

= 36

Hence, £132 in the ratio 3:8 as 36 and 96.

Learn more about ratio here:

brainly.com/question/13419413

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First you add 3 and 8. This equals 11.
£132 / 11 = £12
£12 x 3 = £36
£12 x 8 = £96
So your answer is £36:£96

Please help me to answer this question thank you otherwise I my teacher will be so mad .

Answers

Answer:

2/3 ≈ 0.666667

5/11 ≈ 0.454545

5/6 ≈ 0.833333

6/7 ≈ 0.857143

Step-by-step explanation:

Easiest and fastest way to do this is to use a calculator to find your decimals and then approximate.

Answer:

2/3 = 2 divided by 3 so 2 divided by 3 = 0.666667. We round up because it is a repeating decimal which goes on forever

5/11= 5 divided by 11 = 0.454545

5/6 = 5 divided by 6 =0.833333

6/7 = 6 divided by 7 = 0.857143

rounded up because it is an infinite decimal

Hope this helps

Step-by-step explanation: