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3 years ago

Which graph can be used to find the solution(s) to 8 – 4x = 2x – 4?

Mathematics

2 answers:

nikklg [1K]3 years ago

5 0

it would equal 2x if im correct

Tom [10]3 years ago

3 0

Answer:

The answer in the attached figure

Step-by-step explanation:

Method 1

we have

$8-4x=2x-4$

Rewrite the equation as a compound system of equations

$y=8-4x$ -----> equation A

$y=2x-4$ -----> equation B

Using a graphing tool

The solution of the system of equations is the intersection point both graphs

see the attached figure

the solution is $x=2$

Method 2

we have

$8-4x=2x-4$

Group terms that contain the same variable and move the constant to the other side of equation

$4x+2x=8+4$

Combine like terms

$6x=12$

Divide by $6$ both sides

$x=2$

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Marina86 [1]

Answer:

the answer is 20

Step-by-step explanation:

180+180=360

80+70=150

180-150=20

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3 years ago

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Each home room has to have the same number of girls and boys in each home room.

agasfer [191]

4 for part A
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4 years ago

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a s

Andrew [12]

Answer:

a) 1186

b) Between 1031 and 1493.

c) 160

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean of 1262 and a standard deviation of 118.

This means that $\mu = 1262, \sigma = 118$

a) Determine the 26th percentile for the number of chocolate chips in a bag. 

This is X when Z has a p-value of 0.26, so X when Z = -0.643.

$Z = \frac{X - \mu}{\sigma}$

$-0.643 = \frac{X - 1262}{118}$

$X - 1262 = -0.643*118$

$X = 1186$

(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.

Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a p-value of 0.025, so X when Z = -1.96.

$Z = \frac{X - \mu}{\sigma}$

$-1.96 = \frac{X - 1262}{118}$

$X - 1262 = -1.96*118$

$X = 1031$

97.5th percentile:

X when Z has a p-value of 0.975, so X when Z = 1.96.

$Z = \frac{X - \mu}{\sigma}$

$1.96 = \frac{X - 1262}{118}$

$X - 1262 = 1.96*118$

$X = 1493$

Between 1031 and 1493.

(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?

Difference between the 75th percentile and the 25th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 1262}{118}$

$X - 1262 = -0.675*118$

$X = 1182$

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 1262}{118}$

$X - 1262 = 0.675*118$

$X = 1342$

IQR:

1342 - 1182 = 160

7 0

3 years ago

The area of the top face of a cube is 16 square inches. Use 8 of these cubes to make a rectangular

KengaRu [80]

Answer:

The volume of the rectangular prism is 512 inches³

Step-by-step explanation:

Any cube has 6 square faces

Area of any square = L × L, where L is a length of each side

The volume of the cube = L × L × L

∵ The area of the top face of a cube = 16 inches²

→ Find which number multiply by itself = 16

∵ 16 = L × L

∵ 16 = 4 × 4

∴ L = 4 inches

Let us find the volume of 1 cube

∵ The volume of the cube = L × L × L

∵ L = 4 inches

∴ The volume of each cube = 4 × 4 × 4

∴ The volume of each cube = 64 inches³

∵ We will use 8 of this cube to make a rectangular prism

→ That means the volume of the rectangular prism is 8 times

the volume of 1 cube

∴ The volume of the prism = 8 × volume of 1 cube

∵ The volume of each cube = 64 inches³

∴ The volume of the prism = 8 × 64

∴ The volume of the prism = 512 inches³

The volume of the rectangular prism is 512 inches³

5 0

3 years ago

Need some help with number word problems, tysm if you do :)

lord [1]

Answer:

Read below

Step-by-step explanation:

x is always the smaller number

y is always the larger number

underlined means it's the question

bolded means it's the answer

1.

One number is 6 times as large as another. Their sum is 42. Find the numbers.

The numbers need to fit the criteria:

6x=y
x+y=42

A. 6+36=42 (correct)

B. 7+42=49 (incorrect)

C. 7+35=42 (incorrect because it doesn't follow the 1st rule)

D. 6+42=48 (incorrect)

Only A. 6, 36 fits the criteria.

2.

One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+3=y
4x-4=3y

4+3=7

12-6≠21 (incorrect)

7+3=10

28-3≠30 (incorrect)

13+3=16

52-4=48 (correct)

9+3≠13 (incorrect)

Only C. 13, 16 fits the criteria.

3.

One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+4=y
5x+3=4y

13+4=17

65+3=68 (correct)

-23+4= -19

-115+3≠ -76 (incorrect)

17+4=21

85+3≠84 (incorrect)

-11+4+ -7

-35+3≠ -33 (incorrect)

Only A. 13, 17 fits the criteria.

4.

The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.

The numbers need to fit the criteria:

x+y=23
y-3x=3

5+18=23

18-15=3 (correct)

8+15=23

15-24≠3 (incorrect)

-13+36=23

36+39≠3 (incorrect)

-5+28=23

28+15≠3 (incorrect)

Only A. 5, 18 fits the criteria.

5.

The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.

The numbers need to fit the criteria:

x+y=26
y-2x=2

8+18=26

18-16=2 (correct)

9+17=26

17-18≠2 (incorrect)

7+19=26

19-14≠2 (incorrect)

6+20=26

20-12≠2 (incorrect)

Only A. 8, 18 fits the criteria.

4 0

4 years ago