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3 years ago

Solve by the substitution method. 6x + 8y = 0 -7x + y = 31

Mathematics

1 answer:

jekas [21]3 years ago

7 0

Answer:

(-4, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

6x + 8y = 0

-7x + y = 31

Step 2: Rewrite Systems

-7x + y = 31

Add 7x to both sides: y = 7x + 31

Step 3: Redefine Systems

6x + 8y = 0

y = 7x + 31

Step 4: Solve for x

Substitution

Substitute in y: 6x + 8(7x + 31) = 0
Distribute 8: 6x + 56x + 248 = 0
Combine like terms: 62x + 248 = 0
Isolate x term: 62x = -248
Isolate x: x = -4

Step 4: Solve for y

Define equation: -7x + y = 31
Substitute in x: -7(-4) + y = 31
Multiply: 28 + y = 31
Isolate y: y = 3

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3 years ago

The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]?

ELEN [110]

Question:

The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]?

A. 2/5

B. 1

C.2

D.5/2

The image of the graph is attached below.

Answer:

Option D: 5/2 is the average speed over the interval [9,11]

Explanation:

The graph shows the distance in miles of a runner over x hours.

Now, we need to determine the average rate of speed over the interval $[9,11]$

The x-axis represents the time taken.

The y-axis represents the distance.

To find the average speed, let us use the formula for speed which is given by

$speed=\frac{distance}{time}$

Thus, substituting the coordinates $(9,6)$ and $(11,11)$ , we have,

$speed=\frac{11-6}{11-9} =\frac{5}{2}$

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1. Jadyn started off his long division problem incorrectly. What is his mistake?

Anastaziya [24]

The mistake Jadyn made in the long division is

Mistake in subtraction
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<h3>What is long division ?</h3>

Long division refers to a way of dividing large numbers

performing the long division correctly gives

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8 335 40 8 * 40 = 320 335 - 320 15

8 15 1 8 * 1 = 8 15 - 8 7

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brainly.com/question/1098876

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1 year ago

Mala has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What is the percentage of bangles of each type?

Rainbow [258]

Answer:

Percentage of gold bangles is 66.6 and of silver bangles it is 33.3

Step-by-step explanation:

Given:

Number of gold bangles Mala has = $20$

Number of silver bangles she has = $10$

Total number of bangles = $20+10$ = $30$

We have to find the percentage of each type of bangles.

So,

Percentage of bangles = $\frac{No.\ of \ bangles\ each\ type}{Total\ no.\ of \ bangles} \times 100$

Percentage of gold bangles.

⇒ $\frac{20}{30} \times 100$

⇒ $\frac{20\times 100}{30}$

⇒ $\frac{2000}{30}$

⇒ $\frac{200}{3}$

⇒ $66.6\%$

Percentage of silver bangles.

⇒ $\frac{10}{30}\times 100$

⇒ $33.3\%$

Percentage of gold bangles, Mala has = 66.6 and of silver bangles it is = 33.3

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