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3 years ago

What is the solution to the equation? 5(8 + 7) = 5•x + 5•7

Mathematics

1 answer:

Viefleur [7K]3 years ago

5 0

Answer:

x = 8

Step-by-step explanation:

5( 8 + 7 ) = 5 ⋅ x + 5 ⋅ 7

Add 8 and 7 to get 15.

5 × 15 = 5x + 5 × 7

Multiply 5 and 15 to get 75.

75 = 5x + 5 × 7

Multiply 5 and 7 to get 35.

75 = 5x + 35

Swap sides so that all variable terms are on the left-hand side.

5x + 35 = 75

Subtract 35 from both sides.

5x = 75 − 35

Subtract 35 from 75 to get 40.

5x = 40

Divide both sides by 5.

x = $\frac{40}{5}$

Divide 40 by 5 to get 8.

x = 8

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Sales An apparel shop sells skirts for $45 and blouses for $35. Its entire stock is worth $51,750. But sales are slow and only h

inysia [295]

Answer:

260 skirts and 270 blouses are left in the store after the sale.

Step-by-step explanation:

Let x be the number of skirts and y be the number of blouses.

An apparel shop sells skirts for $45 and blouses for $35

Cost of entire stock = $51,750

Thus, we can write the equation,

$45x + 35y = 51750$

Half the skirts and two-thirds of the blouses are sold for a total of $30,600.

Thus, we can write the equation,

$45(\dfrac{x}{2}) + 35(\dfrac{2y}{3}) = 30600\\\\135x + 140y = 183600$

Solving the two equations by elimination method, we have,

$135x + 140y-(135x + 105y) = 183600 - 155250\\35y = 28350\\\\y = \dfrac{28350}{35} =810\\\\x = \dfrac{51750-35(810)}{45} = 520$

Thus, there were 520 skirts and 810 blouses in the store.

Skirt left =

$520-\dfrac{520}{2} = 260$

Blouses left =

$810 - \dfrac{2}{3}\times 810 = 270$

Thus, 260 skirts and 270 blouses are left in the store after the sale.

5 0

3 years ago

Suppose that a new company that makes yo yos made 560 yoyos the first week the company overestimated its requirements. The manag

KATRIN_1 [288]

Answer:

312 yoyos in 8th week; 3407 yoyos over 8 weeks

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 560 and r = 0.92.

Thus, the formula for your sequence is

aₙ = 560(0.92)ⁿ⁻¹

Eighth term

a₈ = 560(0.92)⁷ = 560 × 0.5578 = 312

The company will manufacture 312 yoyos in the eighth week.

Sum over eight weeks

The formula for the sum of the first n terms of a geometric series is

Sum = a₁[(1 - rⁿ)(1 - r)]

Sum = 560[(1 - 0.92⁸)/(1 - 092)]

= 560[(1 - 0.513 22)/0.08 ]

= 560 × (0.486 78/0.08)

= 560 × 6.0848

= 3407

The company will manufacture a total of 3407 yoyos over eight weeks.

4 0

3 years ago

Solve the folowing equation for "n" 6n - 4= 3n + 8

ipn [44]

Answer:

4/3

Step-by-step explanation:

6n - 4 = 3n + 8

6n - 3n = 8 + 4

3n = 4

n = 4/3

Goodluck with your schoolwork/homework.

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apologies in advance for any errors or bad explanations.

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Mumz [18]

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