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2 years ago

Three sets of a sum of a number and four are added to the sum of 7 times the same number and 13

1 answer:

5 0

Let
x--------------> a number

we know that
<span>three sets of a sum of a number and four----------> 3(x+4)
t</span><span>he sum of 7 times the same number and 13--------> 7x+13

therefore

</span>(Three sets of a sum of a number and four) are added (to the sum of 7 times the same number and 13) ----------> [3(x+4)] + [7x+3]

[3(x+4)] + [7x+3]------> [3x+12] + [7x+3]=10x+15

the answer is 10x+15

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Which ratios are proportional to 6/8 ? Choose all answers that are correct.

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3/4 is one of them and 12/16

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2 years ago

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You have a mean score of 84 after taking five 100-point tests. What do you need to score on the sixth 100-point test to have a m

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The mean of n numbers is the sum of the numbers divided by n.

You have a mean score of 84 after taking 5 tests. Let x be the sum of scores.
$\frac{x}{5}=84 \\
x=84 \times 5 \\
x=420$
You scored a total of 420 points on five tests.

You need to have a mean score of 85 after taking 6 tests. Let y be the score you need to obtain. Your total score on 6 tests is 420+y.
$\frac{420+y}{6}=85 \\
420+y=85 \times 6 \\
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You need to score 90 points on the sixth test.

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2 years ago

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Use the quadratic formula to find the solutions to the quadratic equation below 2x^2-5x+5=0

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Answer:

x = (5 + i sqrt(15))/4 or x = (5 - i sqrt(15))/4

Step-by-step explanation:

Solve for x:

2 x^2 - 5 x + 5 = 0

Hint: | Using the quadratic formula, solve for x.

x = (5 ± sqrt((-5)^2 - 4×2×5))/(2×2) = (5 ± sqrt(25 - 40))/4 = (5 ± sqrt(-15))/4:

x = (5 + sqrt(-15))/4 or x = (5 - sqrt(-15))/4

Hint: | Express sqrt(-15) in terms of i.

sqrt(-15) = sqrt(-1) sqrt(15) = i sqrt(15):

Answer: x = (5 + i sqrt(15))/4 or x = (5 - i sqrt(15))/4

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3 years ago

Which number sentence is always true? Select all that apply.

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2 years ago

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Sue makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 1:4. Yellow paint is s

Lostsunrise [7]

Answer:

Sue's percentage profit = 9% on each tin of green paint she sells.

Step-by-step explanation:

Litres of green paints mixed = 50 litres

Ratio of litres of yellow paint and litres of blue paint = 1:4.

To determine the litres of yellow paint, we say:

$yellow \: paint = \frac{1}{4} \times 50 = 10 \: litres$

To determine the litres of blue paint, we say:

$blue \: paint = \frac{4}{5} \times 50 = 40 \: litres$

Since yellow paint is sold in 5 litres per tin and each tin cost £38; she has 10 litres of yellow paint in all. That implies that she has 10/5 = 2 tin of yellow paint. If one tin cost £38; 2 tin cost 2 × £38 = £76

Similarly,

Since blue paint is sold in 10 litres per tin and each tin cost £58; she has 40 litres of blue paint in all. That implies that she has 40/10 = 4 tin of blue paint. If one tin cost £58; 4 tin cost 4 × £58 = £232

Total cost of yellow and blue paints = £232 + £76

= £308

Since Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin and she has 50 litres in all; we say: 50/10 litres = 5 tins = 5 × £89.32 = £446.60.

Thus, selling price of the green paint = £446.60

$profit \: \% = \frac{selling \: price - cost \: price}{cost \: price} \times \frac{100}{1}$

$profit \: \% = \frac{446.60 - 308}{308} \times \frac{100}{1}$

$profit \: \% = \frac{138.60}{308} \times \frac{100}{1}$

$profit \: \% = 0.45 \times 100$

$profit \: \% = 45\%$

Sue's percentage profit for selling all the tins of green paint is 45%, having sold 5 tins. Therefore, Sue's percentage profit for selling each of the paint will be:

$profit \: \% \: on \: each \: green \: tin = \frac{45}{5} = 9\%$

Hence, Sue's percentage profit for selling each tin of green paint is 9%.

Proof

9% × 5 tins of green paint = 45%

4 0

2 years ago