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3 years ago

Helppppppp! Find the length of PQ if PQR is an isosceles triangle with PQ ≈ QR.

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

5 0

Answer:

Step-by-step explanation:

3x + 10 = 5x - 12

10 = 2x - 12

22 = 2x

x = 11

check:

33 + 10 = 55 - 12

43 = 43

correct

x = 11 so bring this into 3x + 10

we get 43

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Paul has $20,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest

hjlf

Answer:

In the 8% option , $5,000 should be invested

In the 12% option, $15,000 should be invested

Step-by-step explanation:

Let’s start with the total return.

Since the total return expected is 11%, the amount expected to be returned will be;

11/100 * 20,000 = $2,200

Now, let the amount invested at 8% interest be $x while the amount invested at 12% interest be $y

Mathematically;

x + y = 20,000 ••••••(i)

Now let’s work with the interest part;

On the 8% part, amount of interest expected is 8/100 * x

on the 12% part, amount of interest expected is 12/100 * x

8% of $x + 12% of $y = 2,200

Writing this fully mathematically, we have;

(8/100 * x) + (12/100 * y) = 2,200

8x/100 + 12y/100 = 2,200

Multiply through by 100

8x + 12y = 220,000 ••••••(ii)

Now we have two equations to solve simultaneously;

x + y = 20,000

8x + 12y = 220,000

From i, x = 20,000-y

Substitute this into ii

8(20,000-y) + 12y = 220,000

160,000-8y + 12y = 220,000

4y = 220,000 - 160,000

4y = 60,000

y = 60,000/4

y = $15,000

x = 20,000 -y

x = 20,000 - 15,000

x = $5,000

8 0

3 years ago

I need help with this may question

Anastaziya [24]

The answer is 3) 400

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If a muffin costs 7¢, how much will 3 muffins cost?

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Step-by-step explanation:

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Will is w years old <br> Ben is 3 years older <br> Write an expression, in terms of w, for bens age

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Ben is w+3 years old.

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3 years ago

Use the fraction strips to compare 2/4 and 5/8. use the drop-down menus to explain your comparison.

tia_tia [17]

Answer:

$\dfrac{4}{5}$

Step-by-step explanation:

We are given 2 fractional numbers:

$1.\ \dfrac{2}4\\2.\ \dfrac{5}8$

We have to use fraction strips to compare to the fractional numbers.

Let we are Comparing $\frac{2}{4}$ with the length of $x$ number of $\frac{1}4$ sections.

i.e.

$\dfrac{2}{4} = x \times \dfrac{1}{4}\\\Rightarrow x = \dfrac{2 \times 4}{4}\\\Rightarrow x = 2$

Let we are Comparing $\frac{5}{8}$ with the length of $y$ number of $\frac{1}8$ sections.

i.e.

$\dfrac{5}{8} = y \times \dfrac{1}{8}\\\Rightarrow y = \dfrac{5 \times 8}{8}\\\Rightarrow y = 5$

Now, let us have a look at 3rd part of question:

The sections of 2/4 is _____ the length of 5/8. Therefore, 2/4 < 5/8

Let the answer be $z$ .

So, the equation becomes:

$\dfrac{2}{4} = z \times \dfrac{5}{8}\\\Rightarrow z = \dfrac{2 \times 8}{4 \times 5}\\\Rightarrow z = \dfrac{2 \times 2}{5}\\\Rightarrow z = \dfrac{4}{5}$

So, the answers are:

$\dfrac{4}{5}$

5 0

3 years ago

Helppppppp! Find the length of PQ if PQR is an isosceles triangle with PQ ≈ QR.​

Helppppppp! Find the length of PQ if PQR is an isosceles triangle with PQ ≈ QR.