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3 years ago

5x - 3y = 13 3x + 5y = 69

Mathematics

1 answer:

Anni [7]3 years ago

5 0

Here are the answers, combine like terms

X=2

Y=-8

=56

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$20000 is invested in an account that earned 6% p.A. Compounding yearly for 3 years. The interest rate then went up to 8% p.A. F

GuDViN [60]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the first 3 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}$

$\bf A=20000\left(1+\frac{0.06}{1}\right)^{1\cdot 3}\implies A=20000(1.06)^3\implies \boxed{A=2382.032} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the next 4 years}}$

$\bf A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2382.032\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}$

$\bf A=2382.032\left(1+\frac{0.08}{1}\right)^{1\cdot 4}\implies A=2382.032(1.08)^4\implies \boxed{A\approx 3240.73} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{amount for this period}}{2382.032+3240.73}\implies 5622.762$

4 0

4 years ago

A square playing field has an area of 1,255 square yards. About how long is each side of the field?

Sloan [31]

Idk probably A I just wanna answer someone

4 0

3 years ago

A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real num

yKpoI14uk [10]

Answer: hypotenuse = $c^{2} + b^{2}$

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side ( $s_{1},s_{2}$ ) of the right triangle, .i.e.:

$h^{2} = s_{1}^{2} + s_{2}^{2}$

In this question:

$s_{1}$ = $c^{2}-b^{2}$

$s_{2} =$ 2bc

Substituing and taking square root to find hypotenuse:

$h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}$

Calculating:

$h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}$

$h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}$

$c^{4}+b^{4}+2b^{2}c^{2}$ = $(c^{2}+b^{2})^{2}$ , then:

$h=\sqrt{(c^{2}+b^{2})^{2}}$

$h=(c^{2}+b^{2})$

Hypotenuse for the right-angled triangle is $h=(c^{2}+b^{2})$ units

3 0

4 years ago

A store Is having a sale where movies are 15% off their original price. a movien is on sale for $22.10 what was the orgial price

sergeinik [125]

X= original $

Original $ - % of original $= total $

x - 15%x= $22.10
x- 0.15= 22.10
Combine like terms
0.85x= 22.10
Divide both sides by 0.85
x= $26 original price

Hope this helps! :)

3 0

4 years ago

Seth drinks a glass of orange juice every day that contains 0.6 grams of Vitamin C. He eats a serving of strawberries for snack

belka [17]

Answer:

3 week or 21 days consume Vitamin C = 19.95 grams

Step-by-step explanation:

given data

orange juice Vitamin C = 0.6 grams

strawberries Vitamin C = 0.35 grams

to find out

How many grams of Vitamin C does Seth consume in 3 weeks

solution

we first find total Vitamin C consume in 1 day that is

total Vitamin C consume in 1 day = orange juice Vitamin C + strawberries Vitamin C

total Vitamin C consume in 1 day = 0.6 + 0.35

total Vitamin C consume in 1 day = 0.95 grams

in 3 week have 3 × 7 = 21 days

so in 21 days consume Vitamin C = 1 day consume × no of days consume

21 days consume Vitamin C = 0.95 × 21

21 days consume Vitamin C = 19.95 grams

5 0

4 years ago