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alexandr402 [8]
3 years ago
11

Find the solution of this system of equations. x-8y=21 and 3x-8y=15

Mathematics
1 answer:
dusya [7]3 years ago
8 0

Answer:

x = -3 , y = -3

Step-by-step explanation:

Solve the following system:

{x - 8 y = 21 | (equation 1)

3 x - 8 y = 15 | (equation 2)

Swap equation 1 with equation 2:

{3 x - 8 y = 15 | (equation 1)

x - 8 y = 21 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 8 y = 15 | (equation 1)

0 x - (16 y)/3 = 16 | (equation 2)

Multiply equation 2 by 3/16:

{3 x - 8 y = 15 | (equation 1)

0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:

{3 x - 8 y = 15 | (equation 1)

0 x+y = -3 | (equation 2)

Add 8 × (equation 2) to equation 1:

{3 x+0 y = -9 | (equation 1)

0 x+y = -3 | (equation 2)

Divide equation 1 by 3:

{x+0 y = -3 | (equation 1)

0 x+y = -3 | (equation 2)

Collect results:

Answer:  {x = -3 , y = -3

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if Dakota earned $15.75 in interest in account A and $28.00 in interest in account B after 21 months. if the simple interest rat
NISA [10]

keeping in mind that 21 months is more than a year, since there are 12 months in a year,  then 21 months is really 21/12 years.


\bf ~~~~~~ \stackrel{\textit{account A}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill &15.75\\ P=\textit{original amount deposited}\dotfill \\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\to \frac{21}{12}\dotfill &\frac{7}{4} \end{cases} \\\\\\ 15.75=P(0.03)\left( \frac{7}{4} \right)\implies \cfrac{15.75}{(0.03)\left( \frac{7}{4} \right)}=P\implies \boxed{300=P}


\bf ~~~~~~ \stackrel{\textit{account B}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill &28\\ P=\textit{original amount deposited}\dotfill \\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ t=years\to \frac{21}{12}\dotfill &\frac{7}{4} \end{cases} \\\\\\ 28=P(0.049)\left( \frac{7}{4} \right)\implies \cfrac{28}{(0.049)\left( \frac{7}{4} \right)}=P\implies \boxed{326.53\approx P}


so, clearly, you can see who's greater.

3 0
3 years ago
PLEASE HELP! (05.01 MC)
Temka [501]

Answer:

3) Option C is correct.

3 over 3 and 61 hundredths = 6 over 7 and 22 hundredths

Step-by-step explanation:

Triangle BDE is dilated by a scale factor of 2 to obtain triangle BAC.

Dilation by a scale factor of 2 means that all the sides of triangle BAC are twice as much as the corresponding sides of triangle BDE.

And triangle BDE is similar to triangle BAC.

It also means that the corresponding angles are necessarily equal.

BD = 2

BE = 3

ED = 3.61

BA = 2 × BD = 2 × 2 = 4

BC = 2 × BE = 2 × 3 = 6

CA = 2 × ED = 2 × 3.61 = 7.22

Cos ∠D according to trigonometric relations is given as (adj/hyp)

Adj = Adjacent side = BE = 3

Hyp = hypotenuse side = ED = 3.61

Cos ∠D = (3/3.61)

Cos ∠A can also be similarly obtained from trigonometric relations as (adj/hyp)

Adj = Adjacent side = BC = 6

Hyp = hypotenuse side = CA = 7.22

Cos ∠A = (6/7.22)

Since the two angles are corresponding angles of two similar triangles,

We can easily see that

Cos ∠D = Cos ∠A

(3/3.61) = (6/7.22) = 0.8310

Which is necessarily equal to each other

Hence, the proportion that proves that Cos ∠D = Cos ∠A is 3 over 3 and 61 hundredths = 6 over 7 and 22 hundredths.

please mark me brainliest :)

7 0
3 years ago
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hram777 [196]
I did all the work XD

Only now realized you needed only 3 and 4.

3 0
3 years ago
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Minchanka [31]
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Answer:

Step-by-step explanation:

h/c=3/5=15/c

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7 0
3 years ago
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