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Zolol [24]
3 years ago
10

Look at the system of equations below.

Mathematics
1 answer:
Paul [167]3 years ago
7 0

Answer:

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

x=2,\:y=-1

Step-by-step explanation:

Considering the system of the equation

\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}

\mathrm{Subsititute\:}y=-2x+3

\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}

\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11

4x-3\left(-2x+3\right)=11

4x+6x-9=11

10x-9=11

10x-9+9=11+9

10x=20

x=2

\mathrm{For\:}y=-2x+3

\mathrm{Subsititute\:}x=2

y=-2\cdot \:2+3

y=-1

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

x=2,\:y=-1

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sattari [20]

Answer:

The Median of those numbers is 4

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please help, I need to get this done!<br>I need to get number 16, 17, and 18 done please help!!!!​
Tresset [83]

Answer:

16) 62.8 m²

17) 19.4 m²

18) 103.5 m²

Step-by-step explanation:

The formula to find area of a circle is: \pi r^{2}. To find radius, find the half of the diameter.

To solve number 16, first find the area of the unshaded circle using the formula: \pi 4^{2}. This is also 3.14*16. Multiply to get 50.24 m². Now find the area of the larger circle using the formula: \pi 6^{2}. This is also 3.14*36. Multiply to get 113.04 m². Now subtract 113.04 - 50.24 to get the shaded area or 62.8 m².

To solve number 17, first find the area of the square using the formula: side x side. In this case multiply: 5.25 x 5.25 to get 27.5625. Round to the nearest tenth to get 27.6 m². Now find the area of the circle using the formula: \pi 2.625^{2}. This is also 3.14*2.625. Multiply to get 8.2425. Round to the nearest tenth to get 8.2. Subtract 27.6 - 8.2 to get 19.4 m².

To solve number 18, find the area of one unshaded circle using the formula: \pi 1.75^{2}. This is also 3.14*3.0625. Multiply to get 9.61625. Round to the nearest tenth to get 9.6 m². Add 9.6 + 9.6 to find the area of both unshaded circles. You get 19.2 m². Now find the area of the shaded circle using the formula: \pi 6.25^{2}. This is also 3.14*39.0625. Multiply to get 122.65625. Round to the nearest tenth: 122.7. Subtract 122.7 - 19.2 to get 103.5 m².

Hope it helps and is correct!

5 0
3 years ago
You saved $20,000.00 and want to diversify your monies. You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded an
Maru [420]

Compound Interest

A total of $20,000 is invested in different assets.

45% is invested in a Treasury bond for 3 years at 4.35 APR compounded annually.

For this investment, the principal is P = 0.45*$20,000 = $9,000.

The compounding period is yearly, thus the interest rate is:

i = 4.35 / 100 = 0.0435

The duration (in periods) is n = 3

Calculate the final value with the formula:

M=P_{}(1+i)^n

Substituting:

\begin{gathered} M=\$9,000_{}(1+0.0435)^3 \\ M=\$9,000\cdot1.136259062875 \\ M=\$10,226.33 \end{gathered}

The second investment is a CD at 3.75% APR for 3 years compounded annually. The parameters for the calculations are as follows:

P = 15% of $20,000 = $3,000

i = 3.75 / 100 = 0.0375

n = 3

Calculating:

\begin{gathered} M=\$3,000_{}(1+0.0375)^3 \\ M=\$3,000\cdot1.116771484375 \\ M=\$3,350.31 \end{gathered}

The third investment is in a stock plan. The initial value of the investment is

P = 20% of $20,000 = $4,000

By the end of the first year, the stock plan increased by 8%, thus its value is:

M1 = $4000 * 1.2 = $4,800

By the end of the second year, the stock plan decreased by 4$, thus the value is:

M2 = $4,800 * 0.96 = $4,608

Finally, the stock plan increases by 6%, resulting in a final balance of:

M3 = $4,608 * 1.06 = $4,884.48

Finally, the last investment is in a savings account at 2.90% APR compounded annually for 3 years (not mentioned, but assumed).

P = $20,000 - $9,000- $3,000 - $4,000 = $4,000

i = 2.90 / 100 = 0.029

n = 3

Calculating:

\begin{gathered} M=\$4,000_{}(1+0.029)^3 \\ M=\$4,000\cdot1.089547389 \\ M=\$4,358.19 \end{gathered}

To summarize, the final balances for each type of investment at the end of the third year are:

Investment 1; $10,226.33

Investment 2: $3,350.31

Investment 3: $4,884.48

Investment 4: $4,358.19

Total balance: $22,819.32

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Yuki888 [10]
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Sidana [21]

Answer:

C, none of them are equivalent

BECAUSE

For A, the -4q should be positive 4q to apply

For B, the 2q when distributing with the parentheses should be negative 2q to work with the expression above

Hope this helps!

8 0
3 years ago
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