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1 year ago

What is the solution to the system of equations? 7z+3y=-11 2z+ 5y = 1

Mathematics

1 answer:

Readme [11.4K]1 year ago

5 0

Answer:

y=1 , z=-2

Step-by-step explanation:

I will use the method of elimination :

Multiply the top equation by 5 to make equation 3 :

35z + 15y = -55

Multiply bottom equation by 3 to make equation 4:

6z + 15y = 3

Subtract equation 3 from equation 4 to eliminate the y :

-29z = 58

Divide both sides by -29 to solve for z :

z = 58 ÷ -29

z = -2

Substitute this value into either equation 1 or 2 to solve for y :

I chose equation 2 :

2(-2) + 5y = 1

-4 + 5y = 1

Add 4 to both sides :

5y = 5

Divide both sides by 5 :

y = 1

Hope this helped and have a good day

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An observer 2.5 miles from the launch pad of a space shuttle measures the angle of elevation to the base of the shuttle to be 25

kotegsom [21]

Answer:

Height of shuttle at that instant = 1.17 miles

Step-by-step explanation:

Refer the given figure.

C is the position of rocket and B is the position of observer.

Here we need to find AC, that is the height of shuttle at that instant.

Using trigonometric rules on ΔABC, we have

$tan25=\frac{AC}{AB} \\\\tan25=\frac{AC}{2.5}\\\\AC=2.5\times tan25\\\\AC=1.17miles$

Height of shuttle at that instant = AC = 1.17 miles

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3 years ago

Write the expression as a single natural logarithm.3In3+3Inc

k0ka [10]

Answer:

$ln(27c^3)$

Step-by-step explanation:

Given: $3ln(3)+3ln(c)$

If there is a coefficient in front of a $log$ or $ln$ , that means it becomes an exponent.

$ln(3^3)+ln(c^3)$

Simplify the exponent.

$ln(27)+ln(c^3)$

When there is addition between two logarithms or natural logarithms, it means they multiply together.

$ln(27c^3)$

3 0

3 years ago

Read 2 more answers

You and your friend are comparing two loan options for a $165,000 house. Loan 1 is a 15-year loan with an annual interest rate o

Harlamova29_29 [7]

Answer:

No, he is wrong.

Step-by-step explanation:

Since, the total payment of a loan after t years,

$A=P(1+r)^t$

Where,

P = present value of the loan,

r = rate per period ,

n = number of periods,

Given,

P = $165,000,

In loan 1 :

r = 3% = 0.03, t = 15 years,

So, the total payment of the loan is,

$A_1 = 165000(1+0.03)^{15}=165000(1.03)^{15}\approx \$ 257,064.62$

In loan 2 :

r = 4% = 0.04, t = 30 years,

So, the total payment of the loan is,

$A_2 = 165000(1+0.04)^{30}=165000(1.04)^{30}\approx \$ 535,160.59$

Since, $A_1 < A_2$

Hence, total amount repaid over the loan will be less for Loan 1.

That is, the friend is wrong.

7 0

3 years ago

Simplify the expression c+5+10

Darina [25.2K]

Answer:

c+15

Step-by-step explanation:

add the numbers c+15

c+15 is your answer.

5 0

3 years ago

What are the steps to solving 35+3x-11=23

tatuchka [14]

Hello there! Solution given below!

<h3>Solution:</h3>

$35 + 3x - 11 = 23 \\ = > 3x = 23 - 35 + 11 \\ = > 3x = - 1 \\ = > x = \frac{ - 1}{3}$

<h3>Answer:</h3>

$\frac{ - 1}{3}$

Hope it helps you

8 0

3 years ago

Read 2 more answers