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2 years ago

Solving systems by elimination 9x+3y=-3 2x-3y=-8

Mathematics

1 answer:

Alona [7]2 years ago

5 0

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

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Step-by-step explanation:

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Given right triangle MNL what is the value of cos(M)?

FromTheMoon [43]

Step $1$

<u>Find the length of the side MN</u>

we know that

Applying the Pythagorean Theorem

$ML^{2} =NL^{2} +MN^{2}$

Solve for MN

$MN^{2}=ML^{2} -NL^{2}$

in this problem

$ML=25\ units\\ NL=15\ units$

Substitute in the formula above

$MN^{2}=25^{2} -15^{2}$

$MN^{2}=400$

$MN=20\ units$

Step $2$

<u>Find the value of cos (M)</u>

we know that

in the right triangle MNL

$cos (M)=\frac{adjacent\ side\ angle\ M}{hypotenuse}$

$adjacent\ side\ angle\ M=MN=20\ units\\ hypotenuse=ML=25\ units$

Substitute

$cos (M)=\frac{20}{25}$

$cos (M)=\frac{4}{5}$

$cos (M)=0.8$

therefore

The answer is

The value of cos(M) is equal to $0.8$

6 0

2 years ago

If the actual base of the window is 5 ft, what is the height of the actual window

pav-90 [236]

Answer:

5ft

Step-by-step explanation:

...........................

6 0

1 year ago

Question in the attachment!!!!

Verdich [7]

Answer: 90 degress clockwise

Step-by-step explanation: because it is going the way the clock is going and it only went one time which is 90 degrees

5 0

2 years ago

You are opening a savings account with $500 that you have saved. The bank offers 3.2% interest, compounded yearly. How much mone

Nuetrik [128]

Answer:

You will have $623.3441462 in your account after 7 years

Step-by-step explanation:

The formula of the compounded interest is A = P $(1+\frac{r}{n})^{nt}$ , where

A is the new value

P is the initial value

r is the rate in decimal

n is the number of periods

t is the time in years

∵ You are opening a savings account with $500

∴ P = 500

∵ The bank offers 3.2% interest, compounded yearly

∴ r = 3.2% ⇒ divide it by 100 to change it to decimal

∴ r = 3.2 ÷ 100 = 0.032

∵ The interest is compounded yearly

∴ n = 1

∵ The time is 7 years

∴ t = 7

→ Substitute these values in the rule above to find A

∵ A = 500 $(1+\frac{0.032}{1})^{1(7)}$

∴ A = 500 $(1.032)^{7}$

∴ A = 623.3441462

∴ You will have $623.3441462 in your account after 7 years

8 0

2 years ago

Use the tangent identity to

Lunna [17]

Answer:

$tan(x)=\frac{44\sqrt{89}}{89}$

Step-by-step explanation:

tan is defined as: $tan(x)=\frac{opposite}{adjacent}$

sin is defined as: $sin(x)=\frac{opposite}{hypotenuse}$

cos is defined as: $cos(x)=\frac{adjacent}{hypotenuse}$

We can also define tan as: $tan(x)=\frac{sin(x)}{cos(x)}$

because plugging in the definitions of sin and cos in we get: $tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}$

which you'll notice is the original definition of tan(x)

So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

$sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}$

plugging in sin(x) and cos(x) we get:

$tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}$

We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: $\frac{\sqrt{89}}{\sqrt{89}}$ which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

$tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}$

5 0

2 months ago