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1 year ago

Solve for x if the three angles of a triangle are: x, 45 degrees, and 5x degrees

Mathematics

1 answer:

Tcecarenko [31]1 year ago

3 0

Answer: 22.5 degrees

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees.

So we can set up an equation to solve for x.

x + 45 + 5x = 180.

Combine like terms of x:

6x + 45 = 180

Subtract 45 from both sides:

6x = 135

Divide both sides by 6:

x = 22.5 degrees

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Write down the quadratic equation whose roots are $x = -7$ and $x = 1,$ and the coefficient of $x^2$ is 1. Enter your answer in

pav-90 [236]

<h2>Steps:</h2>

So firstly, since we know that the coefficient of x² is 1, this means that this is our base equation:

y = x² + bx + c

Now, since we know that the roots are -7 and 1, set y = 0 and set x = -7 and 1 and simplify:

$0=(-7)^2+b(-7)+c\\0=49-7b+c\\-49=-7b+c\\\\0=1^2+b(1)+c\\0=1+b+c\\-1=b+c\\\\-49=-7b+c\\-1=b+c$

Now with this, we can set up a system of equations to solve for b and c. For this, I will be using the elimination method. For this, subtract the 2 equations:

$\begin{alignedat}{2}-49&=-7b+c\\-(-1&=b+c)\\-48&=-8b\end{alignedat}$

Now that the c variable has been eliminated we can solve for b. For this, divide both sides by -8 and your first part of your answer is b = 6.

Now that we know the value of b, plug it into either equation to solve for c:

$-49=-7(6)+c\\-49=-42+c\\-7=c\\\\-1=6+c\\-7=c$

<h2>Answer:</h2>

<u>Putting it together, your final answer is x² + 6x - 7 = 0.</u>

4 0

2 years ago

What is the lateral area of a right cylinder if the radius of the base is 12 mm and the altitude of the cylinder is 5 times the

schepotkina [342]

Lateral Area of a cylinder is ; 2πR.H

R=12 mm and H= 15 mm

Then LATERAL area = 2π(12)(15) =48π ≈ 150 mm²

5 0

2 years ago

The school water fountain can only fill 3/4 of a jug at a time. With this amount of water, Mr. Kern can water 3/8 of his plants.

Vesnalui [34]

Answer:

$\frac{3}{4} = \frac{3}{3} \\ \frac{3}{8} = x \\ x = \frac{3}{8} \times \frac{4}{3} \\ x = \frac{1}{2}$

5 0

1 year ago

Consider the two expressions 4b(b+1) and (2b+7)(2b-8). Compare their values if b=-3, b=-2, and if b=10. Is it true that for an v

frutty [35]

Answer:

FIRST EXPRESSION:

- If $b=-3$ , the value of $4b(b+1)$ is $24$

- If $b=-2$ , the value of $4b(b+1)$ is $8$

- If $b=10$ , the value of $4b(b+1)$ is $440$

SECOND EXPRESSION:

- If $b=-3$ , the value of $(2b+7)(2b-8))$ is $-14$

- If $b=-2$ , the value of $(2b+7)(2b-8))$ is $-36$

- If $b=10$ , the value of $(2b+7)(2b-8))$ is $324$

Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.

Step-by-step explanation:

Substitute the given values of "b" into each expression and evaluate.

- For the first expression $4b(b+1)$ , you get:

If $b=-3$ → $4(-3)(-3+1)=24$

If $b=-2$ → $4(-2)(-2+1)=8$

If $b=10$ → $4(10)(10+1)=440$

- For the second expression $(2b+7)(2b-8))$ , you get:

If $b=-3$ → $(2(-3)+7)(2(-3)-8)=-14$

If $b=-2$ → $(2(-2)+7)(2(-2)-8)=-36$

If $b=10$ → $(2(10)+7)(2(10)-8)=324$

You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.

7 0

2 years ago

if you were to solve the following system by substitution, what would be the best variable to solve for and from what equation?

Romashka-Z-Leto [24]

Answer:

see below

Step-by-step explanation:

2x+8y=12 3x-8y=11

If we have to solve by substitution, Take the first equation and divide by 2

2x/2 + 8y/2 =12/2

x+4y = 6

Then subtract 4y from each side

x = 6 -4y

Then substitute this into the second equation

This is best solved by elimination

2x+8y=12

3x-8y=11

----------------

5x = 36

x = 36/5

6 0

2 years ago