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4 years ago

Complete the square x squared +18x-64=0

Mathematics

1 answer:

Anestetic [448]4 years ago

3 0

Answer:

x = -9±√145 (= 3.04 or -21.04)

Step-by-step explanation:

x²+18x-64 = 0 (move the constant to the right side, add 64 to both sides)

x²+18x = 64 (divide the x-term by 2, square it, then add it to both sides)

x²+18x + (18/2)²= 64 + (18/2)² (simplify)

x²+18x + 9²= 64 + 9²

x²+18x + 9²= 64 + 81

x²+18x + 9²= 145 (simplify left side using the property (a+b)² = a²+ 2ab+b²)

(x+9)² = 145 (take square root of both sides)

x+9 = ±√145

x = -9±√145 (= 3.04 or -21.04)

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When you multiply a mixed number by a fraction less than 1, will the answer be smaller?

mars1129 [50]

Answer:

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Step-by-step explanation:

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3 years ago

Write the slope-intercept form of the equation of each line.

rewona [7]

Answer:

$y=-\frac{8}{3} x - 3$

Step-by-step explanation:

Slope-intercept form is y = mx + b.

You are given 8x + 3y = -9, so to convert this into slope-intercept form you would solve for y and rearrange the terms (if needed) to follow the format of mx + b.

Start by subtracting 8x from both sides of the equation.

3y = -9 - 8x

Divide both sides by 3 to isolate y.

y = -3 - 8/3x

Rearrange the terms so the "x" variable is first.

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6 0

3 years ago

Question<br> Find the missing side lengths. Leave answer in simplest<br> radical form.

Slav-nsk [51]

Answer:

A) y = $\frac{11\sqrt{3} }{2}$ , x = 11

Step-by-step explanation:

We can use the 60 degree angle to help us solve this.

Remember: tan(angle) = opposite/adjacent

Using this formula, we get that

tan (60 degrees) = y / (11/2)

This is because y is the side opposite to the 60 degree angle and 11/2 is the side adjacent to the 60 degree angle.

Simplifying this expression, we get that

$\sqrt{3}$ = y/(11/2)

Multiplying both sides by 11/2, we get

$\frac{11\sqrt{3} }{2}$ = y

We can now use the pythagorean theorem to help us solve for x

Remember: a² + b² = c²

Since x is the hypotenuse, it is the c value. Therefore, we get:

(11/2)² + ( $\frac{11\sqrt{3} }{2}$ )² = x²

Simplifying this, we get

$\frac{121}{4}$ + $\frac{121 * 3}{4}$ = x²

Simplifying this some more, we get

484/4 = x²

121 = x²

Taking the square root of both sides, we get that

x = 11

I hope this helps!

4 0

3 years ago

In ΔPQR, \overline{PR} PR is extended through point R to point S, \text{m}\angle QRS = (4x-15)^{\circ}m∠QRS=(4x−15) ∘ , \text{m}

mixas84 [53]

Answer:

Step-by-step explanation:

Notice that, the angle QRS is external to the triangle and adjacent to the angle PRQ. According to the theorem of a external/adjacent angle, we have: m∠QRS = m∠PQR + m∠RPQ, where PQR and RPQ are internal angles.

From the hypothesis, we have:

m∠QRS =(10x−12)∘(10x−12)

m∠PQR = (3x+20)∘(3x+20)

m∠RPQ=(3x−8)∘(3x−8)

Using the first equation and replacing the hypothesis:

m∠QRS = m∠PQR + m∠RPQ

(10x−12)∘(10x−12) = (3x+20)∘(3x+20) + (3x−8)∘(3x−8)

Multiplying and applying the remarkable identity:

Then, we use a calculator to find the roots, which are:

In this case, we will see what root is the right one.

Now, we replace it into m∠QRS =(10x−12)∘(10x−12), because we need to find m∠QRS.

m∠QRS =(10x−12)∘(10x−12) = (10(4.7) - 12) (10(4.7) - 12) = (35) (35) = 1225

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Pleaseeee help!!!! I will mark you as brainlinest for correct answer!!!!!!!!

marta [7]

I think the correct answer for that question is C

6 0

4 years ago