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3 years ago

If PR=40, what are PQ and QR?

Mathematics

2 answers:

RUDIKE [14]3 years ago

8 0

Answer:

Step-by-step explanation:

I did it in my head but pretty much just add the 5x-2 and x+ 12 then set it equal to 40. u get x = 5. plug x back in and you get 23 and 17

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

The answer is B

Step-by-step explanation:

5x - 2 + x + 12 = 40

6x + 10 = 40

6x = 30

x = 5

5(5) - 2

25 - 2

PQ = 23

(5) + 12

QR = 17

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Which of the following is an example of a quantitative variable?

Mashcka [7]

Answer:

D. the number of hours the veterinarian works a week

7 0

3 years ago

Solve the equation uding the most direct method: 3x(x+6)=-10?

Tanzania [10]

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

<h3>Distribute</h3>

Use the distributive property to distribute 3x into the term (x + 6):

$3x(x+6)=-10$

$3x^2+18x=-10$

<h3>Rearrange</h3>

To create a quadratic equation, add 10 to both sides of the equation:

$3x^2+18x+10=-10+10$

$3x^2+18x+10=0$

<h3>Use the Quadratic Formula</h3>

The quadratic formula is defined as:

$\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

a = 3
b = 18
c = 10

Set up the quadratic formula:

$\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}$

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

$\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}$

Simplify the radicand:

$\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}$

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

$\sqrt{4\times51}$

Then, using the Product Property of Square Roots, break this into two radicands:

$\sqrt{4} \times \sqrt{51}$

Since 4 is a perfect square, it can be evaluated:

$2 \times \sqrt{51}$

To simplify further for easier reading, remove the multiplication symbol:

$2\sqrt{51}$

Then, substitute for the quadratic formula:

$\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}$

This gives us a combined root, which we should separate to make things easier on ourselves.

<h3>Separate the Roots</h3>

Separate the roots at the plus-minus symbol:

$\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}$

$\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}$

Then, simplify the numerator of the roots by factoring 2 out:

$\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}$

$\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}$

Then, simplify the fraction by reducing 2/6 to 1/3:

$\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}$

$\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}$

The final answer to this problem is:

$\displaystyle x=\frac{-9 + \sqrt{51}}{3}$

$\displaystyle x=\frac{-9 - \sqrt{51}}{3}$

3 0

2 years ago

What is 9/11*4/15 in the simplest form

stiks02 [169]

Answer:

$\frac{12}{55}$

Step-by-step explanation:

$\frac{9}{11}$ × $\frac{4}{15}$

$\frac{3}{11}$ × $\frac{4}{5}$

$\frac{12}{55}$ Answer

Hope this helps!

4 0

4 years ago

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A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point A, the boat's crew measures t

seraphim [82]

Answer: 854.5

Step-by-step explanation:

I got it wrong so it gave me the explanation

7 0

3 years ago

Just need help with this !

777dan777 [17]

Answer:

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3 0

3 years ago

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