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4 years ago

The figures in the pair are similar. Find the missing lenth

Mathematics

1 answer:

Varvara68 [4.7K]4 years ago

7 0

Answer:

In two similar triangles, the ratio of their areas is the square of the ratio of their sides. Try this The two triangles below are similar. Drag any orange dot at P,Q,R. Note the ratio of the two corresponding sides and the ratio of the areas.

Step-by-step explanation:

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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

Im going to give 30 points for this question please answer it please

REY [17]

The answer is 66 because the area of the triangle is 6, and the area of the rectangle is 60, so when you add them together you get 66

6 0

4 years ago

Solve for 8:<br> -0.2 = 8 +(-0.8)

Nookie1986 [14]

S=0.6
Step by step explanation: subtract the greater number by the smaller number. Plug in the decimal after.

6 0

3 years ago

What is the coefficient of x^2 in the expansion of (x+2)^3

goldenfox [79]

(x+2)^3=x^3+2^3+3*x^2*2+3x*2^2=x^3+8+6x^2+12x

The coeficient of the x^2 is 6.

3 0

3 years ago

Asap<br> Select the correct answer.<br> Which function has a restricted domain?

german

Step-by-step explanation:

Check second one

$\\ \rm\Rrightarrow k(x)=(-x+3)^{\frac{1}{2}}$

1/2 means square root

$\\ \rm\Rrightarrow \sqrt{(-x+3)}$

$\\ \rm\Rrightarrow -x+3>0$

$\\ \rm\Rrightarrow -x>-3$

$\\ \rm\Rrightarrow x$

Hence.

Domain is restricted

Option B is correct

8 0

3 years ago