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3 years ago

What value of x will make the triangles similar by the SSS similarity theorem? A. 1.5 B. 20 C. 30 D. 67.5

Mathematics

2 answers:

valentinak56 [21]3 years ago

6 0

just took the test its C.

aleksley [76]3 years ago

5 0

Answer:

The answer is the option C

$x=30$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

$\frac{x}{45}=\frac{50}{75}$

solve for x

$x=45*50/75$

$x=30$

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Find the equation of a circle that has a diameter with the endpoints given by the points A(-4,9) and B (- 2, - 3) )

Aleksandr-060686 [28]

The equation of the circle is $(x+3)^{2}+(y-3)^{2}=37$

Explanation:

Given that the endpoints of the circle are A(-4,9) and B(-2,-3)

We need to determine the equation of the circle.

Center:

The center of the circle can be determined using the midpoint formula,

$Center=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Substituting the coordinates A(-4,9) and B(-2,-3), we get,

$Center=(\frac{-4-2}{2},\frac{9-3}{2})$

$Center=(\frac{-6}{2},\frac{6}{2})$

$Center=(-3,3)$

Thus, the center of the circle is (-3,3)

Radius:

The radius of the circle can be determined using the distance formula,

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Substituting the center (-3,3) and the endpoint (-4,9), we get,

$r=\sqrt{\left(-4+3\right)^{2}+\left(9-3\right)^{2}}$

$r=\sqrt{\left(-1\right)^{2}+\left(6\right)^{2}}$

$r=\sqrt{1+36}$

$r=\sqrt{37}$

Thus, the radius of the circle is $\sqrt{37}$

Equation of the circle:

The standard form of the equation of the circle is given by

$(x-a)^{2}+(y-b)^{2}=r^{2}$

where (a,b) is the center and r is the radius.

Substituting the values, we have,

$(x+3)^{2}+(y-3)^{2}=(\sqrt{37})^{2}$

$(x+3)^{2}+(y-3)^{2}=37$

Thus, the equation of the circle is $(x+3)^{2}+(y-3)^{2}=37$

7 0

3 years ago

8 + 3n ≥ 38 do yall know??? solve please

Sholpan [36]

Answer:

n ≥ 10

Step-by-step explanation:

Given

8 + 3n ≥ 38 ( subtract 8 from both sides )

3n ≥ 30 ( divide both sides by 3 )

n ≥ 10

3 0

3 years ago

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Elena-2011 [213]

The answer is -1. You multiply the 1/4 with the 5x and equal it to 3 multiplied by 5 and have gotten 15x, then multiply the 3 with the 2, as apart of the parentheses. Lasty you just leave the -9 on the side and solve the equation.

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3 years ago

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3 years ago

Which of the binomials below is a factor of this trinomial? x² + 5x-36

IgorLugansk [536]

Answer:

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5 0

3 years ago