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2 years ago

Which of the following is not part of the Triangle Proportionality Theorem?

Mathematics

1 answer:

natka813 [3]2 years ago

3 0

Answer:

A. AA Similarity Theorem . True

B. Two sides divided proportionally. True

C. A parallel line to one side of a triangle. True

D. A perpendicular line to one side of a triangle. False

Step-by-step explanation:

The Triangle Proportionality Theorem says that if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections.

Now, here the given statements are:

A. AA Similarity Theorem

TRUE, as the angles opposite to equal sides are equal.

And if lines are divided proportionally, both the triangles are Similar by AA similarity theorem.

B. Two sides divided proportionally.

TRUE,as the other two sides of the triangle are divided proportionally by the parallel line.

C. A parallel line to one side of a triangle.

TRUE, as the parallel line divides the other two non- parallel sides in equal proportions.

D. A perpendicular line to one side of a triangle.

FALSE, this part is not required anywhere in the given theorem result.

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Which is the value of g(-5) if g(x)=3.4x-8

Dennis_Churaev [7]

G(-5) = -25

to solve:
g(-5) = 3.4(-5) -8

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3 years ago

The sum of the real numbers x and y is 11. Their difference is 5. What is the value of xy

Veseljchak [2.6K]

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Step-by-step explanation:

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3 years ago

Need help with my homework

Volgvan

Answer:

$\displaystyle y=\frac{16-9x^3}{2x^3 - 3}$

$\displaystyle y=-\frac{56}{13}$

Step-by-step explanation:

Equation Solving

We are given the equation:

$\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}$

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

$\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3$

Simplify the radical with the cube:

$\displaystyle x^3=\frac{3y+16}{2y+9}$

Multiply by 2y+9

$\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)$

Simplify:

$\displaystyle x^3(2y+9)=3y+16$

Operate the parentheses:

$\displaystyle x^3(2y)+x^3(9)=3y+16$

$\displaystyle 2x^3y+9x^3=3y+16$

Subtract 3y and $9x^3$ :

$\displaystyle 2x^3y - 3y=16-9x^3$

Factor y out of the left side:

$\displaystyle y(2x^3 - 3)=16-9x^3$

Divide by $2x^3 - 3$ :

$\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}$

ii) To find y when x=2, substitute:

$\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}$

$\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}$

$\displaystyle y=\frac{16-72}{16- 3}$

$\displaystyle y=\frac{-56}{13}$

$\mathbf{\displaystyle y=-\frac{56}{13}}$

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2 years ago

Jada is solving the equation shown below. Negative one-half (x + 4) = 6 Which is a possible first step to begin to simplify the

elena-14-01-66 [18.8K]

The two options that are the possible first step to begin to simplify the equation are (c) Multiply both sides of the equation by –2. and (d). Distribute Negative one-half over (x + 4).

<h3>How to determine which two options are the possible first step to begin to simplify the equation?</h3>

The equation is given as:

Negative one-half (x + 4) = 6

Rewrite the above equation properly

So, we have

-1/2(x + 4) = 6

A possible first step is to multiply both sides of the equation -1/2(x + 4) = 6 by -2

So, we have

x + 4 = -12

Another possible first step is to distribute the expression -1/2(x + 4) in the equation

So, we have

-1/2x - 1/2 * 4 = 6

Hence, the two options that are the possible first step to begin to simplify the equation are (c) Multiply both sides of the equation by –2. and (d). Distribute Negative one-half over (x + 4).