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3 years ago

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Mathematics

1 answer:

Savatey [412]3 years ago

7 0

Answer:

4 : 39

5 : 52

6 : 67

7 : 77

Step-by-step explanation:

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A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of te triangle is 16m to the power of 2, what are the base

Olenka [21]

Answer:

The base of triangle is $\frac{8}{\sqrt{3}} \ m$ and the height of triangle is $\frac{12}{\sqrt{3}} \ m.$

Step-by-step explanation:

Given:

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.

Now, to find the base and height of the triangle.

The base of triangle = $x\times\frac{1}{2} =\frac{x}{2} \ m.$

The height of triangle = $x\times \frac{3}{4} =\frac{3x}{4}\ m.$

The area of triangle = $16\ m^2.$

Now, we put the formula of area to solve:

$Area=\frac{1}{2} \times base\times height$

$16=\frac{1}{2} \times \frac{x}{2} \times \frac{3x}{4}$

$16=\frac{3x^2}{16}$

Multiplying both sides by 16 we get:

$256=3x^2$

Dividing both sides by 3 we get:

$\frac{256}{3} =x^2$

Using square root on both sides we get:

$\frac{16}{\sqrt{3}}=x$

$x=\frac{16}{\sqrt{3}}$

Now, by substituting the value of $x$ to get the base and height:

$Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.$

So, the base of triangle = $\frac{8}{\sqrt{3}} \ m.$

$Height=x\times\frac{3}{4} \\\\Height=\frac{16}{\sqrt{3}}\times \frac{3}{4} \\\\Height=\frac{12}{\sqrt{3}} \ m.$

Thus, the height of triangle = $\frac{12}{\sqrt{3}} \ m.$

Therefore, the base of triangle is $\frac{8}{\sqrt{3}} \ m$ and the height of triangle is $\frac{12}{\sqrt{3}} \ m.$

7 0

4 years ago

Help please! Complete the proof!

Dmitry [639]

Since CM is perpendicular to AB, it follows that ∠1 and ∠2 are 90 degrees. Since they both have 90 degree angles, that must mean they are both right triangles.

And since ∠3 = ∠4 and ∠1 = ∠2, then it follows that ∠A = ∠B. (You can show this by showing that they must add up to 180 degrees.)

So since both right triangles have 3 congruent angles to each, then that makes them similar by AAA (angle angle angle).

5 0

3 years ago

The table shows ordered pairs of the function y = 8 - 2x. When x = 8, the value of y is

Sergeu [11.5K]

The answer will be -8

y=8-2x x=8

8-2(8)
8-16=-8

6 0

3 years ago

At a convention for lawyers it was known that of the 100 present, at least one was honest, yet if you met any two of the lawyers

Temka [501]

From the given condition, there is only one honest lawyer present.

5 0

4 years ago

Translate and solve: 783% of what number is 47,763?

AysviL [449]

Answer:

6,100

Step-by-step explanation:

7.83n= 47,763

Now, we can solve for n by dividing both sides by 7.83 and simplifying.

n=6100

4 0

3 years ago