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harkovskaia [24]

3 years ago

13

The length of a rectangle is 3yd less than twice the width, and area of the rectangle is 27yd^2. Find the dimensions of the rect

angle

1 answer:

Llana [10]3 years ago

3 0

Width= 4.5 yards
length= 6 yards

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Find the number of faces, edges, and veritces of the solid

Nesterboy [21]

This is probably wrong, but from what I know, there are 16 vertices, 24 edges, and 10 faces. I’m not sure if this is wrong, but I did some math and some research, and this is what I got.

7 0

3 years ago

In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

3 years ago

What is the sum of six times a number and 25

mina [271]

six times a number: 6(x)

The sum of 6(x) and 25: 6x + 25

6x + 25 is your expression.

hope this helps

7 0

3 years ago

Read 2 more answers

What is the multiplicative inverse of −9?

Romashka-Z-Leto [24]

Answer:

The answer to your question is: letter C

Step-by-step explanation:

Multiplicative inverse is a pair of numbers which product gives 1.

Then

x will be our number

-9x = 1

x = - 1/9

because

-9 x $\frac{-1}{9}$ = $\frac{9}{9}$ = 1

8 0

3 years ago

According to this diagram what is tan 62

kicyunya [14]

The figure is not attached. So, I have attached it from the link- brainly.com/question/4198293

Answer:

$\tan(62)=1.875$

Step-by-step explanation:

Label the triangle ABC as shown below.

Given:

AB = 8, BC = 15, AC = 17, m∠ABC = 90°, m∠ACB = 28°, m∠BAC = 62°

The tangent of a given angle is given as the ratio of the opposite side and the adjacent side. The opposite side is the side opposite to the angle. The adjacent side is the other leg of the right angled triangle.

Here, the opposite side to angle A is BC and adjacent side is AB.

Therefore, the tan ratio of angle A is given as:

$\tan A=\frac{BC}{AB}\\\tan (62)=\frac{15}{8}=1.875$

Hence, tan 62 = 1.875.

4 0

3 years ago