What is the value of -3/4 ÷ (-3 1/4)<br>

The radius of a circle with area A is approximately √A/3. The area of a circular mouse pad is 54 square inches. Estimate its rad

Gnesinka [82]

Answer:

4.2

Step-by-step explanation:

First I did 54 divided by 3 which is 18. Then I found the square root of 18.

3 0

2 years ago

Riley is building a garden box for his backyard. He wants the perimeter to be 32

babunello [35]

The length of the garden box would be 10ft if the width is 6ft.

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

2 years ago

Find the surface area of this prism please (no links please)

horsena [70]

Answer:

192 ft^2

Step-by-step explanation:

to find the surface area of a shape, you must find the area of each side and add them together. the base of this shape is a rectangle with a length of 11ft and a height of 3ft; to calculate the area of a rectangle, you multiply the length by the height. 3*11 is 33, so the base of this prism has an area of 33ft^2. since this is a prism, we know that the side parallel to the base are the same shape, so they both have an area of 33ft^2. 33*2= 66. the two other large sides have a height of 4.5 and a length of 11; 4.5*11 is 49.5, there are two shapes with these dimensions, so 49.5*2=99. finally, the two shapes on either end of the prism have a height of 4.5 and a length of 3. 4.5*3= an area of 13.5, two of them, so 13.5*2=27. now you just add all of these numbers together: 66+99+27=192.

4 0

2 years ago

What is the partial product of 4.6 x 3.5

PIT_PIT [208]

The partial product of 4.6×3.5 is 16.1

7 0

2 years ago

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What is the value of -3/4 ÷ (-3 1/4)​

What is the value of -3/4 ÷ (-3 1/4)