Find two decimals that are equivalent to

Figure a is dilated by a scale factor of 1/2 to form figure b. What is the length of x?

PIT_PIT [208]

Answer:

The correct option is 3. The value of x is 8 inches.

Step-by-step explanation:

It is given that Figure A is dilated by a scale factor of 1/2 to form Figure B. It means both figure are similar and corresponding sides of similar figures are proportional.

$\text{scale factor}=\frac{\text{Side of image}}{\text{Side of preimage}}$

$\frac{1}{2}=\frac{x}{16}$

Multiply both sides by 16.

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

$8=x$

Since scale factor is 1/2, so we can directly say that the side length of image is half of the corresponding side of preimage.

The length of x is 8 inches. Therefore the correct option is 3.

3 0

3 years ago

Read 2 more answers

How could I get rid of the 3 shown in equation 1?

Tems11 [23]

Answer:

Step-by-step explanation:

3 log 2+log (x-4)=log 2³+log (x-4)=log 8+log (x-4)=log 8(x-4)

8 0

3 years ago

Penelope is going to invest $23,000 and leave it in an account for 11 years. Assuming the interest is compounded continuously, w

madreJ [45]

Answer:

5.3%

Step-by-step explanation: answer fo

r delta math

6 0

3 years ago

The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?

vlabodo [156]

Answer:

<h2>Therefore the length of a side of a cube is $\sqrt[3]{64}\ or\ 4$ </h2>

Step-by-step explanation:

The volume of a cube is expressed as L³ where L is the length of each side of the cube.

Given volume of a cube = 64in³

On substituting;

64 = L³

Taking the cube root of both sides to determine L we have;

$\sqrt[3]{64} = (\sqrt[3]{L})^{3}\\\sqrt[3]{64} = L\\L=4$

Therefore the length of a side of a cube is $\sqrt[3]{64}\ or\ 4$

8 0

3 years ago

An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of

Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = $\pi r^{2} \frac{h}{3}$

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

$r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm$

We will now find the volume of the cone.

Volume of cone $\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}$

We know the density of ice is 0.93 grams per $1cm^{3}$

$1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g$ (Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = $\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}$

Volume of cone being melted = New Volume - Original volume

= $\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}$

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = $\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}$

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = $5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}$

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= $\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}$

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0

1 year ago