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2 years ago

True or face dilations preserve angle measure

Mathematics

1 answer:

Ilia_Sergeevich [38]2 years ago

6 0

Answer:

True

Step-by-step explanation:

Required

Does dilation preserve angle measure?

When a point, side, line, or angle is dilated; the length of the line will be altered by the ratio or scale of dilation.

However, the measure of angle will remain the same.

Hence, the given statement is true.

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Write two ratios equivalent to 24 : 9.

notsponge [240]

Answer:

8:3

16:6

Step-by-step explanation:

First, let's check if 9 and 24 have any common factor. If they do have any common ones, we must find the GCF (greatest common factor).

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors both of the numbers share and 1 and 3. To find the GCF, simply compare one of the factors to the other.

1 < 3

Now that we know the GCF, we can divide the two numbers in the ratio 24 : 9 by it (3).

24:9

24/3:9/3

8:3

Now that our ratio is simplified, it's going to be much easier to find more ratios that are equivalent. 8:3 is already one equivalent ratio, but if we multiply each number in the ratio by any other number, we can get a new equivalent ratio. Let's multiply each number in the ratio by 2:

8:3

8 ⋅ 2:3 ⋅ 2

16:6

So, another equivalent ratio to 24:9 (and 8:3) is 16:6.

3 0

2 years ago

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 16 miles per hou

Verizon [17]

We'll use variables to represent the speeds of the eastbound and westbound trains.

x will represent the speed of the eastbound train.
y will represent the speed of the westbound train.

The eastbound train is 16 mph faster than the westbound train. An equation can be made from this:

$x - y = 16$

Subtraction is used, because it represents the difference in distances between the two trains if they travel the same direction.

After 4 hours, the trains are 800 miles apart. An equation can be made from this:

$4x + 4y = 800$

Addition is used, because the trains are heading in opposite directions, which means their distances from the starting point are added together.

Set the two equations up vertically:

$x - y = 16$
$4x + 4y = 800$

We will use elimination to solve for x.

Multiply the entire first equation by 4 so that the coefficients for y will be opposite numbers:

$(x - y = 16) \times 4 = 4x - 4y = 64$

$4x - 4y = 64$
$4x + 4y = 800$

Combine the two equations together to cancel out y:

$8x = 864$

Divide both sides by 8 to get x by itself:

$x = 108$

The speed of the eastbound train is 108 mph.

5 0

3 years ago

Your school is sponsoring a pancake dinner to raise money for a field trip. You estimate that 150 adults and 280 children will a

soldi70 [24.7K]

Answer:

150x + 280y = 1310

Step-by-step explanation:

5 0

3 years ago

4(2k-3)+1=8k-11 help pls

Fofino [41]

4(2k - 3) + 1 = 8k - 11
8k - 12 + 1 = 8k - 11
8k - 11 = 8k - 11

So, these two equations equal to the same thing.
Glad I could help and gave a fantastic day!

8 0

2 years ago

What is the value of b?

pishuonlain [190]

Answer:

The quadratic function is f(x) = a * x^2 + b * x + c . The b-value is the middle number, the number next to the x. The other letters, a and c, are also numbers like b.

5 0

3 years ago