MATHEMATICS COLLEGE

What is the width of a triangle that has a 15 cm height and hypotenuse of 19 cm​

Answers

Answer 1
Answer:

Answer:

Pythagorean Theorem

Question Answer

Find the width of a triangle that has a 15cm height and a hypotenuse of 19cm. 11.7cm

A helicopter rises straight up 300m then flies west 400m. How far is it from the beginning (if it travels in a straight line back)?

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Find the number of positive integers not exceeding 108 that are not divisible by 5 or by 7.

Answers

Answer:

75

Step-by-step explanation:

The set of positive integer not exceeding 108 divisible by 5 is

D_5=\{5 \quad 10 \quad 15 \quad 20 \quad 25 \quad 30\quad 35 \quad 40 \quad 45 \quad 50 \quad 55 \quad 60 \quad 65\n \quad 70 \quad 75 \quad 80 \quad 85 \quad 90 \quad 95 \quad100 \quad 105\}

and the set of positive integer not exceeding 108 divisible by 7 is

D_7=\{7 \quad 14 \quad 21 \quad 28 \quad 35 \quad 42 \quad 49 \quad 56 \quad 63 \quad 70 \quad 77 \quad 84 \quad 91 \quad 98 \quad 105\}

Moreover, there are exactly three positive numbers not exceedng 108 that are divisible by both 5 and 7, i.e,

D_5 \cap D_7=\{37 \quad 70 \quad 105\}.

Also note that the size of D_5 is \#D_5=21 , the size of D_7 is \#D_5=15 and \# D_7 \cap D_5 = 3.

On the other hand, If a positive integer not exceding 108 is not divisible by 5 or 7, then it doesn't belong to any of this sets. Therefore, the number of positive interges not exceding 108 that are not divisible by 5 or 7 is equal to

108 -(\#D_7 + \# D_5 - \# D_7 \cap D_5)=108 -(21+15-3)=75

If EN=16 and BN=20 what is the scale factor of the dilation?

Answers

The scale factor of the dilation is approximately 1.25.

To find the scale factor of the dilation, we need to compare the corresponding side lengths of the original figure and the dilated figure.

Let's consider the two corresponding side lengths:

Original side: EN = 16 units

Dilated side: BN = 20 units

The scale factor (k) of the dilation is the ratio of the corresponding side lengths in the dilated figure to the original figure. It can be calculated using the formula:

Scale factor (k) = Dilated side length / Original side length

Substituting the given values:

k = 20 / 16 ≈ 1.25

for such more question on scale factor

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In a triangle, the measure of the second angle is twice the measure of the first angle. The third angle is equal to the sumof the other angles,
Which of the following could represent the measures of the three angles?
Ox, 2%, 4%
OX, 2x, 3x
OX, 2x, 2x

Answers

Answer:

x, 2x, 3x

Step-by-step explanation:

If we have angle x as one angle, and the 2nd angle is twice the angle, the 2nd angle will be 2x. If the 3rd angle is the sum of the 1st angle and the 2nd angle, we have 2x + x, which equals 3x.

What point represents the coordinate of point (4, 17) after a reflection about the x-axis​

Answers

Answer:

Step-by-step explanation: do you have a graph?

Zoe walks 4 kilometers and 600 meters, Elijah runs 3 times as far as Zoe walks. Anthony rides his bike 700 meters farthwr than Elijah runs, how far does Anthony ride in meters?

Answers

Answer:

  14,500 m

Step-by-step explanation:

  1 km is 1000 m, so 4 km = 4000 m.

Zoe walks 4000 +600 = 4600 m.

Elijah runs 3(4600 m) = 13,800 m.

Anthony rides 700 m farther, so rides ...

  13,800 m +700 m = 14,500 m

Anthony rides 14,500 meters.

Find the solution of the system of equations . - 5x + 9y = 11 x - 3y = - 7how do i solve this

Answers

Answer:

Solution: x=5, y=4

Step-by-step explanation:

System of Equations

We need to solve:

- 5x + 9y = 11

x - 3y = - 7

There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:

x = - 7 + 3y

Now replace it into the first equation:

- 5(- 7 + 3y) + 9y = 11

Operate:

35 - 15y + 9y = 11

Simplify:

35 - 6y = 11

Rearrange:

- 6y = 11 - 35 = -24

Solve:

y = -24 / -6

y = 4

Finally, since

x = - 7 + 3y

x = - 7 + 3*4

x = - 7 + 12

x = 5

Solution: x=5, y=4
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