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vfiekz [6]
4 years ago
15

one fourth of the 7th grade students made honor roll in the first quarter. the number of honor roll students increased by 18 in

the second quarter. If 105 students made honor roll in the second quarter. How many total 7th graders are there?
Mathematics
1 answer:
Mandarinka [93]4 years ago
3 0

1/4 of x students made the honor roll in the first quarter

1/4 of x plus 18 equals 105

1/4 x + 18 = 105

1/4 x + 18 - 18 = 105 - 18

1/4 x = 87

Reciprocal to isolate variable

4/1(1/4 x) = 87(4/1)

x = 348

There is a total of 348 students in 7th grade

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<span>pi X 2r X 2r X 2h = 8pir^2h </span>

<span>Volume is 8 times </span>

<span>ANSWER IS FALSE</span>
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Find the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4)
Zolol [24]

Answer:

y = 8

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides and three angles of both triangles are equal.

The distance between two points on the coordinate plane is given as:

Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\

In triangle ABC:

|AB|=\sqrt{(2-8)^2+(6-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|AC|=\sqrt{(5-8)^2+(0-4)^2}=5\\\\|BC|=\sqrt{(5-2)^2+(0-6)^2    }=\sqrt{45}

In triangle MNO:

|MN|=\sqrt{(1-7)^2+(2-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|MO|=\sqrt{(4-7)^2+(y-4)^2}\\\\|NO|=\sqrt{(4-1)^2+(y-2)^2    }

Since triangle ABC and triangle MNO are congruent, hence:

|AB| = |MN| = 2√10, |AC| = |MO| = 5, |BC| = |NO| = √45

|AC|=|MO|=5\\\\\sqrt{(4-7)^2+(y-4)^2}=5\\\\(4-7)^2+(y-4)^2=25\\\\9 +(y-4)^2=25\\\\(y-4)^2=16\\\\square\ root\ of\ both\ sides:\\\\y-4=4\\\\y=4+4\\\\y=8

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3 years ago
Saiges spaceship traveled 588 kilometers in 60 seconds. Determine whether or not each spaceship trip below has the same speed as
Fiesta28 [93]

Answer:

Part 1)  441km in 45s   --> Has the same speed as Saige's spaceship

Part 2) 215km in 25s --> Does not have the same speed as  Saige's spaceship

Part 3) 649km in 110s --> Does not have the same speed as  Saige's spaceship

Step-by-step explanation:

<u><em>The complete question is</em></u>

Saige's spaceship traveled 588 kilometers in 60 seconds.

Determine whether or not each spaceship trip below has the same speed as Saige's spaceship.

441km in 45s

215km in 25s

649km in 110s

we know that

The speed is equal to divide the total distance traveled by the total time

In this problem we have that

The speed of Saiges spaceship is equal to

\frac{588}{60}=9.8\ \frac{km}{sec}

case 1) we have

441km in 45s

Find out the speed of the  spaceship trip

\frac{441}{45}=9.8\ \frac{km}{sec}

Compare the speed of the spaceship trip with the speed of Saiges spaceship

9.8\ \frac{km}{sec}=9.8\ \frac{km}{sec}

therefore

Has the same speed as Saige's spaceship

case 2) we have

215km in 25

s

Find out the speed of the  spaceship trip

\frac{215}{25}=8.6\ \frac{km}{sec}

Compare the speed of the spaceship trip with the speed of Saiges spaceship

8.6\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}

therefore

Does not have the same speed as  Saige's spaceship

case 3) we have

649km in 110s

Find out the speed of the  spaceship trip

\frac{649}{110}=5.9\ \frac{km}{sec}

Compare the speed of the spaceship trip with the speed of Saiges spaceship

5.9\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}

therefore

Does not have the same speed as  Saige's spaceship

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Step-by-step explanation:

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