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kifflom [539]
3 years ago
8

Among the eighth-graders in Michael's school, 70% have siblings. The eighth-grade class is 5/6 the size of the seventh-grade cla

ss.
If 112 eighth-graders have siblings, how many students are in the seventh grade?

A. 128

B. 134

C. 160

D. 192
Mathematics
1 answer:
trapecia [35]3 years ago
5 0

Answer:

D. 192

Step-by-step explanation:

This problem involves a few steps.  First, you need to determine how many eighth graders you have given that 112 represent 70% of the total number of eighth graders.  You can solve this using a proportion:

\frac{70}{100}=\frac{112}{x}

Cross-multiply and divide:  70x = 11200 or 70x/70 = 11200/70 or x = 160

Since there are 160 total eighth graders and this is \frac{5}{6} of the amount of seventh graders, we can set up an equation to solve for the total amount of seventh graders:

160 =  \frac{5}{6}x

Multiply by the reciprocal of your fraction on both sides:

\frac{6}{5} x 160 =  \frac{5}{6}x (\frac{6}{5})

Solve for x:  x = 192 seventh graders

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Dilate the the triangle, scale factor = 3 (positive 3, ignore the
HACTEHA [7]

Answer:

The rule of dilation is P'(x,y) = 3\cdot P(x,y).

The vertices of the dilated triangle are A'(x,y) = (-21, -18), B'(x,y) = (-15,-10) and C'(x,y) = (-3,-15), respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)] (1)

Where:

O(x,y) - Center of dilation, dimensionless.

k - Scale factor, dimensionless.

P(x,y) - Original point, dimensionless.

P'(x,y) - Dilated point, dimensionless.

If we know that O(x,y) = (0,0), k = 3, A(x,y) = (-7,-6), B(x,y) = (-5,-2) and C(x,y) =(-1,-5), then dilated points of triangle ABC are, respectively:

A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)] (2)

A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)]

A'(x,y) = (-21, -18)

B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)] (3)

B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)]

B'(x,y) = (-15,-10)

C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)] (4)

C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)]

C'(x,y) = (-3,-15)

The rule of dilation is:

P'(x,y) = 3\cdot P(x,y) (5)

The vertices of the dilated triangle are A'(x,y) = (-21, -18), B'(x,y) = (-15,-10) and C'(x,y) = (-3,-15), respectively.

7 0
3 years ago
What is 71.09 rounded off to the nearest whole number
masha68 [24]

It is 71 because 0 is less than 5, so it stays the same.

5 0
3 years ago
Steve has two pieces of PVC pipe of length 4 ft and 7 ft. Which of the following lengths of PVC pipe could be used as the third
Ratling [72]

Answer:

<em>10 feet</em>

Step-by-step explanation:

here's the reason ; -

let's take the missing side be x

we know, the one side of a triangle should always be greater than the difference between the other two sides, so ,

=》x > 7-4

=》x > 3

and the measure of a side should always be less than the some of the other two sides, hence

=》7 + 4 > x

=》11 > x

now, we have : -

11 > x > 3

value of x should be more than 3 and less than 11 , hence 2 ft , 3 ft and 12 ft can't be the measure of third side,

so, we got our third side as 10 ft

3 0
3 years ago
Jim split up $23 equally among 31 winners. What decimal is
Feliz [49]

Answer:

Each winner received 1.35 dollars

Step-by-step explanation:

I divided 31 by 23 and got 1.34782608696. But we had to round to the hundredths so, I rounded up to 1.35 dollars.

4 0
3 years ago
Work out the perimeter of the semi-circle take pi to be 3.142​
kupik [55]
Answer:
P = 25.71 cm
Step-by-step explanation:
Perimeter of semicircle = πD/2
Where D=10 cm
P = (3.142)(10)/2
P = (3.142)(5)
P = 15.71 cm
Complete Perimeter of Semicircle = P + Diameter
= 15.71 + 10
= 25.71 cm
7 0
3 years ago
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