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3 years ago

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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

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.

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masha68 [24]

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

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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

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=》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,

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Feliz [49]

Answer:

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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.

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kupik [55]

Answer:
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Step-by-step explanation:
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Where D=10 cm
P = (3.142)(10)/2
P = (3.142)(5)
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