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bija089 [108]
3 years ago
11

3/5 of the class were boys. The teacher divided the boys equally into groups so the each group of boys had 1/10 of the number of

students in the class. The teacher then divided the girls equally into groups such that each group of girls had 1/5 of the number of students in the class? How do I do this and what's the answer?
Mathematics
1 answer:
Lana71 [14]3 years ago
4 0
I think boys =18
          girls=12
boys :x
girls:y
student:z
the number of group for the boys :n
the numberof group for the girls :m
so x=(3/5)*z
    y=(2/5)* z
x/y=3/2
3y-2x=0
(1/10)*z*n=(3/5) *z
so n=6
(1/5)*z*m=(2/5)* z
put x=(1/10)*z*6
    y=(1/5)*z*2
 into 3y-2x=0 and z=30
 z=30 so x=(1/10)*30*6=18
               y=(1/5)*30*2=12


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At 2pm two military convoys leave Eagle River Wisconsin one headed North and 1 headed South the convoy headed North averages 50
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Answer:

The answer to the question is

1.5 hours that is;

When the distance between them is more then 135 miles is after 1.5 hours and they will lose radio contact at 3:30 p.m.

Step-by-step explanation:

We note that

The speed of the military convoy headed north =50 mph

The speed of the convoy headed south  = 40 mph

Let t be the time taken for the two convoys to be 135 miles apart

The time taken for the two convoys to be 135 miles apart is given by

50×t miles+ 40×t miles= 135 miles

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Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key
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Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

<h3>1.</h3>

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322}  \\VX \approx 36.36

Also, YW \approx 36.36, beacuse rectangles have congruent diagonals, which intercect equally.

That means, ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18

<h3>2.</h3>

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\  DG \approx 25.75

<h3>3.</h3>

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

\angle 4  = 31\°

Which means \angle 3 = 59\°, beacuse it's the complement for angle 4.

Now, \angle 6 = 59\°, because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

\angle 9=180-59-59=62, by interior angles theorem.

\angle 8 =62, by vertical angles theorem.

\angle 10 = 180- \angle 9=180-62=118\°, by supplementary angles.

\angle 7 = 118\°, by vertical angles theorem.

\angle 5=90-59=31, by complementary angles.

\angle 2 = \angle 5 = 31\°, by alternate interior angles.

\angle 1 = 59\°, by complementary angles.

<h3>4.</h3>

m\angle BCD=90\°, because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

m\angle ABD = 6\° = m\angle BDC, by alternate interior angles and by given.m\angle CBE=90-6=84, by complementary angles.

m\angle ADE=90-6=84, by complementary angles.

m\angle AEB=180-6-6=168\°, by interior angles theorem.

m\angle DEA=180-168=12, by supplementary angles.

<h3>5.</h3>

m\angle JMK=180-126=54, by supplementary angles.

m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63, by interior angles theorem, and by isosceles triangle theorem.

m\angle HLK=90\°, by definition of rectangle.

m\angle HJL=\frac{180-126}{2}=27, by interior angles theorem, and by isosceles triangle theorem.

m\angle LHK=90-27=63, by complementary angles.

m\angle = JLK= m\angle HJL=27, by alternate interior angles.

<h3>6.</h3>

The figure is a rectangle, which means its opposite sides are equal, so

WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5

Then, we replace this value in the expression of side WZ

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<h3>7.</h3>

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Then,

PR=5x+28=5(9)+28=45+28=73

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