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3 years ago

11

Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person

run? (Using equations)

1 answer:

kvasek [131]3 years ago

3 0

Ruby runs 6 miles, Will runs 12

18=3x

6=x

Ruby runs 6

6+12=18

Will runs 12

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Given the equation y = 2x - 8, what is the slope and the y-intercept?

aniked [119]

The answer to this is the second choice

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3 years ago

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Solve the compound inequality 6b < 24 or 4b + 12 > 4.

myrzilka [38]

The answer is a. b>-2 because

6b<24
b< 24/6
b<4

And

4b+12>4
4b>4-12
4b>-8
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2 years ago

A certain number was multiplied by 7. 4 was taken away from the product. Finally, that difference was then divided by 9, resulti

marin [14]

Answer:

7

Step-by-step explanation:

To solve this, we have to work backwards. If you divide something by 9, and it equals 5, to figure out the number, we need to multiply by 9. 5*9= 45. If four was taken away, we have to add it to 45, which is 49. If a number *7 is 49, then we have to divide by 7 to get the answer. 49/7=7

7 0

3 years ago

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0

3 years ago

ycow [4]

Answer:

$11$ bushels of apples were sold

Step-by-step explanation:

Let

x----> bushels of peaches

y----> bushels of apples

we know that

$7x+6y=346$ -----> equation A

$x=y+29$ -----> equation B

substitute equation B in equation A and solve for y

$7(y+29)+6y=346$

$7y+203+6y=346$

$13y=346-203$

$13y=143$

$y=143/13=11$

5 0

3 years ago