What is 1230 divided by 12

A driver drove for 3 hours at a certain speed. If he drove 12 more miles at the same speed, the distance would be 132 miles. At

Zinaida [17]

Distance traveled in 3 hrs was (speed in mph)(3 hrs)

Then s(3 hrs) + 12 mi = 132 mi.

Therefore, 3s = 120, and s = 120 miles / 3 hrs = 40 mph (answer)

7 0

2 years ago

Please help! A chemist has 100ml of 25% acid solution. How much of the solution does she need to drain and replace with 70% acid

ratelena [41]

Answer:

77.78

Step-by-step explanation:

7 0

2 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

2 years ago

PLEASE HELP! (Look at photo)

spayn [35]

Answer:

Starting from the one on the left.

Upper left:

145 degrees

Down left:

35 degrees

Down right:

145 degrees.

-------------

Now for the right image.

Upper left:

153 degrees

Down left:

27 degrees

Down right:

153 degrees

Step-by-step explanation:

Apply the same steps for the second image as for the first.

One thing to keep in mind is that a flat line (horizontal or vertical), as an angle of 180 degrees.

And another useful reminder is that opposed angles have the same degree.

Starting from the one on the left.

Upper left:

180 - 35 = 145 degree

Down left:

since it is opposed to the upper right angle which is 35 degrees this one is also equal to 35 degrees.

Down right:

since it is opposed to the upper left angle which is 145 degrees this one is also equal to 145 degrees.

You can always double check by making sure one flat side (left or right or up or down), is equal to 180 degrees.

example: on the right image, for the down part, I wrote as answers 27 degrees (for down left because it is opposed to upper right) and 153 degrees (for down right because it is opposed to upper left) => 153 + 27 = 180 degrees

8 0

2 years ago

Select the correct answer.<br> Which of the following sets of ordered pairs represents a function?

iogann1982 [59]

Answer: {(-8, -14), (-7,-12), (-6,-10), (-5,-8)}

Step-by-step explanation: A function is a relation in which each x-coordinate corresponds to exactly one y-coordinate.

In the relations show here, notice that the first set

of ordered pairs is the only set where each x-coordinate

appears once with a different y-coordinate.

In the other ordered pairs, there is an x-coordinate that appears more

than once and it corresponds to a different y-coordinate.

For example, in the second relation,

the x-coordinate -9 appears twice.

In one case, -9 corresponds to -12 and

in the other case, it corresponds to -8.

So, this is not a function.

3 0

2 years ago