2. A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles. To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance.

Answers

Answer 1

Answer: given:
angle of 6 : i'm assuming this is 6 degrees.
distance of 5 miles.

tan(6) = rise/5 mi
rise = 5 mi * tan(6)
rise = 5 mi * 0.10510423526
rise = 0.52552117632

rise = 0.53 miles.

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There are a total of 20 lions, tigers and bears. If the number of tigers is 2 more than the number of lions and the number of bears is 1 more than the number of tigers, find the number of each.

Answers

Number of tiguers: x + 2
Number of Lions: x
Number of bears:(x+2)+1=(x+3)

We can suggest this equation:
(x+2) + (x)+(x+3)=20

3x+5=20
3x=20-5
3x=15
x=15/3
x=5.

Therefore:
Number of tiguers: x + 2=5+2=7
Number of Lions: x=5
Number of bears:(x+2)+1=(x+3)=5+3=8.

Answer: there are 7 tiguers, 5 lions and 8 bears.

Final answer:

In the problem, if we denote the number of lions as x, the number of tigers as x+2, and the number of bears as x+3, and considering that the total of all these animals is exactly 20, we can form and solve a simple algebraic equation. We will find that there are 5 lions, 7 tigers, and 8 bears.

Explanation:

This is a problem of simple algebra. According to the problem, let's represent the number of lions as x, the total number of tigers as x + 2 (since it's two more than the lions), and the number of bears as x + 3 (1 more than the number of tigers).

The problem states the total number of all these animals as 20, so we can set up the following equation: x + x + 2 + x + 3 = 20.

Solving this algebra equation gives you:

3x + 5 = 20

Subtracting 5 from both sides gives us:

3x = 15

Dividing both sides by 3 gives us:

x = 5

So, the number of lions is 5, the number of tigers is 7 (5 + 2), and the number of bears is 8 (7 + 1).

Learn more about Algebra here:

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A scale drawing of a square has a side length of 5 millimeters. The drawing has a scale of 1 mm : 5 km. Find the actual perimeter and area of the square.

Answers

Answer:

Actual Perimeter = 100 km

Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

1 mm = 5 km

5 mm = 5 × 5 km

= 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

Perimeter of square = 4 × side

= 4 × 25

= 100 km

Area of the square = side × side

= 25 × 25

= 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

True or False?-If two rectangles have equal areas, then they are congruent.
-If two squares have equal perimeters, then they have equal areas.

Answers

#1

That is false..one could have side lengths of 9 and 1, and the other could have side lengths of 3. Both the areas would be 9, but the figures would not be congruent.

#2

That is true, they must both have the same side length to have the same perimeter, therefore they will also have the same area.

Characteristics of Linear Functions Complete the table below. Function Rate of Change dnitial Value Behavior f(x) = 9.7 – 8 Select an answer Select an answer V(t) = 3 - 9t ODOL ODIO Select an answer v r(a) = 6 Select an answer C(w) = - 3

Answers

ANSWER

EXPLANATION

In linear functions we often have the slope-intercept form of the equation:

$f(x)=mx+b$

Which can also be written in a different order, for example:

$f(x)=b+mx$

m is the slope of the line. The slope of the graph of a function is the rate of change.

b is the y-intercept. This

A total of 584 tickets were sold for the school play. They were either adult tickets or student ticketsThe number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold

Answers

146 adult tickets were sold.
write out your equation first: x+3x=584
4x=584
x=146
Try it out 146+3(146)=584
It worked. That's the solution.

so lets divide the amount of tickets by 4 because there are 4 parts needed in this situation which equals 146 then we know our answer is 146 because the other three parts go to the kids tickets

When is the estimation of products a useful tool?

Answers

The estimation of products are usefull so with you real answer, you can check back and fourth if you answer is reasonable

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