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Usimov [2.4K]
3 years ago
13

Suppose a certain baseball diamond is a square 65 feet on a side. The pitching rubber is located 41.5 feet from home plate on a

line joining homeplate and second base.
a. How far is it from the pitching rubber to first base?
b. How far is it from the pitching rubber to second base?
c. If a pitcher faces home plate, through what angle does he need to turn to face first base?​

Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

Answer:

<h2>a. 41.5 ft</h2><h2>b. 41.5 ft.</h2><h2>c. 90°.</h2>

Step-by-step explanation:

Notice that a baseball diamond is a square, which means all sides are equal. In this case, each side is 65 feet long.

It's important that a square is a symmetric figure, as a symmetric quadrilateral, its diagonals are congruent and the bisect each other. That means that the distance from every corner to the center is the same.

a. Based on square definitions, the distance from the pitching rubber to first base is 41.5 feet.

b. Based on square definitions, the distance from the pitching rubber to second base is 41.5 feet.

c. if the pitcher faces the home plate, he needs to turn his 90° to face the first base, that is because diagonals are perpendicular each other, which means they have a right angle between.

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In isosceles triangle ABC, AC=BC=20, the measure of angle A=68, and CD is the altitude to side AB. What is CD to the nearest 10t
antiseptic1488 [7]

Answer:

Step-by-step explanation:

Comment

The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.

Formula

Sin(A) = Sin(68 = opposite / hypotenuse     Substitute values.

Solution

sin(68) = altitude (side opposite) / 20       multiply both sides by 20

20*sin(68) = 20* altitude / 20                     substitute for sin(68)

20* 0.9272 = altitude

altitude = 18.5

Answer: 18.5 to the nearest tenth

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Read 2 more answers
I need to show the work. Please help
Juliette [100K]

Answer:

x=23

Step-by-step explanation:

The two angles are equal so you can set 8x-77 and 3x+38 equal to each other and write it as:

8x-77=3x+38

Then you get like terms on the same sides by subtracting 3x from both sides and getting:

5x-77=38

Then you add 77 to both sides and get:

5x=115

Then you divide both sides by 5 and get x=23

3 0
3 years ago
You are remodeling your bedroom. You will paint all 4 walls and the door. There are no windows in the room. The floor is 9' by 1
Aleksandr [31]

Answer:

Part 1) The area of the 4 walls is 368\ ft^2

Part 2) You will have to buy 2 gallons

Part 3) You will have to buy 3 gallons

Part 4) \$75

Part 5) The area of the floor is 126\ ft^2

Part 6) \$850.5

Part 7) \$1,008

Part 8) \$472.5

Step-by-step explanation:

Part 1) What is the area of all 4 walls together?

we know that

The area of all 4 walls together is equal to the perimeter of the floor multiplied by the height of the wall (8 ft)

so

The perimeter of the floor is

P=2(9+14)=46\ ft

The area of the walls is

46(8)=368\ ft^2

Part 2) If a gallon of paint covers 350 sq. ft., How many gallons will you have to buy?

using proportion

\frac{1}{350}\ \frac{gal}{ft^2}=\frac{x}{368}\ \frac{gal}{ft^2}\\\\x=368/350\\\\x=1.05\ gal

Remember that you can't buy a fraction of gallon

so

You will have to buy 2 gallons

Part 3) How many gallons will it take to put on 2 coats of paint?

Now the area will be

368(2)=736\ ft^2

using proportion

\frac{1}{350}\ \frac{gal}{ft^2}=\frac{x}{736}\ \frac{gal}{ft^2}\\\\x=736/350\\\\x=2.10\ gal

Remember that you can't buy a fraction of gallon

so

You will have to buy 3 gallons

Part 4) If the paint costs $25 per gallon, and you are applying 2 coats of paint, how much will you spend on paint?

To find the cost multiply the number of gallons by $25 per gallon

so

3(25)=\$75

Part 5) What is the area of the floor?

The area of the floor (rectangle ) is equal to multiply the length of the floor by the width of the floor

A=(9)(14)=126\ ft^2

Part 6) What is the cost to redo the floor in oak?

To find the cost multiply the area of the floor by $6.75 per square foot

so

126(6.75)=\$850.5

Part 7) What is the cost to redo the floor in maple?

To find the cost multiply the area of the floor by $8.00 per square foot

so

126(8.00)=\$1,008

Part 8) What is the cost to redo the floor in carpet?

To find the cost multiply the area of the floor by $3.75 per square foot

so

126(3.75)=\$472.5

5 0
3 years ago
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