MATHEMATICS HIGH SCHOOL

In a 30cm by 25cm rectangle, a quadrant of a circle of radius 7cm has been cut away from each corner. What is the perimeter of the part left? and also what is the area of the part left

Answers

Answer 1

Answer:

Answer:

97.96 cm

596.14 cm²

Step-by-step explanation:

sides become:

30 cm ⇒ 16 cm
25 cm ⇒ 11 cm

and added corners:

4*2πr/4= 2πr = 2*3.14*7 cm= 43.96 cm

then perimeter is:

P= 2*16+2*11+43.96= 97.96 cm

the area left is:

A= 30*25- 4*1/4*3.14*7²= 596.14 cm²

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Answers

Chart are use to represent the visual outcome or status of a business, or an activity or even for any kind of reason as long as the data is complete and relevant. In addition to this, people you charts as a basis or a way of showing the growth of their work. Many people use it so that they can easily makes decision basing to what is the outcome they see in their charts.

"Among 40 students, 20 liters of juice was served. How much juice did each student get?"

Answers

Answer:

How much juice did each student get?"

40/20=2

each student received 2L of juice

Step-by-step explanation:

Each student got 1/2 a litre or 500 ml sa 20 divided by 40 equals half

During a family trip, you share the driving with your dad. At most, you are allowed to drive for three hours. While driving, your maximum speed is 55 miles per hour.Part A) Write a system of inequalities describing the possible numbers of hours “t” and distance “d” you may have to drive.

Part B) Is it possible for you to have driven 160 miles?

Please help and if you don’t mind to explain how you got all of the answers to each part. Offering 20 Points!

Thank you!

Answers

Final answer:

In this question, we create a system of inequalities to describe the possible number of hours and distance you may have to drive. It is not possible to have driven 160 miles.

Explanation:

Part A:

Let t represent the number of hours you drive and d represent the distance you drive.

The constraints for the number of hours are: 0 ≤ t ≤ 3, which means you can drive for at most 3 hours.

The constraints for the distance are: 0 ≤ d ≤ 55t, which means the distance you drive cannot exceed 55 miles per hour multiplied by the number of hours you drive.

Part B:

No, it is not possible for you to have driven 160 miles. Let's substitute t = 3 into the distance constraint:

d ≤ 55t

d ≤ 55(3)

d ≤ 165

Since 160 is greater than 165, it is not within the range of possible distances you can drive.

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Final answer:

The system of inequalities describing the possible numbers of hours and distance is t ≤ 3 and d = t × 55. It is not possible to have driven exactly 160 miles.

Explanation:

Part A:

To describe the possible numbers of hours and distance you may have to drive, we can create a system of inequalities based on the given conditions. Let's denote 't' as the number of hours you drive and 'd' as the distance you cover.

The maximum allowed driving time is 3 hours, so we can write the inequality: t ≤ 3.

Since your maximum speed is 55 miles per hour, the distance 'd' can be calculated using the formula: d = t × 55.

Combining these two inequalities, we have: t ≤ 3 and d = t × 55.

Part B:

To determine if it is possible to have driven 160 miles, we substitute the distance 'd' with 160 in the inequality: d = t × 55. By solving for 't', we can find the allowed range of hours. Plugging in the values, we get: 160 = t × 55. Rearranging the equation, we find t = 160 / 55, which gives t ≈ 2.91.

Therefore, it is not possible to have driven exactly 160 miles, as it falls outside the allowed range of t.

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Solve the rational equation

1/x+3/8=1/4

Answers

Step 1: Subtract 3/8 from both sides
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Step 2: Multiply 1/4 by 1/2
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Step 3: Subtract
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Step 5: Multiply by x on both sides
1/x(x)=-1/8(x)
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Step 6: Divide -1/8
1/(-1/8)=-1/8x/(1/8)
*You can times flip
1(-8)=-1/8x(8)
-8=-x
*Divide by -1
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8=x

If two angles are supplementary, they must __________.add up to
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be congruent

Answers

supplementary angles add up to 180

If two angles are supplementary, their sum is 180º and they can be expressed as x and 180-x. If they are congruent ,then the two angles are equal:
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The 2 angles have to add to 180 degrees

CANT GET WRONG PLZ HELPSimplify
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a. 2x - 26
b. 2x + 28
c. 3x - 27
d. -7x + 1