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storchak [24]
2 years ago
5

Maryam earns a salary of $35,000 a year. Her benefits are equal in value to 35 percent of her salary. What is the value of Mayam

's benefits?
Mathematics
1 answer:
hammer [34]2 years ago
7 0
35% of $35,000 is $12,250
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New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that o
frosja888 [35]
The answer is 80 square meters.

The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.

The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.

After renovations, square garden becomes rectangular.

One side is doubled in length:
a₁ = 2a

The other side is decreased by three meters.
b₁ = a - 3

The new area is 25% than the original square garden:
A₁ = A + 25%A =
     = A + 25/100·A
     = A + 1/25·A
     = a² + 1/25·a²
     = <span>a² + 0.25·a²
</span>     = 1.25·a²

If the starting equation is:
A₁ = a₁ · b₁

Thus, the equation is:
1.25a² = 2a·(<span>a - 3)
</span>1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a

<span>Therefore, the equation that could be used to determine the length of a side of the original square garden is:
</span><u>2a² - 6a = </u><span><u>1.25a²</u></span>


Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0

From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8

If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80

Therefore, the area of the new rectangle garden is 80 square meters.
4 0
3 years ago
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements. Triangle JKL is congruent to triangle . Side LK corre
frosja888 [35]

Answer:

ΔLK ΔJKL

Step-by-step explanation:

I'm not positive cause im still learning this

4 0
1 year ago
Read 2 more answers
The town council wants to know if the residents support beautification of the downtown area. What is the best design for this st
Natasha_Volkova [10]
Experimental census sample survey

7 0
2 years ago
What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = \pi/3? your answer should have at
Serhud [2]
<h3>Answer:</h3>
  • using y = x, the error is about 0.1812
  • using y = (x -π/4 +1)/√2, the error is about 0.02620
<h3>Step-by-step explanation:</h3>

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

___

If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

6 0
2 years ago
Demand for an electric fan is related to its selling price p (in dollars) by the equation n = 1960 − 70 p where n is the number
alexandr402 [8]

Answer:

  $14

Step-by-step explanation:

The revenue from sales of fans is the product of the number of fans sold and the price at which they are sold:

  R(p) = n·p = (1960-70p)p

  R(p) = 70(28 -p)p

This equation describes a parabola that opens downward and has zeros at p=0 and p=28. The axis of symmetry is halfway between those zeros, at p=14. It goes through the vertex or point of maximum revenue.

The price for maximum revenue is p = 14 dollars.

7 0
2 years ago
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