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3 years ago

I need help with this please

Mathematics

1 answer:

goldenfox [79]3 years ago

3 0

Answer:

31/100

Step-by-step explanation:

A percentage can be expressed as a fraction by making use of the fact that the % symbol is essentially equivalent to /100.

31% = 31/100

Rey ate 31/100 of the naxvips.

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211,135.71 merry christmas

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3 years ago

A rectangular field is 75 yards wide and 105 yards long

nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

Width = 75 yards
Length = 105 yards

Area of the field with the given values:

$\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}$

To maintain the same perimeter, but change the area, either:

decrease the width and increase the length by the same amount, or
increase the width and decrease the length by the same amount.

In geometry, length pertains to the longest side of the rectangle while width is the shorter side. Therefore, we should choose:

decrease the width and increase the length by the same amount.

Define the variables:

Let x = the amount by which to decrease/increase the width and length.

Therefore:

$\implies \sf width \times length < 7875\:\:yd^2$

$\implies (75-x)(105+x) < 7875$

Solve the inequality:

$\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}$

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

$\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}$

$\textsf{where } 0 < x < 75$

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

Example 1:

Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

Example 2:

Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

4 0

1 year ago

Read 2 more answers

One endpoint of a line segment has coordinates represented by (x + 4, 1/2y). The midpoint of the line segment is (3, -2). How ar

Marina CMI [18]

Answer:

a. (2 - x, -4 - 1/2y)

Step-by-step explanation:

$\text{Let the coordinates of other endpoint be (a,b)}\\\implies \frac{a+x+4}{2}=3 \:\text{and}\\\frac{b+\frac{y}{2}}{2}=-2\\$

Simplify to get the answer.

4 0

3 years ago

Read 2 more answers

What is the equation of the sinusoid shown in the graph?

ololo11 [35]

Answer:

Answer: C

Step-by-step explanation:

The Cosine Function

The graph of a cosine function is a sinusoid that starts at its maximum value of 1 at x=0 and takes x=2π radians to complete a full cycle. The function of the parent cosine function is:

$y=\cos x$