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elena-s [515]
3 years ago
7

Kate has a rectangular garden that is 8 feet long by 3 feet wide. She wishes to extend the length and width by the same amount i

n order to increase the the area of garden to 104 feet squared. How many feet will she need to add to each side?
Mathematics
1 answer:
elena55 [62]3 years ago
4 0
<span>Let the extension of the length and width be x.
 The new dimensions are: Length = 8+x
  Width =3+x
 Area = 104 ft squared
 Area of a rectangle = Length x Width
 Therefore,
(8+x)(3+x) = 104
 x^2 +11x +24=104
 x^2 +11x +24-104=0
 x^2 +11x-80=0

 Factorize using splitting the middle term method. X^2 +16x-5x-80=0 x(x+16)-5(x+16)=0 (x-5)(x+16)=0 either x-5 = 0 or x+16=0 x=5 or x=-16 length and width measure cannot be negative. Therefore, the extension of the length and width is 5 feet each.</span>
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Question 3 "Try Again." Mary needs 3 feet of boondoggle for a craft project.
kati45 [8]

Answer:

$9.00

Step-by-step explanation:

We can use conversion factors to solve this equation. The multiplication sequence that I got is shown below:

\frac{3ft}{1} × \frac{12 in}{1ft} × \frac{0.25}{1in}

Our feet and inches cancel out and we get the final expression \frac{3*12*0.25}{1}, which is equal to 9, or $9.00.

Hopefully that was helpful! :)

7 0
3 years ago
Previous
worty [1.4K]

No change in area

Step-by-step explanation:

The area is 60 square feet for both rectangles.

4 0
3 years ago
Use the graph to answer the question. Find the slope
Liula [17]
We can take the two points given and plug them into the slope formula.

\sf~m=\dfrac{y_2-y_1}{x_2-x_1}

(-3, 3), (1, -5)
x1  y1  x2 y2

\sf~m=\dfrac{-5-3}{1-(-3)}

Subtract:

\sf~m=\dfrac{-8}{4}

Divide:

\sf~m=-2
8 0
3 years ago
Female athletes at the University of Colorado, Boulder, have a long-term graduation rate of 67% (Source: Chronicle of Higher Edu
VLD [36.1K]

Answer:

Yes, we can assume that the percent of female athletes graduating from the University of Colorado is less than 67%.

Step-by-step explanation:

We need to find p-value first:

z statistic = (p⁻ - p0) / √[p0 x (1 - p0) / n]

p⁻ = X / n = 21 / 38 = 0.5526316

the alternate hypothesis states that p-value must be under the normal curve, i.e. the percent of female athletes graduating remains at 67% 

H1: p < 0.67 

z = (0.5526316 - 0.67) / √[0.67 x (1 - 0.67) / 38] = -0.1173684 / 0.076278575

z = -1.538681 

using a p-value calculator for  z = -1.538681, confidence level of 5%

p-value = .062024, not significant

Since p-value is not significant, we must reject the alternate hypothesis and retain the null hypothesis.

3 0
3 years ago
The answer to this question
Sophie [7]

The answer to this question is D) 13.9 in.

Try using the Pythagorean theorem when solving to get the hypotenuse or other angles for a right triangle.

4 0
3 years ago
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