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lianna [129]
3 years ago
5

A 6-inch-by-10-inch rectangle is cut down to a 5-inch-by-8-inch rectangle. What is the percent of decrease in the area? Express

your answer as a mixed number percent.
Mathematics
1 answer:
Serjik [45]3 years ago
6 0

Answer:

  33 1/3% decrease

Step-by-step explanation:

The original area is (6in)(10in) = 60 in². The reduced area is (5in)(8in) = 40 in². Then the change in area is ...

  ((new value)/(old value) -1) × 100%

  (40/60 -1)×100% = -1/3×100% = -33 1/3%

The area decreased by 33 1/3%.

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Since -5i is a zero, then its complex conjugate +5i is also a zero of the function.

Therefore,

x + 5i, x - 5i , and x - 3 are factors of the polynomial.

Hence, the polynomial function, P(x), of the lowest degree with rational coefficients​ is given by

P(x)=(x+5i)(x-5i)(x-3)

Which implies that

\begin{gathered} P(x)=(x^2-(5i)^2)(x-3)=(x^2-25i^2)(x-3) \\ \text{ Since i}^2=-1,\text{ then we have} \\ P(x)=(x-3)((x^2+25)=x^3+25x-3x^2-75 \end{gathered}

Hence the polynomial is

P(x)=x^3-3x^2+25x-75

5 0
1 year ago
What is the rate of change for a linear function that passes through the points (8, -10) and (-6, 14)
Anna71 [15]

Answer: m=-1.714

Step-by-step explanation:

By definition, the slope of the line is described as "Rate of change".

You need to use the following formula to calcualte the slope of the line;

m=\frac{y_2-y_1}{x_2-x_1}

In this case you know that the line passes through these two points: (8, -10) and (-6, 14).

Then, you can say that:

y_2=-10\\y_1=14\\\\x_2=8\\x_1=-6

Knowing these values, you can substitute them into the formula for calculate the slope of a line:

 m=\frac{-10-14}{8-(-6)}

Finally, you must evaluate in order to find the slope of this line. You get that this is:

m=\frac{-24}{8+6}\\\\m=\frac{-24}{14}\\\\m=-\frac{12}{7}\\\\m=-1.714

8 0
3 years ago
What is 52/100 in a decimal form
Pie

Answer:

0.52

Step-by-step explanation:

The hundredths position is the second spot to the right of the decimal point, so 52/100 can be written as 0.52.

3 0
3 years ago
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kondaur [170]

Answer:

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Step-by-step explanation:

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3 years ago
How to find intersection from -8x+3y=11 and y=3x+4
mash [69]

Answer:

(-1,1)

Step-by-step explanation:

To find where both lines intersect, solve for x and y with substitution.

Equation 1.

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3 years ago
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