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3 years ago

The rectangle below has an area of x^2-25 square meters and a length of x+5.

Mathematics

1 answer:

Archy [21]3 years ago

7 0

Answer:

(x-5)

Step-by-step explanation:

factor the equation and the sign is x-5 because the equation has to be negative at the 25.

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What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)?

olga2289 [7]

Step $1$

Find the slope of the given line

Let

$A(-3,2)\ B(2,-1)$

slope mAB is equal to

$mAB=\frac{(y2-y1)}{(x2-x1)} \\ \\ mAB=\frac{(-1-2)}{(2+3)} \\ \\ mAB=-\frac{3}{5}$

Step $2$

Find the slope of the line that is perpendicular to the given line

Let

CD ------> the line that is perpendicular to the given line

we know that

If two lines are perpendicular, then the product of their slopes is equal to $-1$

$mAB*mCD=-1\\ mAB=-\frac{3}{5} \\ mCD=-\frac{1}{mAB} \\ mCD=\frac{5}{3}$

Step $3$

Find the equation of the line with mCD and the point (3,0)

we know that

the equation of the line in the form point-slope is equal to

$y-y1=m(x-x1)\\\\ y-0=\frac{5}{3} *(x-3)\\\\ y=\frac{5}{3} x-5$

Multiply by $3$ both sides

$3y=5x-15$

$5x-3y=15$

therefore

the answer is

the equation of the line that is perpendicular to the given line is the equation $5x-3y=15$

4 0

2 years ago

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The circumference of a circle

Dmitry_Shevchenko [17]

Use the formula C = pi * d

8 0

3 years ago

A triangular prism and its dimensions are shown in the diagram. What is the lateral surface area of this triangular prism in squ

storchak [24]

Answer: G

Step-by-step explanation:

It said it was correct when I turned it in

3 0

3 years ago

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Multiply: 4(−5 2/3) Enter your answer as a fraction in simplest form, like this: 42/53

8_murik_8 [283]

Answer:

The amount that came is $\frac{-68}{3}$

Step-by-step explanation:

The computation is shown below:

According to the question, it is mentioned that

Multiply 4 by $-5\frac{2}{3}$

First open the equation in a fraction it would be $\frac{-17}{3}$

Now multiplied the above fraction by a 4

That gives the result of $\frac{-68}{3}$

Hence, the amount that came is $\frac{-68}{3}$

We simply multiply the 4 with the given fraction

Thus the above represents the simplest form of the fraction

5 0

2 years ago

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

saveliy_v [14]

Answer: Choice B

12.5 < x < 18.9

================================================

Explanation:

We have a triangle with these side lengths:

a = 10
b = 16
c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need $b^2 < a^2+c^2$ to be true in order for an acute triangle to happen.

So,

$b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5$

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

$c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\$

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

Put together, they form the approximate answer of 12.5 < x < 18.9

6 0

2 years ago