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kiruha [24]
3 years ago
9

Find an equation for the perpendicular bisector of the line segment whose endpoints are (5,-9) and (1,3).

Mathematics
1 answer:
____ [38]3 years ago
3 0

Given coordinates of the endpoints of a line segment  (5,-9) and (1,3).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between (5,-9) and (1,3) is :

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

m=\frac{3-\left(-9\right)}{1-5}

m=-3

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 1/3.

Now, we need to find the midpoint of the given coordinates.

\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)

=\left(\frac{1+5}{2},\:\frac{3-9}{2}\right)

=\left(3,\:-3\right)

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - (-3) = 1/3 (x - 3)

y +3 = 1/3 x - 1

Subtracting 3 from both sides, we get

y +3-3 = 1/3 x - 1 -3

<h3>y = 1/3 x - 4 .</h3>
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Please help me if you can. Please also write how you got the answer thank you.
babunello [35]

Answer:

Question 9: Variables: (smallest) s, q, r (largest)

Question 10: 5 whole numbers (7, 8, 9, 10, and 11)

Step-by-step explanation:

For question nine, there are two given statements... s=q-2 and q<r. Say we plug in 10000 (a really big #) in for q, then we would get s=9998 and r>10000. This way, we can see that s would be the smallest, then q, and r is the largest. <em>(q<r can be written as r>q)</em>

<em />

For question 10, it states \frac{1}{4}. This can be split into \frac{3}{x} and \frac{3}{x} . When x is 12 in the first equation then \frac{3}{12} = \frac{1}{4} and when x is 6 in the second equation \frac{3}{6} =0.5 (0.5 is also  \frac{1}{2}). Therefore, x must be a whole number less than 12 and greater than 6, and it cannot be either 12 or 6. Whole numbers between 6 and 12 are 7, 8, 9, 10, and 11  or  5 whole numbers.

4 0
3 years ago
Anyone know? <br> A. 99 <br> B. 100 <br> C. 121<br> D. Cannot be determined
Verizon [17]

Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.

By being congruent, the corresponding angles and sides are equal.

Therefore, \angle A = \angle F, \angle B = \angle G, \angle C = \angle H, \angle D= \angle I, \angle E = \angle J.

By using \angle A = \angle F

So, 100^\circ = \angle 1

Therefore, the measure of angle 1 is 100 degrees.

So, Option B is the correct answer.

6 0
3 years ago
The perimeter of the flag is 2080 ft what is the flags width and length of the length is 420 ft greater than the width
hram777 [196]

Answer:

The length of the flag is 730 ft and the width is 310 ft

Step-by-step explanation:

<u><em>The correct question is</em></u>

The perimeter of the flag is 2080 ft what is the flags width and length <u>if</u> the length is 420 ft greater than the width

Let

L ----> the length of the flag

W ---> the width of the flag

we know that

The perimeter of the flag (rectangle) is equal to

P=2(L+W)

we have

P=2,080\ ft

so

2,080=2(L+W)

1,040=L+W ----> equation A

L=W+420 ---> equation B

Solve the system by substitution

substitute equation B in equation A

1,040=(W+420)+W

solve for W

1,040=2W+420

2W=1,040-420

2W=620

W=310\ ft

<em>Find the value of L</em>

L=W+420 ----> L=310+420=730\ ft

therefore

The length of the flag is 730 ft and the width is 310 ft

5 0
3 years ago
A young boy has 40 total pets. He has two different types of pets. He has cats and penguins. The total number of the heads of hi
Nina [5.8K]

Answer:

He has 30 penguins and 10 cats.

Step-by-step explanation:

Let's define the variables:

C =  number of cats.

P = number of penguins.

We know that he has a total of 40 pets, then:

C + P = 40

We also know that the total heads (40 heads, each animal has one) plus the number of wings (P*2, each penguin has 2) is equal to the number of feet of his pets (4*C + 2*P, because each cat has 4 paws, and each penguin has 2)

Then we have the equation:

40 + 2*P = 4*C + 2*P

Notice that in the second equation we have the term 2*P in both sides of the equation, then we can just subtract 2*P in both sides to get:

(40 + 2*P) - 2*P = 4*C + 2*P - 2*P

40 = 4*C

Now with this, we can find the value of C.

40/4 = C = 10

Then he has 10 cats.

Now we can replace this in the equation:

P + C = 40

to find the value of P

P + 10 = 40

P = 40 - 10 = 30

P = 30

He has 30 penguins.

3 0
3 years ago
F(x) = 741
Marysya12 [62]

I think its option D

3 0
3 years ago
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