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3 years ago

How is a corollary related to a theorem.

1 answer:

6 0

A statement that follows with little or no proof required from an already proven statement. For example, it is a theorem<span> in geometry that the angles opposite two congruent sides of a triangle are also congruent. A </span>corollary<span> to that statement is that an equilateral triangle is also equiangular</span>

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What is one of the solutions to the following system of equations?

Amanda [17]

Answer:

(8,-1)

Step-by-step explanation:

Given : $x^{2} +y^{2} =65$

$x+y=7$

To Find: solution of given system of equations.

Solution:

Equation a : $x^{2} +y^{2} =65$

Equation b : $x+y=7$

Substitute the value of y from equation b in equation a

y from equation b : y = 7-x

Now substitute value of y in equation a

Thus equation a becomes:

$x^{2} +(7-x)^{2} =65$

$x^{2} +49+x^{2}-14x =65$

$2x^{2} -14x =65-49$

$x^{2} -7x -8=0$

$x^{2} -8x+x -8=0$

$x(x-8)+1(x-8)=0$

$(x+1)(x-8)=0$

⇒ x= -1 and x = 8

Now substitute values of x in equation b to obtains values of y

⇒ $x+y=7$

for x = -1

⇒ $-1+y=7$

⇒ $y=7+1$

⇒ $y=8$

Thus (x,y)=(-1,8)

For x =8

⇒ $8+y=7$

⇒ $y=7-8$

⇒ $y=-1$

Thus (x,y)=(8,-1)

Hence Option A is the correct solution .

6 0

4 years ago

Read 2 more answers

In the diagram below, PQ is parallel to MN . If MP=25, PQ=18, and MN=33, find the length of PO . Figures are not necessarily dra

Ray Of Light [21]

Given that triangles MON and POQ are similar triangles, the length of PO is 30 units.

<h3>What are Similar Triangles?</h3>

The triangles that are similar to each other will have their corresponding sides proportional to each other.

Given:

MP = 25

PQ = 18

MN = 33

Triangles MON and POQ are similar triangles.

Let PO = x

Therefore:

MN/PQ = MO/PO

Substitute

33/18 = (25 + x)/x

Cross multiply

33x = 18(25 + x)

33x = 450 + 18x

33x - 18x = 450

15x = 450

x = 30

Therefore, given that triangles MON and POQ are similar triangles, the length of PO is 30 units.

Learn more about similar triangles on:

brainly.com/question/21874653

8 0

2 years ago

Marco is 6 feet 3 inches tall. There are 2.54 centimeters in 1 inch. What is Marcos height in centimeters?

Anton [14]

190.5 centimeters tall.

8 0

4 years ago

Read 2 more answers

In the solution of the equation 5 + 3x = -2x + 9, 2x is added to the equation first. Which of the following should be done next?

puteri [66]

You should subtract 5 from both sides next.

Adding 2x to both side will give you the following.

5 + 5x = 9

And since you got all the variable terms to the left, you want all the constant terms to the right. You do that by subtracting 5 from both sides. This gives you the below statement.

5x = 4

You can then divide to solve.

x = 4/5 or .8

5 0

3 years ago

1. There are<br> always twice as many girls as boys in school.<br> Mathematical expression

Airida [17]

Answer:

Boys x 2 = Girls

Step-by-step explanation:

If there are twice as many girls in school as boys than take the number of boys and multiply that by 2. For example if there are 400 boys in school and there are twice as many girs your equation would, 400 x 2 = 800 girls.

8 0

3 years ago

Read 2 more answers