If AB=x+4, BC=2x-10, and AC =2x+1, then find the value for x, AB, BC and AC

Answers

Answer 1
Answer:

If A, B and C are collinear, then:

AB+BC=AC\n\nAB=x+4,\ BC=2x-10,\ AC=2x+1

substitute:

(x+4)+(2x-10)=2x+1\n\n(x+2x)+(4-10)=2x+1\n\n3x-6=2x+1\ \ \ |+6\n\n3x=2x+7\ \ \ \ |-2x\n\nx=7\n\nAB=x+4\to AB=7+4=11\n\nBC=2x-10\to BC=2(7)-10=14-10=4\n\nAC=AB+BC\to AC=11+4=15


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A tailor used 2 meters of string to make 10 Halloween masks. He used _ of a meter for each mask.

Answers

Answer: He used (1)/(5) of a meter for each mask.

Step-by-step explanation:

Given : A tailor used 2 meters of string to make 10 Halloween masks.

Here, Total length of string = 2 meters

Number of masks = 10

The the part of a meter of string is used for each Halloween mask will be :-

(2)/(10)=(1)/(5) \text{ meter}  [Divide total length of string by number of masks]

Hence, he used (1)/(5) of a meter for each mask.

one fifth of a meter for each mask
2/10=1/5

The measure of the central angle of a sector of a circle is 90°. The arc length of the sector is 2pi cm. What is the radius of the circle in centimeters?

Answers

Answer:

Step-by-step explanation:

2πr/4=2π

r/4=1

r=4 cm

Simplify the expression x^2+x-2/8x^2+4x/3x^2+10x+8

Answers

Answer:

Step-by-step explanation:

x² + x  - 2 = x² - x +2x -2 = x(x - 1) + 2*(x-1)  = (x-1)(x+2)

8x² + 4x = 4x ( 2x + 1)

3x² + 10x + 8 = 3x² + 6x + 4x + 4*2  =3x  * (x + 2) + 4 * ( x + 2) = (x + 2)(3x + 4)

If the sides of two similar triangles are in the ratio of 3:5, find the ratio of their areas.

Answers

Ratio of areas of similar triangles is 9 : 25.

Solution:

Given data:

Ratio of sides of two similar triangles = 3 : 5

To find the ratio of areas of the triangles:

We know that,

In two triangles are similar, then the ratio of their area is equal to the square of the ratio of their sides.

$\text{Ratio of areas} = \frac{\text{Area of triangle 1}}{\text{Area of triangle 2} }

                      $=\left((3)/(5)\right) ^2

                      $=(9)/(25)

Ratio of areas of similar triangles is 9 : 25.

Answer:

16

:

81

Explanation:

Scale factor for the sides of these triangles.

k

=

4

9

.

Therefore the ratio of area will be:

k

2

=

Area Triangle A

Area triangle B

k

2

=

(

4

9

)

2

=

16

81

How many quarts can be held in 19 gallons

Answers

There are 4 quarts in one gallon:

1 gal = 4 qt

Then, we want to find the number of quarts in 19 gallons. We can write a proportion:

1/4 = 19/x

Cross multiply:

x = 76 quarts.

There are 76 quarts in 19 gallons.

76 quarts in 19 gallons

the number of children in 1st grade has 3 digits the digits in the number are 2 3 and 8 the digits it means 80 in this number write a number that could be the number of children in 1st grade

Answers

I hope this is what you mean, it could be 238, 328, 823, 283, 832, and many more. 

Answer:

I hope this is what you mean, it could be 238, 328, 823, 283, 832, and many more.

Step-by-step explanation: