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TEA [102]
3 years ago
12

What is the value of x? Enter your answer in the box. x =

Mathematics
1 answer:
nikklg [1K]3 years ago
4 0

Answer:

x = 20

Step-by-step explanation:

To find the value of x, write a proportion between the two similar triangles.

A proportion is an equation of equal ratios.

\frac{11}{11+121}=\frac{10}{10+5x+10}  \\\\\frac{11}{132} = \frac{10}{5x + 20}

To solve cross multiply the numerator and denominator of each fraction.

11(5x+20) = 132(10)

55x + 220 = 1320

55x = 1,100

x = 20

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1. What is the solution of the system?
andreyandreev [35.5K]

Answer:

The given system of equations has solutions below:

1) The solution is (2,3)

2) The solution is (\frac{-8}{7}, \frac{5}{7})

3) The solution is infinitely many solutions

4) No solution

Step-by-step explanation:

Given system of equation are

-x+2y=4\hfill (1)

-4x+y=-5\hfill (2)

To solve equation by using elimination method

Multiply eqn (2) into 2

-8x+2y=-10\hfill (3)

Now subtracting (1) and (3)

-x+2y=4

-8x+2y=-10

_________________

7x=14

x=\frac{14}{7}

x=2

Substitute x=2 in equation (1)

-2+2y=4

2y=4+2

y=\frac{6}{2}

y=3

Therefore the solution is (2,3)

2) Given equation is

-2x+y=3\hfill (1)

4y-4=x

Rewritting as below

x-4y=-4\hfill (2)

To solve equation by using elimination method

multiply (2) into 2

2x-8y=-8\hfill (3)

Adding (1) and (3)

-2x+y=3

2x-8y=-8

________

-7y=-5

y=\frac{5}{7}

substitute y=\frac{5}{7} in (1)

-2x+\frac{5}{7}=3

-2x=3-\frac{5}{7}

-2x=\frac{21-5}{7}

x=-\frac{8}{7}

Therefore the solution is (\frac{-8}{7},\frac{5}{7})

3) Given equation is 6x+2y=10\hfill (1)

3x+y=5\hfill (2)

equation (1) can be written as

2(3x+y)=10

3x+y=\frac{10}{2}

3x+y=5

Therefore equations (1) and (2) are same therefore it has infinitely many solutions

4) Given equation is -x-2y=14\hfill (1)

-2x-4y=12\hfill (2)

multiply equation (1) into 2

-2x-4y=28\hfill (3)

To solve equation by using elimination method

subtracting (2) and (3)

-2x-4y=28

-2x-4y=12

_______

28\neq -12

therefore it has no solution

4 0
2 years ago
What is 100,572×135,689
shepuryov [24]

Answer:

13646514108

Step-by-step explanation:

Used calculator.

5 0
3 years ago
Read 2 more answers
line y = 2x+1 is transformed by a dialation with a scale factor of two and centered at (0,-4). what is the equation of the image
Gekata [30.6K]

Answer: y = 2x + 6

Step-by-step explanation:

Here the equation of line,

y = 2x + 1

y-intercept of the line is, (0, 1)

And, the slope of the line is 2.

Since, If a point (x,y) is dilated by a scale factor k about a point (a,b),

Then transformed point are get by,

(x,y)\rightarrow (k(x-a)+a, k(y-b)+b)

Thus, The transformed point of point (0,1) when dilation is occur by the scale factor 2 about the point (0,-4),

(0,-4)\rightarrow (2(0-0)+0, 2(1+4)-4)

(0,-4)\rightarrow (0, 6)

Thus, the point of the new line is (0,6)

And, the slope of the new line is 2 ( because in the dilation, the slope of the line does not change)

Thus, the equation of new line,

(y - 6) = 2 (x - 0)

y - 6 = 2x

y = 2x + 6


5 0
3 years ago
What is 23 inches in centimetres?
Anettt [7]

Answer: 58.42

Formula: Multiply the length value by 2.54

23×2.54 =58.42

12 Inches = 30.48 Centimetres

7 0
3 years ago
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Nezavi [6.7K]
(93+67+78+44+123)/5=405/5=81 pizzas per day on average

C is your answer.
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3 years ago
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