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Elena-2011 [213]
3 years ago
5

If angle A B C is congruent to angle C B D, find x.

Mathematics
1 answer:
Svetlanka [38]3 years ago
6 0
4 x + 30 = 5x + 20
-5x           -5x

-x + 30 = 20
     -30     -30

- x = -10

x = 10
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(7•7•7•7•7)•6•6•6•6•6•6. Write your answer using a exponent.
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Step-by-step

In the exponent we write how many times the number is repeated.

7^{5} x 6^{6}

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A model boat is marked down 15% off the original price of $50. What is the sale price of the
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Answer: $42.5

Step-by-step explanation: So first they take off 15% of of $50 so that means they took $7.5. And now its asking for the price of it after so $7.5-$50= $42.5.

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What is the ratio of the sector area to the area of the entire circle?
inna [77]

Answer:

One fourth

Step-by-step explanation:

\frac{area \: of \: sector}{area \: of \: circle}  =  \frac{ \frac{ 90 \degree}{360 \degree  } \times \pi {r}^{2}}{ \pi {r}^{2}}  \\  =  \frac{ \frac{1}{4}  \times 1}{1}  \\  =  \frac{1}{4}  \\  = 1 : 4

4 0
2 years ago
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Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her
Art [367]

For this case we have the following equation:


y + 1 = 2 (x - 3)

That can be rewritten in the form y = mx + b

Where:


  • m is the slope of the line
  • b is the cut point

So, we have:


y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7

Where:


m = 2 is the slope


b = -7 is the cut point


Carlota has the following points:


(-1, 3) and (2, 9)


To know if the line y = 2x-7 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:


Point (-1, 3):


Substituting:


3 = 2 (-1) -7\\3 = -2-7

3 = -9 It's false, equality is not met. The point (-1, 3) does not go through the line.


The equation written by Carlota is erroneous, the procedure to follow is:


Given(x1, y1) = (- 1, 3) and(x2, y2) = (2, 9), we find the slope:


m=\frac{(y2-y1)}{(x2-x1)}

m=\frac{(9-3)}{(2-(-1))}

m=\frac{6}{3}

m=2

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:


y = 2x + b

Substituting (2,9) we have:


9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is y = 2x + 5

Answer:


The correct equation of the line that passes through the given points is y = 2x + 5

Carlota's mistake was at the cutoff point


5 0
3 years ago
What is the inequality
Korvikt [17]
Problem: Square root of x<12


To solve that, we square both size, x<144

Choices that is less than 144 are the correct answers
5 0
3 years ago
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