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e-lub [12.9K]
3 years ago
6

What is the value of x

Mathematics
1 answer:
olchik [2.2K]3 years ago
4 0
The two angles shown form a linear pair.
The angles are supplementary, which means their measures add to 180 deg.
Now we can write an equation and solve for x.

5x + 120 = 180

5x = 60

x = 12

Answer: x = 12
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Ivanshal [37]
Of the question or answer
6 0
3 years ago
Read 2 more answers
How to get the minimum and maximum temperature​
sukhopar [10]

Put them in order from lowest to highest. Identify the lowest number in the data set, as well as the highest number. Subtract the lowest number in the set from the highest number. The resulting value is the range of the set of temperature values.

6 0
3 years ago
A (0, 2) and B (6,6) are points on the straight line ABCD.
elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points (x_1,y_1) and (x_2,y_2), the distance is denoted by: \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. Let's find the distance between A and B:

d = \sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = \sqrt{(6-a)^2+(6-b)^2}

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0
3 years ago
Read 2 more answers
Find the coordinates of the point 7/10 of the way from A to B
OverLord2011 [107]

Answer:

  (6.8, 1.3)

Step-by-step explanation:

<u>Given</u>:

  A(-3, -5), B(11, 4)

<u>Find</u>:

  P such that AP/AB = 7/10

<u>Solution</u>:

Using the desired relation, we have ...

  (P -A)/(B -A) = 7/10

  10(P -A) = 7(B -A) . . . . . multiply by 10(B-A)

  10P = 7B +3A . . . . . . . . add 10A to both sides

  10P = 7(11, 4) +3(-3, -5) = (77 -9, 28 -15) = (68, 13)

  P = (68, 13)/10 = (6.8, 1.3)

The point 7/10 of the way from A to B is (6.8, 1.3).

7 0
3 years ago
3^x+2=8^x-1 Solve for x.
zubka84 [21]

I assume the equation is supposed to be

3^{x+2}=8^{x-1}

Then we can write

9\cdot3^x=\dfrac18\cdot8^x\implies\left(\dfrac38\right)^x=\dfrac1{72}

Take the logarithm of base 3/8 on both sides:

\log_{3/8}\left(\dfrac38\right)^x=\log_{3/8}\dfrac1{72}

\implies x\log_{3/8}\dfrac38=-\log_{3/8}72

\implies x=-\log_{3/8}72

- - -

If the equation is actually 3^x+2=8^x-1, I'm afraid it cannot be solved exactly.

5 0
3 years ago
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