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Bad White [126]
3 years ago
11

Points A, B, C, and D are collinear and positioned in that order. Find the length indicated 7) Find BC if BC = 2x + 4, AD = 28,

CD = 3x - 2, and AB = 3x + 2. 8) Find BD if BD = -7 + 3x, AB = 2x - 14, AC = 2x - 3, and CD = 9.
Mathematics
1 answer:
belka [17]3 years ago
7 0

Answer:

  7)  BC = 10

  8)  BD = 20

Step-by-step explanation:

7) The segment addition theorem tells you ...

  AB +BC +CD = AD

  (3x+2) +(2x+4) +(3x-2) = 28

  8x +4 = 28 . . . . collect terms

  8x = 24 . . . . . . . subtract 4

  x = 3 . . . . . . . . . divide by 8

  BC = 2x+4 = 2(3) +4

  BC = 10

__

8) AB +BD = AC +CD

  (2x -14) +(-7 +3x) = (2x -3) +(9)

  5x -21 = 2x +6

  3x = 27

  x = 9

  BD = -7 +3x = -7 +3(9)

  BD = 20

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Write the equation of the line for the following table of values.
Luda [366]

Answer:

We conclude that the equation of the line is:

  • y = 5x + 1

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the data table

x      -3 -5 -7 -9 -11

y      -16 -26 -36 -46 -56

From the table taking two points

  • (-3, -16)
  • (-5, -26)

Determining the slope between (-3, -16) and (-5, -26)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-3,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-5,\:-26\right)

m=\frac{-26-\left(-16\right)}{-5-\left(-3\right)}

m=5

Thus, the slope of the line is:  m = 5

substituting m = 5 and (-3, -16) in the slope-intercept form of the line equation  to determine the y-intercept b

y = mx+b

-16 = 5(-3) + b

-16 = -15 + b

b = -16+15

b = 1

Thus, the y-intercept b = 1

now substituting m = 5 and b = 1 in the slope-intercept form of the line equation

y = mx+b

y = 5x + 1

Therefore, we conclude that the equation of the line is:

  • y = 5x + 1
5 0
3 years ago
Noah says to find 20% of a number he divides the number by 5. Is this true explain your answer
Nutka1998 [239]

Answer:

yes

Step-by-step explanation:

note that 20% = \frac{20}{100} = \frac{1}{5}

Hence to find 20% of a number, dividing the number by 5 is correct

20% of £30 = \frac{30}{5} = £6


5 0
3 years ago
Write the explicit<br> rule for the nth term.<br> Then find a71.<br> {O, -8, -16, -24 ...}
yulyashka [42]

Answer:

Step-by-step explanation:

{0, -8, -16, -24,...} here you add -8 each time so the rule is

a_{1} = 0, a_{n} = a_{n-1} -8

the 71 term is

a_{71} = 0 + (71 - 1) * (-8) = 70 * (-8) = -560

3 0
3 years ago
In an ore, 9.8% of its total weight is metal. How many pounds of metal are in 1,950 lb of ore?
Fudgin [204]

Answer

Find out the  how many pounds of metal are in 1,950 lb of ore .

To proof

let us assume that the pounds of metal are in 1,950 lb of ore be x .

As given

In an ore, 9.8% of its total weight is metal.

ore weight = 1,950 lb

9.8% is written in the decimal form

= \frac{9.8}{100}

= 0.098

Than the equation becomes

x = 0.098 × 1950

x = 191.1 pounds

Therefore the 191.1 pounds of metal are in 1,950 lb of ore .

Hence proved



5 0
3 years ago
Can you pls Help it’s math
kaheart [24]

Answer:

B

Step-by-step explanation:

the amount owed is greater than the cost

5 0
3 years ago
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