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Alenkinab [10]
4 years ago
14

Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear

Mathematics
1 answer:
AlladinOne [14]4 years ago
8 0

Answer:

x=\frac{83}{50}

Step-by-step explanation:

we know that

If the three points are collinear

then

m_A_B=m_A_C

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

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

step 1

Find the slope AB

we have

A(1,\frac{2}{3}),B(x,-\frac{4}{5})

substitute in the formula

m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}

m_A_B=\frac{\frac{-12-10}{15}}{x-1}

m_A_B=-\frac{22}{15(x-1)}

step 2

Find the slope AC

we have

A(1,\frac{2}{3}),C(-\frac{1}{2},4)

substitute in the formula

m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}

m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}

m_A_C=-\frac{20}{9}

step 3

Equate the slopes

m_A_B=m_A_C

-\frac{22}{15(x-1)}=-\frac{20}{9}

solve for x

15(x-1)20=22(9)

300x-300=198

300x=198+300

300x=498

x=\frac{498}{300}

simplify

x=\frac{83}{50}

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Oxana [17]

Answer:

B.x>4is a required interval.

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3 years ago
If a cone with a diameter of 10 m has a surface area of 190.6m2, find its slant height. Round to the nearest tenth.
alukav5142 [94]

Answer:  The slant height of the cone is 65.6 m

Step-by-step explanation:

Given: The diameter of a cone = 10 m

Surface area of cone = 190.6 m²

To find: Slant height

Diameter of cone = 10 m

Therefore Radius of cone = \dfrac{\text {Diameter }}{2} = \dfrac{10}{2} =5m

As we know that surface area of a cone is given by

S.A. = \pi r(l+r)

Where S.A. is surface area , r is the radius of cone and l is the slant height of the cone.

Let Slant height = l

So we have

190.6 = \dfrac{22}{7} \times 5 ( 5+l)\\\\\Rightarrow  5+l= \dfrac{190.6 \times 7}{22}\\\\\Rightarrow l=  \dfrac{1334.2}{22}+5\approx 60.64+5 = 65.64\approx65.6

Hence the slant height of the cone is 65.6 m

5 0
3 years ago
Dora goes to a store and buys a phone originally priced at $45. The store is running a discount of 18%. What is the price of the
Alenkinab [10]

Answer: 8.1 $

Step-by-step explanation: 18 percent of 45 is 8.1 ez math hope this helps.

3 0
3 years ago
Can someone help me with factoring by grouping please show step by step
ValentinkaMS [17]
Answer is 3-110x

3 times 1 squared - 11 times 10
1 raised to any power equals 1

calculate the product
3 times 1 -110x

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3-110x

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4 0
3 years ago
A, B and C did a test, A got 3/5 of
Fiesta28 [93]
<h3>Answer:</h3>

C, B, A

<h3>Explanation:</h3>

Simply change all the numbers to decimals

  • A is .6
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After you put them in order from greatest to least. And the anwser is .625, .62, .6. Which is C, B, A.

4 0
3 years ago
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