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1 year ago

For which value of k are the points (0 -5) (6 k) and (-4 -13) collinear?

Mathematics

1 answer:

Sophie [7]1 year ago

6 0

Answer:

Step-by-step explanation:

Use the 2 points for which you have both an x and y coordinate to write the equation of the line containing those 2 points. When you get the equation, sub in the x value of 6 and solve for y.

Begin by finding the slope of the line:

$m=\frac{-13-(-5)}{-4-0}=\frac{-13+5}{-4}=\frac{-8}{-4}=2$

Then use one of the points in point slope form to write the equation in slope-intercept form. I used (0, -5). But either point you choose will give you the exact same line...promise.

y - (-5) = 2(x - 0) and

y + 5 = 2x and

y = 2x - 5

Now sub in the x value of 6 for x and solve for y:

y = 2(6) - 5 and

y = 12 - 5 so

y = 7

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Ria can paint a room in 4 hours. Destiny can paint the same room in 6 hours. How long would it take Ria and Destiny to paint the

Lerok [7]

Time taken by Ria to paint a room = 4 hours

Time taken by Destiny to paint a room = 6 hours

If they work together, they complete 1 job. So,

$\frac{1x}{4}+\frac{1x}{6}=1$

The LCD of 4 and 6 is 12

$\frac{3x+2x}{12}=1$

$\frac{5x}{12}=1$

$5x=12$

$x=\frac{12}{5}$

Hence, both of them can paint the room in $\frac{12}{5}$ hours or 2.4 hours.

4 0

2 years ago

Read 2 more answers

The following numerically ordered sequence of numbers has a mean of 17 and a median of 18.

erastovalidia [21]

Answer:

a = 9

b = 19

Step-by-step explanation:

DO B FIRST

The mean is the average of all the terms (numbers) in the sequence

To find the average you find the sum of the terms and divided the sum by the number of terms there are.

The mean times the number of terms equals the sum of all the terms subtract the terms that you know from the sum to get A

a = 17(10)-7-12-15-17-19-20-22-24-25

a = 170-161

a = 9

The median is found by taking the average of the two middle terms

Our middle terms are 17 and B

the median times 2 equals the sum of the two terms and then subtract the term you know from the sum

b = 18(2)-17

b = 36-17

b = 19

5 0

2 years ago

Read 2 more answers

Ms. Hamby gave a quiz. Two students’ work and the answer key are shown. Ms. Hamby accepts equivalent answers in any form.

Luden [163]

Answer:

Student A and Student B both answered 2 questions correctly.

See explanation below

Step-by-step explanation:

Note: that answers in the form:

$\frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$

ARE ALL EQUIVALENT.

First of all, 4/5 is equivalent to 0.8 if we do long division.

and 19/20 is 0.95 if we do long division.

Now, Student A:

Both of the fractions are correct and the negative sign is equivalent and makes the answer correct, so both are correct.

For Student B:

Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.

Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.

Hence,

Student A and Student B both answered 2 questions correctly.

5 0

1 year ago

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x? StartFraction 2 Over 11 EndFraction plus-or-minus

slamgirl [31]

Answer:

$x=\frac{2}{11}\pm\frac{\sqrt{15}} {11}$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$11x^{2} -4x=1$

equate to zero

$11x^{2} -4x-1=0$

$a=11\\b=-4\\c=-1$

substitute in the formula

$x=\frac{-(-4)\pm\sqrt{-4^{2}-4(11)(-1)}} {2(11)}$

$x=\frac{4\pm\sqrt{60}} {22}$

$x=\frac{4\pm2\sqrt{15}} {22}$

$x=\frac{2\pm\sqrt{15}} {11}$

$x=\frac{2}{11}\pm\frac{\sqrt{15}} {11}$

therefore

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction

7 0

1 year ago

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Convert to the nearest tenth. gal. = 319 qt.

lisov135 [29]

The answer is 79.75 converted to 80.0
Hope this helps!!

5 0

1 year ago