MATHEMATICS MIDDLE SCHOOL

A, B and C are collinear and B is between A and C. The ratio of AB to AC is 1:3. If A is at (2,-6) and B is at (3,-1) what are the coordinates of point C

Answers

Answer 1

Answer:

Answer:

The coordinate of C is (5,9)

Step-by-step explanation:

A, B and C are collinear and B is between A and C.

The ratio of AB to AC is 1:3

If A is at (2,-6) and B is at (3,-1)

AB:AC = 1:3

B is between A and C

AB:(AB+BC) = 1:(1+2)

Therefore, AB:BC = 1:2

Let the point C (a,b)

Using section formula:

$x\rightarrow (mx_2+nx_1)/(m+n)$

$y\rightarrow (my_2+ny_1)/(m+n)$

where,

$m\rightarrow 1$

$n\rightarrow 2$

$x_1m\rightarrow 2$

$y_1\rightarrow -6$

$x\rightarrow 3$

$y\rightarrow -1$

Substitute into formula and solve coordinate point C

$3=(1\cdot a+2\cdot 2)/(1+2)$

$3=(a+4)/(3)$

$a=5$

$-1=(1\cdot b-6\cdot 2)/(1+2)$

$-1=(b-12)/(3)$

$b=9$

Hence, The coordinate of C is (5,9)

Answer 2

Answer:

Answer:

(5, 9)

Step-by-step explanation:

The distance between A and B is 1/3 the distance between A and C.

x coordinates:

3 − 2 = 1/3 (x − 2)

1 = 1/3 (x − 2)

3 = x − 2

x = 5

y coordinates:

-1 − (-6) = 1/3 (y − (-6))

5 = 1/3 (y + 6)

15 = y + 6

y = 9

The coordinates of point C are (5, 9).

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Eli's office recycled a total of 12 kilograms of paper over 6 weeks. After 9 weeks, how many kilograms of paper will Eli's office have recycled

Answers

18 kg

12kgs ÷ 6 weeks = 2kgs a week

2kgs × 9 weeks = 18kgs

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What’s the square root of 50?

Answers

Simplify √50.

Factor out 50.

√50 = √(5 x 5 x 2)

Note that there are 2 5's inside the parenthesis. Two of the same number when multiplied would become a whole number:

√(5 x 5) = 5

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5√2 is your answer

The square root of a number is always going to be done like this. If 50 isn't a square root, what are the square root numbers multiplied by something else to make 50

25 is a square root because of 5 times 5 is 25

√25 x 2 = 50

Next carry out the 5 outside the square root and you would get

5√2 = √50

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Which Two Numbers Add Up To Negative 26 And Multiply To 11?

Answers

xy=11
x+y=-26

x+y=-26
minus x both sides
y=-26-x

sub for y
x(-26-x)=11
-26x-x^2=11
add 26x+x^2 both sides
x^2+26x+11=0

ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

a=1
b=26
c=11

x= $\frac{-26+/-\sqrt{26^(2)-4(1)(11)} }{2(1)}$
x= $(-26+/-√(676-44) )/(2)$
x= $(-26+/-√(632) )/(2)$
x= $(-26+/-2√(158) )/(2)$
x= $-13+/-√(158)$

x= $-13+√(158)$ or $-13-√(158)$

aprox

x=-0.420195 or -25.5698

those are the numbers

Scout wants to jog a total distance of 2 miles so far he has jogged 7545 feet how much farther must he jogged to reach his goal of 2 miles

Answers

Answer:

Step-by-step explanation:

2 miles is 10560 feet

10560-7545=3015

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Convert 15000 ounces to tons

Answers

Answer:

The answer is 0.42525 TONS (METRIC)

Identify each as an expression or an equation y-5=2

Answers

It would be an equation.
In an EQUAtion, it looks like it has the word equal.
In an expression, the problem does NOT have an equal sign.
Hope this helps.

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