A, b, and c are collinear, and B is between a and c. The ratio of AB to AC is 1:2. If A is at (7,-1) and B is at (2,1) what are the coordinates of point C

Answers

Answer 1

Answer:

C(-3,3)

Step-by-step explanation:

Given

A = (7,-1)

B = (2,1)

AB:AC = 1:2

Required

Determine the coordinates of C

Since, B is between A and C; we need to determine ratio BC as follows;

[tex]AB:AC = 1:2[/tex]

Convert to division

[tex]\frac{AB}{AC} = \frac{1}{2}[/tex]

AC = AB + BC;

[tex]\frac{AB}{AB + BC} = \frac{1}{2}[/tex]

Cross Multiply

[tex]2 * AB = 1 * (AB + BC)[/tex]

[tex]2 AB = AB + BC[/tex]

[tex]2AB - AB = BC[/tex]

[tex]AB = BC[/tex]

Divide both sides by BC

[tex]\frac{AB}{BC} = 1[/tex]

Rewrite as

[tex]\frac{AB}{BC} = \frac{1}{1}[/tex]

Write as ratio

[tex]AB:BC = 1:1[/tex]

Next is to determine the coordinates of C as follows;

Because B is between both points. we have:

[tex]B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where

[tex]m:n = AB:BC = 1:1[/tex]

[tex]B(x,y) = B(2,1)[/tex]

[tex]A(x_1,y_1) = A(7,-1)[/tex]

So; we're solving for x2 and y2

[tex]B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where

Solving for x2;

[tex]x = \frac{mx_2 + nx_1}{m+n}[/tex]

[tex]2 = \frac{1 * x_2 + 1 * 7}{1+1}[/tex]

[tex]2 = \frac{x_2 + 7}{2}[/tex]

Cross Multiply

[tex]2 * 2 = x_2 + 7[/tex]

[tex]4 = x_2 + 7[/tex]

[tex]x_2 = 4 - 7[/tex]

[tex]x_2 = -3[/tex]

Solving for y2;

[tex]y = \frac{my_2 + ny_1}{m+n}[/tex]

[tex]1 = \frac{1 * y_2 + 1 * -1}{1+1}[/tex]

[tex]1 = \frac{y_2- 1}{2}[/tex]

Cross Multiply

[tex]2 * 1 = y_2 - 1[/tex]

[tex]2 = y_2 - 1[/tex]

[tex]y_2 = 2 + 1[/tex]

[tex]y_2 = 3[/tex]

Hence, the coordinates of C are: C(-3,3)


Related Questions

√45 rounded to the nearest 0.05 ????​

Answers

Answer:

6.7082039325......tbc

HELLPPPP PLEASE QUICKK ASAP

Answers

Answer:

9

Step-by-step explanation:

The reason why it is 9 is because if you look to the bigger triangle, you can see that 15 is 3/4 the size of 20, so once you find what number is 3/4 of 12, you have the answer, 9! Hope this helps!

What is -4(x+6) can someone pls help

Answers

Answer:

-4x - 24

Step-by-step explanation:

distribute the -4 by multiplying it by what is in the parenthisis. Since it is negative that makes a -4x and a -24

Hey there!

ANSWER: [tex]-4x-24[/tex]EXPLANATION:

[tex]-4(x+6)[/tex]

Let's separate -4 and x+6 with parenthesis.

[tex](-4)(x+6)[/tex]

Now let's separate all with parenthesis.

[tex](-4)(x)+(-4)(6)=-4x-24\\-4x-24(ANSWER)[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

I need help it says what could I change in this polynomial to make them like terms.
[tex] {2x}^{2} + 5x - 6y + 2y - 7[/tex]

Answers

Answer:

2x² + 5x - 4y - 7

Step-by-step explanation:

combine the like terms -6y and 2y

2x² + 5x - 6y + 2y - 7

2x² + 5x - 4y - 7

What is
the circumference of a circle with radius 3.5cm. Take [Pi=22/7]​

Answers

Answer:

22cm

Step-by-step explanation:

Circumference of a circle = 2πr

π = 22/7

r = 3.5

Circumference of a circle = 2 × (22/7) × 3.5

Circumference of a circle = 22cm.

Steven reads 6 books each month as part of his book club. If Steven has read 18 books so far, how many months has he been with his book club?

Answers

Answer:

3

Step-by-step explanation:

18/6 is 3

4 x ((-4)= (-2) - (-3) + (-6))

Answers

Answer:

x=5/16

Step-by-step explanation:

Let's solve your equation step-by-step.

4x(−4)=−2−(−3)−6

Step 1: Simplify both sides of the equation.

4x(−4)=−2−(−3)−6

−16x=−2+3+−6

−16x=(−2+3+−6)(Combine Like Terms)

−16x=−5

−16x=−5

Step 2: Divide both sides by -16.

−16x

−16

=−5/−16

x=5/16

can I be the brainiest please!!

i need answers because it's very hard i need to pass.

Answers

Answer:

whats the question

Step-by-step explanation:

PLEASE HELP, DUE AT MIDNIGHT >>>>>

Answers

Answer:

BELOW

Step-by-step explanation:

7.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-8,\:-11\right),\:\left(x_2,\:y_2\right)=\left(17,\:4\right)\\\\m=\frac{4-\left(-11\right)}{17-\left(-8\right)}\\\\m = \frac{4+11}{17+8}= \frac{15}{25} \\\mathrm{Refine}\\\\m=\frac{3}{5}[/tex]

8.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(10,\:-15\right),\:\left(x_2,\:y_2\right)=\left(13,\:-17\right)\\\\m=\frac{-17-\left(-15\right)}{13-10}\\\\m = \frac{-17+15}{13-10}\\ \\m = \frac{-2}{3}\\ \\Simplify\\m=-\frac{2}{3}[/tex]

9.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-6,\:-7\right),\:\left(x_2,\:y_2\right)=\left(5,\:-7\right)\\\\m=\frac{-7-\left(-7\right)}{5-\left(-6\right)}\\\\m = \frac{-7+7}{5+6}\\ \\m = \frac{0}{11}\\ \\Simplify\\m=0[/tex]

10.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-4,\:-3\right),\:\left(x_2,\:y_2\right)=\left(2,\:-9\right)\\\\m=\frac{-9-\left(-3\right)}{2-\left(-4\right)}\\\\m = \frac{-9+3}{2+4}\\ \\m = \frac{-6}{6} \\\\Simplify\\m =-1[/tex]

11.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\mathrm{When\:}y_1\ne \:y_2\mathrm{\:and\:}\:x_1=x_2\mathrm{\:the\:slope\:is\:}\infty \\\\m = \infty[/tex]

12.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-5,\:3\right),\:\left(x_2,\:y_2\right)=\left(19,\:-6\right)\\\\m=\frac{-6-3}{19-\left(-5\right)}\\\\m = \frac{-6-3}{19+5}\\ \\m = \frac{-9}{24}\\ \\Simplify\\m=-\frac{3}{8}[/tex]

13.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-7,\:-12\right),\:\left(x_2,\:y_2\right)=\left(1,\:-16\right)\\\\m=\frac{-16-\left(-12\right)}{1-\left(-7\right)}\\\\m = \frac{-16+12}{1+7} \\\\m = \frac{-4}{8} \\\\Simplify\\m=-\frac{1}{2}[/tex]

14.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-18,\:0\right),\:\left(x_2,\:y_2\right)=\left(-13,\:1\right)\\\\m=\frac{1-0}{-13-\left(-18\right)}\\\\m = \frac{1-0}{-13+18}\\ \\m = \frac{1}{5} \\[/tex]

15.

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(1,\:-11\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-4\right)\\\\m=\frac{-4-\left(-11\right)}{-2-1}\\\\m = \frac{-4+11}{-2-1}\\ \\m = \frac{7}{-3} \\\\Simplify\\m=-\frac{7}{3}[/tex]

check the image needed more words :p

Answers

i got 16.8 , but she’ll need roughly 17 gallons of paint :)

how i did it :

1. so you know she’ll need 4/5 per book case, and there are 16 bookcases.
2. So you do 16 x 5, then you get 84
3. and you divide 84 by 5. and you’ll get 16.8, that’s how many gallons of paint she needs
i don’t know i’m so sorry

Can somebody help me and answer this question for me f(g(6))=

Answers

f(g(6)) = f(5) = 6(5) - 3 = 27

-5(4x-2)=-2(3+6x) multi step equation

Answers

Answer:

X=2, please mark me brainliest

Step-by-step explanation:

−5(4x−2)=−2(3+6x)

(−5)(4x)+(−5)(−2)=(−2)(3)+(−2)(6x)(Distribute)

−20x+10=−6+−12x

−20x+10=−12x−6

Step 2: Add 12x to both sides.

−20x+10+12x=−12x−6+12x

−8x+10=−6

Step 3: Subtract 10 from both sides.

−8x+10−10=−6−10

−8x=−16

Step 4: Divide both sides by -8.

−8x

−8

=

−16

−8

x=2

6 to the 2nd power x 3 to the 3rd power

Answers

Answer:

972

Step-by-step explanation:

[tex] {6}^{2} \times {3}^{3} \\ = 36 \times 27 \\ = 972[/tex]

Write the algebra expression: six times the sum of four and a number

Answers

Answer:

6(4+x)

Step-by-step explanation:

Answer:

6(x+4)

Step-by-step explanation:

We want to write an algebraic expression for "six times the sum of four and a number"

Let's break this down.

The sum of four and a number:

The words "sum" indicates addition. We can call " a number" x, since it is unknown.

So, the sum of four and a number is: (x+4).

Six times:

The word "times indicates multiplication. We are multiplying six and the sum of four and a number.

So, we have: 6(x+4)

The algebra expression for "six times the sum of four and a number" is 6(x+4)

What is the explicit formula used for?

Answers

Answer:Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms

Step-by-step explanation:

A graph where the horizontal axis shows time (t), numbered 1 to 4, and the vertical axis shows height (h) numbered 10 to 60. Solid circles appear at point (0, 48), point (1, 64), point (3, 0). A solid curved line connects all 3 points. Leon throws a ball off a cliff. The graph represents a relation that models the ball’s height, h, in feet over time, t, in seconds. What is the domain? {t| 0 ≤ t ≤ 3} {t| 0 ≤ t ≤ 48} {t| 0 ≤ t ≤ 64} {t| all real numbers}

Answers

Answer:

{t| 0 ≤ t ≤ 3}

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

It right on edge 2020

There are 7 more sweaters than shirts in the drawer. There are 15 sweaters and shirts in the drawer in all. How many shirts are there in the drawer? Let S represent the number of shirts. Which equation represents the situation

Answers

Answer:

7 + 2s = 15

4 shirts

Step-by-step explanation:

Let's say w denotes sweaters and s denotes shirts.

Since there are 7 more sweaters than shirts:

w = 7 + s

There are a total of 15 sweaters and shirts in all, so:

w + s = 15

Substitute 7 + s in for w in the second equation:

w + s = 15

7 + s + s = 15

7 + 2s = 15

Solving for s:

7 + 2s = 15

2s = 15 - 7 = 8

s = 8/2 = 4 shirts

Thus, the equation is 7 + 2s = 15, and there are 4 shirts.

~ an aesthetics lover

A cylindrical cup has a circular base of radius 7cm and height 10cm, calculate its curved surface area. take pie as 3.1​

Answers

Answer:

264.89cm^2

Step-by-step explanation:

CSA of cylinder=πrl

= 3.1 × 7 ×√149

= 264.89cm^2

Juan, an avid golfer, used two strokes on a miniature golf hole, which was one stroke below par. What was par for this hole?

Answers

1 because two strokes minus 1 for being one stroke above par is 1.

The length of an alligator in a zoo is 14 5/6 feet.The everglades national parks list the longest alligator ever reocord in florida at 17 5/12 feet. Which is the differnce in their lenghth

Answers

Answer:

The difference in the lengths of the two alligators = 3

Step-by-step explanation:

First, let us make the lengths improper fractions, then we will find the difference from there.

Alligator 1:

Length = [tex]14\frac{5}{12} = \frac{173}{12}[/tex]

To convert to improper fraction, multiply the denominator by the whole number, and then add the denominator [(12 × 14) + 5]

Alligator 2:

Length = [tex]17\frac{5}{12} = \frac{209}{12}[/tex]

Now Let us find the difference between the lengths:

[tex]\frac{209}{12} - \frac{173}{12} = \frac{36}{12} =3[/tex]

Therefore the difference in the lengths of the two alligators = 3

please prove this...​

Answers

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2

sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2

Given:  sin Ф = k sin β      -->   (sin Ф)/(sin β) = k

Proof RHS → LHS

[tex]\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}[/tex]

[tex]\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}[/tex]

 [tex]\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark[/tex]

9. Krista and Emily wrote an equation of a line that is parallel to the line y = 3x - 1 and passing
through the point (5,9). Is either of them correct? Explain your reasoning?
Krista:
9 = 3(5) + b
9 = 15 + b
-6 = b
y = 3x - 6
Emily:
y- 9 = 3(x - 5)
y- 9 = 3x - 15
y = 3x - 24
Answer:
Explanation:

Answers

Step-by-step explanation:

Hey there!

The equation, of a st. line that passes through point (5,9) is,

[tex](y - y1) = m1(y - y1)[/tex]

Put the values,

[tex](y - 9) = m1(x - 5)[/tex]

It is 1st equation.

Now, another equation is,

y = 3x-1.........(ii)

Comparing the equation with y = mx+c.

Slope (m2)= 3

As per the parallel lines,

m1=m2=3

Putting,

the value of m1 in equation(i)

(y-9)= 3(x-5)

y-9= 3x - 15

y = 3x - 6.

So, Krista equation is correct.

Hope it helps...

The product of twice the length and the width

Answers

Answer:

The answer to the question is 2(l+w).

Mrs. Bowman spent $110 to rent a popcom machine for the school
carnival and $75 to buy popcorn, oil, and other supplies. If she sold
263 bags of popcorn for $1.50 each, how much money did she make after paying for the machine and the supplies?

Answers

Answer:

200 minutes I am getting poi tea yayyyy

Answer:

$209.50

Step-by-step explanation:

First, find how much she made selling the popcorn:

263(1.5)

= 394.50

Then, find how much she spent on supplies and the machine:

110 + 75

= 185

Subtract the expenses from the profit:

394.50 - 185

= $209.50

Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided. 4(3 - 2x) = 15

Answers

Answer:

x = -3/8

Step-by-step explanation:

4(3 - 2x) = 15

Distribute

12 -8x = 15

Subtract 12 from each side

12-8x-12 =15-12

-8x =3

Divide by -8

-8x/-8 = 3/-8

x = -3/8

The correct answer is: -3/8

-5(k + 6) + 7(k – 4)

Answers

the answer is- 2k-58.

what is the answer to g+3=17

Answers

Answer:

g=14

Step-by-step explanation:

do 17-3, the answer is 14, meaning 14=g

Answer:

g = 14

Step-by-step explanation:

g+3 = 17

Subtract 3 from each side

g+3-3 = 17-3

g = 14

Hugh bought some magizines that cost 3.95 each and some books that cost 8.95 each. He spent a total of 47.65.If Hugh bought 3 magazines,how many books did he buy

Answers

Answer:

4 books

Step-by-step explanation:

We are told that: Hugh bought some magazines that cost 3.95 each

Hugh bought 3 magazines.

Hence, total cost of magazines = 3 magazines × 3.95

= 11.85.

Total cost of magazines = 11.85

From the question, we know that, the total amount Hugh spent = 47.65

Hence, The total cost for books =

Total amount spent - Total cost of magazines

= 47.65 - 11.85

= 35.80

Therefore, the total cost of books = 35.80

We are told in the question that the cost of books is 8.95 each or 8.95 per book.

Hence, the number of books that Hugh bought is calculated as :

35.80/8.95

= 4 books

Therefore, Hugh bought 4 books

PLEASEEEE HELP ASAPPP ILL MARK BRAINLIEST IMPORTANT TO SHOW YOUR WORK

Answers

Answer:

AC = 7.5 cm

Step-by-step explanation:

Given that the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AC}{DE}[/tex] = [tex]\frac{BC}{DE}[/tex] , substitute values

[tex]\frac{AC}{3.5}[/tex] = [tex]\frac{7+8}{7}[/tex] , that is

[tex]\frac{AC}{3.5}[/tex] = [tex]\frac{15}{7}[/tex] ( cross- multiply )

7AC = 52.5 ( divide both sides by 7 )

AC = 7.5 cm

-1/2m=-9 what does m=

Answers

Answer:

m = 18

Step-by-step explanation:

Step 1: Write out equation

-1/2m = -9

Step 2: Multiply both sides by -2

m = 18

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