1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stolb23 [73]
2 years ago
14

On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2.

If location A is at (5,16) and location C is at (3,10). Find the coordinates of location B. A. (1,4) B. (4,13) C. (-1,-2)
Mathematics
1 answer:
koban [17]2 years ago
3 0

Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

You might be interested in
You have to complete at least 10 physics problems and math problems within 2 hours before you playing video games. It will take
Ghella [55]

Answer:2

Step-by-step explanation:

Given

Physics problem requires 20 min

Math problem require 10 min

suppose x question of Physics and y questions of Math are done

so according to the question

x+y\geq 10\ldots 1

Time require for x Physics problem =20 x

Time require for y Math problem =10 y

so,

20 x+10 y\leq 120\ldots 2

On solving (1) and (2)

we get x=2 and y=8

Maximum no of Physics question which can be solved is 2

5 0
3 years ago
Is this the correct way
Anon25 [30]

yes it is hope this helps you


3 0
3 years ago
Read 2 more answers
The price of an item yesterday was $60. Today, the price fell to $42. Find the percentage decrease.
oksian1 [2.3K]

Answer:

-30% or 30% decrease

Step-by-step explanation:

What's percentage decrease?

  • Percent decrease is the difference between the initial value and new value, indicating a loss of value.
  • The formula to find percent decrease is \frac{NV-IV}{IV} * 100, where NV = new value and IV = initial value.

How do we solve this problem?

  • We know that the original value was $60, so that represents IV. Also, now that the price is $42, it represents NV.
  • Now, we plug in the values!
  • \frac{42-60}{60} * 100
  • \frac{-18}{60} * 100
  • -\frac{3}{10} * 100
  • -3 * 10
  • -30

Therefore, the answer is 30% decrease.

6 0
2 years ago
Janet is buying a $28 necklace. The store reduces the price by 20% and then applies a $2 off coupon. How much will Janet pay for
Leokris [45]
Okay well the starting is 28 dollars, right. But since there is a 20 percent discount, you have to turn 20% to a decimal. That means moving the decimal sign twice to the left to make it .20. From the it would be .20*28, that should equal 5.6. Now, that 5.6 is the amount you have to take away, it is the price of the sale. From then, you subtract which is 28-5.6 which should be 22.4. From that 22.4 you now take away two dollars and then it should be 22.4-2 which should be 20.4. Now that is your answer, 20.4.
4 0
3 years ago
Read 2 more answers
Candice leaves on a long trip driving at a steady rate of 35 miles per hour. Her sister Liz leaves from the same location travel
VARVARA [1.3K]

Answer:

<h2>D. 7h</h2>

Step-by-step explanation:

v=\dfrac{d}{t}\\\\v-\text{average speed}\\d-\text{distance}\\t-\text{time}\\\\d=vt,\ t=\dfrac{d}{v}\\\\\bold{Candice:}\ v_C=35\ mph,\ d_C,\ t_C\\\\\bold{Liz}:v_L=50\ mph,\ d_L,\ t_L=t-3\\\\\bold{Equation}:\\\\/\text{the distances are the same}/\\\\d_C=d_L\\\\d_C=v_Ct_C,\ d_L=v_Lt_L\\\\35t_C=50(t_C-3)\qquad\text{use the distributive property}\\\\35t_C=50t_C-150\qquad\text{subtract}\ 50t_c\ \text{from both sides}\\\\35t_C-50t_C=50t_C-50t_c-150\\\\-15t_C=-150\qquad\text{divide both sides by (-15)}

\dfrac{-15t_C}{-15}=\dfrac{-150}{-15}\\\\t_C=10\\\\t_L=10-3=7

4 0
3 years ago
Other questions:
  • in a repeating musical pattern,there are 56 beats in 7 measure.How many measures are there after 104 beats
    12·1 answer
  • I=$54, P=$900, t=18 months what the asnwer
    15·1 answer
  • What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
    11·1 answer
  • If the point (2,4 is rotated 90 degrees clockwise what is the location of the new point
    8·1 answer
  • What percent of 55 is 11
    10·2 answers
  • How do you write 2916 divided by 9 in the Associative Property
    7·1 answer
  • The legs of a right triangle measure 5 inches and 9 inches.
    5·1 answer
  • I will give brainiest to whoever answers correctly !!
    7·2 answers
  • Find x. <br><br>Find x. <br> Find x. find x. <br>find x. <br>find x<br><br><br>​
    6·2 answers
  • Larry is reroofing his house. each side of the roof measures 14 feet from the eave to the ridge. the horizontal distance between
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!