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4 years ago

Find the coordinates of point B on line AC such that AB is 2/3 of AC

Mathematics

1 answer:

ra1l [238]4 years ago

5 0

Answer:

Step-by-step explanation:

Let's calculate the distance between the corresponding coordinates of points A and C.

$A(1,\ -5),\ C(-5,\ 4)\\\\|AC|_x=|-5-1|=|-6|=6\\\\|AC|_y=|4-(-5)|=|4+5|=|9|=9$

We find such B that

$|AB|=\dfrac{2}{3}|AC|=\dfrac{2|AC|}{3}$

Calculate the unit of division

$a_x=\dfrac{6}{3}=2\\\\b_y=\dfrac{9}{3}=3$

Therefore the coordinateso f the point B are:

$B(x+2,\ y-3)\\\\x+2=-5+2=-3\\\\y-3=4-3=1\\\\\boxed{B(-3,\ 1)}$

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Help me with this problem please

gavmur [86]

Answer:

7 yards

Step-by-step explanation:

the absolute value of -2 and 2/3- 51/3 is 7

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3 years ago

Jane does a total of 75 push-ups each week. How many push-ups will Jane do in the 12 weeks? (Show your work).

dedylja [7]

Answer:

900 push-ups

Step-by-step explanation:

75 push-ups in one week

In 12 weeks = 75 × 12 = 900 push-ups

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL :) 

7 0

3 years ago

50 POINTS!!!! Make a box and whisker plot of the data See photo

lara [203]

Let's try it just using test taking skills first, without really knowing anything about what these plots are.

All have a minimum of 13 and a max of 29 so those don't help.

Three have a left box edge of 14.5, one 12.8 or so. The correct answer is probably 14.5.

Three have a median of 19.5, one of 20.5, so 19.5 is probably right.

Similarly 23.5 is the most common right box edge.

So we're looking for the plot with 13/14.5/19.5/23.5/29, which is the first choice.

----

Instead of Einsteining the test, lets review the material. A box and whiskers plot shows the min and max (whisker ends), the 25th and 75th percentiles (box ends) and the 50th percentile, the median, which is the dot in the middle.

Let's start by sorting the 8 data points:

11 13 16 18 21 23 24 29

The minimum is 11 and the maximum is 29. All the charts agree on this.

The median is the middle, which is the average of 18 and 21, so

median = 19.5

That rules out the one selected, it can't be the third one.

The 25th percentile basically the median of the first four numbers, so the average of 13 and 16,

25th percentile = 14.5

The 75th percentile is similarly the average of 23 and 24

75th percentile 23.5

Examining the choices we find our

Answer: first choice

5 0

4 years ago

A. The graph shows four points on the line and the triangles resulting from sketching on the rise and run from one point to the

Gnoma [55]

Answer:

A. Yes

B. The triangles are similar

C. The corresponding sides are proportional

D. The slope of ΔABC = tanθ₁ = tanθ₂ = The slope pf ΔDEF, therefore, the slope of any two points on the line are congruent by similar triangles

E. The rate of proportionality = 2

Step-by-step explanation:

A. From the given graph, given that the angles are formed between the transversal and lines parallel to the R-value axis and the transversal and lines parallel to the thickness axis, the angle formed by the transversal and each parallel lines are corresponding angles and are therefore congruent

The tan of one of the angles on each triangle are

On the uppermost triangle, tanθ₁ = (9.42 - 3.14)/(3 - 1) = 3.14

On the other triangle, tanθ₂ =(25.12 - 12.56)/(8 - 4) = 3.14

tanθ₁ = tanθ₂

∴ θ₁ = θ₂

ΔABC and ΔDEF are right triangles, therefore, all the angles of ΔABC and ΔDEF are congruent

B. Given that the interior angles of the triangles formed by the line the graph are congruent, the triangles are similar by AA similarity postulate

C. Given that the triangles are similar, the length of the corresponding sides of the triangles are proportional

D. Given that the slope is the tangent of the angle between the line of the graph and the Thickness axis, and that the angle is the same for both triangles, (∠θ₁ and ∠θ₂) the slope or the rise-to-run ratio is constant for the two triangles and also for any two points on the line

E. The Unit of proportionality is found using any two points as follows;

Using points used to show the proportional relationship on triangle ΔABC are (8, 25.12) and (4, 12.56) and on triangle ΔDEF, the two points used to show proportional relationship are (3, 9.42), and (1, 3.14)

The ratio of the corresponding sides on ΔABC and ΔDEF are

$\overline {AC}$ / $\overline {DF}$ = (25.12 - 12.56)/(9.42 - 3.14) = 2

$\overline {BC}$ / $\overline {EF}$ = (8 - 4)/(3 - 1) = 2

Therefore, the unit rate of proportionality which is the scale factor = 2.

3 0

3 years ago

What is the prime factor of 4400 by tree method

Mashutka [201]

Answer:

The orange divisor(s) above are the prime factors of the number 4,400. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 5 x 5 x 11 = 4,400. It can also be written in exponential form as 24 x 52 x 111.

Step-by-step explanation:

Hope that this helps! :)

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7 0

3 years ago