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3 years ago

Find the coordinates of point b on ac such that the ratio of AB to BC is 2:1

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

5 0

Answer:

(-2, 3)

Step-by-step explanation:

the point B is

B(x,y)

AB (A to B) is twice BC ( B to C )

AB is 2 - x. BC is x - (-4)= x + 4

2-x=2 (x + 4)

2-x=2x + 8

3x = -6

x = -2

(Same logic as above)

AB is -5 -y. BC is u - 7

-5 -y = 2(y - 7)

-5 - y = 2y - 14

3y = 9

y= 3

the point is (-2, 3)

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An Easter basket contains eggs of three different colors. Find the total number of eggs in the basket if 2 7 of all eggs are gre

sashaice [31]

Answer:

56 eggs

Step-by-step explanation:

If $\frac{2}{7}$ of all eggs are green, $\frac{1}{4}$ of all are blue, then

$1-\dfrac{2}{7}-\dfrac{1}{4}=\dfrac{28-2\cdot 4-7}{28}=\dfrac{13}{28}$

of all eggs are red.

We know that there are 26 red eggs

$26\text{ eggs }-\dfrac{13}{28}\\ \\x\text{ eggs }- 1[=\dfrac{28}{28}]$

Make a proportion

$\dfrac{26}{x}=\dfrac{\frac{13}{28}}{1}\\ \\26\cdot 1=x\cdot \dfrac{13}{28}\ [\text{Cross multiply}]\\ \\13x=26\cdot 28\ [\text{Multiply by 28 to get rid of fraction}]\\ \\x=\dfrac{26\cdot 28}{13}\ [\text{Divide by 13 to get x}]\\ \\x=2\cdot 28\\ \\x=56$

4 0

3 years ago

Enter the ratio as a fraction in lowest terms 2 ft to 10 in.

irga5000 [103]

Answer:

6 / 5

Step-by-step explanation:

1) you take the 2 feet and change it to inches by multiplying 2 by 12 because there is 12 inches in each foot.

2) you find the greatest common factor of 12 and 10 which is 2

3) you divide both of the numbers by your GCF of 2 which is 6/5

8 0

3 years ago

Find the approximate length of EF.

Yuri [45]

Answer:

The correct option is B

Step-by-step explanation:

Given information: ∠F=32°,∠D=54° and DF=18m.

According to the angle sum property of triangle, the sum interior angles of a triangle is 180°.

Using angle sum property, we get

$\angle D+\angle E+\angle F=180^{\circ}$

$54^{\circ}+\angle E+32^{\circ}=180^{\circ}$

$\angle E+86^{\circ}=180^{\circ}$

$\angle E=180^{\circ}-86^{\circ}$

$\angle E=94^{\circ}$

Law of sine:

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Using law of sine we get

$\frac{\sin D}{d}=\frac{\sin E}{e}$

$\frac{\sin D}{EF}=\frac{\sin E}{DF}$

$\frac{\sin 54^{\circ}}{EF}=\frac{\sin 94^{\circ}}{18}$

$\frac{0.809016994375}{EF}=\frac{0.99756405026}{18}$

Cross multiply,

$0.809016994375\times 18=0.99756405026\times EF$

Divide both sides by 0.99756405026.

$EF=14.5978655656$

$EF\approx 14.6$

The value of EF is 14.6 m. Therefore the correct option is B.

7 0

3 years ago

Tina solved an equation incorrectly, as shown below:

Komok [63]

$8x = 24 \\ \\ x = \frac{24}{8} \ / \ divide \ by \ 8 \\ \\ x = 3 \ / \ simplify \\ \\$

Seeing the correct steps above, the mistake that Tina made was that she did not divide 24 by 8.

3 0

3 years ago

Read 2 more answers

The function g(x) = x3 has the point (-3, -27) on its graph. The function g(x) is even or odd

sashaice [31]

Answer:

The function g(x) is odd.

Step-by-step explanation:

Even and odd functions:

If for every value of x, f(x) = f(-x), the function is even.

If for every value of x, f(x) = -f(x), the function is odd.

If those statements are false, the function is neither even nor odd.