Estimate the quotient for the following problem 645 divided by 69

In the diagram below, ABC - DEC. What is the value of x? A 5 B. 3 C. 6 D. 4

Anastaziya [24]

Answer:

C

Step-by-step explanation:

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

$\frac{BC}{EC}$ = $\frac{AC}{DC}$ , substituting values

$\frac{21}{7}$ = $\frac{24-x}{x}$ ( cross- multiply )

21x = 7(24 - x) ← distribute

21x = 168 - 7x ( add 7x to both sides )

28x = 168 ( divide both sides by 28 )

x = 6 → C

7 0

3 years ago

I need help with #1 of this problem. It has writings on it because I just looked up the answer because I’m confused but I want t

belka [17]

In the figure below

1) Using the theorem of similar triangles (ΔBXY and ΔBAC),

$\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}$

Where

$\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}$

Thus,

$\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}$

thus, BC = 7.5

2) BX = 9, BA = 15, BY = 15, YC = y

In the above diagram,

$\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}$

Thus, from the theorem of similar triangles,

$\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}$

solving for y, we have

$\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}$

thus, YC = 10.

4 0

1 year ago

A+5b-c=-20 4a-5b+4c=19 -a-5b-5c=2 Solve for a b and c

ludmilkaskok [199]

Answer:a = - 2

b = - 3

c = 3

Step-by-step explanation:

a + 5b - c = - 20 - - - - - - - - - 1

4a - 5b + 4c = 19 - - - - - - - - - 2

-a - 5b - 5c = 2 - - - - - - - - - - - 3

Adding equation 1 and equation 2, it becomes

- 6c = - 18

c = - 18/ - 6 = 3

Multiplying equation 2 by 1 and equation 3 by 4, it becomes

4a - 5b + 4c = 19

-4a - 20b - 20c = 8

Adding both equations, it becomes

- 25b - 16c = 27

- 25b = 27 + 16c = 27 + 16 × 3

- 25b = 75

b = 75/- 25 = - 3

Substituting b = - 3 and c = 3 into equation 1, it becomes

a + 5 × - 3 - 3 = - 20

a - 15 - 3 = - 20

a - 18 = - 20

a = - 20 + 18 = - 2

5 0

3 years ago

What is y=2x + 1 and y=4x (using algebra to solve linear systems) PLEASE SHOW THE WORK/STEPS

Zina [86]

I would help but i have no idea

6 0

3 years ago

Find the measure of each angle indicated.

Alexandra [31]

50 because 80+50+x=180 (inside triangle) x=130 180-130= 50 (angle outside triangle)

5 0

3 years ago