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padilas [110]
3 years ago
10

8. In the figure, ADC is a straight line.

Mathematics
1 answer:
dlinn [17]3 years ago
4 0

Answer:

a). ΔABC ~ ΔBDC

b). m(BD) = 6 units

Step-by-step explanation:

If ΔABC ~ ΔBDC,

a). Ratio of the corresponding sides of both the triangles will be equal.

\frac{AB}{BD}=\frac{BC}{DC}=\frac{AC}{BC}

\frac{BC}{DC}=\frac{AC}{BC}

\frac{12}{9}=\frac{7+9}{12}

\frac{4}{3}=\frac{4}{3}

Since Ratio of the corresponding sides are same, therefore, both the triangles are similar.

b). \frac{AB}{BD}=\frac{BC}{DC}

\frac{8}{BD}=\frac{12}{9}

BD = \frac{9\times 8}{12}

BD = 6

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Digiron [165]

Answer:

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Step-by-step explanation:

Given the data:

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0 - 1 __________ 11

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5 0
3 years ago
Find the slope of the line that goes through the given points.<br> (0,8) and (- 4,0)
Ronch [10]

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 8) and (x₂, y₂ ) = (- 4, 0)

m = \frac{0-8}{-4-0} = \frac{-8}{-4} = 2

6 0
2 years ago
Read 2 more answers
The ratio of the number of dogs the number of cats is 4:5. There are 270 animals on the rescue Farm. The number of dogs is 4/5.
mafiozo [28]

Answer:

<em>Here is the complete question:</em>

The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:

a. The number of dogs is 4/5 the number of cats.

b. 4/5 of the pets at the farm are dogs.

c. There are exactly 30 more cats than dogs.

d. There are exactly 30 dogs at the farm.

e. 5/9 of the pets at the farm are cats.

a,c and e are true statements.

Step-by-step explanation:

Let the number of dogs be "d' and number of cats be "c".

According to the question:

⇒ c+d=270   ...equation (i)

Arranging the ratio:

⇒ \frac{4}{5} = \frac{d}{c}

⇒ 4c=5d

⇒ c=(\frac{5}{4})d    ...equation (ii)

Plugging (ii) in equation (i).

⇒ c+d=270

⇒ \frac{5}{4} d+d=270

⇒ \frac{5d+4d}{4} =270

⇒ 9d=270\times 4

⇒ d=\frac{270\times 4}{9}

⇒ d=120

Number of dogs "d" = 120

Number of cats "c" = (270-120) = 150

Lets check each statement:

a.

The number of dogs is 4/5 the number of cats.

⇒ \frac{4}{5} \times 150

⇒ \frac{4\times 150}{5}

⇒ 120

Statement is true.

b.

4/5 of the pets at the farm are dogs.

⇒ \frac{4}{5} \times 270

⇒ 216

Number of dogs = 120

So the above statement is false.

c.

There are exactly 30 more cats than dogs.

⇒ c-d =30

⇒ 150-120=30

Statement is true.

d.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

e.

5/9 of the pets at the farm are cats.

⇒ \frac{5}{9} \times 270

⇒ 150

Statement is true.

So,

Statement  a,c and e are true as we could observe in the explanation.

8 0
2 years ago
142 students are going on a field trip. There will be six drivers, and two different types of vehicles. A bus can hold 51 people
otez555 [7]

Answer: 2 buses and 4 vans would be needed

Step-by-step explanation:

Let x represent the number of buses that would be needed.

Let y represent the number of vans that would be needed.

There will be six drivers, and two different types of vehicles. This means that

x + y = 6

142 students are going on a field trip. A bus can hold 51 people while a van can hold 10. This means that

51x + 10y = 142 - - - - - - - - - - - 1

Substituting x = 6 - y into equation 1, it becomes

51(6 - y) + 10y = 142

306 - 51y + 10y = 142

- 51y + 10y = 142 - 306

- 41y = - 164

y = - 164/ - 41

y = 4

x = 6 - y = 6 - 4

x = 2

8 0
3 years ago
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evablogger [386]

The answer choice which represents the quotient of the polynomials given is; 2x² +x -3.

<h3>What is the quotient of the polynomial division?</h3>

According to the task content, the quotient of the polynomial division; (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is required;

Hence, it follows from long division of polynomials that the required quotient is; 2x² +x -3.

Read more on quotients of polynomials;

brainly.com/question/24662212

#SPJ4

7 0
1 year ago
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