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Archy [21]
3 years ago
5

Mr. Smith's wife works at an animal hospital. There is a equivalent fraction relationship between the number of dogs and cats in

the kennels. If there are 20 cats in the kennels, how many dogs?
Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

Answer:

There are 10 dogs in the kennels

Step-by-step explanation:

The equivalent fraction relationship between the number of dogs and cats in the kennels is 1/2.

Which means, if n_d the number of dods and n_c is the number of cats, then,

\frac {n_d}{n_c}=\frac{1}{2}\cdots(i)

Given that there are 20 cats, so n_c=20.

Now, from equation (i) we have,

\frac {n_d}{20}=\frac{1}{2}

\Rightarrow n_d=\frac{1}{2}\times 20

\Rightarrow n_d= 10.

Hence, there are 10 dogs in the kennels.

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Find the area of each regular polygon. Round your answer to the nearest tenth if necessary​
Gnesinka [82]

Answer:

Step-by-step explanation:

13). Area of a square = (Side)²

                                   = (BC)²

     Since, diagonals of a square bisect each other at 90°,

     ΔBOC is a right triangle.

     By applying Pythagoras theorem in the given triangle,

     BC² = OB² + OC²

     BC² = 2(OB)²

     BC² = 2(7√2)²

     BC = \sqrt{196}

     Area of square ABCD = (BC)²

                                          = (√196)²

                                          = 196 units²

14). Measure of interior angles of the regular hexagon = 120°

     Area of the regular hexagon = \frac{3\sqrt{3}}{2}(\text{side})^2

      From the given picture,

      m∠BAC = m∠ABC = m∠ACB = 60°

      Therefore, ΔABC is an isosceles triangle.

      And all sides of this triangle will be equal in measure.

      AB = AC = BC = 9 units

      Area of the given regular hexagon = \frac{3\sqrt{3}}{2}(9)^2

                                                                 = 210.44 square units

                                                                 ≈ 210.4 square units

5 0
3 years ago
The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of inte
11111nata11111 [884]

Area of rhombus = \frac{xy}{2}

where x and y are diagonals.

Given length of one diagonal is 4.5 dm

So, let x= 4.5dm

1 dm = 10 cm

4.5dm= 45cm

area = \frac{xy}{2}

so, 540 = \frac{45y}{2}

y = 24 cm

The two diagonals are x= 45cm and y = 24cm

Since diagonals bisect each other, we get 22.5cm and 12cm

Using right triangle formula

\frac{1}{r^{2} } = \frac{1}{22.5^{2}} + \frac{1}{12^{2}}

\frac{1}{r^{2} } =\frac{12^{2}+22.5^{2}}{22.5^{2}*12^{2}}

r^{2} = \frac{22.5^{2} *12^{2}}{12^{2}+22.5^{2}}

r = 10.588cm

Distance of center to the side = \frac{10.588}{2}  = 5.294 cm

4 0
3 years ago
What is the outlier in this data set ? 14,82,78,89,73,91​
Sergeu [11.5K]

Answer:

14.

Step-by-step explanation:

All of the data can be included of a range from 73 - 91. They are all close in value. However, 14 is much less than the rest of the data, and is therefore an outlier.

5 0
4 years ago
Read 2 more answers
Describe the graph of the equation y = 6x.
Illusion [34]

y = 6x

y = (8.9) (9.8)

y = 6x (8.9)

y = 8.9x

4 0
3 years ago
Find the errors and correct the following mathematical sentences.​
Sergio039 [100]

Answer:

Here is another one solved.

6 0
3 years ago
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