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KATRIN_1 [288]
3 years ago
14

An aquarium is leaking water at the rate of three quarts in 4 days.How many quarts are leaked in 1 week?How many days does it ta

ke for 9 quarts to leak out of the aquarium?
Mathematics
1 answer:
Simora [160]3 years ago
6 0

Answer:

\frac{21}{4} quarts

12 days

Step-by-step explanation:

Given that:

Amount of water leaked in 4 days = 3 quarts

To find:

Number of quarts leaked in 1 week?

Number of days taken for the leakage of 9 quarts of water?

Solution:

We can simply use unitary method or the ratio to find the answers of the questions asked in the statement.

As per question statement:

Amount of water leaked in 4 days = 3 quarts

Dividing by 4 on both sides:

Amount of water leaked in 1 day = \frac{3}{4} quarts

Multiplying by 7 on both sides:

Amount of water leaked in 7 days = \frac{3}{4}\times 7 = \frac{21}{4} quarts

Number of days taken for the leakage of 3 quarts = 4 days

Multiplying by 3 on both sides:

Number of days taken for the leakage of 3 \times 3 = 9 quarts = 4 \times 3 = <em>12 days</em>

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Solve the equation: k^2+5k+13=0
mr_godi [17]

Step-by-step explanation:

k² + 5k + 13 = 0

Using the quadratic formula which is

x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}  \\

From the question

a = 1 , b = 5 , c = 13

So we have

k =  \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)}  \\  =  \frac{ - 5 \pm \sqrt{25 - 52} }{2}  \\  =  \frac{ - 5 \pm \sqrt{ - 27} }{2}  \:  \:  \:  \:  \:  \:  \\  =  \frac{ - 5  \pm3 \sqrt{3}  \: i}{2}  \:  \:  \:  \:  \:  \:

<u>Separate the solutions</u>

k_1 =  \frac{ - 5 + 3 \sqrt{3} \: i }{2}  \:  \:  \:  \: or \\ k_2 =  \frac{ - 5 - 3 \sqrt{3}  \: i}{2}

The equation has complex roots

<u>Separate the real and imaginary parts</u>

We have the final answer as

k_1 =  -  \frac{5}{2}  +  \frac{3 \sqrt{3} }{2}  \: i \:  \:  \:  \: or \\ k_2 =  -  \frac{5}{2}  -  \frac{3 \sqrt{3} }{2}  \: i

Hope this helps you

8 0
2 years ago
In the above figure (not drawn to scale), Find ∠AEC.
n200080 [17]

Answer:

C. 75°

Step-by-step explanation:

We have been given a circle and we are asked to find the measure of angle AEC.

We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.

m\angle AEC=\frac{110^o+40^o}{2}

m\angle AEC=\frac{150^o}{2}

m\angle AEC=75^o

Therefore, measure of angle AEC is 75 degrees and option C is the correct choice.

7 0
3 years ago
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GalinKa [24]

Answer:

i think it is 6 but not sure

Step-by-step explanation:

8 0
2 years ago
Consider the sequence 3, -9, 27, -81, .. Find the 14th term of the sequence.
bagirrra123 [75]

Answer:

let 'a' be the first term, 'd' be the common difference between all the terms of the sequence

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therefore, a = 3,

and, d = -9 -3

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hence the 14th term would be,

=> a + 13d

=> 3 + 13( -12 )

=> 3 - 156

=> - 153

5 0
3 years ago
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In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded regi
Alexeev081 [22]
The area of a circle is <span>πr²
the outer circle area = </span><span>π 4x²
the inside circle area = </span>π.6²=36<span>π
</span>the outer circle area - <span>the inside circle area = </span><span>he shaded region
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the value of x is 8</span>
7 0
3 years ago
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