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3 years ago

A water tank with 265 gallons of water has a leak. After 5 hours, the tank is completely empty.

Mathematics

2 answers:

ddd [48]3 years ago

3 0

The water tank loses 53 gallons of water in 1 hour.

Shtirlitz [24]3 years ago

3 0

265÷5=53, so the water tank loses 5e gallons of water in 1 hour

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Verify that the roots of 5x²- 6x -2 = 0 are <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%20%2B%20%5Csqrt%7B19%7D%20%7D%7B5%7D%2

Mice21 [21]

Answer:

Proof below.

Step-by-step explanation:

Quadratic Formula

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Given quadratic equation:

$5x^2-6x-2=0$

Define the variables:

a = 5
b = -6
c = -2

Substitute the defined variables into the quadratic formula and solve for x:

$\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(5)(-2)}}{2(5)}$

$\implies x=\dfrac{6 \pm \sqrt{36+40}}{10}$

$\implies x=\dfrac{6 \pm \sqrt{76}}{10}$

$\implies x=\dfrac{6 \pm \sqrt{4 \cdot 19}}{10}$

$\implies x=\dfrac{6 \pm \sqrt{4}\sqrt{19}}{10}$

$\implies x=\dfrac{6 \pm2\sqrt{19}}{10}$

$\implies x=\dfrac{3 \pm \sqrt{19}}{5}$

Therefore, the exact solutions to the given quadratic equation are:

$x=\dfrac{3 + \sqrt{19}}{5} \:\textsf{ and }\:x=\dfrac{3 - \sqrt{19}}{5}$

Learn more about the quadratic formula here:

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3 0

1 year ago

Read 2 more answers

The Venn diagram shows the results of two events resulting from rolling a number cube.

gulaghasi [49]

Answer: $P(A\cap B)=\frac{1}{3}$

$P(A)=\frac{1}{3}$

$P(B)=1$

$P(A|B)=\frac{1}{3}$

Step-by-step explanation:

From the given figure it can be seen that

Total number on cube= n(S)=6

Intersection of A and B = n(A ∩ B)= 2

Therefore,

$P(A\cap B)=\frac{n(A\cap B)}{n(s)}=\frac{2}{6}=\frac{1}{3}$

Also, The number of elements in A = 2

Therefore,

$P(A)=\frac{n(A)}{n(s)}=\frac{2}{6}=\frac{1}{3}$

Similarly, The number of elements in B= 6

Therefore,

$P(B)=\frac{n(B)}{n(s)}=\frac{6}{6}=1$

The formula to find the conditional probability is given by :-

$P(A|B)=\frac{P(A\cap B)}{P(B)}\\\\\Rightarrow P(A|B)=\frac{\frac{1}{3}}{1}=\frac{1}{3}$

4 0

3 years ago

Read 2 more answers

Find the distance between the two points.

Ksenya-84 [330]

Hey there!

Distance formula:

d = $\sqrt{(x_{2}-x_{1})+(y_{2}-y_{1}) }$

Plug in variables:

d = $\sqrt{(0-(-6))+(0-(-7))}$

Simplify.

d = $\sqrt{6+7}$

d = $\sqrt{13}$

The distance between the two points is $\sqrt{13}$ units.

Hope this helps!

4 0

3 years ago

A rock weighs 80 g on a triple beam scale. The same rock is then gently placed inside a graduated cylinder containing 30 mL of w

Alexxandr [17]

Answer:

1.78 g/cm³

Step-by-step explanation:

80 g rock displaces water:

75 ml - 30 ml = 45 ml = 45 cm³

Density = mass / volume:

d = 80 g / 45 cm³
d = 1.78 g/cm³ (rounded)

3 0

2 years ago

What is the answer? I am so lost- thanks for any help given.

aev [14]

Answer:

i think that the answer is 13 meters

Step-by-step explanation:

7 0

3 years ago