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3 years ago

Factor the quadratic 6(x-5)* + 126(x - 5) + 324 completely.

Mathematics

1 answer:

den301095 [7]3 years ago

6 0

Answer:

6 • (x + 13) • (x - 2)

tell me if I got it right

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A fish tank has 35 gallons of water in it, but suddenly starts leaking. Water is leaking from the tank at a rate of 1/4 gallon p

Norma-Jean [14]

Answer:

35 - m

Step-by-step explanation:

A tank containing 35 gallons of water is leaking at a rate of gallon per minute.

"m" represents the number of minutes spent

Number of gallons left in the tank = initial amount of water present – leaked amount of water

Number of gallons of water left = 35 gallons – number of minutes spent rate of leakage.

Number of gallons of water left = 35 gallons – m minutes 1 gallons per minute

8 0

3 years ago

the eccentricity of a hyperbola is defined as e=c/a. find an equation with vertices (1,-3) and (-3,-3) and e=5/2

Ksivusya [100]

Answer:

$\frac{(x + 1 )^{2} }{4} - \frac{(y + 3 )^{2} }{21} = 1$ .

Step-by-step explanation:

If (α, β) are the coordinates of the center of the hyperbola, then its equation of the hyperbola is $\frac{(x - \alpha )^{2} }{a^{2} } - \frac{(y - \beta )^{2} }{b^{2} } = 1$ .

Now, the vertices of the hyperbola are given by (α ± a, β) ≡ (1,-3) and (-3,-3)

Hence, β = - 3 and α + a = 1 and α - a = -3

Now, solving those two equations of α and a we get,

2α = - 2, ⇒ α = -1 and

a = 1 - α = 2.

Now, eccentricity of the hyperbola is given by $b^{2} = a^{2}(e^{2} - 1) = 4[(\frac{5}{2} )^{2} -1] = 21$ {Since $e = \frac{5}{2}$ given}

Therefore, the equation of the given hyperbola will be

$\frac{(x + 1 )^{2} }{4} - \frac{(y + 3 )^{2} }{21} = 1$ . (Answer)

6 0

3 years ago

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. the x-inte

wariber [46]

Step-by-step explanation:

Given x intercept is 1, So (x,y) is (1,0)

When x intercept is 1 then y value is 0

Another point on the line is (-2,3)

Two points are (1,0) and (-2,3)

Find out slope using the two given points

$slope m=\frac{y_{2}-y_1}{x_2-x_1} =\frac{3-0}{-2-1} =-1\\m=-1$

Use point slope formula

m=-1 and point(1,0)

$y-y_{1}=m(x-x_{1})\\y-0=-1(x-1)\\y=-1x+1$

Point slope equation is

$y-0=-1(x-1)$

Equation of the line in slope intercept form is

$y=-1x+1$

7 0

3 years ago

What is the probability of rolling a four then a three

spayn [35]

Answer:

$\frac{1}{36}$

Step-by-step explanation:

Total possibilities when we a roll a die at a time are 6

given we should have four for first time and then three

let us assume we rolled the dice we may get 1,2,3,4,5,6(any of these) the probability to get 4 is

PROBABILITY= $\frac{\textrm{FAVOURABLE CHANCES}}{\textrm{TOTAL CHANCES}}$

Favourable chances=1

Total chances=6

Probability= $\frac{1}{6}$

the prabability to get 4 in first roll is $\frac{1}{6}$ .

let us assume we rolled the dice for second time again we may get 1,2,3,4,5,6(any of these) the probability to get 3 is

Favourable chances=1

total chances=6

probability= $\frac{1}{6}$

the probability to get 3 in second roll irrespective of first one is $\frac{1}{6}$

the probability to get 4 in first time and then 3 is

The probability to occur both events at a time is multiplication of individual probabilities

So,

probablility to get 4 in first roll= $\frac{1}{6}$

probability to get 3 in second roll= $\frac{1}{6}$

probability to occur both at a same time is = $\frac{1}{6}$ $\times$ $\frac{1}{6}$ = $\frac{1}{36}$

6 0

3 years ago

Khan academy similarity unit test

shusha [124]

similarity on what

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3 years ago