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3 years ago

A line includes the points (4,10) and ( - 2, - 8). what is its equation in point-slope form?

1 answer:

8 0

Point slope form is written as: $y- y_{1} = m(x- x_{1} )$
The point slope equation for the points given is: $y- 10 = 3(x-4 )$

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The base of a rectangular prism has an area of 12 square centimeters. The height of the rectangular prism is 3 centimeters. What

UkoKoshka [18]

Answer:

36 cubic centimeters

Step-by-step explanation:

In this question, we are tasked with calculating the volume of the rectangular prism.

mathematically, that can be obtained by using the formula for the volume of the rectangular prism.

V = Base area * height

from the question, we have the base area as 12 square centimeters and the height as 3 centimeters.

Plugging these values into the equation, the value of the volume is thus 12 * 3 = 36 cubic centimeters

3 0

2 years ago

Read 2 more answers

At the beginning of my bike ride I feel good, so I can travel 20 miles per hour. Later, I get tired and travel only 12 miles per

Vesnalui [34]

Answer: $3\dfrac{1}{4}$ hours

Step-by-step explanation:

Let x be the time ( in hours ) you feel good and y be the time ( in hours ) that you get tired.

As per given , we have

x+y= 8

Since : $Distance = Speed\times Time$

So , we have

20x+12y=122

According to the given question , we have the following system of equations ,

$x+y= 8--------(1)\\\\20x+12y=122------------------(2)$

Multiply 12 on both sides of equation (1) , we get

$12x+12y=96------------(3)$

Eliminate equation (3) from (2) , we get

$8x=26\\\\\Rightarrow\ x=\dfrac{13}{4}=3\dfrac{1}{4}$

Hence, you felt $3\dfrac{1}{4}$ hours good.

3 0

2 years ago

14% of 60 million gallons is how many gallons?

vichka [17]

Answer:

840,000,0

Step-by-step explanation:

3 0

2 years ago

Can someone please write this as a single logarithm and show work please and thank you

Mazyrski [523]

Answer:

$log_b(w^3y^4)$

Step-by-step explanation:

To write the expression as a single logarithm, or condense it, use the properties of logarithms.

1) The power property of logarithms states that $log_ax^r = rlog_ax$ . In other words, the exponent within a logarithm can be brought out in front so it's multiplied by the logarithm. This means that the number in front of the logarithm can also be brought inside the logarithm as an exponent.

So, in this case, we can move the 3 and the 4 inside the logarithms as exponents. Apply this property as seen below:

$3log_bw+4log_by\\=log_bw^3+log_by^4$

2) The product property of logarithms states that $log_axy = log_ax+log_ay$ . In other words, the logarithm of a product is equal to the sum of the logarithms of its factors. So, in this case, write the expression as a single logarithm by taking the log (keep the same base) of the product of $w^3$ and $y^4$ . Apply the property as seen below and find the final answer.