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2 years ago

A painter leans a 12-foot ladder against a house. The base of the ladder is

Mathematics

1 answer:

tatiyna2 years ago

8 0

11.3 feet.

12 squared (144) minus 4 squared (16) is equal to 128. The square root of 128 is approximately 11.3.

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Which best explains how you know that P(2, 7) is on the same line as Q(7, 4) and R(12, 1)?

Helen [10]

Answer:

See explanation below

Step-by-step explanation:

The best explanation is noticing that in order to get from the point R (12, 1) to the point Q (7, 4) we move 5 units to the left and 3 units up. And to go from point Q (7, 4) to point P (2, 7) we do exactly the same: move 5 units to the left and 3 units up. That means that these points are all connected via the same rate of change: - 3/5, which is in fact the slope of the line the three points belong to.

4 0

3 years ago

Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

7 0

3 years ago

The population of a town was 7652 in 2016. The population grows at a rate of 1.6% annually.

Serggg [28]

Answer:

(A) The population's growth rate in equation form is y = (0.016t * 7652) + 7652

(B) y = (0.016t * 7652) + 7652 =

y = (0.016(8) * 7652) + 7652 =

y = (0.128 * 7652) + 7652 =

y = 979.456 + 7652 =

y = 8631.456 (Or About) 8631

Step-by-step explanation:

(A) Y = the total population of the town. 0.016 is 1.6% just in its original form. T = the year in which were trying to find the town's total population. 7652 is the total population of the town in 2016. With this information, the equation reads, The total population of the town (Y) is equal to 16% (0.016) of the current year's population (T) added to 2016's population of 7652. (This last sentence can also be read what is 1.6% of the towns population in the year were trying to find. Because the population is always growing, 1.6% gets multiplied as to scale with the total population in year T)

(B) We just substitute (T) for 2024, or 8 years after 2016 (2024-2016) and simplify the equation we made.

7 0

3 years ago

The Jackson's are taking out a $35,000 loan to remodel their home. The tables below show the rates for a 1-year and a 5-year loa

Vladimir [108]

Answer:

have a good day :)

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Solve for w: -4u-w = u+6w