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soldi70 [24.7K]
3 years ago
5

Gena attached a dog ramp to her sofa, which allows her oldest dog to easily climb onto a seat cushion. The ramp is 55 inches lon

g. The top of the seat cushion is 28 inches above the floor.
What is the distance from the base of the ramp to the base of the sofa? Enter your answer, rounded to the nearest tenth.
Mathematics
1 answer:
N76 [4]3 years ago
3 0
If we were to view the ramp from its side, the profile would resemble a right triangle with a 90 degree angle where the sofa meets the floor.

In this case, the two legs of the right triangle are 55 inches and 28 inches, and we looking for the length of the hypotenuse.

We can use Pythagorean Theorem which states:

a^2 + b^2 = c^2

 where a and b are the legs, and c is the hypotenuse.

55^2 + 28^2 = c^2

3025 + 784 = c^2

c^2 = 3809

c =  \sqrt{3809}

c = 61.717 inches

To the nearest tenth, the answer is 61.7 inches.
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Angie divides the polynomial function f(x)=x3+3x2−7x−21 by (x + 3). What can she conclude from the fact that the remainder is eq
iren [92.7K]

Answer:

See below

Step-by-step explanation:

<u>Given function</u>

  • f(x)=x³ + 3x²- 7x - 21

<u>We can find its factors:</u>

  • x³ + 3x² - 7x - 21 =
  • x²(x + 3) - 7(x + 3) =
  • (x² - 7)(x + 3)

We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)

Also one of zeros of the function is -3

8 0
3 years ago
Anyone good at composite functions??
sammy [17]

\bf \begin{cases} ~\hfill f(x) = &-3x+4\\ ~\hfill g(x) = &x^2\\ (g \circ f)(0)=&g(~~f(0)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(0) = -3(0)+4\implies \boxed{f(0) = 4} \\\\\\ g(~~f(0)~~)\implies g\left( \boxed{4} \right) = (4)^2\implies \stackrel{(g \circ f)(0)}{g(4)} = 16

6 0
3 years ago
Find the geometric mean of 24 and 32
Maru [420]

Answer:

27√39

Step-by-step explanation:

To calculate the geometric mean we need to first of all multiply 24 and 32 and take the square root of it (i.e. 24*32 is 768, √768 is 27.712.....). However, in this case, we need to represent the answer in a simplified surd. To do this we need to find the highest possible perfect square that is below 768. Here it is 27 because 27*27 equals 729. Now we can go ahead and subtract 768 by 729. We get 39. So now we got two different surds. √729 and √39. We can simplify the √729 to 27. Thus our answer is the combination of both 27*√39 or 27√39.

8 0
3 years ago
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Triangle PQR hAS vertices P (4,-1),Q(-2,7), and R (9,9). find an equation of the median from R
strojnjashka [21]
A median intersects at the midpoint of the opposite length. The midpoint is:

x,m = (4+-2)/2 = 1
y,m = (-1+7)/2 = 3

The midpoint is at (1,3). With this point and point R(9,9), the equation would be:

y = mx + b, where
m = (9 - 3)/(9 - 1) = 0.75
b is the y-intercept
Substituting any point,
3 = 0.75(1)+b
b = 2.25

Thus, the equation for the median is:

y = 0.75x + 2.25
7 0
3 years ago
When rolling a pair of dice at the Bellagio Casino in Las Vegas, there is 1 chance in 36 that the outcome is a 12.
nasty-shy [4]
Yes, that is correct. likewise, the odds of rolling a 1 are \frac{1}{36}
3 0
3 years ago
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