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Semenov [28]
3 years ago
12

Let f(x) = 4 – x^2, g(x) = 2 – x. Find (f + g)(x) and its domain.

Mathematics
1 answer:
PtichkaEL [24]3 years ago
8 0

Step-by-step explanation:

f(x)=4-x^2,\ g(x)=2-x\\\\(f+g)(x)=f(x)+g(x)\\\\\text{therefore}\\\\(f+g)(x)=(4-x^2)+(2-x)=-x^2-x+(4+2)=-x^2-x+6\\\\\text{It's the quadratic function. The domain is the set of all real numbers}\ x\in\mathbb{R}

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Pls help
KATRIN_1 [288]

Answer:

169.04 in² (nearest hundredth)

Step-by-step explanation:

Surface area of a cone = \pir² + \pirl

(where r = radius of the base and l = slant height)

Given slant height l = 10 and surface area = 188.5

Surface area  = \pir² + \pirl

188.5 = \pir² + 10\pir

\pir² + 10\pir - 188.5 = 0

r = \frac{-10\pi +\sqrt{(10\pi )^2-(4\times\pi \times-188.5)} }{2\pi } = 4.219621117...

Volume of a cone = (1/3)\pir²h

(where r = radius of the base and h = height)

We need to find an expression for h in terms of l using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height

r² + h² = l²

h² = l² - r²

h = √(l² - r²)

Therefore, substituting found expression for h:

volume of a cone = (1/3)\pir²√(l² - r²)

Given slant height l = 10 and r = 4.219621117...

volume = 169.0431969... = 169.04 in² (nearest hundredth)

5 0
2 years ago
Read 2 more answers
What is the perimeter of triangle ABC? 20 units 22 units 24 units 26 units
Alex777 [14]
8[2] + 6[2] = c[2]
64 + 36 = c[2]
100 = c[2]
c = 10

8 + 6 + 10 = 24 units
8 0
3 years ago
Read 2 more answers
Nine times a number decreased by four is at least twenty three
Andru [333]
The answer is any whole number larger than 3
6 0
3 years ago
A large spherical balloon is being deflated
artcher [175]

The formula for volume of a sphere is V = 4 /3 x π x r3 (cubed).

The original radius of the balloon is 10 ft, so when we plug that value into the equation we get 4188.79. When the balloon deflated, the new radius was 5 ft, so the new volume is 523.6. The question asks how much volume was lost, so we need to subtract 4188.79 - 523.6 and get approximately 3665.

Hope this helps! I hate taking usa test prep quizzes too haha.

7 0
3 years ago
Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the applicants are qua
Dafna11 [192]

Answer:

\displaystyle P=\frac{7}{15}=0.467

Step-by-step explanation:

<u>Probabilities</u>

When we choose from two different sets to form a new set of n elements, we use the so-called hypergeometric distribution. We'll use an easier and more simple approach by the use of logic.

We have 6 republicans and 4 democrats applying for two positions. Let's call R to a republican member and D to a democrat member. There are three possibilities to choose two people from the two sets: DD, DR, RR. Both republicans, both democrats and one of each. We are asked to compute the probability of both being from the same party, i.e. the probability is

P=P(DD)+P(RR)

Let's compute P(DD). Both democrats come from the 4 members available and it can be done in \binom{4}{2} different ways.

For P(RR) we proceed in a similar way to get \binom{6}{2} different ways.

The total ways to select both from the same party is

\displaystyle \binom{4}{2}+\binom{6}{2}=4+15=21

The selection can be done from the whole set of candidates in \binom{10}{2} different ways, so

\displaystyle P=\frac{21}{\binom{10}{2}}

\displaystyle P=\frac{21}{45}=\frac{7}{15}=0.467

3 0
3 years ago
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