Given:
The functions are
[tex]f(x)=-5x^2+4x-9[/tex]
[tex]g(x)=8x^2-3x-4[/tex]
To find:
The value of (f+g)(x).
Solution:
We know that,
[tex](f+g)(x)=f(x)+g(x)[/tex]
Putting the given functions, we get
[tex](f+g)(x)=-5x^2+4x-9+8x^2-3x-4[/tex]
On combining like terms, we get
[tex](f+g)(x)=(-5x^2+8x^2)+(4x-3x)+(-9-4)[/tex]
[tex](f+g)(x)=3x^2+x-13[/tex]
Therefore, the required function is [tex](f+g)(x)=3x^2+x-13[/tex].
8
BONUS QUESTION: A swimming pool is in the shape of a triangular prism. From the top down, the triangle's base has a length of 22 ft and a height of 11 ft.
The pool is 17.5 ft deep. If it takes 4.83 gallons of Jell-o to fill 2 cubic foot of space, how many gallons of Jell-o will it take to completely fill the pool? (Round the
gallons up).
Answer:
Good luck Dude
Step-by-step explanation:
What is the area of this figure ?
Answer:
52920cm
all you have to do is multiply all the numbers together.
sorry if its wrong.
but hope it helps.
have a great day.
Answer:
102
Step-by-step explanation:
area of the square (36) plus the area of the trapezoid (66)
For the base b of a logarithmic function, b>0 and b≠1
True
False
calcular el tamaño de muestra para una poblacion de 543.098 consumidores de una marca de bebida gaseosa donde el investigador asigna un nivel de confianza de 95% y una margen de error de 3% con una probabilidad de existo de 70% y de fracaso 30%
Answer:
m m m m m m
Step-by-step explanation:
mmmmmmmmm m m m m m m mm m m m m m m
The following stem-and-leaf plot represents the distribution of weights for a group of people.
Stem
Leaves
11
2
4 5 5
6
12
1
3 3
4 5
13
4
6
6
7
14
24
4
7 7
15
0
4
6
6 7
99
16
6
6
7
8
17
2 4
6
6
9
18
5 7
19
0 1
5 9
Step 2 of 3: How many people weigh in the range from 140 to 180 inclusive?
Answer:
the stem and leaf plot is invalid. please provide a diagram.
What is the area of this triangle?
Enter your answer in the box.
Answer:
10 square units
Step-by-step explanation:
Base of triangle (b) = 4 units
Height of triangle (h) = 5 units
Therefore,
Area of triangle
[tex] = \frac{1}{2} bh \\ \\ = \frac{1}{2} \times 4 \times 5 \\ \\ = 2 \times 5 \\ \\ = 10 \: {units}^{2} [/tex]
Colbert's backyard has two trees, shown below. The height of shorter tree is 3/5 of the height of the taller tree. If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree?
Answer:
The height of the taller tree is 7.5 feet.
Step-by-step explanation:
I am going to say that:
The height of the shorter tree is x.
The height of the taller tree is y.
The height of shorter tree is 3/5 of the height of the taller tree.
This means that [tex]x = \frac{3y}{5}[/tex]
If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree?
This means that [tex]x = 4 + \frac{1}{2} = \frac{8+1}{2} = \frac{9}{2}[/tex]
We want to find y.
[tex]x = \frac{3y}{5}[/tex]
[tex]\frac{9}{2} = \frac{3y}{5}[/tex]
[tex]6y = 45[/tex]
[tex]y = \frac{45}{6}[/tex]
[tex]y = 7.5[/tex]
The height of the taller tree is 7.5 feet.
Question 11
Rhonda deposits $5,600 in a savings account that pays 1.36% Interest, compounded semiannually. What is the balance after the first 9 months?
Answer:
follow me please and give thanks
find the inequality represented by the graph
Answer:
y is greater than or equal to -2x-5
Step-by-step explanation:
First find the slope which is -2x and then find the y-intercept which is -5 and then you can just test out if its greater than or equal to, or less than or equal to. To do this you just fill in the point 0,0 and if you do that you should get 0 is greater than (you can ignore the "or equal to") -5 and is that true? Yes it is! so then the side of the line that the point 0,0 is on should be shaded and since it is your answer is right!
Hope this helped!
Eli saves money each month to buy a new computer.
The total amount he has saved, T, can be calculated
by the equation T = 83 + 30m, where m is the
number of months since he started saving. What
does the number 83 represent in the equation?
Answer:
The money he already had when he started saving.
Step-by-step explanation:
Eli begin with $83 during month [m] = 0 and saved money onwards starting from month one.
What does the constant (c) in the equation → y = mx + c indicates?The constant (c) in the equation - y = mx + c, indicates the value of (y) at
x = 0. This means that it indicates the value of (y) even before the value of (x) started to increase.
Given is the equation → T = 83 + 30m representing the money saved by Eli each month to buy a new computer.
The equation given is -
T = 83 + 30m
When compared to the equation of the straight line -
y = mx + c
We get -
c = 80
This shows that Eli begin with $83 during month [m] = 0 and saved the money onwards starting from first month.
Therefore, Eli begin with $83 during month [m] = 0 and saved money onwards starting from month one.
To solve more questions on Amount estimation, visit the link below-
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एक कार की गति 92.4 किमी प्रति घंटा है यह 20 मिनट मे कितना दुरी तय करेगी
Answer:
mate I will surely help if nut pls translate it in English as I can barely read hindi
Use structure: How is subtracting -4x from 9x similar to subtracting -4 from 9?
Answer:
It is the same thing except for subtracting -4x and 9x, you subtract -4 and 9 and just add x at the end
Find 2/3 of 24
Help ASAP plz!! Got to get finished tonight
Answer:
16
Step-by-step explanation:
[tex](\frac{2}{3} )*24=16[/tex]
What is -6k + 7k simplified?
Answer:
1k
Step-by-step explanation:
-6k+7k=1k
or
7k-6k=1k
Answer:
The answer would be found by adding -6 and 7 k so itd be 1k or just k
A rental car company charges $36.41 per day to rent a car and $0.11 for every mile
driven. Kaylee wants to rent a car, knowing that:
• She plans to drive 50 miles.
• She has at most $360 to spend,
Which inequality can be used to determine d, the maximum number of days Kaylee
can afford to rent for while staying within her budget?
360 > 5.5 + 36.41d
360 > 5.50 + 36.41
Submit Answer
360 < 5.5 + 36.41d
360 < 5.5d + 36.41
Answer: 360>5.5+36.41d
Step-by-step explanation:
Exact distance between (-1,-9) and (5,-5)
[tex]2 \sqrt{13} [/tex]
that is your answer
Sylvia had a small box. She filled it with 64 triangle pattern blocks. She said "The volume of this box is 64 cubic units." Do you agree with Sylvia? Why or why not?
Answer:
I do not agree with Sylvia
Step-by-step explanation:
Given
1 small box
64 triangle pattern blocks
Required
Is she right?
From the question, we understand that she fills the box with 64 blocks.
For the fact that she did this; it does not mean that the volume of the small box is 64 cubic units (even if she filled the box completely and the triangle pattern blocks are identical)
The reason for this is that, the volume of each box may not be 1 cubic unit.
So, first she needs to determine the volume of each pattern block, then multiply by 64. If the result is 64, then the volume of the box is 64 cubic units.
Since, it is not stated, we will not make any assumptions.
Hence, I do not agree with Sylvia.
Mary has two sisters. Her younger sister is 5 years younger Her older
sister is twice her age. Their ages add up to 47. How dd is Mary and each
of her sisters?
please help me with this question
Answer:
18
Step-by-step explanation:
Macy has completed 78% of the 50 questions on the test. How
many questions has Macy completed?
Answer:
39
Step-by-step explanation:
Answer:
78% = 78/100
= 0.78
78% of the 50 i equal 0.78 x 50 = 39
Macy has completed 39 questions
Suppose P(t)represents the population of a certain mosquito colony, where. t is measured in days. The current population of the colony is known to be 574 mosquitos; that is, P(0)=574. If P'(0)=50 mosquitos per day, estimate the size of the population in 10 days.
Answer:
The estimated size of the population in 10 days is of 1372 mosquitos.
Step-by-step explanation:
Population after t days:
The population after t days is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
P(0)=574.
So
[tex]P(t) = 574e^{rt}[/tex]
P'(0)=50
[tex]P^{\prime}(t) = 574re^{rt}[/tex]
Since P'(0)=50
[tex]574r = 50[/tex]
[tex]r = \frac{50}{574}[/tex]
[tex]r = 0.0871[/tex]
So
[tex]P(t) = 574e^{0.0871t}[/tex]
Estimate the size of the population in 10 days
This is P(10).
[tex]P(10) = 574e^{0.0871*10} = 1372[/tex]
The estimated size of the population in 10 days is of 1372 mosquitos.
The size of the population of mosquito follows an exponential model.
The size of the population in 10 days is 1370
The given parameters are:
[tex]\mathbf{P(0) = 574}[/tex]
[tex]\mathbf{P'(0) = 50}[/tex]
An exponential function is represented as:
[tex]\mathbf{P(t) = P(0) \times e^r^t}[/tex]
So, we have:
[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]
Differentiate
[tex]\mathbf{P'(t) = 574r}[/tex]
Substitute 0 for t
[tex]\mathbf{P'(0) = 574r}[/tex]
Substitute [tex]\mathbf{P'(0) = 50}[/tex]
[tex]\mathbf{50 = 574r}[/tex]
Divide both sides by 574
[tex]\mathbf{0.087 = r}[/tex]
So, we have:
[tex]\mathbf{r = 0.087 }[/tex]
The function becomes
[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]
[tex]\mathbf{P(t) = 574 \times e^{0.087t}}[/tex]
In 10 days, t = 10.
So, we have:
[tex]\mathbf{P(10) = 574 \times e^{0.087 \times 10}}[/tex]
[tex]\mathbf{P(10) = 574 \times e^{0.87}}[/tex]
Solve
[tex]\mathbf{P(10) = 1370}[/tex]
Hence, the size of the population in 10 days is 1370
Read more about exponential functions at:
https://brainly.com/question/11487261
PLEASE HELP
180% is equiliant of which decimal .....
Answer:
180% is equivalent to the decimal 1.8
Answer:
answer is 1.8 hope it helps
[tex]0.004 \times 0 .81[/tex]
63% of US adults opposed to taxes on junk food and soda. You randomly select 10 US adults. Find the probability that the number of adults who oppose special tax on junk food and soda (a) exactly one, (b) at least four, and (c) less than eight
Answer:
a) 0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.
b) 0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.
c) 0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they are opposed to taxes on junk food and soda, or they are not. Each adult is independent of other adults, which means that the binomial probability distribution is used to solve the question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
63% of US adults opposed to taxes on junk food and soda.
This means that [tex]p = 0.63[/tex]
You randomly select 10 US adults.
This means that [tex]n = 10[/tex]
(a) exactly one
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]
0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.
(b) at least four
This is
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.63)^{0}.(0.37)^{10} \approx 0[/tex]
[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]
[tex]P(X = 2) = C_{10,2}.(0.63)^{2}.(0.37)^{8} = 0.0063[/tex]
[tex]P(X = 3) = C_{10,3}.(0.63)^{3}.(0.37)^{7} = 0.0285[/tex]
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0008 + 0.0063 + 0.0285 = 0.0356[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0356 = 0.9644[/tex]
0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.
(c) less than eight
This is
[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]
In which
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.63)^{8}.(0.37)^{2} = 0.1529[/tex]
[tex]P(X = 9) = C_{10,1}.(0.63)^{9}.(0.37)^{1} = 0.0578[/tex]
[tex]P(X = 10) = C_{10,2}.(0.63)^{10}.(0.37)^{0} = 0.0098[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1529 + 0.0578 + 0.0098 = 0.2205[/tex]
[tex]P(X < 8) = 1 - P(X \geq 8) = 1 - 0.2205 = 0.7795[/tex]
0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.
6xy^3 * 4x^2y^2 answer
what is the area of the figure
Answer:
I can not see the question
Step-by-step explanation:
Please post the question with the picture on your profile so I can attempt it
which expression is equivalent to (5m) ^3
Answer:
5m•5m•5m
Step-by-step explanation:
so you multiply the factor by itself as many times as the exponent says so if the factor is 5m you would multiply it by the exponent which in this case is 3
5m.5m.5m and 125m³ is the equivalent expressions of the expression (5m)³.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (5m)³
We have to find the equivalent expression of (5m)³
Equivalent expressions are expressions that work the same even though they look different
(5m)³ can be written as 5m.5m.5m
The value of five cube is one hundred twenty five.
125m³
Hence, 5m.5m.5m and 125m³ is the equivalent expressions of the expression (5m)³.
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If f(x) = -(5)x , what is f(2)?
Answer:
-10
Step-by-step explanation:
f(2) = 2 x -5
= -10
The answer is -10
Which image below shows the result of an image that has been rotated 180 by the origin O?
7.) Which of the following are some of the possible solutions for the inequality?
-9w <-54
A. 6, 7, 8, 9
B. 6,5, 4,3
C.-6, -5, -4,-3
D. -6, -7,-8,-9
Answer:
A
Step-by-step explanation:
We will solve this inequality by dividing both sides by -9.
Remember, whenever you multiply or divide both sides by a negative number, the sign must be switched.
So we get:
[tex]w>6[/tex]
The only answer that has possible solutions that are greater than 6 is A.