The graph of the function f(x) = (x − 3)(x + 1) is shown.
Which describes all of the values for which the graph is positive and decreasing?
A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3
Answers
Answer:
The correct option is A.
Step-by-step explanation:
The given function is
[tex]f(x)=(x-3)(x+1)[/tex]
Equate f(x)=0 to find the x-intercepts of the function.
[tex]0=(x-3)(x+1)[/tex]
[tex]x=3,-1[/tex]
The x-intercepts of the function are -1 and 3. From the below graph it is clear that,
In x<-1, the function is positive and decreasing.
In -1<x<1, the function is negative and decreasing.
In 1<x<3, the function is negative and increasing.
In x>3, the function is positive and increasing.
Therefore the correct option is A.
Related Questions
the temperature of a pot of water is shown. the temperature of the water changed -2.5 degree F per minute. What was the temperature after 20 minutes?
Answers
=-50
(40 points + Brainliest for right answer).
Answers
Which equation represents the linear function that is shown on the graph below?
ANSWERS:
y= 1/2x +4
y= 1/2x -2
y= 4x -2
y= -2x +4
Answers
which is the same as y = (1/2)x - 2 or can be written as [tex]y = \frac{1}{2}x - 2[/tex]
If you wanted the decimal form version, then the equation would be y = 0.5x - 2
------------------------------------------
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Explanation:
The four points on this line are
(4,0)
(6,1)
(8,2)
(10,3)
Let's pick two of these points to find the slope.
The two points I'll pick are (4,0) and (6,1)
The first point is (4,0) so (x1,y1) = (4,0) meaning that
x1 = 4
y1 = 0
The second point is (6,1) so (x2,y2) = (6,1) meaning that
x2 = 6
y2 = 1
Using the slope formula, we find...
m = (y2 - y1)/(x2 - x1)
m = (1-0)/(6-4)
m = 1/2
m = 0.5
The slope in fraction form is 1/2. This means that each time we move up 1 unit, we move to the right 2 units.
slope = rise/run = 1/2
Rise = 1
Run = 2
The fraction 1/2 is equivalent to the decimal form 0.5
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Let's use the slope m = 0.5, along with the point (x,y) = (4,0) to find the y intercept b
y = m*x + b
y = 0.5*x + b
0 = 0.5*4 + b
0 = 2 + b
0 - 2 = 2 + b - 2
-2 = b
b = -2
The y intercept is -2 meaning that the line crosses the vertical y axis at -2.
Therefore the equation is y = 0.5x - 2 after we update y = mx+b
This is the same as y = (1/2)x - 2 or y = 1/2x - 2 which is why choice B is the answer. The parenthesis help make it clear that x is not in the denominator; though technically they aren't needed.
The equation y = (1/2)x - 2.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
We have points from the graph (6,1) and (8,2).
The slope of the equation is;
m = (2-1) / (8-6)
m = 1/2
And the y-intercept;
We have the slope-intercept form of the equation,
y = mx + b
y = x/2 + b
To find the y-intercept, we substitute the point (6,1)
b = -2
Therefore, we have the equation of the linear function y = (1/2)x - 2.
To learn more about the function;
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50 POINTS!!!
Suzanne ran 3 3/4 miles in the morning and 4 1/2 miles in the afternoon. How many kilometers did she run altogether? Assume 1 mile = 1.6 kilometers.
Answers
3 3/4 = 15/4
15/4 + 18/4 = 8 1/4 or 33/4
33/4 * 1.6/1 = 52.8/4 = 13.2
When assuming 1 mile equals 1.6 kilometers, Suzanne ran 13.2 kilometers in all.
Answer:- Total distance traveled by Suzanne in kilometers=13.2 kilometers.
Explanation:-
Distance traveled by Suzanne in the morning=[tex]3\frac{3}{4}\text{ miles}[/tex]
Distance traveled by Suzanne in the evening=[tex]4\frac{1}{2}\text{ miles}[/tex]
Total distance traveled by Suzanne=[tex][3\frac{3}{4}+4\frac{1}{2}\text{ miles}[/tex]
[tex]=\frac{15}{4}+\frac{9}{2}\text{ miles}[/tex]
[tex]=\frac{15+18}{4}\text{ miles}[/tex]
[tex]=\frac{33}{4}\text{ miles}[/tex]
[tex]=8.25\text{ miles}[/tex]
Total distance traveled by Suzanne in kilometers=[tex]8.25\times1.6\text{ kilometers}=13.2\text{ kilometers}[/tex]
Total distance traveled by Suzanne in kilometers[tex]=13.2\text{ kilometers}[/tex]
Is the symbol (x¯¯) used for the population mean or sample mean?
choices are.....
population mean
sample mean
Answers
x=poluation mean
The symbol x is the sample mean, and the Greek symbol μ is the population mean.
Explanation:The symbol x is the sample mean, and the Greek symbol μ is the population mean. Calculating the Standard Deviation: If x is a number, then the difference x - mean is called its deviation. In a data set, there are as many deviations as there are items in the data set. The deviations are used to calculate the standard deviation. If the numbers belong to a population, in symbols, a deviation is x - μ. For sample data, in symbols, a deviation is x - x.
A condo in Culver City, California, listed for $1.4 million with 20% down and financing at 5% for 30 years. What's the monthly payment?
Answers
Answer:
Step-by-step explanation:
$6,014.40
Convert 5.4 ⋅ 103 to standard form. 0.0054 0.00054 5,400 54,000
Answers
Answer:
5400
Step-by-step explanation:
Convert 5.4 ⋅ 103 to standard form.
[tex]5.4 \ times \ 10^3[/tex]
for 10^3 we add 3 zeros
10^3= 10 times 10 times 10=1000
[tex]5.4 \ times \ 10^3[/tex]
Replace 10^3 by 1000. then multiply with the decimal number
[tex]5.4 \ times \ 1000[/tex]
When we multiply by 1000 we move the decimal point 3 places to the right
5400
A child can explain that 3x2 represents three sets of two
Answers
A child can correctly explain that 3 x 2 represents three sets of two. This child is most likely in Piaget's Concrete Operational stage option (C) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
As we know,
A young toddler may properly identify three sets of two as being represented by 3 x 2.
This child is most likely in Piaget's Concrete Operational stage.
Thus, a child can correctly explain that 3 x 2 represents three sets of two. This child is most likely in Piaget's Concrete Operational stage option (C) is correct.
The complete question is:
A child can correctly explain that 3 x 2 represents three sets of two. This child is most likely in Piaget's _____________ stage.
sensorimotor stagepreoperationalconcrete operationalformal operationalLearn more about the arithmetic operation here:
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The difference in elevation of a helicopter and a submarine is 18 1/2 meters. The elevation of the submarine is -7 3/4 meters. Write and solve an equation to find the elevation h (in meters) of the helicopter
Answers
One way in which to write an equation here is |-7 3/4 meters| + h = 18 1/2.
the difference in elevation = h - s = 18 1/2
the question gives us the value of s: -5 3/4
so sub that into our first equation
h - (-5 3/4) = 18 1/2
h + 5 3/4 = 18 1/2
h = 18 1/2 - 5 3/4
h = 12 3/4
hope it helps :)
Over a 12 hour period from 8 pm to 8 am the tempeture fell a steady rate 8°F to 16°F if the temperature fell at the same rate every hour what was the temperature at 4 am
Answers
12 hour period from 8pm to 8am
temperature dropped from 8°F to 16°F from 8pm to 8am
We need to find temperature at 4 am.
We can start by setting up points:
8pm is are starting point with 8°F, we can express it as (0,8), 0 represents initial time from 0 to 12 hour span.
8am is the ending point with 16°F, we can express it as (12,16), 12 represents the end time of 0 to 12 hours span.
We will use these points to find slope.
slope=m=(16-8)/(12-0)=8/12=2/3
Now, we can set up an expression to find any temperature at a specific time. Aslo, x represents the hours not the the specific time of 4am. We will use 8 since 4am is the 8th hour of the 12 hour span. Using slope of 2/3 and the y intercept of (0,8) since we were already at 8°F at the initial time of 0 we have the function:
f(x)=2/3x+8
f(8)=2/3(8)+8= 40/3≈13.3°
A laptop has a listed price of 715.95 before tax. If the sale tax rat is 9.25%, find the cost of the laptop with the sales tax included. Round your answer to the nearest cent, as necessary.
Answers
About 19/20 of celery is water. What percent is this
Answers
So, 20x5= 100
19x5=95
So, your answer is: 95%
19/20
You need to get the denominator to 100.
20 x 5 = 100
19 x 5 = 95
It is 95%
Hope This Helps You!
Good Luck :)
- Hannah ❤
mrs. baker purchased a number of juice packs at a cost of $0.30 each and a loaf of bread that cost $1.19. the total cost of her purchases was 2.99. which equation would you use the determine how many juice packs mrs. baker purchased
Answers
hope this helps
Answer:
0.30j + 1.19 = 2.99
Step-by-step explanation: Hope this helps! :D
After doing this I got 1/4. Can someone plz show and explain what I did wrong? 7- 3r = r - 4(2 + r)
Answers
7-3r=r-8-4r
Combine like terms
7-3r=-4-3r
Add 3r to both sides
7=-8
The resulting statement is false so there is no real number solution.
Final answer: No solution
sales price is 67.50 sales tax is 5% how much is the total amount paid
Answers
x/67.5=5/100
cross multiply
100x=337.5
divide 100
x=3.375 or 3.38
67.50+3.38= 70.88
At a pet store, Davina counted 12 parrots out of 20 birds. What is an equivalent ratio of parrots to birds in the pet store?
Answers
:what does this problem solve as
1/2(4x−5)+52=10
Answers
Paul is riding his bike 48 miles to the beach. His average rate of speed is 13.8 miles per hour. Paul stopped for a snack after 3 hours. How many miles does he have to go after his snack? Round your answer to the nearest tenth if necessary.
Answers
13.8 miles per hour x 3 hours = 41.4 miles ( what he already rode)
48 - 41.4 = 6.6 more miles to go
Picture above, please make sure to show work:)
Answers
= (3.14)(8^2)(8)
= (3.14)(8*8)(8)
= (3.14)(512)
= 1607.7 in^3
Atif has a z score of 1.02 from a converted iq score. from a z table, the percentage between his score and the mean is 34.61%. what percent of people have iqs at or lower than atif's score?
Answers
Explanation.
Refer to the diagram shown below.
When the z-score is z = 0, then the area under the distribution curve is 50%, which corresponds to the mean, μ.
The given z-score is greater than zero, so the shaded area is 34.61%. to the right of z=0
The area to the left of z = 1.02 is 50% + 34.61% = 84.61%.
This percentage represents the people with IQs at or lower than Atfif's score.
At a sports camp, there is one counselor for every 12 campers. If there are 156 campers attending the camp, which equivalent ratios could be used to find the number of counselors?
Answers
It is 1:12 for counselor to camper
If there are 156 campers, follow these steps:
1 + 12 = 13
156/12 = 13
1 x 13 = 13
12 x 12 = 156
The ratio now is 13:156.
Meaning there are 13 counselors.
Hope This Helps You!
Good Luck :)
- Hannah ❤
The equivalent ratios could be used to get the number of counselors who will be 13.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
At a sports camp, there is one counselor for every 12 campers.
If there are 156 campers attending the camp.
The equivalent ratios could be used to get the number of counselors who will be
⇒ 156 / 12
⇒ 13
The equivalent ratios could be used to get the number of counselors who will be 13.
More about the division link is given below.
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Prove the identity csc^2xsec^2x=sec^2x+csc^2x
Answers
Lucy is thinking of a number.The number is greater than two hundred twenty- five. her number is less than 2 hundred 2 tens 7 ones. what is lucy's number?
Answers
I am trying to add more characters
Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does not react with water but it does react with nitric acid. Silver tarnishes when exposed to air or light. What is a physical property of silver?
Answers
density because everything else would fall under the category of chemical properties instead of physical properties and the other 3 properties would result in a chemical change while density would not
The shortest side of a right triangle measures 11m. The lengths of the other two sides are consecutive integers. Find the lengths of the other two sides.
Answers
Then (11 m)^2 + x^2 = sum of the squares of the 2 shortest sides
= (x+1)^2
121 + x^2 = x^2 + 2x + 1. Then 121 = 2x + 1, and 2x = 120, or x = 60.
Then the hyp. has length 60+1= 61.
We must check these results. Using the Pyth. Thm. (a^2 + b^2 = c^2),
11^2 + 60^2 = 61^2
121 + 3600 = 3721 This is true, so our answers are correct.
The longer side is 60 and the hyp. has length 61.
In a fraternity with 37 members, 18 take mathematics, 5 take both mathematics and art history, and 8 take neither mathematics nor art history. How many take art history but not mathematics?
Answers
fraternity of 32 members with 8 taking neither math or physics
Of the 24, 5 took both. 24 - 5 = 19 taking one. 18 taking just Math.
Just 1 took only Physics.
checking our answer:
just Math 18
just Physics 1
both 5
neither 8
total 32
just physics = 32 - 8 -5 -18 = 1
Answer:
Fraternity of 32 members with 8 taking neither math or physics
Of the 24, 5 took both. 24 - 5 = 19 taking one. 18 taking just Math.
Just 1 took only Physics.
Step-by-step explanation:
What is the quotient of d-2 / d4-6d3+d+17=
A. d3− 4d2 + 9d + 35 B. d3− 8d2 + 17d –17 C. d3− 8d2 + 16d − 31 R 79 D. d3– 4d2– 8d –15 R–13
Answers
We have (d⁴-6d³+d+17) ÷ (d-2)
Step 1:
Multiply d by a term that would give result of d⁴
The aim of this working out is to eliminate on one term at a time, starting from the highest polynomial
We have d⁴ ÷ d = d³ (Write this on the top)
Step 2:
Multiply back d³ by (d - 2) to get d⁴ - 2d³
Step 3:
Then subtract (d⁴ - 2d³) from (d⁴ - 6d³ + 0d² + d + 17)
Notice that the term d⁴ is now eliminated
We have (-6d³ - -2d³) = (-4d³)
Then pull down the third term which is 0d²
We have the sum -4d³ + 0d²
Step 4:
Divide (-4d³) by (d) to get (-4d²)
Write (-4d²) next to (d³) on the top
Step 5:
Then multiply back (-4d²) by (d - 2) to get (-4d³+8d²)
Step 6:
Subtract (-4d³+8d²) from (-4d³ + 0d²) to get (-8d²) then pull down the next term (d) to make the sum (-8d² + d)
Notice that the term -4d³ is now eliminated
Step 7:
Divide -8d² by d to get -8d
Write -8d on the top, next to d³ - 4d²
Step 8:
Multiply back (-8d) by (d - 2) to get (-8d² + 16d)
Step 9:
The subtract (-8d² + 16d) from (-8d + d) to get (-15d + 17)
Notice that the term (-8d²) has been eliminated
The last step is to divide -15d by d to get -15
Write -15 on the top next to the sum d³ - 4d² - 8d
Then multiply -15 by (d-2) to get -15d + 30
Subtract (-15d + 30) from (-15d + 17) to get a REMAINDER of 13
The answer is d³ - 4d² - 8d - 15 R 13
OPTION D
Answer:
Step-by-step explanation:
hey can the other person get brainliest. thanks
4 1/6 divided by 1 2/3 =
Answers
if so then the answer is
5/2 or mixed number form would be 2 1/2
25/6 divided by 5/3. Since the LCD is 6, let's rewrite that as 25/6 div. by 10/6.
Answer: 25/10 = 2.5, or 2 1/2
Lin was waiting to check out at a store. She estimated her total bill to be $20. The actual total was $24.16. What is the difference between Lin’s estimate and the actual total?
Answers
Answer:
4.16
Step-by-step explanation:
Sence Lin estimated $20 and her actucal bill was $24.16. To find the difference, we subtract 20 from 24.16.
[tex]24.16-20=4.16[/tex]
Find f. f '''(x) = cos(x), f(0) = 4, f '(0) = 2, f ''(0) = 6
Answers
f'''(x) = Cos(x)
f''(x) = sin(x) + 6 after f''(0) = 6
f'(x) = -cos(x) + 6x + 2 after f'(0) = 2
f(x) = -sin(x) + 3x^2 + 2x + 4 after f(0) = 4