For two given functions f(x) and g(x), the composite function
(g ° f)(x) is: g(f(x))
Here we will find that the correct option is the last one:
(g°f)(x) = x²-2
To get this, we know that:
g(x) = x + 1
f(x) = x² - 3
Then:
(g°f)(x) = g(f(x))
So here we just need to evaluate g(x) in f(x):
g(f(x)) = f(x) + 1 = ( x² - 3) + 1 = x² - 3 + 1 = x² - 2
Then the correct option is 3:
(g°f)(x) = x²-2
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Write a quadratic function f whose zeros are 2 and 9 .
Substituting these values into the general form of a quadratic equation
f(x) = x² - 11x + 18
A quadratic equation is of the form:
f(x) = x² - (Sum of roots)x + (product of roots)
The given roots are 2 and 9
Sum of roots = 2 + 9
Sum of roots = 11
Product of roots = 2 x 9
Product of roots = 18
Substituting these values into the general form of a quadratic equation
f(x) = x² - 11x + 18
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help........me pls.........
Three times the sum of a number and six is greater than four times the number decreased by two
Final answer:
The mathematical problem is to express 'Three times the sum of a number and six is greater than four times the number decreased by two' as an inequality, resulting in 3(n + 6) > 4n - 2, which simplifies to n < 20.
Explanation:
The question involves translating a word problem into an algebraic inequality. The problem statement 'Three times the sum of a number and six is greater than four times the number decreased by two' can be translated into the inequality 3(n + 6) > 4n - 2, where n represents the unknown number.
To solve this inequality, we would first expand the left side of the equation by distributing, resulting in 3n + 18 > 4n - 2. Then, we would get all n terms on one side and constants on the other, leading to the inequality n < 20.
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What is the difference between the ratio AP:PB and the ratio of AP:AB?
A line segment can be divided into subsegment using ratios. The difference between [tex]AP:PB[/tex] and [tex]AP: AB[/tex] is that:
Ratio [tex]AP:PB[/tex] compares the two subsegments of AB while Ratio [tex]AP: AB[/tex] compares a segment of AB to the whole length of AB.Given:
[tex]AP:PB[/tex] and [tex]AP: AB[/tex]
In [tex]AP:PB[/tex], we can see that AP and PB has a common point (P).
This means that:
[tex]AB = AP + PB[/tex]
i.e. AP and PB are two subsegments of line segment AB.
So, the ratio [tex]AP:PB[/tex] compares the two subsegments of AB
Because AP and PB are two subsegments of line segment AB.
Then, ratio [tex]AP: AB[/tex] compares a segment of AB to the whole length of AB.
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What is the value of 6 in 342.76?
A six ten-thousandths
B six thousandths
C six tenths
D six hundredths
the second digit to the right of the decimal point is the hundredths place
so it is D. 6 hundredths.
What is the value of n?
−6.5(n−5)=18.2
Nicholas bicycled 15.8 kilometers each day for 18 days last month. how many kilometers did he bicycle last month?
Use the number line below to find the midpoint of AD
a sealed rectangular box measuring 8 x 6 x 18 contains 864 sugar cubes, each measuring 1 x 1 x 1. How many sugar cubes are touching the box ?
What's the answer to 1/6d+2/3=1/4(d-2) and can someone explain/work this out with me?
3(t-7) =6. Solve for the and show steps
8(h-9) =8 solve for h and show steps
9+2(z-2) =15 solve for z and show steps
In how money ways can a five-letter license plate be made with the letters from April if none of the letters are repeated ?
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
we have
[tex](x-7)^{2} =36[/tex]
square root on both sides
[tex](x-7)=(+/-)\sqrt{36}[/tex]
[tex](x-7)=(+/-)6[/tex]
[tex]x=(+/-)6+7[/tex]
[tex]x1=6+7=13[/tex]
[tex]x2=-6+7=1[/tex]
therefore
the answer is
[tex]x1=13[/tex]
[tex]x2=1[/tex]
A carpet sells for $27.99 a square yard. what is the price of the carpet per square meter?
I need help with number 26 and 27, thanks.
The number of cars (c) in a parking lot increases when the parking fee (f) decreases. Write the correct equation for this scenario, and solve for the number of cars when the fee is $6. Fee Cars 20 15 30 10
China's population is 1.446×10^9 . Marshall Islands' population is 6.025×10^4 . How many times larger is China's population than Marshall Islands' population? Fill in the blanks.
1.) 0.024
2.) 2.4
3.) 240
4.) 10^4
5.) 10^5
6.) 10^13
___ x ___ times larger
Final answer:
The population of China is approximately 240 times larger than the population of the Marshall Islands. This is calculated by dividing China's population (1.446×[tex]10^9[/tex]) by the Marshall Islands' population (6.025×[tex]10^4[/tex]). (Option 3)
Explanation:
The question asks us to determine how many times larger China's population is compared to the population of the Marshall Islands. To find the answer, we divide the population of China by the population of Marshall Islands:
1.446×[tex]10^9[/tex] (China's population) ÷ 6.025×[tex]10^4[/tex] (Marshall Islands' population).
Carrying out this division, we get a result of approximately 240 times larger. Thus, the population of China is 240 times larger than that of the Marshall Islands.
David played a video game 5 times. The list shows his scores.
4975,5275,4825,5100,4950
What is the difference between the mean and median of the data ?
A.25
B.50
C.75
D.200
E.400
The difference between the mean and median of the data is 50.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
David played a video game 5 times.
The list shows his scores:
4975,5275,4825,5100,4950.
To find the median:
The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. To find the median, firstly arrange the data points in ascending order.
4825, 4950, 4975, 5100 and 5275.
So, the middle number is 4975.
The median is 4975.
To find the mean;
The mean = the sum of the scores / 5
The mean = 25125 / 5
The mean = 5025
The difference:
5025 - 4975 = 50
Therefore, the required difference is 50.
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Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 toher savings. How long will it take her to save enough money to buy the bike?
How many more people attended the Magic's games than attended the pacers' games? 582,295 pacers 715,901 magic
Answer:
133606 persons
Step-by-step explanation:
Number of persons attended the Magic's game= 715,901 games
Number of persons attended the Pacer's game= 582,295 persons
We have to find the number of persons who attend the Magic's game more than Pacer's game.
To find this, we have to find the difference
Number of persons attended the Magic's game= 715,901 games
Number of persons attended the Pacer's game= 582,295 persons
Number of persons who attended More Magic's game= 715901- 582295
Number of persons who attended More Magic's game= 133606 persons
Hence, the correct answer is 133606 persons
What is the distance between points J and K?
-8 to 0 = 8
0 to 4 = 4
8+4 = 12
distance is 12
Which functions have graphs that are less steep than the graph of f(x)= -4x^2
SELECT EACH CORRECT ANSWER
m(x)=5x2
k(x)=4x2
h(x)=−3x2
j(x)=−x2
g(x)=−5x2
The quadratic equations that are less steep than f(x)= -4x² are:
h(x) = -3x² j(x) = -x² Which functions have graphs that are less steep than the graph of f(x)= -4x²?Here we want to identify which equations have graphs less steep than the graph of the quadratic f(x) = -4x²
To identify those, we just need to see which equations have a leading coefficient with a smaller absolute value than |-4| = 4
These equatios are:
h(x) = -3x² ---> With a leading coefficient of -3, absolute value of 3.
j(x) = -x² ---> with a leading coefficient of -1, absolute value of 1.
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Write an equation of the line containing the point (3,5)and perpendicular to the line 2x- 3y
Answer:
The equation of the line would be y = -3/2x + 19/2
Step-by-step explanation:
First we need to solve the original equation for y so that we can find the slope.
2x - 3y = 0
-3y = -2x
y = 2/3x
So since the equation has a slope of 2/3, we know the perpendicular slope would be -3/2 (since perpendicular slopes have opposite and reciprocal slopes). Then we can use this and the ordered pair in point-slope form.
y - y1 = m(x - x1)
y - 5 = -3/2(x - 3)
y - 5 = -3/2x + 9/2
y = -3/2x + 19/2
solve the following equation 3x-5=x+12
What is the range of the following set of numbers? 114, 90, 83, 101, 97, 142, 117, 87, 72
Answer:
The answer is 70
Step-by-step explanation:
Write a story that could describe the expression:-9-5x
Answer:
Step-by-step explanation:
Emily has a lemonade stand she starts with -9 dollars. Everyday Emily loses 5 dollars.
Geometry Help
1. The vertex angle of an isosceles triangle is always acute. (True/False)
2. The base angles of isosceles triangles are always complementary.(True/False)
3.All of the sides of an isosceles triangle are always congruent. (True/False)
i think the first one would be true, second true, and third one would be false... need confirmation
Evaluate the expression (x-2y)^2where x=3and y=2
To evaluate the expression (x-2y)² where x=3 and y=2, substitute the values of x and y into the expression and simplify.
To evaluate the expression (x-2y)² where x=3 and y=2, we substitute the values of x and y into the expression.
Substituting x=3 and y=2 into the expression, we get (3-2*2)².
Solving this expression, we have (3-4)^2 which simplifies to (-1)².
Finally, (-1)² equals 1.
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Find the cost per ounce of a sunscreen made from 100 oz of a lotion that costs $1.50 per ounce and 150 oz of a lotion that costs $4.50 per ounce. (round your answer to the nearest cent.)