Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
f(x) = x-7
g(x) = x^2
f(4) = 4-7 = -3
g(f(4)) = (-3)^2
(-3)^2 = 9
g(f(4)) is 9
Find f(g(4)).
f(g(4)) = f(g(4)) = 9
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
Composition of the functions is sometimes commutative.
hope this helps!! have an amazing day <3
2021 edg
how do the real solution of a quadratic equation show on a graph of that equation?
Answer:
They show as intersections with the x-axis
Step-by-step explanation:
For example, the quadratic y = x² - 1 has roots x = -1 and x = 1.
They show on the graph as intersections of the parabola with the x axis at x = -1 and x = 1.
The value of the expression when n=2 is
Answer:
2/3
Step-by-step explanation:
A random sample of 10 subjects have weights with a standard deviation of 11.6118 kg. What is the variance of their weights? Be sure to include the appropriate units with
the result.
The variance of the sample data is_
(Round to four decimal places as needed.)
To find the variance of the weights from the given standard deviation of 11.6118 kg, you square the value of the standard deviation, resulting in a variance of 134.9143 kg^2.
Explanation:The question pertains to finding the variance of the weights from a given standard deviation. The standard deviation provided is 11.6118 kg. Variance is calculated as the square of the standard deviation, which helps in understanding the dispersion of a dataset relative to its mean. To calculate the variance, you square the value of the standard deviation.
Variance = Standard Deviation2
Thus, Variance = (11.6118 kg)2 = 134.9143 kg2. Therefore, the variance of their weights is 134.9143 square kilograms, rounded to four decimal places as required.
What is the value of x?
Answer:
15
Step-by-step explanation:
Because if you draw a line straight just like the one below the x, it will connect to the 15.
Answer:
18
Step-by-step explanation:
Because you add 9 more angles to the smaller triangle
Write an equation that represents "eight more than twice a number is fifty".
Answer:
8+2x=50
happy to help!!
What's 10 percent of 80
Answer:
8
Step-by-step explanation:
[tex]\frac{is}{of} = \frac{percent}{100}[/tex]
[tex]\frac{x}{80} = \frac{10}{100}[/tex]
80x10 = 800
800 = 100x
800 divide 100 = 8
answer = 8
Hope this helped!! :)
if the function f(x) has a domain of -2≤x≤8 and a range of -4≤y≤6 and the function g(x) is defined by the formula g(x)= 5f(2x) then what are the domain and range of g. explain your thought process
Answer:
Domain: -1 ≤ x ≤ 4
Range: -20 ≤ 5f(2x) ≤ 30
Step-by-step explanation:
Inputs of f are between -2 and 8
Input is now 2x, so
-2 ≤ 2x ≤ 8
-1 ≤ x ≤ 4
(Horizontal stretch, factor 1/2)
Range of f is -4 ≤ y ≤ 6
So,
-20 ≤ 5y ≤ 30
(Vertical stretch, factor 5)
The domain of g(x) is [-1, 4].
The range of g(x) is [-20, 30].
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Domain of f(x) = [-2, 8]
Range of f(x) = [-4, 6]
g(x) = 5 f(2x)
Since -2 ≤ x ≤ 8 and -2 ≤ 2x ≤ 8 = -1 ≤ x ≤ 4.
The domain of g(x) = [-1, 4]
Now,
The range of g(x) = [-20, 30]
Since -4 ≤ y ≤ 6,
5 x (-4) ≤ 5y ≤ 5 x 6
-20 ≤ 5y ≤ 30
Thus,
The domain and range of g(x) are
[-1, 4] and [-20, 30].
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blairs new computer cost 5$ less than twice the cost og her old computer. Her new computer cost 709$. how much did blairs old computer cost?
i need help asap! i will mark brainliest answer and i will give 5 stars for the answer! thank you :)
The cost of old computer is $ 357
Solution:
Let "x" be the cost of old computer
From given,
Cost of new computer = $ 709
Blairs new computer cost 5$ less than twice the cost of her old computer
Therefore,
Cost of new computer = twice the cost of old computer - 5
Cost of new computer = 2x - 5
709 = 2x - 5
2x = 709 + 5
2x = 714
Divide both sides by 2
x = 357
Thus the cost of old computer is $ 357
Answer:
$357
Step-by-step explanation:
709=2x-5
+5 +5
cross the right column out
709+5 = 714
714=2x
divide 714 by 2 and get 357
HOPE THIS HELPS!!!
At midnight the temperature is -6°C. At midday the temperature is 9°C. By how much did the temperature rise?
The temperature increased by 15°C.
What is the temperature?Temperature is a physical quantity that expresses the perceptions of hotness and coldness
Given that at midnight the temperature is -6°C. At midday the temperature is 9°C. Therefore, the difference in the temperature can be written as,
The difference in temperature
= Temperature in Midday - Temperature at midnight
= 9°C - (-6° C)
= 15° C
Therefore, The difference in the temperature is 15°C.
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I need some help here??
x = 11 (or) x = –13
Solution:
Theorem:
If three or more parallel lines are cut by a transversal then they divide the transversals proportionally.
Given lines l, m, n are parallel lines cut by a two transversal lines.
Therefore, they are in proportion by the above theorem.
[tex]$\Rightarrow\frac{x+5}{10}=\frac{12.8}{x-3}[/tex]
Do cross multiplication.
[tex]$\Rightarrow(x+5)\times(x-3)=12.8\times10[/tex]
[tex]$\Rightarrow x^2+5x-3x-15=128[/tex]
[tex]$\Rightarrow x^2+2x-15=128[/tex]
Arrange all terms in one side.
[tex]$\Rightarrow x^2+2x-15-128=0[/tex]
[tex]$\Rightarrow x^2+2x-143=0[/tex]
[tex]$\Rightarrow x^2-11x+13x-143=0[/tex]
Take common terms outside
[tex]$\Rightarrow x(x-11)+13(x-11)=0[/tex]
[tex]$\Rightarrow (x-11)(x+13)=0[/tex]
[tex]$\Rightarrow (x-11)=0\ \text{(or)}\ (x+13)=0[/tex]
⇒ x = 11 (or) x = –13
Hence x = 11 (or) x = –13.
BRAINLIEST PLEASE HELP!!
Determine whether the sequence is arithmetic with a common difference or sequence is geometric with a common ratio. Then select the correct answer from the choices below. 9,12,16,21 1/3,
Answer:
Geometric with common ration of 4/3
Step-by-step explanation:
12/9=4/3
16/12=4/3
What is the value of x?
Enter your answer in the box.
Answer:
Since the two angles are across from each other that tells us that they are equal in length, so we want to set them equal to each other
3x+50=6x-10, Now we want to solve it like a normal equation, get x by itself
First add 10 to each side
3x+50+10=6x-10+10
3x+60=6x
Now we want to subtract 3x from each side
3x-3x+60=6x-3x
60=3x
Now divide both sides by 3
60/3=3x/3
20=x
x=20
Hope this helps ;)
Step-by-step explanation:
What is –36° converted to radians?
Negative 5 pi
Negative StartFraction 5 Over pi EndFraction
Negative StartFraction pi Over 5 EndFraction
Negative one-fifth
Option c: [tex]-\frac{\pi}{5}[/tex] is the correct answer.
Explanation:
The given degree is –36°
Since, [tex]1^{\circ}=\frac{\pi}{180}[/tex]
The radian of –36° can be determined by multiplying it with [tex]\frac{\pi}{180}[/tex]
Thus, the degree can be converted into radians, by multiplying the degree with [tex]\frac{\pi}{180}[/tex]
Hence, it can be written as
[tex]-36^{\circ} \times \frac{\pi}{180}[/tex]
Multiplying, we get,
[tex]\frac{-36^{\circ} \pi}{180}[/tex]
Dividing, we have,
[tex]-\frac{\pi}{5}[/tex]
Thus, the radian of -36° is [tex]-\frac{\pi}{5}[/tex]
Answer:
the answer is c
Step-by-step explanation:
Find the number of terms of this polynomial. 5x^2 + 3x - 4 (2 point)
Number of terms:
There are three terms in polynomial
Solution:
Given polynomial is:
[tex]5x^2+3x-4[/tex]
We have to find the number of terms in polynomial
A term can be a signed number, a variable, or a constant multiplied by a variable or variables
When a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient.
Therefore, terms in polynomial are:
[tex]5x^2+3x-4\\\\Terms: 5x^2 \text{ and 3x and -4 }[/tex]
Thus there are three terms in polynomial
The population of Birmingham is 1,274,589. What is the value of the 7?
Answer:
70,000
Step-by-step explanation:
In the population number 1,274,589 for Birmingham, the 7 is in the ten thousands place. Therefore, its value is 70,000.
Explanation:This problem revolves around understanding of place values in Mathematics. Specifically, we are asked
what is the value of 7
in the population number 1,274,589 for Birmingham. A critical observation is that each position of a digit in a number has a different value. Counting from right (or the ones position) to left, we find that the number 7 is in the ten thousands place. Therefore, the value of 7 in this number is actually 70,000.
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Zachary's family traveled 3/10 of the distance to his aunts house. They traveled 3/7 of the remaining distance. What fraction of the total was traveled to his aunts house
Answer:
1 - 3/10 = 7/10 of the distance left
(3/7)(7/10) = 3/10 of the total distance
Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.
To find the fraction of the total distance traveled to Zachary's aunt's house, we need to combine the distances traveled and express it as a fraction of the total distance.
Given:
1. Zachary's family traveled [tex]\( \frac{3}{10} \)[/tex] of the total distance to his aunt's house.
2. Then, they traveled [tex]\( \frac{3}{7} \)[/tex] of the remaining distance.
Step 1: Calculate the total distance traveled by combining the two distances.
[tex]\[ \text{Total distance traveled} = \frac{3}{10} + \frac{3}{7} \][/tex]
Step 2: Find a common denominator for [tex]\( \frac{3}{10} \) and \( \frac{3}{7} \).[/tex] The least common multiple (LCM) of 10 and 7 is 70.
Step 3: Rewrite the fractions with the common denominator of 70.
[tex]\[ \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \][/tex]
[tex]\[ \frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70} \][/tex]
Step 4: Add the fractions:
[tex]\[ \frac{21}{70} + \frac{30}{70} = \frac{21 + 30}{70} = \frac{51}{70} \][/tex]
Therefore, Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.
How many inches are in 43 yards
Answer:
1548
Step-by-step explanation:
Their are 36 inches in a yard multiply by 43 it’s 1548
I don't think anyone will respond to a good attempt
The answer is gonna be 15
Which set of numbers could represent the lengths of the sides of a right triangle?
8, 15, 17
10, 15, 20
12, 18, 22
7,9, 11
Answer:
The first set: 8, 15, and 17.
Step-by-step explanation:
Pair: 8, 15, 17By the pythagorean theorem, a triangle is a right triangle if and only if
[tex]\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
In this case,
[tex]\text{longest side}^2 = 17^2 = 289[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}[/tex].
In other words, indeed [tex]\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2[/tex]. Hence, 8, 15, 17 does form a right triangle.
Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two
Pair: 10, 15, 20Factor out the common factor [tex]2[/tex] to simplify the calculations.
[tex]\text{longest side}^2 = 20^2 = 400[/tex]
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}[/tex].
[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
Pair: 12, 18, 22[tex]\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}[/tex].
[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
Pair: 7, 9, 11[tex]\text{longest side}^2 = 11^2 = 121[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}[/tex].[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
negative 5 and 3/4 multiplied by 8/23
Answer:
[tex] - 5 \frac{3}{4} \times \frac{8}{23} = - \frac{23}{4} \times \frac{8}{23} = - 2[/tex]
if you have 108 inches of wood to make a picture fram what is the greatest area if a = -w2 + 54w
Answer:
The greatest area possible is 729[tex]inch^{2}[/tex]
Step-by-step explanation:
i) If a = [tex]-w^{2} + 54w[/tex] where w is the width of the picture frame
differentiating on both sides we get
[tex]\frac{da}{dw} = -2w + 54[/tex]
Differentiating the above again on both sides we get [tex]\frac{d^2a}{dw^2}[/tex] = -2
Since the second order derivative is negative then we can get the solution for the maximum area by equating the fist order derivative equation to 0.
Therefore -2w + 54 = 0 therefore w = 27.
ii) If we substitute w = 27 into the equation in ii) we get
a = [tex]-(27)^2 +(54\times 27)[/tex] = (54 - 27) [tex]\times[/tex](27) = [tex]27^{2}[/tex] = 729
40 points please help
Problem:
The altitude of an airplane descending to the airport is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x, represents the number of minutes after descending.
y = -500x + 28,000
Part A:
What is the altitude of the airplane after 5 minutes? after 30 minutes? Show your work then write your answers as ordered pairs (x,y).
Part B:
Create a table for the values when x = 0, 5, 8, 10, 30.
Part C:
Which ordered pair (from the table in part B) represents the initial value? What does the initial value represent in this problem? (1-2 sentences)
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem? (1-2 sentences)
answer:
im not sure. what is ur question
step-by-step explanation:
Ms. Ruiz is 9 years older than 6 times as many years old as Carlos. Ms. Ruiz is 57 years old.
Answer:
Carlos is 8
Step-by-step explanation:
I solved this by subtracting 9 from her age, which gets rid of that. 57-9=48
Carlos is 48/6 years old, or 8
Answer:
The answer is 8
Step-by-step explanation:
pls, help!!!!!!!!!!!!!!!!!!!!! I need help with the problem. I'm stuck!!!!! Write an inequality from this sentence. Kevin sells at most $60 worth of drinks in the concession stand.
Answer:
i) let x be the amount of money worth of drinks that Kevin sold.
ii) Kevin sells at most $60 worth of drinks.
iii) therefore the inequality can be written as
x ≤ $60
Step-by-step explanation:
i) let x be the amount of money worth of drinks that Kevin sold.
ii) Kevin sells at most $60 worth of drinks.
iii) therefore the inequality can be written as
x ≤ $60
The quotient of the complex # below (7-2i)/(4 +3i)
Answer:
Step-by-step explanation:
hello :
(7-2i)/(4 +3i)
=(7-2i)×(4-3i)/(4 +3i)×(4-3i)
but : (7-2i)×(4-3i) =28-21i-8i+6i²
(7-2i)×(4-3i) = 22-29i ....i² = -1
(4 +3i)×(4-3i) = 4²-(3i)²...(identity)
= 16+9 =25
so :
(7-2i)×(4-3i)/(4 +3i)×(4-3i)
=(22-29i)/25
(7-2i)/(4 +3i) = 22/25 -29/25i
(form : a+ib)
To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator.
Explanation:To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 4 + 3i is 4 - 3i. So, we have ((7 - 2i) * (4 - 3i)) / ((4 + 3i) * (4 - 3i)).
Multiplying the numerators and the denominators, we get (28 - 21i - 8i + 6i^2) / (16 - 12i + 12i - 9i^2).
This simplifies to (28 - 29i - 6) / (16 + 9).
Finally, dividing the real parts and the imaginary parts separately, the quotient is:
Quotient = (22 - 29i) / 25
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Solve. 5a−12=−2 plzz help
Answer:
a=2
Step-by-step explanation:
Given: 5a-12=-2
Isolate Variable: 5a=10
Divide: a=2
Answer:
5a - 12= -2
5 x 2= 10 so,
5(2) - 12= -2
^
10-12= -2
What inequality describes the situation?
5. Let t = the amount Thomas earned. Thomas earned $49 or more. (1 point)
Ots49
ta 49
Ot> 49
Ot<49
Answer:
[tex]t \geqslant 49[/tex]
Step-by-step explanation:
If Thomas earned $49 OR more, therefore he could have earned either $49 or greater. Please mark brainliest! : )
The inequality that describes the situation is t >= 49. This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.
Explanation:The inequality that describes the situation is t >= 49.
This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.
For example, if Thomas earned $49, the inequality is true. If Thomas earned more than $49, the inequality is also true.
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a 3 cm x 10 cm rectangle sits inside a circle with radius of 12 cm what is the area of the shaded region
Answer:
Step-by-step explanation:
Since the rectangle sits within the larger circle, let's look at it this way:
Area of Shaded Region = Area of Circle - Area of Rectangle
OR
(X) =( pi * r^2 ) - (rectangle length * rectangle width)
Now we fill in the numbers where we know the numbers:
(X) = (pi * (12 cm)^2) - (3cm * 10cm)
(X) = (pi * 144cm^2) - (30 cm^2)
(X) = 144pi - 30
(X) = 452.39 - 30
(X) = 422.39 cm^2
Take the area of the circle and subtract that with the area of the rectangle.
Area of circle= pi*r^2
Area of circle= pi*12^2
Area of circle=144pi
Area of circle= 452.16 cm^2
Area of rectangle: b*h
Area of rectangle: 10*3
Area of rectangle: 30 cm^3
452.16-30=422.16
So the area of the shaded region is 422.16 cm^2
Hope this helped!
Bananas cost .89cents, I have $11.75, how many bananas can I buy?
Answer: you will be able to buy 13.20224719101124 bananas.
dividing fractions
21/32 ÷ 3/5
Answer:
105/96
Step-by-step explanation:
Answer:
In dividing fractions, you do the inverse. (Also called the reciprocal.)
So take that attachment you attached as a example.
21 3 21 5
---- ÷ ---- = ------ ÷ ------
32 5 32 3
Another reminder, when you find the reciprocal, you now multiply instead of divide. (Do not question the math world. I questioned it, and I paid the price. TnT)
So 21/32 multiplied by 5/3 would be....
21 5 105
----- × ----- = -------
32 3 96
You could leave it that way, or simplify it.
Simplest form is-
1 3/32
Non-simplified form is-
105/96
Good night and have a good day~
(Well at least, I'm going to sleep)