Answer:
[tex](g \circ f)(x) = x^2-10x+25[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=-x+7\\g(x)=x^2-4x+4 \end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The composite function (g o f)(x) means to substitute the function f(x) in place of the x in function g(x).
[tex]\begin{aligned} \implies (g \circ f)(x) & = g\left[f(x)\right]\\& = g(-x+7)\\& = (-x+7)^2-4(-x+7)+4\\& = (-x+7)(-x+7)+4x-28+4\\& = x^2-14x+49+4x-28+4\\& = x^2-14x+4x+49-28+4\\& = x^2-10x+25\end{aligned}[/tex]
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Answer:
x² - 10x + 25
Step-by-step explanation:
The given information is,
→ f(x) = -x + 7
→ g(x) = x² - 4x + 4
The equation we form is,
→ (gof)(x)
→ g[f(x)]
→ f(x)² - 4f(x) + 4
Let's solve the problem,
→ f(x)² - 4f(x) + 4
→ (-x + 7)² - 4(-x + 7) + 4
→ x² - 14x + 49 + 4x - 28 + 4
→ x² - 10x + 25
Hence, answer is x² - 10x + 25.
Solve 2 - ax = -8 for x. Assume a ≠ 0
The expression is simplified to x = 10/ a
What is subject of formula?Subject of formula is defined as a variable which is expressed in terms of other variables involved in a given formula or expression.
Given the expression;
2 - ax = -8
Let's make 'x' the subject of formula
collect like terms
-ax = -8 - 2
Subtract like terms
-ax = - 10
Divide both sides by -a
-ax/ -a = - 10/-a
Find the ratio
x = 10/ a
Thus, the expression is simplified to x = 10/ a
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The coordinates of triangle MNP and triangle QRS are shown in the table.
Triangle MNP
Triangle QRS
M(2, 5) N(6, 4) P(6, 8)
Q(–2, -5) R(–6, -4) S(–6, -8)
Which BEST describes the relationship, in terms of congruency, between triangle MNP and triangle QRS?
Using translation concepts, it is found that the triangles are congruent, as triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.
From the vertices of the triangles MNP and QRS, the following transformation was applied:
(x,y) -> (-x,-y).
Which is a 180º rotation about the origin, that is, triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.
Rotations do not change the side lengths, only the orientation of the triangle, hence the triangles QRS and MNP are congruent.
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The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = -8 and x = -2. Use the line segment to determine the average
rate of change of the function f(x) on the interval -8 ≤ x ≤-2.
Answer:
1x+mx=b
Step-by-step explanation:
1*15+3*15=60
Simplify 9-{X -(7+X)}
A. 16
B. -2x +2
C.-2x +16
D. 2x +2
1) Write 35/
37
in lowest term
Answer:
it is already lowest terms
Step-by-step explanation:
How many pairs of angles are marked as congruent in the figures below?
ДД
X M
0 3
00
2
01
N
Answer: 2 pairs
Step-by-step explanation: You can tell which angles are congruent based on the curved markings. Pairs of congruent angles have matching markings. Since two of the angles are congruent to each other, we can assume that the third angles on the triangles are also congruent to each other, but it is not marked as such. So, there are only two marked pairs of congruent angles.
Using the equation from #5, (d=20g) how many miles can a car drive if it has 13 gallons of gas?
Answer:
If d meaning mile it will be 20x13
Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point.
(3, 2)
Answer:
exterior
Step-by-step explanation:
You want to know if (3, 2) is an interior or exterior point of the circle defined by (x -5)² +(y +3)² = 25.
Distance from centerWe can find the square of the distance of the point from the center of the circle using the equation for the circle.
(x -5)² +(y +3)² = r²
(3 -5)² +(2 +3)² = 4 +25 = 29 > 25 . . . . use (x, y) = (3, 2) in the equation
The point is farther away from the center than points that are on the circle. The point (3, 2) is an exterior point.
23=2 rearrange the equation to solve for f
Answer:
23 doesn't equal 2
Step-by-step explanation:
Sultan Inc. was organized on January 1, 2020. It reported the following for its first two years of operations:
Net earnings for 2020 $ 31,000
Dividends for 2020 14,200
Total shareholders’ equity at end of 2020 130,000
Net earnings for 2021 42,000
Dividends for 2021 18,700
Total shareholders’ equity at end of 2021 250,000
Required:
Compute the ending balance of retained earnings for Sultan Inc. as at December 31, 2021.
The ending balance of retained earnings for Sultan Inc. as at December 31, 2021 is $40,100
What is the retained earnings at the end of 2020?
The retained earnings at the end of 2020 is the net earnings for 2020 minus the dividends paid in 2020 , in other words, the 2020 ending balance of retained earnings are computed as shown below:
retained earnings for 2020=$31,000-$14,200
retained earnings for 2020=$16,800
However, we need to determine additional retained earnings in 2021 which is also ascertained as net earnings minus dividends paid
additional retained earnings in 2021=$42,000-$18,700
additional retained earnings in 2021=$23,300
the ending balance of retained earnings for Sultan Inc. as at December 31, 2021=2021 balance of retained earnings+ additional retained earnings in 2021
the ending balance of retained earnings for Sultan Inc. as at December 31, 2021=$16,800+$23,300
the ending balance of retained earnings for Sultan Inc. as at December 31, 2021=$40,100
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1-131. Lindsay has a paper bag full of Fruiti Tutti Chews in three different fruit flavors. She says, “If you reach into the bag, you have a chance of pulling out a Killer Kiwi. There is a chance that you will get Crazy Coconut.”
The probability of choosing a Kiwi or a coconut is 14/15.
There has to be another flavor in the bag. The probability of picking the third flavor is 1/15.
There can be 15 candies in the bag. There can be more than one possibility.
What is the probability?Probability calculates the odds that a random event would occur. The odds that the random event happens lie between 0 and 1. The more likely the event is to occur, the closer the probability value is to 1. If the probability value is 0.5, it is equally likely and unlikely that the event would happen or not happen. The sum of all probabilities should add up to 1.
The probability of choosing a Kiwi or a coconut = chances of picking a kiwi + chances of picking a coconut
1/3 + 3/5
(5 + 9) / 15 = 14/15
There has to be another flavor in the bag because the sum of the probabilities of picking a coconut or a kiwi does not add up to 1.
The probability of getting another flavor = 1 - sum of the probabilities of picking a kiwi or a coconut
1 - 14/15
15/15 - 14/15 = 1/15
The total number of candies in the bag would be a multiple of 15. The multiple of a number is the product of the number and another number. The possible number of candies are 15, 30, 45, 60, 75, 90
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Which point on the number line best represents
A Point A
B Point B
C Point C
D Point D
A
45°
B C
-3
?
2+
Answer:
A 45 the only reason why I choose number one because you said which point on the line on the bed response point a point b point c point d a 54 or whatever but yeah becauseWhich of the following is most likely the next step in the series?
)DO
O A.
• B.
•
Following the pattern, the most likely next step in the series is given by the pentagon in option B.
What is the most step for the series?We have to look at the number of points in each figure, hence:
The first figure, with the line segment, has two points.The second figure, with the triangle, has three points.The fourth figure, with the rectangle has four points.Hence, the number of points increases by one for each figure, meaning that in the next step, the figure should have 5 points, representing a pentagon.
Among the options given for the answer, only one, option B, has 5 points, with the pentagon, as:
Option A has one point.Option C has four points.Option D has three points.Hence, the most likely next step in the series is given by the pentagon in option B.
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Please Help!! I keep getting this question wrong and have two attempts left
A Global Positioning System satellite orbits d = 13,500 miles above Earth's surface (see figure). Find the angle of depression (in degrees) from the satellite to the horizon. Assume the radius of Earth is 4,000 miles. (Round your answer to two decimal places.)
Using relations in a right triangle, it is found that the angle of depression from the satellite to the horizon is of 89.35º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.First, we consider that:
The opposite side to the internal angle at the satellite is of 4000 mi.The hypotenuse is of 4000 mi + d mi = 17500 mi.Hence the sine of the angle is given as follows:
sin(θ) = 4000/175000
θ = arcsin(4000/175000)
θ = 1.31º.
Twice the angle of depression x and θ are supplementary, hence:
2x + 1.31 = 180
2x = 178.69.
x = 178.69/2
x = 89.35º.
The angle of depression from the satellite to the horizon is of 89.35º.
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Parallel, Perpendicular, or neither? y=3x+3 y=3x-4
-1/2 + 2/3 DO THIS THANKS GUYSSSSS
Answer: 0/5
Step-by-step explanation:
Answer:
1/6 I used a calculator
Step-by-step explanation:
-1/2 + 2/3 =1/6
Use the figure below to list the slopes m₁, m₂, m3, and m4 in order of decreasing size.
the order, from largest to lowest, is:
Purple line, Green line, Blue line, Red line.
How to list the slopes in decreasing order?
A linear equation written in the slope-intercept form is:
y = a*x + b
Such that a is the slope, and it tells us how fast the function changes.
Positive slopes mean that the lines go upwards (purple or green in this case)
Negative slopes mean that the lines go downwards (blue or red in this case)
As larger is the slope, more steep is the function (for the cases with positive slope, is the opposite for negative slopes).
Then the order, from largest to lowest, is:
Purple line, Green line, Blue line, Red line. (y can't see the subindices of the slopes in the lines, so I only can identify the colors).
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In 1920, the record for a certain race was 46.4 sec. In 1970, it was 45.4 sec. Let R(t)=the record in the race and t= the number of years since 1920.
a) Find a linear function that fits the data.
b) Use the function in (a) to predict the record in 2003 and in 2006.
c) Find the year when the record will be sec.
The year will be 2018, the predicted record of 43.74
1920, the record for a certain race was 45.9 sec.
In 1950, it was 45.0 sec.
Let R(t)= the record in the race and t= the number of years since 1920.
How to calculate slope
The equation of slope of any line can be calculated using the following formula, m = rise/run = tanθ = Δy/Δx = (y2 - y1)/(x2 - x1) where, m is the slope. Δy is the change in y-coordinates.
slope = (45-45.9)/30 = -0.9/30 = -0.03
EQUATION:
R(t)= -0.03t + 45.9
b) The predicted record for 2003
t = 83 in 2003
R(83) = -0.03*83 + 45.9
R(83) = 43.41
The predicted record for 2006
t = 86 in 2006
R(86) = -0.03*86 + 45.9
R(86) = 43.32
C) Solve for t
-.02t + 45.7 = 43.74
-.02t = 43.74 - 45.7
-.02t = -1.96
t = +98
1920 + 98 = 2018, the predicted record of 43.74
This type of equations are called linear equations
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
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The simplified expression of
5
x
−
8
−
2.25
x
+
3
5x−8−2.25x+3 is
Answer:
44.5x - 13
Step-by-step explanation:
Combine like term.
Carlos is moving his 14 books. He has packed and equal number of books into each of 3 empty boxes. How many books are in each box? How many books are left over
Answer:
The total ways the textbooks can be arranged in the 3 boxes is , which is equivalent to . If all of the math textbooks are put into the box that can hold  textbooks, there are  ways for the other textbooks to be arranged. If all of the math textbooks are put into the box that can hold  textbooks, there are  ways to choose the other book in that box, times  ways for the other books to be arranged. If all of the math textbooks are put into the box with the capability of holding  textbooks, there are  ways to choose the other 2 textbooks in that box, times  ways to arrange the other 7 textbooks. , , and , so the total number of ways the math textbooks can all be placed into the same box is . So, the probability of this occurring is . If the numerator and denominator are both divided by , we have . Simplifying the numerator yields , and dividing both numerator and denominator by  results in . This fraction cannot be simplified any further, so  and . Therefore, .
Answer:
Step-by-step explanation:
Giving Brainliest!!!
What is 10x + 4 = 22
Answer:
x=1.8
Step-by-step explanation:
10x + 4 = 22
Subtract 4 from both sides.
10x=18
Divide 10 from both sides.
x=1.8
Hope this helps!
Answer: x = 1.8 or x = 9/5
Step-by-step explanation:
1. Subtract 4 from both sides:
10x + 4 - 4 = 22 -4
2. Simplify:
10x = 18
3. Divide by 10 on both sides:
10x/10 = 18/10
4. Solve:
x = 1.8 or 9/5
Type a digit that makes this statement true. 366,5_4 is divisible by 8.
Answer:
required digit is 0.
if we want two answers then 0 &8
Step-by-step explanation:
it is divisible by 8 if last three digits are divisible by 8
504÷8=63
so 366,504 is divisible by 8.
366,504÷8=45813
next term is 584
584÷8=73
so 366,584 is divisible by 8.
A cube has an edge length that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers? (1 point)
O the diagonal of one of the cube's faces
O the volume of the cube
O the surface area of the cube
O the area of one of the cube's faces
Answer:
A) the diagonal of one of the cube's facesStep-by-step explanation:
Let the edge be r, a rational number.
Then the following are:
A) The diagonal of one of the cube's faces,
d = r[tex]\sqrt{2}[/tex], this is always irrational.B) The volume of the cube,
V = r³ - always rational.C) The surface area of the cube,
S = 6r² - this is always rational.D) The area of one of the cube's faces,
A = r²- this is always rational.Write 5.92 x 10^5 in standard notation
Question 8, 11.1.21 A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 9 stocks?
Explanation:
Consider 2 stocks that either go up, down, or stay unchanged. We'd have a 3 by 3 table to show the 3*3 = 3^2 = 9 different outcomes.
This idea can be extended to 3 stocks to have 3*3*3 = 3^3 = 27 outcomes
4 stocks would have 3^4 = 81 outcomes and so on
Therefore, 9 stocks have 3^9 = 19683 outcomes
Distinguish what a ray, line segment and line are in your own words. Then, compare
and contrast the three geometric figures.
Answer: A ray starts from a point and goes to infinity. A line has no end points. A line segment has two endpoints. A line segment connects both endpoints.
Step-by-step explanation:
did this explain it
What are the outputs of the function below?
X
g(x)
O-1, 0, -3, 4
O-1, 0, 7, 10
O6, 2, -3, 4
6, 2, 7, 10
-1
6
0
2
7
3
10
4
Answer:
it a i think
Step-by-step explanation:
The outputs of the function are 6, 2, 3, 4, and the inputs of the function are -1, 0, 7, and 10.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
here,
We have:
x g(x)
–1 6
0 2
7 -3
10 4
The table shows the input and output of the function g(x)
g(-1) = 6
g(0) = 2
g(7) = -3
g(10) = 4
The set of equivalent y-values for the function shown in the table is as follows: 6, 2, 3, 4.
Thus, the outputs of the function are 6, 2, 3, 4, and the inputs of the function are -1, 0, 7, and 10.
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50 POINTS
2( 7w-1)+5w=w+ 3(4w+3)+2 (3w-9)
Answer:
0= -7
Therefore, it has no solutions.
Step-by-step explanation:
Answer:
No solutions.
Step-by-step explanation:
[tex]2\left(7w-1\right)+5w=w+3\left(4w+3\right)+2\left(3w-9\right)[/tex] <- Expand
[tex]19w-2+2=19w-9+2[/tex] <- Add 2 to both sides
[tex]19w=19w-7 \\[/tex] <- Simplify
[tex]19w-19w=19w-7-19w[/tex] <- Subtract 19w from both sides
[tex]0=-7[/tex]
Therefore, this has no solutions.
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If PR = 24 and RS = 11, what is PS?
PS = 42
PS = 13
PS = 27
PS = 35
The length of the line segment PS will be 35 units when PR is 24 units and RS is 11 units.
We are given the length of two line segments as:
PR = 24 units
RS = 11 units
Now, we need to find the length of PS.
We will use the operation of addition here as PS will be equal to the sum of PR and RS. Addition refers to the basic operation of mathematics that is used to simplify and evaluate an expression or an equation.
So, we get that:
PS = PR + RS
Substituting the values, we get that:
PS = 24 units + 11 units
PS = 35 units
Therefore, we get that, the length of the line segment PS will be 35 units when PR is 24 units and RS is 11 units.
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Steve went on holiday.
He recorded the number of photos he took each day.
Steve saves his photos on a memory card.
The memory card has 1000 megabytes of memory space.
Each photo uses 2.4 megabytes of memory space.
Steve has saved 320 photos on the memory card.
Work out how many more photos Steve can save on the memory card.