The sum and product of two linear functions are shown. Which statements are true of the original functions, f(x) and g(x)? Check all that apply. When added, the sum of the y-intercepts must be 4. When multiplied, the product of the the y-intercepts must be 3. f(x) and g(x) have either both positive or both negative rates of change. f(x) could have a rate of change equal to 2, and g(x) could have a rate of change equal to 1. f(x) could have a rate of change equal to 0, and g(x) could have a rate of change equal to 3.
The initial functions f(x) and g(x) can be described by the statements that when added, the sum of the y-intercepts must be 8. The best choice is B.
What do we mean by functions?The expression that established the relationship between the dependent variable and independent variable is referred to as a function.
In order to see the trend of the data, a graph represents the data on the vertical and horizontal axes.
The graphic that is attached to the following response shows the sum and product of two linear functions:
The following calculations will determine the statements that can be used to explain the initial functions f(x) and g(x):
The roles should be:
f(x) = ax + b
g(x) = cx + d
The total is:
j(x) = (a + c)x + b + d
Their product would be:
k(x) = (ax + b)(cx + d)
We can see from the graph that:
f(x) = x + 6
g(x) = -2x² + 8
f'(x) = 1
g'(x) = -4x
Therefore, the initial functions f(x) and g(x) can be described by the statements that when added, the sum of the y-intercepts must be 8. The best choice is B.
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Correct question:
The sum and product of two linear functions are shown Which statements can be used to describe the original functions f(x) and g(x)? Select three options.
a. When added, the sum of the y-intercepts must be 8.
b. When multiplied, the product of the y-intercepts must be 8.
c. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
d. f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of -3.
e. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of -1.
Which statement applies to the transformed function f(x)−4
?
The function is odd, and the graph would be shifted downward. option(2)
The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.
Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.
This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units.
The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.
Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.
This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units. Option(2)
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Solve each equation -3x + 2 = -1
Yana is in the school computer lab writing a paper for history class. The graph represents the number of words Yana has written after a number of minutes
Yana opened her saved paper, wrote, took a break, deleted some of the words, and then began writing again. Then the correct option is A.
What is a function?
A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Yana is in the school computer lab writing a paper for history class. The graph represents the number of words Yana has written after a number of minutes.
The graph is given below.
From the graph, Yana opened her saved paper, wrote, took a break, deleted some of the words, and then began writing again.
Then the correct option is A.
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6x-8 = -4x+7 solve for x
Answer:
so look
Step-by-step explanation:
6x=7+8
2 Simplify 7+87+8 to 1515.
6x=156x=15
3 Divide both sides by 66.
x=\frac{15}{6}x=
6
15
4 Simplify \frac{15}{6}
6
15
to \frac{5}{2}
2
5
.
x=\frac{5}{2}x=
2
5
Done
Decimal Form: 2.5
Answer:
x = 1.5
Step-by-step explanation:
6x - 8 = -4x +7
+ 8 +8
6x = -4x +15
+4x +4x
10x = 15
10x/10 = 15/10
x = 1.5
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
\(w(x)=14\cdot 1.08^{x}\)
w(25) =
\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves
Can the following list represent a complete probability model? P(2)= 1/12 P(3) = 2/3 P(4) = 1/4
Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.
What exactly is probability?The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.
=> P(2) + P(3) + P(4)
=> 1/12 + 2/3 + 1/4
=> (1 + 8 + 3) / 12
=> 12 / 12 = 1
In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.
In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.
Therefore, a complete probability model cannot be represented by this list.
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dul Tunction is shown on the graph below.
A
What are the domain and range for the quadratic function shown on the graph?
A Range: All real numbers less than or equal to 7
B Range: All real numbers greater than or equal to 6 and less than or equal to 7
C Range: All real numbers
D Range: All real numbers less than 7
Answer:
Step-by-step explanation:
A
The following table shows the number and type of properties available in three cities.
City
Key West
Orlando
Miami
Write a matrix that represents the number of each type of property available in Key West.
[ 3 9 13 ] is the Matrix showing all types of property available in key west .
What is matrix ?A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.
Calculationgiven in the table that how many types of property are there in the table
its a simple matrix which u can directly see
its a 3 x 1 matrix ...
[3 9 13] this matrix shows the required value
hope this helps...
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Answer: [3 9 13]
Step-by-step explanation:
A dinner was held to raise money for a children's museum. A ticket for one person cost $200 and a ticket for a couple (two people) cost $350. A total of 130 people attended the dinner, and the ticket sales total was $24,000. What is the total number of tickets that were sold?
Using simultaneous equations, during the dinner to raise money for a children's museum, 90 tickets were sold.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently or at the same time.
Simultaneous equations are also called a system of equations.
The cost of one-person ticket = $200
The cost of two-people ticket = $350
The total number of attendees at the dinner = 130
The total ticket sales = $24,000
Let number of one-person ticket = x
Let number of two-people ticket = 2y
Equations:x + 2y = 130... Equation 1
200x + 250y = 24000... Equation 2
Multiply Equation 1 by 200:
200x + 400y = 26000... Equation 3
Subtract Equation 2 from Equation 3:
200x + 400y = 26000
-
200x + 350y = 24000
50y = 2000
y = 40
x = 130 - 2y
= 130 - 80
= 50
Thus, the number of tickets sold at the dinner was 90.
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John works at Klein’s Dry Cleaning. He earns $8.45 per hour. If John worked 39 hours this week, what is his pay? *
Answer: 329.55
Step-by-step explanation: multiple 8.45 by 39 which is 329.55
8.45 * 39 = 329.55
The daily fee for admission to the Florida Fun 'n Sun
Amusement Park is $45 per adult and $25 per child.
Daily admission fees are paid for a adults and c
children. Which of the following expressions gives the
total amount, in dollars, collected for daily fees?
Options: 45a+25c, 45c+25a, 25(a+c), 70(a+c), 25(a+c)+45a
Answer:
45a + 25c
Step-by-step explanation:
Let;
Adult = A
Child = C
fee per Adult (A) = $45
fee per Child(C) = $25
The expression that gives the total amount collected in daily fees
= ( Adult ( A ) * Daily fee for Adult ) + ( Child(C) * Daily fee for child )
= 45a + 25c
Worth 50 points!I need help plz!
Will mark brainliest to whoever does all the work.
A basket contains:
4 red Santa hats
6 green Elf hats
5 red jackets
7 green jackets.
Determine the probability of randomly selecting a green piece of clothing or a jacket.
(A)Use the addition rule to calculate this probability and explain your answer.
Do this equation P(AorB)=P(A)+P(B)-P(A and B)
(Write your answer as a percent.)
(B) are a green piece of clothing and a jacket mutually exclusive events?
Explanation/Answer:
Total: 4 + 6 + 5 + 7 = 22
Green: 6 + 7 = 13
Probability: 13/22
Note: It Is Not Mutually Exclusive Events
15
25
15
23
15
23
17
21
21
19
15
a.) The standard deviation is(round to two decimal places)
b.) The variance is(round to one decimal place)
c.) The range is
2 of 5
The ratio of boys to girls in a class is
2.3. There are 30 students in the class
How many students are boys?
Answer:
2 boys.
Step-by-step explanation:
If the ratio is 2 : 3 then in a class of 5 there would be 2 boys and 3 girls. So we can say that 2/5 of the class are boys and 3/5 of the class are girls.
help me please ……………
Answer:
c
Step-by-step explanation:
If f(x) = 5 then what does f’ (x) equal?
Answer:
f'(x) = 0
Step-by-step explanation:
the derivative of a constant is zero , that is
f(x) = 5 ( a constant ) , then
f'(x) = 0
HELP ME PLEASE PLEASEPLEASE PLEASEEE
Mathematics
Find the rate
What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?
Show your solution, HELP PLS ASAP!!!
I'LL GIVE 20 POINTS!!
Answer:
Step-by-step explanation:
25%
80%
60%
100%
25%
Convert 12 kilograms to pounds. Use 1kilogram is 2.2 pounds
Answer:
26.4lbs
Step-by-step explanation:
2.2(12) = 26.4 the answer is 26.4Ibs
Powers of ten plz solve
Answer:
The correct answer is A
Step-by-step explanation:
Hope this helps
Answer:
670,000
Step-by-step explanation:
because 10 to the 4 power is 10,000 just add the zero of the number and times 67 give you the answer 670,000
-4x+3 >-5 Solve for a
Answer:
-4x+3>-5
or, -4x>-5-3
or, -4x>-8
or, -4x/-4<-8/-4
so, x<2
What is the vertical distance between the points C(2, -0.8) D(2,1.2)
Answer:
2 units
Step-by-step explanation:
vertical distance will be the magnitude of the difference in the 'y' coordinates
| -.8 - 1.2| = 2 units
Which statement about the zeros of the graphed function is true?
A polynomial function passes through (0.8, 4), (2, minus 4), (4.6, 0.5), (6, 0), and (7.5, 8) also intercepts the x-axis at 1, 4 and 6 units.
A.
The function has three distinct real zeros.
B.
The function has two distinct real zeros and two complex zeros.
C.
The function has four distinct real zeros.
D.
The function has one distinct real zero and two complex zeros.
The function has three distinct real zeros.
The correct answer is A.
To determine the statement about the zeros of the graphed function, let's analyze the given information.
We have the following points on the graph:
(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)
Additionally, the function intercepts the x-axis at 1, 4, and 6 units.
To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.
From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.
These three x-values correspond to three distinct real zeros of the function.
The correct statement about the zeros of the graphed function is:
The function has three distinct real zeros.
The correct answer is A.
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95% of what number is 114?
114 is 95% of 120
100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.
114 is 95 Percent of What Number?
Formula = Number x 100
Percent = 114 x 100
95 = 120
The following shows the steps to derive this formula and find out 95% of the number is 114.
Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.
114
95% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
95Y = 114 x 100
95Y = 11400
Y = 11400
100 = 120
Find the equation of the line with m=6 and b = -7. Write the equation in slope intercept form.
Answer: \(y=6x-7\)
Step-by-step explanation:
We use the formula y=mx+b to put it into slope-intercept form
m=6 (slope)
b=-7 (y-intercept)
Therefore, the answer is y=6x-7
factorise fully:
1) 2014² - 2013²
please explain and help
Which is equivalent to multiplying a number by 10 to the power of 4
Answer: 10,000
Step-by-step explanation:
The graph below shows the relationship between the number of dollars a worker earns and the number of hours worked.
Which statement best describes the rate of change for this situation?
A. The worker earns $40 per hour.
B. The worker earns $8 per hour.
C. The worker earns $10 per hour.
D. The worker earns $320 per hour.
Option B - The worker earns $8 per hour is the correct alternative.
We have a graph that shows the relationship between the number of dollars a worker earns and the number of hours worked.
We have to select the statement which best describes the rate of change for this situation.
How do you calculate the Slope of Line ?The slope of a line can be calculated using -
\($m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)
According to the question, we have two coordinate points marked on the graph -
P(20, 60)
Q(40, 320)
Using the formula to calculate the slope of a line, we get -
\($m = \frac{320-160 }{40 -20 }\)
m = 8
We know that the slope of the line represents the rate of change of y with respect to x. Therefore, the worker earns $8 per hour.
Hence, Option B is correct.
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Find the measure of an angle if it’s supplement measures 30 less than 3 times it’s complement
Answer:
x=52.5
Step-by-step explanation:
x+3x-30=180
4x-30=180
4x=180+30
4x=210
x=52.5