The ratio of the difference in outputs to the input interval is constant and equal to -8. This indicates that the function is a linear function with a slope of -8.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To find the differences of outputs for different input intervals, we can use the given function and the values in the table.
(a) The inputs that are 1 unit apart are -1 and 0. The corresponding outputs are f(-1) = -3 and f(0) = -11. The difference in outputs is:
f(0) - f(-1) = (-11) - (-3) = -8
Therefore, the difference of outputs of any two inputs that are 1 unit apart is -8.
(b) The inputs that are 2 units apart are -2 and 0. The corresponding outputs are f(-2) = 5 and f(0) = -11. The difference in outputs is:
f(0) - f(-2) = (-11) - 5 = -16
Therefore, the difference of outputs of any two inputs that are 2 units apart is -16.
(c) The inputs that are 3 units apart are -3 and 0. The corresponding outputs are f(-3) = 13 and f(0) = -11. The difference in outputs is:
f(0) - f(-3) = (-11) - 13 = -24
Therefore, the difference of outputs of any two inputs that are 3 units apart is -24.
(d) We can observe that the ratios of the differences in the outputs to the input intervals are constant, indicating that the function is linear. For example:
The ratio of the difference in outputs for inputs that are 1 unit apart to the input interval is:
-8 / (0 - (-1)) = -8 / 1 = -8
The ratio of the difference in outputs for inputs that are 2 units apart to the input interval is:
-16 / (0 - (-2)) = -16 / 2 = -8
The ratio of the difference in outputs for inputs that are 3 units apart to the input interval is:
-24 / (0 - (-3)) = -24 / 3 = -8
Therefore, the ratio of the difference in outputs to the input interval is constant and equal to -8. This indicates that the function is a linear function with a slope of -8.
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Original: $100, Discount: 13%
Answer:
Step-by-step explanation:
$87
I need help please solve for x given that TSU ~ FSG
Answer: X = 4
Step-by-step explanation:
TS/FS = SU/SG
3x-2/5 = 6/3
3(3x-2) = 6* 5
9x - 6 = 30
9x -6 + 6 = 30 + 6
9x = 36
x = 36/ 9
x = 4
Answer:
[tex]x = \frac{9}{6}[/tex]
Step-by-step explanation:
The first step is figuring out what the scale factor is
since [tex]2 \overline{\rm US} = \overline{\rm GS}[/tex] we know the scale factor is two
The second step is setting up the equation then solving the equation
[tex]2(3x -5) = 5[/tex]
[tex]6x - 4 = 5[/tex]
[tex]6x = 9[/tex]
[tex]x = \frac{9}{6}[/tex]
In AABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of AABC. Find length of each side of AMNK.
Answer:
4,5,6
Step-by-step explanation:
A midsegment connects two midpoints, and this triangle would be made up of all midsegments. If we know that midsegments are half of the side length, then we can get our answer.
3+x=x^2+3x Rewrite the equation by completing the square. What are the solutions to the equation?
Answer:
hope this helps
Step-by-step explanation:
3+x=x²+3x
Simply the equations.
= x+3=x²+3x
Subtract x²+3x from both sides.
x+3−(x²+3x)=x2+3x−(x²+3x)
−x2−2x+3=0
Factor left side of equation.
(−x+1)(x+3)=0
−x+1=0 or x+3=0
Answer:
x=1 or x=−3
please help me!!!!!!
Answer:
x = 25.5
Step-by-step explanation:
Since there is a pair of parallel lines and a line cutting across the lines, ∠5 and ∠12 are interior angles and add up to 180°.
∠5 + ∠12 = 180°
5x - 11 + x + 38 = 180
Evaluate like terms.
6x + 27 = 180
Isolate 6x.
6x = 180 - 27
= 153
Find x.
x = 153 ÷ 6
x = 25.5
If -1 2/3 is subtracted from 5 1/2, what will be the result?
a. negative
b. greater than 4
c. positive, but less than 4
d. equal to 4
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
When subtracting a negitive number from a positive number the difference ends up being a positive. The answer is 7, therefore, greater than 4.
Jason earns $78,000 per year. If he is paid weekly what is his weekly pay?
In one week he's made $1,500
Answer:
1,500 fffffffffffffffffffffffffffffffff
ab and bc length and midpoint
Emily has 5 packs of gum. Each pack has 50 pieces of gum. If Emily eats 9 pieces of gum, how many pieces of gum are left in all? Emily that’s a lot of gum...
Hurry please!!!!!!!!! It’s a timed test!!!!!!!
The function /(x) is shown on the graph.
What is f(0)?
A.12 only
B. 2 and 3 only
C. -2, -1, -1, and 2 only
D. -2,-1, 1, 2 and 12
Answer:
c
Step-by-step explanation:
please answer thank u i give brainliest to best answer
Answer:
A, B, C,
Step-by-step explanation:
Just use a calculator...?
a)
[tex]2^-^2*2^8=\frac{1}{2^2}*2^8=\frac{2^8}{2^2}=2^8^-^6=2^6=64\\[/tex]
b)
[tex]3^-^5*3^1=\frac{1}{3^5}*3=\frac{3}{243}=\frac{1}{81}[/tex]
c)
[tex]4^4*4^-^3=\frac{4^4}{4^3}=4^1=4[/tex]
d)
[tex]5^3*5^-^1=\frac{5^3}{5^1}=5^2=25[/tex]
e)
[tex]6^-^8*6^-^6=\frac{6^6}{6^8}=6^-^2=\frac{1}{6^2}=\frac{1}{36}[/tex]
f)
[tex]8^2*8^-^4=\frac{8^2}{8^4}=8^-^2=\frac{1}{8^2}=\frac{1}{64}[/tex]
Determine weather the following graph represents a function
Answer:
it doesn't because there are places where there are two y values which just doesn't work out.
how do you write 2x simplified?
Answer:
Simplify the numerator with the sine expression by taking A = B = x and simplify the denominator using A = x and B = 2x. The resulting denominator will have sin (2x) and cos (2x) which you can write in terms of sin (x) and cos (x) using the expressions above.
Step-by-step explanation:
If Frank builds a concrete rectangular walkway that is 4 feet wide by 1.5 feet deep, by 20 feet long from the house to the storage shed, what is the volume of concrete used to pave the walkway?
Feet Cubed
Answer:
120 ft
Step-by-step explanation:
Please review the full explanation below
Answer:
........................................................................................
Step-by-step explanation:
3х + y 2 – 7
Linear inquality
Answer:
xfgn
Step-by-step explanation:
How much fertilizer containing 30% nitrogen should be mixed with a fertilizer containing 10% nitrogen to get 10L of a fertilizer containing 12% nitrogen?
Answer:
1L of 30% fertilizer and 9L of 10% fertilizer
Step-by-step explanation:
Let x = the amount of fertilizer containing 30% nitrogen.
Let y = the amount of fertilizer containing 10% nitrogen
x + y = 10 because the two fertilizers together will be 10L
0.3x will be the amount of nitrogen in the 30% nitrogen fertilizer, and 0.1y will be the amount of nitrogen in the 10% fertilizer. If you add those together, you will get 12% of the nitrogen in the 10L mixture. This makes this equation:
0.3x + 0.1y = 0.12(10)
0.3x + 0.1y = 1.2
Now we have our two equations.
x + y = 10
0.3x + 0.1y = 1.2
We can use substitution to solve this system of equations.
x = 10 - y
Substituting this into the second equation, we have:
0.3(10-y) + 0.1y = 1.2
3 - 0.3y + 0.1y = 1.2
3 - 0.2y = 1.2
1.8 = 0.2y
9 = y
10 - 9 = 1L
There will be 9L of 10% nitrogen fertilizer and 1L of 30% nitrogen fertilizer.
given the function f defined by the formula f (x)=2x+1 find the following:
evaluate f(-5)
f(-5)=
f(-5)=
f(-5)=
Answer:
f(-5)=-9
Step-by-step explanation:
f(x)=y
So knowing that -5 is equal to x plug it in
y=(2)(−5)+1
y=−9
If you have more questions just ask.
A school carnival sold tickets to ride on a Ferris wheel. The charge was $3.00 for adults and $2.00 for students. If 54 tickets were sold for a total of $141.00, how many adult tickets were sold?
Answer:
33 adult tickets and 21 student tickets
Step-by-step explanation:
We will create a system of equations.
Let x = the number of adult tickets sold and let y = the number of student tickets sold
x + y = 54
3x + 2y = 141
We can cancel out the y by multiplying the first equation by -2.
-2x - 2y = -108
3x + 2y = 141
Adding these equations together we get:
x = 33
Plugging this into the equation, we have:
38 + y = 54
y = 21
There were 33 adult tickets and 21 student tickets
HELP ILL GIVE BRAINLIEST AND THANKS
I think my teacher is sleep deprived
I have actually no idea how to do this- none of the answer choices seem to be correct or maybe i'm just... anyways help me!!!
Question: -4pv+ 9= -5
a.3.5
b. -14
c. -45
Answer:
B. -14
Step-by-step explanation:
sana maka tulong ako sayo
at ano ba ang grade nyo
help meeeeeeeeeeeeee
Answer:
18
Step-by-step explanation:
basic math .... hopefully it helped
Answer:
18
Step-by-step explanation:
PLS HELP FOR A GRADE DUE TODAY BRUH PLS
Answer:
A Yes, because every x-vaule has a single y-vaule
Step-by-step explanation:
None of the points share a point on the x axis meaning none of them are directly vertical of each other they are all seperate from each other.
Answer:
A
Step-by-step explanation:
Without graphing, classify each system
independent, dependent, or inconsistent.
3y + 2x= 12
36 - 9y = -6x
Answer:
The solution to the system of equations be:
[tex]y=4,\:x=0[/tex]
As the consistent system of equations has only one solution, it is independent.
Step-by-step explanation:
Given the system of equations
[tex]3y + 2x= 12[/tex]
[tex]36 - 9y = -6x[/tex]
solving the system of equations
[tex]\begin{bmatrix}3y+2x=12\\ 36-9y=-6x\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}3y+2x=12\\ -9y+6x=-36\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}3y+2x=12\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:9y+6x=36[/tex]
[tex]\begin{bmatrix}9y+6x=36\\ -9y+6x=-36\end{bmatrix}[/tex]
so
[tex]-9y+6x=-36[/tex]
[tex]+[/tex]
[tex]\underline{9y+6x=36}[/tex]
[tex]12x=0[/tex]
[tex]\begin{bmatrix}9y+6x=36\\ 12x=0\end{bmatrix}[/tex]
solve 12x=0 for x
[tex]12x=0[/tex]
Divide both sides by 12
[tex]\frac{12x}{12}=\frac{0}{12}[/tex]
[tex]x=0[/tex]
[tex]\mathrm{For\:}9y+6x=36\mathrm{\:plug\:in\:}x=0[/tex]
[tex]9y+6\cdot \:0=36[/tex]
[tex]9y=36[/tex]
Divide both sides by 9
[tex]\frac{9y}{9}=\frac{36}{9}[/tex]
[tex]y=4[/tex]
Thus, the solution to the system of equations be:
[tex]y=4,\:x=0[/tex]
As the consistent system of equations has only one solution, it is independent.
PLS HALP ASAP WILL GIVE BRAINLIEST FOR BEST ANSWER!!!
Steve set up a business making friendship bracelets. He earned $70 in January. He is projected to earn 120% more in February. How much is Steve projected to make in February? (1 point)
Question 30 options:
1)
$84
2)
$98
3)
$154
4)
$190
Answer:
70+120/100x70(1+100/100)=(100/100+120/100)= 220/100 hope helps you
Step-by-step explanation:
Answer:
154 dollary doooos
Step-by-step explanation:
Determine the intercepts of the line.
x-intercept ( , )
y-intercept ( , )
Answer:
y-100
x-250
Step-by-step explanation:
because the lines are insecting the other lines on that line
I NEED HELP ASAP PLEASE AND THANK YOU.
Answer:
C
Step-by-step explanation:
Happy Holidays ❄️☃️
Ms. Ochoa recorded the age and shoe size of each
student in her physical education class. The graph
below shows her data.
Ages and Shoe Sizes of Students
in Ms. Ochoa's Class
9
.
83
8 8
.
Shoe Size of Student
7
6
0
13
14
11 12
Age of Student (years)
Which of the following statements about the graph
is true?
Answer:
The graph shows no trend.
Step-by-step explanation:
See attachment for given graph
Required
What is true about the graph?
From the attached graph, the following points can be deduced:
The data points show no patternThe data points at the same horizontal or vertical level are far away from one anotherWe can not conclude if y increases or decreases as x increase or decreasesBecause of the highlighted points, it is safe to conclude that the graph shows no trend.
Answer:
D
Step-by-step explanation:
A lifeguard can swim at a speed of 6 feet per second and run at a speed of 10 feet per second. The lifeguard is standing at the edge of a beach, looking at the ocean to the south. The lifeguard sees a drowning child in the ocean 100 feet east (down the shore) and 80 feet south (out at sea). How far should the lifeguard run before they start swimming?
The requried distance run and swam by the lifeguard is 100 - x. and √[x² + 80²] respectively.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The question seems to be incomplete, there must be a figure that illustrates the situation,
Since, as of the given data, he might run x distance less toward the east as of the 100 feet east, and than swim, the distance is given as,
= √[x² + 80²].
And the distance run = 100 - x.
Thus, the requried distance run and swam by the lifeguard is 100 - x. and √[x² + 80²] respectively.
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2x^2 - 3x - 2 = X + 4
The equation is represented by the system shown
here.
Check all of the solutions to this equation
-1, 3, 7, (-1, 3), (3, 7)
Answer:-1 and 3
Step-by-step explanation:
Took it on edge :)
The required solution of the given equation is (3, -1) which is the correct option (C).
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The equation is below represented by the system shown here.
2x² - 3x - 2 = x + 4
Rearrange the terms of variables and constants in the above equation
2x² - 3x - 2 - x - 4 = 0
Apply the arithmetic operation in the likewise terms,
2x² - 4x - 6 = 0
2x² - 6x + 2x - 6 = 0
2x(x - 3) + 2(x - 3) = 0
(x - 3)(2x + 2) = 0
(x - 3) = 0 and (2x + 2) = 0
x = 3 and 2x = - 2
x = 3 and x = - 1
Therefore, the required solution of the given equation is (3, -1).
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If f(x)=2x and g(x)=x−3, then find f(x)·g(x).
Question 19 options:
2x2−6x
2x2−6
2x2−3
3x−3
Answer:
2x^2 - 6x
Step-by-step explanation:
2x(x-3)
= 2x^2 - 6x
Complete the square and put this function in vertex form: f(x)=x^2+20x+96
Answer:
f(x) = (x+10)^2 - 4
Step-by-step explanation:
vertex form is y = a(x-h)^2+k
to complete the square, we want to add a number on both sides so x^2+20x+whatver the number is, is the square of something
to find that number take 20, divide by 2, and then square it to get 100.
so, you would get f(x)+100 = x^2+20x+100+96
subtract 96 on both sides: x^2+20x+100 = f(x) + 4
factor: f(x) = (x+10)^2 - 4