[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]
[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]
The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;
x g(x)
1 0
2 3
3 6
We are given;f(x) = x − 1
We want to find; g(x) = 3⋅f(x)
This means that; g(x) = 3(x - 1)
Looking at the options, the input values to be used are x = 1, 2 3.
Thus;When x = 1; g(x) = 3(1 - 1 )
g(x) = 0
When x = 2; g(x) = 3(2 - 1)
g(x) = 3
When x = 3; g(x) = 3(3 - 1)
g(x) = 6
Looking at the options, only the table in option D is correct.
Read more at; https://brainly.in/question/24797649
Pls help me fact than you
Answer:
6/7.
Step-by-step explanation:
The sum of the 2 numbers is greater than 5 in 6 out of 7 throws.
So the required experimental probability is 6/7.
Answer:
The experimental probability that the sum of the next two number rolled is more than 5 is [tex]\frac{6}{7}[/tex].
Step-by-step explanation:
From the given table it is clear that
Roll 1 : 6+6=12>5
Roll 2: 6+1=7>5
Roll 3: 3+5=8>5
Roll 4: 6+2=8>5
Roll 5: 6+4=10>5
Roll 6: 5+1=6>5
Roll 7: 3+2=5
There is information about 7 roll, therefore the total possible outcomes is 7.
6 out of seven rolls resulted in a sum greater than 5, therefore the favorable outcomes is 6.
The experimental probability that the sum of the next two number rolled is more than 5 is
[tex]P=\frac{\text{Favorable outcomes}}{\text{Total possible outcomes}}[/tex]
[tex]P=\frac{6}{7}[/tex]
Therefore the experimental probability that the sum of the next two number rolled is more than 5 is [tex]\frac{6}{7}[/tex].
For which values of P and Q does the following equation have infinitely many solutions?
Px+35=−6x+Q
[tex]\bf Px+35=-6x+Q\implies \stackrel{P}{~~\begin{matrix} -6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}x+35=~~\begin{matrix} -6x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+\stackrel{Q}{35}\implies 35=35[/tex]
whenever you get an equality like so, that's a flat that both equations are exactly one and the same and thus the system has "infinitely many solutions".
The volume of a cube is 27n27 cubic units. What is the lenth of one side of the cube?
Answer: B . on your test
Step-by-step explanation:
A man earns a base salary of 2000$ and every year he got araise of 7% on his total income.huv much total income would he get by end of 4 years
Answer:
his total income by the end of 4 years will be: $2622.
Step-by-step explanation:
A man earns a base salary of $2000, and every year he got a raise of 7% on his total income.
The first year, he will earn: 1.07($2000) = $2140
The second year he will earn: 1.07($2140) = $2289.8
The third year he will earn: 1.07($2289.8) = $2450.086
The fourth year he will earn: 1.07($2450.086) = $2621.59202
Therefore, his total income by the end of 4 years will be: $2622.
A rock dropped on the moon will increase its speed from 0 m/s (its starting
speed) to 8.15 m/s in about 5 seconds. If you were standing on the moon,
measuring the rock's motion, what would you measure for the magnitude of
its acceleration?
O
A. 8.2 m/s2
O B. 41 m/s2
O C. 9.8 m/s2
O D. 1.63 m/s2
The answer is:
The correct option is the option D
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Why?To calculate the acceleration, we need to use the following formula that involves the given information (initial speed, final speed, and time).
We need to use the following free fall equation:
[tex]V_{f}=V_{o}-g*t[/tex]
Where:
[tex]V_{f}[/tex] is the final speed.
[tex]V_{o}[/tex] is the initial speed.
g is the acceleration due to gravity.
t is the time.
We are given the following information:
[tex]V_{f}=8.15\frac{m}{s}[/tex]
[tex]V_{o}=0\frac{m}{s}[/tex]
[tex]t=5seconds[/tex]
Then, using the formula to isolate the acceleration, we have:
[tex]V_{f}=V_{o}-g*t[/tex]
[tex]V_{f}=V_{o}-g*t\\\\g*t=V_{o}-V_{f}\\\\g=\frac{V_{o}-V_{f}}{t}[/tex]
Now, substituting we have:
[tex]g=\frac{V_{o}-V_{f}}{t}[/tex]
[tex]g=\frac{0-8.15\frac{m}{s}}{5seconds}=-1.63\frac{m}{s^{2}}[/tex]
Therefore, since we are looking for a magnitude, we have that the obtained value will be positive, so:
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Hence, the correct option is the option D
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Have a nice day!
Which number sentence does the following number line represent?
0-4+7= 3
3+(-4)=-7
04+3=7
3+(-7)=-4
Answer:
Last option: [tex]3+(-7)=-4[/tex]
Step-by-step explanation:
The number line can help us to make additions and subtractions.
To add a positive number we need to move the point to the right and to add a negative number we need to move the point to the left.
You can observe in the figure that the point on the number line is moved from 3 to -4, then it is moved 7 places to the left. Therefore, you can express it in the following form:
[tex]3+(-7)[/tex]
This is:
[tex]3+(-7)=3-7=-4[/tex]
Then the number line represents this number sentence:
[tex]3+(-7)=-4[/tex]
A population numbers 508 organisms initially and increases by 6.2% each year.
Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.
To find the population after t number of years, multiply the starting population by 1 plus the percent increase raised to the number of years.
The equation would be: P = 508(1.062)^t
What’s the mean
13, 18, 20, 25 , and 11
Answer:
its 17.4
Step-by-step explanation:
if you add all the numbers up then divide it by the amount of numbers you added together you get this answer
Answer 17.4
Explanation: you add them all up so 13+18+20+25+11 then divide by how many numbers there are so divide by 5 you will end up with 17.4
Which table shows a proportional relationship between a and b?
Answer:
Table B
Step-by-step explanation:
we know that
A relationship between two variables, a, and b, represent a proportional variation if it can be expressed in the form [tex]b/a=k[/tex] or [tex]b=ka[/tex]
In this problem the table B shows a proportional relationship because
For a=20, b=25 -----> b/a=25/20=1.25
For a=24, b=30 -----> b/a=30/24=1.25
For a=32, b=40 -----> b/a=40/32=1.25
The constant of proportionality k is 1.25
Answer:
Im pretty sure its B :)
Step-by-step explanation:
What is the vertex for the graph below?
Answer:
(-4, -4)
Step-by-step explanation:
Look for the vertex / minimum point on the graph. If you read the x- and y-axis scales correctly, you'll see that the vertex is located at (-4, -4). Not all the divisions on the x- and y-axes are marked; you have to mark them in your imagination.
Answer:
A.
Step-by-step explanation:
As in the picture we have that the parabola opens up, then the vertex will be the minimum point in the graph. Now, the minimum point of the parabola in the picture is in x= -4 and y = -4 (the points go two by two), I show you that values in the picture below. Then, the vertex of the graph showed in the picture is (-4,-4). Then, the answer is A.
Which expression is a perfect cube?
A. x8
B. y24
C. m28
D. x64
Answer:
B. Y²⁴
Step-by-step explanation:
For perfect cubes, the exponents are a multiple of three. If yᵃ is a perfect cube, then a/3=k where k is a whole number.
Among the provided choices, the exponent of y²⁴ is divisible by 3.
24/3 = 8.
Thus y²⁴ is a perfect cube.
Answer:
B
thats the answer on edge 2020
which equation can be used to find the volumes of the cylinder?
Answer:
π(4)²(16)
Step-by-step explanation:
Given r = 4, h = 16
Use formula for cylinder:
Volume of cylinder,
V = πr²h
= π(4)²(16)
Answer:
Answer:
π(4)²(16)
Step-by-step explanation:
Given r = 4, h = 16
Use formula for cylinder:
Volume of cylinder,
V = πr²h
= π(4)²(16)
Step-by-step explanation:
OBO QBODO 100
Which best describes the function on the graph?
direct variation; k = 1
direct variation; k = 4
inverse variation; k=1
inverse variation; k= 4
Answer:
Inverse variation k=4
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
In this problem
The graph represent a inverse variation
Because
if x increases ----> y decreases
if x decreases ----> y increases
Find the value of k
we have that
For x=2, y=2 -----> see the graph
[tex]k=y*x[/tex]
substitute
[tex]k=2*2=4[/tex]
1 less than the quotient of four and a number X
Answer:
Explanation of the above answer: “One less than the quotient of four and a number x. ""One less"" means you will subtract 1 from it. For that reason the overall expression is 4x-1.
Step-by-step explanation:
Please mark brainliest and have a great day!
Write g(x)=40x+4x^2..
Answer:
g(x)=40x+4x^2
Step-by-step explanation:
[tex]g(x) = 40x + 4 {x }^{2} [/tex]
A parallelogram has a perimeter of 37.2 yards. Two of the sides are each 16.1 yards long. What is the length of each of the other two sides?
Answer:
2.5
Step-by-step explanation:
16.1 + 16.1 = 32.2
37.2 - 32.2 = 5
5 / 2 = 2.5
Mark Me Brainliest!!
One number is 6 times another number. The sum of the two numbers is 84. Find the two numbers.
Answer:
x = 72
y = 12
Step-by-step explanation:
x = 6y
x + y = 84
Just Guess & Check lol
find the solution of this system of equations x=4+y -10x+6y+-28 separate x and y values with a comma.
ANSWER
The solution is (1,-3)
EXPLANATION
The system of Equations are;
[tex]x=4+y[/tex]
and
[tex]-10x+6y=-28[/tex]
We substitute the first equation into the second equation to get:
[tex]-10(4 + y)+6y=-28[/tex]
We expand the parenthesis to get:
[tex]-40 - 10y+6y=-28[/tex]
Group similar terms to get:
[tex]- 10y+6y=-28 + 40[/tex]
Simplify the similar terms to get;
[tex] - 4y = 12[/tex]
Divide both sides -4.
[tex]y = \frac{12}{ - 4} [/tex]
[tex]y = - 3[/tex]
We put y=-3 into the first equation to get:
[tex]x = 4 + - 3 = 1[/tex]
Therefore the solution is (1,-3)
Irina had $300 and then earned $50 each week for 3 weeks. Last week, she bought groceries for $37 and two $25 gift
cards. How much money does she have left?
A.$63
B.$363
C.$578
D.$3,889
Answer:
B)$363
Step-by-step explanation:
since she earned $50 each week
50x3=150
then plus the $300 she has
300+150= 450
then add the groceries and two $25 gifts
25x2=50
37+50=87
then take that away from the amount of money she has
450-87=363
Irina has $63 left.
Explanation:To calculate how much money Irina has left, we need to follow these steps:
Start with $300, which is her initial amount.Add $50 for each of the 3 weeks she earned money. $50 + $50 + $50 = $150.Subtract the amount she spent on groceries and gift cards from the total amount she earned. $150 - $37 - $25 - $25 = $63.Therefore, Irina has $63 left.
Learn more about Calculating remaining money here:https://brainly.com/question/37861577
#SPJ2
(NOTE I PUT THE GRAPH IN SO PLZ HELP )The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.
What is the slope of the line
Answer: -2
Step-by-step explanation:
The slope of a line passing through points (a,b) and (c,d) is given by :-
[tex]m=\dfrac{d-b}{c-a}[/tex]
From the given graph , the line is passing from points (6,33) and (15,15).
Now, the of a line passing through points (6,33) and (15,15) is given by :-
[tex]m=\dfrac{15-33}{15-6}=\dfrac{-18}{9}\\\\\Rightarrow\ m=-2[/tex]
Hence, the slope of the line = -2
plz answer How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
Two solutions
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
Both lines have a slope m = - [tex]\frac{1}{2}[/tex]
Hence the lines are parallel and have no points of intersection
Thus the system has no solution → A
which number produces a rational number when added to 0.42?
The number 0.58 produces a rational number when added to 0.42.
What is a rational number ?A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. It can be expressed as a whole number or in the fractional format.
How to find the number that produces the rational number ?Let us find the nearest rational number which can be expressed in the whole number format.
For 0.42, the nearest rational number is 1 .
Thus the number added to 0.42 is (1 - 0.42) = 0.58 .
Therefore, the number 0.58 produces a rational number when added to 0.42.
To learn more about rational number, refer -
https://brainly.com/question/12088221
#SPJ2
The public debt of Apexistan is 5,446,772,143,940,528 Apex dollars, while its
gross domestic product (GDP) is 13,647,498,222,417,097 Apex dollars. What
is Apexistan's debt-to-GDP ratio?
O A. 5%
O B. 40%
C. 13%
O D. 251%
Answer:40 %
Step-by-step explanation:
Given
Debt=5,446,772,143,940,528 $
Gross domestic product(GDP)=13,647,498,222,417,097 $
Debt to GDP ratio is
=[tex]\frac{5,446,772,143,940,528}{13,647,498,222,417,097}[/tex]
=0.399104
[tex]39.91 \%\approx 40\%[/tex]
Polygon A is similar to polygon B. The sides of polygon A are twice the length
of the corresponding sides of polygon B. The perimeter of polygon Ais 100.
What is the perimeter of polygon B?
Answer:
50
Step-by-step explanation:
half of polygon A is 50 the sides of polygon A are twice the length
of the corresponding sides of polygon B.
It's the sum of the length of the sides used to make the given figure. The perimeter of Polygon A is 50 units.
What is the perimeter?It's the sum of the length of the sides used to make the given figure.
Given Polygon A is similar to polygon B. Also, The perimeter of polygon Ais 100. Now, let the number of sides in Polygon A be n, while the length of a side is 2x. Therefore, the perimeter of the polygon A is,
n × 2x = 100
Given the length of the side of the polygon B is half the length of the side of polygon A. Therefore, the perimeter of polygon B is,
n × x = Perimeter
Now, if the ratio of the two equations is taken then,
(n × 2x)/ (n × x) = 100/ Perimeter
2 = 100/Perimeter
Perimeter = 50 units
Hence, the perimeter of Polygon A is 50 units.
Learn more about Perimeter:
https://brainly.com/question/10466285
#SPJ2
These tables represents a quadratic function with a vertex at (0,3) what is the average rate of change for the interval from x=8 to x=9
There are a few ways to do it; the easiest is just to follow the pattern of taking away two from the average.
The next lines of the table are
6 to 7 -13
7 to 8 -15
8 to 9 -17
Answer: C. -17
Let's find the equation and do it that way.
We have a vertex at (0,3) so we can fill out the vertex form a bit. In general for vertex (p,q) it's
y = a(x-p)^2+q
We have
f(x) = ax^2 + 3
f(1) = 2
a+3 =2
a = -1
So we found our equation,
y = -x^2 + 3
Let's check it at x=5, y=-5^2+3=-25+3=-22, good
We want the rate of change from 8 to 9, which is
[tex]r = \dfrac{f(9)-f(8)}{9-8}=f(9)-f(8)=-9^2 - -8^2 = -17[/tex]
Answer: -17 again, that checks
The average rate of change for the interval from x=8 to x=9 is -17.
The correct option is (C)
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
We have a vertex at (0,3).
In general let us take vertex (p,q) then
y = a(x-p)²+q
We have,
f(x) = ax² + 3
as x=1, f(x)=2
so,
f(1) = 2
a+3 =2
a = -1
Now, the equation
y = -x² + 3
Thus, the rate of change from 8 to 9
= f(9)-f(8)/9-8
= -9²-(-8)²
=-81+64
=-17
Hence, the average rate of change for the interval from x=8 to x=9 is -17.
Learn more about this concept here:
https://brainly.com/question/14372714
#SPJ2
what do both dependent and inconsistent systems have in common
Answer:
both equations represent the same line
Step-by-step explanation:
Find y if the line through (1,y) and (5,7) has a slope of 6.
What number should be added to –2 to get a sum of 2?
Answer:
4
Step-by-step explanation:
4 - 2 = 4 + -2 = -2 + 4
To build a cottage, Mia loaded her wheelbarrow with 39.50 kg of bricks, 70.32 kg of lumber, and 67.39 kg of miscellaneous supplies. What was the weight of the heaviest supply?
Answer:
70.32 kg
Step-by-step explanation:
70.32 is bigger than 39.50 and 67.39
so it is the heaviest supply.
Answer:
70.32 kg
Step-by-step explanation:
Put the numbers from smallest to largest, since the units are the same
39.5, 67.39, 70.32
The largest is 70.32, so that is the heaviest
Using the given points, determine the delta symbol y. (-3,-5) and (0,10)
Answer:
Δy = 15
Step-by-step explanation:
Δy represents the change in the y-coordinates
We are given points (-3,-5) and (0,10)
here y₁ = -5 and y₂ = 10
so, delta y will be
Δy = y₂ - y₁
Δy = 10 -(-5)
Δy = 10 + 5
Δy = 15
So, delta y Δy =15