Answer:
[tex]f(6) = f(-6)[/tex] --- True
[tex]f(6)=2 * f(3)[/tex] --- False
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2}{3} - 2[/tex]
Solving (a): f(6) = f(-6)
First, we solve for f(6) by substituting 6 for x in [tex]f(x) = \frac{x^2}{3} - 2[/tex]
[tex]f(6) = \frac{6^2}{3} - 2[/tex]
[tex]f(6) = \frac{36}{3} - 2[/tex]
[tex]f(6) = 12 - 2[/tex]
[tex]f(6) = 10[/tex]
Next, we solve for f(-6) by substituting -6 for x in [tex]f(x) = \frac{x^2}{3} - 2[/tex]
[tex]f(-6) = \frac{-6^2}{3} - 2[/tex]
[tex]f(-6) = \frac{36}{3} - 2[/tex]
[tex]f(-6) = 12 - 2[/tex]
[tex]f(-6) = 10[/tex]
We have that:
[tex]f(6) = f(-6) = 10[/tex]
Hence, the statement is true
Solving (b): [tex]f(6)=2 * f(3)[/tex]
We have that:
[tex]f(6) = 10[/tex]
Next, we solve for f(3) by substituting 3 for x in [tex]f(x) = \frac{x^2}{3} - 2[/tex]
[tex]f(3) = \frac{3^2}{3} - 2[/tex]
[tex]f(3) = \frac{9}{3} - 2[/tex]
[tex]f(3) = 3 - 2[/tex]
[tex]f(3) = 1[/tex]
[tex]2 * f(3) = 2 * 1[/tex]
[tex]2 * f(3) = 2[/tex]
So:
[tex]f(6)=2 * f(3)[/tex]
[tex]10 \neq 2[/tex]
Hence, the statement is false
Write an equation for the line in slope- intercept form. 2. Х -4 -2 o 2 4. -2 4
Answer:
y= -2x-3
Step-by-step explanation:
this is because the y intercept is at negative 3 and the rise over run is down 1 over 2
Lawrence bought 2/3 pound of roast beef. He used 3/4 of it to make a sandwich. How much beef did he use for his sandwich A 5/12 pound B 1/2 pound C 5/7 pound D 6/7 pound
Answer:
B) 1/2 pound
Step-by-step explanation:
Lawrence bought 2/3 pound of roast beef.
He used 3/4 of it to make a sandwich.
The amount of beef that he used for his sandwich is calculated as:
3/4 of 2/3 pounds of roast beef
3/4 × 2/3
= 6/12 pound
= 1/2 pound
Option B is the correct Option.
The cost of printing 200 business cards is $23. The cost of printing 500 business cards is $35. What linear equation that could be used to solve this problem?
***Answer when you can!***
Evaluate functions from their graph
g(-4)=??
Answer:
1
Step-by-step explanation:
That is the y coordinate when x is -4The monthly payment for a car lease is $530 for 18 months. The down payment is $2,000. The residual value is $7,000. What is the total cost of the lease? A. $18,540 B. $20,540 C. $25,540
Answer:
18540
Step-by-step explanation:
18 times 530 = 9540
9540 + 2,000 + 7,000= 18540
I did 18 times 530 because it said 530 for 18 months
The triangles in the picture are congruent by which method
A negative multiplied/divided by a negative (same signs) equals a _
positive
negative
Answer:
When you multiply two negative numbers or two positive numbers then the product is always positive. 3 times 4 equals 12. Since there is one positive and one negative number, the product is negative 12.
Step-by-step explanation:
In the diagram below, what is the equation that represents the relationship between the number of triangles and the perimeter of the figure they form? Use this table to help you create an equation.
Answer:
The perimeter of the figure as a function of the number of triangles is [tex]y = 6 + 4\cdot x[/tex].
Step-by-step explanation:
According to the diagram, we get the following facts:
i) For one triangle ([tex]x=1[/tex]), the total perimeter is ([tex]y=2\cdot 3 + 1\cdot 4 = 10[/tex]).
ii) For two triangles ([tex]x = 2[/tex]), the total perimeter is ([tex]y = 2\cdot 3 +2\cdot 4 = 14[/tex])
iii) For three triangles ([tex]x = 3[/tex]), the total perimeter is ([tex]y = 2\cdot 3 +3\cdot 4 = 18[/tex])
iv) For four triangles ([tex]x = 4[/tex]), the total perimeter is ([tex]y = 2\cdot 3 +4\cdot 4 = 22[/tex])
From these information we conclude that the equation that determines the perimeter of the figure as a function of the number of triangles is [tex]y = 6 + 4\cdot x[/tex].
Rewrite each linear equation in standard form. Then, state the values for A, B, and C.
0.09x-0.01y=0.39 _____
A=_______,B= _______,C= _______
Answer:
A = 9/100
B = -[1/100]
C = -[39/100]
Step-by-step explanation:
Given:
0.09x - 0.01y = 0.39
Find:
A,B,C
Computation:
Linear equation;
Ax + By + C = 0
So,
0.09x - 0.01y = 0.39
9x/100 - 1y/100 = 39/100
9x/100 - 1y/100 - 39/100= 0
So,
A = 9/100
B = -[1/100]
C = -[39/100]
THESE 2 QUESTIONS ASAP PLS! BRAINLIEST!!
Answer:
1=y=4x+-2 2=y=4x-3
Step-by-step explanation:
What is the opposite integer of –(–7)?
20 points
Need help ASAP!!!!!!!
Answer:
I can't see the assignment question. It says there is nothing attached...
Step-by-step explanation:
Write the recurring decimal 0.63as a fraction
Answer:
63/100, this can't further more simplified
Step-by-step explanation:
i hope it helped you please give me brainliest
Select the equation which represents the graph.
Question 1 options:
A: y − 3 = 3/2(x − 4)
B: y − 3 = 2/3(x − 4)
C: y − 3 =− 2/3(x − 4)
D: y − 3 = −3/2(x − 4)
Answer:
B. [tex] y - 3 = \frac{2}{3}(x - 4) [/tex]
Step-by-step explanation:
We can create an equation to represent the graph in point-slope form, given as [tex] y - y_1 = m(x - x_1) [/tex], by using a point (x1, y1) on the line, (4, 3) and the slope (m) of the line.
Let's find slope using the two points (4, 3) and (-2, -1).
[tex] slope (m) = \frac{y_2 - y_1}{x_2 -x_1} = \frac{-1 - 3}{-2 - 4} = \frac{-4}{-6} = \frac{2}{3} [/tex]
Substitute m = ⅔, x1 = 4, and y1 = 3 in [tex] y - y_1 = m(x - x_1) [/tex].
The equation that represents the graph would be:
✅[tex] y - 3 = \frac{2}{3}(x - 4) [/tex],
Which set of points represents a function? { ( 1 , − 2 ) , ( 3 , − 5 ) , ( 3 , − 2 ) , ( 5 , − 7 ) , ( 7 , − 8 ) } { ( 1 , − 2 ) , ( 3 , − 5 ) , ( 3 , − 2 ) , ( 5 , − 7 ) , ( 7 , − 8 ) } { ( 0 , 1 ) , ( 1 , − 3 ) , ( 2 , − 5 ) , ( 3 , − 7 ) , ( 4 , − 9 ) } { ( 0 , 1 ) , ( 1 , − 3 ) , ( 2 , − 5 ) , ( 3 , − 7 ) , ( 4 , − 9 ) } { ( − 1 , 1 ) , ( − 1 , 3 ) , ( − 1 , 5 ) , ( − 1 , 7 ) , ( − 1 , 9 ) } { ( − 1 , 1 ) , ( − 1 , 3 ) , ( − 1 , 5 ) , ( − 1 , 7 ) , ( − 1 , 9 ) } { ( − 4 , 0 ) , ( − 3 , − 1 ) , ( − 3 , 1 ) , ( 0 , − 2 ) , ( 0 , 2 ) } { ( − 4 , 0 ) , ( − 3 , − 1 ) , ( − 3 , 1 ) , ( 0 , − 2 ) , ( 0 , 2 ) }
Given:
The set of points.
To find:
Which set of points represents a function?
Solution:
A set of points represents a function if there exist a unique y-value for each x-value.
It option A, the set of points is
{(1,-2), (3,-5), (3,-2), (5,-7), (7, -8)}
This is not a function because there exist two y-values y=-5 and y=-2 for x=3.
It option B, the set of points is
{(0,1),(1,−3),(2,−5),(3,−7),(4,−9)}
This is a function because there exist a unique y-value for each x-value.
It option C, the set of points is
{(−1,1),(−1,3),(−1,5),(−1,7),(−1,9)}
This is not a function because there exist five y-values y=1,3,5,7,9 for x=-1.
It option D, the set of points is
{(−4,0),(−3,−1),(−3,1),(0,−2),(0,2)}
This is not a function because there exist two y-values y=-1 and y=1 for x=-3.
Therefore, the correct option is B.
Answer:
problem ...
Which of the following sets represents a function?
{(3, 5), (-1, 7), (3, 9)
{(1, 2), (3, 2), (5, 7)}
{(1, 2), (1, 4), (1, 6)}
Step-by-step explanation:i think is
{(1, 2), (3, 2), (5, 7)}
BRAINLIEST ON THE LINE INFO IN PHOTO BELOW
Answer:
32 days is my final answer
Step-by-step explanation:
The First-person to get correct will get BRAINLESIT
I think of a number, multiply it by four, and subtract three. I get eleven. a) Using the statement above, form an equation. Use the letter 'x' for the unknown number.
b) Solve the equation
Use the table. Make a scatter plot relating the distance of various cities from the metro area to the population of the cities. SOMEONE HELP ASAP ILL GIVE BRAINLIEST
Answer:
Option (A)
Step-by-step explanation:
From the table attached,
Independent variable 'x' is will be represented by the distance from Metro area.
Similarly, dependent variable 'y' will be on y-axis.
Scatter plot relating the distances of various cities from the metro area (x) to the population of the cities (y) will be represented by the ordered pair as (x, y).
Set of ordered pairs to be plotted,
[(1, 300), (5, 275), (10, 208), (15, 135), (20, 108)]
Therefore, graph given in Option (A) will be the answer.
whats the slope of the line y-9=15 x-5
Answer:
Slope= 15
Hope this helps! :)
All of the points in the picture are on the same line.
YA
(6, 10)
(a, 8)
(4,5)
(2, 2)
1. Find the slope of the line. Explain or show your reasoning,
2. Write an equation for the line.
3. Find the values for a and b. Explain or show your reasoning
4. What is the y-coordinate when x = 0? Explain or show your reasoning.
Answer:
Did you ever get the answers??
The equation of the line is y = 2x - 2.
What is the point-slope form of a line?If m is the slope of the line that passes through the point (x₁, y₁), then the equation of the line is y - y₁ = m (x - x₁).
The graph of the line is given.
(1)
The line passes through points (2,2) and (6,10).
The slope of the line is:
m = (10 - 2)/(6 - 2)
m = 8/4
m = 2
(2)
The equation of the line with a slope of m =2 and passes through (2,2) is:
y - 2 = 2(x - 2)
y = 2x - 4 + 2
y = 2x - 2 (1)
(3)
The line passes through points (4,b) and (a,8), therefore, from equation (1):
b = 2(4) - 2
b = 6, and
8 = 2a - 2
2a = 10
a = 5
(4)
Substitute x = 0 into equation (1):
y = 2(0) - 2
y = -2
Hence, the equation of the line is y = 2x - 2.
Learn more about the point-slope form of a line:
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Which has a slope of -2?
Answer:
The answer would be line be because it goes down 2 and forward one.
Which of Earth’s spheres encompasses all of
Earth’s water?
a. the hydrosphere
b. the atmosphere
c. the asthenosphere
d. the geosphere
Answer:
The answer is A.
Step-by-step explanation:
All of earths bodies of water including groundwater. the hydrosphere also includes the cryosphere, which is made up of the worlds ice sheets and sea ice.
Answer:
a. the hydrosphere
Step-by-step explanation:
hydro means water
Leila was asked to solve the equation 2 over 3 left parenthesis x plus 5 right parenthesis equals 29. The first step she did to solve the equation was 2 over 3 left parenthesis x right parenthesis plus 2 over 3 left parenthesis 5 right parenthesis equals 29. What property did she use in this step?
A.associative
B.commutative
C.distributive
D.reflexive
Which answer is right !
It’s almost your birthday and you are saving up to buy a car. So far, you have $300 in your account. Each month, you will deposit another $200
Answer:
300+200
Step-by-step explanation:
did not give a equation
Answer:
300 + 200x
Step-by-step explanation:
200 is the one that's changing so it has the x.
What is the slope of the line?
Answer:
-1/2.
Change in y above change in x (don't mix that up)
The first coordinate is 3,-2 the second is 2,-4.
The change is x was -1 . (2-3)
The change in y was 2. (-4-(-2))
Select the expressions that are equivalent to 6u + U.
7u
U times 7
40 + 2u + u
3u + 4u
Answer:
7u, U times 7, and 3u + 4u.
2 The perimeter of a square is given as 12x + 20. Write two different expressions to
represent its perimeter. Use factoring for one way.
Answer:
The two expressions are;
4(3x + 5)
and
(6x + 10) + (6x + 10)
Step-by-step explanation:
Here, we want to write two different expressions to represent the perimeter of the square
The perimeter is given as 12x + 20
Using factoring, we can have this as;
4(3x + 5)
Otherwise, we can have
(6x + 10) + (6x + 10)
The town of Paxton has a population of 4.81 × 104 residents. The town of Oakville has twice the number of residents than Paxton. Which values represent the number of residents for the town of Oakville? Select all the values that apply
.A.9.62 × 10^8
B.4.81 × 10^6
C.9.62 × 10 ^4
D.4.81 × 10^8
E.4,810,000
F.96,200
plz help
Answer: A,F
Step-by-step explanation:
Sandy receives a $50000 salary for working as an engineer. If Sandy spends 60% of her
salary on expenses each year, then how much money does Sandy have to spend on
expenses? Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
50,000 * 60%= 30,000
If Sandy receives a $50000 salary for working as an engineer. If Sandy spends 60% of her salary on expenses each year, then Sandy spends $30,000 on expenses.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that, Engineer Sandy earns a salary of $50000 per year. If Sandy spends each year 60% of her income on expenses,
We have to find the amount Sandy has to spend on expenses,
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
The amount spend on the expenses is,
Expenses = 60% of the salary
Expenses =60/100 × $50000
Expenses = 30,000
Thus, if Sandy receives a $50000 salary for working as an engineer. If Sandy spends 60% of her salary on expenses each year, then Sandy spends $30,000 on expenses.
Learn more about the percentage here:
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I will give brainliest
A. 2x-1+3x=0
B. 5x-1=0
1) How can we get Equation B from Equation A?
Choose 1 answer:
(Choice A) Add/subtract the same quantity to/from both sides
(Choice B) Add/subtract a quantity to/from only one side
(Choice C) Rewrite one side (or both) by combining like terms
(Choice D) Rewrite one side (or both) using the distributive property