Both A and B represent functions, as the same x value is not used twice.
However, with option C, the x value -2 is used twice, and thus it is not a function.
The concept of functions in mathematics is determined by whether each input (or 'x' value) corresponds to exactly one output (or 'y' value). Upon examination, the sets of ordered pairs in option A qualify as functions, while the sets in options B and C do not.
Explanation:A function in Mathematics is a relation between a set of inputs and a set of outputs where each input is related to exactly one output. In your question, you have three different sets of ordered pairs. Let's examine them.
A. [(-2,3)], [(-1,5)], [(0,7)], [(1,9)]
Here every 'x' value is paired with only one 'y' value, so this one is a function.
B. [(-3,3)], [(3,3)], [(0,0)], [(1,1)], [(-1,1)]
For this one, we see that 'x' values -1 and 1 are both paired with 'y' value 1. This implies that a single 'x' value has more than one 'y' value which is not allowed for a function. So this one is not a function.
C. [(-2,5)], [(-1,4)], [(0,3)], [(-1,2)], [(-2,1)]
This one is similar to the second case where 'x' values -1 and -2 are both paired with multiple 'y' values. So, this one is not a function either.
So, only the first set constitutes a function.
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Graph the equation on the coordinate plane.
y=−2x
Use editing software or windows paint to edit dots, thanks!
Solution :
Given, the equation [tex]y=-2x[/tex].
To graph the equation on the coordinate plane, we first need to derive the different points of the equation [tex]y=-2x[/tex],
[tex]at\:\;x=0\Rightarrow y= -2(0)=0\\\\at\:\;x=1\Rightarrow y= -2(1)=-2\\\\at\:\;x=2\Rightarrow y= -2(2)=-4\\\\at\:\;x=3\Rightarrow y= -2(3)=-6\\\\at\:\;x=-1\Rightarrow y= -2(-1)=2\\\\at\:\;x=-2\Rightarrow y= -2(-2)=4\\\\at\:\;x=-3\Rightarrow y= -2(-3)=6[/tex]
The graph plotted using these points is shown in the figure,
Gabriel needs d more dollars to buy a new video console that coast $156.75. He has saved $98.26. Solve the equation $98.26 + d = $156.75 to find out how much more money Gabriel needs.
Just subtract 98.26 from 156.75. It equals $58.49.
you can use subtraction by doing 156.75 minus 98.26 when you do that the amount he still needs is 58.49
Triangle ABC has vertices at A(−1 , 2), B(4, 2), and C(3, −1). Classify the triangle according to the side lengths.
A) equilateral
B) isosceles
C) right
D) scalene
Answer:
B) Isosceles
Step-by-step explanation:
The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).
We must first determine the length of the sides of the triangle, before we can classify it.
We apply the distance formula to find length of the sides.
[tex]|AB|=\sqrt{(4--1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{5^2+(0)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{25}[/tex]
[tex]\Rightarrow |AB|=5 units[/tex].
The length of side BC
[tex]|BC|=\sqrt{(3-4)^2+(-1-2)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{1+9}[/tex]
[tex]\Rightarrow |BC|=\sqrt{10}[/tex]
The length of side AC
[tex]|AC|=\sqrt{(3--1)^2+(-1-2)^2}[/tex]
We simplify to obtain;
[tex]|AC|=\sqrt{(3+1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{16+9}[/tex]
[tex]|AC|=\sqrt{25}[/tex]
[tex]|AC|=5\:units[/tex]
Since [tex]|AC|=5\:units=|AB|[/tex], the given triangle is an isosceles triangle.
The correct answer is
Answer:
B) isosceles
Step-by-step explanation:
10x=-80
I could us some hlp
10x = -80
Note the equal sign. What you do to one side, you do to the other.
Divide 10 from both sides
10x/10 = -80/10
x = -80/10
x = -8
-8 is your answer for x
---------------------------------------------------------------------------------------------------------------------
~Rise Above the Ordinary, Senpai
answer: x = -8
work:
you're working to solve for x.
this means you want to isolate x, and get it alone.
to do so, divide both sides by 10 to get rid of the 10.
once you divide both sides by 10, x is on its own, and you have the solution to your equation, x = -8!
to check your work you can plug the value for x into the original equation and solve.
10(-8) = -80
-80 = -80
so we can verify this is in fact correct.
i hope this helps, and have a great day! don't hesitate to ask if you need more help with this specific question! ♥ - eviezoom
Evaluate –4 – w for w = –7
i think the answer might be 3
The answer is 3. Have a great day!
Car dealerships claim to make most of their money from servicing cars. In a certain month, an Acura dealership sold fifteen less used cars than twice the number of new cars. In the smae month, they serviced fifty more than twelve times the number of new cars sold. If the dealership either sold or services a total of 335 cars that month, how many new cars were sold that month? How many use? How many serviced?
Answer:
New cars sold = 20,
Used cars sold = 25
Cars serviced = 290
Step-by-step explanation:
In a month they sold fifteen less used cars than twice the number of new cars.
Lets say 'x' number of new cars were sold, then:
The number of used car sold is:
[tex]2\times x-15=2x-15[/tex]
In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:
[tex]12\times x+50=12x+50[/tex]
Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:
[tex]x+(2x-15)+(12x+15)=335[/tex]
Solving for 'x' we get:
[tex]x+2x+12x-15+50=335[/tex]
[tex]15x+35=335[/tex]
[tex]15x=335-35=300[/tex]
[tex]x=\frac{300}{15}=20[/tex]
Therefore, the number of new cars sold in that month is 20.
Number of used car sold [tex]=2x-15=2\times 20-15=40-15=25[/tex]
Number of cars serviced [tex]=12\times x+50=12\times20+50=240+50=290[/tex]
We can also cross check by summing them up:
[tex]290+25+20=335[/tex]
Evaluate the algebraic expression for the given variable
-x- -3,x=-5
which expression represents “seventeen more than one-fourth y”
hello again
17-1/49 is your correct answer thank you and have a great day please mark me as brainliest if can
Answer:
Expression which represents “seventeen more than one-fourth y” is:
[tex]\dfrac{1}{4}y+17[/tex]
Step-by-step explanation:
We have to find a expression which represents
“seventeen more than one-fourth y”
one-fourth y= [tex]\dfrac{1}{4}y[/tex]
So, seventeen more than one-fourth y= [tex]\dfrac{1}{4}y+17[/tex]
Hence, expression which represents “seventeen more than one-fourth y” is:
[tex]\dfrac{1}{4}y+17[/tex]
I am very confused lol... So I'm doing a worksheet for Algebra 1 (highschool) and we're doing division and multiplication with fractions at the moment to review what we learned last year and I'm stuck. Right now I'm doing #1 and ended up getting 7 1\2... so I ended up doing this as my equation..
[tex]3 \frac{3}{4} \div \frac{1}{2} [/tex]I have no idea if I'm supposed to do division with this but I tried division and multiplication and got 7 1\2 Everytime I did it. And I know the answer is 1 7/8 cause I may have found a cheat sheet online but I still need to know how to do it. Anyways this is what I did:
[tex]3 \frac{3}{4} \div \frac{1}{2} [/tex]
[tex] \frac{15}{4} \times \frac{2}{1} = \frac{30}{4} [/tex]
[tex] \frac{30}{4} = \frac{15}{2} = 7 \frac{1}{2} [/tex]
I don't understand what I'm doing wrong lol.
OK first change 3 3/4 to an improper fraction and that will give you 15/4. so you got that part right. Next, change the division sign to multiplication. then flip the 1/2 to 2/1. Then multiply 15 times 2 and that will give you 30. Then multiply 4 times 1 and that will give you 4. then you will have an answer of 30/4. Finally, since you a have a big number over a small number you divide 30 by 4 and that will give you 7 1/2. So it turns out that your little cheat sheet is wrong because when you check your answer you should go on Math-way to check it. Also, a little background about me is that I am in 8th grade and I am taking algebra 1 too.
How much longer is a 1 inch button than a 3 over 8 inch button
Subtract.
1 - 3/8 = 5/8
x intercept and y intercept
x + 8y = 0
x - intercept when y = 0:
x + 8(0) = 0
x + 0 = 0
x = 0
y - intercept when x = 0:
0 + 8y = 0
8y = 0 |:8
y = 0
Answer:
The x-intercept is 0
The y-intercept is 0
What is the midpoint of AB?
The formula of a midpoint:
[tex]\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have
[tex]A(-2,\ 5),\ B(3,\ -3)[/tex]
Substitute:
[tex]\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\\dfrac{5+(-3)}{2}=\dfrac{2}{2}=1[/tex]
Answer: (0.5, 1).
Answer:
The midpoint of AB is (0.5,1).
Step-by-step explanation:
From the given graph it is clear that the vertices of the triangle ABC are A(-2,5), B(3,-3) and C(-4,-1).
If end points of a line segment are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the midpoint of that segment is
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We need to find the midpoint of AB.
[tex]Midpoint=(\frac{-2+3}{2},\frac{5+(-3)}{2})[/tex]
[tex]Midpoint=(\frac{1}{2},\frac{5-3}{2})[/tex]
On further simplification we get
[tex]Midpoint=(\frac{1}{2},\frac{2}{2})[/tex]
[tex]Midpoint=(0.5,1)[/tex]
Therefore the midpoint of AB is (0.5,1).
if ( 6^2) ^x =1 what is the value of x
What is the slope and y intercept of y= 3
the slope is 0 over 1 and the y-intercept is 3
Help!! I have no clue
okay so you just plug in the x and ys. x is the first number, y is the second. then you just do them all out
So we know that an ordered pair looks like (x,y), right? For this inequality, we're supposed to plug in the values of x and y. If it isn't true, then the inequality does not represent the ordered pair.
First option: (0,1)
[tex]2x + 3y \geq -1[/tex] --> [tex]2(0) + 3(1) \geq -1[/tex] --> [tex]5 \geq -1[/tex]
So this option is correct.
Second option: (-2,1)
[tex]2x + 3y \geq -1 --> 2(-2) + 3(1) \geq -1[/tex]
--> [tex]-4 + 3 \geq -1 --> -1 \geq -1[/tex]
This is also correct.
Third option: (-6,0)
[tex]2(-6) + 3(0) \geq -1 --> -12 \geq -1[/tex]
This is not true, so this option is not correct.
Fourth option: (0,-1)
[tex]2(0) + 3(-1) \geq -1 --> -3 \geq -1[/tex]
This is not correct.
Fifth option: (2,-1)
[tex]2(2) + 3(-1) \geq -1 --> 4 - 3 \geq -1[/tex]
This is correct.
Sole the equation for the indicated variable.
zm= a+b/a, for a
zm= a+b/a, for a
Switch sides to have a on left side
a+b/a=zm
Now multiply both sides by a
A+b= zm(a)
A+b= ama
Now subtract azm both sides
A+b-azm=0
Subtract b both sides
A-azm= -b
Factor out a from ask
A(1 -zm)= -b
Divide each term by 1 - zm to get
A= - b/1-zm
Choose the graph below that correctly represents the equation 2x + 4y = 24.
A. line through the points 0 comma 6 and 12 comma 0
B. line through the points 0 comma negative 6 and 12 comma 0
C. line through the points 0 comma negative 12 and 6 comma 0
D. line through the points 0 comma 12 and 6 comma 0
a line through the point (0, 6 )
to find a point on the line, choose any value of x , substitute into the equation and solve for y
x = 0 : 0 + 4y = 24 ( divide both sides by 4 )
y = [tex]\frac{24}{4}[/tex] = 6
hence line goes through (0, 6 )
The correct graph that represents the equation 2x + 4y = 24 is option A, which shows a line through the points (0, 6) and (12, 0).
Explanation:The equation 2x + 4y = 24 can be rearranged to y = -0.5x + 6. This means that the equation represents a linear function with a slope of -0.5 and a y-intercept of 6.
Option A, which shows a line through the points (0, 6) and (12, 0), is the correct graph since it satisfies the equation. The slope is -0.5 and the y-intercept is 6.
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Please help. Thanks!
B. The equation of this line is x = 3.
E. This graph is not a function because the value x = 3 is assigned to more than one y-value.
7-3x=x-4(2+x)
helppp
is 1000 a perfect cube?
Think of a cube with side lengths of 10.
The volume of the cube will be L*W*H = 10*10*10 = 1000
This volume of 1000 is what we consider a perfect cube.
Answer: yes
10*10*10=[tex]10^{3}[/tex]
10*10*10=1,000
1,000 is a perfect cube, because 10^3 is 1,000.
I hope this helps :)
Colton solved an equation incorrectly, as shown below:
Step 1: x − 13 = 26
Step 2: x = 26 − 13
Step 3: x = 39
Which statement best explains why Step 2 is incorrect in Colton’s solution?
He did not subtract 13 from 26.
He did not multiply 26 by 13.
He did not add 13 to 26.
He did not divide 26 by 13.
Answer:
He did not add 13 to 26.
Step-by-step explanation:
Given : Step 1: x − 13 = 26
Step 2: x = 26 − 13
Step 3: x = 39
To Find: Which statement best explains why Step 2 is incorrect in Colton’s solution?
Solution:
Correct steps
Step 1:[tex]x- 13 = 26[/tex]
Step 2:[tex]x = 26+13[/tex]
Step 3:[tex]x = 39[/tex]
So, this concludes that He did not add 13 to 26 in step 2
So, Option C is correct.
Hence He did not add 13 to 26.
Answer:
he did not add 13 to 26
Step-by-step explanation:
A case of 24 pairs of the same kind of sports shoes costs a little more than $800.Explain whether $28 per pair with tax included is a good estimate.
Answer:
$28 per pair is not a good estimate.
Step-by-step explanation:
Let x represent cost of each pair with tax.
We have been given that a case of 24 pairs of the same kind of sport shoes cost a little more than $800.
The cost of 24 pairs would be [tex]24x[/tex].
[tex]24x>800[/tex]
[tex]\frac{24x}{24}>\frac{800}{24}[/tex]
[tex]x>33.33[/tex]
Since the cost of each pair is greater than $33.33, therefore, $28 is not a good estimate.
The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function. Which equation represents that function? f(x) = 2x f(x) = 3x f(x) = 4x f(x) = 5x
Answer:
Option D is the correct answer.
Explanation:
The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function.
We need to find f(x)
Checking each options.
a) f(x) = [tex]2^x[/tex]
For (0,1)
f(0) = [tex]2^0=1[/tex]
For (1,5)
f(1) = [tex]2^1=2[/tex], given that f(1) = 5, so option A is wrong.
b) f(x) = [tex]3^x[/tex]
For (0,1)
f(0) = [tex]3^0=1[/tex]
For (1,5)
f(1) = [tex]2^1=3[/tex], given that f(1) = 5, so option B is wrong.
c) f(x) = [tex]4^x[/tex]
For (0,1)
f(0) = [tex]4^0=1[/tex]
For (1,5)
f(1) = [tex]4^1=4[/tex], given that f(1) = 5, so option C is wrong.
d) f(x) = [tex]5^x[/tex]
For (0,1)
f(0) = [tex]5^0=1[/tex]
For (1,5)
f(1) = [tex]5^1=5[/tex]
For (2,25)
f(2) = [tex]5^2=25[/tex]
For (3,125)
f(3) = [tex]5^3=125[/tex]
So all values are satisfied Option D is the correct answer.
Which of the inequalities represents the statement, "Two times a number x, less 15, is greater than or equal to 4 times the number y"? A) 2x - 15 ≤ 4y B) 2x - 15 ≥ 4y C) 2x + 15 ≤ 4y D) 15 - 2x ≤ 4y
Therefore, the best and most correct answer among the choices provided by the question is the fourth choice "15 - 2x ≥ 4y". I hope my answer has come to your help.
Answer:
Step-by-step explanation: B) 2x - 15 ≥ 4y is the correct answer
a rock fell from a cliff at 108 feet high and landed on an embankment feet from the ground. find the amount if time it would have taken the rock to fall.
To solve this problem we will directly use the formula:
[tex]h=\frac{1}{2}gt^2[/tex]..........Equation 1
where symbols have their usual meanings.
Here g=32.2 ft/s^2 and h=108 feet
Therefore, from Equation 1 we will get:
[tex]t=\sqrt{\frac{2h}{g}}[/tex]....Equation 2
Plugging in the values in Equation 2 we get:
[tex]t=\sqrt{\frac{2\times 108}{32.2}}\approx 2.59[/tex] seconds.
Therefore, the amount of time it would have taken the rock to fall is 2.59 seconds.
What is the value of the discrimination for the quadratic equation 0=2x2+x-3
Remark
The formula for a discriminate is b² - 4*a*c
a = 2
b = 1
c = - 3
So the discriminate =
D = (1)² - 4*2*(-3)
D = 1 - - 24
D = 25
The lateral surface area of cone A is equal to the lateral surface area of cylinder B.
True or false
Answer:
TRUE
Step-by-step explanation:
Lateral area of cone is given by: πrl
where r is the radius and l is the slant height
Here r=r and l=2h
Hence, lateral area of cone A= π×r×2h
= 2πrh
Lateral area of cylinder is given by: 2πrh
where r is the radius and h is the height
Lateral area of cylinder B=2πrh
Clearly, both the lateral areas are equal
Hence, the statement that:The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is:
True
What is f(–3) for the function f(a) = –2a2 – 5a + 4?
Answer:
The value of f(-3) is 1.
Step-by-step explanation:
Given expression,
[tex]f(a)=-2a^2-5a+4----------(1)[/tex]
For finding the value of f(-3),
Put a = - 3 in equation (1),
We get,
[tex]f(-3)=-2(-3)^2-5(-3)+4[/tex]
[tex]=-2(9)+15+4[/tex]
[tex]=-18+19[/tex]
[tex]=1[/tex]
Hence, the value of f(-3) is 1 for the given function.
choosing the 6 winning lottery numbers when the numbers are chosen at random from 0 to 9 A) 1/1,000,000 B) 1/100,000 C) 1/10,000,000 D) 531,441
Answer:
A 1/1,000,000
Step-by-step explanation:
****BRAINLIEST GOES TO THE FIRST CORRECT ANSWER****
The two equations are vertical angles, which mean they are equal.
Set each equation to equal each other and solve for x.
3x-3 = 6(x-10)
Simplify the right side:
3x-3 = 6x-60
Subtract 3x from each side:
-3 = 3x - 60
Add 60 to each side:
57 = 3x
Divide both sides by 3:
x = 57 / 3
x = 19