Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
A.
{-4, 4, 14}
B.
{2, 4, 9}
C.
{-12, -4, 6}
D.
{12, 4, -6}
Answers
Answer:
The range is {12, 4, -6} ⇒ D
Step-by-step explanation:
The range of the relation is the values of y corresponding to the values given for x which is the domain of the relation
∵ The relation is 12x + 6y = 24
∵ The domain of the function is {-4, 0, 5}
→ That means x = -4, 0, 5, we need to find their corresponding values of y
∴ Substitute the values of x in the relation
∵ x = -4
∴ 12(-4) + 6y = 24
∴ -48 + 6y = 24
→ Add 48 to both sides
∴ -48 + 48 + 6y = 24 + 48
∴ 6y = 72
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{72}{6}[/tex]
∴ y = 12
∵ x = 0
∴ 12(0) + 6y = 24
∴ 0 + 6y = 24
∴ 6y = 24
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{24}{6}[/tex]
∴ y = 4
∵ x = 5
∴ 12(5) + 6y = 24
∴ 60 + 6y = 24
→ Subtract 60 from both sides
∴ 60 - 60 + 6y = 24 - 60
∴ 6y = -36
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{-36}{6}[/tex]
∴ y = -6
∵ The range is the values of y which corresponding to the domain
∴ The range is {12, 4, -6}
The answer is down below have a good day!!!
Related Questions
The yield in bushels from a grove of orange trees is given by Y = x(600 − x), where x is the number of orange trees per acre. How many trees will maximize the yield?
Answers
Answer:
90000
Step-by-step explanation:
Y = x(600 - x)
Let's rearrange the equation so that we have
Y = x(-x + 600)
Y = -x² + 600
When you take a look at parabolas, we know that their maximum or minimum values are usually on the axis of symmetry. This axis of symmetry has an equation of
x = -b/2a,
In this question, the axis of symmetry is
x = -600 / -2
x = 300
This means that planting 300 trees will maximize your yield. If you substitute for x = 300 into the equation, the maximum yield will be
y = 300 (600 - 300)
y = 90000.
Answer: 300
Step-by-step explanation:
use the formula X=-b/2a
x=-600/-2
x=300
9. Determine whether KM and ST are parallel, perpendicular, or neither. K(-1, -8), M(1,6), S(-2,-6), T(2, 10) A Parallel B Perpendicular C Neither Hint(use slope formula)
Answers
bob is on his way home in his car. he has driven 30 miles so far, which is three-fifths of the way home. what is the total length of his drive?
Answers
The length of Bob's drive as a fraction = 5/5
Let the length of his total drive be = x
30 miles driven by Bob as a fraction =
= 3/5 of x = 30
= 3/5x = 30
= 5/x = 30 ÷ 3 ( transposing ×3 from LHS to RHS changes ×3 to ÷3 )
=5/x = 10
= x = 10 × 5 ( transposing ÷5 from LHS to RHS changes ÷5 to ×5 )
= x = 50
Now we have to see what is =
= 2/5 of 50
= 2/5 × 50
= 100/5
= 20 miles
So , total length of Bob's drive = 30 miles + 20 miles = 50 miles .
∴ The total length of Bob's drive is 50 miles .
2/15 = h/125 need a step by step please
Answers
====================================
Work Shown:
2/15 = h/125
2*125 = 15*h .... cross multiply
250 = 15h
15h = 250
h = 250/15
h = (5*50)/(5*3)
h = 50/3
-----------------
Extra info:
50/3 = (48+2)/3
50/3 = (48/3)+(2/3)
50/3 = 16 + (2/3)
50/3 = 16 & 2/3
The improper fraction 50/3 converts to the mixed number 16 & 2/3
Another way to see this is to use long division to get 50/3 = 16 remainder 2.
Tabithas living room is rectangle that measures 19 3/4ft by 12ft find the perimeter and the area of the room
Answers
Answer:
237ft²
63.5ft
Step-by-step explanation:
Given parameters:
Length = 19[tex]\frac{3}{4}[/tex] ft
Width = 12ft
Unknown:
Area of rectangle = ?
Perimeter of rectangle = ?
Solution:
Area of rectangle = length x width
= 19[tex]\frac{3}{4}[/tex] x 12
= [tex]\frac{79}{4}[/tex] x 12
= 79 x 3
= 237ft²
Perimeter of rectangle = 2(length + width)
= 2 (19.75 + 12 )
= 63.5ft
To win a trivia game you must score 90 points each correct answer is worth 1 3/4 points, each incorrect point is worth -1/4 points if he gets 58 questions correct and 22 questions incorrect, what is his score?
Answers
Follow the steps to find the value of x
1.Addition property of equality.
1/5(x)-2/3=4/3
1/5(x)-2/3+2/3=4/3+2/3
2.Multiplicative property if equality.
1/5(x)5/1=6/3(5/1)
The solution is x=
Answers
X= 10
Answer:
its 10
Step-by-step explanation:
I got it right
7 x7 dived by 5 plz helppppvme
Answers
Answer:
Step 1) 7*7 = 49
Step 2) 49/5 = 9.8
Answer:
Step-by-step explanation:
7x7=49, 49 divided by 5=9.8, hope I helped! :P
ayer 100% A company sells cases of tomato juice. Each case contains 24 cans of juice and sells for $18. The equation y = 18x represents the total price ( y), in dollars, when x number of cases are sold. Choose all statements about the situation that are correct based on the information. A. The cost per can is dependent on the number of cases sold. B. The number of cans sold is dependent on the price per can. C. The total price for a sale is dependent on the number of cases sold. D. The number of cases sold is independent from the number of cans in each case.
Answers
Answer:
c
Step-by-step explanation:
Answer:
C is the answer
The angle measures of triangle QRS are given:
The measure of angle Q is (5x−15)°.
The measure of angle R is 75°.
The measure of angle S is (3x)°.
What is the value of x?
Answers
Answer:
x = 15°
Step-by-step explanation:
(5x-15) + 75 + 3x = 180
8x + 60 = 180
8x = 120
x = 15°
Evaluate 8 ÷ -2 · 4²+9. Thanks! Will give brainiest if possible
Answers
In order to test for the significance of a regression model involving 5 independent variables and 123 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
Answers
Answer: The numerator and denominator degrees of freedom (respectively) for the critical value of F are 4 and 118 .
Step-by-step explanation:
We know that , for critical value of F, degrees of freedom for numerator = k-1
and for denominator = n-k, where n= Total observations and k = number of independent variables.
Here, Numbers of independent variables(k) = 5
Total observations (n)= 123
So, Degrees of freedom for numerator = 5-1=4
Degrees of freedom for denominator =123-5= 118
Hence, the numerator and denominator degrees of freedom (respectively) for the critical value of F are 4 and 118 .
Solve for X please :(( Will give brainliest.
Answers
5x+6+92 = 22x-4
5x+98 = 22x-4
add 5x to both sides
98 = 27x-4
add 4 to both sides
102 = 27x
divide both sides by 27
x = 3 and [tex]\frac{7}{9}[/tex]
Convert 139 pounds to kilograms
Round answer to the nearest tenth.
Conversion table:
1 kilogram = 2.205 pounds
Answers
Answer: 63.1
Step-by-step explanation:
Need help ASAP with my math
Answers
Answer: The answer is -2
Step-by-step explanation: I want points and trust me this answer is correct
Megan had $235.17 in her bank account. She withdrew $77.98 from the account to spend
on clothing. How much money does she have left in her bank account now?
Answers
Answer: 157.19
Step-by-step explanation:
Show that each conjecture is false by finding a counterexample.
1.For any integer n, n3 > 0.
2. Each angle in a right triangle has a different measure.
3.For many years in the U.S, each bank printed its own currency. The variety of different bills led to widespread counterfeiting. By the time of the Civil War, a significant fraction of the currency in circulation was counterfeit. If one soldier had 48 bills, 16 of which were counterfeit, and another soldier had 39 bills, 13 of which were counterfeit, make a conjecture about what fraction of bills were counterfeit at the time of the Civil War.
Answers
Answer:
1. [tex]n: n^3 > 0[/tex] is not true for negative integers
2. [tex]45\ and\ 45[/tex] show that all angles do not have different measure
3. [tex]Fraction = \frac{1}{3}[/tex]
Step-by-step explanation:
Solving (1):
[tex]n: n^3 > 0[/tex]
Take
[tex]n = -1[/tex]
[tex]-1^3 = -1[/tex]
[tex]n: n^3 > 0[/tex] is not true for negative integers
Solving (2):
The angles of a right angled triangle are:
[tex]45, 45\ and\ 90[/tex]
[tex]45\ and\ 45[/tex] show that all angles do not have different measure
Solving (3):
When
[tex]Bills = 48[/tex]
[tex]Counterfeit = 16[/tex]
The fraction is calculated as thus:
[tex]Fraction = \frac{Counterfeit}{Bills}[/tex]
[tex]Fraction = \frac{16}{48}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
Similarly, when
[tex]Bills = 39[/tex]
[tex]Counterfeit = 13[/tex]
[tex]Fraction = \frac{Counterfeit}{Bills}[/tex]
[tex]Fraction = \frac{13}{39}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
The difference of two integers is 1. The product of the integers is 30. What
are the integers?
Answers
[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]
Let us take ,
First integer be x .Second integer be y .Also let us consider x > y .
According to first Condition :-
⇒ x - y = 1.
⇒ x = y + 1. .............(i)
According to second Condition :-
⇒ x × y = 30 .
⇒ ( y + 1 )y = 30 . [ From (i) ]
⇒ y² + y = 30.
⇒ y² + y - 30 = 0 .
⇒ y² + 6y - 5y -30 = 0.
⇒ y ( y + 6 ) -5 ( y + 6 ) = 0 .
⇒ ( y + 6 ) ( y - 5 ) = 0 .
[tex]\red{\bf \longmapsto y = 5 , (-6)}[/tex]
Here y can sustain both values 5 and minus 6 as y is an integer.
So , x = -6 , 5 .
Hence possible answers are ,
[tex]\boxed{\purple{\bf x = -6 , y = -5 }}[/tex]
[tex]\qquad\qquad\qquad \bf Or [/tex]
[tex]\boxed{\purple{\bf x = 6 , y = 5 }}[/tex]
.
Pls I need help ASAP
Answers
Answer:
the answer is 1/8
thank you
if you loved my answer then please like it and mark as brainliest
Simplify and find the value for 1) x = -1, y = 1 and z = 2 (x – 2y) (3x2 + 4xy – y 2 )
Answers
Answer:
Step-by-step explanation:
(1-2*1) (3*2+4*-1*1- 1*2)
=-1 (6+4-1-2)
-1*7
-7
Which correctly solves the equation ab+c=d solve for b.
Answers
Answer:
b=(d-c)/a
Step-by-step explanation:
Just gotta switch them around a bit
бx + 8 = 50
I need that answer
Answers
Answer:
=
7
Step-by-step explanation:
ax+6=15 a is a negative, what must be true about x?
Answers
Answer:
x= 9/a
Step-by-step explanation:
Simplest form of 8/36
Answers
Answer:
8.36 I think
Step-by-step explanation:
Answer: 2/9
Steps: 8/36 simplified is 2/9.
Plz mark brainliest:)
11. Factor for
12 – 8.1 + 16
Answers
Answer:
2(6-4.05+8)
Step-by-step explanation:
2(6-48+43.05+8)
(-8) X 2/3 i NEED the answer help me
Answers
-5.33333333333
I used a calulator can I get brainliest please
Tara's website, verdantveggies.com, specializes in the sale of rare or unusual vegetable seeds. Tara sells packets of sweet-pepper seeds for $2.85 each and packets of hot-pepper seeds for $4.29 each. She also offers a 16-packet mixed-pepper assortment combining packets of both types of seeds at $3.30 per packet. How many packets of each type of seed are in the assortment?
Answers
Answer:
Let's define the variables:
S = # of sweet pepper seeds in the mix pack.
H = # of hot pepper seeds in the mix pack.
Let's suppose that $3.30 is the mean price of the seeds in the mix pack.
Then we have two equations:
S + H = 16.
(S*$2.85 + H*$4.29)/16 = $3.30
Now let's solve this system.
The first step is isolating one variable in one of the equations, i will isolate S in the first equation.
S = 16 - H.
Now we can replace this in the second equation, and solve it for H.
( (16 - H)*$2.85 + H*$4.29)/16 = $3.30
( (16 - H)*$2.85 + H*$4.29) = $3.30*16 = $52.80
$45.60 + H*$1.44 = $52.80
H*$1.44 = $52.80 - $45.60 = $7.20
H = $7.20/$1.44 = 5
Then in the mix pack there are 5 hot-pepper seeds.
And the other 11 must be sweet-pepper seeds
Algebraic equations are equations that contain unknown variables.
The number of packets of sweet-pepper seeds is 11 and the number of packets of hot-pepper seeds is 5.
Let's represent:is
The number of packets of sweet-pepper seeds = s
The number of packets of hot-pepper seeds = h
Based on this question, our system of equations are:
$2.85 x s + $4.29 x h = $3.30(16)
2.85s + 4.29h = 52.8...........Equation 1
s + h = 16...........Equation 2
s = 16 - h
We substitute 16 - h for s in Equation 1
2.85(16 - h) + 4.29h = 52.8
45.6 -2.85h + 4.29h = 52.8
Subtract 45.6 from both sides
45.6 - 45.6 -2.85h + 4.29h = 52.8 - 45.6
1.44h = 7.2
h = 5
There are 5 hot-pepper seeds in the assortment.
Solving for the number of sweet-pepper seeds.
s = 16 - h
s = 16 - 5
s = 11
There are 11 sweet-pepper seeds in the assortment.
Therefore, the number of packets of sweet-pepper seeds is 11 and the number of packets of hot-pepper seeds is 5.
To learn more, visit the link below:
brainly.com/question/12978834
Quadrilateral GHJK has vertices G(2, 3), H(8, 2), J(6, 8), and K(3, 6). It is transformed according to the rule T(–4, –5).
What are the coordinates of G”?
(–7, 3)
(–2, 2)
(–1, –7)
(2, –2)
Answers
Answer:
the transformation T(a, b) can be change the pre image to the final image by following the rule as we explain below
if A(x, y) is a pre image, then A ' ( x', y') is its image, and x' = a+x, y' = b + y, where because of T(a, b) transformation
in our case Quadrilateral GHJK has vertices G(2, 3), so the coordinates of G”
can be found with
T(-4, -5) applied to G(2, 3) ⇒ G' (-4 +2, -5+3)=G' (-2, -2)
T(-4, -5) applied to G' (-2, -2) ⇒ G"(-4-2, -5-2) =G"(-6, -7)
the coordinates of G” are (-6, -7)
Step-by-step explanation:
i hope it helps?Answer:
its c on edg (-1, -7)
Step-by-step explanation:
The Riley family has 3 children all born 1 year apart. Kate is the youngest, Bradley is the middle child, and Cameron is the oldest. Together, the children's ages total 36. How old is Kate?
Answers
Step-by-step explanation:
12
Answer:
11
Step-by-step explanation:
11+12+13 =36
So Kate would be 11. Bradley would be 12. And Cameron would be 13
Use a system of linear equations with two variables and two equations to solve.
175 students enrolled in a freshman-level chemistry class. By the end of the semester, 4 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answers
Answer:
35 failed and 140 passed
Step-by-step explanation:
Let p = number who passed
f = number who failed
p+f = 175
4 times the number of students passed as failed, so we need to balance this to set it equal
4f = p
Substitute this into the first equation
4r+f = 175
5f = 175
5f/5 =175/5
f = 35
Now find the number who passed
p = 4f
p = 4*35
p =140