Determine whether the table of values below represents a linear function. If it represents a linear function, write the function. If it does not represent a linear function, explain why not.
Answer:
The equation of a linear function is:
[tex]y = 2x+4[/tex]Step-by-step explanation:
Given the table
x y
-10 -16
-3 -2
1 6
2 8
Determining the slope between the points (-10, -16), (-3, -2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-10,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)[/tex]
[tex]m=\frac{-2-\left(-16\right)}{-3-\left(-10\right)}[/tex]
[tex]m=2[/tex]
Determining the slope between the points (-3, -2), (1, 6)
[tex]m=\frac{6-\left(-2\right)}{1-\left(-3\right)}[/tex]
[tex]m=2[/tex]
Determining the slope between the points (1, 6),(2, 8)
[tex]m=\frac{8-6}{2-1}[/tex]
[tex]m = 2[/tex]
As the slope between the points is the same. Thus, the table represents the linear function.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 2 and any point let say (1, 6)
[tex]y - 6 = 2(x-1)[/tex]
[tex]y-6 = 2x-2[/tex]
[tex]y = 2x-2+6[/tex]
[tex]y = 2x+4[/tex]
Therefore, the equation of a linear function is:
[tex]y = 2x+4[/tex]WILL GIVE BRAINLIEST
Given the system of equations presented here:
4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?
Multiply the first equation by −4 to get −16x − 4y = −16.
Multiply the second equation by −4 to get −8x − 24y = −96.
Multiply the first equation by −2 to get −8x − 2y = −8.
Multiply the second equation by −2 to get −4x − 12y = −48.
Answer:
Multiply the second equation by −2 to get −4x − 12y = −48.
Step-by-step explanation:
Given:
4x + y = 4 (1)
2x + 6y = 24 (2)
Multiply the second equation by −2 to get −4x − 12y = −48.
4x + y = 4 (1)
−4x − 12y = −48 (3)
Variable x can be eliminated by adding the equations
4x + (-4x) + y + (-12y) = 4 + (-48)
4x - 4x + y - 12y = 4 - 48
0 - 11y = -44
-11y = -44
Divide both sides by -11
y = -44/-11
= 4
y = 4
Answer: Multiply the second equation by −2 to get −4x − 12y = −48.
Step-by-step explanation:
Help me out here please find the value of x
Answer:
6. 51
7. 31
8. 20
Step-by-step explanation:
2x+8=110
2x=102
x=51
2x+x-3=90
3x-3=90
3x=93
x=31
7x+x+20=180
8x+20=180
8x=160
x=20
Aubree invested $500 into a mutual fund that paid 3% interest each year compounded annually. Find the value of the mutual fund in 12 years.
Answer:
FV= $712.88
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $500
Number of periods (n)= 12 years
Interest rate (i)= 3% compounded annually
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
FV= 500*(1.03^12)
FV= $712.88
Answer:
25%
Step-by-step explanation:
Because she divided it
CAN SOMEONE PLEASE HELP ME!!
Consider the polynomial function h(x) = -7x6 + 3x4 – 5x2.
What is the end behavior of the graph of h ?
Answer: As x -> ♾, h(x) -> -♾, and as x -> -♾,h(x) -> -♾
Step-by-step explanation:
The end behavior is x ----> ∞ then h(x) ----> -∞, and when x ----> -∞ then h(x) -----> -∞.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
h(x) = -7[tex]x^6[/tex] + 3 [tex]x^4[/tex]– 5x².
If we plot the Equation on the Graph we can see a parabolic Curve.
This Curve tells as x tends to ∞ the value of h(x) tends to -∞.
and, when x tends to -∞ the value of h(x) tends to -∞.
Hence, the end behavior is x ----> ∞ then h(x) ----> -∞.
and, when x ----> -∞ then h(x) -----> -∞.
Learn more about Function here:
https://brainly.com/question/2541698
#SPJ5
Decrease £2123 by 8%
- A fish tank filter cleans 3 gallons of water every 1/4 hour. Set up and solve a proportion to determine how many gallons of water are cleaned in 4 hours.
Answer: 48 gallons in 4 hours
Step-by-step explanation:
3 gallons every .4 hours > 12 gallons every 1 hour > 48 gallons every 4 hours
find the linear equation from the points (-2,-6) and (2,-3)
Answer:
y = 3/4 x - 9/2
Step-by-step explanation:
find the slope by (y2-y1)/(x2-x1) and then substitute a point in
Use the drop-down menus to choose steps in order to correctly solve
4k - 6= -2k - 16 - 2 for k.
Mr. Patel bought his 3 friends Casio G-Shock watches for Christmas. The retail price for each watch on Amazon was $39.91. How much did he pay for all 3 watches, excluding tax?
Answer:
Mr. Patio paid $312.00 for the three watches
Step-by-step explanation:
The price of one of the Casio G-Shock watches that Mr. Patel bought his 3 friends for Christmas is $39.91.
For Mr. Patio to have bought this watch for each of his 3 friends, we have that the cost will be multiplied by three. He is spending three times the amount he would have spent if he is buying for only a single person.
Cost = 39.91 X 3 =$312.00
Mr. Patio paid $312.00 for the three watches
In triangle JKL what is the value of x° if JK = KL
A) 38°
B) 60°
C) 69°
D) 71°
Answer:
A: 38º
Step-by-step explanation:
Triangle JKL is an isosceles triangle as JK=KL:
That means ∠J=∠L=71ºThe sum of a triangle's interior angles is 180º, so ∠K=180º-∠J-∠L. We know ∠J=∠L=71º, so ∠K=180º-71º-71º=38Sam is interested in buying a TV. At Walmart, the TV is regularly prices at $599.99 and is on sale for 20% off the regular price. At Best Buy, the same TV is regularly prices at $899.99 and is on sale for 30%off the regular price.
What is the difference in the sale price of the TV between these two stores?
Show your work.
Answer:
If 30% of 599.99 is 197.99 and 30% of 899.99 is 269.99 then you subtract 269.99-197.99= $72
Step-by-step explanation:
Hope this helped you!! Give brainliest.
bruh math problems really be like
"sALLY aTe 7 PenCiLs, iF sHe vOmitS 3 hOw mAnY arE LeFt?"
smh.
Answer:
Bruu for real and they don't make sense LOL
Step-by-step explanation:
Answer:
FACTS lmbooo
Step-by-step explanation:
Which phrase matches the algebraic expression below?
2(x - 7) +10
Answer:
2 times the difference of x minus 7 plus 10
Step-by-step explanation:
When dealing with equations, you ALWAYS do the parentheses first. The first relationship x and 7 are going to have is being subtracted from eachother. Once you do that, you can do the rest of the equation. Hope this helps!
دائرة مركزها o فيها الوتران cd,ab اذا علمت ان النقطة n نقطة منتصف الوتر cd والنقطة m نقطة منتصف الوترab وكان om=on وطول cn=6cm
فان طول AB يساوي :
c 24cm
b 12 cm
a 6 cm
Step-by-step explanation:
12cm
...............
Answer:
c 24cm
Step-by-step explanation:
A taxi in myrtle beach charges $2 per mile and $1 per person. If a taxi cab ride for 2 people cost $12, how far did the taxi cab travel ( don’t include units (miles) in the answer)
Answer:
I belive the answer is 5
Step-by-step explanation:
$12- $2 for ppl= $10
$10÷$2 per mile = 5
A farmer has 300 feet of fence available to
enclose a 4500 square foot region in the
shape of adjoining squares, with sides of
length x and y. The big square has sides of
length x and the small square has sides of
length y. Find x and y.
UUUULTTUUL
x= ? feet
y = ? feet
Given :
A farmer has 300 feet of fence available to enclose a 4500 square foot region in the shape of adjoining squares, with sides of length x and y.
The big square has sides of length x and the small square has sides of length y.
To Find :
The value of x and y.
Solution :
From attached figure perimeter is given by :
x + x + x + y + y + y + ( x-y ) = 300 ft
4x + 2y = 300
2x + y = 150 ...1)
Now, area is given by :
A = x² + y²
x² + y² = 4500 ...2)
Putting value of y in equation 2), we get :
[tex]x^2 + ( 150 - 2x)^2 =4500\\\\x^2 + 4x^2 + 22500-600x =4500\\\\5x^2 -600x + 18000=0\\\\x^2 - 120x +3600=0\\\\x^2-2\times x\times 60 + 60^2 =0\\\\(x-60)^2 =0\\\\x = 60\ ft[/tex]
y = 150 - ( 2× 60 )
y = 30 ft
Therefore, the value of x and y is 60 ft and 30 ft respectively.
In training for a swim meet, Logan swam 750 meters in \large \frac {1}{3} 3 1 of an hour. His swimming partner, Mila, swam \frac {2}{3} 3 2 of Logan's distance in \frac {1}{4} 4 1 of an hour. what is milas average speed
Answer:
2 km/hr
Step-by-step explanation:
Distance traveled by Logan = 750 m = 0.75 km = [tex]\frac{3}{4}\ km[/tex]
Time taken by Logan = [tex]\frac{1}{3}\ hours[/tex]
To calculate the speed using time and distance, following formula is used:
[tex]\text{Average Speed =} \dfrac{\text{Total Distance}}{\text{Total Time}}[/tex]
Speed of Logan :
[tex]\dfrac{\frac{3}{4}}{\frac{1}{3}}\\\Rightarrow \dfrac{9}4\ km/hr[/tex]
Distance traveled by Mila = [tex]\frac{2}{3}[/tex] of Logan's distance:
[tex]\frac{2}{3}\times \frac{3}{4} = \frac{1}{2}\ km[/tex]
Time taken by Mila = [tex]\frac{1}{4}\ hr[/tex]
As per formula above:
Average Speed of Mila is given as:
[tex]\dfrac{\frac{1}{2}}{\frac{1}{4}}\\\Rightarrow \dfrac{4}{2}\\\Rightarrow \bold{2 km/hr}[/tex]
6x +1.5x = 2
What is x=

[tex]\boxed{x=\frac{4}{15},~0.2667}[/tex]
Solution Steps:______________________________
1.) Combine 6x and 1.5x:[tex]6x+1.5x=7.5x[/tex]- You combine since these are like terms.
Equation at the end of Step 1:
[tex]7.5x=2[/tex]2.) Divide both sides by 7.5:[tex]7.5x[/tex] ÷ [tex]7.5=x[/tex][tex]2[/tex] ÷ [tex]7.5=[/tex]- We divide because we want to get x alone.
Equation at the end of Step 2:
[tex]x=\frac{2}{7.5}[/tex]3.) Expand the fraction by multiplying both numerator and the denominator by 10:[tex]2[/tex] × [tex]10=20[/tex][tex]7.5[/tex] × [tex]10=75[/tex]- We turned this into a fraction because we couldn't divide properly.
4.) Reduce the fraction to lowest terms by extracting and canceling out 5:[tex]20[/tex] ÷ [tex]5=4[/tex] [tex]75[/tex] ÷ [tex]5=15[/tex]- This step just means divide the lowest amount possible, which in this case is 5.
______________________________
Amelia is making a cookie recipe that requires 4 cups of sugar for every 12 cups of flour. Amelia only has 9 cups of flour. She concludes that she will only need 3 cups of sugar Is Amelia correct? Why or why not?
A Amelia is correct. She needs 3 cups of sugar because the ratio 3:9 is equivalent to 4:12.
B Amelia is correct. One-quarter the amount of sugar is needed because only one-quarter of the recipe will be made.
C Amelia is incorrect. The number of cups of sugar must be reduced by 3 because the number of cups of flour is reduced by 3.
D Amelia is incorrect. She needs 4 cups of sugar because decreasing the number of cups of flour by 3 requires increasing the number of cups of sugar by 3.
Answer:
B
Step-by-step explanation:
Because if you will divide the ratio 4:12 by three- we will get a ratio 1:3. Then we need the last 3 in the ratio 1:3 become a 9. For this we need to multiply it by 3= 1:3 *3= 3:9. This is only 3/4 of whole of recipe.
Answer: Choice A)
Amelia is correct. She needs 3 cups of sugar because the ratio 3:9 is equivalent to 4:12
=======================================================
Explanation:
It might help to think of the ratio 4:12 as the fraction 4/12. Dividing both parts by 4 leads to 1/3.
Similarly, the ratio 3:9 becomes 3/9 which reduces to 1/3.
This shows that 4/12 = 3/9, so the ratios 4:12 and 3:9 are the same.
------------
Another way to show two fractions are equal is to do the steps below
4/12 = 3/9
4*9 = 12*3 ... cross multiply
36 = 36
Since the last equation is true, the first equation must be true.
-------------
Here's another way to see Amelia is correct.
So we know that 4 cups of sugar go with 12 cups of flour. This forms the fraction 4/12.
We also know that she has 9 cups of flour. Let's say we don't know how much sugar she needs, so we'll call this x. We have x cups of sugar go with 9 cups of flour. This forms the fraction x/9.
Equate the two fractions and solve for x
4/12 = x/9
9*4 = 12*x ... cross multiply
36 = 12x
12x = 36
x = 36/12 ... divide both sides by 12
x = 3
She needs 3 cups of sugar
The steps in this section are very similar to the steps in the last section.
A prime number has two factors, itself and 1? *
Answer:
That is true. More information below.
Step-by-step explanation:
A prime number has to have only two factors: 1 and itself. 1 only has one factor (itself) so it is, as you were saying, neutral.
A truck is working to carry a batch of goods including sand and
stone but it can only carry 20 tons at most. The carriage
charges of each ton of sand and stone are 10 and 15 dollars
respectively. Its owner wants to earn at least 250 dollars. Write
a system of inequalities to express this situation. What is the
least possible number of tons of stone the owner needs to
carry to meet his own goal?
tons
Enter the answer
Check it
Answer:
Y=10
Step-by-step explanation:
No
Which expression is equivalent to 1/5 divided by 1/2?
A- 1/5 x 1/2
B- 1/5 x 2/1
C - 5/1 x 2/1
D 5/1 x 1/2
PLZZ HELP I NEED IT NOWW
plss can someone do this ive been trying for hourss
Answer:
(6+y) (6-y) / 6-y
Step-by-step explanation:
Answer:
Negative Infinity
at an amusement park, children are charged an entrance fee of $20 plus $3 per ride and adults are charged an entrance fee of $28 plus $4 per ride. Identify your variable with a 'let' statement and write expressions for both children and adults that represent the cost for each group.
Answer:
T=3r+20 for the children and T=4r+28 for the adults
Step-by-step explanation:
Let r equal the amount of rides the person took, let T equal the total cost of the trip
please help first will be brainliest
Answer:
Just multiply or divide the numbers they give you try both
Step-by-step explanation:
Pls help I'm gonna give brainliest but just help pls I need to do this but I don't get it.
Ellen wants to purchase a book that is regularly priced at $18. The book is discounted 15%. She also needs to pay a 6% sales tax on the discounted price.
What is the total amount Ellen will pay for the book?
Answer:
$16.22
Step-by-step explanation:
When 18 dollars is discounted by 15%, we first need to find what 15% of 18 is. 18 times .15 is 2.7, and 18-2.7 is 15.3.
Then, we need to find the sales tax, which applies to the discounted price. 15.3 times 0.06 is 0.918. Add that to 15.3 and you get 16.218, or about $16.22. Hope this helped! :D
Help pls!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
No
Please help on 5 and 6
I’m not sure of what the answer is. Can u help me, please and thank you.
Answer:
3
Step-by-step explanation:
