Answer:
✅The table can be represented by the equation, [tex] y = 4x + 4 [/tex]
✅The relation is a function.
✅The graph of the function is linear.
Step-by-step explanation:
✍️The first statement: The table can be represented by the equation, [tex] y = 4x + 4 [/tex].
To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).
Using two pairs, (1, 8) and (2, 12),
Slope = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4 [/tex].
Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.
Thus:
8 = (4)(1) + b
8 = 4 + b
Subtract 4 from each side
8 - 4 = b
4 = b
Plug in the values of b and m into y = mx + b.
Thus, the equation that represents the table would be:
[tex] y = 4x + 4 [/tex].
✅Therefore, the first statement is correct.
✍️The second statement: The graph of the function is non-linear.
This is NOT TRUE because the equation of the function, [tex] y = 4x + 4 [/tex], represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.
✍️The Third statement: The relation is a function.
This is TRUE because each input value (x-value) has exactly one output value (y-value).
✍️The Fourth statement: The rate of change is NOT constant.
This standby is NOT TRUE.
The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.
Therefore, this statement is not correct.
✍️The Fifth statement: The graph of the function is linear.
This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.
The true statements are:
(a) The equation of the function is [tex]\mathbf{y = 4x +4}[/tex](c) The relation is a function(e) The graph is linear(a) The equation of the function
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{12 - 8}{2 -1}}[/tex]
[tex]\mathbf{m = 4}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x -x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{y = 4(x -1) + 8}[/tex]
[tex]\mathbf{y = 4x -4 + 8}[/tex]
[tex]\mathbf{y = 4x +4}[/tex]
Hence, this statement is true
(b) The graph is nonlinear
Because of (a) above, the graph is linear
Hence, this statement is false
(c) The relation is a function
A linear relation is a function
Hence, this statement is true
(d) The rate of change is not constant
Because of (a) above, the rate of change is constant
Hence, this statement is false
(e) The graph is linear
Because of (a) above, the graph is linear
Hence, this statement is true
Read more about linear relations at:
https://brainly.com/question/7988877
The sum of three number is 126. The third number is 4 times the second. The second number is 6 less than the first. What are the numbers?
Step-by-step explanation:
ASK

ALGEBRA II
Ingrid H.
asked • 04/02/20
The sum of three numbers is 126 . The third number is 3 times the first. The second number is 6 more than the first. What are the numbers?
The sum of three numbers is 126
. The third number is 3
times the first. The second number is 6
more than the first. What are the numbers?
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Mackenzie K. answered • 04/02/20
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Lets define a=1st number, b=2nd number, and c=3rd number
We know that a+b+c=126
We also know that the second number is 6 more than the first, so we can represent this as b=a+6
We also know that the third number is 3 times the first which can be represented as c=3a
We can plug these new values into our original equation and get:
a+(a+6)+(3a)=126
2a+6+3a=126 COMBINE LIKE TERMS
5a+6=126
5a=120
a=24
Our first number is 24.
Our second number is 6 more than our first number, so the second number is 24+6=30
Our third number is 3 times the first number, so the third number is 3(24)=72
We can check by plugging these numbers in for a, b, and c in our original equation
a+b+c=126
24+30=72=126
126=126
The numbers are 26, 20, and 80.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Three numbers:
First = a
Second = b
Third = c
Now,
a + b + c = 126 ____(1)
c = 4b ____(2)
b = a - 6 _____(3)
From (1), (2), and (3) we get,
a + (a - 6) + 4b = 126
a + a - 6 + 4b = 126
2a + 4b = 126 + 6
2a + 4b = 132
2a + 4(a - 6) = 132
2a + 4a - 24 = 132
6a = 132 + 24
6a = 156
a = 26
Now,
a = 26
b = a - 6 = 20
c = 4b = 4 x 20 = 80
Thus,
The numbers are 26, 20, and 80.
Learn more about expressions here:
https://brainly.com/question/3118662
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evaluate -19.2 + 87.31 please shoe work!
Answer:
the answer is 68.11
Step-by-step explanation:
use symbolab I use it all the time
Answer:
68.11
Step-by-step explanation:
Since one number is negative, your equation is basically
87.31 - 19.2= 68.11
Hope I can be brainliest (:
What is 48,020,000 expressed in scientific notation?
A. 4.802 x 10^7
B. 0.48 x 10^-8
C. 0.4802 x 10^8
D. 4.802 x 10^8
Answer:
im pretty sure it is answer A. 4.802 x 10^7
Step-by-Step explanation
The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
Calculating scientific notation for a positive integer is simple, as it always follows this notation:
a x 10b
Follow the steps below to see how 48,020,000 is written in scientific notation.
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 48,020,000
New Number: 4.8020000
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 4 . 8 0 2 0 0 0 0
Decimal Count: 1 2 3 4 5 6 7
There are 7 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 4.802 (Please notice any zeroes on the end have been removed)
b = 7
Now the whole thing:
4.802 x 107
Step 4
Check your work:
107 = 10,000,000 x 4.802 = 48,020,000
Help on this please
Answer:
99% sure its D
Step-by-step explanation:
Triangles A B C and L M N are shown. Angle B A C is 58 degrees. Angle M L N is 78 degrees. Sides A B and L M are congruent. Sides A C and L N are congruent.
Given AC = LN and BA = ML, which statement must be true?
BC < MN
BC > MN
BC = MN
BA = LN
Answer:
the correct answer is A on edge
Step-by-step explanation:
Answer:
The answer above is correct!
Option A. BC < MN is the answer :)
Step-by-step explanation:
Here's a screenshot for proof - hope this helped :D
What is the solution to this system 2x + y = 1 3x – y = –6 (–1, 3)
Answer: 2x+y=1
3x-y=-6
==>5x=-5
==>x=-1 and y=1-2*(-1)=3
Sol={(-1,3)}
Answer A
1) Noah ate all of his Takis for breakfast, but he forgot that he owed Jason 16
Takis. London gave Noah 27 Takis at lunch the next day. How many Takis
will Noah have in total after he give Jason the Takis?
Answer:
noah will have 11 takis
Step-by-step explanation:
Need help on Homework
Answer:
go to tiger algebra on google and type in question
Step-by-step explanation:
PLEASE HELP I'LL GIVE YOU 23 POINTS
THERE IS A SCREEN SHOT BUT JUST IN CASE YOU CANT ACCESS IT I'LL ADD THIS!
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 65 degrees, angle QPR is equal to x, angle PRD is equal to 120 degrees.
Answer:
45 degrees
Step-by-step explanation:
pretty sure
Answer:
x = 55
Step-by-step explanation:
to find angle BPR you would do:
180 - 120 = 60
so BPR is 60°
now to find x you do this:
65 + 60 + x = 180
125 + x = 180
x = 55
What is the solution of the system of equations shown in the graph ?
A) (1,0) and (-3,0)
B) (0,-3) and (0,-1)
C)(-1, -2)
D) (-2,-1)
Translate the sentence into an equation.
Twice the difference of a number and 8 is 6.
Use the variable c for the unknown number.
Answer:
c-8=6
Step-by-step explanation:
C-8=6
is the and
Thank me
∆GHI is an isosceles triangle with a vertex angle H If the m∠H=80°, then find the m∠I.
Answer:
m∠I = 50 degrees
Step-by-step explanation:
Mathematically, the base angles of an isosceles triangle are equal
So in this case, since H is a vertex;
m∠I + m∠H + m∠G = 180
m∠I = m∠G = x
2x + 80 = 180
2x = 180-80
2x = 100
x = 100/2
x = 50
Answer:
d is the answer on edge 2022
Step-by-step explanation:
9 Helen measures a rectangular sheet of paper as 197 mm by 210 mm, each correct to the nearest
millimetre. Calculate the upper bound for the perimeter of the sheet of paper.
Answer:
Perimeter of the sheet of paper = 814 mm²
Step-by-step explanation:
Given:
Length of side = 197 mm
Width of side = 210 mm
Find:
Perimeter of the sheet of paper
Computation:
Perimeter of the sheet of paper = 2[l+b]
Perimeter of the sheet of paper = 2[197+210]
Perimeter of the sheet of paper = 814 mm²
Mrs. Roberts plants tomatoes and radishes in the areas shown in the model below.
A model with 7 rows of 5, representing 35 acres of tomatoes, and 7 rows of 4, representing 28 acres of radishes.
Which expression is equivalent to the sum of the two areas?
5 (7 + 4)
5 (7 + 7)
7 (5 + 4)
7 (4 + 7)
Answer: C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Select all ratios that are in their simplest form.
4:24 28:15 3:13 18:30 12:14
Answer:
1. 28:15
2. 3:13
Step-by-step explanation:
The ratios above have no common factor.
4:24 .
Common factor : 4
18:30
Common factor : 6
12:14
Common factor : 2
Answer:
28:15
3:13
Step-by-step explanation:
The ratios 28:15 and 3:13 are in their simplest form, meaning that they cannot be simplified any further.
Meanwhile, the other 3 ratios are not in their simplest form and can still be simplified if they are divided by either 2 or 4.
1. 5 3/4+("-" 1/4)
2. "-" 2/3+1/6
3. "-" 8/5+("-" 3/4)
Answer:
BELOWStep-by-step explanation:
1.
[tex]5\frac{3}{4} +(-\frac{1}{4} )\\\\5\frac{3}{4}=\frac{5\times4+3}{4}=\frac{23}{4}\\\\\frac{23}{4} +(-\frac{1}{4} )\\\\=\frac{23}{4}-\frac{1}{4}\\\\=\frac{23-1}{4}\\\\=\frac{22}{4}\\\\=5\frac{1}{2}[/tex]
2.
[tex]-\frac{2}{3} +\frac{1}{6} \\\\L.C.M \:OF\:3,6\: =6\\\\Adjust\:fractions\:based \:on \:their\:L.C.M\\\\=-\frac{4}{6}+\frac{1}{6}\\\\=-\frac{4}{6}+\frac{1}{6}\\\\=\frac{-3}{6}\\\\=-\frac{3}{6}\\\\=-\frac{1}{2}[/tex]
3.
[tex]-\frac{8}{5} +(-\frac{3}{4} )\\\\L.C.M \:OF\:5,4\: =20\\\\Adjust\:fractions\:based \:on \:their\:L.C.M\\\\=-\frac{32}{20}-\frac{15}{20}\\\\=\frac{-32-15}{20}\\\\=\frac{-47}{20}\\\\=-\frac{47}{20}\\\\=-2\frac{7}{20}[/tex]
Change 9.65kg into grams.
Answer:
9.65 kilograms = 9650 grams
Step-by-step explanation:
In square ABCD, m∠AED=(8x−6)°.
What is the value of x?
Enter your answer in the box.
x =
Answer:
12
Step-by-step explanation:
The angle equals 90 degrees so (8*12-6) would equal 90
Write an
equivalent expression by distributing the "-" sign outside the parentheses:
-(0.39 + 75 – 5)
Answer:
(-0.39 - 75 + 5)
Step-by-step explanation:
If you multiply a positive by a negative, it becomes a negative. If you multiply a negative by a negative, it becomes positive. Remember that, it will help you later on.
Answer:-70.39
Step-by-step explanation: im in college
The points in the table lie on a line. Find the slope of the line.
Answer:
this is given by Rishabh 3456
Step-by-step explanation:
- X is and why is right answer6 - 2 and 2 6The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 80I I2 + I + 9 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
Answer:
At ; I = 3, P is at maximum
Step-by-step explanation:
P ( I ) = [tex][ \frac{80 I}{I^2 + I + g } ][/tex]
at I = 3
P" ( I ) < 0
therefore at I = 3 the value of P( I ) is at maximum
attached below is the detailed solution
Marian wishes to buy a new computer that will cost her $300. She receives $5 per hour for babysitting her younger brother and $4 per hour for helping her mother with chores. Each week she babysits her brother for 4 hours and helps her mother with chores for 10 hours. How many full weeks must she work to earn enough money to buy the computer?
Answer:
4 weeks . ∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴
5w - 4 > 11
Help please
Answer:
w > 3
Step-by-step explanation:
5w - 4 > 11
5w > 15
w > 3
I think the answer is w= 6 or more
Step-by-step explanation:
I think it's this bc if u do 5 times 6 equals 30 then minus 4 is 26. 26 or more is greater than 11
Given that sin x = 3/4
where x is an obtuse angle, find the exact value of cos x.
Answer:
Step-by-step explanation:
sin x =3/4
x is an obtuse angle and sin x is positive .
∴ x lies in 2nd quadrant.
Hence cos x is negative.
[tex]cos x=-\sqrt{1-sin^2x} =-\sqrt{1-(3/4)^2} =-\sqrt{1-\frac{9}{16} } =-\sqrt{\frac{7}{16} } =-\frac{\sqrt{7} }{4}[/tex]
Solving a trigonometric equation, it is found that:
[tex]\cos{x} = -\frac{\sqrt{7}}{4}[/tex]
The sine and the cosine of an angle x are related by the following equation:
[tex]\sin^2{x} + \cos^2{x} = 1[/tex]
In this problem:
x is an obtuse angle, which means that it is the second quadrant, in which the sine is positive and the cosine is negative.[tex]\sin{x} = \frac{3}{4}[/tex], thus:
[tex]\sin^2{x} + \cos^2{x} = 1[/tex]
[tex](\frac{3}{4})^2 + \cos^2{x} = 1[/tex]
[tex]\frac{9}{16} + \cos^2{x} = 1[/tex]
[tex]\cos^2{x} = 1 - \frac{9}{16}[/tex]
[tex]\cos^2{x} = \frac{7}{16}[/tex]
[tex]\cos{x} = \pm \sqrt{\frac{7}{16}}[/tex]
Since the cosine is negative.
[tex]\cos{x} = -\frac{\sqrt{7}}{4}[/tex]
A similar problem is given at https://brainly.com/question/24680641
what are you doing right now?
Answer:
Nun u
Step-by-step explanation:
DOING YA MOM
Just kidding, I am eating Chicken Pot Pie while working on my day off (:
Which ones measure to 92 degrees
Answer:
angles 4 7 and 6........
Please help me with this problem!
240THE ANSWER IS 240
HELP PLEASE ! ASAP !
Answer: i think 23x
Step-by-step explanation: i might be incorrect
Answer:
23x + 250
Step-by-step explanation:
x representing the amount of jerseys and 250 representing the one time fee and the y intercept
4. An acre is 43,560 square feet. How much would it cost to fence in a 4 acre rectangle of land at
$0.55 cents per foot?
Answer:
174,242.2
hope tis help
Step-by-step explanation:
If you use the distribution property on 2(4 - 3x), what is the result?
Answer:
8 - 6x
Step-by-step explanation:
2(4-3x)
multiply 2 to both 4 and -3x
8-6x
Answer:
-6x + 8 or 6x - 8 if you want to remove the negative sign in x