What are the slope and the y-intercept of the linear function that is represented by the table?
-1
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3
2
1
2
0
0
اني انا
3
1
2
Answers
Answer:
[tex]m = -\frac{2}{5}[/tex] ---- slope
[tex]y = -\frac{1}{3}[/tex] --- y intercept
Step-by-step explanation:
Given
The attached table
Required
Calculate the slope and y intercept
First, we need to calculate the slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From the table, the following relationships exist:
[tex](x_1,y_1) = (-\frac{3}{4},-\frac{1}{30})[/tex]
[tex](x_2,y_2) = (\frac{1}{4},-\frac{13}{30})[/tex]
So, the expression for calculating slope becomes:
[tex]m = [-\frac{13}{30} - (-\frac{1}{30})] / [\frac{1}{4} - (-\frac{3}{4})][/tex]
[tex]m = [-\frac{13}{30} +\frac{1}{30}] / [\frac{1}{4} +\frac{3}{4}][/tex]
Take LCM
[tex]m = [\frac{-13+1}{30}] / [\frac{1+3}{4}][/tex]
[tex]m = [\frac{-12}{30}] / [\frac{4}{4}][/tex]
[tex]m = [\frac{-12}{30}] / 1[/tex]
[tex]m = \frac{-12}{30}[/tex]
[tex]m = \frac{-2}{5}[/tex]
[tex]m = -\frac{2}{5}[/tex]
To calculate the y intercept:
x must be 0. i.e.
[tex]x = 0[/tex]
So, we have:
[tex](x_1,y_1) = (-\frac{3}{4},-\frac{1}{30})[/tex]
[tex](x_2,y_2) = (0,y)[/tex]
[tex]m = -\frac{2}{5}[/tex]
Substitute these values in:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{2}{5} = [y - (-\frac{1}{30})] / [0- (-\frac{3}{4})][/tex]
[tex]-\frac{2}{5} = [y +\frac{1}{30}] / [0+\frac{3}{4}][/tex]
[tex]-\frac{2}{5} = [y +\frac{1}{30}] / [\frac{3}{4}][/tex]
Multiply through by 3/4
[tex]-\frac{2}{5}*\frac{3}{4} = y +\frac{1}{30}[/tex]
[tex]-\frac{6}{20} = y +\frac{1}{30}[/tex]
[tex]-\frac{3}{10} = y +\frac{1}{30}[/tex]
Collect Like Terms
[tex]y = -\frac{3}{10}-\frac{1}{30}[/tex]
[tex]y = \frac{-9-1}{30}[/tex]
[tex]y = \frac{-10}{30}[/tex]
[tex]y = \frac{-1}{3}[/tex]
[tex]y = -\frac{1}{3}[/tex]
Related Questions
What is the equation of the line in slope-intercept form?
Answers
Answer:
y=1/2x-2
Step-by-step explanation:
RIse / run
find a point then go up one and right two to the next point which gives you 1/2
the y intercept is -2 because thats where the line is interceting
I need help i my math homework
Answers
Answer:
Domain: (-7, 4]
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
According to the graph, the line's x-values span from -7 to 4. Since -7 is an open dot, it is exclusive in the domain. Since 4 is a closed dot, it is inclusive in the domain:
(-7, 4] or -7 < x ≤ 4
Tina plans to make wooden frames to put her two triangular art pieces in.
How much wood would she need fortriangle DFG?
Enter your answer in the box.
in.
Answers
Answer: 54 in.
Step-by-step explanation: So, the problem does something a little sneaky, and that is they ask for the TOTAL amount of wood needed for triangle DFG. And to find that, we simply have to multiply side AC by 3 to get side DG. We do this because triangle ABC is 3 times as small as triangle DFG. Then, add your side DG that you just got, (21) to side FG and FD to get the total amount of wood needed, 54 in.
The length of wood needed for triangle DFG is 54 inches
Start by calculating the side length DG in triangle DFG
The side lengths of DFG are three times the corresponding side length of ABC
So, we have:
[tex]DG = 3 \times AC[/tex]
[tex]DG = 3 \times 7\ in[/tex]
[tex]DG = 21\ in[/tex]
The perimeter of triangle DFG is then calculated as:
[tex]P = DF + FG + DG[/tex]
This gives
[tex]P = 15 + 18 + 21[/tex]
[tex]P = 54[/tex]
Hence, the length of wood needed is 54 inches
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A person invests $1000 in a bank. The bank pays 6% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches $3300
Answers
Answer:
20 years approx
Step-by-step explanation:
Step one:
given data
Principal= $1000
rate= 6%
Final amount A= $3300
Required
Time t
Step two:
the expression for the compound interest is given data
A= P(1+r)^t
t = ln(A/P) / r
substitute
t= ln(3300/1000)/0.06
t= ln3.3/0.06
t= 1.193/0.06
t=19.88 years
t= 20 years approx
Please and thank you
Answers
Answer:
is this free points. cuz why you said please and thank you?
Step-by-step explanation:
Mrs. Jones has a recipe for cooking roast beef. It takes half an hour for one pound of beef in an oven heated to 325° Fahrenheit to cook. How long should it take to cook a roast that weighs 5 34 pounds?
Answers
_______________________________
1lbs = 30min
= 5.34lbs × 30mins= 160.2mins= 160.2mins ÷ 60mins= 2.67hrsIt Should Take Mrs. Jones 3hrs & 7mins________________________________
5. What do you notice about the numbers in the last two columns of the table?
Answer?
Answers
I will give brainiest to whoever answers correctly !!
Answers
Answer:
Step-by-step explanation:
The principal amount is
P=3000.
The time for which money is borrowed is ,
[tex]t=9 months[/tex]
The interest rate is ,
[tex]R=3\frac{1}{2}[/tex]
Determine the time in terms of year by division of time by 12.
[tex]t=\frac{9}{12} years\\= \frac{3}{4} years\\[/tex]
The formula for the interest is ,
[tex]I=\frac{P.r.t}{100}[/tex]
Substitute the known calues in the formula to obtain the value of interest.
[tex]I=\frac{3000.\frac{3}{4} .3\frac{1}{2} }{100} \\=\frac{3000.3.7}{2.4.100} \\=78.75\\[/tex]
So interest paid by the woman is $78.75
(b)
Determine the amount paid by the woman .
[tex]A=P+I\\=3000+78.75\\=3078.75[/tex]
So woman repay $3078.75 to the bank.
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QL
Find the x- and y-intercepts of the equation.
-x + 2y = 4
O (4,0). (0,2)
O None of these
O (-4.0), (0.-2)
O (4.0), (0, -2)
O (-4.0), (0.2)
pls help
Answers
Answer:
Option 2: none of these
Step-by-step explanation:
-x +2y= 4
x-intercept occurs at y=0.
When y=0,
-x +2(0)= 4
-x= 4
x= -4
Thus, x-intercept is (-4,0).
y-intercept occurs at x=0.
When x=0,
0 +2y= 4
2y= 4
y= 4 ÷2
y= 2
Thus, y-intercept is (0,2).
*When writing coordinates, the x and y coordinates are separated by a comma in the bracket. If the 3rd option is a comma instead of a dot (which could instead denote a multiplication sign), it would be the correct option.
A point (–7, –6) is rotated counterclockwise about the origin to map onto (–6, 7). The angle of rotation is
Question 18 options:
A)
180°.
B)
90°.
C)
270°.
D)
360°.
Answers
Because you going from-,- to -,+
With is half way around it and a full circle is 360 and half of 360 is 180 with it half a circle so I believe it is A
Answer:
C
Step-by-step explanation:
took the quiz and got it right
Let sugar be the explanatory variable and calories be the response variable; which scenario best describes ŷ = 57 + 2.5x?
Select one:
a. The amount of calories in fruit juice increases by 57 for every one gram of sugar. The calorie amount estimated by this model is 2.5 if there are zero grams of sugar.
b. The amount of sugar in fruit juice increases by 2.5 grams for every one calorie. The sugar amount estimated by this model is 57 grams if there are zero calories.
c. The amount of sugar in fruit juice increases by 57 grams for every one calorie. The sugar amount estimated by this model is 2.5 grams if there are zero calories.
d. The amount of calories in fruit juice increases by 2.5 when there are zero grams of sugar. The calorie amount estimated by this model is 57 if there is one gram of sugar.
e. The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.
Answers
Answer: Choice E)
The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.
=============================================================
Explanation:
x = amount of sugar (in grams)
y = number of calories in the juice
ŷ = estimate of y, so its the estimate of calories in the juice
The regression equation rearranges to ŷ = 2.5x + 57
This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.
The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5
The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.
All of these facts point to choice E as the final answer.
Answer:
e.
Step-by-step explanation:
calories is y or response variable and sugar is the explanatory variable, x.
if x(sugar) is 1
y = 57 + 2.5(1) = 59.5, a 2.5 increase.
if it is 2
y = 57 + 2.5(2) = 62, another 2.5 increase.
if zero grams of sugar x = 0
y = 57 + 2.5(0) = 57 calories.
Denise doesn't describe tabletop with an area of 36 x 16 squared white boy squared units running expression to represent one side length of the table top
Answers
Step-by-step explanation:
Side length = √Area = √(36x¹⁶y⁴)
= √[(6x⁸y²)²] = 6x⁸y².
Hence the expression for side length is 6x⁸y².
The length of the side of the table top will be 6x⁴y².
Based on the information given, it was stated that the area of the table top was given in the question.
It should be noted that the area of a square is gotten by squaring the sides. Therefore, the length of the side of the square will be 6x⁴y².
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The larger of two numbers is eight more than five times the smaller number the sum of two numbers is 80 find the two numbers
Answers
Answer:
y=68
x=12
Step-by-step explanation:
Variables= x and y
Lets make y the larger variable.
x+y=80
y=5x+8
substitution
x+5x+8=80
6x+8=80
x=12
plug 12 back in to find y
5(12)+8=68
y=68
x=12
Perform the operation and get
your answer in the form a + bi.
(5 – 2i)(5 + 2i)
[?] + [ ]i
Answers
Answer:
Step-by-step explanation:
(5-2i) ( 5+2i) = (5^2) - ((2i)^2) = 25 - 4i^2
= 25 - 4(-1) = 25 +4 = 29 + 0i
The Solution is 29 + 0i.
What are complex numbers?The sum of a real number and an imaginary number is called a complex number. A complex number is usually represented by z and has the form a + ib. Here, both a and b are real numbers. The real part, denoted by Re(z), is represented by the value "a," and the imaginary part, represented by "b," is represented by Im(z). Also known as an imaginary number, ib.
Given Expression (5 – 2i)(5 + 2i)
we know a² - b² = (a - b)(a + b)
(5 – 2i)(5 + 2i) = 5² - (2i)²
= 25 - 4i²
and i² = -1
= 25 - 4(-1)
= 25 + 4 = 29
since the solution has 0i
so the equation is 29 + 0i
where a = 29 and b = 0
Hence, equation is 29 + 0i.
Learn more about complex numbers;
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30 points ans brainliest
plz i really need this awnser asap
Answers
the quotient of 18 and a number a
Answers
Answer:
18÷n or 18a
Step-by-step explanation:
Help plssssssssssssssssss
Answers
Hope this helps
Have a great day
Answer:
131.2 ft
Step-by-step explanation:
12.8*10.25=131.2
Find the value of X so that the function has the given value t(x)=3x; t (x)= 24
Answers
Answer:
here is your answer....
Step-by-step explanation:
lets take x as 8
t(8)=3*8
t(8)=24
Therefore:
we get t(x)=24 from equation t(x)=3x
Please help me. My other question I need help on. 2- g(x)=x^2-4 is what is g(-3) 3- F(x)=3x+7 what is f(2) please help me please please
Answers
Answer:
[tex]g(-3) = 5[/tex]
[tex]f(2) = 13[/tex]
[tex](f + g)(x) = x^2 +2x- 1[/tex]
Step-by-step explanation:
Solving (a):
[tex]g(x) = x^2 - 4[/tex]
Required
Determine g(-3)
[tex]g(x) = x^2 - 4[/tex]
Substitute -3 for x
[tex]g(-3) = (-3)^2 - 4[/tex]
[tex]g(-3) = 9- 4[/tex]
[tex]g(-3) = 5[/tex]
Solving (b):
[tex]f(x) = 3x + 7[/tex]
Required
Determine f(2)
[tex]f(x) = 3x + 7[/tex]
Substitute 2 for x
[tex]f(2) = 3*2 + 7[/tex]
[tex]f(2) = 6 + 7[/tex]
[tex]f(2) = 13[/tex]
Solving (c):
[tex]f(x) = 2x + 3[/tex]
[tex]g(x) = x^2 - 4[/tex]
Required
[tex](f + g)(x)[/tex]
In functions:
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 2x + 3 + x^2 - 4[/tex]
Collect Like Terms
[tex](f + g)(x) = x^2 +2x- 4+3[/tex]
[tex](f + g)(x) = x^2 +2x- 1[/tex]
simplify -5 + 3d + 6 - 4d
Answers
-5+3d+6-4d
anwers is 12/-30
Find the length of the radius of the circle.
A)
2 inches
B
B)
3 inches
)
6 inches
D)
8.5 inches
Answers
Answer:
C) 6 inches
Step-by-step explanation:
(√72)² = x² + x²
72 = 2x²
72/2 = x²
36 = x²
√36 = √x²
6 = x
x = 6 inches
Answer:
By Pythagoras theorem, we get
[tex] {x}^{2} + {x}^{2} = {( \sqrt{72}) }^{2} \\ 2 {x}^{2} = 72 \\ {x}^{2} = 36 \\ \boxed{x = 6}[/tex]
C) 6 inches is the right answer.Tom, Brad, Angela, and Mona went to a theater. In how many different ways can they sit on four adjacent seats in a line in the theater?
Answers
Answer:
16
Step-by-step explanation:
4x4 = 16
Please answer quickly
Answers
Answer:
I answered the first two Q but i dont know the third one sorryy
Step-by-step explanation: i put the answers as pics
Lawrence is half as old as Jonathan. The sum of their ages is 54. How old is Jonathan?
Answers
Answer:
Jonathan is 36 years old.
Step-by-step explanation:
Jonathan=2 Lawrence
J= 2L
54 divided by 3 equals 18.
18 times 2 equals 36.
Hope this helped! :)
A car travels 104 kilometers in 2 hours. What is its speed?
Answers
Answer:
52 kilometers per hour
:)
Solve the following system of equations using the elimination method. 5x + y = 9 –10x + 7y = 18 Question 6 options: A) (2,–6) B) (–7,3) C) (3,–4) D) (1,4)
Answers
Answer:
Step-by-step explanation:
5x + y = 9
-10x + 7y = 18
10x + 2y = 18
-10x + 7y = 18
9y = 36
y = 4
5x + 4 = 9
5x = 5
x = 1
(1,4)
answer is D
find the value
any help
Answers
Which of the following best describes the equation y= -2/7x +12
A. Linear
B. Both linear and nonlinear
C. Nonlinear
D. Neither linear or nonlinear
Answers
Write an equivalent equation by combining like terms.
5x - 7y + 2x + 10y + 4
Answers
Answer:
7x+3y+4Step-by-step explanation:
A bamboo plant grows about 3.9 feet each day find the growth in 9 weeks
Answers
Answer:
The answer is 245.7
Step-by-step explanation:
7 days in a week. 9 weeks. 9 x 7 = 63.
63 x 3.9 = 245.7