Step-by-step explanation:
Slope / gradient of a line is obtained by making an equation in the form of:
y=mx+c
where ' m ' gives the slope/gradient of the line and ' c ' gives y-intercept.
2x+y=17
y = −2x+17
Here comparing this with y=mx+c gives:
m = -2 (slope/gradient) and
c = 17 (y-intercept)
So slope / gradient of line :
m=−2
convert to standard form y=-4x-8
Answer:
[tex]4x + y = - 8[/tex]
Step-by-step explanation:
write in standard form :
[tex]ax + by = c[/tex]
Mel works as a delivery person for Amazon. The graph shows a linear model for his delivery times on
different days.
(a) What is the equation of the line, first written in point-slope form and then written in slope-intercept
form? Show how you determined the equation.
(b) Based on the linear model, predict how long it initially took Phillip to deliver his packages.
Approximately how much did his delivery time decrease per day?
Answer:
Point slope form: -9 = m(3)
Slope intercept form: y = -3x + 30
At x = 0, his delivery time was 30 minutes. It decreased by 3 minutes per day.
Step-by-step explanation:
We have 2 points to calculate the line.
(3, 21) x1 y1
(6, 12) x2 y2
First, we need to calculate the slope.
m =
m =
m = -3
Point slope form is:
y - y1 = m(x - x1)
So for our case:
-9 = m(3)
And slope intercept form is:
y = mx + b
We need to solve for the y intercept (b)
y = -3x + b --- enter the slope
21 = -3(3) + b --- enter in any point on the line for x and y
21 = -9 + b
b = 30 --- solve for b
Now our slope intercept form of the line is:
y = -3x + 30
At x = 0, his delivery time was 30 minutes. It decreased by 3 minutes per day.
Review the graph. On a coordinate plane, a vector has origin (6, 2) and terminal point (0, 4). What is the component form and magnitude of the vector shown? LeftAngleBracket negative 2, 7 RightAngleBracket and StartRoot 53 EndRoot LeftAngleBracket negative 2, 7 RightAngleBracket and 53 LeftAngleBracket negative 7, 2 RightAngleBracket and StartRoot 53 EndRoot LeftAngleBracket negative 7, 2 RightAngleBracket and 53
Answer:
I think C
Step-by-step explanation:
The component form and magnitude of the vector is < -6, -2>, √ 40, the correct option is A.
What is a Vector?A vector is a quantity that needs both magnitude and direction for its representation.
A vector has origin (6, 2) and terminal point (0, 4).
The component of vectors is determined by the formula
<x,y> = < (x₂- x₁ ) , (y₂-y₁)>
<x,y> = < (0-6), (4-2)>
<x,y> = < -6, -2>
The magnitude of the vector is determined by
[tex]\rm |v| = \sqrt{x^2 +y^2[/tex]
|v| = √ 40
The correct options are
LeftAngleBracket negative 6, 2 RightAngleBracket and StartRoot 40 EndRoot LeftAngleBracket negative 6, 7 RightAngleBracket and 40 LeftAngleBracket negative 2,6 RightAngleBracket and StartRoot 47 EndRoot LeftAngleBracket negative 2, 6 RightAngleBracket and StartRoot 40
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Please help me asap
Select the correct answer from each drop-down menu.
A system of linear equations is given by the tables. x y -1 1 0 3 1 5 2 7 x y -2 -7 0 -1 2 5 4 11
Answer:
1) The first equation of the system is y = 2·x + 3
2) The second equation of the system is y = 3·x - 1
3) The solution of the system is (4, 11)
Step-by-step explanation:
1) From the coordinates of the first table, we have;
The points of the y-coordinate have a common difference of two
The rate of change of the function using the first and the last point is given as follows;
Rate of change = Slope, m = (7 - 1)/(2 - (-1)) = 2
The, equation of the line in point and slope form is, y - 7 = 2 × (x - 2)
∴ The equation of the line in slope and intercept form is y = 2·x + 3
Therefore, the first equation of the system is y = 2·x + 3
2) Similarly from the coordinates of the second table, we have;
The points of the y-coordinate have a common difference of six
The rate of change of the function using the first and the last point is given as follows;
Rate of change = Slope, m = (11 - (-7))/(4 - (-2)) = 3
The, equation of the line in point and slope form is, y - 11 = 3 × (x - 4)
∴ The equation of the line in slope and intercept form is y = 3·x - 1
Therefore, the second equation of the system is y = 3·x - 1
3) Equating both equations in the system of equations to find a common solution gives;
2·x + 3 = 3·x - 1
∴ x = 4
From y = 3·x - 1 or y = 2·x + 3, we have the value of y at the solution point as y = 3 × 4 - 1 = 11 or 2 × 4 + 3 = 11
∴ y = 11 at point of the common solution of the system of equations
Therefore, the coordinates of the common point which is the solution of the system is (4, 11).
Answer:
Select the correct answer from each drop-down menu.
A system of linear equations is given by the tables.
x y
-1 1
0 3
1 5
2 7
x y
-2 -7
0 -1
2 5
4 11
The first equation of this system is y =
2
x + 3.
The second equation of this system is y = 3x −
1
.
The solution of the system is (
4
,
11
).
Step-by-step explanation:
Find the length of the missing side. Round to the nearest tenth (one decimal place).
Answer: pretty sure it is 56.5
Step-by-step explanation:
A submarine is 105 feet below the surface of the water, and it begins to ascend at a rate of 3 feet per minute. After how many minutes will the submarine be 81 feet below the surface?
Answer:
8 minutes
Step-by-step explanation:
Step one:
given
A submarine is 105 feet below the surface of the water
depth of submarine= 105 feet
let the time of ascending be x
Required
The time taken to ascend up to 81 ft
Step two:
the expression for the situation is
81=105-3x
solve for x
3x=105-81
3x=24
divide both sides by 3
x= 24/3
x=8 minutes
This year, a small business had a total revenue of $89,700. If this is 38% more than their total revenue the previous year, what was their total revenue the previous year?
Answer:
The business' total revenue last year was $65,000.
Step-by-step explanation:
So, if you need to find the previous year's total revenue, you would set up an equation like this:
x + 0.38x = 89,700
I think it would work out something like this:
x + 0.38x = 89,700
1.38x = 89,700
x = 65,000
To check, we would substitute 65,000 into the equation x + 0.38x = 89,700.
x + 0.38x = 89,700
(65,000) + 0.38(65,000) = 89,700
65,000 + 24,700 = 89,700
89,700 = 89,700
Ralph and Joe leave school walking in opposite directions. Ralph walks 1 km per hour faster than Joe. After 2 hours they are 30 km apart. What is the rate of each
Answer:
Joe's rate = 7 mph
Ralph's rate = 8 mph
Step-by-step explanation:
Give. That:
Joe's rate = x
Ralph rate = x + 1 kmph
Travel time = 2 hours
Hence, distance traveled = Speed * time
Joe's distance : 2 * x
Ralph's distance = 2 * (x + 1)
2x + 2(x + 1) = 30
2x + 2x + 2 = 30
4x + 2 = 30
4x = 30 - 2
4x = 28
x = 28/4
x = 7
Joe's rate = 7
Ralph's rate = 7 + 1 = 8
Which is equivalent to 6x-8y
Answer:
24 i guess. im not sure
Explain how to estimate the quotient using compatible numbers. 27 and two-thirds divided by 3 and nine-tenths
Answer:
the estimation of the quotient is 7
Step-by-step explanation:
The computation of estimating the quotient is shown below:
It is given that the number is 27
After that the two-third would be divided by 3
And, then the nine-tenth
Based on the above information, the estimation of the quotient is
= 27 + 2 ÷ 3 ÷ 3 + 9 ÷ 10
= 27 + 0.67 ÷ 3 + 0.9
= 27.67 ÷ 3.9
= 28 ÷ 4
= 7
hence, the estimation of the quotient is 7
Write P(x) = x^3 + x^2 − 17x + 15 as a product of two factors, using x − 3 as one factor.
A. (x − 3)(x^2 + x − 17)
B.(x − 3)(x^2 + 4x − 17)
C.(x − 3)(x^2 – 4x − 5)
D.(x − 3)(x^2 + 4x − 5)
Answer:
D. (x-3)(x^2 + 4x - 5)
Step-by-step explanation:
P(x) = x³ + x² - 17x + 15 can be written as (x - 3) (x² + 4x - 5) as a product of two factors.
What is Polynomials?Polynomials are expressions in algebra which consist of variables, constants and exponents combined using the basic operations in mathematics like addition, subtraction, multiplication and division.
Polynomials can be classified as monomials, binomials and trinomials depending on the degree of the variables as 1, 2 and 3 respectively.
The given polynomial is P(x) = x³ + x² - 17x + 15.
We already have x - 3 is the factor of this polynomial.
To get the other factor which is a binomial, we have to divide the given polynomial with x - 3.
On dividing, we get x² + 4x - 5 as the quotient and remainder equals zero.
So x² + 4x - 5 is the other factor of the given polynomial.
Hence, the polynomial P(x) = x³ + x² - 17x + 15 can be written as (x - 3) (x² + 4x - 5) as a product of two factors.
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find the slope of the line graphed below
Answer:
To find the slope of a line, we need to know the slope formula. The slope formula is:
m = , with m being the slope and (x₁, y₁) being the coordinates of one point and (x, y) being the coordinates of the other. Now we can substitute the values of the points in our problem ( (-1,-1) and (1, -4) ) into the slope formula. Substituting, we get:
=
==
=-1.5
That means the slope of our line is -1.5
Step-by-step explanation:
which is the better value 36 pictures for $8 or 24 pictures for $5
Answer:
24 pictures for $5
Step-by-step explanation:
To find out the better value, we have to find the price of a singular picture. To do this, we will divide each number by the amount of pictures.
For the first deal, 36 pictures cost $8, so 1 picture costs about $0.22.
For the second deal, 24 pictures cost $5, so 1 picture costs about $0.21.
Since the second deal costs less, it is a better deal.
Answer:
The best deal is 24 pictures for $5.
Step-by-step explanation:
In order to find out which price is better, we need to find the amount of pictures per dollar. This is also known as the unit rate.
36 ÷ 8 = 4.5 or 5 when rounded to the nearest whole number.
24 ÷ 5 = 4.8 or 5 when rounded to the nearest whole number.
However, since 4.8 is in fact higher than 4.5, the best deal is 24 pictures for $5.
Hope this helps! :D
The cost of 5 cans of dog food is 4.35. At this price how much do 11 cans of dog food cost? Explain!
Answer:
Ok so it would be 9.57
Step-by-step explanation:
4.35÷5 = 0.87
so 1 can is 0.87
$0.87*11=$ 9.57
If 5p - 2r = 19 and 2p + r = 4, find (p+r)
Answer:
5p-2r =19 in this one 5*5-2*3 so in this one p is =5 and r =3 and in the next one 2p+r=4 the answer is for p =1 and r =2 this means 2*1=2 and 2+2=4 and the first one is 5*5=25 and 2*3= 6 and 25-6=19 so that's it I guess
Giving brainleest for brainly.
Square ABCD was translated using the rule (x. y) «-4,y + 15) to form A'B'CD. What are the coordinates of point
D in the pre-image if the coordinates of point D' in the image are (9, -8)?
TE
O (13, -23)
(5, 7)
O (18, 1)
O (6,4)
Answer:
[tex](13,-23)[/tex]
Step-by-step explanation:
Given
Translation: [tex](x,y) -> (x-4,y+15)[/tex]
Required
Determine the pre-image of (9,-8)
In (9,8)
[tex]x = 9[/tex] and [tex]y = -8[/tex]
So:
[tex](x,y) -> (x-4,y+15)[/tex]
Becomes
[tex](9,8) ->(x-4,y+15)[/tex]
By comparison:
[tex]x - 4 = 9[/tex]
[tex]y + 15 = 8[/tex]
Solving for (x):
[tex]x - 4 = 9[/tex]
[tex]x = 9 + 4[/tex]
[tex]x = 13[/tex]
Solving for (y):
[tex]y + 15 = -8[/tex]
[tex]y = -8 - 15[/tex]
[tex]y = -23[/tex]
Hence, the pre -image has a coordinate of [tex](13,-23)[/tex]
What is the value of x In this equation?
75 + 10x = 225
150
15
25
10
Answer:
15
225-75=150
150÷10=15
Find the missing angle measure Angle STU?
2
A small business collected data each month to find out if money spent on advertising
affected the total sales for the company. The table shows the data collected over
several months.
Total Sales
Money Spent on
Advertising ($)
200
250
1,500
1,505
1,600
1,650
260
300
350
1,700
450
1,825
525
1,875
What is the correlation coefficient between money spent and total sales?
Answer:
Step-by-step explanation:
3
how to use standard form
Answer: Standard form is another way to write slope-intercept form (as opposed to y=mx+b). It is written as Ax+By=C. You can also change slope-intercept form to standard form like this: Y=-3/2x+3. Next, you isolate the y-intercept(in this case it is 3) like this: Add 3/2x to each side of the equation to get this: 3/2x+y=3.
Step-by-step explanation: hope this helps
grams of fish
number of calories
1000
2001
Enter the missing values in the boxes below.
b=0
Answer:
♂️ but if you know please answer
Answer:
12344567891011121314151617181920
Step-by-step explanation:
12344567891011121314151617181920
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w 12
2l + 2w 12
l + w < 30
Answer:
a i the answer
Step-by-step explanation:
l ≤ 12
2l + 2w < 30
Answer: a
Step-by-step explanation:
These two triangles are similar. If the base of △ A B C is 3 cm and the base of △ D E F is 7 cm, and the area of △ A B C is 7 cm², calculate the area of △ D E F. Round your answer to two decimal places.
Answer:
38.11 cm^2
Step-by-step explanation:
DEF is larger than ABC
therefore find the height of ABC
7 = 1/2 * 3 * h
h = 7 * 2/3
h = 14/3
So, lets find height for DEF, 7/3 = H/ 14/3
H = 98/9
A = 1/2 * 7 * 98/9
A = 38.11 cm^2
what is the answer to 3c-7c+a+b
I don't understand this question. I was hoping someone could help.
Answer:
A
Step-by-step explanation:
The constant rate of change in this question simply means the slope
To get the slope, we simply get two points and apply the slope equation;
The points are;
(3,60) and (6,30)
The slope equation is;
m = (y2-y1)/(x2-x1) = (30-60)/(6-3) = -30/3 = -10 ft/s
So our answer is the first option as it represents a decent of -10 ft/s
Using the Arc length formula s = r θ, find the missing variable.
Find s when r = 18.4 and θ 3π/4
13.8π
15.2π
24.5π
Step-by-step explanation:
13.8pie is correct answer of your question
Equal to the opposite of -45
Answer:
45 or 1/45
Step-by-step explanation:
not sure
Question 4
Write an algebraic expression for the following.
Joe spent three dollars less than twice as much as Fernando did.
Use x for the variable.
Question 5
Ayliah is 7 years more than 1/2 of Deb's age
use x for the variable
Which graph represents the solution set of and ?
graph I
graph II
graph III
graph IV
A.
graph I
B.
graph II
C.
graph III
D.
graph IV
Answer:
GRAPH IIIStep-by-step explanation:
Look at the picture.
We have
y = x² - 4 → move the graph of x² 4 units down (the vertex is (0, -4))
x + y + 2 = 0 subtracy x and 2 from both sides
y = -x - 2 → move the graph of -x 2 units down (the y-intercept os -2)
Only graph III and IV meets these conditions.
The solution is the points of intersection of the graphs.
Therefore your answer is GRAPH III
Answer:
[tex]\fbox {C. graph lll}[/tex]
Step-by-step explanation:
The solution of the system of equations can be found at their intersections.
The graph which is correct is graph III as it has the correct representations of the equations and correctly indicates the points of intersection.