Write an equation of the line that passes through the pair of points.
(-5,-4), (5,-3)
Answers
Step-by-step explanation:
the most common form of line equation is
y = ax + b
a is the slope of the line. it is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
b is the y-intercept (the y value when x = 0).
once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.
for the slope a :
x changes by +10 (from -5 to 5)
y changes by +1 (from -4 to -3)
the slope is +1/+10 = 1/10
the equation looks now like
y = (1/10)x + b
let's use the first point.
-4 = (1/10)×-5 + b = -1/2 + b
-3 1/2 = -7/2 = b
the equation is
y = (1/10)x - 7/2
so, the second answer option is correct.
Related Questions
A trader has a mixture of 5c and 10c coins. He has 50 coins in all, with a total value of $4.20. How many of each coin does he have?
Answers
Answer:
16 5c coins
34 10c coins
Step-by-step explanation:
(I prefer to use whole numbers)
5x + 10y = 420
x+y=50
multiply the bottom problem by -5
5x +10y =420
-5x -5y = -250
combine the problems
5y = 170
divide by 5
y = 34
that means x = 16
34 10c coins
16 5c coins
-- Gage Millar, Algebra 1/2 tutor
The number of 5 cent coins are 16 and the number of 10 cent coins are 34.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, a trader has a mixture of 5 c and 10 c coins.
Let the the number of 5 c coins be x and the number of 10 c coins be y.
He has 50 coins in all, with a total value of $4.20.
So, x+y=50 ---------(I)
5x+10y=420 ---------(II)
Multiply equation (I) by 5, we get
5x+5y=250 ---------(III)
Subtract equation (III) from (II), that is
5x+10y-(5x+5y)=420-250
⇒ 5y=170
⇒ y=34
Substitute y=34 in equation (I), we get
x=16
Therefore, the number of 5 cent coins are 16 and the number of 10 cent coins are 34.
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any of these please i don't get this
Answers
Answer:
33. $5.75
34. 15 ft
35. 8
36. 32
Step-by-step explanation:
These questions pretty much cover the sorts of things you're supposed to learn in an Algebra course. If you don't get any of it, you may have a problem with follow-on courses.
__
33.You are expected to understand this question gives you two relations in two unknowns. The first step is to assign a variable to each of the unknowns. We can use ...
x = cost of a milk shakey = cost of a sundaeThe given relations have to do with the prices of different quantities of these:
2x +3y = 26.25 . . . . . . cost of 2 shakes and 3 sundaes
4x +2y = 29.50 . . . . . . cost of 4 shakes and 2 sundaes
These two equations in two unknowns can be solved several ways. Here, it is convenient to use the method of "elimination", because the coefficients of x are related by a small integer. Subtracting the second equation from 2 times the first eliminates the x-variable (hence the name of the method).
2(2x +3y) -(4x +2y) = 2(26.25) -(29.50)
4y = 23.00 . . . . . . simplify
y = 5.75 . . . . . . . . . divide both sides by 4
The cost of an ice cream sundae is $5.75.
We can substitute this value into either equation and solve for x. We would find the cost of a shake to be x=4.50. However, the question only asks for the price of a sundae.
__
34.There are formulas for the perimeter, area, and volume of various geometric figures of a generally circular or rectangular shape. You might find it convenient to memorize them. Here, you need the formulas for the volume of a cylinder and of a cone. You also need to know that the diameter of a circle is 2 times the radius of the circle, since most of the circle-related formulas are in terms of the radius.
Volume of a cone of radius r and height h: V = 1/3πr²h
Volume of a cylinder of radius r and height h: V = πr²h
It can be convenient to remember that a cone has 1/3 the volume of a cylinder the same height.
The relation of interest here is the volume of the silo is the sum of the volumes of the bottom cylinder and the top cone.
V = π(20 ft)²(60 ft) + 1/3(20 ft)²(x ft) = 26000π ft³
V = 24000π ft³ +(400/3)x·π ft³ = 26000π ft³ . . . . simplify a bit
400/3·x = 2000 . . . . . . . divide by π ft³, and subtract 24000
x = 2000(3/400) = 15 . . . . multiply by 3/400
The height of the top portion is 15 feet.
__
35.This has to do with understanding the meaning of a table and of an expression relating table values. The expression f(a) = g(b) means you're looking for table entries such that the number in the f(x) column is equal to the number in the g(x) column.
We find the only common function value to be -1, so f(-6) = -1 = g(1). Comparing this to f(a) = g(b), we see that a=-6.
The question asks for |g(a)|. The table tells us g(-6) = -8. Its absolute value will be the value without the negative sign:
|g(-6)| = |-8| = 8 = |g(a)|
__
36.This is a polynomial division problem. It tells you the quotient of the quadratic, divided by (ax +2), is (3x -4) with a remainder of 66. We're concerned with the leading coefficient of the divisor, 'a'.
Polynomial long division is much simpler than numerical long division, because each quotient term is the leading dividend term divided by the leading divisor term. Here, that means ...
96x²/(ax) = 3x
Multiplying by ax gives ...
96x² = 3ax²
Dividing by 3x², we see that ...
(96x²)/(3x²) = (3ax²)/(3x²)
96/3 = a = 32
The value of 'a' is 32.
To earn an a in mr.whites math class students must score a total of at at least 135 points on three test. On the first two test , kaylees scores were 47 and 48 . What is the minimum score she must get on the third test to earn an a
Answers
Answer:
Set an equation x+47+48= 136
solve for x
x+95=136
x= 40
so they need to score a 40
Х
у
-2
3
2
-9
6
-21
10
-33
Answers
Answer:
y = - 3x - 3Step-by-step explanation:
Given table:
x | -2, 2, 6, 10 y | 3, -9, -21, -33Use two pairs of points to work out the equation of the line y = mx + b:
(-2, 3) and (2, - 9)Find the slope:
m = (-9 - 3)/(2 - (-2)) = - 12/4 = - 3Use one pair to find the y-intercept:
3 = - 3*(-2) + b3 = 6 + bb = 3 - 6b = - 3The line is:
y = - 3x - 3m = (-9 - 3)/(2 + 2) = -12/4 = -3 ==> (x)
3 = (-3)•(-2) + b
3 = 3•2 + b
3 = 6 + b
b = -3 ==> (a)
Soo :
y = -3x - 3PLEASE HELP ASAP
A shop sells a washing machine for £236.25, making a profit of 5%. At what wholesale price did the shop buy the washing machine?
Original price = £
Answers
Answer:
£225
Step-by-step explanation:
The relationship between the cost price (cp) and the selling price (sp) is ...
cp + 5% × cp = sp
cp(1.05) = sp . . . . . . collect terms
cp = sp/1.05 . . . . . . divide by 1.05
cp = £236.25/1.05 = £225
The original wholesale price was £225.
Which sequence is geometric?
Group of answer choices
-2, 1, 6, 13...
-1, 2, 7, 14
-4, 20, -100, 500...
-7, 7, 21, 35...
Answers
Hi there! :)
A geometric sequence is a sequence where we use multiplication or division to get to the next term.
We use multiplication in the third sequence (we multiply by -5)
So the answer is Option C
Hope it helps
~Just a gloomy teen who misses her best friend
#CarryOnLearning
[tex]SilentNature[/tex]
If the sum of two consecutive
even integers is - 18, find the
integers.
Answers
-10 and -8????
I believe because -10 + -8 = -18 and they are both consecutive
-3 and -5 what is less, greater than , and or equal
Answers
Answer:
-3 is less and -5 is greater
Step-by-step explanation:
Answer:
less than
Step-by-step explanation:
because -5 would be less than -3 because it is bigger
Determine the number of solutions you will have for the system: 1/3x+y=2 and 3y=6-x
One solution.
No solutions.
Infinite solutions.
Impossible to determine.
Answers
Answer:
infinity solution
solution:
-x-3y=-6
x+3y=6
What is the value of the rational expression when x = –3?
-1/12
0
1/6
undefined
Answers
Option D is correct, the value of the rational expression when x = –3 is undefined.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is x/x²-9
x divided by x square minus nine.
Now let us find the value of the expression when x is minus three,
Plug in x as -3 in the above expression.
-3/(-3)²-9
-3/9-9
-3/0
Anything divided by zero then the value is undefined.
Hence, Option D is correct, the value of the rational expression when x = –3 is undefined.
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What is the value of the rational expression x/x2-9 when x = –3?
A. -1/12
B. 0
C. 1/6
D. Undefined
Orion buys 3 books for a total of 25.50. He pays $8 plus sales tax for each book. He wants to know how much the sales tax is for one book.
Let "t" equal the sales tax Orion pays for each book. Write an equation that represents this situation.
Answers
The equation that represents this situation is 8 + 3t = 25.50.
How to calculate the value?Let the sales tax for each book be represented as t.
Since Orion buys 3 books for a total of 25.50 and he pays $8 plus sales tax for each book. This will be illustrated as:
Cost of book + Tax = Total amount
8 + (3 × t) = 25.50
8 + 3t = 25.50
Collect like terms
3t = 25.50 - 8.
3t = 17.50
Divide
t = 17.50 / 3
t = 5.83
The sales tax is $5.83.
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(sinx + cosx)(1 − sinx cosx) ≡ sin3x + cos3x
Answers
Step-by-step explanation:
We will use the LHS to find the RHS.
Step 1: Expand the LHS by multiplying through the brackets and simplify
(sinx + cosx)(1 − sinx cosx) ≡ sinx + cosx - (sinx + cosx (sinx cosx))
≡ sinx + cosx - sin²x cosx - sinx cos²x
Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation
≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)
Step 3: Simplify the equation by adding like terms
≡ sinx + cosx - cosx + cos³x - sinx + sin³x
≡ sin³x + cos³x [QED]
Reminder:
1 - cos²x = sin²x 1 - sin²x = cos²x (cosx)(cosx) = cos²x
1. A linear function can be represented by the equation y = 7x - 4. Identify the slope and y-intercept.
y-intercept:
Slope:
Answers
Hello!
Remember y=mx+b.
m is the slope and b is the y intercept.
So
the slope is 7 and the y intercept is 4.
Hope this helps!
~Just a felicitous teen
#CarryOnLearning
[tex]SIlentNature[/tex]
Answer:
slope: 7
y-intercept:4
Step-by-step explanation:
There are 16 mangoes in a basket.They are ONLY Julie and east indian.If you take out a Julie and replace it with an east indian ,there will be an equal number of Julie and east indian mangoes.If you take you three east indian mangoes and replace them with Julie,the number of Julie will be three fi me the number of east Indians? At present there are how many east indian and Julie mangoes in the basket?
Answers
Answer:
11 Julie's and 5 East Indians
simplify, (xy+yz)² - 2x²y²z² and find the value when x=-1, y=2 and z=1
plz answer this fast plz u will give you brainly plz help me fast only 5min left to answer
Answers
We have
(xy + yz)² - 2x²y²zIf,
x = -1, y = 2 and z = 1Putting value:
(xy + yz)² - 2x²y²z➡ (-1×2 + 2×1)² - 2×-1²×2²×1
➡ (-2 + 2)² - 2×1×4×1
➡ (0)² - 8
➡ 0 - 8 = -8,answer
A radar station is 2000 ft from the launch site of a rocket. If the rocket is launched vertically at the
rate of 500 ft/sec, how fast is the distance between the radar station and the rocket changing 10 seconds
later?
Answers
Answer: f 500 Ft./sec
Step-by-step explanation:
By evaluating the derivate of the distance in t = 10s, we will see that at t = 10s the distance is changing at a rate of 464.2 ft/s
We can think of the situation as in a right triangle, one cathetus is equal to 2000ft, and the other cathetus increases at a rate of 500ft/sec.
The hypotenuse would be the distance between the radar and the rocket.
Then the distance function is:
[tex]D(t) = \sqrt{(2000ft)^2 + (500ft/s*t)^2}[/tex]
Now we need to get the rate of change, this is given by:
[tex]\frac{dD(t)}{dt} = (1/2)*\frac{2*(500ft)^2*t}{\sqrt{(2000ft)^2 + (500ft/s*t)^2} }[/tex]
Now we evaluate this in t = 10s to get:
[tex]\frac{dD(10s)}{dt} = (1/2)*\frac{2*(500ft/s)^2*10s}{\sqrt{(2000ft)^2 + (500ft/s*10s)^2} } = 464.2 ft/s[/tex]
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An Earth worm Moves at a
distance of 45cm in 90 secondo
find the speed of the earth
worm
(I need to know how to lay it out as well)
Answers
Answer:
if the units is in m/s
Step-by-step explanation:
first work out using this triangle.
distance= speed x by time
so if we're trying to find out the speed we reaarange the triangle to :
distance
---------------------
speed x time
so speed = distance divided by time
distance = 45cm
divided by time = 90 seconds
But the units are cm and should be metres per second
change 45cm to m
that is 45cm = 45/ 100 = 0.45
0.45/ 90= 0.005cm
answer = 0.005 metres per second( m/s)
plz say thanks + rate !
Find two integers whose sum is -3 and product is -18
Answers
With this in mind,
x + y = -3
x * y = -18
[] Let's think about the factors of -18Then we will think about which ones could add up to 3
1 & 18, 2 & 9, 3 & 6 are factors of 18 (one being negative results in -18)
Well 1 and 18 cannot make 3, same for 2 and 9, that leaves us with 3 and 6.
[] Last, we will testYou can see our test shows this solution works!
-6 + 3 = -3
-6 * 3 = -18
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Which describes the slope of the line that passes through the points (2, 5) and (– 4, 5)?
Answers
Answer:
m is the slope of line and x1, y1= 2,5 , and x2, y2= -4, 5
m = 5-2/-4-5 = -1/3
Step-by-step explanation:
A shop sells orange juice in the following ways:
500 ml bottle for £1.25
1.5 litre carton for £2.35 each or 2 cartons for £3.50
2 litre carton for £3.25
What's the cheapest way of buying exactly 8 litres with no extra?
Find the amount of each type of bottle or carton you need and the total cost of buying 8 litres
Answers
Answer:
1.
1.5 litre carton for $2.35 is the cheapest way since it's the cheapest out of all the other options.
2.
a. 1.25 / 0.5 = $2.50 per L
2.35 / 1.5 = $1.57 per L
3.25 / 2 = $1.63 per L
b. 2.50 x 8 = $20.00 per 8 L
1.57 x 8 = $12.56 per 8 L
1.63 x 8 = $13.04 per 8 L
Step-by-step explanation:
find unit rate (cost / quantity)
Rewrite 4/6 and 1/3 as a unite rate
Answers
Answer: B
Step-by-step explanation: Hope this helps :)
Please help me! my teacher didn't teach me this!!
Answers
Answer:
skew
skew
parallel
parallel
Step-by-step explanation:
First see the below figure to understand parallel and skew lines
As you can see parallel lines lie on the same plane
skew lines lie on different plane and do not intersect
1)AB and GF
AB lies on ABCD plane
GF lies on EFGH plane
and they will never meet / intersect
so skew
2)DH and BF
DH lies on ADHE plane
BF lies on BCGF plane
they seem parallel but they are on different plane, so skew
3)EF and HG
EF and HG both lie on the same plane EFGH
and they both are parallel
4)for this see the second picture
both these planes are parallel
Hope this helps!
What is the slope of the line with equation 2x−5y=52?
Answers
Answer:
m = 2/5
Step-by-step explanation:
2x - 5y = 52
-5y = -2x + 52
y = 2/5x - 52/5
The slope of the line with equation 2x−5y=52 is 2/5.
The given equation of line is 2x−5y=52.
What is the slope of a equation?The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis.
The given equation 2x−5y=52 can be rewritten as
2x-52=5y
⇒ y = 2x/5-52/5
Now, compare y = 2x/5-52/5 with the standard form of an equation y=mx+c
So, m=2/5
Therefore, the slope of the line with equation 2x−5y=52 is 2/5.
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Part 2
Directions: Use the information in the charts to answer the questions.
Type of Fruit Cost
Estimated
Cost
apple
$1.75/pound
orange
$2.35/pound
banana
$1.50/pound
Answers
Answer:
i think you need to add all that up
Step-by-step explanation:
x^8+8x^7+15x^6−9x^5−72x^4−135x^3+8x^2+64x+120 Factor completely given the following factors: (x+5) and (x+3) There should be 6 factors (2 given, 2 binomials, and 2 trinomials.) show steps
Answers
Answer:
(×+3)(×+5)(×2)(×-1) (×^2+2×+4)(×^2+×+)Step-by-step explanation:
Where the given one is bolded the 2 binomials is italicized Ang the 2 trinomials is underlinedpa BRAINLEST pls
pls help plsss
help
plss
Answers
Answer:
number 2 is c, number 3 is c
what is the common denominator of 6/7 and 3/8(please help i'm failing math)
Answers
Answer:
56
Step-by-step explanation:
Owen invested $81,000 in an account paying an interest rate of 3\tfrac{7}{8}3 8 7 % compounded continuously. Zoe invested $81,000 in an account paying an interest rate of 3\tfrac{1}{4}3 4 1 % compounded monthly. After 9 years, how much more money would Owen have in his account than Zoe, to the nearest dollar?
Answers
Answer: $6322
114800.8806 - 108478.6929
= 6322.1877
Rounded to the nearest dollar = $6322
Answer:6761
Step-by-step explanation:
I need 30 please thank you
Answers
Answer:
ok good morning
have a nice day
Step-by-step explanation:
#toxicsquad
Answer:
i think its 7, but you should probably check that...
What is the graph of y=3/4x-3
Answers
Answer:
the answer is graph C
Step-by-step explanation:
babyface_wee
Answer: Graph A
Step-by-step explanation:
y-intercept = -3 So, Not Graph B
Slope = 3/4x = rise 3 run 4 or up 3 right 4. So not Graph C
Graph A meats all the criterias.