Answer:
[tex]\displaystyle (y + 2) = -\frac{1}{3}\, (x - 9)[/tex].
Equivalently:
[tex]\displaystyle (y - 2) = -\frac{1}{3}\, (x + 3)[/tex].
Step-by-step explanation:
Let [tex](x_{1},\, y_{1})[/tex] and [tex](x_{2}\, y_{2})[/tex] denote the coordinates of two points in the plane. If [tex]x_{1} \ne x_{2}[/tex] (i.e., the two points aren't on the same vertical line,) the slope of the line that goes through the two points would be:
[tex]\begin{aligned} m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\end{aligned}[/tex].
In this question, [tex]x_{1} = 9[/tex] and [tex]y_{1} = (-2)[/tex] (for [tex](9,\, -2)[/tex]) while [tex]x_{2} = (-3)[/tex] and [tex]y_{2} = 2[/tex] (for [tex](-3,\, 2)[/tex].) Given that [tex]x_{1} \ne x_{2}[/tex], the slope of the line that goes through these two points would be:
[tex]\begin{aligned} m &= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ &= \frac{2 - (-2)}{(-3) - 9} \\ &= -\frac{1}{3}\end{aligned}[/tex]
If a line in a plane is of slope [tex]m[/tex] and goes through the point [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line would be:
[tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of this line is [tex]m = (-1/3)[/tex]. If the point [tex](9,\, -2)[/tex] is chosen as [tex](x_{0},\, y_{0})[/tex] ([tex]x_{0} = 9[/tex] and [tex]y_{0} = (-2)[/tex],) then the point-slope equation of this line would be:
[tex](y - (-2)) = (-1/3)\, (x - 9)[/tex].
Simplify to obtain:
[tex]\displaystyle (y + 2) = -\frac{1}{3}\, (x - 9)[/tex].
Similarly, if the point [tex](-3,\, 2)[/tex] is chosen as [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this would be:
[tex]\displaystyle (y - 2) = -\frac{1}{3}\, (x + 3)[/tex].
This diagram shows the dimensions of a concrete piece used to build a deck.
What is the volume of the concrete piece?
Enter your answer in the box.
Answer: 2,200 I took the quiz.
Step-by-step explanation: Hope this helps!✪ ω ✪
You bought a winter coat for S48.75. The original price was $75. What percent of the original price did you pay for the coat?
Answer:
53.85%
Step-by-step explanation:
75-48.75= 26.25
26.25/48.75x100= 53.8461538462 Round 53.85%
Check Answer:
48.75 x 53.85%=26.251875 Round 26.25
48.75 + 26.25=75
Hence, the correct answer is 53.85%.
One-Step Equations 20 points if you solve them
Answer:
All answers below in explanation!
Step-by-step explanation:
1. x / 3 = 15 - 5
2. 2x = 11 + 6
3. x = -12
4. 400 - 20x = 60
what is 3x [8 divided by (4-2)]
Answer:
3(8/4-2)=12
Step-by-step explanation:
3(8/2)=3*4=12
Find the 7th term in the following sequence (n = 7)
f(n) = 8 + 5(n-1)
Also, for this question, state what a1 is (first term) and the common difference (a2 - a1).
Answer:
n= - 3/5
Step-by-step explanation:
1- Substitute f ( n ) = 0 remove the parentheses
2- Calculate
3- Move the variable to the left
4- Divide both sides
solve for I when 3/5 +I-1/15
Answer:
23 over 15 or 1.533
Step-by-step explanation:
Group like terms:
1+(3/5+-1/15)
Find LCD:
1+9/15+-1/15
Combine numerators:
15/15+8/15
And you get 23/15
Simplified:1 8/15
Decimal: 1.533
Santosh bought a refregator for rupees 9000 and forced to sell it in 8100 find loss percent
Answer:
10%
Step-by-step explanation:
original price = 9000
sold for 8100
price lost = 900
percentage of price lost = 900/9000 × 100
= 10 %
Hope this helps.
The ratio of the measures of the sides of a triangle is 3:7:9. If the perimeter of the triangle is 266 inches, find the length of the shortest side
Answer: I simplified it for you lol
Step-by-step explanation: Simplify the matrix.
19 + 266 inches
Solve the inequality for x.
-24 > x +4
Step-by-step explanation:
[tex] - 24 > x + 4[/tex]
[tex] - 28 > x[/tex]
Higher income Here is the distribution of the adjusted gross income in
thousands of dollars) reported on individual federal income tax returns
in a recent year. Given that a return shows an income of at least
$50,000, what is the probability that the income is at least $100,000?
Probabilities are used to determine the chances of events
The probability that the income is at least $100,000 is 0.106
How to determine the probabilityFrom the table, we have the following parameters:
Salary 100 - 499 = 0.100
Salary >= 500 = 0.006
The probability that the income is at least $100,000 is then calculated as:
p = 0.100 + 0.006
Evaluate the sums
p = 0.106
Hence, the probability that the income is at least $100,000 is 0.106
Read more about probability at:
https://brainly.com/question/25870256
Please may I have help with these questions. I’m really confused
Thank you
Answer:
Step-by-step explanation:
So what you need to do is take the two points (1, -5) and (3, -1) and subtract them. You take y of the second group and subtract y of the first group.
-1 - (-5) = 4
Now you do the first numbers in each group with the second set being the number you subtract from.
3 - 1 = 2
Now you do [tex]\frac{Rise}{Run}[/tex]. Rise = 4 Run = 2
[tex]\frac{4}{2}[/tex] = 2
Now the second part is saying y = 3x + c with your first set of numbers being x and y.
x = 1
y = -5
-5 = 3(1) + c
-5 = 3 + c
Subtract 3 from -5
-8 = c
The final answer is:
y = 3x - 8
Sharon completed the proof below. Which statement about Sharon’s proof is true
Answer:
1
Step-by-step explanation:
If it's given then it must be true
A 2-column table with 2 rows. The labels for the columns and rows are blank. First column entries are 5 x squared, 10 x. Second column entries are negative 2 x, negative 4. Which factors can be multiplied together to make the trinomial 5x2 8x – 4? Select two options. (x 1) (2x 1) (x 2) (5x 1) (5x – 2).
The factors of the binomial 5x²+8x-4 whose multiplication will give us the trinomial are (5x-2)(x+2).
What are the factors whose product will give us the binomial 5x²+8x-4?To solve the problem we will find the roots of the binomial 5x²+8x-4,
[tex]5x^2+8x-4 \\\\\text{Finding the roots of 8}\\\\=5x^2+10x-2x-4\\\\=5x(x+2) -2(x+2)\\\\=(5x-2)(x+2)[/tex]
Hence, the factors of the binomial 5x²+8x-4 whose multiplication will give us the trinomial are (5x-2)(x+2).
Learn more about Binomial expression:
https://brainly.com/question/15265533
4x^2+2x-5-3x and 6x^2-x+3-2x^2-8
Are these two expressions equal? Show how you know
Step-by-step explanation:
Simply Equation 1
R. H. S
6x^2 -x +3-2x^2-8
==> 6x^2-2x^2 -x +3-8
==> 4x^2-x-5 .....(1)
Simply equation 2
L. H. S
4x^2+2x-5-3x
==> 4x^2 +2x-3x-5
==> 4x^2-x-5 ....(2)
Since here, RHS = LHS
both eqn (1) = eqn(2)
hence they are equal.
Answer:
yes they are equal
Step-by-step explanation:
for the equation [tex]4x^{2} +2x-5-3x[/tex] you're going to collect like terms
2x-3x=5x
so your final equation is [tex]4x^{2} -x-5[/tex]
for the equation [tex]6x^{2} -x+3-2x^{2} -8[/tex] you're going to collect like terms
[tex]6x^{2} -2x^{2} =4x^{2}[/tex]
then you're going to calculate the difference
3x-8=-5
so your final equation is [tex]4x^{2} -x-5[/tex]
hcf of 738, 1080 and 1332.
Answer:
72 is the HCF for 738, 1080 and 1332.
the way I worked this out was by trial and error/improvement
What is 11.25 x 34.67 + 34.67 divided by 2?
Answer:
407.3725
Step-by-step explanation:
write two equelivant ratios 11 and 4
Answer:
The answer is 8 : 22, 12:33 as they are two equelivant ratios 11 and 4
Find the distance between (7,1) and (-3,-4)
Answer:
5
step explanation:
Use the distance formula to determine the distance between the two points.
Distance=√(x2−x1)2+(y2−y1)2
Substitute the actual values of the points into the distance formula.
√(1−(−3))2+(7−4)2
Simplify
5
What is the solution set of -11 > 1+ a?
o ac-12
Oa>-12
O a<-10
a>-10
Answer:
[tex] - 11 > 1 + a \\ - 11 - 1 > a \\ - 12 > a[/tex]
In a class there are 10 students who play football and cricket 7 students who do not play football or cricket 14 students who play football 21 students who play cricket Find the probability that a student chosen at random plays football and cricket
Answer:
110 members of a sports club play atleast one of the games, football, basketball and volleyball. If 20 play football and basketball only, 15 play football and volleyball only, 26 play basketball and volleyball only, x play all the three games, 2x each play
math
Of 45 students 30 play badminton and 26 play tennis. Each student play either badminton or tennis,determine how many students play:(a)badminton only (b) tennis only
probability and statistics
At a particular school with 200 male students, 58-play football, 40-play basketball, and 8 play both. What is the probability that a randomly selected male student plays a) At least one sport b) Neither sport c) Only basketball
The perimeter of a triangle is 74 inches. The two longer sides are equivalent and measure 1.5n+3. The shorter side measures 0.5n+1.5 What is the value of n
Answer:
n = 135/7
Step-by-step explanation:
2 x long side + short side = 75
substitute measures ⇒ 2(1.5n + 3) + (0.5n + 1.5) = 75
multiply out brackets ⇒ 3n + 6 + 0.5n + 1.5 = 75
gather like terms ⇒ 3n + 0.5 n + 6 + 1.5 = 75
combine like terms ⇒ 3.5n + 7.5 = 75
subtract 7.5 from both sides ⇒ 3.5n = 67.5
divide both sides by 3.5 ⇒ n = 135/7
What is the vertex of y = x2 + 2x +2
O (1,-1)
O (2,-2)
O (1, 2)
0 (-1, 1)
Answer:
vertex = (- 1, 1 )
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 2x + 2 ← is in standard form
with a = 1 and b = 2 , then
x = - [tex]\frac{2}{2}[/tex] = - 1
substitute x = - 1 into the equation for y- coordinate of vertex
y = (- 1)² + 2(- 1) + 2 = 1 - 2 + 2 = 1
vertex = (- 1, 1 )
Write a system of equations for the scenario
JUSD is selling tickets to a district-wide concert. They offer a two-dollar discount off the regular price ticket for bringing a canned food item for donation. On the first day of ticket sales, JUSD collected a total of $213 by selling 14 regular price tickets and 23 tickers with a donation. How much does each type of ticket cost?
Answer:
System of equation : 14x+23y = 213 and y = x-2
The cost of regular tickets is $7 and the cost of tickets with donation is $5.
Step-by-step explanation:
Let regular ticket's cost be x and tickets with donation's cost be y.
14x+23y = 213
y = x-2
Now,
14x+23y = 213
or, 14x+23(x-2) = 213
or, 14x + 23x - 46 = 213
or, 37x = 259
so, x = 7
again,
y = x-2
or, y = 7-2
so, y = 5
Lily earns $29.75 an hour. If she works 6 hours each day during the week and 4 hours a day
during the weekend, find her weekly wage.
Answer:
the answer is $1062.10
Step-by-step explanation:
explanation above
Guys does that mean multiply or like fractions?
Answer:
multiply
Step-by-step explanation:
It says for you to multiply.
Answer:
Multiplication...
Product means to multiply
1. K + 8 > 19, if k = 11 is this a true statement
Answer:
No, it isn't.
Step-by-step explanation:
The correct statement would be K + 8 = 19 <<<<<<<<\
11 + 8 equals 19 not greater than 19.
Asma will donate up to 500$ to charity. The money will be divided between two charities: the City Youth Fund and the Educational Growth Foundation. Asma would like the amount donated to the Educational Growth Foundation to be at least four times the amount donated to the City Youth Fund. Let "x" denote the amount of money (in dollars) donated to the City Youth Fund. Let "y" denote the amount of money (in dollars) donated to the Educational Growth Foundation. Shade the region corresponding to all values of "x" and 'y" that satisfy these requirements.
PLEASE PROVIDE THE GRAPH
Answer:2y>x or x<2y
x+y < 500
The points satisfying the 2nd inequality is a triangle bordered by the x and y axes and a downward sloping line connecting points (0,500) and (500,0)
the 1st inequality is half a plane, above the line x=2y or a line through the origin, with slope 1/2
the two overlap in a triangle bordered by the y axis, the line x+y=500 and the line x=2y
It's a triangle with vertices (333 1/3, 166 2/3) (0,500) and the origin (0,0)
Basically
Step-by-step explanation:
Answer:
See attachment
Step-by-step explanation:
y = 4x [ the amount, y, donated to the Educational Growth Foundation to be at least four times the amount donated to the City Youth Fund, x]
y + 4x ≤ $500
whats 12x12 +3x8-10+19=?
Answer:
172 = y
Step-by-step explanation:
Using PEMDAS(parentheses, exponents, multiplication, division addition subtraction.)
Given:
12 x 12 + 3 x 8 - 10 + 19 = y
12x 12 = 144
3 x 8 = 24
144 + 24 = 168
168 - 10 = 158
158 + 19 =
177
so
177 = y
Answer:
177
Step-by-step explanation:
i dont know if its right but it might help
hope it does :)
Write an algebraic expression for the word phrase below.
twelve more than m machines
Answer:
12 + m
Step-by-step explanation:
it's 12 more, which would be +12 because it's adding 12
Pls help, show work! Thank you
Answer:
126 miles
Step-by-step explanation:
1/4 inches = 9 miles
Divide 3.5 by 1/4 or 0.25
3.5 ÷ 0.25 = 14
Multiply 14 by 9
14 x 9 = 126
126 miles
