Write an equation of the form y = mx for the line shown below. If appropriate,use the decimal form for the slope.(4,3)
Answers
SOLUTION
Step 1 :
In this question, we are expected to find the equation of the line,
y = m x + c
where y = dependent variable,
x = dependent variable,
m = gradient of the line
c = intercept on the y - axis.
Step 2 :
We are given that :
[tex]\begin{gathered} \text{The gradient of the line, } \\ m\text{ }=\text{ }\frac{y_2-y_1}{x_{2_{}}-x_1} \\ \text{where (x }_{1\text{ , }}y_{1\text{ }}\text{ ) = ( 4, 3)} \\ (x_{2\text{ , }}y_2\text{ ) = ( -4 ,- 3 )} \\ \text{Then we have that :} \\ m\text{ = }\frac{(\text{ -3 - 3 ) }}{-\text{ 4 - 4}} \\ m\text{ = }\frac{-6}{-8} \\ m\text{ =}\frac{3}{4} \end{gathered}[/tex]Step 3 :
Since ( x 1, y 1) = ( 4, 3 ) and
[tex]\begin{gathered} \text{the gradient m = }\frac{3}{4}\text{. } \\ y-y_{1\text{ }}=m(x-x_1) \\ y\text{ - 3 =}\frac{3}{4}\text{ ( x - 4 )} \\ \text{simplifying further, we have that:} \\ 4\text{ y - 12 = 3 x - }12 \\ 4y\text{ - 3x - 12 + 12 = 0} \\ 4\text{ y - 3 x = 0} \\ \operatorname{Re}-\text{arranging the equation, we have that:} \\ 4\text{ y = 3 x } \end{gathered}[/tex]CONCLUSION:
The final answer is :
[tex]y=\text{ }\frac{3}{4}\text{ x }[/tex]Related Questions
The product of the ages (in days) of two newborn babies Simran and Jessie in two dayswill be 48 more than the product of their ages today. How old are the babies if Jessie is 2days older than Simran?
Answers
Given that:
- The product of the ages (in days) of babies Simran and Jessie in two days
will be 48 more than the product of their ages today.
- Jessie is 2 days older than Simran.
Let be "j" Jessie's age (in days) and "s" Simran's age (in days).
You can set up the following System of Equations using the data given in the exercise:
[tex]\begin{cases}(j+2)(s+2)=js+{48} \\ j={s+2}\end{cases}[/tex]You can use the Substitution Method to solve the system:
1. Substitute the second equation into the first one:
[tex](s+2+2)(s+2)=(s+2)s+48[/tex]2. Solve for "s":
[tex](s+4)(s+2)=s^2+2s+48[/tex][tex](s)(s)+(s)(2)+(4)(s)+(4)(2)=s^2+2s+48[/tex][tex]s^2+2s+4s+8=s^2+2s+48[/tex][tex]\begin{gathered} 4s=48-8 \\ \\ s=\frac{40}{4} \\ \\ s=10 \end{gathered}[/tex]3. Substitute "s" into the second original equation and evaluate:
[tex]\begin{gathered} j=10+2 \\ j=12 \end{gathered}[/tex]Hence, the answer is: Jessie is 12 days old and Simran is 10 days old.
use the values of the vertex and point to write the equation of the graph in standard form
Answers
The vertex form of a quadratic function is:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{ Where} \\ (h,k)\text{ is the vertex of the parabola } \end{gathered}[/tex]The standard form of a quadratic function is:
[tex]y=ax^2+bx+c[/tex]We can do the following steps to solve the exercise.
Step 1: We replace the values of h,k, x, and y into the vertex form of a quadratic equation, and we solve for a.
[tex]\begin{gathered} h=1 \\ k=-5 \\ x=3 \\ y=-1 \end{gathered}[/tex][tex]\begin{gathered} y=a(x-h)^{2}+k \\ -1=a(3-1)^2-5 \\ -1=a(2)^2-5 \\ -1=4a-5 \\ \text{ Add 5 from both sides} \\ -1+5=4a-5+5 \\ 4=4a \\ \text{ Divide by 4 from both sides} \\ \frac{4}{4}=\frac{4a}{4} \\ 1=a \end{gathered}[/tex]Step 2: We replace the values of a,h, and k into the vertex form of a quadratic equation.
[tex]\begin{gathered} y=a(x-h)^{2}+k \\ y=1(x-1)^2-5 \end{gathered}[/tex]Step 3: We expand the expression inside the parentheses and combine like terms to convert the function into its standard form.
[tex]\begin{gathered} y=1(x-1)^{2}-5 \\ y=(x-1)^2-5 \\ y=(x-1)(x-1)-5 \\ \text{ Apply the distributive property} \\ y=x(x-1)-1(x-1)-5 \\ y=x*x-x*1-1*x-1*-1-5 \\ y=x^2-x-x+1-5 \\ y=x^2-2x-4 \end{gathered}[/tex]AnswerThe equation of the graph in standard form is:
[tex]y=x^{2}-2x-4[/tex]17. Testing Lipitor In a clinical trial of the cholesterol drug Lipitor, subjects were partitioned into groups given a placebo or Lipitor doses of 10 mg, 20 mg, 40 mg, or 80 mg. The subjects were randomly assigned to the different treatment groups (based on data from Pfizer, Inc.). would it be a random,systematic, onvience, stratified, or cluster.
Answers
Answer:
Stratified
Explanation:
In Stratified Sampling, members of the population are divided into subgroups before a random sample of each group is taken.
Therefore in the case of the clinical trial presented, the sampling method used is stratified.
Write an algebraic expression for each verbal expression.1. x more than 7 2. a number less 35 3. 5 times a number4. one-third of a number5. f divided by 106. the quotation of 45 and r7 three times a number plus 168. 18 decreased by 3 times d9. k squared minus 1110. 20 divided by t to the fifth power
Answers
Part 1
'x more than 7' written as an algebraic expression is:
= 7 + x
Part 2
Let the number be n
Therefore, 'a number less 35' written as an algebraic expression:
=n - 35
Part 3
Let the number be y
'5 times a number' written as an algebraic expression:
=5 x y = 5y
Part 4
[tex]\text{One}-\text{third}=\frac{1}{3}[/tex]Let the number be x.
[tex]\begin{gathered} \text{One}-\text{third of a number}=\frac{1}{3}\text{ of x} \\ =\frac{1}{3}x \end{gathered}[/tex]Part 5
[tex]f\text{ divided by 10}=\frac{f}{10}[/tex]im confused on what goes with what
'
Answers
Answer: b
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
you have to divide it so 7 1/2 ÷ 1 1/2
15/2 × 3/2 then you swap the 3/2 to 2/3 so it will be 15/2 × 2/3 you don't have to cross multiplication so you just multiply across so it would be 15×3=30 and then 2×3=6 so it would be 30/6 but that's not the final answer because it and improper fractions so you divide 30÷6=5 and that's how you get 5
The cross-section of a lean-to shelter is in the shape of a triangle. The base of the triangle is 88 feet more than twice its height. If the area of the triangle is 6060 square feet, determine the length of the base and the height of the triangle in feet.
Answers
The length of the base and the height of the triangle are 7.7 feet and 15.7 feet
How to determine the length of the base and the height of the triangleFrom the question, we have the following parameters that can be used in our computation:
Base = 8 feet more than twice the height
Area = 60
This means that
b = 8 + h
A = 60
The area of a triangle is
A = 0.5bh
So, we have
0.5(8 + h)h = 60
This gives
4h + 0.5h² = 60
Rewrite as
0.5h² + 4h - 60 = 0
Using a calculator, we have
h = 7.7
Recall that
b = 8 + h
So, we have
b = 8 + 7.7
Evaluate
b = 15.7
Hence, the base is 15.7 feet
Read more about areas at
https://brainly.com/question/24487155
#SPJ1
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
You used `14` ounces of cheese to make `2` pizzas.
How much cheese do you need for `3` pizzas?
Answers
Answer:
You need 21 ounces of cheese for 3 pizzas.
Step-by-step explanation:
If you use 14oz for 2 pizzas, then if you divide it by 2, you have 7oz for 1 pizza.
Now multiply by 3 to get 21oz for 3 pizzas.
Gary makes $7.48 an hour. He grossed $310.42 last week. How many hours did he work?
Answers
Answer:
Gary worked 41 and a half hours
Step-by-step explanation:
$310.42 divided by $7.48 per hour = 41.5 hours
WILL GIVE BRAINLIEST IF RIGHT
The following is a list of grades that students received on a recent math exam:
77, 78, 81, 62, 63, 65, 81, 92, 93, 89, 91, 78, 66, 75, 78, 80, 91, 93, 95, 93, 91, 88, 76, 89, 91, 96.
The teacher wants to highlight the lower quartile, median, and upper quartile. Which of the following displays would represent the data in this way?
Bar chart
Box plot
Histogram
Stem-and-leaf plot
Answers
The display that would represent the data in the best way that lower quartile, median, and upper quartile would be highlighted would be box ploy. That is option B.
What is box plot?Box plot which is also called box and whisker plot is a type of graphical representation that is used to represent the five number summary of a data set that include the following:
Minimum,lower quartile, median,upper quartile andMaximum.Therefore, among the listed displays, the graphical representation method that can best be used is the box plot.
Learn more about upper quartile here:
https://brainly.com/question/28277179
#SPJ1
Answer:
B - Box Plot
Step-by-step explanation:
I took the test :)
simplify: 3√45 -4 √225 + √200 - √50
Answers
According to the given data we have the following:
3√45 -4 √225 + √200 - √50
Then to simplify we would have to make the following:
[3 × √3 × √3 × √5] - [√5 × √5 × √5] + [√2 × √2 × √2 × √5 × √5] - [√2 × √5 × √5]
=[3 × 3 × √5] - [5 × √5] + [2 × 5 × √2] - [5 × √2]
=3√5 - 5√5 + 10√2 - 5√2
=√5(3 - 5) + √2(10 - 5)
=(-2√5) + 5√2
Therefore, the answer would be 16√5 + 75√2
Miranda has $50 to buy 6 swim caps for the members of a swim team.
Which expression shows the amount of money she will have left if each swim cap costs c dollars?
Answers
Answer:
50÷6=8 R2
Step-by-step explanation:
8
6 ⟌50 R2
- 0
-------------
50
-48
--------------
2
So, Miranda will have $8 left to buy.
Write a systems of equations for each problem define variables used. Please show all work.On a table are 20 coin., quarters and dimes. Their value is $3.05 how many of each kind of coin are there?
Answers
We have 20 coins in total, lets say that we have X amount od quarters(0.25 dollar) and Y amount of dimes(0.1 dollar), and in total we have $3.05, with this we can write the system:
[tex]X+Y=20[/tex]Wich means that we have 20 coins, and:
[tex]0.25X\text{ + 0.1Y=3.05}[/tex]Thats the amount of money we have.
So, from the first equation, we can isolate X, as follows:
[tex]X=20-Y[/tex]And with that we can substitute X in the second equation, as follows:
[tex]0.25X\text{ + 0.1Y=3.05 }\rightarrow\text{ }0.25(20-Y)\text{ + 0.1Y=3.05 }\rightarrow\text{ }5-0.25Y+0.1Y=3.05[/tex][tex]5-0.25Y+0.1Y=3.05\rightarrow-0.15Y=-1.95\rightarrow Y=13[/tex]So, if Y=13, we have that X=7. So 13 dimes and 7 quarters.
can you explain to me what a voronoi diagram is?and what are the edges, and other things?
Answers
A Voronoi diagram is a division of a plane into areas near each of a given set of objects in mathematics. These things are just infinitely many points in the plane in the simplest scenario (called seeds, sites, or generators). There is a region, known as a Voronoi cell, for each seed that is made up of all points in the plane that are closer to that seed than to any other point. A set of points' Voronoi diagram and Delaunay triangulation are identical.
We are aware that any intersection of half-planes results in a convex region bordered by a collection of linked line segments. Voronoi edges are the line segments that define the limits of Voronoi regions. These edges' termini are known as Voronoi vertices.
Voronoi diagram:
A Voronoi diagram in mathematics is a division of a plane into areas near to each of a given set of objects. These things are simply infinitely many plane points in the most basic scenario (called seeds, sites, or generators).
To learn more about Voronoi diagram visit: https://brainly.com/question/26309607
#SPJ9
In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 5 feet of fence for the shortest side and 13 feet of fence for the longest side,
how many feet of fencing is needed for the entire animal pen?
Answers
Answer:
The answer is 12.
Step-by-step explanation:
First you need to draw a right triangle. Then the shortest side of the triangle is 5 and the longest is 13 so you would have to do a^2 + b^2 = c^2. So the problem would look like this 5^2 + b^2 = 13^2. 5 x 5= 25 and 13 x 13= 169. Now the problem looks like this 25 + b^2 = 169, since you can't do 25 + b you would have to bring it to the other side. Afterwards the problem should look like this b^2 = 144. Now you would have to square the b and 144 so the answer is 12. Sorry for spelling and grammar mistakes. Hoped this helped!
Answer:
15
Step-by-step explanation
Consider the equation 2x+5y=1Identify the slope and y intercept
Answers
Solution
Given the equation 2x+5y=1
We are required to Identify the slope and y intercept
The general equation of a straight line is in the form y = mx + c
Where m = slope and c= y-intercept
To solve the problem before us, we need to re-write 2x+5y=1 in the form y = mx + c
[tex]\begin{gathered} 2x+5y=1 \\ 5y=-2x+1 \\ y=-\frac{2}{5}x+\frac{1}{5} \\ \\ Comparing\text{ the resulting equation with y=mx+c} \\ m=-\frac{2}{5},\text{ c=}\frac{1}{5} \end{gathered}[/tex]Thus, the slope = -2/5 while the y-intercept is 1/5
An orchard has 40 rows of trees. Each row is a set number
of trees longer than the one preceding it. If the first row
has 24 trees and the last row has 180 trees, find the
following:
a. How many trees are there in the whole orchard?
b. How many trees are there in the 21st row of the orchard?
ar:
Answers
Answer:
a)4080 trees
b)104 trees
Step-by-step explanation:
1st - 24 trees
last (40th) - 180 trees
If differences between any row (except 40th) and next row are equal then
2nd - 24 trees+X
3rd - (2nd+X) or 24 trees + 2X
coefficient of X is number of row minus 1, therefore 40th row has 24 trees + 39X, and it is equal to 180. We can make an equation from this:
24tr+39X=180tr
39X=156tr
X=4tr
By this we can find how many trees are there in the 21st, 21st row has 24 trees+20X=24 trees+80 trees=104 trees
To find how many trees are there in the whole orchard, we add them all:
1st - 24 trees, 2nd - 24 trees + X, 3rd - 24 trees + 2X,
easily, it is just 24 trees x 40 + 39X x 20 = 4080 trees
Answer:
(a) 4,080 trees
(b) 104 trees
Step-by-step explanation:
If the first row has 24 trees and the fortieth row has 180 trees, how many additional trees are in each succeeding row?
[tex](40-1)x=180-24[/tex]
[tex]39x=156[/tex]
[tex]x=4[/tex]
That means that each row has 4 more trees than the preceding row. For example, the second row has 28 trees, the third row has 32 trees, and so on. We can write a formula to tell us how many trees are in any given row:
[tex]n=4(r-1)+24[/tex]
where [tex]r[/tex] is the row number between 1 and 40.
(a) 24 + 28 + 32 + 36 + 40 + 44 + 48 + 52 + 56 + 60 + 64 + 68 + 72 + 76 + 80 + 84 + 88 + 92 + 96 + 100 + 104 + 108 + 112 + 116 + 120 + 124 + 128 + 132 + 136 + 140 + 144 + 148 + 152 + 156 + 160 + 164 + 168 + 172 + 176 + 180 = 4,080
(b) Using our formula above:
[tex]n=4(21-1)+24[/tex]
[tex]n=4(20)+24[/tex]
[tex]n=80+24[/tex]
[tex]n=104[/tex]
Make a table of values for the function Y=-4x
Answers
The table of values for the function y = -4x.
The table is attached below-
Hence, the values for the function is giiven below
To understand more about Simple equations refer -
https://brainly.com/question/25020119
#SPJ1
14 Betsy works as waitress. Today she worked an 8 hour shift, and was paid $ 92.00. Plot
a graph of the amount Betsy earns against the time she works for. Then find how much
Betsy is paid per hour. Write an equation using Y = MX + B Form.
Answers
Answer:
11.50 per hour
Step-by-step explanation:
Y = 92
8 = Mx
Y = mx
92 = m(8)
m = 11.50 per hour
simplify and solve the following linear equations.15 (Y - 4 - 2) Y - 9 + 5 (Y + 6)=0
Answers
Solution
We want to solve
[tex]\begin{gathered} 15(y-4)-2(y-9)+5(y+6)=0 \\ Exapnd\text{ the brackets } \\ 15y-60-2y+18+5y+30=0 \\ 15y-2y+5y-60+18+30=0 \\ 18y-12=0 \\ 18y=12 \\ \text{Divide both sides by 18} \\ \frac{18y}{18}=\frac{12}{18} \\ y=\frac{12}{18} \\ y=\frac{2}{3} \\ \\ \text{The answer is y = }\frac{2}{3} \end{gathered}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Absolute value can never be negative,
true or false?
Answers
Answer:
Yes, an absolute value can never be false. So, the answer is true.
I just need to know the answer for question 12
Answers
Given:
The given inequalities are:
[tex]3x+1>7\text{ and 4x}\leq24[/tex]Solving first inequality, we get:
[tex]\begin{gathered} 3x+1>7 \\ 3x>7-1 \\ 3x>6 \\ x>\frac{6}{3} \\ x>2 \end{gathered}[/tex]Solving the second inequality, we get:
[tex]\begin{gathered} 4x\leq24 \\ x\leq\frac{24}{4} \\ x\leq6 \end{gathered}[/tex]Merging the solutions of both inequalities, we get:
[tex]\begin{gathered} x>2\text{ and x}\leq6 \\ \Rightarrow x\epsilon\text{ (2,6\rbrack} \end{gathered}[/tex]So, the graph will be a number line with an open circle at 2 and a closed circle on 6 and shading in between.
Therefore,
Option A is correct.
w/2+3=5 help w/2 is a fraction Btw solve for w pleasee..!
Answers
Answer:
w = 4
Step-by-step explanation:
[tex]\frac{w}{2}[/tex] + 3 = 5 ( subtract 3 from both sides )
[tex]\frac{w}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )
w = 4
9- (4x + 4) = 3x - 10 + 8x
Answers
Answer: 1=x
Step-by-step explanation:
9-4x-4=3x-10+8x
9-4+10=3x+8x+4x
15=15x
1=x
Expand the brackets :
9 - 4x - 4 = 3x - 10 + 8x
-> 9 - 4x - 4 - (3x - 10 + 8x) = 0
-> 9 - 4x - 4 - 3x + 10 - 8x = 0
-> (9 - 4 + 10) - (4x + 3x + 8x) = 0
-> 15 - 15x = 0
15x = 15
x = 1
Might be confusing so just leave a comment if you don't understand (because I do the more detailed way really ;-;)
) In triangle XYZ, angle Y is right angle, and angle X and angle Y are complementary angles.If sin x =3/5 and cos x=4/5 then what is the value of sin y?
A) 3/5
B)4/5
C) 3/4
D)4/3
Answers
The value of sin Y is 4/5. The correct option is B) 4/5
Calculating the value of the sine of an angleFrom the question, we are to determine the value of sin Y.
From the given information, we have that
sin X = 3/5
and
cos X = 4/5
Also,
We have that angle X and angle Y are complementary angles.
That is,
X + Y = 90°
From the Trigonometric ratios of complementary angles, we have that
sin Y = cos (90° - Y)
From X + Y = 90°
X = 90° - Y
Therefore,
sin Y = cos X
From the given information,
cos X = 4/5
Hence, sin Y = 4/5
Learn more on Calculating the value of the sine of an angle here: https://brainly.com/question/16127404
#SPJ1
Question 12(Multiple Choice Worth 1 points)(07.04 LC)Factor completely 36x² - 49.(3x + 7)(12x-7)(3x-7)(12x+7)(6x-7)(6x-7)(6x + 7)(6x-7)
Answers
The factor the binomial
[tex]a^2-b^2[/tex]Find the square root of a and the square root of b, then put them as the product of the sum and difference of these square roots
[tex]\begin{gathered} \sqrt{a^2}=a \\ \sqrt{b^2}=b \\ a^2-b^2=(a+b)(a-b) \end{gathered}[/tex]We will use this rule to factor in the given expression
[tex]36x^2-49[/tex]Find the square root for each term
[tex]\begin{gathered} \sqrt{36x^2}=6x \\ \sqrt{49}=7 \end{gathered}[/tex]Write the two factors
[tex]36x^2-49=(6x+7)(6x-7)[/tex]The answer is the last choice (6x + 7)(6x - 7)
Given the point slope form of a line equation write in the slope form equation y+1=-3(x-2)
Answers
Given the line in point slope form:
y + 1 = 3(x - 2)
Let's rewrite the equation in slope intercept form.
Using the point slope form:
y - y1 = m(x - x1)
Thus, we have the following:
x1 = -2
y1 = 1
slope, m = 3
To write in slope intercept form, all you have to do is to isolate the y.
Thus,
y + 1 = 3(x - 2)
Expand the parenthesis:
y + 1 = 3x - 6
Subtract 1 from both sides:
y + 1 - 1 = 3x - 6 - 1
y = 3x - 6 - 1
y = 3x - 7
Therefore, the equation in slope intercept form is:
y = 3x - 7
ANSWER:
y = 3x - 7
Answer:
Step-by-step explanation:
1 Divide both sides by -3−3.
-\frac{y+1}{3}=x-2
−
3
y+1
=x−2
2 Add 22 to both sides.
-\frac{y+1}{3}+2=x
−
3
y+1
+2=x
3 Regroup terms.
2-\frac{y+1}{3}=x
2−
3
y+1
=x
4 Switch sides.
x=2-\frac{y+1}{3}
x=2−
3
y+1
pls helpp
I dont understand this
Answers
Answer:
third expression
Step-by-step explanation:
the surface area (SA) is the area of the 6 faces.
Note that opposite faces are congruent.
the surface area is the the area of each face multiplied by 2 , since they are congruent.
SA = 2(front area ) + 2(side area ) + 2(area of base)
= 2(5 × 7 ) + 2(4 × 7 ) + 2(4 × 5 ) ← third option
= 2(35) + 2(28) + 2(20)
= 70 + 56 + 40
= 166 cm²
HELP ME PWEASE (what is A^2 + B^2 =)
YOUR WELCOME FOR THE POINTS
Answers
Answer:
i think it is 61
correct me if im wrong
Answer:
a2 + b2 = (a + b)2 -2ab.
Step-by-step explanation:
Your Welcome:)
- 2ab