The equation given has a slope of -3. See it? The equation we are looking for must have the same slope because the lines are parallel to each other. This means the lines never meet or touch on the xy-plane.
We use the point-slope formula to find the equation.
Here is the point-slope formula:
y - y_1 = m(x - x_1)
y - 4 = -3(x - (-3))
y - 4 = -3(x + 3)
y - 4 = -3x - 9
We now isolate y to find our equation.
y = -3x - 9 + 5
y = -3x - 4
Done.
Following are the calculation to the given line which is parallel:
Given:
[tex]\bold{ line: \ y=-3x+4}\\\\\bold{ point: (-3,4)}[/tex]
To find:
Calculating the equation=?
Solution:
General equation of a line: [tex]\bold{y = mx + c}[/tex]
Equation of a line: [tex]\bold{y-y_1=m(x-x_1)}[/tex]
By comparing the line equation with the general equation of a line:
[tex]\to \bold{m=-3}\\\\\to \bold{c=4}\\\\[/tex]
Using a line equation and put the point and slope value in it:
[tex]\bold{Point: (-3,4)}\\\\\bold{m=-3}[/tex]
[tex]\to \bold{y-4=-3(x-(-3))}\\\\\to \bold{y-4=-3(x+3)}\\\\\to \bold{y-4=-3x-9}\\\\\to \bold{y=-3x-9+4}\\\\\to \bold{y=-3x-5}\\\\[/tex]
Therefore, the final answer is "[tex]\bold{y=-3x-5}[/tex]"
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HELP PLEASE 20 POINTS
Adrian is a songwriter who collects royalties on his songs whenever they are played in a commercial or movie. Adrian will earn $40 every time one of his songs is played in a commercial and $130 every time one of his songs is played in a movie. Adrian earned a total of $1010 in royalties on 14 commercials commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Adrian's songs were played. Define the variables that you used to write the system.
Answer:
commercial = 9
movie = 5
Step-by-step explanation:
Step one:
let the number of commercials be x and movies be y
so
40x+130y=1010-------------1
since there are a total of 14 commercials and movies combined
x+y=14--------------2
Hence the systems of equation is
40x+130y=1010------1
x+y=14-------------------2
Step two:
from equation 2
x=14-y
substui]te the value of x in equation 1
40(14-y)+130y=1010
560-40y+130y=1010
collect like terms
130y-40y=1010-560
90y=450
divide both sides by 90
y=450/90
y=5
movies is 90
put y=5 in equation 2
x+5=14
x=14-5
x= 9
commercial is 9 in numbers
and movie is 5
Answer:
40c+130m=1010
c+m=14
Step-by-step explanation:
Let c=the number of commercials
Let m=the number of movies
system of equations:
40c+130m=1010
c+m=14
3) 7.NS.1.b *
The temperature on Sunday was 87°F. On Saturday the
temperature was 4°F higher. On Friday the temperature was 7°F
lower than on Saturday. What was the temperature on Friday?
Answer:
84°
Step-by-step explanation:
Answer:
84
Step-by-step explanation: It says 4 high which meanS added by four then it says 7 lower than it means subtract by it.
When Judy worked 4 hours and Ben worked 1 hour, their combined pay was $75. When Judy worked 2 hours and Ben worked 6 hours, their combined pay was $120. Find the hourly rate of pay for Ben and Judy.
Answer:
$15
Step-by-step explanation:
let the hourly rate of pay for Ben = B
let the hourly rate of pay for Judy = J
Judy worked 4 hours and Ben worked 1 hour, their combined pay was $75;
4J + B = 75 ----- i
Judy worked 2 hours and Ben worked 6 hours, their combined pay was $120
2J + 6B = 120 --- ii
Now, we should solve the expression;
Multiply equation ii by 2 and equation i by 1;
4J + B = 75 ----- i x 1 ; 4J + B = 75 -- iii
2J + 6B = 120 --- ii x 2 ; 4J + 12B = 240 ---iv
Now,
equation iv - iii;
11B = 165
B = $15
So, solving for J;
4J + B = 75
4J + 15 = 75
4J = 75 - 15 = 60
J = $15
Describe the set of all complex numbers that are at a distance of 2 units from the origin.
Answer:
The description of the set is [tex]A = \{s\in \mathbb{C}|\|s\| = 2\}[/tex].
Step-by-step explanation:
From Complex Analysis, we remember that complex numbers are numbers whose form is:
[tex]s = a+i\, b[/tex], [tex]a,b \in \mathbb{R}[/tex] (1)
Where [tex]i = \sqrt{-1}[/tex].
In addition, the distance from the origin is defined by the following Pythagorean identity:
[tex]\|s\| = \sqrt{a^{2}+b^{2}}[/tex] (2)
The following condition must be satisfied:
[tex]\|s\| = 2[/tex]
Then, the set of all complex numbers that are at a distance of 2 units from the origin is described below:
[tex]A = \{s\in \mathbb{C}|\|s\| = 2\}[/tex] (3)
The set of all complex numbers that are at a distance of 2 units from the origin is [tex]\{z\in \mathbb{C} :\text{ }|z|=2\}[/tex]
A complex number, written in rectangular form is
[tex]z=a+ib\\a,b\in \mathbb{R}[/tex]
The distance of a complex number from the origin (the modulus of the complex number, denoted by [tex]|z|[/tex]) is given by the formula
[tex]|z|=\sqrt{a^2+b^2}[/tex]
Since we want all the complex numbers to be at the distance of 2 units from the origin, they must satisfy
[tex]|z|=2[/tex]
thus, the set we are looking for is
[tex]D=\{z\in \mathbb{C} :\text{ }|z|=2\}[/tex]
where [tex]\mathbb{C}[/tex] is the set of all complex numbers
Learn more about complex numbers here: https://brainly.com/question/12274048
what’s the slope of (1,7) and (6,10)
Sort each equation according to whether it has one solution, infinitely many solutions, or no solution.
5(x - 2) = 5x - 7
One Solution
Infinitely Many Solutions
No Solution
-30% - 4) =-3x + 12
4(x + 1) = 34+4
-2x - 3) = 2X-6
6(x + 5) = 6x + 11
5) Intro
Answer:
Equations with one solution: [tex]-2(x-3) = 2x-6[/tex]
Equations with no solution:
[tex]6(x+5) = 6x+11\\5(x-2) = 5x-7[/tex]
Equations with infinite many solutions: [tex]-3(x-4) = -3x+12[/tex]
Step-by-step explanation:
We will solve each equation to see if it has one solution, no solution or infinite many solutions.
An equation where the value of variable can be found has one solution.
An equation with no solution has both sides different.
An equation with infinite solution will have both sides equal after solution(number)
So,
Equation 1:
5(x-2) = 5x-7
[tex]5(x-2) = 5x-7\\5x-10 = 5x-7\\5x-5x = -7+10\\0 = 3[/tex]
As both sides are not equal, equation has no solution.
Equation 2:
[tex]-3(x-4) = -3x+12\\-3x+12 = -3x+12\\-3x+3x = -12+12\\0=0\\[/tex]
As both sides are equal the equation has infinite many solutions.
Equation 3:
[tex]-2(x-3) = 2x-6\\-2x+6 = 2x-6\\-2x-2x = -6-6\\-4x = -12\\\frac{-4x}{-4} = \frac{-12}{-4}\\x = 3[/tex]
As x=3, the equation has only one solution.
Equation 4:
[tex]6(x+5) = 6x+11\\6x+30 = 6x+11\\6x-6x+30 = 11\\30 =11[/tex]
The equation has no solution.
Hence,
Equations with one solution: [tex]-2(x-3) = 2x-6[/tex]
Equations with no solution:
[tex]6(x+5) = 6x+11\\5(x-2) = 5x-7[/tex]
Equations with infinite many solutions: [tex]-3(x-4) = -3x+12[/tex]
what is the answer to this question. PLEASE HELP
Answer:
Im going to guess a i have no idea tho
Step-by-step explanation:
What is 5 Left-bracket cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) right-bracket raised to the 3rd power?
Answer:
C
Step-by-step explanation:
I took it on edg 2020
The Complex Alternative form to the expression (5[cos(π/4) + i sin(π/4)])^3 is given as: (Option C).
What is a complex Alternate form?A complex number of equations will take the form x + yi, where x and y are real numbers and i is an indeterminate that satisfies the rule i² = -1.
Hence, the solution to the above is given as follows:
Step 1 - Ludooph's number pi is given as:
π ≈ 3.14159265
Step 2 - Divide 3.14159265/4
= 0.78539816
Step 3
Cos (0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 4
Divide: 3.14159265 / 4
= 0.78539816
Step 5 - find the Sin of the result of step 4
sin(0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 6
Multiply i by the result of Step No 5
= i * 0.70710678
= 0.7071068i
Step 7 - Add the result of step no. 3 and the result of step number 6
= 0.70710678 + 0.7071068i
= 0.7071068+0.7071068i
Step 8 Multiply 5 by the result of step 7
= 5 * (0.7071068+0.7071068i)
= 5 * 0.70710678118655 + 5 * 0.70710678118655i
= 3.53553391+3.53553391i
= 3.53553391 +i(3.53553391)
= 3.5355339+3.5355339i
Step 9 - Exponentiate the results of Step 8 to the third power:
= (3.5355339+3.5355339i) ^ 3
= (5 × ei π/4)3 = 53 × ei 3 × π/4
= 125 × ei 3π/4
= -88.3883476+88.3883476i
If left in the Alternate Complex form, we have:
125[cos(3π/4) + i sin(3π/4)]
Learn more about Complex Forms at:
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0.6(x + 2) = 0.55(2x + 3)
Answer:
-0.9
Step-by-step explanation:
0.6(x+2)=0.55(2x+3)
Use the distributive property to multiply 0.6 by x+2.
0.6x+1.2=0.55(2x+3)
Use the distributive property to multiply 0.55 by 2x+3.
0.6x+1.2=1.1x+1.65
Subtract 1.1x from both sides.
0.6x+1.2−1.1x=1.65
Combine 0.6x and −1.1x to get −0.5x.
−0.5x+1.2=1.65
Subtract 1.2 from both sides.
−0.5x=1.65−1.2
Subtract 1.2 from 1.65 to get 0.45.
−0.5x=0.45
Divide both sides by −0.5.
x= 0.45/−0.5
x= -0.9
xoxo,your highness...Please help ASAP I will give brainliest
Answer:
the answer is -3
have a nice day
Please answer as soon as possible!
Answer:
lol is this a test? are u cheating!!!!???
Step-by-step explanation:
Given g(x) = -4x-2, find g(-2)
Answer:
g(-2) = 6
General Formula and Concepts:
Pre-Algebra
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
g(x) = -4x - 2
g(-2) is x = -2
Step 2: Evaluate
Substitute: g(-2) = -4(-2) - 2Multiply: g(-2) = 8 - 2Subtract: g(-2) = 6What is the area of a circle with a diameter of 200cm? Use 3.14 for pie.
Answer:
A≈31415.93cm²
Step-by-step explanation:
PLEASE HELP, DUE SOON!!
Answer:
x= 34 y= 99 z= 41
Step-by-step explanation: A.
Answer:
D
Step-by-step explanation:
First I solved for the triangle on the right by adding 58 and 81 then subtracting by 180 and I got 41 degrees for the missing angle. Now for the left triangle you subtract 47 from 180 and you get 133. Answer choice D is the only answer choice that has x and y equal to 133 this is why answer choice D is the correct solution.
If you liked my answer then please mark it as the brainliest it would be much appreciated. Thanks!
Brainliest for whoever gets it right!
Of the 34 cars in a parking lot, 12 are blue, 8 are red, 4 are white, and 10 are silver. In simplest form, what are the odds in favor that the next car that leaves the lot will be red or white?
A. ) 6:11
B. ) 6:17
C. ) 17:6
D. ) 11:6
Answer:
B (6:17)
Step-by-step explanation:
The values of red and white are 8 and 4, so you add them. The ratio should then be 12:34 because 34 is the total of all values. When simplified, 12:34=6:17
Answer:
im thinking c add them all together and you get that 17:6 if u kow how to add :^
Step-by-step explanation:
write a linear equation given the two points 3,4 and 0,5
Answer:
where is the graph
Step-by-step explanation:
did your teacher put in a graph
Tara owns a pizza shop. She sells pizzas for $6.00 plus a $10 delivery fee.If you are having a party and you have $58 how many pizzas can you buy?
Answer:
You can buy 8 pizzas
Step-by-step explanation:
$58 - $10 = $48
$48/$6 = 8
A box has 5 marbles numbered from 1 to 5. Determine the following theoretical probabilities of the totals of two marbles ( a marble is taken from the box, the number noted, put back in the box, and then a second marble taken from the box and the number noted)
a) P(a total of 4)
b) P(a total of 5)
c) P(an odd total)
Answer:
4
Step-by-step explanation:
How many solutions does the linear equation have?
x + 3 + 2x = 4 + 3x - 1.
1. infinite
2. none
3. one
Answer:
infinite solutions
Step-by-step explanation:
Given
x + 3 + 2x = 4 + 3x - 1 ( simplify both sides )
3x + 3 = 3x + 3
Since the equation is the same on both sides.
This indications the equation has an infinite number of solutions
Which angle is supplementary to the
Please helppp
Answer:
[tex]\angle FCB[/tex]
Step-by-step explanation:
Supplementary angles are angles that sum to [tex]180^{\circ}[/tex]. In this case, [tex]\angle FCB[/tex] is supplementary to [tex]\angle DCF[/tex] since they add up to the angle of a straight line which is [tex]180^{\circ}[/tex].
Hope this helps :)
I needddd helppppp pleaseee
Answer:
w = 59°
Step-by-step explanation:
sides AC and BC are congruent thus Δ ABC is isosceles, then the 2 base angles are congruent, that is
∠ A = ∠ B , so
w = [tex]\frac{180-62}{2}[/tex] = [tex]\frac{118}{2}[/tex] = 59°
what is it called when a sea bird lands on a channel maker
Answer:
This question is actually a riddle. The answer to this riddle is, "Buoy meets gull."
Step-by-step explanation:
Answer:
ligand-gated channel.
Step-by-step explanation:
If the angle opposite of the height of a right angle triangle is 15 degrees and the base is 215 cm how much is the height of the triangle.
Answer:
86.1
Step-by-step explanation:
because if it it trigonometry u do the inverse operation of tan
so its tan-1 (215/15)
=86.0090869
if u want to round to 3sf its 86.1
hope it helped
Need help on my math only have today till I turn int tomorrow
Hope this helps explain what was needed to be solved! :)
HLEP PLEASE ANSWER IM SERIOUS NO JOKE STOP THE TROLLING I NEED HLEP
you got find out if the 800 is in ml or a diffent one
The ticket sales for a concert started at 4:00 P.M. The table shows the linear relationship
between the number of tickets remaining and the number of hours since 4:00 P.M.
Ticket Sales
Answer: I just took the test so the answer would be y=3,000x+12,000
Step-by-step explanation: hope this help thx for the points :D
⦁ A local pizzeria sold 75 pizzas yesterday.
⦁ The owner offers the employees a bonus if the number of pizzas sold increases by 20% today.
⦁ How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning. Show your work!
⦁ Suppose the actual number of pizzas sold today was 66. Describe the number of pizzas sold as a percent increase or decrease.
Answer:
a. 90 pizzas
b. 12% decrease
Step-by-step explanation:
To receive a bonus, there must be 20% increase in the number of pizzas
Thus;
20% of 75 = 20/100 * 75 = 1500/100 = 15
So the number of pizza to be sold to receive the bonus will be 15 + 75 = 90
So now, we have 66 pizza sold today;
We can see that there was a decrease from 75
Percentage decrease will be;
(new value - old value)old value * 100%
= (66-75)/75 * 100%
= -9/75 * 100%
= -0.12 * 100% = -12%
This shows a 12% decrease
Rachel earned $54.79 last week. Morgan earned $50.23. About how much more did Rachel earn
Answer:
105.2
Step-by-step explanation:
54+50=104
.79+.23=1.02
104+1.02=105.2
Hope this helps.
Answer:$4.56
Step-by-step explanation:Take $54.79 and subtract it by $50.23, to see the difference in how much more money Rachel earned.
please answer for me appreciate it