Answer:
y = - 3x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x - 3y = 3 ( subtract x from both sides )
- 3y = - x + 3 ( divide all terms by - 3 )
y = [tex]\frac{1}{3}[/tex] x - 1 ← in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, then
y = - 3x + c ← is the partial equation
To find c substitute (5, - 9) into the partial equation
- 9 = - 15 + c ⇒ c = - 9 + 15 = 6
y = - 3x + 6 ← equation of perpendicular line
On the average it takes the factory 4.2 hours to produce 6 truckloads of steel how many truckloads would the factory produce in 7 hours ?
WILL MARK BRAINLYIST
Answer:
what's the question
Step-by-step explanation:
lol but u could mark me brainlyist
Answer:
.....................................
Step-by-step explanation:
Nathan buys coffee and hot chocolate for his co-workers. Each cup of coffee costs $1.55 and each cup of hot chocolate costs $1.05. If he pays a total of $9.35 for 7 cups, how many of each does he buy?
Answer:
he buys 6.78
Step-by-step explanation:
Sam lives 8 miles from work and Mike lives 30 miles from work. How much farther is Mike’s trip to work than Sam’s?
CORRECT ANSWER AND I WILL THANK, GIVE 5 STARS, AND GIVE BRAINLIEST!!!!
System Of equations:
Solve by elimination:
7x + 2y = 13
x - 2y = 11
Group of answer choices
(3 . -4)
(3 , 4)
(4 , 3)
(-4 , -3)
[tex](7x + 2y) + (x - 2y) = 13 + 11 \\ 8x = 24 \\ x = \frac{24}{8} \\ x = 3[/tex]
Substitute x = 3 in any given equations.[tex]x - 2y = 11 \\ 3 - 2y = 11 \\ 3 - 11 = 2y \\ - 8 = 2y \\ \frac{ - 8}{2} = y \\ - 4 = y[/tex]
Answer Check
Substitute x = 3 and y = - 4 in both equations.[tex]7x + 2y = 13 \\ 7(3) + 2( - 4) = 13 \\ 21 - 8 = 13 \\ 13 = 13[/tex]
[tex]x - 2y = 11 \\ 3 - 2( - 4) = 11 \\ 3 + 8 = 11 \\ 11 = 11[/tex]
Both equations are true for x = 3 and y = 4.
Answer[tex] \large \boxed {(3, - 4)}[/tex]
Feel free to ask if you have any questions related to the answer or the explanation.
express the surface area A of a cube in terms of its volume V
The general manager, marketing director, and 3 other employees of Company A are hosting a visit by the vice president and 2 other employees of Company B. The eight people line up in a random order to take a photo. Every way of lining up the people is equally likely.
(a) What is the probability that the general manager is next to the vice president?
(b) What is the probability that the marketing director is in the leftmost position?
(c) Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.
Solution :
Let the three places be 1, 2, 3, 4, 5, 6, 7, 8
a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2
= 14
[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]
Therefore the required probability is
[tex]$=\frac{14}{8!}$[/tex]
= [tex]$\frac{14}{40320} = 0.000347$[/tex]
b). The probability that the marketing director to be placed in the leftmost position is
[tex]$=\frac{7!}{8!}$[/tex]
[tex]$=\frac{1}{8} = 0.125$[/tex]
c). The two events are not independent because
[tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]
[tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]
where A is the case a and B is the case b.
(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].
(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].
(c) So, the two events are dependent on each other.
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.
Total people in company A and company B is [tex]=8[/tex]
Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]
[tex]=40320[/tex]
(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]
Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].
by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]
[tex]=5040[/tex]
Again, combine the general manager and vice president in one line[tex]=2![/tex]
[tex]=2[/tex]
Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]
[tex]=\frac{10080}{40320}[/tex]
[tex]P(A)=\frac{1}{4}[/tex]
(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]
Now, fixing the position of marketing director in the leftmost.
arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]
Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]
[tex]=\frac{1}{8}[/tex]
[tex]P(B)=\frac{1}{8}[/tex]
(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.
Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.
So, the two events are dependent on each other.
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Rewrite as a simplified fraction. 0.51 = ?
Answer:
51/100
Step-by-step explanation:
Work out the surface area of this cylinder 8.2cm 17.5cm
Answer: 1324.12 sq. cm.
Step-by-step explanation:
A=2πrh+2πr2
A = 2π x 8.2 x 17.5 + 2π x 8.2^2
A = 2π x 143.50 + 2π x 67.24
A= 1324.12
4p + 3p = 49
solve for p
Answer:
4p + 3p = 49
p(4+3)=49
p=49/7
p=7
Step-by-step explanation:
..........
Graph the system of inequalities
Jessica locates her garden using a coordinate grid with yards as the units. The two points
(-5, -2) and (-8, -3) represents the two corners of the garden. Approximately how far
apart are the two corners?
Answer:
These two corners are [tex]\sqrt{13}[/tex] units apart.
Step-by-step explanation:
Distance between two points:
Suppose we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Approximately how far apart are the two corners?
We have to find the distance between the points (-5,-2) and (-8-3). So
[tex]D = \sqrt{(5-(-8))^2+(-2-(-3))^2} = \sqrt{13}[/tex]
These two corners are [tex]\sqrt{13}[/tex] units apart.
Help me with this thx <3
12) Two rectangles are similar. The length of small rectangle is 4 and the length of the big
rectangle is 12. If the perimeter of the smaller rectangle is 28, then what is the perimeter
of the larger rectangle
Answer:
84
Step-by-step explanation:
To get from 4 to 12, you multiply with 3.
Everything is 3 times as big in the larger rectangle.
This includes the perimeter.
Example:
small rect 4x10, perimeter 4+4+10+10 = 28
large rect 12x30, perimeter 12+12+30+30 = 84
but also 28x3 = 84
The perimeter of the larger rectangle is 84.
What is perimeter?Its the sum of length of the sides used to made the given figure.
We are given that length of small rectangle is 4 and the length of the big
rectangle is 12. If the perimeter of the smaller rectangle is 28,
The small rectangle
length = 4
perimeter = 28
The big rectangle
length = 12
perimeter = ?
The small rectangle perimeter = 2l + 2w
28 = 2 * 4 + 2 w
28 - 8 = 2w
20 / 2 = w
10 = w
The big rectangle perimeter;
4 w = 10 * 12
w = 120 / 4 = 30
Perimeter = 2*12 + 2*30
= 24 + 60 = 84
The perimeter of the big rectangle is 84.
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I need help plz I will mark brainliest
how do you create a graph for linear equation? I need to graph 3x=4
Answer:
Look at the graph below, hope this helped.
Step-by-step explanation:
Translate and solve: fifty times n is at most 500.
Answer:
n must be less than or equal to 10
Step-by-step explanation:
Order from least to greatest: 0.84, 0.084, 84, 8.4
Group of answer choices
Answer:
0.084 , 8.4, 0.84, 84 sorry if im wrong
Step-by-step explanation:
What is the measure of the missing leg of a right triangle if the hypotenuse measures 10 ft and the other leg measures 8 ft?
Answer:
2?
Step-by-step explanation:
−2y−8+4yminus, 2, y, minus, 8, plus, 4, y
Answer:
a number 12
Step-by-step explanation:
duh bro
How do I solve a hanger diagram?
Answer:
con un lapizStep-by-step explanation:
por que con un lapiz escribesA convex polygon has 6 sides what is the sum of its interior angles 1980°.
Step-by-step explanation:
Sum of interior angles in a polygon
= 180°(n - 2), where n is the number of sides.
Hence a convex polygon with 6 sides
=> 180°(6 - 2) = 720°.
What is the product of (2x – 3)(4x + 1)
Answer: 8x^2 - 10x - 3
Step-by-step explanation:
first, we multiply the parentheses.
2x x 4x + 2x - 3 x 4x - 3
then, we calculate all of that junk.
8x^2 + 2x - 12x - 3
finally, we collect the like terms.
8x^2 - 10x - 3
Answer:
8x^2-10x3
Step-by-step explanation:
8x^(add the 2 upbove the x)-10x-3
Where art thou smart people
Answer:
a smart person is not me clearly lol
Step-by-step explanation:
U-substitutions only work for specific kinds of expressions. Below, you are asked to choose a value of n for which u-substitutions will be a useful integration technique. Then, you are to compute the antiderivative with that specific n. (E.g., if n = 5 makes u-subs work, then solve the integral with a 5 in place of n).
(a) [ zºeke*+1 "'de
(b) /co cos(1/2) dr
(c) / r+n dr 22 + 8x - 4
Answer:
Step-by-step explanation:
(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]
Suppose [tex]5x^4 + 1 = f[/tex]
by differentiation;
[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]
Suppose n = 3
Then, the integral
[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]
[tex]= \int e^f \ \dfrac{df}{20}[/tex]
[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]
[tex]= \dfrac{1}{20} e^f + C[/tex]
recall that [tex]f = 5x^4 + 1[/tex]
Then;
[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]
(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]
suppose; [tex]\dfrac{1}{x^3} = f[/tex]
[tex]x^3 = f[/tex]
[tex]\implies -3x^{-4} \ dx = df[/tex]
[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]
If n = u, then the integration is:
[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]
[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]
Since; [tex]x^3 = f[/tex]
Then;
[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]
(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]
Suppose [tex]x^2 + 8x - 4 = f[/tex]
Then, by differentiation of both sides
[tex](2x + 8) \ dx = df[/tex]
[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]
Suppose n = 4 in integration, then:
[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]
By substitution;
[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]
[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]
[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]
The suitable substitutions of n are 3,4,4 respectively.
What is integration?The process of finding integrals is called integration.
a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
Suppose
[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]
So, we need n=3 for easy integration.
[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]
[tex]I=\frac{e^{t} }{20}[/tex]
[tex]I = e^{5x^{4}+1 }/20 +c[/tex]
b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]
n=4 is needed for easy integration.
I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]
c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]
n=4 is needed for easy integration.
[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]
Hence, the suitable substitutions of n are 3,4,4 respectively.
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Point D (-5, 3) and point E (6, -2) are located on a coordinate grid.
Which measurement is the best representation of the distance between point D and point E in units?
Answer:
Rounding to the nearest number, the answer would be 12 units
Step-by-step explanation:
I hope this helped! Please mark me as brainliest if you can!
Pls find this asap I am already late for this pls
Answer:
Step-by-step explanation:
I'm not sure about number 3, but I have the answer for number. The answer is 1:32.
3: 69
3/69
Then we reduce the fraction to the lowest term
3/69 = 1/32
1:32
Just divide 96/3 and you can see that one bus can hold 32 students
how might you ask for 1/10 of a liter of water
Answer:
weird questions but...
May I have 4 cups of water please?
Answer:
deciliter of water
Step-by-step explanation:
a unit of capacity equal to 1/10 of a liter.
175 plus what equals 405
Answer:
i hope this answers your question!
Step-by-step explanation:
175+x=405
Step 1: Simplify both sides of the equation.
x+175=405
Step 2: Subtract 175 from both sides.
x+175−175=405−175
x=230
The number that, when added to 175, equals 405 is 230.
To find the number that, when added to 175, equals 405, we can subtract 175 from 405. This will give us the missing number.
405 - 175 = 230
Therefore, 175 plus 230 equals 405.
To explain this process further, we can think of subtraction as the inverse operation of addition. By subtracting the known quantity (175) from the total (405), we are left with the missing quantity (230).
In other words, if we start with 175 and add 230 to it, we will end up with the desired sum of 405. This demonstrates the relationship between addition and subtraction and allows us to determine the missing number needed to reach the target sum.
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order 9%, 0.03, 0.7% and 0.004 from least
to greatest