Answer:
Point D: [tex](0,-4, 1 )[/tex]
d = √41
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightPre-Calculus
Midpoint Formula [3D]: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} )[/tex]Distance Formula [3D]: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point A(1, 2, -1)
Point B(-3, -6, 2)
Point C(3, -2, 0)
Step 2: Find Point D
Simply plug in your coordinates B and C into the midpoint formula to find midpoint
Substitute [MF]: [tex](\frac{-3+3}{2},\frac{-6-2}{2}, \frac{2+0}{2} )[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-8}{2}, \frac{2}{2} )[/tex]Divide: [tex](0,-4, 1 )[/tex]Step 3: Find distance d
Simply plug in the 2 coordinates A and D into the distance formula to find distance d
Substitute [DF]: [tex]d = \sqrt{(0-1)^2+(-4-2)^2+(1+1)^2}[/tex]Subtract/Add: [tex]d = \sqrt{(-1)^2+(-6)^2+(2)^2}[/tex]Exponents: [tex]d = \sqrt{1+36+4}[/tex]Add: [tex]d = \sqrt{41}[/tex]Patterns and functions
A pair of equations is shown below:
y=7x- 8
y= 5x-2
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)
Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points
Answer:
x=3, y=13. (3, 13).
Step-by-step explanation:
7x-8=5x-2
7x-5x-8=-2
2x-8=-2
2x=-2+8
2x=6
x=6/2=3
y=5(3)-2=15-2=13
Answer:
given y=7x-8 i
y=5x-2 ii
Step-by-step explanation:
equating equation i and ii which is i=ii
7x-8=5x-2
7x-5x= -2+8
2x=6
x=6÷2
x=3
now
putting the value of xbin equation i
y=7x-8
y=7×3-8
y=21-8
y=13
hence the value of x and y is 3 and 13 respectively
Please help with these 3
Answer:
3) 146 degrees
4) 471 degrees
5) x = 100 and 3x = 300
Step-by-step explanation:
all three are polygons whose sum of all interior angles can be found by using the formula (n - 2)*180 where 'n' refers to the number of sides
In #3 and 5 there are 5 sides, so (5 - 2)*180 = 3(180) giving a total of 540 degrees. Add all known angles and deduct from 540.
#4 has 7 sides, so (7 - 2)*180 = 1260 degrees. Add all known angles and deduct sum from 1260.
#5 Add all integers plus 'x' + '2x' to get 240 + 3x = 540
Which expression uses the associative property to make it easier to evaluate 6(3/2x1/5) ?
A: 6(2/3x1/5
B: 6(1/5x3/2)
C: (3/2x1/5)6
D: (6x3/2)1/5
a train is running at a speed of hundred kilometre per hour how much distance will it run in 12 minutes
Step-by-step explanation:
In an hour, there are 60 minutes.
100km * (12/60) = 20km.
Hence the train runs 20km in 12 minutes.
Samantha invested $660 into an account that pays 3.5% interest compounded annually . Samantha did not make any additional deposits or withdrawals .
What is the total amount of interest paid by this investment at the end of five years?
A- $115.50
B-$783.87
C-$123.87
$2,755.50
The amount of money after five years will be $783.87. Then the correct option is B.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
Samantha put $660 into a record that pays 3.5% interest accumulated every year. Samantha put aside no extra installments or withdrawals. And for yearly, the value of n will be one. Then the equation is given as,
[tex]\rm A = 660\times (1 + 0.035)^t[/tex]
The total amount of interest paid by this investment at the end of five years will be given as,
A = 660 x (1.035)⁵
A = $660 x 1.1876
A = $783.87
The amount of money after five years will be $783.87. Then the correct option is B.
More about the compound interest link is given below.
https://brainly.com/question/25857212
#SPJ2
Choose all the equations that are true if x=9
Answer:
A, C, E
Step-by-step explanation:
I don't really know how to explain it but you can kinda substitute 9 for the variable to confirm if you want.
Jack use 25% of the memory card on his digital camera while taking pictures at a family reunions if jack took 96 pictures at a family reunions how many pictures can the memory card hold
PLEASE HELP I NEED THIS ANSWERED
An integer from 300 through 780, inclusive is to be chosen at random, find the probability that the number is chosen will have 1 as at least one digit.
Answer:
93/481Step-by-step explanation:
Total number of integers from 300 through 780, inclusive:
780 - 299 = 481Number of integers with at least one of digit 1:
Hundreds - 0,Tens - 5*10 = 50 (31th, 41th, 51th, 61th, 71th)Units - 4*9 + 7 = 43 (300 till 699 and 700 till 780)So in total 50 + 43 = 93The probability is:
P = favorable outcomes/total outcomes = 93/481Hi! please help me the blue line is what I have to find.
Answer:
Pretie sure answer is 0
Step-by-step explanation:
first you take the 1 and subtract it from -3
which is -2 then add the other 2 to the -2 which is 0
then you devide 5 with 5 and 5 with zero which leaves you with zero and 0=x
John has 16 boxes of apples. Each box holds 14 apples. If 8 of the boxes are full, and 8 of the boxes are half full, how many apples does John have?
A. 44
B. 112
C. 224
D. 168
Answer:112
Step-by-step explanation:multiply and divide for your answer
A conical water tank with vertex down has a radius of 10 feet at the top and is 24 feet high. If water flows out of the tank at a rate of 20 ft3/min, how fast is the depth of the water DECREASING when the water is 6 feet deep?
Answer:
Depth of water is increasing at 0.143 ft/min.
Step-by-step explanation:
Nate biked 56 miles in 4hours. what was Nates average speed for 1 hour?
Find the area of this figure 115 ft 2 125 ft 2 60 ft 2 100 ft 2
Answer:
125
Step-by-step explanation:
divide the Figure into 3 parts
1 st = 5 X 10 =50
2nd = 5×10 =50
3rd = 5×5 = 25
total = 50+50 + 25 = 125
You are stuck at the Vince Lombardi rest stop on the New Jersey Turnpike with a dead battery. To get on the road again, you need to find someone with jumper cables that connect the batteries of two cars together so you can start your car again. Suppose that 16% of drivers in New Jersey carry jumper cables in their trunk. You begin to ask random people getting out of their cars if they have jumper cables. Use Scenario 6-17. On average, how many people do you expect you will have to ask before you find someone with jumper cables
Answer:
The expected number of people you will have to ask before you find someone with jumper cables is 6.25.
Step-by-step explanation:
The geometric distribution is the distribution of the number of X Bernoulli trials required for one success. If the one success requires k independent trials, each with the probability of success as p, then the probability that the kth trial is the one success is:[tex]p_{X}(k)=(1-p)^{k-1}p;\ k={1, 2, 3...}[/tex]
The geometric distribution is the distribution of the number of Y = X – 1 failures required before the first success. If the first success requires k failures, each trial with the probability of success as p, then the probability that the 1st success occurs after k failures is:[tex]p_{X}(k)=(1-p)^{k}p;\ k={0, 1, 2, 3...}[/tex]
In this case the first scenario follows.
X = number of people you will have to ask before you find someone with jumper cables.
p = 0.16
Compute the expected number of people you will have to ask before you find someone with jumper cables as follows:
[tex]E(X)=\frac{1}{p}\\\\=\frac{1}{0.16}\\\\=6.25[/tex]
Thus, the expected number of people you will have to ask before you find someone with jumper cables is 6.25.
y is inversely proportional to the cube of x if y = 7 when x=4 what is y when x is 5
Answer:
8.75
Step-by-step explanation:
7/4 = 1.75 and ?/5 (5x1.75) = 8.75
What is the area of this
Consider the function represented by the equation x – y = 3. What is the equation written in function notation, with x as the independent variable? f(x) = y + 3 f(x) = –y – 3 f(x) = –x + 3 f(x) = x – 3 ANSWER WITHIN 1O MINUTES AND WILL GIVE BRAINLIEST
Answer:
d
Step-by-step explanation:
Answer:
the answer is D i think.
Bro help please I don’t know that answer I’ll give brainiest
Answer:
the awnser is 8 as is it it the awnser
Step-by-step explanation:
It's C.
8x8 = 64,
64/8 = 8
im so confused how to get the answer.
Answer:
A
Step-by-step explanation:
9 items at $50 each would be 9 × $50 = $450, which is more money than he has.
it takes shonda 2/5 of an hour to dry one load of laundry in her dryer. How many hours will it take her to dry 5 loads of laundry?
2 hours Step-by-step explanation:
Answer: 2 hours.
Step-by-step explanation:
2/5 hour = one load of laundry
2/5 x 5 = 10/5 = 2 hours.
It will take Shonda 2 hours to dry 5 loads of laundry.
Hope this helps!
If f(x) = x/2 - 3 and g(x) = 4x ^ 2 + x - 4 , find (f + g)(x)
Why might a person donate money to an organization focused on curing a deadly disease?
O To be part of a solution
O To be tax free this year
To satisfy receive discounts at a store
To satisfy a requirement
Jamal ran a distance of 360 feet. Lonnie ran a distance of 30 yards. What is the ratio of the distance Jamal ran to the distance Lonnie ran?
The ratio of the distance Jamal ran to the distance Lonnie ran is 4:1.
Note that 1 yard = 3 feet
Since Jamal ran a distance of 360 feet, this will be converted to yard and this will be: = 360/3 = 120 yards
Lonnie ran a distance of 30 yards.
Then the ratio of the distance that Jamal ran to the distance Lonnie ran all be: = 120/30 = 4/1 = 4:1
The ratio of the distance is 4:1
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https://brainly.com/question/21806098
What is the angle measure of angle ABC?
Answer:
92°
Step-by-step explanation:
First, find the value of x.
3x + 23 = 4x (corresponding angles are congruent)
Subtract 3x from each side
23 = 4x - 3x
23 = x
x = 23
Angle ABC = 4x
Plug in the value of x
Angle ABC = 4(23)
Angle ABC = 92°
IT WUU Tate for school on a
Given that 35.5% of them were men, 40% of them were women and the rest were
OXFORD
particular day, find the number of students who were punctual for school.
1800 people attended the National Day dinner in a certain constituency.
children, find the number of children who attended the dinner.
Answer:
Number of students = 441 Students
Step-by-step explanation:
Given:
Percent of women = 40%
Percent of women = 35.5%
Total number of people = 1,800
Find:
Number of students
Computation:
Percent of student = 100% - 35.5% - 40%
Percent of student = 24.5%
Number of students = 1,800 x Percent of student
Number of students = 1,800 x 24.5%
Number of students = 441 Students
42.1 in expanded form
Answer:
40+2+0.1
Step-by-step explanation:
5/6 divided 2/3 pls help
Answer:
exact form: -5/4
Decimal Form: -1.25
Step-by-step explanation:
Please help me thank you I appreciate it
Answer:
68°
Step-by-step explanation:
PRQ = SRQ gives:
3x-8 = 2x+6
x = 6+8 = 14
So PRQ = SRQ = 34
and
PRS = PRQ+SRQ = 68
A 1000-liter tank initially contains a mixture of 450 liters of cola and 50 liters of cherry syrup. Cola is added at the rate of 8 liters per minute, and cherry syrup is added at the rate of 2 liters per minute. At the same time, a well mixed solution of cherry cola is withdrawn at the rate of 5 liters per minute. Let S(t) be the amount (measured in liters) of cherry syrup in the tank at time t, where t is measured in minutes.(a) Formulate an initial-value problem for the the amount of cherry syrup in the tank overtime.(b) Solve the initial-value problem using an integrating factor.(c) What percentage of the mixture is cherry syrup when the tank is full?
Answer:
A) dS/dt = 2 - S/(100 + t) ; S(0) = 50
B) S(t) = (100 + t) - 5000/(100 + t)
C) 35%
Step-by-step explanation:
A) Let;
t = time in minutes
S = amount of syrup
dS/dt = rate at which syrup is flowing through tank
We are told that initially, the tank contains a mixture of 450 liters of cola and 50 liters of cherry syrup.
Thus,
At t = 0
Amount of cola = 450 litres
Amount of syrup = 50 litres
Total mixture = 450 + 50 = 500 litres
We are told that a well mixed solution of cherry cola is withdrawn at the rate of 5 liters per minute.
Thus, amount of liquid in the tank at a time "t" is; 500 + 5t
We are told that cherry syrup is added at the rate of 2 liters per minute.
Thus, rate at which syrup is flowing through tank is given as;
dS/dt = 2 - 5[S/(500 + 5t)]
Factorizing out, we have;
dS/dt = 2 - 5[S/5(100 + t)]
5 will cancel out to give;
dS/dt = 2 - S/(100 + t)
Since we have 50 liters of cherry syrup initially, the initial value problem is;
dS/dt = 2 - S/(100 + t) ; S(0) = 50
B) We have our initial value problem as;
dS/dt = 2 - S/(100 + t)
Rearranging, we have;
dS/dt + S/(100 + t) = 2
Multiplying through by 100 + t gives;
(dS/dt)•(100 + t) + S = 2(100 + t)
Integrating each term with respect to t gives;
(100 + t)S = (100 + t)² + c
Divide both sides by (100 + t) to get;
S = (100 + t) + c/(100 + t)
At t = 0;
S(0) = (100 + 0) + c/(100 + 0)
S(0) = 100 + c/100
Recall earlier in our initial value problem where we stated that S(0) = 50.
Thus;
100 + c/100 = 50
Subtract 100 from both sides to givw;
c/100 = 50 - 100
c/100 = -50
c = -50 × 100
c = -5000
Thus;
S(t) = (100 + t) - 5000/(100 + t)
C) The capacity of the tank is given as 1000 liters.
Earlier, we saw that amount of liquid in the tank at a time "t" is; 500 + 5t
Thus;
500 + 5t = 1000
5t = 1000 - 500
5t = 500
t = 500/5
t = 100 minutes
We want to find What percentage of the mixture is cherry syrup when the tank is full.
Thus we will plug in t = 100 minutes into S(t) = (100 + t) - 5000/(100 + t)
Thus;
S(100) = (100 + 100) - 5000/(100 + 100)
S(100) = 200 - 25
S(100) = 175 litres
We saw earlier that total mixture initially was 500 litres.
Thus, percentage of the mixture that is cherry syrup when the tank is full is;
175/500 × 100% = 35%