Let P be the point (1,1,-2). Suppose that the point P0(2, -5, 2) is 1/5 of the way from P to Q. Find the point Q.
Answers
Q = 4P0 -4P +P0
Q = 5P0 -4P
Q = 5(2, -5, 2) -4(1, 1, -2)
Q = (6, -29, 18)
Related Questions
If guy walks from his house to school which is 5/10 away and back, how far does he walk?
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jen collects toy sports cars. she has 1568 orange cars and 448 blue cars. she wants to line up the cars in groups so that each group has the same number of cars and contains only orange cars or only blue cars. What is the largest number of cars that she can have in a group?
Answers
Answer:
224 cars.
Step-by-step explanation:
We have been given that Jen has 1568 orange cars and 448 blue cars. she wants to line up the cars in groups so that each group has the same number of cars and contains only orange cars or only blue cars.
To solve our given problem, we will find greatest common factor of 1568 and 448.
Prime factorization of 1568: [tex]2\times 2 \times 2\times2\times2\times7\times7[/tex]
Prime factorization of 448: [tex]2\times 2 \times 2\times2\times2\times2\times7[/tex]
We can see that 448 and 1568 is [tex]2\times 2 \times 2\times2\times2\times7=224[/tex]
Therefore, each group will have 224 cars.
A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting coats $22 per square foot. (1 yd=3 ft)
Answers
A = bh
A = 15(12)
A = 180
The area of the bedroom is 180 square feet. The cost of carpeting the entire bedroom will be the amount of square feet of the bedroom (its area) times the cost per square foot of carpet. Multiply the area by the cost per square foot.
180 × 22 = 3960
It will cost $3,960 to carpet the bedroom.
A high fountain of water is in the center of a circular pool of water. you walk the circumference of the pool and measure it to be 190 meters. you then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. it is 55°. how high is the fountain?
Answers
2 * pi * R = 190
From here, we clear the radio:
R = (190) / (2 * pi)
R = 30.23943919 m
Then, you can see the problem as a rectangle triangle, where the height of the source will be given by the following trigonometric relationship:
tan (55) = H / R
From here, we clear the height H:
H = R * tan (55)
H = (30.23943919) * tan (55)
H = 43,1863948 m
Amswer:
the fountain is 43.19 m high
The height of the fountain is 43.20m
Data;
circumference = 190mangle = 55 degrees.Circumference of a CircleThe circumference of a circle is given as
[tex]c = 2\pi r[/tex]
Let's calculate the radius of the circle
[tex]c=2\pi r\\r=c/2\pi \\r=190/(2*3.14)\\r=30.25m[/tex]
Assuming the radius of the pool makes a right angle triangle with the top of the fountain;
[tex]tan\theta=\frac{opposite}{adjacent}\\tan55=\frac{x}{30.25}\\ x= 30.25tan55\\x=43.20m[/tex]
From the calculations above, the height of the fountain is 43.20m
Learn more on right-angle triangles here;
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explain how you would take a survey to find your classmates favorite shirt color
Answers
Older Orchards need more hives per acre Caleb has decided to place 6 hives for every 2 acres on an older peach orchard Zeke one of Caleb workers delivery 10 hives to a 30 acre peach orchard did Zeke follow Calebs decision.how does the table prove your answer.
Don't do a table
Answers
If there are 30 acres, this means he would 15 groups of 6 hives (90 hives). He only brought 10.
Please see picture for work.
Solve this equation: 3x-1/5-2/9x=124/5
Step 1: Simplify by combining like terms. Which terms can be combined?
A) 3x and -1/5
B) -1/5 and -2/9x
C) 3x and -2/9x
Answers
Answer:
The correct option is C.
Step-by-step explanation:
The given equation is
[tex]3x-\frac{1}{5}-\frac{2}{9}x=\frac{124}{5}[/tex]
If two terms have the same variables having same powers, then they are known as like terms.
In the given equation [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] are like terms.
So, when we simplify the given equation by combining like terms. we need to combined [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] .
Therefore the correct option is C.
The solution to the equation is approximately x = 45.48.
To solve the equation 3x - 1/5 - 2/9x = 124/5, to combine like terms. Like terms are terms that have the same variable and exponent.
The terms in the equation are:
3x (coefficient is 3, and the variable is x)
-1/5 (coefficient is -1/5)
-2/9x (coefficient is -2/9, and the variable is x)
Now, let's identify the like terms that combined:
C) 3x and -2/9x
The terms 3x and -2/9x both have the variable x, so they are like terms and can be combined.
Step 1: Combine the like terms:
3x - 2/9x = (3 - 2/9)x = (27/9 - 2/9)x = (25/9)x
Now, after combining the like terms, the equation becomes:
(25/9)x - 1/5 = 124/5
Step 2: Isolate x on one side of the equation. To do this, we can first get rid of the fraction by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 45 (LCM of 9 and 5):
45 × [(25/9)x - 1/5] = 45 × (124/5)
This simplifies to:
25x - 9 = 1128
Step 3: Now, isolate x by moving the constant term (-9) to the other side of the equation:
25x = 1128 + 9
25x = 1137
Step 4: Finally, divide by 25 to solve for x:
x = 1137 / 25
x ≈ 45.48
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Average speed of Car 1 = 55 mph.
Average speed of Car 2 = 70 mph.
Time elapsed between start of Car 1 and start of Car 2 = 4 minutes.
How long before Car 2 overtakes Car 1? __hour(s).
Answers
Answer: 11/45 hour (≈15 min.)
Let p: x = 4 Let q: y = −2 Which represents "If x = 4, then y = −2”? p ∨ q p ∧ q p → q p ↔ q
Answers
Have a brainy day!
Answer:
C. p → q
Step-by-step explanation:
We are given that,
'p' is represented by 'x = 4' and 'q' is represented by 'y = -2'.
That is, we have,
p: x = 4
q: y = -2
The given statement is, 'If x = 4, then y = -2'.
This means that whenever x = 4, then y = -2.
That is, 'x = 4 implies y = -2'.
Thus, it will be represented by p → q.
One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function?
Answers
Answer:
Solutions are[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]
Step-by-step explanation:
The given expression is
[tex]f(x)=x^{3}-9x^{2} +26x-24[/tex]
First, we need the divisors of the independent term, which is 24.
24 divisors: 1, 2, 3, 4, 6, 8, 12, 24.
Now, we replace each divisor in the function, and those which gives zero as result, those are gonna be the roots of the equation.
For [tex]x=1[/tex]
[tex]f(1)=(1)^{3}-9(1)^{2} +26(1)-24=1-9+26-24=-6[/tex]
This means [tex]x=1[/tex] is not a solution.
For [tex]x=2[/tex]
[tex]f(2)=(2)^{3}-9(2)^{2} +26(2)-24=8-36+52-24=0[/tex]
So, [tex]x=2[/tex] is the first solution.
For [tex]x=3[/tex]
[tex]f(3)=(3)^{3}-9(3)^{2} +26(3)-24=27-81+78-24=0[/tex]
It's solution.
For [tex]x=4[/tex]
[tex]f(4)=(4)^{3}-9(4)^{2} +26(4)-24=64-144+104-24=0[/tex]
Therefore, all roots are
[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]
what is 87/96 feet in inches
Answers
A wall map has a scale of 128 miles = 6 inches. The distance between Springfield and Lakeview is 2 feet on the map. What is the actual distance between Springfield and Lakeview? Question 4 options: 42.7 miles 1.13 miles 512 miles 384 miles
Answers
2 feet = 24 inches
128 miles/6 inches is the scale.
I would create an equivalent ratio using this scale and the 24 inches.
128 miles/6 inches=x miles/24 inches
To go from 6 inches to 24 inches, you will need 4 groups of 6 inches.
You would also need 4 groups of 128 miles.
4 x 128 = 512 miles
The distance between these 2 towns is 512 miles.
Mariah collects 3 spiders each spider has eight legs.Brian gives her 1more spider. how many legs do Mariah's spiders have altogether?
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what function is vertically stretched by a factor of 3 and translated 4 units right from the parent function
A. log_(5) (3x+4)
B. 3log_(5) (x-4)
C. 3(5^x+4)
D. 5^3x-4
Answers
Final answer:
The correct function is B, 3log_5(x-4), which represents a logarithmic function that is vertically stretched by a factor of 3 and translated 4 units to the right.
Explanation:
The student is asking about transformations of a parent function, specifically a vertical stretch and a horizontal translation. When a function is vertically stretched by a factor of 3, this involves multiplying the function by 3. A translation of 4 units to the right would mean adjusting the input variable x by subtracting 4. Considering the options given, option B, 3log5(x-4), is the correct answer because it represents a function that has been vertically stretched by a factor of 3 and horizontally translated 4 units to the right from its parent function log5x.
Suppose your club is selling candles to raise money. It cost $100 to rent a booth from which to sell the candles. If the candles cost your club $1 and are sold for $5 each, how many candles must be sold to equal your expenses?
Answers
100 + x = 5x
4x = 100
x = 25
answer
25 candles must be sold to equal expenses
25 candles
What is profit and loss ?
Profit or Gain = Selling price – Cost Price
Loss = Cost Price – Selling Price
According to the given question,
Candles sold must cover the expenses = 100
Let x be the no. of candles that needs to be sold to cover the expenses
rent = 100
Cost price of 1 candle = CP = 1
Cost price of x candles = CP = 1x
Selling price of 1 candle = SP = 5
Selling price of x candles = SP = 5x
Therefore, from the above statements we can infer that the profit generated must be equal to the expenses,
So, SP - CP = Profit = 100
5x - x = 100
4x = 100
x = 25
Therefore, we need 25 candles that needs to be sold to cover the expenses
Read more about SI units at:
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Identify the quadratic term in the function, f(x)=2x^2-3x+5
Answers
The three terms are
2x^2
-3x
5
as they are separated by a plus sign. You can think of it as 2x^2 + (-3x) + 5 if you want. The quadratic term is the term with the exponent of 2
Trigonometric Identities and Applications? help
Answers
[tex]\bf cos^{-1}\left( \frac{8}{-15}\right)=\stackrel{radians}{\stackrel{II~quadrant}{\approx 2.13}~~,~~\stackrel{III~quadrant}{\approx 4.15}}\qquad \qquad t= \begin{cases} \frac{5}{2\pi }\cdot 2.13\\\\ \frac{5}{2\pi }\cdot 4.15 \end{cases}[/tex]
On Monday, the office staff at your school paid $8.77 for 4 cups of coffee and 7 bagels. On Wednesday, they paid $15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel? Explain.
Answers
The pricing is inconsistent. The double order should be double the price, $17.54. There are no prices for bagels or coffee that will match both purchases.
Your friend scores a 22.5 on a normally distributed new logic test with a mean of 20 and a standard deviation of 2.5, and you're confident that 13.59% of people are more logical than your friend but not as logical as you. if you're really as smart as you think you are, what would you score on the test?
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The number of diagonals in any polygon is whole number. But on the other side the formula of the number of diagonals in any convex polygon is in a fraction form \frac{n(n-3)}{2[tex] . How can you explain this?
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[tex]N=n(n-1)/2[/tex]
This will always give a result of a whole number because
if n is odd, then n-1 is even, or
if n is even, n-1 must be odd.
So the division by 2 will always give a whole number because there is always an even number in the numerator.
By the way, this number is also solution to the "hand-shake" problem, which is "how many possible handshakes in a group of n people, if everyone shakes hand with everyone else exactly once?" Therefore, again, it is a whole number.
What is 51.875 rounded to the nearest tenth
Answers
what is the LCM of 6 and 8
Answers
LCM stands for "Least Common Denominator."
The LCM is the smallest common multiple of two numbers.
To find the LCM of 6 and 8, follow these easy steps.
1. Find the prime factorization of both numbers.
6 = 2 × 3
8 = 2 × 2 × 2
Next, multiply each factor the number of times we did above.
LCM = 2 × 2 × 2 × 3
LCM = 24
ANSWER:
The LCM of 6 and 8 is 24.
6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
===================================================================
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
Now find the multiple that matches first (which is 24)
Your LCM is 24
Class records at rockwood college indicate that a student selected at random has probability 0.75 of passing french 101. for the student who passes french 101, the probability is 0.91 that he or she will pass french 102. what is the probability that a student selected at random will pass both french 101 and french 102? (round your answer to three decimal places.)
Answers
Signed General Penguin
P - potassium
S - sodium
L - lithium
M - magnesium
C - calcium
A - aluminium
Z - zinc
I - iron
L - lead
H - hydrogen
C - copper
S - silver
G - gold
P - platinum
To get the probability of two individual events both occurring, you have to multiply the probabilities of their individual events occurring. Therefore in this problem, the probability that a student selected at random will pass both French 101 and French 102 is 0.683 (.75 x .91). The answer is already rounded to three decimal places.
if a seed is planted it has a 75% chance of growing into a healthy plant. If 7 seeds are planted what is the probability that exactly 4 don't grow
Answers
7C4*. 75^4*. 25^(7-4)
35*. 75⁴*. 25³
35*. 316*. 016
11.06*. 016
. 1769
=. 177
How much Will be left after
45 hours if an isotope has a half life of 15 hours and you have 371 MGS
Answers
and surely you know how much that is.
After 45 hours, approximately 46.375 mg of the isotope will be left, given its half-life is 15 hours. This was determined by calculating the amount remaining after each of three half-lives. Each half-life reduces the amount by half.
To determine how much of the isotope is left after 45 hours, we need to use the concept of half-life. The half-life of the isotope is 15 hours. This means that every 15 hours, half of the isotope decays. We start with 371 mg.
First, calculate how many half-lives have passed:
45 hours / 15 hours per half-life = 3 half-livesAfter each half-life, the amount of isotope remaining is halved:
After the first half-life (15 hours): 371 mg / 2 = 185.5 mgAfter the second half-life (30 hours): 185.5 mg / 2 = 92.75 mgAfter the third half-life (45 hours): 92.75 mg / 2 = 46.375 mgTherefore, after 45 hours, approximately 46.375 mg of the isotope will be left.
A runner ran 2/3 of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
a. How long did it take to run the entire race?
b. How many minutes did it take to run 1 kilometer?
Answers
Answer:
it take 31.53 minutes to run the entire race
it take 6.3 minutes to run the 1 km
Step-by-step explanation:
A runner ran 2/3 of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
[tex]\frac{2}{3} \cdot 5= \frac{10}{3}[/tex]
3.33 km is covered in 21 minutes
So 5 km is covered in [tex]\frac{5 \cdot 21}{3.33}=31.53[/tex]minutes
it take 31.53 minutes to run the entire race
[tex] \frac{10}{3}[/tex] km is covered in 21 minutes
1 km is covered in [tex]\frac{21}{\frac{10}{3} } =6.3[/tex]
It takes to run the entire race is 31 minutes and 30 seconds and it takes to run 1 kilometer is 6 minutes and 18 seconds.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
[tex]\rm speed = \dfrac{distance}{time}[/tex]
A runner ran 2/3 of a 5 kilometers race in 21 minutes. They ran the entire race at a constant speed.
2/3 of 5 km is given as x
[tex]x = \dfrac{2}{3}* 5 = \dfrac{10}{3}[/tex]
Then the speed will be
[tex]\rm speed = \dfrac{\frac{10}{3}}{21} = \dfrac{10}{3*21} = \dfrac{10}{63}[/tex]
a. It takes to run the entire race will be
[tex]\rm Time = \dfrac{5}{ \frac{10}{63}} = \dfrac{63* 5 }{10} =31.5[/tex]
It takes to run the entire race is 31 minutes and 30 seconds.
B. It takes to run 1 kilometer will be
[tex]\rm Time = \dfrac{1}{ \frac{10}{63}} = \dfrac{63* 1}{10} = 6.3[/tex]
It takes to run 1 kilometer is 6 minutes and 18 seconds.
More about the speed link is given below.
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The world's smallest gecko is 3/4 inch long. An adult male Western Banded Gecko is 7 1/3 times as long. How long is an adult male Western Banded Gecko
Answers
To solve this problem, you can multiply the numbers 3/4 and 7 1/3 since it is times as long as the world's smallest gecko . . .
3/4 = 3/4
7 1/3 = 22/3
3 x 22 = 66
4 x 3 = 12
Simplifying 66/12 . . .
66/12 = 5 1/2 <-------
An adult male Western Banded Gecko is 5 1/2 inches long.
Hope this helps you.
Have a great day!
You are making lemonade for your lemonade stand. Each liter of lemonade you make uses 3.5 tablespoons of lemonade powder, and you have 14 tablespoons of lemonade powder. Can you make 5 liters of lemonade?
Answers
What is the sum of the measures of < 1 and < 2?
180°
118°
236°
59°
Answers
Answer:
118
Step-by-step explanation:
You can use a calculator for this question.
Greg builds a new pond which has a volume of 7.35 m3.
It is 4.2 m long and 50 cm deep.
What is the width of the pond? m
There will be a circular patio with a diameter of 7 metres.
Greg is going to put a tiled edge around the patio.
What is the circumference of the patio? m
Circumference of a circle = 2πr
Use π = 3.14
Answers
2) C = 7pi = 21.98 m