The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
How to determine the location of a point within a line segment
By geometry we know that a line segment is generated from two distinct points set on a plane. The location of the point P within the line segment can be found by means of the following vectorial formula:
P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)], 0 < k < 1 (1)
Where:
A(x, y) - Initial pointB(x, y) - Final pointk - Distance factorIf we know that A(x, y) = (- 8, - 2), B(x, y) = (6, 19) and k = 2/5, then the location of the point P is:
P(x, y) = (- 8, -2) + (2/5) · [(6, 19) - (- 8, -2)]
P(x, y) = (- 8, -2) + (2/5) · (14, 21)
P(x, y) = (- 12/5, 32/5)
The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
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2=10 3=18 4=28 6=54 then 8=?
Answer:
72
Step-by-step explanation:
2*5=10
3*6=18
6*8=54
8*9=72
find the value of x
I have to show the work
Answer:
x = 39
Step-by-step explanation:
A circle is made up of 360 degrees
235+ 54+ x+32 = 360
Combine like terms
x+321=360
Subtract 321 from each side
x+321-321 = 360-321
x = 39
5 2/5 is ___ 3 1/2, is it greater than or less than
Answer:
5 2/5 > 3 1/2. 5 2/5 is greater than 3 1/2
Step-by-step explanation:
Answer:
I believe that 5 2/5 is greater than 3 1/2
solve the linear equation 7x-3=67 for x
Answer: x=10
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
when we see something like 7x-3=67, we have to get x alone. the first step is to always cancel out the constant (the number that does not have a variable such as x connected to it). so to make -3 equal to 0 we have to add 3. what we do to one side we have to do to the other so after adding 3 on each side we get 7x=70. now here, we still have to get x alone. 7x means 7 times x so to undo this we have to do the opposite and divide each side by 7. 7 divided by 1 (and 1x is 1 times x which is just x so now we have x alone yaay) and 70 divided by 7 is 10. so x = 10.
I hope this helped :))
Determine the density in g/cm3 of a mineral that has a volume of 3.8 cm3 and a mass of 22.4 g.
Answer:
5.89 g/cm³
Step-by-step explanation:
givens,
Mass = 22.4 g
volume = 3.8 cm³
Density = mass / volume
= 22.4 / 3.8
= 5.89 g/cm³
The density with a volume of 3.8 cm³ and a mass of 22.4 g is 5.89 g / cm³.
Given,
The volume of a mineral = 3.8 cm3
And the mass of the mineral = 22.4 g
We need to find the density.
What is density?It is the ratio of mass and volume.
Density = mass / volume
Find the density.
Volume = 3.8 cm³
Mass = 22.4 g
Density
= Mass / Volume
= 22.4 / 3.8
= 5.89 g / cm³
Thus the density with a volume of 3.8 cm³ and a mass of 22.4 g is
5.89 g / cm³.
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Swedish researchers concluded that viewing and discussing art soothes the soul and helps relieve medical conditions such as high blood pressure and constipation. This conclusion was based on a study in which 20 elderly women gathered once a week to discuss different works of art. The study also included a control group of 20 elderly women who met once a week to discuss their hobbies and interests. At the end of 4 months, the art discussion group was found to have a more positive attitude, to have lower blood pressure, and to use fewer laxatives than the control group.
Required:
a. Why would it be important to determine if the researchers assigned the women participating in the study at random to one of the two groups?
b. Explain why you think that the researchers included a control group in this study.
Step-by-step explanation:
1. By assigning women at random. It would make these 2 groups comparable abc the result from the research or investigation would be more useful and valid. It is very important that there are two comparable groups.
2. A control group is useful in comparing both groups. It would help us to check if there's really an effect or if there is none. If all women were in in art group then all would likely make improvements and there would be no means of verifying this.
324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues
An investor wants to save money to purchase real estate. She buys an annuity with monthly payments that earn 5.6% interest, compounded monthly. Payments
will be made at the end of each month, Find the total value of the annuity in 16 years if each monthly payment is $65.
Do not round any intermediate computations, and round your final answer to the nearest cent
Answer:
1040
Step-by-step explanation:
just took 65 and mutiply 65$
Answer:
1040
Step-by-step explanation:
just took 65 and mutiply 65$
Ivan has 32 baseballs and 48 basketballs. If he wants to divide them into identical groups without any balls left over, what is the greatest number of groups Ivan can make
Here we will show you step-by-step with detailed explanation how to calculate 48 divided by 32 using long division.
Before you continue, note that in the problem 48 divided by 32, the numbers are defined as follows:
48 = dividend
32 = divisor
Step 1:
Start by setting it up with the divisor 32 on the left side and the dividend 48 on the right side like this:
3 2 ⟌ 4 8
Step 2:
The divisor (32) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
3 2 ⟌ 4 8
Step 3:
Multiply the divisor by the result in the previous step (32 x 0 = 0) and write that answer below the dividend.
0
3 2 ⟌ 4 8
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
3 2 ⟌ 4 8
- 0
4
Step 5:
Move down the 2nd digit of the dividend (8) like this:
0
3 2 ⟌ 4 8
- 0
4 8
Step 6:
The divisor (32) goes into the bottom number (48), 1 time(s). Therefore, put 1 on top:
0 1
3 2 ⟌ 4 8
- 0
4 8
Step 7:
Multiply the divisor by the result in the previous step (32 x 1 = 32) and write that answer at the bottom:
0 1
3 2 ⟌ 4 8
- 0
4 8
3 2
Step 8:
Subtract the result in the previous step from the number written above it. (48 - 32 = 16) and write the answer at the bottom.
0 1
3 2 ⟌ 4 8
- 0
4 8
- 3 2
1 6
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 48 divided by 32 calculated using Long Division is:
1
16 Remainder
Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far are the divers from each other?
Answer:
66.25 ft
Step-by-step explanation:
25.5 + 40.75
66.25
They are 66.25 feet away from each other.
Please let me know if I'm wrong!
68% of johns school are boys. There are 180 more boys than girls. How many students are there in johns school
Answer:
500 students in the school
Step-by-step explanation:
100 - 68% = 32%
boys percentage 68%
girls percentage 32%
difference 68 - 32 = 36% = 180
36 ÷ 18 = 2 × 50 = 100
180 ÷ 18 = 10 × 50 = 500
Answer:
500 students.
Step-by-step explanation:
This a system of equations you could write where t is the total amount of students in the school, b is the number of boys, and g is the number of girls:
0.68t=b
b+g=t
180+g=b
0.68t+g=t
g=0.32t
180+g=b
180+0.32t=0.68t
180=0.36t
t=500
Which of the following numbers is a perfect square?
222
141
196
124
Answer:
196
Step-by-step explan
Scarlett stopped at a campground along the Appalachian trail. The campground had a 1
2
acre area for tents, divided into 6 equal campsites. Scarlett picked one of the sections to pitch her tent.
Which expression would give you the size of Scarlett’s campsite? Check all that apply.
One-half divided by 6
StartFraction 6 Over 7 EndFraction divided by 6
6 divided by one-half
StartFraction 6 Over 12 EndFraction divided by 6
6 divided by StartFraction 3 Over 6 EndFraction
Answer:
1/2 divided by 6
6/12 divided by 6
Step-by-step explanation:
Answer:
a - d
Step-by-step explanation:
How to estimate the sum of using different methods. 187,176,154,207
Answer:
tuff
guess you will fail
Step-by-step explanation:
what is the solution of 7k+2=4k-10? (anwser asap plz)
1.- Divison property of Equality
2.- Simplify
3.-Subtraction Property of Equality
4.- Subtract
Answer:
3
Step-by-step explanation:
Answer:
k = -4
division property
Step-by-step explanation:
I will give brainliest :D
Which equation matches this scenario?
A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.
• 5x+8=61
• 61+8x=5
• 8+5x=61
• 8x+5=61
Answer: 8x + 5= 61
Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.
Simplify the expression:
27
simplifying square roots
Answer:
3^2
Step-by-step explanation:
3x3x3 = 27
Because if you have 3^2 then that is 3 to the power of 2 and 3 to the power of 2 is 27.
Answer:
3 by the power of 2
Step-by-step explanation:
Solve for X please :(( Will give brainliest.
5x+6+92 = 22x-4
5x+98 = 22x-4
add 5x to both sides
98 = 27x-4
add 4 to both sides
102 = 27x
divide both sides by 27
x = 3 and [tex]\frac{7}{9}[/tex]
What is the value of j
If the area of the base of the box is 112 square inches and the height is 3.5 inches, what is the volume of the box?
Answer: uh i think its 392 inches squared
Step-by-step explanation:
The volume of the box whose area is 112 inch² and height 3.5 inch is
392 inch³
What is the Volume of a Rectangle?
The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
The area of the box = 112 inch²
The height of the box = 3.5 inch
Now , the volume of the box is given by the equation
Volume of the box = Area of the box × Height of the box
Volume of the box = 112 inch² x 3.5 inch
Volume of the box = 392 inch³
Therefore , the volume of the box is 392 inch³
Hence , the volume of the box whose area is 112 inch² and height 3.5 inch is 392 inch³
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How many quarts does a 100 liter tank hold?
Answer: 84.535 Quartas.
Step-by-step explanation:
a tourist information center charges $10 per hour to rent a bicycle
Answer:
10per the other side of alloys
Will Give Branieliest!!!!!!!
A farmer placed an order for 11 tons of fertilizer. He calculates that the corn fields will require 6 5/8 tons of it. How much fertilizer will the farmer have left for his other crops?
Write your answer as a fraction or as a whole or mixed number.
Answer:
4.375
Step-by-step explanation:
11 tons
He needs 6 5/8
Convert 11 tons to a fraction with the same denominator:
[tex]\frac{11}{1} *\frac{8}{8} =\frac{88}{8}[/tex]
Now calculate 6 5/8:
[tex]\frac{6}{1} *\frac{8}{8} =\frac{48}{8}[/tex] and add [tex]\frac{5}{8}[/tex]
[tex]\frac{48}{8} +\frac{5}{8} =\frac{53}{8}[/tex]
Now subtract
[tex]\frac{88}{8} -\frac{53}{8} =\frac{35}{8}[/tex]
As a mixed number:
[tex]\frac{35}{8} = 4 \frac{3}{8}[/tex]
As a fraction:
4.375 is how much he has left for his other crops.
A furniture manufacturer makes two types of furniture: chairs and sofas. The production of the sofas and chairs requires three operations: carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The prfit per chair is $90 and the profit per sofa is $75. The manufacturer wants to know how many chairs and how many sofas should be produced each day to maximize the profit.
Formulate a linear programming (LP)problem you would use to find a solution.
Answer:
Chair x₁ = 10
Sofa x₂ = 18
z(max) = 2250 $
Step-by-step explanation:
Information:
Operation-Profit Carpentry Finishing Upholstery Profit
hours hours hours $
Chair (x₁) 3 9 2 90
Sofa (x₂) 2 4 10 75
Objective Function z:
z = 90*x₁ + 75*x₂
Constrains:
1.-66 hours of carpentry available
3*x₁ + 2*x₂ ≤ 66
2.- 180 hours of finishing available
9*x₁ + 4*x₂ ≤ 180
3.- 200 hours of upholstery
2*x₁ + 10*x₂ ≤ 200
Model:
z = 90*x₁ + 75*x₂ to maximize
Subject to:
3*x₁ + 2*x₂ ≤ 66
9*x₁ + 4*x₂ ≤ 180
2*x₁ + 10*x₂ ≤ 200
x₁ >= 0 x₂ >= 0
From simplex method solver we get the answer
x₁ = 10 x₂ = 18 z = 2250
The linear programming model is:
Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]Subject to [tex]\mathbf{3x + 2y \le 66}[/tex], [tex]\mathbf{9x + 4y \le 180}[/tex], [tex]\mathbf{2x + 10y \le 200}[/tex], [tex]\mathbf{x,y \ge 0}[/tex]Represent sofa with y and chairs with x.
The given parameters are:
Carpentry:
[tex]\mathbf{Chair =3\ hours}[/tex]
[tex]\mathbf{Sofa =2\ hours}[/tex]
[tex]\mathbf{Available = 66\ hours}[/tex]
So, we have:
[tex]\mathbf{3x + 2y \le 66}[/tex]
Finishing
[tex]\mathbf{Chair =9\ hours}[/tex]
[tex]\mathbf{Sofa =4\ hours}[/tex]
[tex]\mathbf{Available = 180\ hours}[/tex]
So, we have:
[tex]\mathbf{9x + 4y \le 180}[/tex]
Upholstery
[tex]\mathbf{Chair =2\ hours}[/tex]
[tex]\mathbf{Sofa =10\ hours}[/tex]
[tex]\mathbf{Available = 200\ hours}[/tex]
So, we have:
[tex]\mathbf{2x + 10y \le 200}[/tex]
The profit is given as: $90 per chair, and $75 per sofa.
So, the objective function is:
[tex]\mathbf{Z = 90x + 75y}[/tex]
Hence, the linear programming model is:
Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]
Subject to
[tex]\mathbf{3x + 2y \le 66}[/tex]
[tex]\mathbf{9x + 4y \le 180}[/tex]
[tex]\mathbf{2x + 10y \le 200}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
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Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use cross products to demonstrate whether or not the two ratios are equivalent:
4/6 and 14/21.
PLEASE ANSWER, I WILL MARK BRAINLYEST. IF YOU PUT AN ABSURD ANSWER I WILL REPORT. 50+ POINTS
Answer:
The umbrella will fit in, but there will be a lot of extra room.
Step-by-step explanation:
Remember the Pythagorean theorem:
x^(2) + y^(2) = n^(2)
where "x" and "y" are the legs of the right triangle and "n" is the hypotenuse
In this problem it is given that the sides (legs) are:
38in, and 24in
and diagonally across is 29in
so the hypotenuse is 29in
therefore we can form the equation:
38^(2) + 24^(2) = 29^(2)
without solving it is clear that
38^(2) + 24^(2) > 29^(2)
because 38 is a leg, but it is greater than 29, which means that 38 - 24 - 29 is not a Pythagorean triple,
but because 38 > 29, then the 29 in umbrella will fit into the suitcase, but it will not be a snug fit, there will be a lot of extra room
Answer:
see below
Step-by-step explanation:
The umbrella should fit
The umbrella is the diagonal in a right triangle so we can use the Pythagorean theorem
a^2+b^2 = c^2
18^2 + 24^2 = c^2
324 + 576 = c^2
900 = c^2
Take the square root of each side
sqrt(900) = sqrt(c^2)
30 =c
As long as the umbrella is less than 30 inches, it should fit
The umbrella is 29 inches so it should fit
A Giant Sequoia tree is planted in Trevor's
backyard when it is 2 ft tall. The tree grows an
average of 4 ft each year. Write a function and
graph the height of the tree over this time period.
I need to know the answer and what points to graph please help
I need help like serious help
Answer:
AB is equal to AD because if you move from A to B, you would have to go 3 points toward the B, and then move one point toward B. Same for D. You must move 3 points toward D, then move one down.
Step-by-step explanation:
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm.
What is its surface area?
Show your reasoning.
I got 48 cm2
Answer:
i got 48
Step-by-step explanation:
2(5*2)
2(2*5)
2(2*2)
Please answer question a & b.
a) Work out the following:
3/4 - 7/9 + 2
b). Which is the largest of the following numbers?
0.1, 0.02, 0.003, 0.0004, 0.00005
Please help due today.
Answer:
a)
b)0.1
pls refer to the pic