Find an equation for the plane that is perpendicular to v = (1, 1, 1) and passes through (1, 0, 0).
Final answer:
The equation for the plane that is perpendicular to the vector v = (1, 1, 1) and passes through the point (1, 0, 0) is x + y + z = 1.
Explanation:
To find an equation for the plane that is perpendicular to the vector v = (1, 1, 1) and passes through the point (1, 0, 0), we need to use the normal vector v as the coefficient of the variables in the plane equation.
Step 1: The vector v is perpendicular to the plane, so its components are the coefficients of x, y, and z in the plane equation. Since v has components (1, 1, 1), the plane equation can be written as x - y - z = D, where D is a constant.
Step 2: The plane passes through the point (1, 0, 0). Substituting these coordinates into the plane equation allows us to find D.
Substituting, we get 1(1) + 1(0) + 1(0) = D. Hence, D = 1. Therefore, the equation of the plane is x + y + z = 1.
On Monday, three hundred twenty students went on a trip to the zoo. All seven buses were filled and five students had to travel in cars. How many students were in each bus?
11. What other information do you need to prove the triangles congruent using the AAS Congruence Postulate?
BAC=DAC
AV=AD
AB=AD
CBA=CDA
From the diagram, we are given that triangle ABC and triangle ADC shares the same side AC, so it means both triangles have one congruent side.
We are also given that angle BAC and angle DAC are equal.
If we want to prove the triangles congruent using Angle-Angle-Side congruent postulate, we need to see one angle in each triangle that is congruent. We will need the information either: ACB = ACD or ABC = ADC
Correct answer: fourth option
Determine whether the equation 14+3x-7=7x+7-4x has one solution, no solution, or infinite solutions. Show work to support your answer.
Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 300. Its cost (in dollars) for a run of x hockey jerseys is
C(x) = 3000 + 10x + 0.2x2 (0 ≤ x ≤ 300)
Gymnast Clothing sells the jerseys at $110 each. Find the revenue function.
R(x) =
Find the profit function.
P(x) =
How many should Gymnast Clothing manufacture to make a profit? HINT [See Example 2.] (Round your answer up to the nearest whole number.)
The revenue function for Gymnast Clothing is R(x) = 110x. The profit function is P(x) = 110x - (3000 + 10x + 0.2x^2). To determine the profit maximizing quantity, we need to find the value of x that makes P(x) greater than zero.
Explanation:To find the revenue function for Gymnast Clothing, we need to multiply the number of hockey jerseys sold (x) by the selling price per jersey ($110). Therefore, the revenue function is R(x) = 110x.
To find the profit function, we subtract the cost function C(x) from the revenue function R(x). Therefore, the profit function is P(x) = R(x) - C(x). Substituting the given cost function, we have P(x) = 110x - (3000 + 10x + 0.2x^2).
To determine how many jerseys Gymnast Clothing should manufacture to make a profit, we need to find the value of x that makes P(x) greater than zero. We can solve this mathematically or graphically. In this case, it is more efficient to solve it graphically by plotting the profit function and finding the quantity that corresponds to a positive profit.
Select the correct answer.
Roberta is thinking about joining the food co-op store. If she pays $10.00 to join, she will get 10% off on all the groceries she buys there. How much must she buy before her savings equal her membership fee?
$10.00
$50.00
$100.00
$1,000.00
Simplify the expression 3bx4b
You are asked to determine the perimeter of the cover of your textbook. you measure the length as 48.28 cm and the width as 24.83 cm. how many significant figures should you report for the perimeter?
Step-by-step explanation:
The length of the textbook, l = 48.28 cm
The breadth of the textbook, b = 24.83 cm
The shape of the textbook is a rectangle. The perimeter is equal to the sum of all sides. Mathematically, it is given by :
[tex]p=2(l+b)[/tex]
[tex]p=2\times (48.28+24.83)[/tex]
p = 146.22 cm
So, the perimeter of the textbook is 146.22 cm. There are 5 significant figures in this number since non zero digits are always significant. Hence, this is the required solution.
What is the midpoint of the line segment whose endpoint are (-8,12) and (-13,-2)
Determine the type of triangle that has side lengths of 18, 24, and 42. scalene triangle isosceles triangle equilateral triangle it's not a triangle.
The triangle with the given side lengths are scalene triangles.
What are triangles?
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees
An isosceles triangle has two sides of equal length. A scalene triangle has sides lengths of different sizes. A right angled triangle have side length in which the sum of the square of the two sides is equal to the square of the third side.
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Name the property shown by the statement.
3(x + 7) = 3x + 21
Based on the box-and-whisker plot shown below, match each term with the correct value.
(1)Median
a0
(2)Range
a1
(3)25th percentile
a2
(4)75th percentile
a3
(5)Inter-quartile Range
a4
Median will be 18, Range will be 15 to 21, 25th percentile will be 15 to 17, 75th percentile 15 to 20, and Inter-quartile Range will be 17 to 20.
What is a box-and-whisker plot?Solid lines on either outside of the rectangle represent the minimum and maximum interquartile range.
Based on the box-and-whisker plot shown below.
1) Median will be 18.
2) Range will be 15 to 21.
3) 25th percentile will be 15 to 17.
4) 75th percentile 15 to 20.
5) Inter-quartile Range will be 17 to 20.
More about the box-and-whisker plot link is given below.
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#SPJ2
1)Solve G(x) for the given domain.
G(x) = 3x 2 - 2x - 1
G(6) =
a)287
b)95
c)23
2)Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x 2 + 2
F(x2) =
3)Solve F(x) for the given domain.
F(x) = x 2 + 3x - 2
F(-1) =
a)-4
b)-6
c)2
4)Solve F(x) for the given domain.
F(x) = x 2 + 3x - 2
F(3) =
a)13
b)16
c)40
Answer:
1-287
2- x^4 + 2
3 -6
4 16
Step-by-step explanation:
Answer:
1) is 95 G(6) = 3(6) ^2 - 2(6) - 1
2) is F(x²) = x⁴ + 2
3)is -4 f(-1)=-1^2+3(-1)-2
4) is 16 F(3) = (3) 2 + 3(3) - 2
Step-by-step explanation:
2) F(x) = x 2 + 2
F(x2) = F(x^2) = (x^2)^ 2 + 2x^4+2
= f(x^2)=x^4+2
A jet ski company charges a flat fee of $26.00 plus $1.00 per hour to rent a jet ski. Another company charges a fee of $14.75 plus $3.25 per hour to rent the same jet ski.
find the number of hours which the cost are the same. Round your answer to the nearest whole number.
Final answer:
The number of hours when the cost of renting a jet ski from two different companies is the same is 5 hours, when rounded to the nearest whole number.
Explanation:
To find the number of hours where the cost to rent a jet ski from two different companies is the same, we can set up two equations to represent the cost from each company and solve for the number of hours.
For the first company, the cost C is given by C = 26 + 1h, where h represents the number of hours.
For the second company, the cost C is given by C = 14.75 + 3.25h.
To find when the costs are the same, we set the two equations equal to each other:
26 + 1h = 14.75 + 3.25h
Now we solve for h:
Subtract 1h from both sides: 26 = 14.75 + 2.25h
Subtract 14.75 from both sides: 11.25 = 2.25h
Divide both sides by 2.25: h = 11.25 / 2.25
Calculate h: h = 5 hours
Therefore, the number of hours at which the costs are the same, when rounded to the nearest whole number, is 5 hours.
A boy found a bicycle lock for which the combination was unknown. the correct combination is a four-digit number,
The difference between consecutive prime numbers is always an even number, except for two particular prime numbers. What are those numbers?
Sally can paint a room in 5 hours while it takes steve 9 hours to paint the same room. how long would it take them to paint the room if they worked together
Final answer:
Sally and Steve will take approximately 3.21 hours to paint a room together. This is calculated by adding their individual rates of painting and then finding the reciprocal of their combined rate.
Explanation:
To determine how long it would take Sally and Steve to paint a room together, we need to calculate their combined work rate. Sally's rate of painting is 1 room per 5 hours, while Steve's rate is 1 room per 9 hours. Their combined rate is the sum of their individual rates. This can be expressed as:
Combined rate = Sally's rate + Steve's rate = (1 room / 5 hours) + (1 room / 9 hours)
The least common multiple (LCM) of 5 and 9 is 45, so to add these rates together, we convert them into a common denominator:
Combined rate = (9 rooms / 45 hours) + (5 rooms / 45 hours) = (9+5) rooms / 45 hours = 14 rooms / 45 hours
To find out how long it takes them to paint one room together, we take the reciprocal of their combined rate:
Time to paint one room = 1 / (Combined rate) = 45 hours / 14 rooms
Therefore, rounding to two decimal places, Sally and Steve would take approximately 3.21 hours to paint the room together.
Each of the 212 pages in the largest fashion catalog measured 1.2m by 1.9m. whats was the perimeter of a page what was the area
Final answer:
To find the perimeter of the catalog page, we add the length and width and multiply by 2, resulting in 6.2 meters. For the area, we multiply the length by the width, resulting in 2.28 square meters.
Explanation:
The question asks for the perimeter and area of a page from a fashion catalog with dimensions of 1.2 meters by 1.9 meters. To calculate the perimeter of a rectangle, the formula is 2(length + width), and to calculate the area, the formula is length × width.
For the perimeter:
2(1.2m + 1.9m) = 2(3.1m) = 6.2 meters.
For the area:
1.2m × 1.9m = 2.28 square meters.
Byron has 1 7/10 kilograms of black pepper. He uses 7/8 of the black pepper and splits between 7 pepper shakers. How much pepper will be in each shaker?
what is (4−5y)−2(3.5y−8)?
Thank you!!
How many lines does wide ruled paper have?
12(3w+8)=25 what is the w
match the distance with their respective endpoint coordinates
distance coordinate
3.6 units A (-3,4) and (3,4)
4.5 units B (-5,3) and (-5,11)
6 units C (-20-18) and (-22-21)
8 units D (2,4) and origin
15 units E (7,8) and (-2,20)
correct sequence of the matching
A. BDAEC
B. BCDAE
C. CDABE
D. CADBE
The density of an object can be calculated by dividing the object's mass by its volume. A rectangular prism has a density of 15g/cm3. The prism has a mass of 5,625 g. The length of the object is 5 cm. The width of the object is 3 cm. What is the height of the object?
density = mass/ volume
volume = mass/ density
volume = 5625 / 15 = 375 cm^3
volume = l x w x h
375 = 5 * 3 * X
375 = 15
x = 375/15 = 25
height = 25 cm
The height of the object is 25 cm and this can be determined by using the formula of density and volume.
Given :
The density of an object can be calculated by dividing the object's mass by its volume.A rectangular prism has a density of 15g/[tex]\rm cm^3[/tex]. The prism has a mass of 5,625 g. The length of the object is 5 cm. The width of the object is 3 cm.The height of the object can be determined by using the formula of density. The formula of density is given by:
[tex]\rm d = \dfrac{m}{V}[/tex]
where d is the density, m is the mass, and V is the volume.
Now, substitute the known terms in the above formula.
[tex]\rm V = \dfrac{5625}{15}= 375\;cm^3[/tex]
Now, the volume of an object is given by:
[tex]\rm V = l \times w\times b[/tex]
Now, substitute the known terms in the above formula.
375 = 5 [tex]\times[/tex] 3 [tex]\times[/tex] h
h = 25 cm
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Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which statement comparing the two swimmers is accurate?
1 mile 1,609 meters
Alina swims about 0.7 miles per hour faster than Talia.
Talia swims about 0.7 miles per hour faster than Alina.
Alina swims about 1.5 miles per hour faster than Talia.
Talia swims about 1.5 miles per hour faster than Alina. pls help
Answer:
Talia swims about 1.5 miles per hour faster than Alina.
Step-by-step explanation:
Since, 1 miles = 1609 meter and 1 hour = 60 seconds,
⇒ [tex]\text{ 1 miles per hour } = \frac{1609}{3600}\text{ meter per seconds}[/tex]
⇒ [tex]\text{ 1 meter per seconds } = \frac{3600}{1609}\text{ miles per hours}[/tex]
Here, The speed of Alina = 2.5 miles per hour = 2.5 × 1609/3600
[tex]=\frac{4022.5}{3600} \text{ meter per seconds }[/tex]
[tex]=1.11736111\text{ meter per seconds}[/tex]
And, the speed of Talia = 1.8 meter per second,
Since 1.8 > 1.11736111
⇒ Talia swims faster than Alina.
And, the difference between their speeds = 1.8 - 1.11736111 = 0.68263889 meter per seconds
= 0.68263889× 3600/1609 miles per hour
= 1.52734618 miles per hour ≈ 1.5 miles per hour ,
⇒ Fourth option is correct.
What is 0.96 as a fraction in simplest form?
Answer:
I agree as well, the answer is 24/25. =)
Step-by-step explanation:
Simplify 7 - (-4) + 3(-6).
it would become 11 - 18 which would equal -7
Can someone please explain this to me? I've been staring at this for 10 minutes.
answer choices:
always, always
always, never
never, always
never, never
never and never
2 negatives multiplied by each other = a positive number
lets look at the first one:
let a = -2
you then have -2*(1/-2) = -2 * (-.5) = 1 ( positive 1 )
2nd eq, multiply a negative by a negative:
a = -3, b=-4, -3*-4 = 12 ( positive 12)
both equations give positive numbers for answers
A garden table and a bench cost $1025 combined. The garden table costs $75 more than the bench. What is the cost of the bench?
Two candidates running for the same office received a total of 1,926 votes. If the winning candidate had 410 more votes than the other candidate, how many votes did the winner receive?
The number of votes received by winner is: 1168
Step-by-step explanation:Let the number of vote that is received by winning candidate be: a
and the number of votes received by other candidate be: b
It is given that:
Two candidates running for the same office received a total of 1,926 votes.
i.e.
[tex]a+b=1926--------------(1)[/tex]
and
The winning candidate had 410 more votes than the other candidate.
This means that:
[tex]a-b=410--------------(2)[/tex]
Now on solving the equation by the method of elimination .
i.e. on adding both the equation we have:
[tex]2a=1926+410\\\\i.e.\\\\2a=2336\\\\i.e.\\\\a=1168[/tex]
Now on putting the value of a in equation (1) we get:
[tex]1168+b=1926\\\\i.e.\\\\b=1926-1168\\\\i.e.\\\\b=758[/tex]
Hence, the answer is: 1168