Answer:
in 9 days
Step-by-step explanation:
..
Given points A(2,1,3) and B(0,5,0), find a point C in the xy-plane that creates an isosceles right triangle such that:_______
a. AB and BC are the legs of the right triangle
b. AB is the hypotenuse of the right triangle (for part ii, just doing all the set-up work is sufficient; you do not need to solve and find the points)
Answer:
a.)Point C will be either (4.82, 7.41) or ( -4.82, 2.59)
b.) -x² + 2x + 6y - y² - 5= 0 , 8y - 4x = 11
Step-by-step explanation:
As given A(2,1,3) and B(0,5,0)
a.)
We have to find C in the xy-plane
⇒ C is of the form (x, y, 0) ( Because in xy plane , z coordinate is zero)
Now, given AB and BC are the legs of the right triangle .
AB = (0, 5, 0) - (2, 1, 3) = ( -2, 4, -3)
BC = (x, y, 0) - (0, 5, 0) = ( x, y-5, 0)
As AB and BC are legs of triangle
⇒AB is perpendicular to BC
⇒(AB).(BC) = 0
⇒( -2, 4, -3).( x, y-5, 0) = 0
⇒ -2x + 4(y-5) -0 = 0
⇒ -2x + 4y- 20 = 0
⇒ -x + 2y- 10 = 0
⇒ 2y = 10 + x
⇒ y = 5 + [tex]\frac{x}{2}[/tex] ......(1)
As ABC is making an isosceles right triangle
It means two sides of the triangle are equal
Now,
|AB| = √(-2)² + (4)² + (-3)² = √4+16+9 = √29
|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²
Now,
AS AB = BC
⇒|AB| = |BC|
⇒|AB|² = |BC|²
⇒29 = (x)² + (y-5)²
⇒29 = (x)² + (5 + [tex]\frac{x}{2}[/tex] -5)²
⇒29 = (x)² + ( [tex]\frac{x}{2}[/tex] )²
⇒29 = x²( 1 + [tex]\frac{1}{4}[/tex] ) = x²( [tex]\frac{5}{4}[/tex] )
⇒ x² = [tex]\frac{116}{5}[/tex] = 23.2
⇒ x = 4.82 , -4.82
⇒y = 7.41 , 2.59
so, Point C will be either (4.82, 7.41) or ( -4.82, 2.59)
b.)
As given AB is the hypotenuse of the right triangle
S, AC and CB will perpendicular to each other
Now,
AC = (x, y, 0) - ( 2, 1, 3) = ( x-2, y-1, -3)
CB = (0, 5, 0) - (x, y, 0) = (-x, 5-y, 0)
As, AC and CB is perpendicular
⇒(AC).(CB) = 0
⇒( x-2, y-1, -3).(-x, 5-y, 0) = 0
⇒(x-2)(-x) + (y-1)(5-y) - 0 = 0
⇒-x² + 2x + 5y - y² - 5 + y = 0
⇒-x² + 2x + 6y - y² - 5= 0 ..........(2)
As ABC is making an isosceles right triangle
It means two sides of the triangle are equal
Now,
|AC| = √(x-2)² + (y-1)² + (0-3)² = √(x-2)² + (y-1)² + 9
|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²
Now,
AS AC = BC
⇒|AC| = |BC|
⇒|AC|² = |BC|²
⇒(x-2)² + (y-1)² + 9 = (x)² + (y-5)²
⇒x² + 4 - 4x + y² + 1 - 2y + 9 = x² + y² + 25 - 10y
⇒ 4 - 4x + 1 - 2y + 9 = 25 - 10y
⇒14 - 4x - 2y = 25 - 10y
⇒10y - 2y - 4x = 25 - 14
⇒8y - 4x = 11 ........(3)
Now, we have 2 equations
-x² + 2x + 6y - y² - 5= 0 , 8y - 4x = 11
Solve these equations to find x, y
What is the value of the x?
Answer:
53
Step-by-step explanation:
37+90=127
180-127=53
Explain whether the following statement is true or false. The function notation f-1(x) means 1/f(x)
Answer:
True
Step-by-step explanation:
f-1(x) otherwise known as the inverse of f(x) is the mathematical equivalent as 1/f(x).
Being inverse simply means that it "reverses" the operation that was applied to it with the original function .
For example: suppose f(x) = x+1, then if x = 1, f(1) = 1+1 =2
Now if we do f-1(x) or 1/f(x), then 1/f(1) = 1/1 +1 = 1/2
So, 2/1 is in fact the inverse of 1/2.
Hence, f-1(x) is the same as 1/f(x)
Researchers for the National Institute of Child Health and Human Development studied 208 infants whose brains were temporarily deprived of oxygen as a result of complications at birth. These babies were subjects in an experiment to determine if reducing body temperature for three days after birth improved their chances of surviving without brain damage. What is the population
Answer: All infants
Step-by-step explanation:
In statistics,
Population is a term that is used to represent the largest group sharing similar charcteristic from the researcher's point of view.
A sample is a subset of the population.
Here, a sample is collected of infants which were subjects for the study.
Objective of study: To check if reducing body temperature for 3 days after birth improved their chances of surviving without brain damage.
Here, the population of interest is "All infants".
A trawler caught 2/3 ton of fish on Monday and 1/2 on Tuesday. What was the total amount of fish caught?
Answer:
1 1/6
Step-by-step explanation:
(1/2×3/3)+(2/3×2/2)=
3/6+4/6=
3+4/6=7/6 or 1 1/6
3+4 is the numerator over 6
Help plz:)))I’ll mark u Brainliest
Answer: 3
Step-by-step explanation:
pls awnser asap plplplplplplplplplplplplp
Answer:
14/6
Step-by-step explanation:
37. Simplify to find x:
3-(4 X 3) = x
(483) - 7
Answer:
-0.003 x 2+.195 x -.483=0. -0.003x^2+.195x-.483=0 2,3,3,3,5,3,2,3,
Prime factors. 1000,200,1000
square root of (x-(65/2))2 is (x-(65/2))2/2 = (x-(65/2))1 = x-(65/2)
Step-by-step explanation:
−0.003 x 2+.195 x −.483=0. Enter an ... -0.003x^2+.195x-.483=0 ... {Left,Right}. 2, 3, 3, 3. 5, 3, 2, 3. Product of all. Prime Factors, 1000, 200, 1000 ... Step 7 : ... Note that the square root of (x-(65/2))2 is (x-(65/2))2/2 = (x-(65/2))1 = x-(65/2)
find the missing value in the ration table
The total cost of a jacket and a belt was $57.07. If the price of the jacket was $9.21 less than the belt, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer:
48.26
Step-by-step explanation:
subtract and thats the answer its 48.26 less than the belt
Find the perimeter of the following shape:
Sarah Sandoval is a coffee farmer trying to decide how many tons of coffee to produce. She can sell each ton of coffee for $2,400. The cost of producing her first ton of coffee is $600, and the second ton costs $1,200. Each additional ton of coffee costs $600 more to produce. How many tons of coffee should Sarah produce, and what is the total cost of her coffee production
Answer:
Sarah should produce four tons of coffee and total cost for four ton is $6,000.
Step-by-step explanation:
According to the scenario, calculation of the given data are as follows,
Selling price per ton = $2,400
Cost of production is increasing by $600 for each ton.
So, Cost of production first ton = $600
Cost of production for second ton = $600 + $600 = $1,200
Similarly, Cost of production for third ton = $1,200 + $600 = 1,800
Cost of production of fourth ton = $1,800 + $600 = $2,400
Here, Sarah can produce coffee till selling price = cost of production.
As, cost of production of four ton = selling price, then Sarah can produce only four tons of coffee.
Total cost for four ton coffee = $600 + $1,200 + $1,800 + $2,400
= $6,000
Sarah can produce 4 tons of coffee and the total cost of the production is $6000 and this can be determined by using the arithmetic operations.
Given :
Sarah Sandoval is a coffee farmer trying to decide how many tons of coffee to produce.She can sell each ton of coffee for $2,400. The cost of producing her first ton of coffee is $600, and the second ton costs $1,200. Each additional ton of coffee costs $600 more to produce.The following steps can be used in order to determine the total amount of coffee (in tons) should Sarah produce and the total cost of her coffee production:
Step 1 - Remember that Sarah can produce coffee unitil selling price is equal to the cost of production.
Step 2 - According to the given data, each additional ton of coffee costs $600 more to produce.
Step 3 - From the above steps, it can be concluded that Sarah can produce 4 tons of coffee because the cost of 4 tons of coffee is equal to the selling price.
[tex]600\times 4 = $2400[/tex]
Step 4 - So, the total cost of producing four tons of coffee is:
Total Cost = 600+ 1200 + 1800 + 2400
Total Cost = $6000
For more information, refer to the link given below:
https://brainly.com/question/1957976
108x25^2divided by
2^6 x 5^2
Answer:
108 x 25² divided by 2⁶ x 5² is equal to [tex]42\frac{3}{16}[/tex]
Step-by-step explanation:
Given;
108 x 25² divided by 2⁶ x 5²
The expression is simplified as follows;
[tex]\frac{108\times 25^2}{2^6 \times 5^2} = \frac{108\times 625}{64\times25} =\frac{675}{16} = 42\frac{3}{16}[/tex]
Therefore, 108 x 25² divided by 2⁶ x 5² is equal to [tex]42\frac{3}{16}[/tex]
7/8 divided by 1/16 in simplest form?
Answer:
14
Step-by-step explanation:
Keep, change, flip!
7/8 / 1/16
7/8 x 1/16
7/8 x 16/1
Equals...
112/8
Which can be simplified to...
14!
Hope this helped!
Answer:
14
Step-by-step explanation:
(7/8)/(1/16) = 7/8 × 16/1
7 × 16/8 = 7 × 2 = 14
There are three car salespeople at the local car dealership. The table below shows how many cars each salesperson has sold.
Car salesperson Years of employment Cars sold
Ronaldo 222 104104104
Maria 777 322322322
Bruno 121212 516516516
Which car salesperson sold the most cars per year?
Choose 1 answer:
Choose 1 answer:
Answer:
bruno
Step-by-step explanation:
1+2+1+2+1+2+5+1+6+5+1+6+5+1+6=45
64 people ordered a veggie burger at a local hamburger stand out of 160 people in an hour. What percentage of the customers ordered a veggie burger ?
A 40%
B 60%
C 64%
Answer:
A
Step-by-step explanation:
R the midpoint of overline OP and overline QR perpendicular to OP In the diagram below. 20 in. 26 in. Q Find the length of QR .
Answer:
24
Step-by-step explanation:
PLEASE HELP ME 12 POINTS
Answer:
Streamers cost 2.50 and balloons cost 1.25.
Step-by-step explanation:
Pls mark brainliest.
Answer:
Balloon : $1.25
Streamer : $ 2.50
Step-by-step explanation:
Form simultaneous equations.
Let streamer be represented by ------------s
Let balloons be represented by ------------b
So the equations will be;
3s + 2b = 10 ----------------i
2s + 1b = 6.25---------------ii
Make the terms with s equal by multiplication
[3s + 2b = 10 ]2
[2s + 1b = 6.25]3
Perform subtraction
6s + 4b = 20
6s + 3b = 18.75
b = 1.25 ---------iii
Use iii in ii as;
2s + 1b = 6.25
2s + 1.25 = 6.25
2s = 6.25 - 1.25
2s = 5.00
s= 5.00 / 2
s= 2.5
Hence ; a balloon is $1.25 and a streamer is $2.5
THIS HOMEWORK IS SO HARD WALLAHI CAN SOMEONE HELP PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
may be 5 I'm not a 100%sure
The width of a rectangle is 7 inches less than the length. The perimeter is 62 inches. Find the length and the width.
Answer: Perimeter = 2(L) + 2(W) Length = 7W - 2 Perimeter = 60 60 = 14W - 4 + 2(W) 60 =16W - 4 64 = 16W Width = 4 Length = 7(4) - 2 Length = 26
I hope this helped!
Step-by-step explanation:
Find the vertex of the parabola defined by the following equation. 3x^2-12x+11
Answer:
y= 3(x-2)^2-1
Step-by-step explanation:
A cliff diver jumps from a height of 58 feet with an initial velocity of 4 feet per second.
Answer:
The answer is 6 seconds
How many 1/6 are in 2/3
Answer:
4
Step-by-step explanation:
2/3 ÷ 1/6 = 2/3 · 6/1 = 4
Answer:
It takes 4 one-sixth sized pieces to make the two-thirds. and we can see that there 1 \times 6 = 6 sixths in a whole.
Hope you enjoy !
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!
Answer:
55 degrees
Step-by-step explanation:
Mr. Santor cuts 1/2 of a piece of construction paper. He uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does he use to make the flower?
Answer:
1/12
Step-by-step explanation:
1/2 multiplied by 1/6 equals 1/12
PETS Each month Travis spends $20 for premium food$10 for treats $18 for grooming, and $3 for toys for his pet. Write an expression that could be used to determine the amount he spends on these items for his pet over a period of 12 months.
Answer:
$492 per year
Step-by-step explanation:
The first step we take towards solving this question is to add all the numbers we were given as money spent(excluding that of the month)
$20 + $10 + $18 + $3 = $41 per month
This means that a total of $41 was spent per month.
Going further, since we're told it's 12 months, we then multiply it by 12, and thus, we have
$41 * 12 = $492 per year
Therefore, the total money spent is $492 per 12 months, or per year
Which expressions are solutions to the equation 3/4x=15
Answer:
3/4x=15 you flip 3/4 to 4/3 and cancel it out on one side leaving x by itself then you multiply 4/3 by 15 and you get 60/3 and that equals 20 x=20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
3/4x=15 you flip 3/4 to 4/3 and cancel it out on one side leaving x by itself then you multiply 4/3 by 15 and you get 60/3 and that equals 20 x=20
Who is the protagonist?
A. the magician
b. Aladdin
c. the princess
D. the tailor
Answer:
it is a) the magician
Step-by-step explanation:
comment if its wrong mark me brainlest if it is right
The graph of a linear function is shown on the grid . What is the slope of the line
A) -10
B) -3/2
C) -2/3
D) 2
The slope of the equation is 2. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The graph of a linear function is shown on the grid.
From the graph, the points are (-2.5, 0) and (0, 5) and the y-intercept is 5. The slope of the line is given as,
m = (5 - 0) / (0 + 2.5)
m = 5 / 2.5
m = 2
The slope of the equation is 2. Then the correct option is D.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
The missing graph is attached below.
Evaluation 6ab when a = 1/2 and b = 7
Answer:
21
Step-by-step explanation:
6x1/2x7
6 x 1/2=3, 3 x 7=21
I hope this helps and have a nice day!
