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
Which type of interest will earn you more money in a savings account?
Answer:
a compound interest that has the lowest interest rate .
Step-by-step explanation:
Promise Easy Points
Calculate the average monthly expenses for these individuals?
Kelsey spent $350 in May, $432 in June and $420 in July. Her average monthly expenses are:____
Michael spent $700 in April and May and $800 in June and July. His average monthly expenses are:____
$420+$350+$432=kelsey's monthly expenses
$700+$800=Micheal's Monthly expenses
Michael's average monthly expenses are $750.
What is the average?The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, Kelsey spent $350 in May, $432 in June and $420 in July.
Now, average monthly expenses are
(350+432+420)/3
= 1202/3
= 400.67
Michael spent $700 in April and May and $800 in June and July.
Here, (700×2+800×2)/4
= (1400+1600)/4
= 3000/4
= $750
Therefore, Michael's average monthly expenses are $750.
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An environmental study was conducted. It reported that houses with more inhabitants do not necessarily produce more or less trash. What can be determined?
A. There is no correlation between number of inhabitants and amount of trash produced.
B. There is a correlation between number of inhabitants and amount of trash produced. However, there is no causation. This is because there is probably an increase in the amount of trash produced with an increase in the number of inhabitants.
C. There is a correlation between number of inhabitants and amount of trash produced. There may or may not be causation. Further studies would have to be done to determine this.
Answer:
C.
Step-by-step explanation:
There's no problem for now but it still needs to be monitored in case something might happen.
Photo attached please help
Can you help me please with this
-39/100 is the answer according to me ..
Plz mark me as brainliest if u found it helpful
PLEASE HELP
Consider the expressions (3m+2n−6) and (−4−6m+7n).
Part A
What is the sum of the expressions for n=−2 and m=5?
The sum is
Answer:
5, -20
Step-by-step explanation:
Given the equation (3m+2n−6) and (−4−6m+7n).
Also, given that we're told that
n = -2 and
m = 5, if we take a rather direct approach by substituting like for like, we have
(3m+2n−6) = (3 * 5 + 2 * -2 - 6)
(3m+2n−6) = 15 - 4 - 6
(3m+2n−6) = 15 - 10
(3m+2n−6) = 5
(−4−6m+7n) = (-4 - 6 * 5 + 7 * 2)
(−4−6m+7n) = -4 - 30 + 14
(−4−6m+7n) = -34 + 14
(−4−6m+7n) = -20
Therefore, we proceed to conclude that the answers are 5 and -20 respectively
What is the equation in slope-intercept form for the line that passes through the points (–1, 3) and (–2, –3)?
Answer:
The answer is y = 6x + 9.
-
Step-by-step explanation:
☆Remember: [tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
☆Slope-intercept: [tex]y = mx + b[/tex]
---
☆We need to find the slope first. So just plug in according to the slope formula!
[tex]m = \frac{ - 3 - 3}{ - 2 - ( - 1)} = \frac{ - 6}{ - 1} = 6[/tex]
---
☆Now we need to find the y-intercept. We are going to plug in the slope and a set of coordinates to find the y-intercept.
[tex]y = mx + b \\ 3 = 6( -1 ) + b \\ 3 = - 6 + b \\ \frac{ + 6 = + 6 \: \: \: \: \: \: \: \: \: \: }{9 = b \: \: \: \: \: \: \: \: \: \: \: } [/tex]
---
☆Now all we need to do is plug in and we are done!
[tex]y = 6x + 9[/tex]
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Isabella is making a display board for the school trip. The display board is 2.50m by 2m rectangle. She needs to cover the entire display board with card. How much card would she needs?
Answer:
5m^2
Step-by-step explanation:
Given data
Length of board= 2.50m
Width of board= 2m
The cover need should have the same area as the board
Area= Length*Width
Area= 2.5*2
Area=5m^2
Hence the area of the cover is 5m^2
A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices. Of the devices checked, 84% are not defective. What is the probability of an incorrect conclusion? Round your answer to the nearest tenth of a percent.
The probability of an incorrect conclusion is,
In 84 % of inspection, [tex]7.56\%[/tex] of them labeled as not defective but they are actually defective
Probability :It is given that,
A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices.
Of the devices checked, 84% are not defective.
Actual not defective is,
[tex]\frac{91*84}{100} = 76.44\%[/tex]
In [tex]84\%[/tex] of inspection,[tex]76.44\%[/tex] are actually not defective
But [tex]84- 76.44 = 7.56\%[/tex] of them labeled as not defective but they are actually defective
Learn more about Probability here:
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my friend needs help with this can someone help
Answer:Sorry
Step-by-step explanation:
Hi would help but i dont know and im not in collage sorry.
Mr. Jones charged Roberta $105 for parts and $25 per hour for labor to repair her bicycle. He spent 2 hours repairing her bike. Which expression would be used to correctly calculate the amount Roberta owes him?
a.(2 × 25) + 105
b.(105 x 2) + (25 x 2)
c.2 x (25 + 105)
d.2 x 25 × 105
Answer:
a.(2 × 25) + 105
Step-by-step explanation:
Let the number of hours spent repairing the bike = x
Mr. Jones charged Roberta $105 for parts and $25 per hour for labor to repair her bicycle.
Therefore, our algebraic expression
= $25× x + $105
= 25x + 105
We were told in the question that He spent 2 hours repairing her bike.
Hence:
25 × 2 + 105
Therefore, the correct option is option a
a.(2 × 25) + 105
if sarah has 800 marbles and her teacher gave her 3,00 more and she have 100 to her 2 friends how much will sarah have??
Answer:
3600
Step-by-step explanation:
If she has 800 her teacher gives her 3000= 3800 and she gave 100 to both of her friends - 200 then she will have 3600.
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At a restaurant, the bill comes to $30. If you decide to leave a 10% tip, how much total do you need to pay? Give your answer to the nearest dollar.
Answer:
33dollors if I'm not mistakin
Solve for x:
3x – 2(6 - x) = 7x + 2(5 + x) – 6
Answer:
-4
Step-by-step explanation:
3x-2(6-x)=7x+2(5+x)-6
First, distribute.
3x+ −12+ 2x = 7x + 10 + 2x −6
Combine like terms on each side.
5x − 12= 9x + 4
To solve for x, pick a side to solve. I will solve the right x.
5x - 12 = 9x + 4
-5x -5x
-12 = 4x + 4
Subtract 4 to isolate the variable.
-16 = 4x
Divide 4.
-4 = x
How heavy is a 225 meter cable if a 3 meter section weighs 1.3 kg?
What’s the answer pls
Answer:
Step-by-step explanation:
There is no bird on the spinner. therefore the answer is impossible because there is no bird.
Answer:
Impossible - There's no bird on the wheel.
Step-by-step explanation:
three and two forths - one and two thirds =
3 2/4 - 1 2/3 =
Answer:
1.83333333333
Step-by-step explanation:
pls mark me brainliest
ok thanks :) :) :) :)
Estimate the value of 50.
O A. between 5 and 6
O B. between 6 and 7
C. between 7 and 8
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D. between 8 and 9
PLEASE HELPP
Answer: c
Step-by-step explanation: because 7 squared is 49 and 8 squared is 64
nvm i read the question wrong
Step-by-step explanation:
the person above is correct
How do you graph y=−x−2.
Helppppppppppppp meeeeee
Answer:
9
Step-by-step explanation:
because 9 in a third is 3
3 + 12 is 15
9x2 is 18
and 15 is 3 less than 18
[tex] \sqrt{361} [/tex]
Answer:
19
Step-by-step explanation:
Answer:
19
Step by step explanation:
A professor in one city earns $61,000 a year. A bioengineer earns $95,750. A nurse earns $50,600. What is the difference in salary between the professor and nurse?
Answer:
The difference is 10,400$.
Step-by-step explanation:
$61,000-$50,600=$10,400
What is the area of the composite figure?
Hello! :)
[tex]\large\boxed{A = 32.5cm^{2}}[/tex]
We can use the following area to solve for the area of the trapezoid pictured:
[tex]A = \frac{1}{2}(b_{1} + b_{2})h[/tex]
Where:
h = height
b1 = bottom base
b2 = top base
Plug in the given values:
[tex]A = \frac{1}{2}(9 + 4)(5)[/tex]
Simplify:
[tex]A = \frac{1}{2}(65)\\\\A = 32.5 cm^{2}[/tex]
What is the measure of angle M?
Answer:
35°
Step-by-step explanation:
4x+11 = 5x-24
5x-4x=x
x=24+11
x=35
Use the exchange rate £1 = $1.38 to convert $276 into £.
Answer:
£200
Step-by-step explanation:
List all factors of 72
Answer:
1,2,3,4,6,8,9,12,18,24,36,72.
Step-by-step explanation:
What you are looking for are numbers that multiply by each other to equal 72, like 1 and 72 or 8 and 9. Factor tree may help, search it up :)
PLZ HELP ME What shape is this cross-section?
Answer:
i'm not sure if i'm right but think is cube
HELP QUICK ILL GIVE TOU BRAINLIEST
find the surface area...
5/= 1.5 x 25
What is 1.5 × 25
A. 22.5
B. 37.5
c. 52.5
D. 85.5
Answer:
37.5 is the answer
Step-by-step explanation:
all you do is just multiply the 2 numbers
how much is 1/2÷8×57÷13+15
Answer:
Use the BODMAS method and at the end work the fraction left by adding it to 15
My answer was 15.274
