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
Two hundred people responded to a survey. Of those who had green eyes, 7 had blonde hair, 9 had brown hair, and 2 had red hair. Construct a two-day table to display these data. Then identify the least common combination of eye and hair color. Explain.
Answer:
18
Step-by-step explanation:
Marcin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
Find the cost of one crayon.
Answer: 28 p is the cost of one crayon.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Marcin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
now,
To solve this problem we're going to use an equation.
First let's write down the information that we do know.
Let's use (r) for ruler and (c) for crayon.
So 7 rulers and 15 crayons cost £7 (or 700 pennies)
--> 7r + 15c = 700
But we also know that r = c +12
So we can substitute c + 12 into the first equation where r is at the moment.
7(c+12) + 15c = 700
Now let's expand the brackets.
We multiply 7 by c to get 7c
and 7x12 t0 get 84
7c + 84 +15c = 700
22c + 84 = 700
Here I'm going to take 84 away from both sides.
22c = 616
616 divided by 22 is 28
so c = 28
hence, Each crayon therefore costs 28p.
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If the triangles are congruent,
then y = [?].
4x+1
13
2x+y
8x-2y
Answer:
4x+1
Step-by-step explanation:
The way i got this was because sometimes on shapes there are 4 side and so you would multiply the number of sides then add some more to it.
Which of these must be true
what do you call two math teachers who bowl?
Answer:
69
Step-by-step explanation:
Find the vertex and focus of the parabola.
y^2 - 12y + 4x + 4 = 0
Answer:
Vertex: (8,6) Focus (7,6)
Step-by-step explanation:
32/4=8
Half of 12=6
What is the remainder when
12345×54321 is divided by 9?
Answer:
0
Step-by-step explanation:
there isn't a reminder, you get 670592745
The value of the equation is A = 7,45,10,305 and the remainder is 0
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 12345
Let the second number be q = 54321
Now , A = ( p x q ) / 9
Substituting the values in the equation , we get
A = ( 12345 x 54321 ) / 9
On simplifying the equation , we get
A = 67,05,92,745 / 9
On further simplification , we get
A = 7,45,10,305
And , the remainder of the equation is 0
Therefore , the value of A is 7,45,10,305
Hence , the equation is A = 7,45,10,305 and the remainder is zero
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7x
5x+18
Find the size of the smallest angle
Answer
Not sure is there supposed to be a pic?
Step-by-step explanation:
emily paints at a constant rate. she can paint 32 square feet in 5 minutes. what area,A, in square feet, can she paint in t minutes? a. write the linear equation in two variables that represents the number of square feet Emily can paint any given time interval.
Answer: A(t) = (6.4 ft^2/min)*t
Step-by-step explanation:
We know that Emily paints at a constant rate, and she can paint 32 ft^2 in 5 minutes.
Then if we take the quotient of these two quantities, we will find the amount she can paint in one minute, this is:
32ft^2/5min = (32/5) ft^2/min = 6.4 ft^2/min.
Then if she paints for t minutes, the area that she can cover can be written as:
A(t) = (6.4 ft^2/min)*t
This is the linear equation we wanted to find.
Predict whether the product will be greater than, less than or equal to the second factor. 1/5 x 3/4
Answer:
14
Step-by-step explanation:
* Use order of operations to solve the following.
* Use order of operations to solve the following.
3 + 5 2 × 2 −7
Answer:
5
3+5 2×2 -7
8+4-7
12-7
5
^^^^
62.837 expanded form decimal
Answer:
60+2+0.8+0.03+0.007
Step-by-step explanation:
Rewrite the expression using the Distributive Property. Explain your answer or show your work.
6(x−4)
Answer:
6x - 24.
Step-by-step explanation:
Distributive Property is:
a(b + c)
= ab + ac
So for this expression
6(x - 4)
= 6*x + 6 * -4
= 6x - 24.
(-Z - 8) - (62-5)
Help me please thank
Answer: -z-65
Step-by-step explanation:
Taylor charges $15 for the first hour of dog walking and $10 for each additional
hour or fraction of an hour. The rates that Lucy charges for x hours of dog walking
are modeled with the function shown.
f(x) =
{
20x, 0
10x. 2
5x, x >4
Who will charge more to walk a dog for 2.5 hours, Taylor or Lucy? How much more?
Who?:
How much more?:
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of hours of dog walking. Taylor charges $15 for the first hour and $10 for each additional hour. Therefore:
Let g(x) represent how much Taylor charges. Hence:
g(x) = 15 for 0 ≤ x ≤ 1
g(x) = 15 + 10(x - 1) = 15 + 10x - 10 = 10x + 5 for x > 1
g(x) can be represented by the piecewise function:
[tex]g(x)=\left \{ {{15\ \ \ \ \ \ for\ 0\leq x\leq 1} \atop {10x+5\ \ for\ x>1}} \right.[/tex]
Lucy charges f(x) is modeled by the piecewise function:
[tex]f(x)=\left \{ {{20x\ \ \ \ \ \ for\ 0\leq x\leq 2} \atop {10x\ \ \ for\ 0< x< 4}} \right.[/tex]
Therefore the charge for walking a dog for 2.5 hours by either Taylor or Lucy is:
For Taylor; f(2.5) = 10(2.5) + 5 = $30
For Lucy; g(2.5) = 10(2.5) = $25
Therefore Taylor charges more by walking a dog for 2.5 hours. Taylors charge is $5 more than Lucy charge ($30 - $25).
Find the coordinates the intersection of the diagonals of parallelogram QRST if with vertices Q(-2,-1), R(-3,6), S(1,5), and T(2,-2) HELP PLS
Answer:
(-0.5, 2)Step-by-step explanation:
Diagonals of a parallelogram bisect each other.
Intersection point is the midpoint of either diagonal.
Let's take QS and calculate midpoint using midpoint formula:
Q(-2, -1), S(1, 5)x = (x1 + x2)/2 = (-2 + 1)/2 = -1/2 = -0.5y = (y1 + y2)/2 = (-1 + 5)/2 = 4/2 = 2Point (-0.5, 2) is the answer
A particular electric utility charges customers different rates depending on their daily rate of energy consumption: $0.05/kWh up to 20 kWh, and $0.10/kWh for all energy usage above 20 kWh in any 24-hour period. (a) Calculate how many 100 W light bulbs can be run continuously for less than $10 per week. (b) Calculate the daily energy cost if 2000 kW of power is used continuously.
Answer:
(a) the number of 100W light bulbs is 11
(b) the daily cost of 2000 kW is $4,800
Step-by-step explanation:
charge of energy consumption up to 20 kWh = $0.05/kWh
charge of energy consumption above 20 kWh = $0.10/kWh
(a) number of 100 W light bulbs that can be run continuously for less than $10 per week
Total energy consumed by 100 W in 1 week = (0.1 kW) x (7 x 24 h)
= 16.8 kWh
Charge associated with this consumption = $0.05/kWh
let the number of 100 W light bulbs = n
[tex]n(\frac{\$ 0.05}{kWh} \times 16.8 kWh) = \$10\\\\n(0.84) = 10\\\\n = \frac{10}{0.84} \\\\n = 11.9[/tex]
Since 0.9 is not a whole number, the number of 100 W light bulbs is 11.
(b) if 2000 kW is used continuously
total energy consumption = 2000 kW x 24 h = 48,000 kWh
The daily cost is calculated as;
[tex]= \frac{\$0.10 }{kWh} \ \times \ 48,000 kWh\\\\= \$ 4,800[/tex]
A particular electric utility charges customers different rates depending on their daily rate of energy consumption :
(a) the number of 100W light bulbs is 11
(b) the daily cost of 2000 kW is $4,800
"Energy Consumption"Given :
Charge of energy consumption up to 20 kWh = $0.05/kWh
Charge of energy consumption above 20 kWh = $0.10/kWh(
Part a)
Number of 100 W light bulbs that can be run continuously for less than $10 per week
Total energy consumed by 100 W in 1 week = (0.1 kW) x (7 x 24 h)Total energy consumed by 100 W in 1 week = 16.8 kWhCharge associated with this consumption = $0.05/kWh
Let the number of 100 W light bulbs = n[tex]n\left(\frac{\$0.05}{kWh}\cdot16.8kWh\right)=\$10\\n\left(0.84\right)=10\\n=\frac{10}{0.84}\\n=11.9[/tex]
Since 0.9 is not a whole number.
Thus, the number of 100 W light bulbs is 11.
Part b)
2000 kW is used continuously
Total energy consumption = 2000 kW x 24 h
Total energy consumption = 48,000 kWh
The daily cost is calculated by:
[tex]\frac{\$0.10}{kWh}\cdot48000\ kWh
Daily cost=\$4800[/tex]
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The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.
Technician Shutdowns
Taylor 2
Hurley 1
Gupta 3
Rousche 5
Huang 4
A. How many samples, without replacement, of size two are possible?
B. Compute the mean of the sample means and compare it to the population mean.
C. The mean of the sample means is_____.
D. The population mean is_____.
E. Both means are:_____.
a. not equal
b. equal.
Answer:
it is a
Step-by-step explanation:
i dont realy like its hard for me to explain
HELP NOW PLEASE ASAP
A government agency hires you to provide consulting on new rules regarding vehicle license plates. The agency is considering an all-numbers license plate that has six slots (digits 0-9 with no duplicate digits allowed). How many possible license plates are there
Answer:
There are 151,200 possible license plates.
Step-by-step explanation:
The order in which the digits are positioned is important(for example, 012345 is a different plate than 102345). No repeat digits are allowed, which means that we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
There are 10 possible digits(from 0 to 9).
The plate has 6 slots.
So
[tex]P_{(10,6)} = \frac{10!}{(10-6)!} = 151200[/tex]
There are 151,200 possible license plates.
help me asap pls pls
Answer:
11(7+4)=22 7+4=18 here i think it help for u
Given that WXYZ is a rectangle and ZY=2x + 3, and WX=x +4, then WX=
Answer:
7
Step-by-step explanation:
Answer:
WX = 5
Step-by-step explanation:
2x + 3 = x + 4
x = 1
WX = 2(1) + 3 = 5
Sarah interviewed for a job that promised her a starting salary of $37,000
with a $1550 raise at the end of each year. What will her salary be during
her sixth year if she accepts the job
help fast plz with that
the sum of 17 and 3 times x
Answer:
20x?
Step-by-step explanation:
Answer:
it will = 17+3x. hope it helps
at the beginning of the school year Anderson Middle School had 480 students at the end of the year it had 504 students what is the percent of change in the enrollment
Answer:
The number of enrollments increased by 5%.
Step-by-step explanation:
Given that:
Number of students at the beginning of the year = 480
Number of students at the end of the year = 504
Change = 504 - 480 = 24
This indicates increase.
Percent of change = [tex]\frac{Change}{Old\ number\ of\ students}*100[/tex]
Percent of change = [tex]\frac{24}{480}*100[/tex]
Percent of change = 5%
Hence,
The number of enrollments increased by 5%.
Divide. Reduce the answer to lowest terms. 2/7 • 15/7
On Sunday, Sheldon bought 412 kg of plant food. He used 123kg on his strawberry plants and used 14 kg for his tomato plants.
How many kilograms of plant food did Sheldon have left? Write one or more equations to show how you reached your answer.
Answer:
275
Step-by-step explanation:
412kg - 123kg - 14kg = 275kg left
Because he used 275 kg out of 412kg
9. When Diego's phone is fully charged, it will last 18 hours. How much time 1 point
is left on his phone when the battery has 15% charge remaining? *
Answer:
2.7 hours
Step-by-step explanation:
Assuming that each percentage is worth the same amount of time. Then we can use the Rule of three since this is a ratio problem and we are given three values and a variable which is the amount of time that the battery lasts at 15%. This variable is represented by the letter x. To solve this we simply multiply the diagonal values and divide by the last remaining value which gives us the value of the variable like so...
100% <====> 18 hours
15% <====> x hours
(15 * 18) / 100 = 2.7 hours
Finally, we can see that 15% charge on the phone will last 2.7 hours
Account A has a simple annual interest rate of 2% and Account B has a simple annual interest rate of 3.5%. How much more interest do you eam per year when
you deposit x dollars in Account B instead of A?
9514 1404 393
Answer:
0.015x
Step-by-step explanation:
The amounts earned at the different rates are ...
at 2%: 0.02x
at 3.5%: 0.035x
The difference in earnings is ...
0.035x -0.02x = 0.015x