Can someone please help me answer this!!!

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

Answer:

24

Step-by-step explanation:

Answer:

Step-by-step explanation:

we have to remember the power rules, power raised to the power-we use the multiplication

(7^2)^-7=7^-14= 1/7^14

Answer:

first you choose one of the varibles to solve for so im going to start with s you would add them up and subtract them that way there on the other side of the = sighs so you equation would be 8+2d+3=-7s then you add the 8 and the 3 and you would get 11+2d=-7s i dont know what you do after this i think this is the answer.

Answer:

the other guy is right trust him

Answer:it took  the particle 50,000,000 seconds to travel the specified distance

Step-by-step explanation:

Given that distance = Rate x time

Distance traveled by Particle= 9.0×10^12 meters

and rate= 1.8×105 meters per second

Time taken for particle to travel the specified distance  using our equation that

distance = Rate x time

time = Distance / Rate

=9.0×10^12 meters/ 1.8×105 meters per second

=50,000,000 seconds

Answer:

y= 3(x-2)^2-1

Step-by-step explanation:

Answer:

its loading but ill help!

Step-by-step explanation:

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

Answer: -2.4f-18

Step-by-step explanation:

Add 0.2f to -2.6f then subtract 3 from -15

Answer:

1/2 > 1/4

Step-by-step explanation:

1/2 = 2/4

2/4 > 1/4

Answer:

1/2 > 1/4

Step-by-step explanation:

1/2= 2/4

2/4 > 1/4

Answer:

−x+y+1

Step-by-step explanation:

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

Answer: Identify and use the commutative properties for addition and multiplication. Here, the same problem is worked by grouping 5 and 6 first, 5 + 6 = 11. The example below shows how the associative property can be used to simplify. The sum is 14. 7 + 2 + (8.5 + (−3.5)). 7 + 2 + 5. 9 + 5. 14. Group 8.5 and –3.5=5

Step-by-step explanation:

Answer:

7 × (9 + 6) = (7 × 9) + (7 × 6)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The month of June has  40 sweets

Let the number of sweets in the month of June be  P

Given that April,  May and June collectively have 90 sweets

Given that May has three quarters of number of sweets as that of June

So we can write

[tex]\rm Number\; of \; sweets\; in \; May = \dfrac{3P}{4 } .......(1) \\[/tex]

Similarly it is given that April has two third of sweets as that of May month and hence we can write

[tex]\rm Number\; of\; sweets \; in \; April = \dfrac{2}{3} \times \dfrac{3P}{4} = P/2 ......(2)\\[/tex]

As the total number of sweets in  April,  May and June is  90

Let the number of sweets in  May be "M" and in April be "A"

We can write the following equation and solve it further

[tex]\rm M + A + P = 90\\From \;equations \; (1) \; and \; (2) \\[/tex]

[tex]\rm P + 3P/4 + P/2= 90\\\\2.25 \; P = 90\\P = 40[/tex]

So we can conclude that the month of June has  40 sweets

For more information please refer to the link given below

https://brainly.com/question/1301963

Answer:

1 1/3

Step-by-step explanation:

or 1.33333333333333333333333333333333333333333333

Answer:

20 weeks

Step-by-step explanation:

30/15=2

300/15=20

20 weeks

Answer:

x2

Step-by-step explanation:

x2 82

Answer: 32

Step-by-step explanation: since y=5, 4y= 20. 12+20=32

Answer:

[tex]r=\frac{5}{9}(y-32)[/tex]

Step-by-step explanation:

The Celsius scale was developed by Swedish astronomer Andres Celsius in 1742. It is used to measure temperature in degree Celsius in which 0 degrees represents the freezing point of water, and 100 degrees represents boiling point of water at the standard atmosphere.

The Fahrenheit scale was proposed in 1724 by the physicist Daniel Gabriel Fahrenheit. It is used to measure temperature in degree Fahrenheit in which 32°F represents the freezing point of water, and 212°F represents boiling point of water at the standard atmosphere.

Let r represent the temperature in degrees Celsius and y represent the temperature in degree Fahrenheit. The relationship between r and y is:

[tex]\frac{r-freezing\ point(^oC)}{boiling\ point\ (^oC)-freezing\ point(^oC)} =\frac{y-freezing\ point(^oF)}{boiling\ point\ (^oF)-freezing\ point(^oF)} \\\\Substituting:\\\\\frac{r-0}{100-0}=\frac{y-32}{212-32}\\\\\frac{r}{100} =\frac{y-32}{180}\\\\r= \frac{y-32}{180}*100\\\\r=\frac{5}{9}(y-32)[/tex]

Answer:

it's times 4 every time

Step-by-step explanation:

4.5 times 4 is 18 etc

Answer:

The kind of hypothesis testing we can use is z-test for means

Step-by-step explanation:

Given that;

sample mean x" = 500

standard deviation σ = 100

sample size n = 6

What kind of hypothesis testing do we use?

There are two cases where z-test can be use;

first, when we know the population standard deviation or variance

and secondly, when the population size is more than 30.

So from the question, the population standard deviation was given, which is 100.

Since we know the S.D, it meets the first condition.

Therefore, The kind of hypothesis testing we can use is z-test for means

Answer:

I believe that the one that is NOT true is Option, letter C.  Pls mark brainliest.

Answer:The answer is D

Step-by-step explanation:The Line could intercept the x axis but Sometimes it can only intercept the x axis such as x=7 it only intercepts (7,0) and not (0, any real number.) so that is why that is the answer.

Also brainly pls.

the third one, you have written not clearly

bwhwhsbsh hsbsvs bw wjw wjw whe

Answer:

20

Step-by-step explanation:

what is 42-22?

it is 20. Next time, use a calculator or get your additon and normal calulations really good.

Answer:

im not sure

Step-by-step explanation:

Answer:

Integers are always closed under subtraction, addition and multiplication, not division though. Hope this helped! :D

Step-by-step explanation: