What is the slope of the line? What is the y-intercept of the line? y = 1/2x + 7

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Explanation:

The 90 degree counterclockwise rotation rule we use is

[tex](x,y) \to (-y,x)[/tex]

the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.

After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.

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Extra info (optional section):

Define the following three points

A = (0,0)

B = (8,4)

C = (-4,8)

Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.

Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.

for the to be parallel both the angle must be equal

so 7x - 20 = 3x + 20 - > 4x = 40⁰

x = 10⁰

Answer:

P is maximum at I = 2

Step-by-step explanation:

Here is the complete question

The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 100I/(I² + I + 4) where I is the light intensity (measured in thousands of foot candles). For what light intensity P is a maximum?

To find the value of I at which P is maximum, we differentiate P with respect to I and equate it to zero.

So, dP/dI =  d[100I/(I² + I + 4)]/dI

= [(I² + I + 4)d(100I)/dI - 100Id(I² + I + 4)/dI]/(I² + I + 4)²

= [(I² + I + 4)100 - 100I(2I + 1)]/(I² + I + 4)²

= [100I² + 100I + 400 - 200I² - 100I]/(I² + I + 4)²

= [-100I² + 400]/(I² + I + 4)²

=  -100[I² - 4]/(I² + I + 4)²

Since dP/dI = 0,  -100[I² - 4]/(I² + I + 4)² = 0 ⇒ I² - 4 = 0 ⇒ I² = 4 ⇒ I = ±√4

I = ±2

Since I cannot be negative, we ignore the minus sign

To determine if this is a maximum point, we differentiate dP/dI. So,

d(dP/dI)/dI = d²P/dI² = d[-100[I² - 4]/(I² + I + 4)²]/dI

= [(I² + I + 4)²d(-100[I² - 4])/dI - (-100[I² - 4])d(I² + I + 4)²/dt]/[(I² + I + 4)²]²

= [(I² + I + 4)²(-200I) + 100[I² - 4]) × (2I + 1) × 2(I² + I + 4)]/(I² + I + 4)⁴

= [-200I(I² + I + 4)² + 200[I² - 4])(2I + 1)(I² + I + 4)]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I(I² + I + 4) - [I² - 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + I² + 4I - I² + 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + 4I + 8])(2I + 1)]]/(I² + I + 4)⁴

Substituting I = 2 into d²P/dI², we have

= [-200(2² + 2 + 4)[2³ + 4(2) + 8])(2(2) + 1)]]/(2² + 2 + 4)⁴

= [-200(4 + 2 + 4)[8 + 8 + 8])(4 + 1)]]/(4 + 2 + 4)⁴

= [-200(10)[24](5)]]/(10)⁴

= -240000/10⁴

= -24

Since d²P/dI² = -24 < 0 at I = 2,  this shows that it I = 2 is a maximum point.

So, P is maximum at I = 2

Answer:

The expressions that give the value of y are A - 3B and (1/3)A - B

The solution is (27/13, -60/13)

Step-by-step explanation:

We can see both equation A and equation B.

Equation A: 2x + (1/4)y = 3

Equation B: (2/3)x - y = 6

To find the value of y, we have to solve both equations A and equation B simultaneously. This is done by multiplying equation B by 3 and subtracting from equation A (A - 3B) to get:

(13/4)y = -15

y = -60/13

you can also get y by dividing equation A by 3 and subtracting equation B (1/3A - B)

Put y = -60/13 in equation A to get x:

2x + (1/4)(-60/13) = 3

2x = 3 + 15/13

2x = 54/13

x = 27/13

The solution is (27/13, -60/13)

Answer:

x = 3     y = 5

Step-by-step explanation:

     y=x+2

+    y=-x +8

2y = 10

y = 5

y = -x + 8

5 = -x + 8

x = 3

Answer:

C

Step-by-step explanation:

[tex]4(x + 3) \leqslant 44 \\ \\ 4x + 12 \leqslant 44 \\ 4x \leqslant 44 - 12 \\ 4x \leqslant 32 \\ 4x \div 4 \leqslant 32 \div 4 \\ x \leqslant 8[/tex]

Answer:

x^2 - 9

Step-by-step explanation:

length = 2x - 6 = 2(x-3)

Area = [2(x-3) * (x + 3)]/2 = (x-3)(x+3) = x^2-9

Answer: x = 9

2x -6= x +3

2x -x= 3 +6

x= 9

Step-by-step explanation:

yes they are because they have the same variables which are X& Y

Answer:

5yx-7xy

they are like terms, it's all multiplication just a different arrangement

5xy-7xy=-2xy

Step-by-step explanation:

hope this is helpful

Answer:

for (a)

Step-by-step explanation:

15 and 25 are the numbers that come in A union to B

Answer:

g(x)=f(x+3)+5

Step-by-step explanation:

Answer:

(B)

Step-by-step explanation:

Can't explain lol, but that's the answer

Answer:

{0,-3,-9,5,7}

Step-by-step explanation:

range = all y values

function =(x,y)

so all the second values are ranges

Answer:

[tex]9p^2-16q^2[/tex]

[tex](3p)^{2} -(4p)^{2}[/tex]

[tex]\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}[/tex]

[tex]\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)[/tex]

[tex]=\left(3p+4q\right)\left(3p-4q\right)[/tex]

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hope it helps....

have a great day!!

Answer:

The smallest number is 10

Step-by-step explanation:

x+y=24---equation 1

x-y=¹/6×24=>x-y=4---equation 2

Add both equations

2x=28

x=14

put x=14 into equation 1

14+y=24

y=24-14=10

Answer:

There are 80 questions on the test

Step-by-step explanation:

I think this is right, but don't quote me on this.

Answer:

so if its actually 1000 and that map thing is 250

250 goes into 1000 4 times so

4cm

Hope This Helps!!!

Answer:

3, 5, 7

Step-by-step explanation:

Substitute n = 1, 2, 3 into the nth term rule

a₁ = 2(1) + 1 = 2 + 1 = 3

a₂ = 2(2) + 1 = 4 + 1 = 5

a₃ = 2(3) + 1 = 6 + 1 = 7

Answer:

3, 5, 7

Step-by-step explanation:

n = 1, 2, 3 into the nth term rule

a₁ = 2(1)+1=2+1=3

a2=2(2)+1=4+1=5

a3 = 2(3)+1=6+1=7

Answer:

y is 4

Step-by-step explanation:

x is 3

y is 4 coordinate is (3,4)

Answer:

4

Step-by-step explanation:

Answer:

10 friends can go to the amusement park

Step-by-step explanation:

214.25 = 6.75 + 20.75x

207.50 = 20.75x

x = 10 friends can go

Answer:

Step-by-step explanation:

You just need to sum up the values according to arc addition postulate:

Now we have to find,

The measure of arc AD according to the Arc Addition Postulate.

AD is the sum of the measures of the other two arcs. Then measure of AD is,

→ AC + CD

→ 35° + 45°

→ 80° (final answer)

Hence, the measure of arc AD is 80°.

Answer:

54°

Step-by-step explanation:

Here :-

Measure of 6 :-

Answer:

m<6 = m<2 = 54º

Step-by-step explanation:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162 / 18

x = 9

13x + 9

13(9) + 9

126

180 - 126

54

m<6 = m<2 = 54º

Answer:

d  || if its wrong cancel me lol <3

Step-by-step explanation:

Answer:

y = 7/5x + 7

Step-by-step explanation:

Answer:

15.52 ft

Step-by-step explanation:

the length of the rope can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√15² + 4²

= √225 + 16

=√ 241

= 15.52 ft

Answer:

the answer is b the square root of 160

Step-by-step explanation:

i did it on the assignment

Answer:

see explanation

Step-by-step explanation:

Angles on the circumference subtended on the same arc are equal

Angle at the centre is twice the angle at the circumference subtended on the same arc.

Then

∠ BAC = ∠ BDC = 29°

∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

Answer:

(i) - rectangular prism

(Ii) - triangular prism

(iii) - square pyramid

Step-by-step explanation: