enter a formula using k to connect the two variables. y is proportional to 1/x

Step-by-step explanation:

To solve both questions you will have to use the Pythagoras theorem

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

c being the hypotenuse

so to find AB we say

[tex] {ap}^{2} = {pb}^{2} + {ab}^{2} [/tex]

To make AB the subject of the formula, we take PB over. Therefore:

[tex] {ab}^{2} = {ap}^{2} - {pb}^{2} [/tex]

now we just substitute

[tex] {ab}^{2} = {13}^{2} - {5}^{2} [/tex]

[tex] {ab}^{2} = 169 - 25[/tex]

[tex] {ab}^{2} = 144[/tex]

square root both sides of the equation

[tex]ab = 12[/tex]

We then use the same formula to find AQ(which is a hypotenuse)

[tex] {aq}^{2} = {ab}^{2} + {bq}^{2} [/tex]

[tex] {aq}^{2} = {12}^{2} + {9}^{2} [/tex]

[tex] {aq}^{2} = 144 + 81[/tex]

[tex] {aq}^{2} = 225[/tex]

square root both sides

[tex]aq = 15[/tex]

Answer: the answer is C

Step-by-step explanation: trust me took the final yesterday ‍♀️

Answer:

C) [tex]f(x)=(x-1)^\frac{1}{2}[/tex]

Step-by-step explanation:

The graph shows a radical function that starts at (0,1). This must mean that the original function had been translated to the right one unit. Therefore, [tex]f(x)=(x-1)^\frac{1}{2}[/tex] is correct.

Answer:

x-3=-x+3

2x=6

x=3 y=0

the solution is the intersection of those two lines!

Answer:

(-1,1)

Step-by-step explanation:

To find where both lines intersect, solve for x and y with substitution.

Equation 1.

-8x+3y=11

Equation 2.

y=3x+4

Substitute y from equation 2 into equation 1.

-8x+3(3x+4)=11

-8x+9x+12=11

x=-1

Now plug x into the second equation to solve for y.

y=3(-1)+4

y=-3+4

y=1

Both lines intersect at (-1,1)

Answer:

  (-1, 1)

Step-by-step explanation:

It's somewhat difficult to find the point of intersection when graphing these by hand, but a graphing calculator can show it easily.

The lines intersect at (-1, 1).

__

You are given an expression for y, which makes it easy to use substitution as a solution method. Using the second equation to substitute for y in the first equation, we get ...

  -8x +3(3x +4) = 11

  x +12 = 11 . . . . simplify

  x = -1 . . . . . . . subtract 12

Substituting back into the second equation, we find y to be ...

  y = 3(-1) +4 = 1

The lines intersect at (x, y) = (-1, 1).

_____

Additional comment

The slopes are 8/3 and 3. When hand-drawn lines have nearly the same slope, it is difficult to tell exactly where they intersect. Of course, a graphing calculator does not have the problem of finite line width and an apparent long region of intersection. It can pinpoint the intersection exactly.

Of course, "substitution" is not the only way this system of equations can be solved. However, for this system, it is one of the easiest when doing the solution by hand.

The selling price of the item is $835.49

The given parameters are:

Original cost = $784.50

Markup = 6.5%

The selling price is calculated as

Selling price = Original cost * (1 + Markup)

So, we have:

Selling price =$784.50 * (1 + 6.5%)

Evaluate the expression

Selling price =$835.49

Hence, the selling price of the item is $835.49

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Answer:

option C can be used.

Step-by-step explanation:

hope this helps you.

Answer:

Equation in cubed form is x^3+7x^2+7x-15

Step-by-step explanation:

Answer:

-8/7

Step-by-step explanation:

First, find the slope of line c.

(x1, y1) = (9, 10)

(x2, y2) = (1, 3)

The slope formula is:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Solve for the slope using the given values:

[tex]m=\frac{3-10}{1-9}\\\\m=\frac{-7}{-8}\\\\m=\frac{7}{8}[/tex]

The slope of line c is 7/8. To find the slope perpendicular to it, you need to find the negative reciprocal of that number. An example of that would be 2 and -1/2. Basically, flip the fraction and the +/-.

In this case, the negative reciprocal of 7/8 is -8/7. The image below doesn't account for the y-intercept, but it does show that the slopes are perpendicular.

Answer:

slope = - [tex]\frac{8}{7}[/tex]

Step-by-step explanation:

Calculate the slope m of line c using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 10 ) and (x₂, y₂ ) = (1, 3 )

m = [tex]\frac{3-10}{1-9}[/tex] = [tex]\frac{-7}{-8}[/tex] = [tex]\frac{7}{8}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{7}{8} }[/tex] = - [tex]\frac{8}{7}[/tex] ← slope of line d

h(x)=3x−3, find h(3)

h(3)= 3(3)−3

= 9-3

= 6

Answer:

f(0) = 0

f(22) = 11

f(-22) = -11

Step-by-step explanation:

Substitute the values for x.

[tex]1.)~f(0)=1/2(0)=0\\\\2.)~f(22)=1/2(22)=11\\\\3.)~f(-22)=1/2(-22)=-11[/tex]

Answer:

48350.06

Step-by-step explanation:

nvm I'm wrong is there a way to delete answer

Use the simple interest formula:

Total = start value x( 1+ (interest rate x time In years))

Total = 48350 x (1+(0.03 x 2))

Total = 48350 x 1.06)

Total = $51,251

Answer:

I think it's 25 meters.

Hope that helps. x

Answer:

I think it will be 25 meters

Answer:

The diagonals are congruent.

Step-by-step explanation:

Answer:

1) The diagonals are congruent.

3) The opposite angles are congruent.

4) The opposite sides are parallel.

Step-by-step explanation:Two pairs of opposite sides are congruent. The diagonals are perpendicular to each other. 4 In parallelogram QRST, diagonal is drawn. Which statement must always be true?

if it does not work sorry

Answer:

-4y²- 16y

Step-by-step explanation:

   2y(-2y - 8)

   2y (-2y) + 2y (-8)  Distributive

      -4y² - 16y                Multiply (+)(-) = -   and (y)(y) = y²

Answer:

1/3 ^ 1/3 * 1/3 = (1/3)^3 = 1/27

Answer:

In total she works 21 hours and for the equation its gn=g+n

Step-by-step explanation:

got the equation i just put gn but that can be replaced with 21 since g and n both represent the number of hours fawzia works

If the pair of points (5, 6) and (10, y) lie on a line with slope 4/5, then the value of y is 10

The slope m of the line passing through the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is calculated as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For the line passing through points (5, 6) and (10, y)

[tex]x_1=5, y_1=6, x_2=10, y_2=y[/tex]

The slope, m = 4/5

Substitute these value into the slope formula and solve for y

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\\frac{4}{5}=\frac{y-6}{10-5} \\\\\frac{4}{5}=\frac{y-6}{5}[/tex]

Cross  multiply:

4(5)  =  5(y-6)

4   =  y  -  6

Collect like terms

y  =  4  +  6

y  =  10

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Answer:

C

Step-by-step explanation:

Answer:

2.5 ×  [tex]10^{-5}[/tex]

Step-by-step explanation:

I hope this helps!!

Answer: 24 of 80 is 30%

Step-by-step explanation:

24 of 80 can be written as: 24/80

To find percentage, we need to find an equivalent fraction with denominator 100. multiply both numerator & denominator by 100: 24/80 x 100/100

= (24x100 / 80 ) x 1/10 = 30/100

Therefore, the answer is 30%

If you are using a calculator, simply enter 24÷80×100 which will give you 30 as the answer.

Answer:

4.8 $

Step-by-step explanation:

5 cans = 3 $

then:

1 can  = 0.6 $ because 0.6*5 = 3

Now 0.6*8 cans = 4.8 $

Answer:

  $4.80

Step-by-step explanation:

The cost will be proportional to the number of cans. If the number of cans goes up by a factor of 8/5, so does the cost.

  cost of 8 = (8/5)($3.00) = $4.80

Answer:

10m

Step-by-step explanation:

Answer:

3 I believe im not 100% sure tho sorry if its wrong

Answer:

There is 7 students in each group

Step-by-step explanation:

So it's basically easy math 42 divided by 6 equals 7 :)

Hopes This Helps :)

The number of basket balls donated is; 28 basket balls

We are told that;

Ratio of basket balls to soccer balls = 7:6

Now, the number of soccer balls donated was 24.

This, means fraction of the total number of balls x for soccer balls was; [6/(7 + 6)]x

Thus;

[6/(7 + 6)]x = 24

6x/13 = 24

6x = 24 × 13

6x = 312

x = 312/6

x = 52 balls

Now, since total balls are 52 and soccer balls are 24, then;

Number of basketballs = 52 - 24

Number of basketballs = 28 basketballs

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Answer:

e

Step-by-step explanation:

e

Given to us:

[tex](a)\ x^2+3x-2;\ -x^2-3x+2\\\\(b)\ -y^7-10;\ -y^7+10\\\\(c)\ 6z^5+6z^5-6z^4;\ (-6z^5)-(6z^5)+6z^4;\\\\(d)\ x-1;\ -x+1\\\\(e)\ (-5x^2) + (-2x) + (-10);\ 5x^2 - 2x + 10[/tex]

Additive inverse means changing the sign of the number and adding it to the original number to get 0(zero) as our answer.

(a)

[tex]x^2+3x-2;\ -x^2-3x+2)\\x^2+3x-2 +( -x^2-3x+2)\\[/tex] on solving this we will get zero.

hence, this is an additive inverse.

(b)

[tex]-y^7-10;\ -y^7+10\\-y^7-10+( -y^7+10)[/tex]  on solving this we will not be getting zero.

hence, this is not an additive inverse.

(c)

[tex]6z^5+6z^5-6z^4;\ (-6z^5)-(6z^5)+6z^4,\\\\6z^5+6z^5-6z^4+[ (-6z^5)-(6z^5)+6z^4}[/tex]  on solving this we will get zero.

hence, this is an additive inverse.

(d)

[tex]x-1;\ -x+1\\x-1+( -x+1)[/tex]    on solving this we will get zero.

hence, this is an additive inverse.

(e)

[tex]-5x^2 + -2x -10;\ 5x^2 (- 2x) + 10\\-5x^2 + -2x -10+ 5x^2 (- 2x) + 10[/tex]  on solving this we will not be getting zero.

hence, this is not an additive inverse.

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