Which graph represents a proportional relationship?

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{h}{-3}~~,~~\stackrel{k}{4})\qquad \implies f(x) = a[x-(-3)]^2+4\implies f(x) = a(x+3)^2+4 \\\\\\ \textit{we know that} \begin{cases} x=0\\ f(x) = -5 \end{cases}\implies -5=a(0+3)^2+4\implies -5=9a+4 \\\\\\ -9=9a\implies \cfrac{-9}{9}=a\implies \boxed{-1=a}~\hfill \blacktriangleright f(x)=-(x+3)^2+4 \blacktriangleleft[/tex]

Answer:

twice the difference gives 2(difference). 7 = 14  20 = 40

Step-by-step explanation:

Answer:

x=11/17

Step-by-step explanation:

determine the defined range

11/x  17

11/x =17 then x is canceled out  

11=17x

17x=11 dividing both sides

x=11/17

Check the picture below.

Bearing in mind that the angle is not changing all the wihle, namely is constant

[tex]tan(32^o)=\cfrac{y}{x}\implies x = \cfrac{y}{tan(32^o)}\implies x = \cfrac{1}{tan(32^o)}y \\\\\\ \stackrel{\textit{taking the derivative on bot sides}}{\cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}\cfrac{dy}{dt}}\implies \cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}200\implies \cfrac{dx}{dt}\approx 320.07~\frac{km}{hr}[/tex]

Answer:

150

Step-by-step explanation:

The ration is 2/3 in this example means they are twice as many boys than girls. If boys = 2/3, than girls = 1/3.

So, to find the answer, you must multiply 75 by 2, which is 150.

You don't need this, but they are 75 + 150 = 225 boys and grils in grade 10.

Answer:

D.

y = 4(x − 3)^2 + 2

Step-by-step explanation:

A.    y = 4(x + 3)^2 + 2   = ( − 3 ,  2 )

B.    y = (x + 3)^2 + 2     = ( − 3 ,  2 )

C.    y = 19(x − 2)^2 + 3  = ( 2 ,  3 )

D.    y = 4(x − 3)^2 + 2   = ( 3 ,  2 )

[tex]10+y=5x+x^2~~~~.....(i)\\\\5x+y =1~~~....(ii)\\\\\text{From (i):}\\\\10+y = 5x +x ^2\\\\\\\implies y = 5x +x ^2 -10\\\\\text{Substitute y in equation (ii):}\\\\5x+5x+x^2-10=1\\\\\implies x^2 + 10x -11 =0\\\\\implies x^2 +11x -x -11=0\\\\\implies x(x+11) -(x+11) =0\\\\\implies (x-1)(x+11) =0\\\\\implies x =1 ~~ \text{or}~~ x = -11\\\\\text{Substitute x =~1 in equation (ii):}\\ \\5+y =1 \implies y =-4[/tex]

[tex]\\\text{Substitute}~ x =-11~ \text{in equation (ii):}\\\\\ 5(-11) + y = 1 \implies y = 1 +55 = 56 \\\\\text{Hence} (x,y) = (-11,56) ~~\text{and}~~ (x,y)=(1,-4)[/tex]

The lengths of the other two sides are 6 inches and 5 inches

Let b represent the base of the right triangle, h represent the height of the right triangle and x represent the hypotenuse.

Since the area of the triangle is 15 in², hence:

Area(A) = (1/2) * base * height

15 = (1/2)bh

bh = 30  

b = 30/h         (1)

Applying Pythagoras theorem also:

x² = b² + h²

(√61)² = b² + h²

61 = (30/h)² + h²

61 = 900/h² + h²

61h² = 900 + h⁴

h⁴ - 61h² + 900 = 0

h = -6, -5, 5, 6

Since the length cant be negative, hence h = 5 or h = 6

When h = 5; b = 30/5 = 6

When h = 6; b = 30/6 = 5

Therefore the lengths of the other two sides are 6 inches and 5 inches

Find out more at: https://brainly.com/question/2773823

9514 1404 393

Answer:

  (b)  6x −7y = −11

Step-by-step explanation:

Perhaps the easiest way to approach this is to look at the y-intercept. To find it, set the value of x to zero, and divide by the y-coefficient. The y-intercepts of these equations are ...

  a) 11/-7 = -1 4/7

  b) -11/-7 = 1 4/7 . . . . possible candidate

  c) 11/-6 = -1 5/6

  d) -13/-5 = 2 3/5

The only y-intercept that matches the graph is the one for equation ...

  6x -7y = -11

_____

You can use any of several other strategies to verify this choice:

1) Putting the given point values into the equation:

  for (-3, -1): 6(-3) -7(-1) = -18 +7 = -11 . . . . yes

  for (1/2, 2): 6(1/2) -7(2) = 3 -14 = -11 . . . . yes

__

2) Finding the equation from the given points.

  m = (y2 -y1)/(x2 -x1) = (2 -(-1))/(1//2 -(-3)) = 3/(3 1/2) = 6/7

Then the point-slope equation is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-1) = 6/7(x -(-3)) . . . . . substitute known values

  7y +7 = 6x +18 . . . . multiply by 7, simplify

  6x -7y = -11 . . . . . . . add -18 -7y to both sides

Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

In this problem:

The percentages associated with a positive test are:

Hence:

[tex]P(A) = 0.8(0.3) + 0.09(0.7) = 0.303[/tex]

The probability of both a positive test and the body attempting to reject the kidney is:

[tex]P(A \cap B) = 0.8(0.3) = 0.24[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{0.24}{0.303} = 0.7921[/tex]

0.7921 = 79.21% probability that the body is attempting to reject the kidney.

A similar problem is given at https://brainly.com/question/25553471

Answer: Varies

Step-by-step explanation:

It involves any that is not concerned with making a profit.

Answer:

x + 4 < 27

-4. -4

x > 24

Step-by-step explanation:

put lines under signs

Answer:

1/2

Step-by-step explanation:

b is directly proportional to h.

b = kh

take any (h, b) point

using (28, 14)

14 = k(28)

Divide both sides by 28

1/2 = k

1/2

Answer:

$ 1.94

Hope I helped

Answer: A. True.

Step-by-step explanation:

A relationship is linear when the points on a scatterplot follow a somewhat straight line pattern. This is the relationship that we will examine. Linear relationships can be either positive or negative. Positive relationships have points that incline upwards to the right. As x values increase, y values increase.

Answer:

The selling price cost 472.5

Step-by-step explanation:

Let's find the profit first.

To find that, let's turn 5% to decimal form.

5 % = 0.05

Then, lets multiply it to the initial price which is 450

450 * 0.05 = 22.5

So the profit costs 22.5

Now, let's add the profit to the initial cost to find the selling price

450 + 22.5 = 472.5

That's it.

Answer:

-30.28

Step-by-step explanation:

Answer:

[tex]y=5x[/tex]

Step-by-step explanation:

Insert the information into the point-slope formula to find slope-intercept form.

[tex]y-y_1=m(x-x_1)\\\\y-5=5(x-1)\\\\y-5=5x-5\\\\y=5x[/tex]

Answer:

range is { - 17, 1, 22 }

Step-by-step explanation:

Substitute the values from the domain (input) into f(x) for range

f(- 4) = 3(- 4) - 5 = - 12 - 5 = - 17

f(2) = 3(2) - 5 = 6 - 5 = 1

f(9) = 3(9) - 5 = 27 - 5 = 22

range is { - 17, 1, 22 }

Answer: If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 => Percentage decreased number = 0.8 × Initial value

Step-by-step explanation: Number 100 decreased by 20% (20 percent) of its value (percentage decrease) and calculated absolute change (actual difference)

Answer:

$2,100

Step-by-step explanation:

'regular' pay is 375/10 or $37.50 per hour

'time-and-a-half' would be 37.50 + 18.75 = $56.25 per hour

'double time' would be (2)37.50 = $75.00

35 hours in 2 weeks and 7 hours at 'double time' and 28 at 'time-and-a-half'

so:

(7)75 + (28)56.25 = 525 + 1575

Total overtime pay for 2-week period is $2,100

Answer:

D  [tex]\sqrt{x+4}[/tex]

Step-by-step explanation:

Answer:

5.5 hours

Step-by-step explanation:

time = distance/speed

t = 330/60

t = 5.5 hours

Answer:

7(x-y)

Step-by-step explanation:

difference of x and y=x-y

product of 7=7 times the expression

so,

Answer is 7(x-y)

Answer:

3%

Step-by-step explanation:

[tex] \frac{0.03}{1} \times 100[/tex]

0.03=3/100 So

[tex] \frac{3}{100} \div 1 \times 100[/tex]

=3%

Answer:

f¹(x) = x - 3

To find the inverse of a function, just "trade" and y and solve for the "new" y. The graph of the inverse is the reflection of the original function over the line y = x.

Rewrite the function f(x) = x + 3

as the equation y = x + 3

Trade x and y.

x = y + 3

Solve for the "new" y.

= y + 3

3 - 3

Subtract 3 from both sides

y = x= 3

The symbol for the inverse is f-¹(x)

f¹(x) = x - 3

Step-by-step explanation:

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[tex]f(x) = x -3 \\\\\text{Write f(x) as}~ y = x -3}\\\\\text{Now replace x and y,}\\\\x = y-3\\\\\text{Solve for y:}\\\\y = x+3 \\\\\implies f^{-1}(x) = x +3 ,~ \text{This is the inverse of given function.}[/tex]

Answer:

the median of 0 1 2 3 16 38 34 12 is 9.5