Y varies directly with the square of X and when Y= 80, X=4

Answer:

-3 x - 6 = -9

Step-by-step explanation:

s = side length of square

4s = perimeter of square

L = length of rectangle

W = width of rectangle

P = 2L+2W = perimeter of rectangle

4s = 2L+2W .... since we want the perimeters the same

4s = 2(L+W)

s = 0.5(L+W)

s^2 = (0.5(L+W))^2 ... square both sides

s^2 = 0.25(L+W)^2

The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.

-----------------------------------

The area of the rectangle is LW

Let's subtract this from the area of the square and see what we get

A = area of square = s^2

B = area of rectangle = LW

C = difference in area

C = A - B

C = s^2 - LW

C = 0.25(L+W)^2 - LW

C = 0.25(L^2+2LW+W^2) - LW

C = 0.25L^2+0.5LW+0.25W^2-LW

C = 0.25L^2-0.5LW+0.25W^2

C = 0.25(L^2-2LW+W^2)

C = 0.25(L-W)^2

Regardless of what we pick for L and W, the expression (L-W)^2 is always positive. Squaring a negative number leads to a positive result.

So C is always positive as long as [tex]L \ne W[/tex]

If C > 0, and C = A - B, then

C > 0

A-B > 0 .... replace C with A-B

A > B .... add B to both sides

This shows the square area is always larger than the rectangle.

Again this only works if L and W are different values. If L = W, then the argument falls apart because the rectangle becomes the square.

We make [tex]L \ne W[/tex] to have a nonsquare rectangle.

Answer:

p[

Step-by-step explanation:

p[

Answer:

p = (200 + 7.5t) psi

Step-by-step explanation:

The initial pressure inside a closed container is 200 psi. Since the container is closed, the pressure inside it can not be less than 200 psi.

The pressure increases 7.5 psi with a degree rise in temperature (t) = 7.5t

so that;

p = 200 + 7.5t

  = (200 + 7.5t) psi

If the temperature increases by [tex]1^{o}[/tex] F, then;

p = 200 + 7.5(1)

  = 200 + 7.5

  = 207.5 psi

If the temperature increases by [tex]10^{o}[/tex] F, then;

p = 200 + 7.5(10)

  = 200 + 75

  = 275 psi

Answer:

Step-by-step explanation:

432 ÷ 6 = 72

8 = 1% of 800

8 x 9 = 72 = 9%

Step-by-step explanation:

I = P×r%×t

432 = 800 × r/100 × 6

432 = 4800 × r/100

[tex]r = \frac{432 \times 100}{4800} [/tex]

r = 9%

By completing squares we will see that the solutions are:

[tex]x =\pm \sqrt{35} + 8[/tex]

Here we have the quadratic equation:

[tex]x^2 - 16x + 50 = 21[/tex]

We can rewrite it as:

[tex]x^2 - 2*8*x + 50 - 21 = 0\\\\x^2 - 2*8*x + 29= 0[/tex]

Then we must have a 8² term to complete squares, then we need to add and subtract 35.

[tex]x^2 - 2*8*x + 29 +35 - 35= 0\\\\(x - 8)^2 - 35 = 0\\\\(x - 8)^2 = 35[/tex]

Now we can solve this:

[tex]x =\pm \sqrt{35} + 8[/tex]

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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Answer:

y = 1.5m

Step-by-step explanation:

Since we are finding the length after a certain number per month, that means we will be multiplying.

1.5 for EVERY month so it would look like

_ = 1.5m

We can replace the blank with the variable y.

y = 1.5m

Hope that helps and have a great day!

Answer:

[tex]y=\frac{1}{2}x+4[/tex]

Step-by-step explanation:

Find the slope of the line first using the slope formula:

Substitute the two given points into this formula.

Now that you have a slope and a point that the line passes through, you can use the point-slope formula to find the equation of the line.

Point-slope formula:

Substitute m = 1/2 for the slope and one of the points; I'm going to use (2, 5).

Simplify the equation so it's easier to read.

Distribute 1/2 inside the parentheses.

Add 5 both sides of the equation.

Answer:

The slope is the change in y over the change in x.

(7-5) / (6-2) = 2 / 4 = 1 / 2

In y = mx + b, we know y, m, and x. Now solve for b:

Let's use the point (2, 5).

5 = (1/2)(2) + b

5= 1 + b

b = 4

Now put it together:

y = (1/2)x + 4

Step-by-step explanation:

Answer:

792

Step-by-step explanation:

Sorry if im wrong :)

Answer:

$216

Step by step

Explanation:

First we subtract  $ 20 from  $ 84  giving us a total of  $ 64 and when we add that to  $ 152  we get  $ 216

.

Answer:

-60

Step-by-step explanation:

Using it's concept, it is found that the vertex of the quadratic function is given by:

B (800, 10).

It is the point in which the parabola changes from increasing to decreasing, or vice versa, that is, the point in which it turns.

In this problem, it turns at x = 10 and y = 800, hence option A is correct.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

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Answer:

Step-by-step explanation:

Answer:

No, The graph does not represent two proportional quantities, because the line does not passes through the origin point (0, 0)

Step-by-step explanation:

To solve the question graphically, we will use the ordered pairs on the table

→  x  →  y  ⇒  ordered pair

→  1  →  3  ⇒  (1, 3)

→  7  →  1  ⇒  (7, 1)

→  4  →  2 ⇒  (4, 2)

Plot the points

→ Look at the attached graph down

∵ The line does not cut the y-axis at the origin point (0, 0)

→ That means the equation of the line can not be in the form y = k x

∴ The line does not represent a proportional equation

∴ The number of people and the number of hours are not proportion

Answer:

The Left side (0) is greater then the right side (-15)

Step-by-step explanation:

(x - 3) is greater than -3(3+2)

Given:

The amount of fuel remaining in a gas grill is a function of the number of hours.

[tex]F(h)=100-2h[/tex]

To find:

The domain for this situation.

Solution:

Domain is the set of input values.

The amount of fuel remaining in a gas grill F(h) is

[tex]F(h)=100-2h[/tex]

where, h is the number of hours.

Here, domain is the set of all possible values of h.

We know that, time and remaining fuel cannot be negative. So,

[tex]h\geq 0[/tex]      ...(i)

[tex]F(h)\geq 0[/tex]

[tex]100-2h\geq 0[/tex]

[tex]100\geq 2h[/tex]

[tex]50\geq h[/tex]       ...(ii)

Using (i) and (ii), we get

[tex]0\leq h\leq 50[/tex]

Therefore, the domain of the given function is [tex]0\leq h\leq 50[/tex].

Answer:116

Step-by-step explanation:

By definition, a rhombus will have equal opposite angles.

Also by definition, the two angles on the same side of a rhombus are supplementary, or add up to 180 degrees.

Using this, we can make the equation 2c-12+c=180, 3c-12=180, 3c=192, and c =64

Now that we have found out c is 64, we plug it into the angle 2c-12 to get

2*64-12=116.

So again by definition, angle J will be 116 degrees since its an opposite angle.

Answer: your picture doesnt have all the options for the answer but the first two are incorrect. The correct one would have both little dots filled in with black

Step-by-step explanation:

Answer: 3 ≤ x ≤ 7

Step-by-step explanation:

The number line will have a filled in circle at 3 and a filled in circle at 7.

A filled in circle indicates that the number IS a solution.

An open circle indicates that the number is NOT a solution.

Hope this helps!

Answer:

Diet

Step-by-step explanation:

Health & fitness level has multiple factors. Some internal choice factors, some externally ascribed factors. Eg(s) - Diet, Excercise & Heredity, pollution respectively.

In my opinion, biggest factor affecting health is : Diet. As, it can affects health positively & negatively, by major extent. It can also help overcoming other health detrimental factors - eg lack of excercise, heredity issues, pollution related issues etc.

Answer:

y=3/2x+15

Step-by-step explanation:

Answer:

y=3/2+15

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x ( 4x - 5 ) + 3

12x^2 - 15x + 3

12 × 3^2 - 15 × 3 + 3

12 × 9 - 45 + 3

= 108 - 45 + 3

= 66

Hope this helps

plz mark as brainliest!!!!!!

Answer:

50 dollars an hour

Step-by-step explanation:

Answer:

19.04

Step-by-step explanation:

convert 170% into decimal form number:

1.7

Then multiply by 11.2:

1.7 × 11.2 = 19.04

Pls consider marking my answer as Brainliest! It would mean a lot!

Answer:

B=3

Step-by-step explanation:

Answer:

Range: [tex]y\in[-4,0)\cup[2,+\infty)[/tex]

Step-by-step explanation:

Range of a Function

Given a real function f(x), the Range of f is the set of all the values the function can take when x varies within the domain of f.

If we have the graph of the function, a practical rule can be used to find the Range. Imagine a horizontal rule moving from minus infinity to plus infinity. If that rule touches the graph of the function, the vertical height or y-value belongs to the range.

Consider the function provided in the image. If our horizontal rule comes from minus infinity, it won't touch the graph until it reaches the value y=-4. Note the endpoint has a filled dot, meaning the point belongs to the function. The range starts from -4.

Going up in values of y, we touch the function until y=0. But that endpoint is marked with an empty dot, so that point does not belong to the function.

The first interval of the range is [-4,0)

Moving up the rule, we touch the function again when y=2 (included) and we note the function continues to go up to plus infinity (signaled with the arrow). Thus, the second interval is [2,+∞).

The range of f is the union of both intervals:

Range: [tex]y\in[-4,0)\cup[2,+\infty)[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Uh- I cant ;w;

Step-by-step explanation:

Answer:

yes I can if you still want one

Step-by-step explanation:

Answer:

the equation is x=-3

Step-by-step explanation:

no matter what, the x values are the same, if you have the same values in the same line, it is most likey a vertical line

x-intercept: 4

y-intercept: 20

Answer:

Step-by-step explanation:

x-intercept: 4

y-intercept: 20

Answer:

C

Step-by-step explanation:

2-(p*6)

minus=the difference of

(p*6)=p times 6

Fully written out: The difference of two and p times six

Answer:

9/5

Step-by-step explanation:

3/5 ÷ 1/3

9/5