MATHEMATICS MIDDLE SCHOOL

The function f(x)=-(x-3)^2 +9 can be used to represent the area of a rectangle with the perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

Answers

Answer 1
Answer:

Maximum area of the rectangle is 9cm^(2)

Explanation:

Considering the dimensions to be in cm

f(x) = -(x-3)^(2) +9\nf(x) = -(x^(2) +9 - 6x)+9\nf(x) = -x^(2) +6x\nf'(x) = -2x+6\n-2x+6 = 0\n2x=6\nx=3cm\n\n

Putting the value of x = 3

Perimeter = 2(x+b)\n12 = 2(3+b)\n6 = 3+b\nb= 3cm

Area of rectangle = x X b\n = 3 X 3\n = 9cm^(2)

Therefore, maximum area of the rectangle is 9cm^(2)

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One-hundredth of 60 is what?

Answers

Answer:

40

Step-by-step explanation:

In the diagram, x/15=y/6. What ratio completes the equivalent proportion x/y=?

Answers

The equivalent proportion is x/y = 5/2.

What is a Ratio?

A ratio indicates the number of times one number contains another.

Given that, x/15 = y/6.

The equivalent proportion is:

x/15 = y/6

x/y = 15/6

x/y = 5/2

Hence, the equivalent proportion is x/y = 5/2.

To learn more about ratios, click here:

brainly.com/question/13419413

#SPJ2

Answer:

(5)/(2)

Step-by-step explanation:

given (x)/(15) = (y)/(6) ( cross- multiply )

15y = 6x ( divide both sides by y )

15 = (6x)/(y) ( divide both sides by 6 )

(x)/(y) = (15)/(6) = (5)/(2)

Mike observed that 75% of the students of a school liked skating. If 35 students of the school did not like skating, the number of students who liked skating was ______. (only put numeric values, no other symbols)

Answers

100-75=25% did not like
25%=35 students how about 75%
75 x 35 divided by 25=105 students 
105
100-75=25%
25%=35 students but you have 75%
so 75*30divided by 25=90 students

Determine whether y varies directly with x. If so, find the constant of variation and write the equation. yes; k = 1/4 and y = 1/4x

No

yes; k = 4 and x - 4y

yes; k = 4 and y - 4y

Answers

Answer:

Yes, 4 and  y = 4x

Step-by-step explanation:

By looking at the graphic you see it's a straight line, not a hyperbolic curve, not a logarithm curve either, not a curve at all in fact.  And the line is neither totally horizontal nor totally vertical... so there's a direct relation, a direct positive relation, since the greater the x-value, the greater the y-value.

Then we have to find the constant of variation, or the slope of the line.

We'll take two points on the line (1,4) and (0,0) and examine their variance of Y over their variance of X... that will give us the constant of variation:

slope = (4-0)/(1-0) = 4

So the constant of variation is 4.

Now that we have the slope, its easy to find the full equation:

y = mx + b where m is the slope (we have it) and b is the value for y when x = 0.

By looking at he graph, we see that when x = 0, y = 0 as well.

So, the equation is: y = 4x

LeBron has 6 yards of cable.he needs 15 feet of cable to install a stereo.does he have enough cable to install the stereo?explain your answer

Answers

PLEASE MARK BRAINLIEST!

Answer:

Yes!

Step-by-step explanation:

This is because 6 yards equals 18 feet. If there is 15 feet needed to install a stereo, and we have 18 feet of cable, we have MORE THAN ENOUGH cable to install the stereo. So yes, there is enough cable to install the stereo.

I hope this helps!

- sincerelynini

Answer:

Yes.

Step-by-step explanation:

There is 3 feet in every yard. So LeBron has 18ft of cable.

Least to greatest

1/2 0.4. 30%

Answers

1/2=50/100=0.5
0.4=0.4
30%=30/100=0.3

0.5,0.4,0.3 order
0.3,0.4,0.5

aka
30%, 0.4, 1/2
I would change all these to decimals. 1/2 is 0.5, 0.4, and 30% is 0.3
Therefore, least to greatest, it is 30%, 0.4, and 1/2. Good luck!
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