The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 15 cm and the width is 12 cm, how fast is the area of the rectangle increasing?

Answer:

~10.8 (ft)

Step-by-step explanation:

Apply the Pythagorean theorem, you can work out the measure of diagonal.

[tex]Diagonal = \sqrt{9^{2}+6^{2} } =\sqrt{81 + 36} =\sqrt{117} =~10.8(ft)[/tex]

The measure of the diagonal of a rectangle is 10.8 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, a rectangle measures 9 feet by 6 feet.

Let the length of diagonal be x.

x²=9²+6²

x²=81+36

x²=117

x=√117

x=10.8 feet

Therefore, the measure of the diagonal of a rectangle is 10.8 feet.

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Answer:

The y-intercept of the line is 2

Step-by-step explanation:

You could try to find the slope of the line and then find the intercept with y axis by sloving b = y - ax

But here it seems easy enough once you see that the x values in the table increase by a factor of 8 and the y values in the table increase by a factor of 20.

(By the way, this is enough to give you the slope, because it is 8/20 ). But why bother?

Just extrapolate the table to the left, and you will find the y value where x = 0

x 0 8 16 24 32

y 2 22 44 64 84

So the y-intercept of the line is 2.

Extra:

The full equation of the line is:

y = 8/20x + 2

Answer:

(0,4)

Step-by-step explanation:

Answer:

66.67% probability that all selected components function properly

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the components are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Desired outcomes:

2 components which function properly, from a set of 5. So

[tex]D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]

Total outcomes:

2 components, from a set of 6. So

[tex]T = C_{6,2} = \frac{6!}{2!(6-2)!} = 15[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{10}{15} = 0.6667[/tex]

66.67% probability that all selected components function properly

Answer:

x = 5

Step-by-step explanation:

Since TV bisects (equally divides) EF hence <EKT = 90°

Also <EKT = 5x+65

So

5x+65 = 90

5x = 90-65

5x = 25

Dividing both sides by 5

x = 5

Answer:

Problem: 3x/5x + 5 ≤ 8 + 2x

Solution: x ≥ -15/7

Step-by-step explanation:

Example of this inequality is:

3x/5x + 5 ≤ 8 + 2x

3x/5x - 2x ≤ 8 - 5

(3x - 10x)/5 ≤ 3

-7x ≤ 15

x ≥ -15/7

Answer:

52

Step-by-step explanation:

24+28 = 52

52 - 24 = 28

Answer: D with the open circles at -10 and 10 with a line in between them.

Step-by-step explanation:

Since x has an absolute value sign around it this means that all the values will be positive which includes negative numbers.

Since the solution must be less than 10 we need all values under 10 which is 1-9.9 repeating. we can show the 9.9 repeating with an open circle on the value of 10. This also goes for the negative values for x as we can go up to -9.9 repeating because it will become positive.

The only graph that shows these values is D with the open circles at -10 and 10 with a line in between them.

Answer:

D

Step-by-step explanation:

Hope this helps

Answer:

volume= 5,184 cubic inches

Step-by-step explanation:

Step-by-step explanation:

To find the inverse we just switch f(x) and x so we get :

x = 2f(x) + 1

2f(x) = x - 1

h(x) = 1/2x - 1/2

Hope this helps!

Answer:

x = 2f(x) + 1

2f(x) = x - 1

h(x) = 1/2x - 1/2

Step-by-step explanation:

Answer:

1.  D) 75 inches

2. A)  27 square feet

Step-by-step explanation:

1.  You need to convert 6 feet to inches.  In one foot, there are 12 inches.  Multiply 6 by 12 to find the number of inches in 6 feet.  Add 3 inches to the product to find the total number of inches.

6 × 12 = 72

72 + 3 = 75

You will have 75 inches in total.

2.  Use the formula to solve.  You are given the base and the height already.  Simply plug in and solve.

A = 1/2BH

A = 1/2(6)(9)

A = 3(9)

A = 27 ft²

The area is 27 ft².

Answer:

Step-by-step explanation:

Answer:

About 0.642

Step-by-step explanation:

Answer:

The Sum of two number is 15: x + y = 15

One of the numbers is 12 times the other: x = 12y:

System of equations:

x + y = 15

x = 12y

Plug x = 12y into equation one(x + y = 15)

12y + y = 15

13y = 15

y = 15/3

y ≈  1.15

Now we know x = 12y

x = 12(15/13) = 180/13

x = 180/13

x ≈ 13.85

The biggest number is x = 180/13.

Solution,

radius=21 cm

Circumference of circle=2 pi r

=2*3.142*21

=131.964 cm

hope it helps

Good luck on your assignment

Solution,

42+7x+12x-8

Combine like terms,

= 7x+12x+42-8

Simplify

=19x+34

hope it helps

Good luck on your assignment

Answer:

36+19x

Step-by-step explanation:

Ok, first, combine like terms, so the two values with X.

42 + 7x + 12x – 8

42 +19x – 8

Now, we combine the two values that have no X

42+19x– 8  Imagine there is a plus sign in front of the 42 because it's positive.

So 42-8=36

36+19x

That's your solution, that's the most this can be simplified.

Answer:

a. lts diameter = 13.540550005146 cm

b. Its circumference​ = 42.538892421732 cm

Step-by-step explanation:

suppose A the area ; d the Diameter ; P the circumference and r the radius

A = πr²

P = d×r = 2πr

then

r² = A/π = 144÷π = 45.836623610466

then

→ r = √(45.836623610466) = 6.770275002573

d = 6.770275002573×2 = 13.540550005146

→ P = 13,.540550005146×π = 42.538892421732

Answer:

a) The observed proportion of wallets that were returned

  p = 0.45625

b) 95% of confidence intervals for Population proportion

 0.40168  , 0.51082)

c) The lower bound of the 95% confidence interval = 0.40168

d) The upper bound of the 95% confidence interval = 0.51082

Step-by-step explanation:

Step(i):-

a)

Given data the  researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them

Given sample size 'n' = 320

  Given data          'x ' = 146

Sample proportion

              [tex]p = \frac{x}{n}[/tex]

             [tex]p = \frac{x}{n} = \frac{146}{320} = 0.45625[/tex]

Step(ii):-

b) 95% of confidence intervals for Population proportion

Level of significance = 95% or 0.05%

[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

95% of confidence intervals for Population proportion are determined by

[tex](p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]

[tex](0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })[/tex]

(0.45625 - 0.05457 , 0.45625 + 0.05457)

(   0.40168  , 0.51082)

c) The lower bound of the 95% confidence interval = 0.40168

d) The upper bound of the 95% confidence interval = 0.51082

Answer:

140672

Step-by-step explanation:

formula for cone volume=pi*r^2*h*1/3

80^2*3.14*21=422016

422016*1/3

=140672

Answer:

The answer is A.

Step-by-step explanation:

First, recall the vertex form of a quadratic equation: [tex]f(x)=a(x-h)^2+k[/tex], where [tex]h[/tex] represents the horizontal change and [tex]k[/tex] represents the vertical change.

The original equation is [tex]g(x)=x^2[/tex], or, in other words, [tex]g(x)=1(x-0)^2+0[/tex].

We are told that the graph is shifted up 3 and right 1. Thus, both values are positive (right and up). Note that up 3 corresponds to a positive vertical change of 3 while right 1 represents a positive horizontal change of 1.

Thus, put these back into the equation in place of [tex]h[/tex] and [tex]k[/tex].

We have:

[tex]f(x)=1(x-(+1))^2+(+3)[/tex]

Or, simplified:

[tex]f(x)=(x-1)^2+3[/tex]

The answer is A.

Answer:

22+2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Expanded it is

24-4[tex]\sqrt{2}[/tex]+6

This simplified leads to 22+2[tex]\sqrt{2}[/tex]

Hope this helps

Answer:

1385.622

Step-by-step explanation:

A=πr2=π·212≈1385.622

hope this helped

Answer:

calculate the area of a square using the length * width formula, and then add the areas of the other triangles, of which you can calculate by using the base * height formula

Step-by-step explanation:

Answer:

Multiply the side length of the base by the slant height and divide by two. Then, multiply by 4. This will give you the lateral surface area of the pyramid.Step-by-step explanation:

Answer:

Length of segment PZ = 6 units

Step-by-step explanation:

As per theorem of intersecting chords in a circle ;

"Product of lengths of line segments on each chord are equal".

From the figure attached,

Chords XY and WZ are intersecting at point P in a circle.

By theorem;  XP × PY = WP × PZ

7 × 12 = 14 × PZ

PZ = [tex]\frac{84}{14}[/tex]

PZ = 6 units

Therefore, length of the segment PZ = 6 units.

Answer: Rectangular pyramid

Step-by-step explanation:

When you think about it, a pyramid has 3 faces that are triangular!

If you found this answer helpful, give it a five-star rating and a thanks! I would really appreciate it!

You can even give it a brainliest if you want! ;)

Answer:

6 ≤ b.

(6).

Step-by-step explanation:

So, we are given in the question that the amount that Myra wants to say is $500 at the end of her summer vacation and she has saved up to $350. Thus, it remain ($500 - $350 = $150) for completion.

Also, "She can earn $25 cutting a lawn in her neighborhood."

Therefore, the total amount of money she wants to save = a = 500. Then,

Total amount of money, a = 350 + 25b.

500 = 350 + 25b.

=> 500 ≤ 350 + 25b.

Note that the ' =' sign has changed to '≤' sign since she wants that amount(at least). Also, the question specified that she used inequality.

Hence, the amount remaining for it to complete is $150. Therefore;

150 ≤ 25b.

6 ≤ b.

Thus, Myra will have to mow at least 6 lawns

Answer:

6

Step-by-step explanation:

Took the quiz on edge!

Volume of the bottom rectangle:

12 x 4.5 x 5.5 = 297 cubic cm

Volume of triangle:

1/2 x 12 x 5 = 30 x 4.5 = 135 cubic cm

Total volume = 297 + 135 = 432 cubic cm

Answer:

  [-4, 9]

Step-by-step explanation:

The range is the vertical extent of the relation.

__

The minimum value of g is marked by the solid dot at (x, y) = (4, -4). That minimum is -4.

The maximum value of g is the peak at (x, y) = (-2, 9). That maximum is 9.

The function is continuous between these values, so the range includes all values between -4 and +9, inclusive.

  range: [-4, 9]

Answer:

Step-by-step explanation:

range: [-4, 9]

Answer: A

Step-by-step explanation:

First, the problem is g(f(x)). You would plug in f(x) wherever you see an x in g(x). To find the domain, you take the bottom function, and set it equal to 0.

[tex]\sqrt{x-2} =0[/tex]

When you solve that, you get x=2. You know your domain is x≥2, but there is as asymptote at x=11. That means the graph never reaches x=11, but gets very close. You find that by setting the entire equation equal to 0 and solve from there.

Answer:

56 and 42

Step-by-step explanation:

3:4

3 + 4 = 7

98 / 7 = 14

14 x 3 = 42

14 x 4 =  56

56 + 42 = 98

The dimensions of the pool can be categorized as below:

Length equals 28 feet

Width equals 21 feet

The perimeter of a rectangle is the outside length of the rectangle. To find the perimeter we add all the 4 sides of the rectangle.

Perimeter = 2(length) + 2 (width )

The ratio of the width to the length is 3:4. The width of the rectangle is 3x  

We know,

Length of the rectangle is 4xWidth =3x  

Length = 4x

Substitute it in the perimeter formula and solve for x.

Given that,

Perimeter of a rectangle = 98 feet

Perimeter = 2(length )+2(width)

98 = 2(4x)+2(3x)

98 = 8x+6x

98 = 14x

∵ x = 7

Now, we will find out the length and width of the pool.

Length = 4x

= 4(7)

= 28 ft.

and,

Width = 3x

= 3(7)

= 21 ft.

Thus, the length of the pool is 28 feet and the width of the pool is 21 feet

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