What is the side length of the smaller square in the diagram?

Answer:

I think is 50m.

Step-by-step explanation:

The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;

10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.

b. After 9 hours, the change in the water ls 15.75 inches

c. The change in the water level after 23 hours is 40.25 inches

A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?

The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;

Hours Draining  [tex]{}[/tex]           Change in Water Level (inches)

2   [tex]{}[/tex]                                   -35

9  [tex]{}[/tex]                                     ?

17  [tex]{}[/tex]                                    -29.75

23  [tex]{}[/tex]                                    ?

The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.

Let H represent the hours draining and let C represent the change in water level, we have;

C ∝ H

C = k·H
[tex]k = \dfrac{C}{H}[/tex]

Where;

k = The constant of proportionality, which is the rate at which the water level is changing per hour

a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;

The first pair of points = (2, -3.5)

[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]

The rate at which the water level is changing per hour is -1.75 inches per hour

The water level is decreasing at 1.75 inches per hour

b. The change in water level after 9 hours is found by using the formula;

C = k × H

Where, H = 9, we have;

Change in water level, C = -1.75 × 9 = -15.75

The change in water level after 9 hours is 15.75 inches

c. The change in water level after 23 hours is found by plugging in H = 23 as follows;

C = -1.75 × 23 = -40.25

The change in water level after 23 hours is -40.25 inches

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The value of the expression in the form of k² will be (T²/4π²)-h²).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is T² = 4π² (h² + k²). The expression for the value of k² will be calculated as,

T² = 4π² (h² + k²)

(h² + k²) = T² / 4π²

k² =  (T² / 4π²) - h²

Therefore, the value of the expression in the form of k² will be (T²/4π²)-h²).

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Answer:

(-4,-1) and (3,1), respectively.

Step-by-step explanation:

I am not quite sure if the question is necessarily asking for this, but the x and y values are switched to get the points of the inverse. (-1,-4) --> (-4,-1) and (1,3) --> (3,1). I hope that makes sense!

Answer:22.5

Step-by-step explanation:

Answer:

g(10)=-33, x=3

Step-by-step explanation:

g(x)=-4x+7. --------(1)

a) g(10)=?

since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x

g(10)=-4(10)+7

g(10)=-40+7

g(10)= -33

b.)find x if g(x)=-5. ---------(ii)

g(x)=-4x+7. we will place (I) in (ii)

g(x)=-5

-4x+7=-5

-4x=-5-7

-4x=-12

cancel the minus(-) sign in both sides

4x=12

x=12/4

x=3

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Answer:

9 km

Step-by-step explanation:

1/2 hr = 1800 seconds

3.7 m/s * 1800s    +   1.3 m/s * 1800 s  = 9000 m in 1 hr

   ( he walked AND ran this far)

Answer:

Here ,

sigma x=50+60+65+70+70+80+90=485

N=7

now,

Mean =sigma x÷N

=485÷7

=69.28

The coordinates of point N are (8.66, 21)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -

x =  [tex]$\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]$\frac{my_2+ny_1}{m+n}[/tex]

We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.

Assume the coordinates of point N are (a, b).

We can write -

9 =  (2b + 3)/5

4 = (-6 + 3a)/5

2b + 3 = 45

b = 21

3a - 6 = 20

3a = 26

a = 8.66

Therefore, the coordinates of point N are (8.66, 21)

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Answer:

x-intercept(s): (−5,0)

y-intercept(s): (0,−5)

Explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Im also in K12 so Ez Good Luck

Hope this helped!

The given formula can be written as 5F = 9C + 160.

A measurement unit is a unit to measure certain quantities. To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The conversion formula for °C into °F is 9C  = 5(F - 32)

The given formula can be written in the form of cF = aC + b as,

9C = 5(F - 32)

⇒ 5F = 9C + 160

Hence, the given formula can be written by making F as the subject as 5F = 9C + 160.

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Answer: 14=2x

Step-by-step explanation:

the answer is 14=2x7=14

The set of positive integers less than 1000 that are:

a)Divisible by 7 are 142

b)Divisible by 7 but not by 11 are 130

c)Divisible by both 7 and 11 are 12

d)Divisible by either 7 or 11 are 220

e)Divisible by exactly one of 7 and 11 are 220

f)Divisible by neither 7 nor 11 are 780

g)Having distinct digits are 576

f)Having distinct digits and even are 337

A whole number that is greater than zero is known as positive integer

a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.

Total terms: 994, divided by 7, plus (n-1)

There are 142 total terms below 1000 that are divisible by 7.

b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.

The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.

c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.

There are 12 total integers below 1000 that can be divided by 77.

d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.

The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.

Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.

e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.

f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.

Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),

=> Unique digits from 1 to 100 equal 90.

=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),

=> Unique digits from 101 to 200 are: 100 to 28, 72.

=> Unique numbers between 201 and 1000 = 72 x 8 = 576.

h)Different digits and even values equal to 337

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A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

So we know that the perimeter of rectangle is

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

As we know the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

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Student B has raised the least amount of money after walking for 7 miles.

A unit rate means a rate for one of something.

Given that, three students are participating in a walkathon,

Student A's money is represented by the equation y = 13x, where y is money raised for walking x miles.

Student B raised $36 money for 3 miles and Student C has raised  $52 and $65 money for 4 and 5 miles respectively.

Money raised by each of them for a mile =

Student A = $13

Student B = $12

Student C = $13

Money raised by them by walking 7 miles =

Student A = $13*7 = $91

Student B = $12*7 = $84

Student C = $13*7 = $91

Hence, Student B has raised the least amount of money after walking for 7 miles.

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Answer:  how

Step-by-step explanation: love

The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)

Given,

In the question:

Use distributive property to remove parenthesis.

-9(-3w + 3u - 4)

Now, According to the question:

First, we know:

What does parentheses mean distributive property?

The distributive property allows us to multiply all terms in a parentheses by a number outside of it. a(b +c) = ab + ac.

We have:

-9(-3w + 3u - 4)

Solve by Distributive Property :

-9(-3w + 3u - 4)

Open the bracket:

27w - 27u +36

Hence, The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)

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40 freezers could be shipped in the container.

What is a variable?

A variable is a quality that may be measured and take on several values.

We are given that

A railroad container can hold weight=42,000 pounds

Total number of ovens for ship=90

Weight of each oven=200 lbs

Weight of each freezer=600 pounds

We have to find the number of freezers that can be shipped in the container.

Let x be the number of freezers that can be shipped in the container.

According to the question,

42000=90(200)+600x

42000=18000+600x

600x=42000-18000=24000

x=24000/600=40

Hence, 40 freezers can be shipped in the container.

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Answer:

x = -12

Step-by-step explanation:

Get X all on one side

7x - 8x = 8x - 8x + 12

-x = 12

x = -12

Answer:

x = -12

Step-by-step explanation:

To solve this, you will need to get all of the variables on one side, and the 12 on the other. You will subtract 8x from both sides to get the equation -x = 12. You can then divide both sides by -1 to get the x alone, and thus you get x = -12.

Answer: 60 degrees

Step-by-step explanation: Because all sides are equilateral, and in an equilateral triangle all angles are 60 degrees, hope that helps.

The equation of the line that passes through the point (8, 6) and has a slope of 0 is  y = 8.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through the point (8, 6) and has a slope of 0.

Therefore,

m = 0

Hence, let's find the y-intercept using the (8, 6)

y = mx + b

6 = 0(8) + b

b = 8

Therefore, the equation is y = 8

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By applying the concept of rate of a reaction, The graph B never saturates because the enzyme is always in excess.

What is the enzyme substrate reaction?

The enzyme is called a catalyst as it has an active site where the substrate can bind and convert into the product. Here in the graph the enzyme is amylase, and its substrate is starch. When there is an excess of enzymes in the solution, they can convert it into a product till substrates are available. If the substrate runs out, the reaction will come stop.

As per the concept of rate of a reaction, The graph B never saturates as the enzyme in the reaction is always in excess. These excess enzymes present will convert the starch into simple glucose molecules. Hence, there will be no upper limit, as both are in abundance.

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The given two equations are Perpendicular to each other .

What is intersection of lines ?

 It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.

Here the equation of line is y=mx+b .

Where m = slope . then,

=> y = x-7 where here slope m1= 1 and

=> y = -x+3 where here slope m2 = -1 .

Here the m1= -m2

Hence the given two equations are Perpendicular to each other .

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Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.

The probability of drawing a second red in the event that this red is not changed is 9/15,

hence the probability of A is 10/16 * 9/15, or 0.375.

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