The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch.

From the given coordinates, we can say that the Midpoint of AC = a/2, b/2 and the Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

From the given image, we see that the coordinates of parallelogram ABCD are;

A (0, 0)

B (a, 0)

C (a , b)

D (0, b)

Thus;

1) The coordinates of the midpoint of AC are;

Midpoint of AC = (0 + a)/2, (0 + b)/2

Midpoint of AC = a/2, b/2

2) The coordinates of the midpoint of BD are;

Midpoint of BD = (a + 0)/2, (0 + b)/2

Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

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Answer:

B)

Step-by-step explanation:

8 is even number which uses each of the digits exactly once.

The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

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Answer: r=2

Step-by-step explanation:

We can use the given 2 points to find slope. Since we are given the slope, we can plug it into the formula and solve for r.

\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =2\)                                        [plug in values]

\(\frac{12-r}{-6-(-11)} =2\)                                   [combine like terms]

\(\frac{12-r}{5} =2\)                                          [multiply both sides by 5]

\(12-r=10\)                                      [subtract both sides by 12]

\(-r=-2\)                                          [divide both sides by -1]

\(r=2\)

The total number of boxes is the sum of all boxes each day

The total number of boxes he filled in the five days is \(23 \frac 18\)

The box each day is given as:

So, the total number of boxes is:

\(Total = 4\frac 78 + 5\frac 34 + 4\frac 72 + 4\frac 38 + \frac 58\)

Add the fractions

\(Total = 23 \frac 18\)

Hence, the total number of boxes he filled in the five days is \(23 \frac 18\)

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The sοlutiοn οf the system οf equatiοn is x = 0 and y = 7/3.

If there is nο sοlutiοn tο a system οf equatiοns, it is incοnsistent system; οtherwise, there must be at least οne sοlutiοn. If a set οf equatiοns has infinitely many sοlutiοns, it is dependent.

Every οne οf the equatiοns in a system οf equatiοns must have a sοlutiοn in οrder fοr the system tο be cοnsistent. This demοnstrates that a set οf values fοr the variables may simultaneοusly satisfy all οf the system's equatiοns and shοw that they are nοt mutually exclusive.

There is nο sοlutiοn tο an equatiοn system that satisfies all οf the equatiοns in the system. This indicates that nο cοmbinatiοn οf values fοr the variables can cοncurrently satisfy all οf the system's equatiοns since they are incοmpatible.

The given equatiοns are:

y = 2/3x + 7/3

-4x+6y=14

Substituting the value of y in the second equation:

-4x + 6y = 14

-4x + 6(2/3x + 7/3) = 14

-2x + 4x + 14 = 14

2x = 0

x = 0

Substitute the value of x = 0 we have:

y = 2/3(0) + 7/3

y = 7/3

Hence, the solution of the system of equation is x = 0 and y = 7/3.

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Complete question:

Given system of equations y = 2/3x + 7/3 and -4x + 6y = 14

Find the value of x and y.

Answer: The printer costs 310 and the computer costs 930.

Step-by-step explanation:

p = printer

c = computer

p + c = 1240 <- their combined total is 1240

c = 3p <- a computer costs 3 times the amount of a printer

p + 3p = 1240 <- substitute c for 3p

4p = 1240

p = 310 <- cost of printer

c = 3*310 <- substitute into the 2nd equation

c = 930

930 + 310 = 1240 <- double check

Answer

F.More than 5% of the children chose “other” as the favorite type of cereal.

Step-by-step explanation:

The answer is F

Answer:The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. Then the correct option is A.

What is the area of the parallelogram?

The vertices of the parallelogram are (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄).

Then the area of the parallelogram will be

Area = 1/2 [(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)]

(x₁, y₁) ⇒ (0, 2)

(x₂, y₂) ⇒ (2, 6)

(x₃, y₃) ⇒ (4, 6)

(x₄, y₄) ⇒ (4, 0)

Then the area of parallelogram 1 will be

A₁ = 1/2 [(0 x 6 + 2 x 6 + 4 x 0 + 4 x 2) – (2 x 2 + 6 x 4 + 6 x 4 + 0 x 0)]

A₁ = 16 square units

(x₁, y₁) ⇒ (2, 0)

(x₂, y₂) ⇒ (4, -6)

(x₃, y₃) ⇒ (2, -6)

(x₄, y₄) ⇒ (0, -2)

Then the area of parallelogram 2 will be

A₂ = 1/2 [(2 x -6 + 4 x -6 + 2 x -2 + 0 x 0) – (0 x 4 + -6 x 2 + -6 x 0 + -2 x 2)]

A₂ = 12 square units

The difference of area will be

A₁ - A₂ = 16 – 12

A₁ - A₂ = 4 square units

Then the correct option is A.

Step-by-step explanation:

Based on the image given, the area of parallelogram 1 is option A: 4 square units greater than the area of parallelogram 2.

To know the problem, one need the calculate the area of all of the parallelogram. So it will be:

Area of first Parallelogram (lets call it P-1) ,

Area of P-1 = Area of the red-figure - Area ΔA - Area ΔB - Area ΔC - Area ΔD

= (6 x 6) - (0.5 x 4 x 2) - (0.5 x 2 x 4)- (0.5 x 4 x 2) - (0.5 x 2 x 4)

= 36 - 4 - 4 - 4 - 4

= 20 units²

Area of Parallelogram 2 (lets call it P-2) ,

Area of P-2  = Area of the Blue-figure - Area ΔP - Area ΔQ - Area ΔR - Area ΔS

(8 x 4) - (0.5 x 2 x 2) - (0.5 x 6 x 2) - (0.5 x 2 x 2) - (0.5 x 6 x 2)

= 32 - 2 - 6 - 2 - 6

= 16 units²

The differences that is seen in the area of the parallelogram are:

= Area of P-1 - Area of P-2

= 20 - 16

= 4 units²

So, the area of parallelogram 1 is option A: 4 square units greater than the area of parallelogram 2.

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Answer:

x²-3x+2=0

x²-2x-x+2=0

(x²-2x)(-x+2)=0

x(x-2)-1(x-2)=0

(x-2)(x-1)=0

x-2=0 or x-1=0

x=2 or x=1

Answer: x²-x+6

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). Since we are given the values of f(x) and g(x), we can directly subtract them.

x²+1+(5-x)                     [distribute +1]

x²+1+5-x                      [combine like terms]

x²-x+6

Answer:

\(\huge\boxed{(f+g)(x) = x^2 - x+ 6}\)

Step-by-step explanation:

\(\sf f(x) = x^2 + 1\\g(x) = 5-x\)

Adding both functions

\(\sf (f+g)(x) = x^2 + 1+ 5 - x\\(f+g)(x) = x^2 - x+ 6\)

9514 1404 393

Answer:

  40

Step-by-step explanation:

If the number of questions on the test is Q, then we have ...

  35% × Q = 14

Dividing by the coefficient of Q gives ...

  Q = 14/0.35 = 40

There are 40 questions on the test.

Answer:

Yesthe data table and the statment mean the same thing:)

Step-by-step explanation:

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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His bottom line was a gain from selling and 3% commission is $257.50.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The cost price of 200 shares of BUI is (19.50×200) = $3900.

The selling price of 200 shares of BUI is (20.75×200) = $4150.

The net gain is (4150 - 3900) = $250 and with 3% commission it is,

= (103/100)×250.

= $257.50.

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Answer:x=5

Step-by-step explanation:

2x-4=6 Then you at 4 to both sides

2x=10 Divide

x=5

For this equation you simply have to graph it.

First, you have to remember that these equations follow a formula: y=mx+b. m is the slope of you line and b is the y-intercept.

Next, you need to graph it. First, graph your b, in this case 2. You would go up 2 on you graph (graph (0,2)). Then, you would graph your slope which is 3.

Now, remember that slope equals y/x, so think of the number 3 being like 3/1. You would start at (0,2) and go up 3 points in the graph, then over 1 point (graph where you end up). You repeat that from each new point you make until you have enough points to create a straight line.

Hope this helps a bit,

Answer:

(6, 6)

Step-by-step explanation:

The formula to find midpoint is (xm, ym) = (x1+x2)/2, (y1+y2)/2

In this case, x1= 9

x2= 3

y1= 5

and y2= 7

so, (xm, ym) = (9+3)/2, (5+7)/2

which can be simplified to

(xm, ym)= 12/2, 12/2

which equals (xm, ym) = 6,6

so the x value of the midpoint is 6 and the y value of the midpoint is 6

which makes the midpoint (6,6)

By using division, it can be concluded that

Number of math problem she can be able to complete within given time is  \(24 \div \frac{2}{3}\)

This is the required expression

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a word problem on division

Zareen has 24 minutes to work on her math homework

Fraction of time taken to do each sum =\(\frac{2}{3}\)

Number of math problem she can be able to complete within given time is

\(24 \div \frac{2}{3}\)

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Answer:

89

Step-by-step explanation:

Given:

Combine weight of two cats, Zeus and Athena = 13 pounds

Zeus weighs 5 pounds less than Athena.

To find:

The weight of Athena.

Solution:

Let x pounds be the weight of Athena.

Zeus weighs 5 pounds less than Athena.

Weight of Zeus = x - 5 pounds

Combine weight of two cats, Zeus and Athena = 13 pounds

\(x+(x-5)=13\)

\(2x-5=13\)

Add 5 on both sides.

\(2x=13+5\)

\(2x=18\)

Divide both sides by 2.

\(x=\dfrac{18}{2}\)

\(x=9\)

Therefore, the weight of Athena is 9 pounds.

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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The equation shows that the number of toys that must be bought for them to have equal profit will be 212 toys.

From the information, it should be noted that the equation that can be used to represent the information about Jaclyn company will be:

= 2125 + (49.99 × x)

= 2125 + 49.99x

The equation that can be used to represent the information about Richie company will be:

= (39.95 × x)

= 39.95x

Therefore, we will equate both equations:

2125 + 49.99x = 39.95x

49.99x - 39.95x =2125

10.04x = 2125

x = 212

Therefore, the number of toys that must be bought for them to have equal profit will be 212 toys.

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Answer:

43!

Step-by-step explanation:

i added it up

Answer:

Step-by-step explanation:

= 45+ 15

=60

The first step is replacing the given trigonometric functions by simpler ones and then taking the product of the denominators.

Here we have the expression:

\(\frac{tan(x)}{1 + sec(x)}\)

Remember that:

\(tan(x) = \frac{sin(x)}{cos(x)}\\ \\sec(x) = \frac{1}{cos(x)}\)

Replacing that would be the "step zero", we can write:

\(\frac{tan(x)}{1 + sec(x)} = tan(x)*\frac{1}{1 + sec(x)} = \frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} }\)

The first step to simplify this, is taking the product between the denominators:

\(\frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} } = sin(x)*\frac{1}{cos(x) + \frac{cos(x)} {cos(x)} } = \frac{sin(x)}{cos(x) + 1}\)

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Answer:

tanx(1-secx)/(1+secx)(1-secx)

Step-by-step explanation:

aP E

Answer:

Derivative of y=(x⁴-2x³+5x²-4)³

Step-by-step explanation: