a rectangle has an area of 240 square inches and a length which is six inches more than three times the width. find the length and the width of the rectangle.

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

⇒To check if the given point (2,-8) is the solution to the system you should have a general knowledge that 2 is the input that is represented by variable x and -8 is the output variable represented by letter y.

⇒Now to check if the point is a solution we will have to check for both cases  ....y<x-1 and .....y>-x+2

x=2 and y=-8 in the system y< x-1

LHS=-8

RHS=(2)-1

RHS=1

-8<1

The result is true for the first inequality

for the second system inequality

x=2 and y=-8

LHS=-8

RHS=-(2)+2

RHS=-2+2

RHS=0

-8<0 but in the inequality it is saying that -8>0 which is not true but False

⇒As a conclusion point (2,-8) is not a solution to the system as it does not apply to both the conditions.

⇒The answer is no.

Answer:

I think it would be a

Step-by-step explanation:

Im really srry if im wrong but I hope this helped! also pls correct me if im wrong ty!

Answer:

-800/100 and 80 ÷ (–10)

Step-by-step explanation:

I did the test and I got 100%

The true statement is that Jana has completed more than 75%

To determine the fraction of Jana's homework that she has completed, we need to add 1/4 and 2/3.

However, these fractions have different denominators, so we need to find a common denominator first.

A common denominator for 1/4 and 2/3 is 12.

To convert 1/4 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 3:

1/4 = (1 x 3)/(4 x 3) = 3/12

To convert 2/3 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 4:

2/3 = (2 x 4)/(3 x 4) = 8/12

Now we can add the fractions:

1/4 + 2/3 = 3/12 + 8/12 = 11/12

Therefore, Jana has completed 11/12 of her homework.

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The given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.

Amount is a numerical quantity that is used to measure the size or magnitude of something. It is typically expressed in terms of a unit of measure such as a dollar, pound, or other currency.

The given k-value of 0.1459 corresponds to the rate of decay of the 9 gram sample of the substance over time. The equation for determining the amount of the sample left after a certain amount of time (t) is: N = -kt, where N is the amount of the sample left after the given amount of time, k is a positive constant that depends on the substance itself and on the units used to measure time, and t is the amount of time in days.

N = N0 e^(-kt)

for half life N/N0 = 1/2 and k = 0.1459

1/2 = e^(-0.1459t)

=> -0.1459 t = ln(0.5)

t = - ln(0.5) /0.1459

= 4.8 days       

Therefore, with the given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.

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Complete question is:

A 9 gram sample of a substance that's used for drug research has a K value of 0.1459

Find the substances half-life in days, and round answer to the nearest ten. ( exponential decay )

The exact value of the expression \(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16\ is\ (2 + \sqrt2)/4\).

We can use the following trigonometric  identity:

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

We have:

\(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16 \\= cos(3\pi /16 - \pi /16) \\= cos \pi /8\)

Now, using the half-angle identity \(cos(\theta/2) = ^+_-\sqrt{[(1 + cos \theta)/2]\), we can simplify cos π/8:

\(cos \pi /8 \\= cos(\pi /4 - \pi /8) \\= cos \pi /4\ cos \pi /8 + sin \pi /4\ sin \pi /8 \\= 1/\sqrt{2} \times \sqrt{[(1 + cos \pi /4)/2]} + 1/\sqrt{2} \times \sqrt{[(1 - cos \pi /4)/2]} \\= 1/\sqrt{2} \times \sqrt{[(1 + 1/\sqrt{2})/2]} + 1/\sqrt{2} \times \sqrt{[(1 - 1/\sqrt{2})/2] }\)

\(= 1/\sqrt{2} \times \sqrt{[(2 + \sqrt{2})/4] }+ 1/\sqrt{2} \times \sqrt{[(2 - \sqrt{2})/4]} \\= 1/2 \times \sqrt{(2 + \sqrt{2})} + 1/2 \times \sqrt{(2 - \sqrt{2})} \\= \sqrt{2}/2 + \sqrt{2}/2\sqrt{2} + \sqrt{2}/2 - \sqrt{2}/2\sqrt{2} \\= \sqrt{2}/2 + \sqrt{2}/4 \\= (2 + \sqrt{2})/4\)

Therefore, the exact value of the expression \(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16\ is\ (2 + \sqrt2)/4\).

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The expression that represents the volume of the rectangular prism, in terms of the width w, is given as follows:

6w³ cubic units.

A rectangular prism is composed by three dimensions, given as follows:

The volume of the rectangular prism is given by the multiplication of these three dimensions, as follows:

V = lwh.

From the image given at the end of the answer, the dimensions of the prism are given as follows:

Hence the expression that gives the volume of the rectangular prism is given as follows:

V = w x 2w x 3w = 6w³ cubic units.

The prism is given by the image shown at the end of the answer.

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Properties of the multiplication

The associative property states that the product of three factors can be grouped in any order and they will produce the same result.

The statement

(3x4)x7 can be written in two equivalent forms by associating another pair of elements:

3x(4x7)

(3x7)x4

Selecting the first form:

(3x4)x7 = 3x(4x7)

Thus the correct choice is:

a. Associative

Answer:

Step-by-step explanation:

(

81

m

6

)

1

2

Simplify the expression.

9

2

(

1

2

)

(

m

6

)

1

2

Cancel the common factor of

2

.

9

1

(

m

6

)

1

2

Simplify the expression.

9m3

Answer:

Step-by-step explanation:

Given

(81 m^6) ^ (1/2)

Solution

change 81 to 9^2

(9^2 m^6)^(1/2)

Now multiply the 1/2 by each of the powers

9^2*(1/2)  m^6^1/2

Answer 9 m^3

Comment

It's hard to show this, but the 1/2 only multiplies by power. It doesn't influence the base. That's because 1/2 is a power itself.

The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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The NPV is -$37.65 and the IRR is approximately 11.55%. To calculate the net present value (NPV) and internal rate of return (IRR), we need to consider the cash flows and the discount rate.

Given cash flows:

Year 0: $0

Year 1: -$860

Year 3: $920

Discount rate: 8%

First, let's calculate the present value (PV) of each cash flow using the discount rate:

Year 0: $0 (no cash flow)

Year 1: PV = -$860 / (1 + 0.08)^1 = -$796.30

Year 3: PV = $920 / (1 + 0.08)^3 = $758.65

Now we can calculate the NPV by summing up the present values of all cash flows:

NPV = PV(year 1) + PV(year 3)

= -$796.30 + $758.65

= -$37.65

The NPV is -$37.65.

To calculate the IRR, we need to find the discount rate that makes the NPV equal to zero. In this case, we can use the trial and error method or utilize financial software or calculators to find the IRR. Let's assume the IRR is r%.

Using the cash flows and the IRR:

Year 0: $0

Year 1: -$860

Year 3: $920

Setting the NPV equal to zero:

0 = PV(year 1) + PV(year 3)

\(0 = -$860 / (1 + r)^1 + $920 / (1 + r)^3\)

Solving this equation for r gives us the IRR. However, solving this equation analytically can be complex, so it's better to use financial software or calculators.

Using a financial calculator or software, the IRR for these cash flows can be calculated as approximately 11.55%.

Therefore, the NPV is -$37.65 and the IRR is approximately 11.55%.

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Calculating this expression will give us the probability that a person's Badger 5 lottery ticket will have exactly two winning numbers.

To find the probability of a person's Badger 5 lottery ticket having exactly two winning numbers, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes in the Badger 5 game is given by the number of ways to choose 5 numbers out of 31 without repetition and in numerical order.

The number of favorable outcomes is the number of ways to choose exactly two winning numbers out of the 5 numbers drawn in the lottery drawing.

To calculate these values, we can use the binomial coefficient formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of available numbers (31 in this case) and r is the number of numbers to be chosen (5 in this case).

The probability of exactly two winning numbers can be calculated as:

P(exactly two winning numbers) = (number of favorable outcomes) / (total number of possible outcomes)

Substituting the values into the formula, we can calculate the probability:

P(exactly two winning numbers) = (5C2 * 26C3) / (31C5)

Calculating this expression will give us the probability that a person's Badger 5 lottery ticket will have exactly two winning numbers.

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The number of hours in a week a student played basketball is \(11\frac{3}{8}\).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= \(11\frac{3}{8}\).

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The solution to the equation is x = 24.The equation is given as follows:\(\sqrt{x} (x - 8) - 3 = 1\).We can add 3 to each side of the equation as follows:\(\sqrt{x} (x - 8) = 4\).Now, we can square each side of the equation to get rid of the square root as follows:\(\sqrt{x} (x - 8))^2 = 4^2x - 8 = 16x = 16 + 8x = 24\)

Therefore, x = 24 is the solution to the equation.The given equation is:sqrt (x - 8) - 3 = 1.\(\sqrt{x} (x - 8) - 3 = 1\)To solve for all possible values of x, we can perform the following steps:

Step 1: Add 3 to each side of the equation to get rid of the negative 3:\(\sqrt{x} (x - 8) = 4\)

Step 2: Square each side of the equation to get rid of the square root:\(\sqrt{x} (x - 8))^2 = 4^2x - 8 = 16\)

Step 3: Add 8 to each side of the equation to isolate the variable:x - 8 + 8 = 16 + 8x + 8x = 24

Step 4: Combine like terms:16x = 24

Step 5: Solve for x:x = 24.

Therefore, the solution to the equation is x = 24.

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Given:

The figure of a right triangle.

To find:

The measure of x.

Solution:

According to the altitude on hypotenuse theorem, the length of the altitude is the geometric mean of segments of the hypotenuse.

Let "h" be the height  of the altitude and it divides the hypotenuse if two pieces of lengths "a" and "b", then

\(h=\sqrt{ab}\)

In the given figure, 14 is the height  of the altitude and it divides the hypotenuse if two pieces of lengths 24 and x. So, by using the altitude on hypotenuse theorem, we get

\(14=\sqrt{24x}\)

Taking square on both sides.

\(196=24x\)

\(\dfrac{196}{24}=x\)

\(\dfrac{49}{6}=x\)

Therefore, the value of x is \(\dfrac{49}{6}\) units and its approximate value is 8.167 units.

Answer:

12.5

Step-by-step explanation:

Keep dividing by 2, 25 divided by 2 is 12.5

A. To find the area of a circle you need to use the formula A= π r²  

The radius (R) is half of the diameter . . . that's 6.5 cm .

r² = ( 6.5)² = 42.25 cm²

Area =  π r² = 42.25 π  =  132.7 cm²

B. Area of a rectangle is just (length) x (width).

Length = 12 cm

Width = 5 cm

Area = (12 cm) x (5 cm) = 60 cm²

C. The shaded portion is the part of the circle that's NOT in the rectangle. So its area is (area of the circle) - (area of the rectangle)

Area = (132.7 cm²) - (60 cm²) = 72.7 cm²

Answer:

3006

Step-by-step explanation:

this is

Answer:

aa

Step-by-step explanation:

Answer:

12/7 or 1 5/7

Step-by-step explanation:

6 * 2 = 12

so

12/7 = 1 5/7

Answer:

1.714 and/or 1 5/7

Step-by-step explanation:

You're welcome :P

Answer:

it's option 3

Step-by-step explanation:

1/6y+1/6y gives you 2/6y or 1/3y simplified

12/6=2

so1/6y+1/6(y+12)-2= 1/3

Answer:

El lado del cuadrado inicial es 17 m.

Step-by-step explanation:

El área de un rectángulo se calcula a partir de los dos lados diferentes. Siendo a y b el valor de ambos lados, el área de la figura es el producto de los dos lados contiguos del rectángulo.

A los lados de un cuadrado se le aumenta en 3 y 5 m respectivamente la superficie del nuevo rectángulo es 440 m². Siendo x el lado del cuadrado inicial, entonces el área del rectángulo se puede expresar como:

(x+3)*(x+5)= 440 m²

Resolviendo:

x*x + 5*x + 3*X + 3*5= 440

x² + 8*x + 15=440

x² + 8*x + 15 -440= 0

x² + 8*x -425= 0

Una función cuadrática de la forma a*x² + b*x + c= 0 se puede resolver mediante la expresión:

\(\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}\)

En este caso, a=1, b=8 y c=425. Reemplazando:

\(\frac{-8+-\sqrt{8^{2}-4*1*(-425) } }{2*1}\)

Resolviendo:

\(\frac{-8+\sqrt{8^{2}-4*1*(-425) } }{2*1}= \frac{-8+\sqrt{64+1700} }{2*1}= \frac{-8+\sqrt{1764 } }{2}= \frac{-8+42 }{2}= \frac{34}{2} = 17\)

y

\(\frac{-8-\sqrt{8^{2}-4*1*(-425) } }{2*1}= \frac{-8-\sqrt{64+1700} }{2*1}= \frac{-8-\sqrt{1764 } }{2}= \frac{-8-42 }{2}= \frac{-50}{2} = -25\)

Como las longitudes no pueden ser negativas, el lado del cuadrado inicial es 17 m.

The equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

What is point slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

One of the formulas used to determine a line's equation is the point slope formula. According to the point slope formula, y - y1 = m (x - x1) is the equation for a line with slope "m" and the points (x, y1) on it.

We have to find the equation of line that passes through the points (6, 5) and (0, -7).

First to find the slope of the line,

\(m = \frac{y_2-y_1}{x_2-x_1} = \frac{-7-5}{0-6}= \frac{-12}{-6} = 2\)

Now, consider the point slope form of the line

\(y-y_1=m(x-x_1)\)

Plug \(m = 2, (x_1, y_1) = (0, -7)\)

⇒

\(y-(-7)=2(x-0)\\y+7=2x\\y=2x-7\)

Hence, the equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

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Answer:

Step-by-step explanation:

After Diane buys 4 candy bars and Susan buys 2, they will both have 13 dollars left.

Hope this helps!

The value of C that satisfies the mean value theorem for f(x) = x²³ − x on the interval [0, 2] is 1.174. So the option is none of the above.

The mean value theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there is at least one point c in (a, b) such that

f′(c)=(f(b)−f(a))/(b−a).

The given function is

f(x)=x²³ −x.

The function is continuous on the interval [0, 2] and differentiable on the open interval (0, 2).

Therefore, by mean value theorem, we know that there exists a point c in (0, 2) such that

f′(c)=(f(2)−f(0))/(2−0).

We need to find the value of C satisfying the theorem.

So we will start by calculating the derivative of f(x).

f′(x)=23x²² −1

According to the theorem, we can write:

23c²² −1 = (2²³ − 0²³ )/(2 − 0)

23c²² − 1 = 223

23c²² = 224

\(c = (224)^(1/22)\)

c ≈ 1.174

Therefore, the value of C that satisfies the mean value theorem for f(x) = x²³ − x on the interval [0, 2] is approximately 1.174, which is not one of the answer choices provided.

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Answer: C (x = 4/3)

Step-by-step explanation: Solve for x by simplifying both sides of the equation, then isolating the variable.

Other forms of the answer: x = 4/3 in improper fraction form, 1.3  ( 3 as the repeating decimal/ recurring decimal) in decimal form, and 1 1/3 in decimal form.

The given expression [(4) = 3x + 1] in exponential form is [(2)² = 3x + 1].

So, the given expression is:

(4) = 3x + 1

Now, convert the given function into exponential form as follows:

(4) = 3x + 1

(2×2) = 3x + 1

(2)² = 3x + 1

Therefore, the given expression [(4) = 3x + 1] in exponential form is [(2)²=3x+1].

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