Find the area of the rectangle below be sure to include the correct unit in your answer

Answer:

Step-by-step explanation:

Solving by factoring is a strategy used to find the solutions or roots of a quadratic equation in the form of ax^2 + bx + c = 0. The goal of factoring is to rewrite the equation in the form of (x-r)(x-s) = 0, where r and s are the solutions or roots of the equation. Once the equation is in this form, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Here is an example to illustrate the process:

Example: Solve the equation x^2 + 5x - 14 = 0 using factoring.

Step 1: Rewrite the equation in standard form (ax^2 + bx + c = 0). In this case, a = 1, b = 5, and c = -14.

Step 2: Factor the equation by looking for two numbers that multiply to give c and add to give b. In this case, the two numbers are -7 and 2, since (-7)(2) = -14 and -7 + 2 = -5.

Step 3: Rewrite the equation as (x + 7)(x - 2) = 0.

Step 4: Use the zero product property to set each factor equal to zero and solve for x.

x + 7 = 0 or x - 2 = 0

x = -7 or x = 2

So the solutions or roots of the equation are x = -7 and x = 2.

It's important to note that not all quadratic equations can be factored, and in such cases, other methods like completing the square or using the quadratic formula should be used.

It's also important to understand that when factoring, it's important to make sure that you have correctly factored the equation, if not the solution will be wrong.

Answer:

  rhombus

  (b) The diagonals are perpendicular but not congruent.

Step-by-step explanation:

You want to know what sort of figure the parallelogram JKLM is, given the vertices J(-2,7), K(7, 2), L(-2,-3), M(-11,2).

The x-values of points J and L on diagonal JL are the same, so that diagonal is a vertical line. Its length is 7 -(-3) = 10.

The y-values of points K and M on diagonal KM are the same, so that diagonal is a horizontal line. Its length is 7 -(-11) = 18.

The diagonals are perpendicular and not congruent, so the parallelogram is a rhombus.

The requried, score is given as 42, as of the given condition,

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Let the total score after finishing the game be x,
Receive one point for each card you played and lose two points for each card remaining in your hand. and the score is tripled.
According to the quesiton,
x =3 [1 × 18 - 2 × 2]
x = 3[ 18 -4]
x = 3 × 14
x = 42

Thus, The requried, score is given as 42, as of the given question,

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Answer:

Step-by-step explanation:

The required expression is x³ + 5x² + 6x as an expanded form.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

x(x + 2)(x + 3)

We have to expand and simplify the given factors.

As per the question, we have

⇒ x(x + 2)(x + 3)

Open the first parentheses, and distributes

⇒ (x² + 2x)(x + 3)

⇒ x²(x + 3) +  + 2x(x + 3)

Combine the likewise terms in the above expression,

⇒ x³ + 3x² +2x² + 6x

⇒ x³ + 5x² + 6x

Thus, the required expression is x³ + 5x² + 6x.

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So on solving the provided question we can say that - the function is  y = (-8x + - 74) and y = -82

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here, we have

y = (-8x + - 74)

and from data we have x = 1

so, y = (-8-74)

y = -82

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The probability of randomly picking a peach from from the fruit bowl is 29 %

To find the probability of picking a peach from the fruit bowl at random, you first need to sum up the number of fruit :

= 10 Limes + 5 peaches + 2 mangoes

= 17 fruit

The probability of picking a peach from the fruit bowl can then be found to be :

= Number of peaches in fruit basket / Number of fruit in the fruit basket

= 5 / 17

= 29 %

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The rest of the question is:

The probability of randomly picking a peach from from the fruit bowl is _________.

The domain of the function 5h + 2d = 15 is [0, 3].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function 5h + 2d = 15

Where h is the number of hours and d is the distance remaining after h hours.

Now,

5h + 2d = 15

2d = 15 - 5h

d = (15 - 5h)/2

For h = 0, d = 15/2 = 7.5

For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.

For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.

For h = 3, d = (15 - 15)/2 = 0 miles

The domain of the function is [0, 3].

Thus,

The domain is [0, 3].

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The solution to the given complex number expression is; 0 + [1/(-2√6))]i

We are given the expression as;

(√-4)/[(√-8)√-12)]

Now, when it comes to complex numbers, we know that the square root of a negative number for example √-25 would result in 5i.

Similarly, i² = -1

Thus, our expression is now;

2i/(2i√2 * 2i√3)

= 2i/(-4√6)

= i/(-2√6))

= 0 + [1/(-2√6))]i

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Answer:

[tex]\frac{8}{27}[/tex]

Step-by-step explanation:

This means

[tex]\frac{2}{3}[/tex] x [tex]\frac{2}{3}[/tex] x [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{27}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(\dfrac{2}{3})^3}[/tex]

[tex]\mathsf{= \dfrac{2}{3}(\dfrac{2}{3})(\dfrac{2}{3})}}[/tex]

[tex]\mathsf{= \dfrac{2(2)(2)}{3(3)(3)}}[/tex]

[tex]\mathsf{= \dfrac{4(2)}{9(3)}}[/tex]

[tex]\mathsf{= \dfrac{8}{27}}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{8}{27}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

This is a mathematical problem that can be solved using algebra. Let P be the original amount borrowed, and R be the interest rate as a decimal (for example, 5% would be represented as 0.05).

We know that at the end of 25 years, the amount borrowed has trebled, so the total amount is 3P. We also know that the interest is calculated using simple interest, which is calculated as P x R x T, where T is the number of years.

So we can set up the equation:

3P = P + P x R x 25

To find R, we can solve for R by dividing both sides of the equation by P:

3 = 1 + 25R

Then by subtracting one from both sides we have :

2 = 25R

Then by dividing both sides by 25 we can find the rate as :

R = 2/25

Finally, to find the interest rate as a percentage, we multiply R by 100:

rate = 2/25 x 100 = 8%

So the interest rate is 8% per annum

The approximate surface area of the tower is 156.33 feet².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

The given tower is a composite of a cylinder and a cone.

But cylinder does not have the bases and cone also does not have it's base.

Surface area of the curved surface of cylinder = 2π r h

where r is the radius of the base and h is the height of the cylinder.

Given h = 8 feet and r = 2.5 feet

Curved surface area of cylinder = 2π × 2.5 × 8 = 40π feet²

Surface area of the curved surface of the cone = π r √(h² + r²)

where r is the radius of the base of the cone and h is the perpendicular height of the cone.

Given r = 2.5 feet and h = 3 feet

Curved surface area of cone = π × 2.5 [√(2.5² + 3²)]

                                                = 9.76π feet²

Total surface area = 40π + 9.76π

                              = 156.33 feet²

Hence the total surface area of the tower is approximately 156.33 feet².

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The value of cot(x/2) is -3.73

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, Csc(x) = -2

Since,

cscx = 1/sinx

Therefore,

1/sinx = -2

sinx = -1/2

sinx = -sin30°

x = -30°

Therefore,

cot (x/2) = cot(-15)

= -1/tan15

= -3.73

Hence, the value of cot(x/2) is -3.73

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3 of mixed cereal and 2 of tropical fruit

The required expression is 21.29 × 38 = 809.02. has an exact value of the given product.

The estimate is a process, and it includes the rough over-calculation that makes one have a close value to the exact value.

here,
Given expression,
21.29 × 38 = (21 + 0.29) 38
Using distributive property,
               = 21× 38 + 0.29 × 38

               = 798 + 11.02
               = 809.02

The required expression is 21.29 x 38 = 809.02. has an exact value of the given product.

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Answer:

one's place

Step-by-step explanation:

Answer:

exponential growth

Step-by-step explanation:

The rate of change is $6 per hour while the initial value is $20

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let y represent the total amount of money that Larry would have after working x hours.

From the graph, the y intercept is at (0, 20). Using point (0, 20) and (5, 50):

Slope = (50 - 20)/(5 - 0) = 6

The slope is $6 per hour

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Answer:

0.7 mile high

Step-by-step explanation:

tan 30 = height /1.2

so height =1.2 *tan30 = 1.2*0.58 = 0.7

Answer:

[tex]y=-(x-6)^2+6[/tex]

Step-by-step explanation:

Vertex form of a parabola is expressed as: [tex]y=a(x-h)^2+k[/tex]

It's also important to note that the axis of symmetry is a vertical line which passes through vertex, so in this form, that axis of symmetry can be defined as such: [tex]x=h[/tex]

So if we're given the axis of symmetry we know the x-coordinate of the vertex.

Since we're given the axis of symmetry to be: [tex]x=6[/tex] then that means the x-coordinate of the axis of symmetry is six. Another important thing to note about the vertex is it's y-value is either a minimum or maximum depending on whether it's opening up or down. So when we're given the maximum height to be 6, that's the y-coordinate of the vertex.

So now we know the coordinates to the vertex: [tex](6, 6)[/tex]. Using this we can plug in some values into the vertex form: [tex]y=a(x-6)^2+6[/tex], but we still don't know the "a" value in front (besides that it's negative). Luckily we're given a point on the equation! We can plug in the coordinates given: [tex](7, 5)[/tex] into the vertex form as (x, y) to solve for the "a" value, so let's do that.

Original Equation:

[tex]y=a(x-6)^2+6[/tex]

Passes through the point (7, 5), so substitute it for (x, y)

[tex]5=a(7-6)^2+6[/tex]

Simplify inside parenthesis:

[tex]5=a(1)^2+6[/tex]

Square the one:

[tex]5=a+6[/tex]

Subtract 6 from both sides:

[tex]-1=a[/tex]

So now let's plug this back into our equation: [tex]y=-1(x-6)^2+6[/tex], although we don't have to explicitly put the one, and just put the negative sign which does the same thing: [tex]y=-(x-6)^2+6[/tex]

Answer:

1/560

Step-by-step explanation:

So the x input which is the top row the numbers increase by 1 so that is your top number of your slope (rate of change)

And your bottom row increases by 560 so that is your bottom number of your slope

So your rate of change is 1/560

How do I know where to get these numbers?

Well if you take the first 2 numbers from the top row (in your case 1 and 2) and subtract them from each other (2-1=1) you get your first number. Then you do the same for the bottom (in your case 560 and 1120) subtract them (1120-560=560) and get your bottom....If needed you can simplify your fraction but sometimes your slope can come out as a whole number instead of a fraction but in your case you have a fraction.

That is where you get 1/560

Hope this helped!

Answer: C

Step-by-step explanation:

10000(1+0.10)³
=10000(1.10)³
=10000*1.331
=13310

Answer:

Step-by-step explanation:

The area of the rectangle is 48 square feet.

Write an equation you can use to find the value of x.

48 : 4 = x

12 = x

48=4x is the equation which can be used to find the value of x.

Given that area of the rectangle is 48 square feet.

We have to find the value of x.

We know that area of rectangle is length times width.

Area = length × width

Length =x ft

Width = 4 ft

Area = 48 square feet.

Plug in the values of length, width and area in above formula.

48=4x

Divide both sides by 4:

x=12

Hence, 48=4x is the equation which can be used to find the value of x.

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The required equation modeled as of the given condition is 46x + 1 / x².

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Let the number be x, and its reciprocal is 1/x
According to the question, the product of 46 and a number added to the reciprocal of a number squared is given as,
= 46 × x + 1/x²
= 46x + 1/x²

Thus, the required equation modeled as of the given condition is 46x + 1 / x².

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Yes, Rob can ship all 4,056 eggs in the same shipment.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Rob lives on an egg farm with 5,287 chicken hens. Rob collects the chicken eggs every day. One day Rob collects 4,056 eggs.

The eggs are placed in egg cartons of twelve eggs per carton and are shipped to stores.

Here, number of cartons required =4,056/12

= 338 cartons

The egg cartons must be carefully placed in shipping boxes. Each shipping box holds twenty-four egg cartons.

Number of shipping boxes =338/24

= 14.08

The shipper can deliver no more than fifteen shipping boxes of eggs at a time.

Yes, Rob can ship all 4,056 eggs in the same shipment.

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The slope intercept form is  y= 2x+1

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let's take 2 points :

(x1,y1) = ( 1,  -1)

(x2,y2) = ( 2,  -3)

slope  , m = (y2-y1) /(x2-x1)

                = (-3-(-1))/(2-1)

                = (-3+1)/1

                = -2

Slope intercept form:

y-y1=m(x-x1)

y-(-1) = -2 (x-1)

y+1=-2x+2

=> y=2x+2-1

=> y= 2x+1

Thus, the slope intercept form is  y= 2x+1

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Answer:

So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.

Step-by-step explanation:

Ingrid's time of 13.9 seconds was originally measured to 2 decimal places, which means that her actual time could be rounded to 13.9 seconds. To find the slowest time she could have run, we need to find the greatest value that could have been rounded down to 13.9 seconds.

Since the time was measured to 2 decimal places, this means that the hundredths place is known and the thousandths place can be anything between 0 and 9. So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.

Answer:

If Becky had a 40% off coupon, that means she saved 40/100 = 0.4 of the original price.

To find how much she paid for dinner, we can multiply the original price by the percentage of the price that she paid:

30 * (1- 0.4) =30*0.6 = $18

Becky paid $18 for her dinner.

The length of the car in Ivans drawing is given as 8 cm

We are to solve for the length of this car by using the figure we have in the scale drawing. The length of car in Megan's drawing is 6 cm. The scale is 3 : 2

Ivan's drawing is in the relation of 2 : 1 cm

We would have to find the actual length of this car but by the use of Megan's ratio

This is given as

6 * 2 / 3

12 / 3

= 4 cm

Next we have to find Ivans length.

4 * (2/1)

= 8 / 1

= 8 cm

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