Find the area of the composite figure

The solution to the equation [tex]4x^2 = 5(4x - 5)[/tex] is x = 5/2."

To solve the equation [tex]4x^2[/tex] = 5(4x - 5), we first simplify the right-hand side by using the distributive property:

Next, we bring all the terms to one side of the equation by subtracting 20x and adding 25 to both sides:

[tex]4x^2 - 20x + 25 = 0[/tex]

This equation is now in the form of a quadratic equation [tex]ax^2[/tex] + bx + c = 0, where a = 4, b = -20, and c = 25. We can solve for x using the quadratic formula:

[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]

Substituting the values of a, b, and c, we get:

x = (-(-20) ±  - 4(4)(25))) / 2(4)

x = (20 ± sqrt(400 - 400)) / 8

x = 5/2

Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.

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Answer:

$624

Step-by-step explanation:

The width is the smaller side and there are four sides to a rectangle so 2 sides are 36 cm and 2 sides are 42cm. The perimeter formula follows this P=(L+W)*2 so plugging the variables (42+36)*2= 156. So there are 156 meters of fencing and each meter costs $4.00. Thus, 156*4=$624

Step-by-step explanation:

y ( 2y + 5 )   + 4 ( 2y+3)

2y^2 + 5y     +  8y + 12  

 2y^2   + 13 y   + 12

the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.

To find the probability of drawing three green marbles from the bag, we need to use the formula for calculating the probability of multiple independent events. The probability of multiple independent events occurring together is the product of the individual probabilities of each event.

Let's first calculate the probability of drawing a green marble on the first draw. We have a total of 6 + 4 + 7 = 17 marbles in the bag, and 7 of them are green. So the probability of drawing a green marble on the first draw is:

P(green on first draw) = 7/17

After we draw a green marble on the first draw, we have 16 marbles left in the bag, including 6 red marbles and 4 blue marbles. Since we don't replace the marble after we draw it, the probability of drawing a green marble on the second draw is:

P(green on second draw) = 6/16

Finally, after we draw a green marble on the second draw, we have 15 marbles left in the bag, including 5 green marbles. So the probability of drawing a green marble on the third draw is:

P(green on third draw) = 5/15

To find the probability of drawing three green marbles in a row, we need to multiply these probabilities:

P(three green marbles) = P(green on first draw) x P(green on second draw) x P(green on third draw)

P(three green marbles) = (7/17) x (6/16) x (5/15)

Simplifying this expression, we get:  

P(three green marbles) = (7 x 6 x 5) / (17 x 16 x 15)

P(three green marbles) = 0.0735

Therefore, the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.

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Mercy will be 27 years old, and her mom will be 37 years old, 7 years from now.

To find Mercy's and her mom's ages, follow these steps:
1. Set up an equation: Let Mercy's age be 2x and her mom's age be 3x.

Their combined age is 50 years, so the equation is 2x + 3x = 50.
2. Solve the equation: Combine the terms on the left side to get 5x = 50.

Then, divide both sides by 5 to find x = 10.
3. Find their present ages: Mercy's age is 2x = 2(10) = 20 years old, and her mom's age is 3x = 3(10) = 30 years old.
4. Find their ages 7 years from now:

In 7 years, Mercy will be 20 + 7 = 27 years old, and her mom will be 30 + 7 = 37 years old.

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The area of the rectangle is 40 square inches.

For a rectangle that is 8 inches long, 3 inches on the bottom, and 5 inches on the side, there are a few things you can do.

The perimeter of a rectangle is the sum of the lengths of all four sides.

To calculate the perimeter, add the lengths of the top and bottom sides (8 + 3 = 11) and the lengths of the two side lengths (5 + 5 = 10).

To find the area of a rectangle with an 8-inch long side, a 3-inch bottom side, and a 5-inch side, follow these steps:
Identify the dimensions of the rectangle.
The dimensions are given as 8 inches long, 3 inches on the bottom, and 5 inches on the side.

However, a rectangle only has two different side lengths, so we can assume that the 3-inch measurement is irrelevant.
Confirm the side lengths.
In this case, the side lengths are 8 inches and 5 inches. The 8-inch side is the length, and the 5-inch side is the width.
Calculate the area of the rectangle.
To find the area, multiply the length by the width. In this case, that is 8 inches (length) multiplied by 5 inches (width).
Area = Length × Width
Area = 8 inches × 5 inches
Area = 40 square inches

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Answer:

Step-by-step explanation:

use a calculator it's free

Answer:

a) 2 new printers

b) 11 min

Step-by-step explanation:

Given:

5 old printers take 30 min to produce a batch of comic books

4 new printers take 18 min to produce a batch of comic books

.

a) First, we need to find how long does one old and new printer take to produce a batch of comic books:

.

Since 5 old printers take 30 min to do the job, one printer would take 5 times more than this (5 printers work together and they do the job faster than one, that's why we have to multiply):

.

1 old printer does the job in:

5 × 30 = 150 min

1 new printer does the job in:

4 × 18 = 72 min

.

Since one old printer does the job in 150 min, 6 old printers would do this job 6 times faster (that's why we divide):

6 old printers would take:

150 / 6 = 25 min

2 new printers would take:

72 / 2 = 36 min

.

25 < 36

That means, 2 new printers would do this job faster

.

b) In order to find how much less time would this take, we have to subtract:

.

36 - 25 = 11 min

The volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.

What is volume ?

Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape.

It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.

the length of the prism is 7 feet, the width is 2 feet, and the height is 3.5 feet.

Volume = Length x Width x Height

Volume = 7 ft x 2 ft x 3.5 ft

Volume = 49 cubic feet

So, the volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.

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Answer:

approximately 0.0018 feet, or about 0.0216 inches.

Step-by-step explanation:

The volume of the suitcase is:

V_suitcase = height x length x width

V_suitcase = 5 ft x 4 ft x 4 ft

V_suitcase = 80 cubic feet

The volume of each supply is:

V_supply = base area x height

We know that the base area of each supply is 9 square feet. Let's assume that the height of each supply is h.

So, the total volume of all the supplies that can be put in the suitcase is:

V_total_supplies = V_supply x number of supplies

V_total_supplies = (9 ft^2 x h) x 5120

We want to find the height of each supply, so we can rearrange the equation above to solve for h:

h = V_total_supplies / (9 ft^2 x 5120)

Substituting the values we know:

h = (80 ft^3) / (9 ft^2 x 5120)

Simplifying, we get:

h = 0.0018 ft

So the height of each supply is approximately 0.0018 feet, or about 0.0216 inches.

Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

The proportion of a circle's circumference to its diameter is denoted by the mathematical constant pi (). It cannot be written as a simple fraction since it is an irrational number. Pi is approximately equal to 3.141592, or 3.15.

We must first determine the circle's radius in order to determine the length of Mr. Chang's string.

C = 2πr, where C is the circle's circumference and r is its radius, is the formula for a circle's circumference.

Given that the circle's circumference is 31.4 meters, we can solve for r using the following method:

C = 2r 31.4

=2x3.14xr

= 31.4/(2x3.14)r

= 3.14/6.28r

r = 5

Thus, the circle's radius is roughly 5 meters.

The diameter of the circle, which is twice as long as its radius, will be equal to Mr. Chang's stake because it is in the center of the circle.

Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

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Since lines l and m are parallel, we know that angles 1 and 5 are corresponding angles and are therefore congruent. Also, angles 4 and 8 are corresponding angles and are congruent.

We also know that angles 1 and 4 are vertical angles, so they are congruent, and angles 2 and 3 are vertical angles, so they are congruent.

Thus, we can set up the following equation:

m∠7 = m∠8 - m∠5 = m∠4 - m∠5

We are given that m∠2 = 120°, so we can use this to find m∠1:

m∠1 + m∠2 = 180° (since angles 1 and 2 are supplementary)

m∠1 + 120° = 180°

m∠1 = 60°

Since angles 1 and 5 are congruent, we know that m∠5 = 60°.

We are also given that angles 1 and 3 are complementary, so we can use this to find m∠3:

m∠1 + m∠3 = 90°

60° + m∠3 = 90°

m∠3 = 30°

Now we can find m∠4:

m∠1 + m∠4 = 180° (since angles 1 and 4 are supplementary)

60° + m∠4 = 180°

m∠4 = 120°

Finally, we can use these values to find m∠7:

m∠7 = m∠4 - m∠5

m∠7 = 120° - 60°

m∠7 = 60°

Therefore, m∠7 is 60°.

Ans:-

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Solution:-

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The value of x is 2 !

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hope it helps:)

The value of solution of expression is,

⇒ x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 7 + 4x - 9 = 6

Now, We can simplify as;

⇒ 4x - 2 = 6

⇒ 4x = 4 + 2

⇒ 4x = 8

⇒ x = 2

Thus, The value of solution of expression is,

⇒ x = 2

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Answer:

A. 500 yards

Step-by-step explanation:

By the Pythagorean Theorem:

[tex] \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

The distance from the park to Anita's house is 5 blocks, which is

5 blocks × 100 yards/block = 500 yards.

Answer:

A. 500 yards

Step-by-step explanation:

1 block = 100 yards

one leg: 4*100= 400 yards

second leg: 3*100= 300 yards

hypotenuse:

pythagorean theorem

hypotenuse ^2 = (one leg)^2 + (second leg)^2

hypotenuse ^2= (400)^2 + (300)^2

hypotenuse ^2 = 160,000 + 90,000

hypotenuse = sqrt(250,000)

hypotenuse = 500 yards

Answer:

Step-by-step explanation:

The steps that should be taken to calculate the volume of the right triangular prism are;

Base = 8 meters

Height = 14 meters

Length of the prism = 7 meters

Area = ½ × base × height

= ½ × 8 × 14

= 56 square meters

Volume of the rectangular prism = Area × length of the prism

= 56 square meters × 7 meters

= 392 cubic meters

Ultimately, the volume of the right triangular prism is 392 cubic meters

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The correct answer is "The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80."

The slope of the line of fit represents the rate of change in the dependent variable (total cost, y) with respect to the independent variable (number of donuts, x). In other words, it represents the amount by which the total cost increases or decreases for each unit increase in the number of donuts sold.

In this case, the slope of the line of fit is 4/5, which means that for each additional donut sold, the total cost is predicted to increase by $0.80. This indicates that the donut shop should expect to make a profit of $0.80 for each donut sold, assuming that all other factors remain constant. This information can be used by the donut shop to determine the optimal price to sell its donuts and maximize its profits.

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This statement is false. Therefore, the original equation has no solution.

How to solve an equation?

To solve the equation 5x + 3x = 2(4x - 5) - 2, we need to simplify each side of the equation using the order of operations (PEMDAS).

First, we simplify the left side of the equation by combining like terms. 5x + 3x equals 8x, so we have:

8x = 2(4x - 5) - 2

Next, we simplify the right side of the equation using the distributive property of multiplication. We multiply the 2 by each term inside the parentheses:

8x = 8x - 10 - 2

We can simplify further by combining like terms on the right side of the equation:

8x = 8x - 12

Now we have an equation with variables on both sides. To solve for x, we want to isolate the variable on one side of the equation. We can do this by subtracting 8x from both sides:

0 = -12

This statement is false. Therefore, the original equation has no solution.

The equation 5x + 3x = 2(4x - 5) - 2 is an example of a contradiction. It means that there is no value of x that makes both sides of the equation equal. In this case, we can see that the left side of the equation is always greater than or equal to the right side, no matter what value of x we choose. Therefore, the equation has no solution.

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The function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal p = $8100

Rate of interest r = 3.7% = 3.7/100 =0.037

Compounded daily then n= 365

Now using compound interest formula then,

=> CI = [tex]P(1+\frac{r}{n})^{nt}[/tex]

=> CI = [tex]8100(1+\frac{0.037}{365})^{365t}[/tex]

=> CI = [tex]8100(1+0.000101369)^{365t}[/tex]

=> CI = [tex]8100(1.000101369)^{365t}[/tex]

Then the function is f(t) = [tex]8100(1.000101369)^{365t}[/tex] .

Now percentage of growth per year is ,

=>  [tex]8100(1.000101369)^{365t}[/tex][tex]\times\frac{1}{100}\%[/tex]

Put t=1 then

=> 8,405.30[tex]\times\frac{1}{100}\%[/tex]

=> 84%

Hence the function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

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The simplified ratio of [tex]2.4:3/4:1 2/3[/tex]  is [tex]28.8:9:20[/tex].

A ratio refers to the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

To solve this ratio, we need to convert all the fractions to a common denominator:

2.4 : 3/4 : 1 2/3 = 2.4 : (3/4) : (5/3)

To eliminate the fractions, we can multiply all terms by the LCD of 12:

2.4 * 12 : (3/4) * 12 : (5/3) * 12

= 28.8 : 9 : 20

So the simplified ratio for the given ratio is: 28.8 : 9 : 20

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The missing property is the distributive property of multiplication.

The distributive property of multiplication is a mathematical property that allows you to simplify expressions that involve multiplying a number or variable by a sum or difference of other numbers or variables.

For the addition of 5 terms with 1z, we have that the term 1 is common to all the factors in the expression, hence the expression can be written as follows:

1z + 1z + 1z + 1z + 1z = 1(z + z + z + z + z) = 5z.

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The equation for the new function F(t) is F(t) = 9t - 256/9.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The conversion formula for converting temperature from Celsius to Fahrenheit is:

F = 9/5C + 32

Substituting the equation for C(t) into F(t) = 9/5C(t) + 32, we get:

F(t) = 9/5(5t - 160/9) + 32

Simplifying this equation, we get:

F(t) = 9t - 320/9 + 32

F(t) = 9t - 256/9

Therefore, the equation for the new function F(t) is F(t) = 9t - 256/9.

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The surface area of the rectangular prism is 348 square meters.

Hello! I'd be happy to help you find the surface area of a rectangular prism with dimensions 6 m by 4 m by 15 m. The surface area can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

where l = length, w = width, and h = height.

Given the dimensions 6 m (length), 4 m (width), and 15 m (height), we can plug in the values

The surface area can be calculated using the formula:

Surface Area = 2(6)(4) + 2(6)(15) + 2(4)(15)
Surface Area = 48 + 180 + 120
Surface Area = 348 m²

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Answer: it is one of the last two

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

balls

Step-by-step explanation:

[tex]\:\: \:\: \:\star[/tex] We are asked to find out the distance between (1,5) and (-6,-2).We know the formula to find the distance between two points is given by -

[tex] \:\: \star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

As per question, points are -

Now that we are given the points, so we can put them into the formula and solve for distance between them.Which is -

[tex]\:\: \:\: \:\star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

[tex] \longrightarrow \sf Distance_{(AB)} = \sqrt{ (-2-5)^2 + (-6-1)^2 }\\[/tex]

[tex]\:\:\:\:\:\longrightarrow \sf Distance_{(AB)}= \sqrt{ (-7)^2 + (-7)^2 }\\[/tex]

[tex]\:\:\:\:\longrightarrow \sf Distance_{(AB)} = \sqrt{ 49+49 }\\[/tex]

[tex]\: \:\:\:\: \:\longrightarrow \sf Distance _{(AB)}= \sqrt{ 98}\\[/tex]

[tex]\: \:\:\: \:\longrightarrow \sf Distance_{(AB)} = \sqrt{49 \times 2}\\[/tex]

[tex]\:\: \:\: \:\:\longrightarrow \sf\underline{ Distance_{(AB)} = 7√2}\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf Distance_{(AB) }= 9.89949......\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf \underline{Distance_{(AB) }= 9.9\:(Approx)}\\[/tex]

Therefore, the distance between (1,5) and (-6,-2) is 7√2 or, 9.9 ( Approx).

The van would have traveled approximately 8 miles of distance after 12 minutes.

To calculate the distance traveled by the van after 12 minutes, we can use the formula:

y = mx

Where m is the rate of travel, and x is the time in minutes.

To find the value of m, we can use the first two data points:

m = (y2 - y1) ÷ (x2 - x1)

m = (8 - 0) ÷ (10 - 0)

m = 8 ÷ 10

m = 4 ÷ 5

Therefore, the formula becomes:

y = (4 ÷ 5) x

Now, we can substitute x = 12 to find the distance traveled after 12 minutes:

y = (4 ÷ 5) × 12

y = 0.8 × 12

y = 9.6

y ≈ 8 miles

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The complete question is:

A van travels at a constant speed. The table shows the distance y (in miles) that the van travels after x minutes. How far does the van travel after 12 minutes?

Time (minutes), x 0 10 20 30

Distance (miles), y 0 8 16 24