Finding area of composite figure

an equation to model this situation is 200 = x+ 2 *t and 220 pounds is  his total weight after 30 weeks

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

x  initial weight of John

weight gained 1 week = 2 pounds

no. of weeks = 20=t

Final weight of John = 200 pounds

200 = x+ 2 *t ---------(1)

no. of weeks = 20=t

From eq(1)

x = 160 pounds= intial weight

So,

[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]

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Answer:

The cost of a single pack would be $2.45.

Step-by-step explanation:

If a 5 pack costs 12.25 then to find the cost of 1 packet we need to divide.

We would divide by 5.

$12.25/5=$2.45

Tasha, because she has the lowest ratio since 0.7 < 0.625

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The ratio of hits compared to total attempts is their batting average

Each player on the team wants to have the highest batting average to help their team the most.

Jana has hit the ball 7 times out of 10 attempts.

Average is 7/10=0.7

Tasha has hit the ball 10 times out of 16 attempts.

Tasha Average is 10/16=0.625

We need to find the player who has better batting average

Tasha, because she has the lowest ratio since 0.7 < 0.625

Hence, Tasha, because she has the lowest ratio since 0.7 < 0.625

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If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

The amount earned In a month is 3250.

There are 12 months In a year.

The total month in 10 years = 10× 12 = 120 months

The total amount in the account for 10years = 120×3250 = 390,000

Therefore there will be 390000 in the account at the end of 10th year.

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By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

What is the value of 1meter in terms of centimeter ?

1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .

Given,

1 meter= 3.28 feet

1 Liter= 0.26 gallons

1 kilogram = 2.20 pounds

we know that ,

1yard = 0.0009144 km

so ,

26.794 yard = 26.794*0.0009144 km

= 0.024500

Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

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Explanation:

The zeros in 0.00798516 are not considered significant because they are not between nonzero values.

If we had something like 1.207, then that zero would be considered significant.

The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.

Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.

Answer: 0.00799

0.00798516 rounded off to three significant figures is 0.00799

hope that helps...

Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

Answer:

he will do 34 the next month

Answer:

(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180

Step-by-step explanation:

A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:

p = 2w + 2l

We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.

We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.

Plugging these values into our equation we get:

p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.

Or in the form of a quadratic equation:

p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162

=

p = 4k^2 - 24k + 180

Hope this helps!

The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.

The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).

Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.

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A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]

B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]

c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]

are the value of given algebraic expression.

The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".

here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]

Given .

[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]

upon solving two complex number we solve coefficient of iota together and real number together.

A) to find [tex]$(x+y)$[/tex]

[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]

B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]

c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]

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The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;

p(x) = x(1 + 6/100)

g(x) = (1500 - x)(1 + 3.8/100)

The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.

We are given that;

The total amount invested in the two mutual funds = $1500.

The growth rate of the first mutual fund = 6%.

The growth rate of the second mutual fund = 3.8%.

If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.

The growth for both mutual funds can then be represented by;

First mutual fund; p(x) = x(1 + 6/100)

The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)

Thus, the polynomial expression for both the mutual funds are;

p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.

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Using mathematical operations, the construction worker requires C. 2 pounds of cement to mix 3 pounds of sand.

The basic mathematical operations are subtraction, addition, division, and multiplication.

These mathematical operations combine numbers, variables, mathematical operands, and the equation symbol to solve mathematical problems.

In this situation, we can apply the mathematical operation of multiplication to determine the quantity of cement required for 5 pounds of gravel.

The quantity of gravel per pound of sand = 1²/₃ = 1.667 pounds

For 3 pounds of sand, the quantity of gravel required = 5 pounds (1²/₃ x 3)

The quantity of cement per pound of gravel = ²/₅ pounds or 0.4

For 3 pounds of sand and 5 pounds of gravel, the quantity of cement required = 2 (5 x 0.4) or (5 x ²/₅)

Thus, 2 pounds of cement are needed to mix with 3 pounds of sand and 5 pounds of gravel.

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Answer:

yes

Step-by-step explanation:

The angle of elevation of the fly's flight path is approximately 57.74 degrees.

In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side of the triangle and is the side opposite to the 90 degrees angle. It is also the side that forms the "hypotenuse" of the right triangle.

The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where a and b are the legs of the triangle and c is the hypotenuse. This theorem can be used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known.

Let's call the angle we're trying to find "theta". The horizontal distance is 30 feet, the vertical distance is 32 feet and the height is 9 feet.

Using pythagorean theorem:

$c^2 = a^2 + b^2$

$c = \sqrt{30^2 + 32^2}$ = $\sqrt{900 + 1024}$ = $\sqrt{1924}$

Now we can use the tangent function:

$\tan(\theta) = \frac{opposite}{adjacent} = \frac{32}{30}$

Now we can find the angle, theta, by using the inverse tangent function:

$\theta = \tan^{-1}(\frac{32}{30})$

The angle of elevation of the fly's flight path is approximately 57.74 degrees.

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The equation 3y + 2 = 2x is not a direct variation

From the question, we have the following parameters that can be used in our computation:

Variation = direct variation

3y + 2 = 2x

A direct variation is represented as

y = kx

Where k is the constant of proportion

When the equations y = kx and  3y + 2 = 2x are compared, we can see that

The equation 3y + 2 = 2x has a constant term

Hence, the equation is not a direct variation

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The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.

A stew recipe uses 3 teaspoons of salt for every 4 cups of water.

There is a ratio issue here.

As X is to three, 3 is to 4.

3 : 4 :: X : 3

To eliminate the fractions, multiply each integer in the ratio by 12.

9 : 12 :: 9X : 12

This is a portion of what is

9 / 12 = 9X / 12

to obtain, cross-multiply.

9 / 12 = 3 teaspoons of salt,

Check: 3 cup of flour yields 3 cups, which is a 4x increase.

The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.

The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.

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The angles add up to 180° so the angles are supplementary.

The value of x is 31.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

From the figure,

Two angles:

3x + 25  and 2x

These two angles form a straight angle.

Now,

3x + 25 + 2x = 180

5x = 180 - 25

5x = 155

x = 31

When the sum of two angles is 90°, then the angles are known as complementary angles.

When the sum of two angles is 180°, then the angles are known as supplementary angles.

Now,

3x + 25

= 3 x 31 + 25

= 93 + 25

= 118

2x

=2 x 31

= 62

Now,

118 + 62 = 180

Thus,

The angles are supplementary.

The value of x is 31.

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Answer: 21.3

Step-by-step explanation:

1. Cross multiply

8(8) = 3(x)

2. Simplify

64 = 3x

3. Divide by 3 on both sides to get the variable by itself

64/3 = 3x/3

4. Simplify

21.3333333333 = x

you can round the answer to the nearest tenth, which would be 21.3

Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).

The mathematical field of trigonometry investigates relationships between triangle sides and angles. Because every straight-sided form may be reduced to a collection of triangles, trigonometry is a fundamental concept in all of geometry. The relationships between trigonometry and other branches of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly intricate.

Here,

[tex]e^{x}[/tex] is a function that increases across all of space  (d[[tex]e^{x}[/tex] ]/dx = [tex]e^{x}[/tex]  which is never negative), it must be that so it must be that [tex]e^{u}[/tex] crosses y=1 just once, or at u = 0. To demonstrate this:

In[tex]e^{sinx}[/tex]= In 1

sin x = 0

And when x = "0, 0", "2", we would have that sin x = 0 in [0, 2"]. In general, we would then have that x = n, where n Z, because of the periodicity of sin (where n is an integer).

Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).

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Answer: $1794.28

Step-by-step explanation:

280*5.95= 1666

0.077*1666= 128.282

1666+128.282= 1794.282

We round cause its money

Need to find the x and y: The Graph asking in question is attached below:

A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.

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The trinomial (x - 12)² in standard form is x² - 24x + 144

From the question, we have the following parameters that can be used in our computation:

(x-12)^2

Express properly

So, we have the following representation

(x - 12)²

Expand the expression

This gives

(x - 12)² = (x - 12) * (x - 12)

Open the brackets

This gives

(x - 12)² = x² - 12x - 12x + 144

Evaluate the like terms

(x - 12)² = x² - 24x + 144

Hence, the trinomial is x² - 24x + 144

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[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3

Substitute:

[tex]8-2(3)+3(4+9)[/tex]

[tex]8-6+39[/tex]

Solve:

[tex]8-6+39\\=\fbox{23}[/tex]

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

[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]

[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]

[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]

[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]

[tex]\mathsf{= 2 + 12 + 27}[/tex]

[tex]\mathsf{= 14 + 27}[/tex]

[tex]\mathsf{= 41}[/tex]

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

[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]

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

Answer:16

Step-by-step explanation: If henry hits 80% of pitches, then the easiest way is to make 80% of 10, which is half of 20, is 8. So if it is 20 times he is up to bat, then 8*2, 2*8 is 16, so he hits the ball 16 times.

Answer: $26.81

Step-by-step explanation: the tank holds 16.5 gallons. Meaning, half of the tank is 8.25 gallons. Multiply that by the cost of the gas, 3.25, and you get 26.81

Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.

A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages ​​are:

L1, which has exactly one "a" but any number of "bs".

L2, which has an odd number of "as" and an even number of "bs".

L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.

L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".

L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.

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Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2

A mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.

Here,

Given : synthetic division for

x³ + 3x² + 8x + 14

------------------------

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

         -2 -2  

------------------------

     1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

           -2 -2

---------------------------

         1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

        -2 - 2

------------------

     1    1   6

=> We get:

As

x² +x+6+ [tex]\frac{2}{x+2}[/tex]

and remainder is 2

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.

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Answer: Simplify the expression.

6.1b − 4.9