Find the area of the figure below formed from a triangle and a parallelogram

The simplified equation of \(\frac{x^{2}-9 }{3x^{2} +8x-3}+\frac{x-3}{x+2}\)  is \(\frac{(x-3)(4x+1)}{(3x-1)(x+2)}\)

Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler. Therefore,

\(\frac{x^{2}-9 }{3x^{2} +8x-3}+\frac{x-3}{x+2}\)

3x² + 8x - 3 = (3x - 1)(x + 3)

x² - 9 = (x - 3)(x + 3)

Therefore,

\(\frac{(x-3)(x+3)}{(3x-1)(x+3)} +\frac{x-3}{x+2} =\frac{(x+2)(x-3)(x+3)+(x-3)(x+3)(3x-1)}{(3x-1)(x+3)(x+2)}\)

Therefore,

\(\frac{(x+2)(x-3)(x+3)+(x-3)(x+3)(3x-1)}{(3x-1)(x+3)(x+2)}=\frac{((x+3)(x-3)((x+2)+(3x-1)))}{(3x-1)(x+3)(x+2)}\)

\(\frac{((x+3)(x-3)((x+2)+(3x-1)))}{(3x-1)(x+3)(x+2)}=\frac{(x-3)((x+2)+(3x-1))}{(3x-1)(x+2))}\)

Therefore,

\(\frac{(x-3)((x+2)+(3x-1))}{(3x-1)(x+2))} = \frac{(x-3)(x+2+3x-1)}{(3x-1)(x+2)}\)

\(\frac{(x-3)(x+2+3x-1)}{(3x-1)(x+2)}=\frac{(x-3)(4x+1)}{(3x-1)(x+2)}\)

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Answer:

i am confused on what you are asking but if you explain it i would love to help

Step-by-step explanation:

Answer:

You are still broke because you forgot that you have no money to add with

Step-by-step explanation:

Answer:

x = 2

y = - 1

Step-by-step explanation:

Please see the step by step solution in the picture attached below.

Hope it can help you. Have a nice day!

Answer:

16a

Step-by-step explanation:

14a+2=14+2+a=16a.

Given:

The semicircle with dimeter 6 cm.

Required:

FInd the area.

Explanation:

We have figure of semicircle and area of semicircle

Radius is half of diameter. That is radius equal 3cm.

In poetry, the two main types of feet are iambic and trochaic.

Iambic foot: An iambic foot consists of two syllables, with the first syllable being unstressed and the second syllable being stressed. This creates a rhythmic pattern of "da-DUM" that gives iambic meter its characteristic "rising" sound. Iambic meter is one of the most common types of meter in English poetry, and is often associated with a natural, conversational rhythm.

Trochaic foot: A trochaic foot consists of two syllables, with the first syllable being stressed and the second syllable being unstressed. This creates a rhythmic pattern of "DA-dum" that gives trochaic meter its characteristic "falling" sound. Trochaic meter is less common than iambic meter in English poetry, but is still used in a variety of forms and styles. It can create a sense of tension or urgency, and is often used in poetry that is meant to be dramatic or suspenseful.

It's important to note that these two types of feet are just two of many possible metrical patterns that can be found in poetry. However, they are two of the most basic and widely recognized, and a good starting point for understanding the rhythms and structures of poetic meter.

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Answer:

a, the letter is a and you welcome

Answer:

A) x+4y=13

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(2-4)/(5-(-3))

m=-2/(5+3)

m=-2/8

simplify

m=-1/4

y-y1=m(x-x1)

y-4=-1/4(x-(-3))

y-4=-1/4(x+3)

y=-1/4x-3/4+4

y=-1/4x-3/4+16/4

y=-1/4x+13/4

y-(-1/4x)=13/4

y+1/4x=13/4

4(y+1/4x)=4(13/4)

4y+4/4x=13

4y+x=13

x+4y=13

Answer:

x = 6 gallons (of 30% alcohol)

y = 12 gallons (of 60% alcohol)

Step-by-step explanation:

Let

x = liters of 30% alcohol

y = liters of 60% alcohol

There are two unknowns, we need two equations

x + y = 18. (1)

0.30x + 0.60y = 0.50(x+y) (2)

From (1)

x + y = 18

y = 18-x

Substitute the value of y into (2) and solve for x:

0.30x + 0.60y = 0.50(x+y)

0.30x + 0.60(18-x) = 0.50(x+18-x)

0.30x + 10.8 - 0.60x = 0.50(18)

10.8 - 0.30x = 9

-0.30x = -1.8

Divide both sides by -0.30

x = 6 gallons (of 30% alcohol)

Substitute x=6 into (1) and solve for y:

x + y = 18

6 + y = 18

y = 12 gallons (of 60% alcohol)

13:13

2 cubes=8

3-1=2

2 squared=4

4+1=5

5+8=13

Answer:

the

Step-by-step explanation:

sale would be $20 for every item, duh

Answer:

y=3x+5

y=-2x-1

y=-4x

y=1/2x+2

Step-by-step explanation:

These are linear functions(y=mx+b).  m stands for the slope and b stands for the y intercept.  After plugging in your slope, you use the coordinates they give you to find the y intercept.  To find the y intercept plug in the y coordinate into the y in y=mx+b, and plug in the x coordinate into the same equation.  

You can also check your answer on desmos graphing calculator.

Hope my explanation made sense! I suck at explaining things lol.

To find the slope of a line you need to know at least 2 points on that line to use their coordinates in the following formula:

That is the formula to find the slope of a line, m is the slope, y2 and y1 are the y coordinates of the known points and x2 and x1 are the x coordinates.

For example, find the slope of the line that passes through (1,4) and (3,12)

The slope of the line is 4.

===================================================

Explanation:

We multiply each side of the triangle (8,6,and 10) by the height of the prism. This will give us the area of each rectangular panel.

The total lateral surface area is therefore 320+240+400 = 960 square cm. This excludes the area of the triangular bases.

You could compute it alternatively like this:

40*(8+6+10) = 40*24 = 960

The 8+6+10 portion represents finding the perimeter of the triangular base.

The area of rectangular surfaces of the prism will be equal to 960 square cm. If the sides of the base of the prism are 8 cm, 6 cm and 10 cm

A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces.

We multiply each side of the triangle (8,6,and 10) by the height of the prism. This will give us the area of each rectangular panel.

\(8\times 40 = 320\\\\6\times 40 = 240\\\\10\times 40 = 400\)

The total lateral surface area is therefore

320+240+400 = 960 square cm.

This excludes the area of the triangular bases.

You could compute it alternatively like this:

\(40*(8+6+10) = 40\times 24 = 960\)

Hence the area of rectangular surfaces of the prism will be equal to 960 square cm.

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Answer:

false is the answer ........

Solution:

So the statement is false and the correct statement is:

For any two integers a and b, (a+b)^2 = a^2+2ab+b^2.

Numbers which are co- prime number which have greatest common factor one are 1, 7, 13, 17, 19, 23, 29, 31

Two integers a and b are coprime, comparatively prime, or mutually prime in mathematics if and only if the single positive integer that divides both of them is 1. As a result, every prime integer that divides a does not divide b, and the opposite is also true. This translates to having a greatest common divisor of 1 for them. Co-prime numbers are collections of numbers with just one common factor between them. Their highest common factor (HCF) is 1, which signifies. For Co-Primes to exist, there must be at least two Numbers. Relatively Prime Numbers is another name for co-prime numbers.

Given,

A date is called weird if the number of its month and the number of its day have greatest common factor 1.

Numbers which are co- prime which have greatest common factor one are:

1, 7, 13, 17, 19, 23, 29, 31

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\(7x + 8 = ( - 5x) + 32 \\ 7x + 5x = 32 - 8 \\ 12x = 24 \\ x = \frac{ \cancel{24} {}^{ \: \: \: 2} }{ \cancel{12}}\\x=2 \)

\( \Large{\boxed{\sf x = 2}} \)

\( \\ \)

Given equation:

\( \sf 7x + 8 = -5x + 32 \)

\( \\ \)

Substract 8 from each side :

\( \sf 7x + 8 - 8 = -5x + 32 - 8 \\ \\ \sf 7x = -5x + 24 \)

\( \\ \)

Add 5x to both sides :

\( \sf 7x + 5x = -5x + 24 + 5x \\ \\ \sf 12x = 24 \)

\( \\ \)

Divide both sides by 12 :

\( \sf \dfrac{12x}{12} = \dfrac{24}{12} \\ \\ \\ \boxed{\boxed{\sf x = 2}} \)

\( \\ \\ \)

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well,  the hypotenuse is always a positive value, since it's just the distance from the center to the arc in a circle or between two points, so is never negative, hmmm we know the sine is -1/5, and we also know the cosine is >0, which is another way to say is positive, hmmm let's use that, keeping in mind that the sine is negative and the cosine positive only in the IV Quadrant.

\(sin(\theta )=\cfrac{\stackrel{opposite}{-1}}{\underset{hypotenuse}{5}}\impliedby \qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\)

\(\pm\sqrt{5^2 - (-1)^2}=a\implies \pm\sqrt{24}=a\implies \stackrel{IV~Quadrant}{+\sqrt{24}=a} \\\\[-0.35em] ~\dotfill\\\\ cot(\theta )=\cfrac{\stackrel{adjacent}{\sqrt{24}}}{\underset{opposite}{-1}}\implies cot(\theta )=-\sqrt{24}\)

To find the value of V*(s'), The Bellman equation relates the Q*(s, a) values to the state-value function V*(s) by taking the maximum Q-value over all possible actions. Given the Q*(s, a) values and the transition information:

V*(s') = max(Q*(s', a)) for all actions a

In this case, the Q* values for state s are:

Q*(s, \(a_{1}\)) = 10

Q*(s, \(a_{2}\)) = -1

Q*(s, \(a_3}\)) = 0

Q*(s, \(a_{4}\)) = 11

Since s' can be reached from s by taking action a1, we consider the Q* values for state s' and select the maximum value:

V*(s') = max(Q*(s', \(a_{1}\)), Q*(s', \(a_{2}\)), Q*(s', \(a_{3}\)), Q*(s',\(a_{4}\) )

Substituting the given Q* values for s', we have:

V*(s') = max(Q*(s', \(a_{1}\)), Q*(s', \(a_{2}\)), Q*(s', \(a_{3}\)), Q*(s', \(a_{4}\))

         = max(10, -1, 0, 11)

         = 11

Therefore, the value of V*(s') is 11.

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Answer:

The answers are;

a. None

b. None

c. Infinite

d. None

e. None

Step-by-step explanation:

The number of non congruent triangles that can be drawn depends on the uniqueness of the triangle

The parameters of a unique triangle are;

Knowing the Side Side Side (SSS)

Knowing the Side Angle Side (SAS)

Knowing the Angle Side Angle (ASA)

Knowing the Angle Angle Side (AAS)

However, knowing only the Side Side Angle it is possible to draw two non-congruent triangles

Therefore, considering each of the triangles gives;

a. Sides 7 inches, 8 in., and 16 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided properties

b. Similarly, the given triangle parameters are 4 in., 4 in., and 6 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided information

c. The parameters of the triangle given here are angles 30°, 60°, and 90° which is of the form Angle Angle Angle, or AAA for which the sides can be scaled to form an infinite number of non-congruent triangles

d. The parameters given are three angles measuring 120° which does not form a triangle as the sum of triangles in a triangle = 180°

Hence the number of non-congruent triangles that can be drawn in this case = 0

e. The parameters given are two angles measuring 45° and one side length of 10 in., hence the parameter is of the forms AAS or ASA hence the triangle is unique and it is not possible to draw two non-congruent triangle with the provided properties.

i'm sorry i can't answer because i can't see the marks but i would help if i could

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Edward has 12 coins of the quarter and 8 coins of nickel with him

Total number of coins = 20

The total amount of money = $3.40

Let x represent the number of quarters and y represent the number of nickels

Formulating the equations we get:

x + y = 20-------(1)

0.25x + 0.05y = 3.40

Simplifying by removing the decimals and solving

25x + 5y = 340------(2)

Multiplying equation (1) by 5 and subtracting with equation (2) we get the following:

5x + 5y = 100

25x + 5y = 340

= 20x = 240

x = 12

So, y = 8

So, the number of quarters is 12 and the number of nickels is 8

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Answer:

see explanation

Step-by-step explanation:

The restriction a ≠ 0 and b ≠ 0 is applied since division by zero would make

\(\frac{a}{b}\) and its reciprocal \(\frac{b}{a}\) undefined, thus meaningless

Answer: 11

Step-by-step explanation:

Given

Jim's mom distributed  a bag of 440 Jelly beans evenly in to 20 Plastic bags

i.e.each bag has \(\frac{440}{20}=22\)  Jelly.

After the hunt, Jim has 242 Jelly. This much Jelly constitutes

\(\Rightarrow \dfrac{242}{22}=11\ \text{bags}\)

Therefore, Jim has 11 bags of Jellys