Determine the measure of the indicated angle in the following triangle:

If a certain store is selling packages of 10 pencils and 4 pens for back to school . The number of pencils that are in the larger package is 25 pencils.

First step is to find the  number of pencils per pen

Number of pencils per pen = 10 / 4

Number of pencils per pen = 2. 5

Now let find the number of pencils  that are in the larger package

Number of pencils = Number of pens x Pencils per pen

Number of pencils  = 10 x 2.5

Number of pencils = 25 pencils

Therefore we can conclude that the number of pencils is 25 pencils.

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If XV =27-2x and VZ =3x+2, then the diagonal of parallelogram XZ = 34 units and VZ = 17 units.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

The length of line XV = 27 - 2x.

The length of line VZ = 3x + 2.

According to the properties of a parallelogram the diagonals bisect each other .

Hence, XV = VZ.

Equating the expressions -

27 - 2x = 3x + 2

-2x - 3x = 2 - 27

-5x = -25

x = 5

The value of line XV = 27 - 2x

27 - 2(5)

27 - 10

17 units

The value of line VZ = 3x + 2

3(5) + 2

15 + 2

17 units

The value of line XZ = XV + VZ

17 + 17

34 units

Therefore, the value of VZ = 17 units and value of XZ = 34 units.

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The value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

The Integral is [tex]$$\int \frac{t}{t^4+5} d t$$[/tex]

Indefinite integrals are not defined using the upper and lower limits. The indefinite integrals represent the family of the given function whose derivatives are f, and it returns a function of the independent variable.

Let [tex]$t^2=u= > t d t=\frac{d u}{2}$[/tex]

The above Integral becomes

[tex]$\frac{1}{2} \int \frac{1}{u^2+(\sqrt{5})^2} d u=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{u}{\sqrt{5}}\right)+C$$[/tex]

Substitute u In terms of t

[tex]$$\int \frac{t}{t^4+5} d t=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

Therefore, the value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex].

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Answer:

2x^7

Step-by-step explanation:

To simplify this expression, there are two steps. You have to act as though the exponents are whole numbers and add them together to combine like terms.

[tex]2x^4 \times x^3\\= 2x^{4+3}\\= 2x^7[/tex]

Hope this helps!

The solution to the given system of equations y = x² + 10x + 11, y = x² + x - 7 is x = -2, y = -5.

The given set of equations

y = x² + 10x + 11 --- eqn(1)

y = x² + x - 7 --- eqn(2)

Solving the equations by elimination method

⇒ Subtracting eqn 2 from eqn 1, we get

⇒ y - y = x² + 10x + 11 - (x² + x - 7)

⇒ 0 = x² + 10x + 11 - x² - x + 7

⇒ 0 = 9x + 18

⇒ 9x = -18

⇒ x = -2

Put the value of x in eqn 1, and we get

⇒ y = (-2)² + 10(-2) + 11

⇒ y = 4 - 20 + 11

⇒ y = -5

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Answer: B

Step-by-step explanation: You are adding the shirts times the amount, hence X the variable plus the money already spent to then be less then the 200 dollar maximum.

Sound decibel are not additive because humans listen to sound logarithmically and LaTrenda is correct

Osman is not correct in his claim that 88 + 75 decibels would be 163 decibels. The decibel unit is not an additive unit, meaning that when you add the decibel levels of two different sound sources, you do not simply add the decibel levels.

Instead, adding the decibel levels of two different sound sources together would give you the total sound pressure level (SPL) of the combined sound.

To calculate the SPL of the combined sound, you would need to add the intensities of the two sounds and then calculate the decibel level of the combined sound using the formula:

SPL (dB) = 10 log10 (I1/I0) + 10 log10 (I2/I0)

Where I1 and I2 are the intensities of the two sound sources and I0 is the reference intensity, which is the threshold of human hearing.

It would make more sense to add the intensities of the two sounds and then calculate the number of decibels, because the human ear perceives loudness of sounds logarithmically, not linearly.

So, LaTrenda would be correct in this scenario.

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A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days

How to find the number of members ?

When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.

A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.

Total receipts for the period of time the tournament took place was $132,000.

This means the tournament took place throughout how many days?

since total divide by per night is equal to number of days

now 132000/11000= 12

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Polynomial [tex]$-1+x^3-\frac{1}{3} x^3$[/tex] and its conventional form, [tex]x^5-\frac{x^2}{3}-1$$[/tex] , are both used.

[tex]$$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$[/tex]

steps

[tex]$$-1+x^5-\frac{1}{3} x^2$$[/tex]

[tex]\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}[/tex]

rephrase in proper grammar

[tex]=x^5-\frac{x^2}{3}-1$$[/tex]

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.

Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.

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The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”.

Now, According to the question:

What is inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

We use the equal sign "=" to say that two things are the same. However, sometimes we just want to show that something is bigger or smaller than something else. Or maybe we just want to say that two things are not equal. These cases are called inequalities.

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Answer:

  4y

Step-by-step explanation:

You want to simplify the expression (12x²y)/(3x²).

When reducing any fractions, common factors in the numerator and denominator are cancelled. Here, the factor 3x² in the numerator is cancelled by the same factor in the denominator.

  [tex]\dfrac{12x^2y}{3x^2}=\dfrac{(3x^2)(4y)}{(3x^2)}=\boxed{4y}[/tex]

Answer:

Three lines of symmetry.

Step-by-step explanation:

A figure is symmetrical when it is made up of exactly similar parts facing each other or around an axis.

See the attached photo.

There are 3 symmetrical lines:

Please let me know it this helped!!!

Answer: Value of p= 28

Step-by-step explanation:

Use remainder theorem to find the value of p

K(x) = 2x^3+4x^2+px-12  is take f(x)

           (x + 3)  

 f(3)  = 21

f(3)    = 2*3^3+4*3^2+p*3-12

           = 2*27+4*9+3p-12

           = 54+36+3p-12= -6

           =  90-12+3p = -6

           =78+3p = -6

           = 3p = 78--6

                     =78+6

              3p  = 84

              p = 84/3

                 = 28

The value of p is 28

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The y-intercept of Y = - 10 is -10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, b, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y =  - 10 = 0x -10

m = 0 and c = -10

As we know the c is the y-intercept which is equal to -10.

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The value 255 in pixels means the code for the image is white. Therefore, any image with 255 pixels means it is white color.

Pixel values are the numerical values that make up the matrix in which images are stored in computers. The byte image, the most popular pixel format, stores this number as an 8-bit integer with a possible value range of 0 to 255.

Normally, zero and 255 are considered to be black and white, respectively. The many colors of gray are composed of values in between. This has the tremendous benefit of allowing computers to operate with color values that can be stored in a tidy number of bytes.

It is represented in 8 bits because 2⁸ equals 256 (from 0 to 255).

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Answer:

17°

Step-by-step explanation:

m∠1 = m∠2.

Set the expressions for 1 and 2 equal to each other.

6x + 5 = 9x - 46

Separate x's on one side.

3x = 51

x = 17

Using the quadratic function for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.

A quadratic function is an equation in which the highest power of the unknown is 2.

Since we have the function f(x) = -0.5x² + 32.5x - 375, to determine the value of x at which the company breaks even, we equate f(x) to zero and solve for x.

So, f(x) = 0

⇒ -0.5x² + 32.5x - 375 = 0

So, using the quadratic formula, we solve for x

so, [tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where

So, substituting the values of the variables into the equation, we have that

[tex]x = \frac{-32.5 +/- \sqrt{(32.5)^{2} - 4\times(-0.5)\times(-375)} }{2\times(-0.5)}\\= \frac{-32.5 +/- \sqrt{1056.25 - 750} }{-1}\\= \frac{-32.5 +/- \sqrt{306.25} }{-1}\\= \frac{-32.5 +/- 17.5 }{-1} \\x = \frac{-32.5 - 17.5 }{-1} or x = = \frac{-32.5 + 17.5 }{-1} \\x = \frac{-50}{-1} or x = \frac{-15}{-1} \\x = 50 or x = 15[/tex]

So, for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.

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The percentage of his income that he pays in taxes would be = 32%

Taxes is defined as the amount that is paid to the government by working class individuals as a way of generating internal revenue for the country.

The total amount of money made by Mr. Sullivan = $24,000

The amount of tax paid for the wedges = $7,700

The percentage of the income paid as tax would be calculated as;

= 7700/24000 × 100

= 770000/24000

= 32.01

= 32%

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Answer:4 individuals

Step-by-step explanation:

Two pairs refers to 2 sets of two things. In general terms, a pair refers to two items and when you have two of them, it would be two sets of two things, or simply "four items".

For example, two pairs of socks would be four socks.

The Area of a triangle whose height is 8 feet and has a base length of t feet is; 20 ft².

It follows from the task content that the area of the triangle whose height is 8 feet and base length is 5 feet be determined.

Since the area of a triangle is given by;

A = 1/2 × b × h

Therefore, the area of the triangle in discuss can be determined as follows;

Area, A = 1/2 × 8 × 5

Area, A = 20 ft².

On this note, it follows that the area of the triangle is; 20 ft².

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Answer:

20 square feet

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

Given the base of the triangle is 5 feet, and the height is 8 feet, substitute b = 5 and h = 8 into the formula and solve for A:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot 5 \cdot 8\\\\&=\dfrac{5}{2} \cdot 8\\\\&=\dfrac{5 \cdot 8}{2}\\\\&=\dfrac{40}{2}\\\\&=20\; \sf ft^2\end{aligned}[/tex]

Therefore, the area of a triangle that has a height of 8 feet and a base length of 5 feet is 20 square feet.

The result for the error interval has already been rounded to the nearest integer, which is 4.8.

The numbers 10.3 and 10.5 are below and above, respectively (to 1 decimal place)

For the lower bound, we need to look halfway between 10.3 and 10.4 and for the upper bound, we need to look halfway between 10.4 and 10.5.

For the number to be rounded to 10.4 with one decimal point, it has to be between 10.35 and 10.45.

An inequality can be used to describe this.

10.35 ≤ x < 10.45

Thus, the error interval with the lower bound and upper bound are: 10.35 ≤ x < 10.45.

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Answer:

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

Step-by-step explanation:

The solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=5/2 x.

Substitute x=0, 1, 2, 3, 4,......

When x=0

y=0

When x=1

y=5/2=2.5

When x=2

y=5

When x=3

y=7.5

Therefore, the solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

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"Your question is incomplete, probably the complete question/missing part is:"

Use the equation y=5/2 x to complete the table. Is y proportional to x? Explain why or why not.

Answer:

12.375 hours

Step-by-step explanation:

We know that car travel

400 miles = 5.5 hours

900 miles = ?

We take 900 times 5.5, then divide by 400 and get 12.375 hours

So, the car take 12.375 hours to travel 900 miles

Answer:

12.375

Step-by-step explanation:

400+400+100=900miles

5.5+5.5=11

5.5÷4=1.375

11+1.375=12.375

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

Given that,

An open box length [tex]l[/tex] = 5 feet

An open box breadth b = 5 feet

An open box height = h

An open box area = 605 cubic feet

A square is a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The shape of the square is such as, if it is cut by a plane from the center, then both the halves are symmetrical. Each half of the square then looks like a rectangle with opposite sides equal.

Area = [tex]l * b * h[/tex]    (Equation - 1)

So,

We can substitute l , b , h values in the equation - 1,

605 = 5 * 5 * h

605 = 25 * h

605/25 = h

24.2 = h

Therefore,

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

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yes there is no work show below

The values of x and y that are solutions to the system of simultaneous equations are; y = 573/25 and x = 17.1

We are given the simultaneous equations;

²/₃x + ³/₅y = 12    -----(eq A)

⁵/₂y - 3x = 6       ------(eq B)

Multiply eq A by 9 and eq B by 2 to get;

6x + ²⁷/₅y = 108    -----(eq C)

5y - 6x = 12       ------(eq D)

Add eq C to eq D to get;

5y + ²⁷/₅y = 120

Multiply through by 5 to get;

25y + 27 = 600

25y = 600 - 27

25y = 573

y = 573/25

Thus;

5(573/25) - 6x = 12

6x = 5(573/25) - 12

6x = 102.6

x = 17.1

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Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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The amplitude of a sine or cosine function is the vertical stretch or compression factor of the function. In this case, the function f(x) = sin(x) has been stretched vertically by a factor of 3. Therefore, the amplitude of the function g(x) is A = 3.

The function g(x) = 3sin(12x) + (-5)