If PQRS is a rectangle, ST = 12, and mzPRS = 23°, find each measure.

SQ =
PT =
measurement of angle QPR =

The height of the popcorn box is 8.75 inches.

What is the rectangular prism?

A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as a rectangular cuboid, or simply a cuboid. It has three dimensions: length, width, and height. It can be represented by the formula: V = lwh where l is the length, w is the width, and h is the height.

We can use the formula for the volume of a rectangular prism to solve this problem. The formula is:

V = l * w * h

where V is the volume, l is the length, w is the width, and h is the height. We know that the volume of the box is 35 cubic inches and that the length and width are 2 inches each. So we can substitute those values into the formula and solve for h:

35 = 2 * 2 * h

To find h, we'll divide both sides of the equation by 4.

h = 35/4 = 8.75

Hence, the height of the popcorn box is 8.75 inches.

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The value for the input when the output is −3 is 6.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given y = f(x)

and f(x) = -2/3x + 1

to find the value of x when f(x) = -3

substitute the value of f(x)

f(x) = -2/3x + 1

-3 = -2/3x + 1

-2/3x = -3 - 1

2/3x = 4

x = 4*3/2

x = 6

Hence the input is 6.

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The line's slope is -6, and its y-intercept is 2. In this equation, the slope is the value of x, which is -6, and the y-intercept is the value of b, which is 2. This is known as the slope-intercept format.

All linear equations, with the exception of vertical lines, cross the y-axis at a certain location known as the y-intercept. When our linear equation is written as y = m x + b, the slope-intercept form, the value of b is the value of the y-intercept.

Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).

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Answer:

  f(x) = 3x

Step-by-step explanation:

You want the relation 3x -y = -6x +2y written as a function of x.

This is solved the same way any 3-step linear equation is solved:

Now you have the function written in terms of x:

  y = 3x

In functional notation, this is ...

  f(x) = 3x

Answer:

The values are calculated with the help of table.

Step-by-step explanation:

We are given the following information in the question:

A table is shown showing trees on two different plots of land which are tested for disease.

     Tree:        1           2           3           4          5           6          7        

      Plot:         A          A           B           B         B           A          B

Disease:        Y          N           Y           Y          Y          N         N

We have to find:

Calculating from the table, we can fill the values as:

                                              Plot A                Plot B

Disease Present                        1                          3

Disease not Present                2                          1

the of is .

The formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides

Given data ,

Let the be

Now , the value of k is determined by

The values of Time be x = { 2 , 4 , 6 , 8 }

The values of distances be y = { 8,16,24,32 }

Now , the constant of proportionality is given by

y = kx

Divide by x on both sides of the equation , we getk = y/x

Substituting the values in the equation , we get

k = 8/2

k = 4

And , k = 16/4

k = 4

Therefore , the value of is .

Hence , the constant of is

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The value of constant or K is found to be 4.

The formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides

Given data ,

Let the be

Now , the value of k is determined by

The values of Time be x = { 2 , 4 , 6 , 8 }

The values of distances be y = { 8,16,24,32 }

Now , the constant of proportionality is given by

y = kx

Divide by x on both sides of the equation , we getk = y/x

Substituting the values in the equation , we get

k = 8/2

k = 4

And , k = 16/4

k = 4

Hence , the constant of is 4.

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The first angle is 80 and the other angle is  100.

What are supplementary angles?

The pair of angles known as supplementary angles always add up to 180 degrees. These two perspectives are known as each other's supplements.

Let one angle to be 'x', other angle to be 'y' and the number to be 'c'.

So, according to the question:

one angle is forty more than four times a number and the other angle is

twenty less than twelve times a number.

So, x = 4c + 40

and, y = 12c - 20

We know that, the sum of x and y would be 180 because these are supplementary angles.

So, x + y = 180

  4c + 40 + 12c - 20 = 180

 16c + 20 = 180

 16c = 160

   c = 10

Hence, x = 4(10) + 40 = 80

and, y = 12(10) - 20 = 100

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The measures of the angles are (a) 180-C, and 180-A (b) 180 (c) 180 and supplementary.

You should understand that  cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle

For better understanding note the following

Opposite angles of a cyclic quadrilateral are supplementary

opposite angles of a cyclic quadrilateral = 180 degrees

(a) m<A = 180 - m<C

m<C = 180 - m<A

(b)  m<A + m<C = 180 .......... (opposite angles are supplementary)

(c) m<A + m <C = 180 (Sum of opposite angles = 180⁰)

(d) <A and <C are supplementary angles

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The additive inverse of 3/7 is -3/7.

The additive inverse of any number is the opposite of that number. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

3/7

So, the additive inverse of 3/7:

⇒3/7 + Additive inverse = 0

⇒Additive inverse = -3/7

Thus the additive inverse of is 3/7 is -3/7.

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Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

To make a 360mL mixture that contains 9% vinegar, use 288 mL of the first brand and 72 mL of the second brand.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 360 milliliters of a dressing that is 9% vinegar.

to set up an equation that will match the word problem. Let's call the amount of the first brand, F, and the amount of the second brand, S.

We want the total mixture to be 360mL so: F + S = 360

Also, you want the total mixture to contain 8% vinegar so:

.08F + .13S = .09(360)

Now, we can solve the system of equations using substitution.

F + S = 360

.08F + .13S = .09(360)

F = 360 - S      [solve 1st equation for F]

.08(360 - S) + .13S = .09(360)    [substitute into 2nd equation]

28.8 -0.08s+0.13s = 32.4

0.05s = 3.6

S = 72

F + 72 = 360     [substitute answer for S back into original equation]

F = 288

Therefore, To make a 360mL mixture that contains 9% vinegar, use 288 mL of the first brand and 72 mL of the second brand.

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The strength and direction of a force are shown by an arrow. Its length indicates the strength (size) of the force, while the arrowhead points towards the force's direction of application.

Gravity and the air's resistance act on the arrow as it goes in the direction of the target. Frictional force is another name for the air resistance force.

Science fundamentals:

Scientists employ arrows to depict a force's intensity and direction.

The force's direction is indicated by the arrow's direction.

The force's strength is represented by the length of the arrow.

A smaller, weaker force is represented by a shorter arrow than a greater, stronger force by a longer arrow.

The strength and direction of a force are shown by an arrow. Its length indicates the strength (size) of the force, while the arrowhead points towards the force's direction of application.

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The number from greatest to least in the given set of numbers are:

-14/5 < -2.25 < 1 ¼ < 3/2

A group of numbers is referred to as an element and makes up a set of numbers. The collection of numbers in the set may be infinite or finite. Roster notation is a method for indicating sets. For example, the set "2,31" contains the elements 2 and 31.

We need a way to say which numbers are included when a set has an infinite number of elements because it is impossible to list them all. Our number system is based on a few well-known infinite sets.

Given mixed fractions and decimals:

-14/5, -2.25, 1 ¼, 3/2

So,

-14/5 = −2.8

-2.25

1 ¼ = 1.25

3/2 = 1.5

As, −2.8 < -2.25 < 1.25 < 1.5, The numbers from greatest to least are:

-14/5 < -2.25 < 1 ¼ < 3/2.

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Complete question:

There are different ways to represent an inequality, but two correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 - 5x

-6x + 15 + 5x < 10

-x < -5

and

2x - 5 < -5 + 2x

0 < -5x

x > 0

Both options are correct as each of them represents a different way to simplify the inequality but still holds the same meaning.

Answer:b=294

Step-by-step explanation: b/14=21 21*14=b

Answer: B=294

Step-by-step explanation:

From the given shapes, The value of c and d are 4 and 6.

An region in two dimensions known as a shape is determined by a collection of lines, curves, or angles.

The locations of its points define its perimeter.

Geometric (such as a square, triangle, circle, etc.) or organic (such as free-form) shapes are both possible. Images, symbols, and designs are all made out of shapes in art and design.

According to its attributes, such as area, perimeter, and angle, forms are characterised and categorised in mathematics.

Space, such as that found in a plane or in three dimensions, can also be described by shape.

To construct things like bridges and buildings, architects and engineers use forms.

Objects and their interactions with one another are described by forms in physics.

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The probability  that a student chosen at random speaks Spanish but not French is 0.66

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

At a college, 20% of students speak Spanish, 6% speak French, and 4% speak both languages.

Conditional probability

let P(I) = 0.06, P ( S & I) = 0.04 and P (S) = 0.20

Finally to find P ( S  given I )

we use the theorem

P ( S given I ) = P (S & I) / P (I)

=  0.04 / 0.06

= 4/6

= 2/3 = 0.66

Hence, The probability  that a student chosen at random speaks Spanish but not French is 0.66

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After solving the quotient (2x^3 - 3x - 10) ÷ (x - 2) is 2x^2 + 4x + 5.

In the given question, we have to find the quotient (2x^3 - 3x - 10) ÷ (x - 2).

The given expression is (2x^3 - 3x - 10) ÷ (x - 2).

We must use the synthetic division approach to determine the quotient.

By artificial division,

1) Identify the term's coefficients.

2) Decrease the initial coefficient, which is 2.

3) Putting 4 under the second coefficient 0 (2×2 = 4) now. Together, we get 4.

4) We take 4 and double it by 2, which gives us 8. Put 8 under coefficient 3 in the third place. Together, we get 5.

5) Next, divide 5 by 2. We get 10. Under the fourth coefficient, put 10. Together, we get 0.

x-2 ) 2x^3          - 3x - 10 ( 2x^2 + 4x + 5

        2x^3 - 4x^2

       -       -

      ___________

                   4x^2 - 3x

                   4x^2 - 8x

                  -       -

              ______________

                               5x - 10

                               5x - 10

                              -      -

                         ____________

                                  0

Hence, after solving the quotient (2x^3 - 3x - 10) ÷ (x - 2) is 2x^2 + 4x + 5.

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The complete question is:

What is the quotient (2x^3 - 3x - 10) ÷ (x - 2)?

The product of (4y - 3)(2y²+ 3y - 5) is 8y³+ 6y²- 29y+15.

The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 20 is the product of 4 and 5, and so on. The term "product" refers to the result of one or more multiplications.

Given expression is

(4y - 3)(2y²+3y-5)

⇒ 4y(2y²+3y-5) -3(2y²+3y-5)

⇒ 8y³+ 12y²- 20y - 6y²- 9y + 15

⇒ 8y³+ 6y²-29y+15

Therefore, the product of (4y - 3)(2y²+3y-5) is 8y³+6y²- 29y+15.

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The equation of the line if the y-intercept i (0,6) and the lope i 15 is:

B. y = 15x 6

The equation of the line is given in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis and is given as (0,6). Therefore, the value of b is 6. The slope is given as 15. Therefore, the equation of the line is y = 15x + 6. This equation means that for every unit increase in x, y increases by 15 units and the line passes through the point (0,6)

This method is applicable for other equations as well, as long as they are in slope-intercept form (y = mx + b). The slope-intercept form is a way to represent a linear equation where the slope and the y-intercept are known. If the equation is not in that form, it can be rearranged to make it so. Once the equation is in slope-intercept form, you can identify the slope and the y-intercept which can be useful in understanding the characteristics of the line such as its direction and position in the coordinate plane.

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The product of 2/3 and ¾ is 6/12 that is 0.5.

To find the product of the given equation

[tex]\frac{2}{3} * \frac{3}{4} \\\\\frac{2*3}{4*3} \\\\\frac{6}{12\\}\\\\\\frac{1}{2} \\\\0.5[/tex]

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Simply the fraction to its lowest word before multiplying it. Simplify it in the case of mixed fractions. Multiply the denominator by the denominator and the numerator by the numerator once the fraction has been made simpler. The fractional product is then obtained in p/q form.

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Answer:

x = 10

Step-by-step explanation:

Based on the given conditions, formulate: 140 - 12 X x = 20

Rearrange unknown terms to the left side of the equation: -12x = 20 - 140

Calculate the sum or difference: -12x = -120

Divide both sides of the equation by the coefficient of variable: x = -120/-12

Determine the sign for multiplication or division: x = 120/12

Cross out the common factor: x = 10

get the result: x = 10

Answer: x = 10

The partial sum is called  the sum of part of the sequence, they are also called as finite series.

Since adding all the terms does not yield the sums of these series, we can study their behaviour by looking for patterns in the partial sums. A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums. For instance, is the total of an infinite series' first six terms.

The first five partial sums are in the following order: 1, 4, 9, 16, and 25. This trend will persist, and the terms will keep expanding without limit. In other words, because the infinite total is infinitely huge, the partial sums keep increasing.

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The recommended range for longitude and latitude coordinates is -180 to 180 and -90 to 90, respectively.

The use latitude and longitude to coordinates

To denote degrees, use the degree sign.

To denote decimals, use periods.

Your spreadsheet should have Latitude listed before Longitude.

When plotting a point, (x, y)-coordinates are used. The horizontal movement from the origin along the x-axis is represented by the value of x, while the vertical movement along the y-axis is represented by the value of y. A helpful hint is to always put latitude (either north or south) before longitude when providing a coordinate (east or west). Degrees, minutes, and seconds are used to divide latitude and longitude.

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The requried solution of the given system of equations is x = -9 and y = 2.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
1/3x + y = -1  - - - - - - -(1)

1/3x + 8y = 13 - - - -- - (2)

Subtract equation 1 from 2,
8y - y = 13 + 1
y = 2

Now,
1/3x + 2 = -1
x = -9

Thus, the requried solution of the given system of equations is x = -9 and y = 2.

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The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.

The formula for a polynomial in its standard form is [tex]f(x)=a_a x^n+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+\ldots . .+a_1 x+a_0[/tex]

A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power. Leading term and leading coefficient are terms used to describe the first term and its coefficient, respectively, in the polynomial's standard form.

According to the definition of a polynomial in standard form, exponents must be written in decreasing order. The standard form of polynomials is used to facilitate calculations. Exponents must be expressed in decreasing order in order to be considered a polynomial in standard form. To make calculations easier, polynomials are expressed in their standard form.

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Answer:

Four folk love legends: "Cowhand and Weaver Girl", "Meng Jiangnu crying at the Great Wall" (cry Wan Xiliang), "Liang Shanbo and Zhu Yingtai", "The Legend of the White Snake", the author does not know

The development history of the Four ancient Chinese folk legends: China is a country with a vast territory and abundant resources and a long history, which contains extremely rich national cultural heritage. Among them, the four most Chinese ones are the famous "Cowhand and Weaver Girl", "Meng Jiangnu", "Liang Shanbo and Zhu Yingtai" and "The Legend of the White Snake". The most widespread, the most influential.

Brief introduction: the gigolo knit legend began in the book of songs, cable ":" Qi he vega ", "Huan he cow". "Nineteen Ancient Poems · Long Distance Star" has called the cowherd and weaver girl husband and wife. Ying Shao "custom" Yi wen: "Zhinv Tanabata when crossing the river, make magpie bridge, legend has it that the magpie head without reason all Kun, because beam (note: bridge) to cross Zhinv also. The story has been preliminarily formed and combined with the Qixi Festival custom.

The legend of Meng Jiangnu originated from the record of Qi Liang's wife refusing to hang herself in the area of the Marquis of Qi and adhering to the rules of etiquette in the Zhuan. Later, it was added in the Dangong that "Duke Zhuang of Qi attacked Ju and took away (tunnel) and Qi Liang died. The weeping wife who greeted his coffin on the road is the archetype of the story. Han Liu Xiang's Biography of Liannu (IV) : "Qi Liangzhu died in battle, his wife cried in the city, ten days the city collapsed." And Tang (anonymous) "carved jade collection" record "Qin when Yan Qi Liang, married Meng Chao female Zhongzi wife, because good was built the Great Wall officials killed, Zhongzi cry under the Great Wall, the city collapsed. It is known that this legend was popular in the Tang Dynasty, but Meng Zhongzi and Qiliang were renamed Meng Jiangnv and Fan Xiliang in the legend. The story of Butterfly lovers first appeared in Tang's "Ten Taoist and Four Tibetan Records", which recorded the story of Liang and Zhu "having a taste of schoolmates" and "sharing the tomb". There are more detailed records in Xuanbaozhi of late Tang Zhang Reading. To the Ming Dynasty Feng Menglong's "Ancient and modern novels", and added to the British Taiwan confused belt, Liang Shanbo doubts and butterflies.

The story of White Snake came into being the latest. The origin of the story is as follows. It originates from the Three Towers of West Lake. To the Ming Dynasty Feng Menglong's "Lady White Forever Town Leifeng Pagoda" (" Warning Word "), the story has been preliminarily finalized.

Answer: 7.5 cm; 1.6 cm

Step-by-step explanation:

If that is a right triangle, it is probably a 30 60 90 triangle and we can use this special property to say that the leg facing the 30 degree angle is half of the hypotenuse. The hypotenuse measures 15 cm, which means we can say that the leg facing the 30 degree angle is 7.5 cm. Next, since 21 cm is the sum of the 2 legs, we can add 21 cm to 15 cm to get 36 cm. Now that we know our hypotenuse, perimeter, and one of our legs, we can find the other leg by using basic algebra to get 1.6 cm. Hopefully this helps! I'm not sure tho.

The answer is the equation can have many solutions. the given equation is the linear equation that may have infinitely many  solutions.

The equation given in the question is  

2x + y – 5 = 0  

4x + 2y – 10 = 0  

For the given equation it can be written as:  

[tex]a_{1} x+ b_{1}y - c_{1} = 0[/tex]

[tex]a_{2} x+ b_{2}y - c_{2} = 0[/tex]

Here, [tex]a_{1}[/tex] = 2, [tex]b_{1}[/tex] = 1, [tex]c_{1}[/tex] = −5  

[tex]a_{2}[/tex]= 4, [tex]b_{2}[/tex]= 2,  [tex]c_{2}[/tex]= −10

So, according to the question given for the equation:

[tex]\frac{a_{1} }{a_{2}} = \frac{2}{4} = \frac{1}{2}[/tex]

[tex]\frac{b_{1} }{b_{2}} = \frac{1}{2}[/tex] and

[tex]\frac{c_{1} }{c_{2}} = \frac{-5}{10} = \frac{1}{2}[/tex]

⇒  [tex]\frac{c_{1} }{c_{2}} = \frac{b_{1} }{b_{2}} = \frac{c_{1} }{c_{2}}[/tex]

From the above solution, we see the end result for the equation given so, we can say that this given equation can have infinitely many solutions.

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