One positive integer is 2 less than twice another. The sum of their squares is 745.

The proof that Q R S T is a parallelogram is given and enumerated in the following paragraph.

A mathematical proof is a deductive argument for a mathematical declaration that demonstrates that the provided assumptions logically ensure the conclusion.

The proof that the above-named geometrical shape is a parallelogram goes thus:

Statements                                            Reasons

1. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex]                                 Given

2. [tex]\overline{RS}[/tex] ≅ [tex]\overline{QT}[/tex]                                 Given

3. [tex]\overline{RT}[/tex] ≅ [tex]\overline{TR}[/tex]                                 Reflexive Property

4. [tex]\Delta QRS[/tex]  ≅ [tex]\Delta STQ[/tex]                  SSS Congruence Theorem

5. A 1  ≅  A 4                   CPCTC Property

6. A 2  ≅  A3            CPCTC Property

7. QR | ST                    Alternate Interior Angles Converse

8. QT | RS                    Alternate Interior Angles Converse

9. Q R S T is a parallelogram         Definition of parallelogram      

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The first triangle is an Isosceles triangle:

2 equal sides

2 equal angles ( opposite to the sides)

The sum of all interior angles of a triangle is 180°

So, for the left triangle:

51+x+x2 = 180

x+x2 = 180-51

x+x2 = 129

Since both angles are equal:

129/2 = 64.5°

x= 64.5°

x+y = 90°

64.5 + y = 90

y= 90-64.5

y= 25.5°

Right triangle:

25.5+25.5 +z = 180

z= 180-25.5-25.5

z= 129°

Multiplication of all of the integers from -10 to -1, including -10 and -1 is positive.

What is integer?

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 3/4, 3.14.

According to question,

multiplication of  all of the integers from -10 to -1, including -10 and -1 is

-10 × -9 × -8 × -7 × -6 × -5 × -4 × -3 × -2 × -1 = +3628800

Answer is positive because - × - gives + and there are five such pairs of number, all of the minus sign become positive after multiplication.

Hence, multiplication of all of the integers from -10 to -1, including -10 and -1 is positive.

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We will have the following:

So, the simplification is equal to 1.1.

***Explanation***

First, we multiply all the values that are asked to be multiplied, and we also operate all the exponents. [We recall that a value at the power of a number is the number of times the value is multiplied by itself], then we get that:

Finally we operate the simpler and lower in the hierarchy of operations expressions:

Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:

• You can find the length of the rectangle by applying the following Trigonometric Function:

In this case, you can set up that:

Then, substituting values and solving for "l", you get:

• In order to find the width of the rectangle, you can use this Trigonometric Function:

In this case, you can say that:

Therefore, substituting values and solving for "w", you get:

• Now you need to use the following formula for calculating the area of a rectangle:

Where "l" is the length and "w" is the width.

Substituting the length and the width of the given rectangle into the formula and evaluating, you get:

Hence, the answer is: Option C.

Hi there. To solve this question, we'll have to remember some properties about parabolas and its roots.

Given the function:

that models the height of the football Armando kicked from the ground, in feet, with respect to time x in seconds, we have to determine:

The time it takes for the ball to return to the ground after being kicked.

Let's suppose that the ball was kicked from x = 0, since the times x is given in seconds and we can't have negative time.

Before supposing it, in fact we have to determine which moments the ball was at the ground, that is, f(x) = 0. We're finding the roots of the function:

To solve this quadratic equation, remember the general solution to a quadratic equation

Is given by the formula:

Plugging a = -7, b = 38 and c = 0.22, we get:

Multiply the values, square the number and add inside the radical.

Separing the solutions and calculating their values, we get

In this case, we before had supposed the ball started from x = 0. This is not really necessary because we found that the roots of this functions are contained in the positive x-axis.

To find the time for the ball to return to the ground, we make:

Or 5.42 seconds.

Graphically, what we have is:

Aisha age is 5 year and Aisha's mother age is 25 year.

The formula for a linear equation is the way in which a linear equation is expressed. It can be expressed in the standard form, the slope-intercept form or the point-slope form. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is the coefficient of x, and B is a constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, and A, B, and C are any real numbers.

Given that,

Aisha's mother is 5 times older than Aisha.

Let Aisha age = x year

Aisha's mother = 5x year

After 15 years Aisha's mother will be twice the age her daughter.

5x+15 = 2(x+15)

5x+15 = 2x+30

3x = 15

x = 5

Aisha age = 5 year

Aisha's mother age = 5x = 5×5 = 25 year

Hence, Aisha age is 5 year and Aisha's mother age is 25 year.

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Step-by-step explanation:

[tex]\sqrt[3]{t^{2} } + 4\sqrt{t^{3} } \\=t^{\frac{2}{3} } + 4t^{\frac{3}{2} }\\\\then, \\u` = \frac{2}{3}t^{-\frac{1}{3}} + 6t^{\frac{1}{2} }[/tex]

Answer:

D. 17.4 yards

Step-by-step explanation:

Since the area of the rectangle is 17.36 square yards, and the width is 3.1 yards, we set up and solve this equation to find the length:

17.36 = 3.1h, so h = 5.6 yards.

From this, the perimeter of the rectangle is 2(3.1 + 5.6) = 2(8.7) = 17.4 yards.

So D is the correct answer.

Answer:

Yes, it is a linear function.  For every input there is only 1 output.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]x^2 - 2x - 1 = 0\\x^2 = 2x + 1\\x^4 = 4x^2 + 4x + 1\\x^4 = 4(2x + 1) + 4x + 1\\x^4 = 8x + 4 + 4x + 1\\x^4 = 12x + 5[/tex]

The composite function's value, (gof)(5), is equivalent to 6.

A mathematical procedure called composite combines two functions, f and g, to produce a third function, h(x), where g(x) is the sum of f(x) and h(x).

Given the aforementioned functions,

f(x) = x^2-6x+2 and;

g(x) = -2x

The composite function is known as the gof (5)

(gof) = g(f(x)) where;

f(x) = g(x2-6x+2) and;

f(x) = -2(x2-6x+2).

Substitute the given functions into the composite;

g(f(5)) = -2(5^2-6(5)+2)

g(f(5)) = -2(-3) = 6

The comparable composite value is provided by this.

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We are given that Brianna needs to receive $199300 and that she also needs to allow for a 3 percent commission. Let "x" be the amount Brianna needs to sell her house. We need to subtract from this amount the 3% commission. To do that we will use the following relationship:

Now, we solve for "x" first by adding the fractions using the following model:

Therefore, we will multiply the 100 from the denominator by "x" and subtract 3 from the result, like this:

Solving the operations we get:

Now we multiply both sides by 100:

Now we divide both sides by 97:

Therefore, the amount is $205463.92. Since we are told to round to the nearest hundred dollars we round the answer to $205500.

The graph of function d is a reflection across the y-axis of the graph of function t.

In Geometry, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function t(x) = -4x + 72 would be transformed to function d:

d(x) = -(-4x) + 72.

d(x) = 4x + 72.

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Complete Question:

The temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x) = -4x + 72. The temperature x hours after 10 a.m. is represented by d(x) = 4x + 72. Describe the transformation from the graph of t to the graph of d.

Answer:

48 gallons of paint are needed.

Step-by-step explanation:

Set up a proportion.

Like this: x is for the unknown number of gallons.

[tex]\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer[/tex]

length:15 cm

width: 14 cm

Explanation

Step 1

Let

w represents the width of the rectangle

l represents the length of the rectangle

a)The width of a rectangle is 4 less than the length,hence

write this in math terms, replace

b)the area of the rectangle is 165 square cm

the area of a rectangle is given by

Step 2

now, solve the equations

a) replace the w from equation (1) into equation(2)

b) now, we have a quadratic equation in the form

hence, we can use the quadratic formula to solve

let

a=1

b=-4

c=-165

replace

therefore

as we are searchinf for a distance, the only valid answer is 15

so, the answer is length= 15 cm

c) finally, replace the l value into equation (1) to find the width

therefore, the width is 11 centimeters

I hope this helps you

The equation of the line with slope -2 and passing through the point (3,-2) is y+2x-4=0.

The point-slope formula is used to find the equation of the line passing through a point (a,b) and having a slope of m.

A straight line equation of the form (y-b) = m(x-a), where m is the slope of the line and (a,b) are the coordinates of a given point on the line, is the standard form given for the point-slope form of the line.

A point (3,-2) and a slope -2 are given.

Use the standard Point-slope form of the line to find the equation of the line.

(y-b) = m(x-a)

Put the given values in the Point-slope equation.

y-(-2)=-2(x-3)

Simplify the equation to get the equation of the line.

y+2=-2x+6

y+2x-4=0

So, the equation of the line is y+2x-4=0.

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The total cost of transporting 12 tons is $8000 and number of tons the company transporting is 23.

The total cost of transporting 12 tons can be calculated by keeping the value of number of tons in the formula.

Total cost = 6500 + 125×12

Performing multiplication on the Right Hand Side of the equation

Total cost = 6500 + 1500

Performing addition on the Right Hand Side of the equation

Total cost = 8000

The number of tons can be calculated by keeping the total cost in the formula.

9375 = 6500 + 125n

125n = 9375 - 6500

Performing subtraction on Right Hand Side of the equation

125n = 2875

n = 2875 ÷ 125

Performing division

n = 23

So, the total cost is $8000 and number of tons is 23.

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Answer:

0.053

Step-by-step explanation:

the probability of taking a Boston creme first is 6/19 (19 is the total doughnuts in the box), then the probability of taking a chocolate glazed second would be 3/18 (bc there would be 18 left after taking one first). then multiply these fractions together. as a decimal you get 0.053 to 3 decimal places

To find the answer, we just have to look for the complement fraction of 9/10, which is found by subtracting from 1

Observe that the complement of 9/10 is the answer because that's the amount of energy that stays in the plant.

It is an Irrational number.

Mathematics Number Types

The numbers are divided into many sorts based on their characteristics and how they are shown on a number line. To help readers comprehend each kind of number, descriptions, features, and examples are included. Here are the many kinds of numbers:

Natural Numbers

Natural numbers, which include the range of positive integers from 1 to infinity, are sometimes known as "counting numbers." The letter "N" stands for the set of natural numbers. The definition of the natural number set is:

N = {1, 2, 3, 4, 5, ……….}

For instance, 35, 59, 110, etc.

Natural Numbers' Characteristics

Natural number addition is commutative, associative, and closed.

Multiplication of Natural Numbers is closed, associative, and commutative.

Zero is the identity component of a natural number when added.

A natural number's identity component under multiplication is one.

Complete numbers

Natural numbers with a zero are another name for whole numbers. The set is made up of non-negative integers without any fractional or decimal parts. The entire set of numbers is "W" which stands for the concept. The definition of the natural number set is:

W = {0,1, 2, 3, 4, 5, ……….}

For instance, 67, 0, 49, 52, etc.

Whole-number properties:

Under addition and multiplication, whole numbers are closed.

The identity component of the whole numbers that are additive is zero.

The multiplicative identity element is 1, which.

It complies with addition and multiplication's commutative and associative properties.

The distributive property that favors multiplication over addition and vice versa is satisfied.

Here is further information about the entire numbers.

The set of all whole numbers with a negative set of natural numbers is known as an integer. The letter "Z" stands for the integer set. The definition of the set of integers is:

Z = {-3, -2, -1, 0, 1, 2, 3}

For instance: -52, 0, -1, 16, 82, etc.

Characteristics of integers

For addition, subtraction, and multiplication, integers are closed.

For integer addition and multiplication, the commutative property is met.

It abides by the addition and multiplication operations' associative feature.

For addition and multiplication, it abides by the distributive property.

The integers' additive identity is 0.

Integers have a multiplicative identity of 1.

Actual Figures

Real numbers are any number, including positive and negative integers, fractional and decimal numbers, and quantities without imaginary numbers. The letter "R" is used to signify it.

Examples are 34, 0.333, 2, 0, -10, 20.

Real Numbers' Characteristics

Under addition and multiplication, Real Numbers are commutative, associative, and distributive.

The opposite property applies to real numbers.

Real numbers have identity elements that are 0 and 1, respectively, for addition and multiplication.

Rational  Numbers

Any integer that can be expressed as p/q, or as a ratio of one number to another, is referred to be a rational number. The letter "Q" can be used to signify a rational number.

Examples include 7/1, 10/2, 1/1, and 0/1.

Rational number properties include:

Addition, subtraction, multiplication, and division all result in closed rational numbers.

With regard to addition and multiplication, it meets the commutative and associative properties.

For addition and subtraction, it abides by the distributive property.

Unrealistic Numbers

The amount that cannot be represented by p/q. It denotes a number as being irrational if it cannot be expressed as a ratio of one to another. The letter "P" is used to signify it.

Examples include 2 and Euler's constant.

Irrational number characteristics include:

Irrational numbers do not meet the property of closure.

Under addition and multiplication, it complies with the commutative and associative properties.

Irrational numbers can be added to and subtracted from in distributive ways.

Large Numbers

Complex numbers are those that take the form a+bi, where a and b should be real values, and I should be an imaginary number.

Examples are 1 + 2i, -2 + 3i, and 4 + 4i.

Complex number properties include:

The complex numbers have the following characteristics:

a characteristic of addition and multiplication that is associated.

Commutative addition and multiplication properties.

Multiplication's distributive advantage over addition.

Unreal Numbers

The complex numbers category includes imaginary numbers. It is the result of adding actual numbers with the hypothetical unit "i." It defines the imaginary portion of complex numbers.

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Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. The tax rate t that maximizes revenue for the government is 66.992%.

Revenue can be defined as the amount or the income a person or an organization generated from the sales of goods and services.

Given function :

Total sale  = S(t) = 7−6∛t

Hence,

Expression for Revenue rate = r(t) = tS(t)

Now let substitute and solve  expression

r(t) = t (7−6∛t)

= 7t−6(t)^4/3

Differentiate the expression

d[r(t)] dt = r′(t)

r′(t) = 7− (4/ 3) 6(t)^1/3

=7−8(t) ^1/3 ........ expression (1)

Maximum revenue

r′(t) = 0

Substitute and solve expression (1)

0 =7−8(t)^1/3

(t) = (7/8)^3

= 0.66992 × 100

= 66.992%

Therefore we can conclude that the tax rate t that maximizes revenue is 66.992%.

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The complete question is :

Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)

S(t)=7−6∛t

-7a - 2y + 7 + 2y + 5a

Reordering:

(-7a + 5a) + (-2y + 2y) + 7 =

= -2a + 7 =

= 7 - 2a

Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.

The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality.

Given Mean (X) = 3.86, Standard deviation (SD) = 3.36

According to Chebyshev’s Theorem,

1-1/k^2  proportion of values lies between Mean ± (k × SD )

Given k = 2.

k = x - mean /SD

1-1/k^2 =1-1/2^2

⇒1-1/4=1-0.25

⇒0.75

Therefore Proportion Value = 75%

If k= 2

75% Chebyshev’s intervals are

Lower Limit = Mean - (k × SD )

⇒3.86 - (3.36×2)

⇒3.86 - 6.72 = - 2.86

Upper Limit = Mean + (k × SD )

⇒3.86 + (3.36 × 2)

⇒3.86+6.72 = 10.58

Hence the Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.

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The Quadrilateral can best be described as a trapezoid with it's two parallel sides and two non- parallel sides.

A Quadrilateral is a type of polygon that is known to have four sides from which the name is being derived.

Examples of quadrilateral include the following:

The quadrilateral represented in the coordinate grid is a trapezoid because it has two parallel sides which are AB and DC and two non parallel sides such as AD and CB.

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According to the table of values, y has a value of 15 when equals 5

The table of values represents the given parameter

On the table of values, we can see that:

The value of x multiplied by 3 gives the corresponding value of y

This can be represented as

y = 3 * x

Evaluate

y = 3x

As a proof, we have

1.5 * 3 = 4.5

3 * 3 = 9

5.2 * 3 = 15.6

So, when x = 5;

We have

y = 3x

This gives

y = 3 * 5

Evaluate

y = 15

Hence, the value of y when x= 5 is 15

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Check the picture below.