Explain how the Distributive Property can be used to solve the equation.
3(x + 4) = 36.

Answer:   The mystery number is 5.5

5.5 converts to the fraction 11/2.

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

Explanation:

The phrasing "subtract 10 from the number, then square the result" leads to the expression [tex](\text{x}-10)^2[/tex]

The phrasing "Square the number, then subtract 10 from the result" means we have [tex]\text{x}^2-10[/tex]

Set those expressions equal to one another so we can solve for x like shown in the steps below.

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\\text{x}^2-20\text{x}+100 = \text{x}^2-10\\\\-20\text{x}+100 = -10\\\\-20\text{x} = -10-100\\\\\text{x} = -110/(-20)\\\\\text{x}=11/2\\\\\text{x} = 5.5[/tex]

The x^2 terms cancel out in the third step (since we subtract x^2 from both sides).

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

Check:

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\(5.5-10)^2 = (5.5)^2-10\\\\(-4.5)^2 = (5.5)^2-10\\\\20.25 = 30.25-10\\\\20.25 = 20.25[/tex]

The answer is confirmed.

On solving the provided question we can say that - area of the given triangle will be A = 60 cm sq.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

B = 8cm

H = 15 cm

A = 1/2 BH = 1/2 X 8 X 15 = 60cm sq.

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The percentage of people who are satisfied with the car are 60%.

In mathematics →

Given is that in a survey of 2000 people who owned a certain type of​ car, 1200 said they would buy that type of car again.

The percentage of people who are satisfied with the car are -

{x}% = (1200/2000) x 100

{x}% = (12/20) x 100

{x}% = 12 x 5

{x}% = 60

Therefore, the percentage of people who are satisfied with the car are 60%.

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Answer:

Step-by-step explanation:

In addition and subtraction, the identity is 0. In multiplication and division, the identity is 1. That means that if 0 is added to or subtracted from n, then n remains the same. Also, if n is multiplied or divided by 1, then n remains the same  

ORRRRRRRRR

Five Properties of Addition

Closure property of Addition.

Commutative property of Addition.

Associative property of Addition.

Additive identity property of Addition.

Additive inverse property of Addition.

The ordered array will be 9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2

What is leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

In this instance, the number on the left of the division stands in for the number in the tens place. The value or values on the right side are the ones that fall between the tens and ones places. The number "9.1" is the equivalent of the word "911," for instance. When a number appears more than once on the right side of a division, that number appears more than once in the tens place. In this case, the three numbers 9.1, 9.4, and 9.7 are represented by the string "9 | 147".

Hence, There is an ordered array when reading the stem and leaf plot from top to bottom:

9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2

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Answer:

p + s = 45

s = 2p + 5

Step-by-step explanation:

Let s = number of students.

Let p = number of parents.

p + s = 45

s = 2p + 5

Growth that is slower than the Nuttall Oak growth rate is h=5t.

An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.

This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.

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Answer:180 degrees

Step-by-step explanation: add the angles

Answer:

Step-by-step explanation:

Given: Polynomial y = 5x²+3x⁶-10x-8

here, 5 is the coefficient of x², 3 is the coefficient of x⁶, -10 is the coefficient of x and -8 is the constant term.

option (D)

Answer:

down there.

Step-by-step explanation:

Look for a term that has no variables with it. Once you've found it you've found ur constant. The only such term is -8 so the constant is -8 or choice d.

hence choice d

Answer: solving by forming simple algebra equation

Step-by-step explanation:

8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)

We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y

& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80

& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
      = 6 (10) = 60

so the cost of basketball is $80 & 1 volleyball is $60

Hope it helps :)

p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!

f(x)=[tex]x^{2}[/tex]-x-4 + g(x)=x+4 = the product is with process [tex]x^2+7 x+8$$[/tex] . It is the solution of f(x) and g (x) .

[tex]$$f(x)=x^2-x-4, g(x)=x+4: x^2+7 x+8$$$$\begin{aligned}& \text { Find } f \circ g \text { given } f(x)=x^2-x-4, g(x)=x+4 \\& f \circ g=f(g(x)) \\& g(x)=x+4 \\& =f(x+4)\end{aligned}$$$$\begin{aligned}& f(x+4): \quad x^2+7 x+8 \\& =x^2+7 x+8\end{aligned}$$[/tex]

When a number is multiplied by another number, its products can be found. Because 9 x 3 Equals 27, for instance, 27 is a product of 9 and 3. What you get when you multiply two numbers together is their product. As a result, the product of three and four is twelve, followed by five and four, and so on.

A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product. For instance, the result of multiplying 2 by 5 is 10 when the two numbers are combined. Byproducts include things like straw from grain harvesting operations, salt from desalination plants, sawdust from sawmills, and manure from feedlot operations.

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Ms. Wickham folded 200 report cards and Ms. Cho folded 300 report cards, giving Ms. Cho an average of 100 report cards.

Ms. Wickham and Ms. Cho together folded 500 report cards.

Ms. Wickham folded 200 report cards

(200/500 = 2/5)

Ms. Cho folded 300 report cards

(300/500 = 3/5)

Mr. Leiva and Mr. Gamory folded 300 report cards.

Ms. Cho folded more report cards than Ms. Wickham, by

100 (300 - 200 = 100).

Ms. Wickham and Ms. Cho together folded 500 report cards, with the ratio of Ms. Wickham's report cards to Ms. Cho's being 2:3. Ms. Wickham folded 200 report cards, while Ms. Cho folded 300. At the end of the day, Mr. Leiva and Mr. Gamory folded an average 300 report cards. This meant that Ms. Cho folded more report cards than Ms. Wickham, by 100. Therefore, Ms. Cho folded 400 report cards in total, while Ms. Wickham only folded 300.

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The value of x in its simplest radical form is (25)^1/3

When a given number is in the form of a whole number, it is said to be an integer. Thus it can not be in the form of a fraction or does not have a decimal part. Examples include: 20, 345, 10, etc.

Radical form is a type of number which is expressed with a square root. This it could give a whole number or a number with a decimal part as the final answer.

To solve for x in either as an integer or in its simplest radical form;

-42 = 8 - 2x^3

-42 - 8 = -2x^3

- 50 = -2x^3

divide through by -2 to have;

x^3 = 25

find the cube root of both sides,

x = 25^1/3

Therefore in it simplest radical form, the value of x is 25^1/3

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The number is 35.

What is an equation?

An equation is a statement of equality between two expressions. It uses the equal sign (=) to show that the expressions on either side of the sign have the same value.

For example 2x+3=5y-7z, and x+y=5 are examples of equations.

In solving your problem,

25 less than the sum of a number and 5 results in 15, can be written as an equation like this:

let x be the number we want to find.

x + 5 =15+25 (25 less than the sum of x+5)

x + 5 = 40

then

x=40-5

x=35

So the number is 35.

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The confidence interval is (22.68,29.52).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

n = 10

x = 26.1

s = 4.2

Two-sided confidence interval :

CI = [tex](x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )[/tex]

    = [tex](26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )[/tex]

    = (26.1−3.42,26.1+3.42)

    = (22.68,29.52)

Hence, the confidence interval is (22.68,29.52).

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The outer perimeter of the figure will be 62.3 ft.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The figure is shown in figure.

Now, The total outer perimeter is,

⇒ Outer perimeter of triangle = 12.2 ft + 6 ft

                                              = 18.6 ft

And, Outer perimeter of rectangle = 14 ft + 14 ft

                                                     = 28 ft

And, Outer perimeter of semicircle = πr

                                                      = 3.14 × 10 / 2

                                                      = 3.14 × 5 ft

                                                      = 15.70 ft

Thus, The total outer perimeter is = 18.6 ft + 28 ft + 15.70 ft

                                                    = 62.3 ft

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Vivian and her dad travelled for a total distance of 12 miles

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

Time taken = 4 hours

Rate of travel = 3 miles per hour

The distance travelled can be calculated using the following equation

Distance = Rate of travel * Time taken

Substitute the known values in the above equation, so, we have the following representation

Distance = 3 miles per hour * 4 hours

Evaluate the product

So, we have the following representation

Distance = 12 miles

Hence, the distance is 12 miles

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Complete question

Vivian and her dad drive 4 hours to the rock and roll hall of fame in Cleveland, Ohio. if they drive at the same rate how far do they travel if the rate is 3 miles per hour

The greatest number of classrooms is 4, Joanne can distribute materials

5 flyers and 4 buttons.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor or GCF.

Given:

Joanne is campaigning for class president and plans to distribute some campaign materials.

20 flyers and 16 buttons.

She wants each classroom to receive an identical set of campaign materials, without having any materials left over.

In order to find the greatest number of classrooms, Joanne can distribute materials:

We have,

the number of flyers = 20.

Number of buttons = 16

We need to find the GCF.

GCF of 16 - 1,2,4,8,16

GCF of 20-1,2,4,5,10,20

Clearly, 4 is the GCF.

Therefore, total number of classrooms = 4

Number of flyers distributed to each classroom

= Total number of flyers / Total number of classroom

= 20/4

= 5

Number of buttons distributed to each classroom

= Total number of buttons/ Total number of classrooms

= 16/4

= 4

Therefore, the Joanne can distribute 5 flyers and 4 buttons to each classroom.

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a) Attached at the end.

b) Strong positive linear correlation.

c) The length of time is 220 minutes.

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).

Given:

a) The Scatter plot Associated with data is attached below.

b) The Scatter plot shows the positive linear correlation between number of pieces in a jigsaw puzzle and time required for a person to complete it.

c) To complete the puzzle with 650 pieces it will take 220 minutes.

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Answer:

a)  See attachment.

b)  Strong positive correlation.

c)  247 minutes

Step-by-step explanation:

Plot the points from the given table on the given coordinate plane.

Draw a line of best fit.

(See attachment).

As the line of best fit has a positive gradient, the two variables are positively correlated.

As the line of best fit lies close to most of the points, this indicates there may be a strong correlation.

To predict the length of time it will take Dave to complete a 650-piece puzzle, locate 650 on the x-axis of the scatter plot, trace up to the line of best fit and read the y-value:

Therefore, it will take Dave approximately 247 minutes to complete a 650-piece puzzle.

The ratio is 1:4, which means for every 1 butterfly, there are 4 caterpillars.

This ratio represents the relationship between the number of butterflies and the number of caterpillars. In this case, the ratio is saying that for every 1 butterfly, there are 4 caterpillars. This could mean that for every butterfly that is observed, there are 4 caterpillars that are also present or for every butterfly that is caught, there are 4 caterpillars that are also caught.

This ratio may also indicate that for every butterfly that is born, 4 caterpillars are also born. It could also indicate the population ratio of butterflies to caterpillars in a specific habitat.

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f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

We note that x=7 is on 1<x< 9 so we use the second piece. Replace x with 7 and

evaluate to find f(7):

f(7)=2(7)

f(7)=14

so f( 7 ) = 14

f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.

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The 40 50 90 triangle can be solved using Pythagoras theorem.

A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.

Given:

We have 40 50 90 triangles.

A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.

Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.

So, Such type of Triangles can be solved using Pythagoras theorem.

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Using the provided values and the conditions, The inequality equations required are : [tex]x+y \leq 20[/tex] and [tex]450x+200y \geq 4800[/tex].

An equation is a mathematical statement in which two expressions are set equal to each other. It is typically written using an "=" sign, with the expressions on either side of the sign representing equivalent values. For example, the equation 2 + 2 = 4 states that the value of 2 plus 2 is equal to the value of 4. Equations can be used to express relationships and to solve problems.

An inequality is a mathematical statement that compares two values or expressions. It is similar to an equation, but instead of using the "=" sign to indicate that the two sides are equal, it uses one of the following symbols: ">", "<", "≥", "≤" to indicate that the two sides are not equal. For example, the inequality 2 + 2 > 4 states that the value of 2 plus 2 is greater than 4. Similarly, the inequality 2 + 2 < 4 states that the value of 2 plus 2 is less than 4. Inequalities can be used to express constraints in a problem or to define a range of solutions. They can also be represented graphically by using a number line.

x= number of tables sold

y= number of chair sold

max furniture in a day = 20

so, [tex]x+y \leq 20[/tex].

least selling amount = 4800

so, [tex]450x+200y \geq 4800[/tex]

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The meaning of the 4! ( factorial ) in mathematics is equal to                    ( 4 × 3 × 2 × 1 ).

As given in the question,

Given expression in mathematics is written as :

4! ( factorial )

In standard form meaning of the n! ( factorial ) is given by multiplication of all the terms in decreasing order till 1.

It is expressed as:

n! = n × ( n - 1 ) × ( n - 2 ) × ( n - 3 ) × ........× 3 × 2 × (n - (n - 1) ).

Apply this formula for 4! ( factorial ) we get,

4! ( factorial )

= 4 × ( 4 - 1 ) × ( 4 - 2 ) ×( 4 - 3)

= 4 × 3 × 2 × 1

= 12

Therefore, the meaning of 4! ( factorial ) in mathematics is given by

4 × 3 × 2 × 1 .

The above question is incomplete , the complete question is :

What does 4! ( factorial ) mean in mathematics?

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It is false that the cost of two pounds of apple cast is more than $ 3.50.

Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.

Given that  

Andrew buy 8 pounds of apples for $ 12.00  

Let 'x' be the cost of 1 pound of apples

By the given data,

=> 8x = $ 12

=> x = 12/8

=> x = 1.5  

The cost of 1 pound of apples = $ 1.5

Cost of 2 pounds apples = 2 × 1.5 = 3

Therefore,

It is false that the cost of two pounds of apple cast is more than $ 3.50.

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The appropriate scale for a drawing are-

The appropriate scale for a drawing that fits on a regular sheet of paper

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The correct question is attached-

On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

city - north at (0,65)

city-east at (59,0)

Slope is m=(-65/59)

[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]

The equation of the line between the cities is y = (-65/59)x + 65

[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]

the intersection points are:

(20.698, 42.197) and (43.998,16.527)

The transmitter is within range between those to points along the line.

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The value of all four numbers will be 91, 98, 105, 112 respectively.

Let the first multiple be 7x

As the multiple of any number can be determined by simply multiplying the given number by the natural number or the counting numbers.

So, the value of the second multiple of 7 will be 7(x+1)

The value of third multiple of 7 will be = 7(x+2)

The value of fourth multiple of 7 will be = 7(x+3)

As all the multiple are consecutive so we have taken the multiplying factor as x, (x+1), (x+2) and (x+3)

From the data given in the question:

Sum = 7x+7x+7+7x+14+7x+21 = 406

=>28x+42=406

=>28x=364

=>x=(364/28)=13

So, the value of first multiple = 7x = (7*13) =91

So, the value of the second multiple of 7 will be 7(13+1)=98

The value of third multiple of 7 will be = 7(x+2)=7(13+2)=105

The value of fourth multiple of 7 will be = 7(x+3)=7(13+3)=112

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The exponential function showing the relationship between y and t is y = 4800e^(0.0625t).

An exponential function is a function of the form f(x) = bx, where b is a positive real number and x is a real number. This type of function is commonly used to model the rate of growth or decay of a quantity over time. Exponential functions have the property that their derivatives (slope) are proportional to the value of the function itself. This property makes them useful for modeling phenomena with compound growth or decay, such as populations, interest rates, and radioactive decay.

In this equation, 4800 is the original principal, 0.0625 is the interest rate (6.25%) and t is the number of years since the start of the investment. This equation can be used to calculate the value of the investment after any number of years. For example, if t = 5, then y would equal 6,842.50. This means that after 5 years, the value of the investment would be 6,842.50.

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Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.

The equation of two-degree polynomial having one variable is called quadratic equation.

The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.

given equation, x² = 6x -10

                x²-6x +10 =0

This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.

we know that standard form of a quadratic equation is given by

ax² + bx +c = 0

where a is the coefficient of x², b is the coefficient of x and c is the constant.

the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a

Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1

                                                                     x = 6 ± √ (36 -40) / 2

                                                                x = 6 ± √-4 / 2

                                                   as        √-4 = √-1 ×2

                                                            x = 6 ± 2 √-1 /2  

                                        divide both numerator and denominator by 2

                                              x = 3± i     as √-1 = i

this is the solution in (a + bi) form a = 3 and b = 1

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