True or False:

The Commutative Property of Addition states that for all expressions a and b, ab = ba

From the data provided, we can consider the following function as a good approximation:

Therefore:

The answer is:

a quadratic function with a negative value of a

Given the expression:

2.5x

Let's determine the situation which best represents the expression.

Let's start from the first statement:

• A. The total amount of change received to pay for an item that cost $2.50:

The best representation for this is: C = A - 2.50

Where A is the amount paid, C is the amount of change.

• B. The area of a rectangle with side lengths 2.5 and x:

The best representation for this situation is:

2.5x

• C. The total cost of an item that is 2.50 more than x dollars:

T = 2.50 + x

• D. The total square footage of a yard when 2.50 yards is divided into equal parts:

This expression cannot be represented by 2.5x

Therefore, the situation which can be represented by the expression 2.5 is:

The area of a rectangle with side lengths 2.5 and x

ANSWER:

B. The area of a rectangle with side lengths 2.5 and x

Answer:

.0025 inches

Step-by-step explanation:

[tex] \frac{.15}{150} = \frac{x}{2.5} [/tex]

[tex]150x = 3.75[/tex]

[tex]x = .0025[/tex]

Answer:

3/4

Step-by-step explanation:

up 3 right 4

Answer:

Slope = 2

Step-by-step explanation:

See attached graph/worksheet.

Answer:

6 oranges

Step-by-step explanation:

1) I know that 5 oranges equals to $2.85

2)I need to find the cost of 1 orange

3)Divide the 3.42 to the cost of 1 orange

MY WORK:

2.85 / 5=  $0.57 ( the cost per orange )

3.42 / 0.57= 6 oranges

Hope this helps!

The ball takes 6.3 seconds to reach the ground when thrown upwards.

The height of the baseball thrown is 5 feet.

The function or equation for the height of the ball at a certain time t is given as:

h( t ) = - 16t² + 100t + 5

When the ball will reach the ground the height of the ball will be h = 0.

Therefore,

- 16t² + 100t + 5 = 0

Comparing the equation with general quadratic equation ax² + bx + c =0

We have, a = - 16, b = 100, and c = 5

Using the quadratic formula,

[tex]t=\frac{-b\pm \sqrt{b^{2} - 4ac } }{2a}[/tex]

[tex]t = \frac{-100\pm \sqrt{(100)^{2} - 4(-16)(5) } }{2(-16)}[/tex]

[tex]t=\frac{-100 \pm \sqrt{10000+320} }{-32}[/tex]

[tex]t = \frac{-100\pm \sqrt{10320} }{32} \\[/tex]

t = [ 25 ± √(645) ] / 8

When,

t = [ 25 + √(645) ] / 8 = 6.299 = 6.3 seconds

t = [ 25 - √(645) ] / 8 is false as the time cannot be negative.

The correct option is (b) 6.3 seconds.

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If radium-221 has half life of 30 seconds. To decay 86% of the the sample, it will take 85.09 seconds

The half life of the radium-221 = 30 seconds

To decay 86% of the sample

The equation of the half life N = [tex]N_0(\frac{1}{2} )^\frac{t}{t_1}[/tex]

Where N is the quantity of substance remaining

[tex]N_0[/tex] is the initial quantity of substance

t is the time elapsed

[tex]t_1[/tex] is the half life of the substance

Substitute the values in the equation

0.14[tex]N_0[/tex] = [tex]N_0(\frac{1}{2} )^\frac{t}{30}[/tex]

Cancel the [tex]N_0[/tex] from each side

0.14 = [tex](\frac{t}{30} )^\frac{t}{30}[/tex]

[tex]2^\frac{t}{30}=\frac{1}{0.14}\\ \frac{t}{30}=log_2\frac{1}{0.14}\\ t = 30log_2\frac{1}{0.14}[/tex]

t = 85.09 seconds

Hence, if radium-221 has half life of 30 seconds. To decay 86% of the the sample, it will take 85.09 seconds

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Answer:

a = 11cm

Step-by-step explanation:

We can use the Pythagorean theorem to find the value of a.

Let us solve it now.

[tex] \sf {a}^{2} + {12}^{2} = {15}^{2} [/tex]

Now solve for a and and find the length of the side.

[tex] \sf {a}^{2} + 144 = 225 \\ \sf {a}^{2} = 225 - 144 \\ \sf{a}^{2} = 121 \\ \sf \: a = \sqrt{121} \\ \sf \: a = 11[/tex]

She need 15 quarts to cover the walls of a room with perimeter 50 feet and wall height 15 feet.

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Given Data

Veronica needed 11.2 quarts of paint to paint a room with perimeter 40 feet and wall height 14 feet.

Area of room = 40(14)

Area of room = 560

She need to cover the walls of a room with perimeter 50 feet and wall height 15 feet

Area = 50(15)

Area = 750

Let q be the number quarts of paints

[tex]\frac{560}{750}[/tex] = [tex]\frac{11.2}q{}[/tex]

Cross multiplying,

560q = 11.2(750)

q = [tex]\frac{11.2(750)}{560}[/tex]

q = 15

She need 15 quarts to cover the walls of a room with perimeter 50 feet and wall height 15 feet.

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The equation to represent the number of pages is: 0.25x = 10.

What is equation?

In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.

According to the question, the given parameters to form the equation are as follows:

The cost of each print is: $10

The cost of each page printed: $0.25

Now, let us assume number of printed pages are: 'x'

Therefore, the equation which shows the relationship between the number of pages and the cost of order is: 0.25x = 10

Hence, the equation to represent the number of pages is: 0.25x = 10

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The equation of the line in slope intercept form is found as y = x/5 + 24/5, where slope is (-1/5) and y-intercept is 24/5.

For the given question;

Two points are given as;

(x1, y1) = (-6, 6)

(x2, y2) = (9, 1)

The slope of the line is found as;

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

m = (1 - 6)/(9 + 6)

m = -5/15

m = -1/5

The equation of the line in slope-intercept form is found as;

y  - y1 = m(x - x1)

y - 6 = (-1/5)(x + 6)

5y - 30 = -x - 6

5y = -x + 24

y = -x/5 + 24/5

Thus, the equation of the line is found as y = x/5 + 24/5, where slope is (-1/5) and y-intercept is 24/5.

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It is the average amount by which the function changed per unit throughout that time period. The average rate of change of a linear function exists 9/3.

It exists the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

The average rate at which one quantity changes in relation to another's change exists directed to as the average rate of change function. A method that defines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

The average rate of change of a linear function (the slope) exists constant. The rate of change of the linear relationship = change in y / change in x

The rate of change from x = 1 to x = 4

= (5 - -4) / (4 - 1) = 9 / 3

Therefore, the average rate of change of a linear function exists 9/3.

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The most appropriate choice for trigonometry will be given by -

AB = 32

AC = [tex]16\sqrt{3}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta,[/tex] [tex]cos\theta[/tex], [tex]tan\theta[/tex], [tex]cot\theta[/tex], [tex]sec\theta[/tex], [tex]cosec\theta[/tex]

[tex]sin\theta=\frac{perpendicular}{hypotenuse}\\\\cos\theta=\frac{base}{hypotenuse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here,

The figure has been attached here.

Since this is a right angled triangle, trigonometry can be applied here,

Since ∠C = 90°, AB is the hypotenuse of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex] as the side opposite to 90° angle is the hypotenuse.

Let BC be the base of  [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex]

BC = 16

m∠B = 180 - (90 + 30)

        = 180 - 120

        = 60°

cos 60 = [tex]\frac{BC}{AB}[/tex]

[tex]\frac{1}{2} = \frac{16}{AB}\\AB = 16\times 2\\AB = 32[/tex]

sin 60 = [tex]\frac{AC}{AB}[/tex]

[tex]\frac{\sqrt{3}}{2} = \frac{AC}{32}\\\\AC = 32 \times \frac{\sqrt{3}}{2}\\\\AC = 16\sqrt{3}[/tex]

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The value of variable x in the equation is 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Therefore, let's solve for variable x in the equation below.

2x - 8 + 3x - 10 = 10x - 43

A variable is number represented with a letter in an equation.

Hence,

2x - 8 + 3x - 10 = 10x - 43

2x + 3x - 8 - 10 = 10x - 43

5x - 18 = 10x - 43

5x - 10x = - 43 + 18

-5x = - 25

divide both sides of the equation by -5

-5x / - 5= - 25 / -5

Therefore,

x = 5

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Applying the triangle sum theorem, the value of w in the triangle is calculated as: w = 29.

The triangle sum theorem states that if we add up all the three interior angles of any given triangle, we will have a sum of 180 degrees.

This means that, irrespective of whatever triangle that is given, the sum of all the interior angles of such triangle will be equal to 180 degrees.

The diagram attached below shows the following interior angle measures of a triangle: 35°, 2w, and 3w.

To find the value of w in the triangle given, we have to create an equation using the triangle sum theorem that will enable us solve for the value of w.

Thus:

35 + 2w + 3w = 180° [according to the triangle sum theorem]

Combine like terms

35 + 5w = 180

Subtract both sides by 35

35 + 5w - 35 = 180 - 35 [subtraction property of equality]

5w = 145

Divide both sides by 5

5w/5 = 145/5 [division property of equality]

w = 29

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The answer to the question is A-

16.6

Answer:

A. 16.6

Step-by-step explanation:

d = sqrt{(x2 - x1)^2 + (y2-y1)^2}

so this is our distance formula

now we need the two points

(-6, -6) and (3, 8)

lets plug these into our formula

d = sqrt{(3 - (-6))^2 + (8 - (-6))^2}

lets simplify

d = sqrt{(9)^2 + (14) ^2}

d = sqrt{277}

d = 16.64 or 16.6

The most appropriate choice for Linear equation will be given by-

[tex]2000T = -9X+206000[/tex]

This is the required equation to find the temperature T at an elevation X on the mountain.

What is linear equation?

Equation shows the equality between two expressions by connecting the expressions with an equal to sign.

A one degree equation is called linear equation.

Here,

Let X denotes the elevation of the mountain and T is the temperature

Let the equation be T = pX + c

It is 76 at the 6000 foot level of a mountain

Putting T = 76 and X = 6000

6000p  + c = 76 .........(1)

It is 49 at the 12000 foot level of the mountain

Putting T = 49 and X = 12000

12000p + c = 49..........(2)

Subtracting (2) from (1),

6000 p = -27

[tex]p = \frac{-27}{6000}\\\\p = \frac{-9}{2000}[/tex]

Putting the value of p in (1),

[tex]6000 \times \frac{-9}{2000} + c = 76\\-27 + c = 76\\c = 27 + 76\\c = 103[/tex]

Equation

[tex]T = \frac{-9}{2000}X+103[/tex]

[tex]2000T = -9X+206000[/tex]

This is the required equation to find the temperature T at an elevation X on the mountain.

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Consider the following matrix equation:

Applying the additive property, this is equation is equivalent to:

This is equivalent to the following linear system of equations:

Equation 1:

Equation 2:

Equation 3:

Equation 4:

From equation 1, we get:

From equation 2, we get:

From equation 3, we get:

From equation 4, we get:

we can conclude that the correct answer is:

and

A ribbon is 3 4/5 feet long. Each hair tie needs 2/5 feet. Number of hair ties is 6

No of hair ties = 6

How to find number of hair ties :

Length of the ribbon = 3 4/5 feet

Length of each hair tie needed = 2/5 feet

To find how many ties , divide the total length of ribbon by 2/5

That is  = [tex]\frac{3 (4/5)}{2/5}[/tex]

= 6 You can make 6 no.  of hair tie from 3 4/5 feet ribbon.

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The given statement is not true because the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.

We are given the scale of the map as;

1 inch : 100 miles

What this means is that 1 inch on the map represents an actual distance of 100 miles.

Now, from conversion values, we know that;

1 mile = 63360 inches

Now, the question is trying to suggest that the actual distance between two towns 100 times the map distance between the two towns

The given statement is not true because as seen from the conversion above, the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.

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Applying the transitive property of congruency and other postulates, lines l and m are proven to be parallel as explained below.

The transitive property of congruency states that when two angles are sides are congruent to another third angle or side, then the three sides or angles are all congruent to each other.

For example, if <A = <C, and <B = <C, then <A = <B.

The proof that shows that lines l and m are congruent is explained below:

Statement                                      Reason                                        

1. r║s, <5 is congruent to <6    1. Given

2. <5 is supplementary to <4    2. Same-side interior angles theorem

3. <4 is supplementary to <6    3. Transitive property of congruency

4. l║m                                         4. Converse of same-side interior <s theorem

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Answer:

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.

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The  five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).

Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.

A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.

Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.

Let the value of

x = 0,

then,

0 + y = 3

⇒

y = 3

One of the solutions

for x + y =3, is =(0,3)

Similarly, If x = 1,

then,

1 + y =3 ⇒ y = 3 - 1 = 2

One of the solutions for x + y =3, is

(1,2)

If x = 2,

then,

2 + y = 3

⇒ y = 3 - 2 = 1

One of the solutions for x + y =3, is

(2,1)

If x = 3, then,

3 + y = 3

⇒ y = 3 - 3 = 0

One of the solutions for x + y =3, is

(3,0)

If x = 4,

then,

4 + y = 3

⇒ y = 3 - 4 = -1

One of the solutions for x + y =3, is

(4, -1)

Hence,

five

solutions of the equation x + y = 3, are:

(0,3), (1,2), (2,1), (3,0) and (4, -1).

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Answer:

1.056

Step-by-step explanation:

We convert 2 into 6/3.

Now, we add the fraction part of the mixed number with 6/3
-> 5/3 + 6/3 = 11/3

So, it is equal to 4(11/3)

Now, we convert 11/3 into 3(2/3)
-> 4(11/3) = 4+3(2/3) = 7(2/3).

Answer:

based on the bodmass 4×5÷3=6.7+2=8.7

Answer:

r ≤ -24.32

Step-by-step explanation:

r/-3.2 > 7.6

r /-3.2 × 3.2 > 7.6 × -3.2

r ≤ -24.32

Answer: r ≤ −24.32

Step-by-step explanation:

The inequality you provided is:

r/-3.2 >= 7.6

To solve for r, we can multiply both sides of the inequality by -3.2 to get:

r <= -24.32

Therefore, r is less than or equal to -24.32.

I hope this helps! Let me know if you have any other questions.

Solution

I think the interest is compounded yearly, if so

First, convert R as a percent to r as a decimal

r = R/100

r = 6.25/100

r = 0.0625 per year

A = 10000

P = 5000

Use logarithms or a scientific calculator

t = 11.5

In 11.5 years $5000 investment be worth of $10000

>>>>>>>>>>>>>

In case the interest is simple interest

Interest = Amount - Principal = $10000-$5000 = $5000

Time = 100*Interest / (Principal*Rate

= 100*5000 / (5000*6.25)

t = 16 years

In 16 years $5000 investment be worth of $10000