what is 5x² - (2x - 3)² ?​

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 formula for calculating the volume of a sphere is expressed as

Volume = 4/3 x pi x radius^3

From the information given,

pi = 3.14

radius = 6.2

By substituting these values into the formula, we have

Volume = 4/3 x 3.14 x 6.2^3

Volume = 997.7999

Rounding to the nearest tenth,

Volume = 997.8 m^3

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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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 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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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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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.

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!

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

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

By definition, Scientific notation has the following form:

Where the coefficient "a" is a number from 1 to 10, but not including 10 and the exponent "n" is an Integer. The base will be always 10.

When you write a number in Scientific notation, the decimal point must be after the first digit of the coefficient.

In this case, you have:

So, in order to write that product in Scientific notation, you must move the decimal point one space to the left. This must be represented in the exponent. If you move it just one space, to the left, then the exponent will be 1 and will be positive.

Therefore, you get that this is:

Therefore, you can determine that the answer is:

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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Answer: 16 inches

Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.

Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents

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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Answer:

x= -2, y= 3

Step-by-step explanation:

5. Solve the system using substitution.

4x + 5y = 7

y= 3x + 9

What variable in the top equation will you substitute the bottom equation into? y

6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation?

4x + 5(3x+9) = 7

7. Using the equation you came up with for question 6, what does it look like simplified?

4x+5(3x+9) = 7, distribute 5 over the sum in parenthesis

4x+15x+45 = 7, subtract 45 from both sides of the equation

4x+15x+45-45 = 7-45, combine like terms

19x = -38, divide both sides by 19

x = -2

8. What is the solution to the equations from question 5?

y= 3x+9, substitute x for -2

y = 3(-2) +9

y = -6+9

y = 3

The solution for the system of equations

4x + 5y = 7

y= 3x + 9

is x= -2, y= 3

This means that the point (-2, 3) is the intersection of line 4x+5y=7 and line y=3x+9 and that point belongs to both lines.

Answer:

Below in bold.

Step-by-step explanation:

5. 4x + 5y = 7

y= 3x + 9

Substitute for y from the top equation.

5y = -4x + 7

y = (-4x + 7)/5

Substituting:

(-4x + 7)/5 = 3x + 9

6. Substituting from bottom equation, we get:

4x + 5(3x + 9) = 7

7. Simplifying the above:

4x + 15x + 45= 7

19x = -38

8. Solving equations from part 5:

(-4x + 7)/5 = 3x + 9

-4x + 7 = 15x + 45

-38 = 19x

x = -2.

Now substitute x = -2 into y = 3x + 9

y = 3(-2) + 9

= 3.

Solution is x = -2, y = 33

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

Answer:

1.056

Step-by-step explanation:

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

The ordered pair is [4k , 3k]

In first equation, 3x - 4y = 0

∴ 3x = 4y

  x = 4y/3.   ----1

Placing the value of x in second equation:

 4x - 5y = k

 4[4y/3] - 5y = k

16y/3 - 5y = k

[tex]\frac{16y - 15y}{3}[/tex] = k

16y - 15y = 3k

y = 3k

Replacing the value of y in eq. 1, we get

x = 4k

∴ The ordered pair is [4k , 3k]

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Answer:

its A

Step-by-step explanation

i took this test

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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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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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:

.0025 inches

Step-by-step explanation:

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

[tex]150x = 3.75[/tex]

[tex]x = .0025[/tex]

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:

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 variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match.  A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies

The classification of various types of functions can be done using four primary categories. depending on a factor Onto function, one-to-one relationship, many-to-one relationship, and into function are all examples of relationships between function.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.

Equations' true strength is in their ability to explain numerous aspects of the world in a highly accurate manner. (This is why, if one can be found, an equation's solution can be helpful.)

Hence, A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies

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