Ross made a scale drawing of his workshop as shown below. What is the actual width
of his workshop?

To make the quadratic polynomial x² + 18x into a perfect square, we add 81 to it.

A quadratic polynomial is a polynomial in which the highest power of the unknown is 2.

A perfect square is a number suvh that it is equal to another number multiplied by itself

Since we have the quadratic polynomial x² + 18x, and we wnat to convert it to a perfect square.

To be a perfect square, we want it in the form (x + a)² = x² + 2ax + a²  (1)

Compring the quadratic polynomial with equation (1), we have that

2a = 18

a = 18/2

a = 9

⇒ a² = 9² = 81

So, substituting a = 9 into equation (1), we have

(x + a)² = x² + 2ax + a²

(x + 9)² = x² + 2(9)x + 9²

= x² + 18x + 81

Thus we see that to make  x² + 18x into a perfect square, we add 81 to it.

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Answer:

The length of side B is 6.25, The length of side A is 8.75, The scale factor is 0.25

Step-by-step explanation:

Divide the left side of the first model by the left side of the scaled version

60 / 15 = 4

divide side A and B by the result

35 / 4 = 8.75

25 / 4 = 6.25

The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL

The number of water bottles = 6

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of water bottles required be = A

Now , the equation will be

The total distance of the bush walk = 3.5 km

Bernard's requirement of water for every 1.4 km = 1.2 L of water

So , Bernard's requirement of water for every 3.5 km = ( total distance of the bush walk / 1.4 ) x 1.2 L

Substituting the values in the equation , we get

Bernard's requirement of water for every 3.5 km = ( 3.5 / 1.4 ) x 1.2 L

Bernard's requirement of water for every 3.5 km = 2.5 x 1.2 L

Bernard's requirement of water for every 3.5 km = 3 L

Now , the amount of water one water bottle can hold = 500 mL

The value of 3 L = 3000 mL

So , the number of water bottles required to hold 3 L = 3000 / amount of water one water bottle can hold

Substituting the values in the equation , we get

The number of water bottles required to hold 3 L = 3000 / 500

The number of water bottles required to hold 3 L = 6 water bottles

Therefore , the value of A is 6 water bottles

Hence , The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL

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The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.

We have the following information:

A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.

Now, we know the combined ounces of meat and cheese for 1 sandwich will be given as follows:

Ounces of meat + ounces of cheese

4+3

7 ounces

Now, in an hour 91 ounces of combined cheese and meat are used.

So, we have the following expression:

Number of sandwiches made in 1 hour = Total ounces used/ounces used in 1 sandwich

Number of sandwiches = 91/7

Number of sandwiches = 13

Ounces of meat used in 13 sandwiches = 13*4

Ounces of meat used in 13 sandwiches = 52 ounces

Ounces of cheese used in 13 sandwiches = 13*3

Ounces of cheese used in 13 sandwiches = 39 ounces

Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.

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By using the property of congruency of triangles,

[tex]\angle V \cong \angle S[/tex] has been proved

What is congruency of triangles?

Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.

There are different axioms of congruency. They are

SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom

UV [tex]\cong[/tex] ST [Given]

QR [tex]\cong[/tex] PQ [Given]

QT [tex]\cong[/tex] QU [Given]

PV [tex]\cong[/tex] RS [Given]

PT = PQ + QT [Additive Property of Length]

RU = QR + QU [Additive Property of Length]

PT = QR + QU [Substitution]

PT = RU [Transitive Property of Equality]

TV = UV + TU [Additive Property of Length]

SU = ST + TU [Additive Property of Length]

TV = ST + TU [Substitution]

SU = TV [Transitive Property of Equality]

[tex]\angle[/tex]SUR [tex]\cong[/tex] [tex]\angle[/tex]VTP [QT = QU]
[tex]\Delta USR \cong \Delta TVP[/tex] [SAS axiom]

[tex]\angle V \cong \angle S[/tex] [Corrosponding parts of congruent triangles are congruent]

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Answer:

height = 4

Step-by-step explanation:

b = 3h

b * h = 48

3h * h = 48

3h² = 48

3/3 h² = 48/3

h² = 16

h = √16

h = 4

b = 4 * 3

b = 12

No, because being older than 55 and being pregnant are not independent events.

If we randomly select a U.S. female, is (pregnant and over 55) = (0.06)(0.27) = 0.0162 because being older than 55 and being pregnant are not independent events.

A random number is one that is selected by chance, or randomly, from a set of numbers, as the name suggests. There is an equal chance that any one of the numbers in a given distribution will be chosen at random.

The concepts of randomness are formally defined in the fields of mathematics, probability, and statistics. A random variable in statistics is the process of assigning a numerical value to each potential result of an event space. The identification of the events and the estimation of their probabilities are made easier by this association.

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If the degree of the equation is two, then the result leads to the quadratic equation. The following equations are entitled to the quadratic equations.

[tex]- $\mathrm{y}=2 \mathrm{x}^2$- $\mathrm{y}=2 \mathrm{x}^2-8$- $y=2 x^2-3 x-8$[/tex]

What is a quadratic equation?

In the quadratic equation, the maximum power of the variable is 2 . It consists of  [tex]$x^2, x$,[/tex] and the constant term.

Given

1 .[tex]$y=2 x^2$[/tex]

2. [tex]$y=2 x^2-8$[/tex]

3. [tex]$\mathrm{y}=-2+2 \mathrm{x}-8$[/tex]

4.[tex]$\mathrm{y}+3 \mathrm{x}=2 \mathrm{x}^2-8$[/tex]

5. [tex]$\mathrm{y}+3 \mathrm{x}^2=2 \mathrm{x}+3 \mathrm{x}^2-8$[/tex]

[tex]y=2 x^2[/tex]

The above expression is a quadratic equation.

2.

[tex]y=2 x^2-8[/tex]

The above expression is a quadratic equation.

3.

[tex]y=2 x-10[/tex]

The above expression is not a quadratic equation.

4.

[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x} & =2 x^2-8 \\\mathrm{y} & =2 x^2-3 x-8\end{aligned}[/tex]

The above expression is a quadratic equation.

5.

[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x}^2 & =2 x+3 x^2-8 \\\mathrm{y} & =2 x-8\end{aligned}[/tex]

The above expression is not a quadratic equation.

Thus, the third and fifth are not quadratic equations and the first, second, and fourth are quadratic equations.

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The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔUST and ΔVRQ, then we have

TU = QV (Given)

ST = QR (Given)

UV = SR

Add RU on both sides, then we have

UV + RU = SR + RU

RV = SU

The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.

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It takes Sandra 6.44 hour to word process 29 pages.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

It takes Sandra 1 hour to word process 4.5 pages.

Now,

Since, It takes Sandra 1 hour to word process 4.5 pages.

Hence, The time to make 29 pages = 29/4.5

                                                        = 290/45

                                                        = 58/9 hours

Thus, It takes 6.44 hours to complete 29 pages.

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Answer: True

Step-by-step explanation:

If I remember not to mistake y=x is the parent functions. So y=b is the parent function! So this question is true.

Answer:

A

Step-by-step explanation:

y = - 2² + 4

y = - 4 + 4

y = 0

(2,0)

The equation that has a real zero at x = 2 is y = -[tex]2^x[/tex] + 4.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The graph shows an x-intercept at x = 2, which means that the function has a real zero at x = 2.

Now,

We can check which of the given equations has this property by plugging in x = 2 and seeing if the corresponding y-value is zero.

For y = [tex]-2^x[/tex] + 4,

y = -2² + 4 = 0

This equation has a real zero at x = 2.

For y = 2^x,

y = 2² = 4,

This equation does not have a real zero at x = 2.

For y = log₂(x + 2) + 1,

y = log₂(2 + 2) + 1 = log₂4 + 1 = 3

This equation does not have a real zero at x = 2.

For y = log₂(-x + 2),

-x + 2 < 0, which means that x > 2.

This equation does not have a real zero at x = 2.

Therefore,

The equation that has a real zero at x = 2 is y = -[tex]2^x[/tex] + 4.

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The rate of change is 2 and initial value is 3.

Given points A (0,3) B(2,7)

What is the slope of line joining between point A and point B

if let's suppose A(x1,y1) B(x2,y2)

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

x1=0,y1=3

x2=2 y2= 7

slope(m) = 4/2 = 2

The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the rate of change. The rate of change is the slope of the line if the rate of change is linear and constant.

Rate of change of linear function is also know as slope of that linear function.

So here slope itself is the rate of change.

Initial value is 3 as Coordinate of A is (0,3).

Given Question is incomplete Complete Question here

A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3)and ending at point B (2, 7) .

What is the rate of change for the linear function and what is its initial value?

Select from the drop-down menus to correctly complete the statements.

The rate of change is____ and the initial value is___ .

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Given graph will be a line parallel to [x] axis.

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have Mrs. Rao pays the same amount each month for Internet service.

Assume that he pays amount [k], each month. Then, we can write the equation representing the graph as -

y = k

The graph will be a line parallel to [x] axis.

Therefore, the given graph will be a line parallel to [x] axis.

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Answer:

She can make 12 pizzas

Step-by-step explanation:

There are 2 halves in a pound, so you'll need to do 6 × 2 = 12.

The number of child tickets sold is 99.

A system having more than two equations is known as a system of equations.

Given that, the cost of a child ticket and the cost of an adult ticket are $5.60 and $9.50 respectively.

Let the number of child tickets sold and the number of adult tickets sold be s and a, then

s + a = 170

a = 170 - s

The total cost of s child tickets and a adult tickets is:

5.6s + 9.5a = 1228.90

Substitute a= 170 -s into the above equation:

5.6s + 9.5(170 - s) = 1228.90

5.6s + 1615 - 9.5s = 1228.90

3.9s = 386.1

s = 99

Hence, the number of child tickets sold is 99.

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A sample of 38 adults who has own an answering machine,

a) The probability that in a sample of 38, exactly 15 people own an answering machine is 0.061.

b) The probability that in a sample of 38, at most 15 people own an answering machine is 0.92381.

We have three in ten adults own an answering machine . That is probabilty of success, p = 3/10

Sample size, n = 38

Using Binomial Probability distribution,

X ~ Binom( 38, 0.3)

where X is random variable of adults has own an answering machine.

P(X= x) = ⁿCₓ (p)ˣ1-p)⁽ⁿ⁻ˣ⁾

The probability that in a sample of 38, exactly 15 people own an answering machine. , P(X= 15)

= ³⁸C₁₅(0.3)¹⁵ )(1 - 0.3)²³

= 38!/15!23! (0.3)¹⁵5(0.7)²³

= 0.06075 ~ 0.061

so, P(X= 15) = 0.061

b) The probability that in a sample of 38, at most 15 people own an answering machine, P(X<= 15)

Now, P(X≤ 15) = P( X= 1 ) + P(X= 2) + ... + P(X= 15) or 1 - P(X>15)

= 0.923814121

Hence, required probabilities

are 0.061 and 0.9238.

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The distance between the two parallel lines with the equations y = 7 and

y = -1 is 8 units

What is the distance of a line between 2 points?

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Given data ,

Let the equation of line be y = 7 and y = -1

Now , the slope of both the lines is 0

Slope m = 0

And the y intercept of the equation 1 or line 1 is = 7

So , the point is ( 0 , 7 )

And the y intercept of the equation 2 or line 2 is = -1

So, the point is ( 0 , -1 )

Now , the distance between the points ( 0 , 7 ) and ( 0 , -1 )  is given by the equation ,

[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Substituting the values in the equation , we get

Distance D = √ ( 7 - ( - 1 ) )²

Distance D = √ ( 8 )²

Distance D = 8 units

Therefore , the value of D is 8 units

Hence , The distance between the two parallel lines with the equations y = 7 and y = -1 is 8 units

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Answer:

640[tex]\pi[/tex]

Step-by-step explanation:

Answer:

640π

Step-by-step explanation:

The formula for a cone volume is

[tex]V = \pi r^{2} \frac{h}{3} \\\\V = \pi 8^{2} \frac{30}{3} \\\\V = \pi 64 * 10 \\\\V = 640\pi[/tex]

All potential values of x are represented by the inequality x≤20.

A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.

An inequality displays the difference between two variables, whereas an equation displays the equivalence of two variables.

So, the inequality that also represents all the possible values of x is:

On Mondays, Kelli walks no more than 25 dogs.

Also, Ms. Lincoln's five dogs are walked by Kelli.

Along with Ms. Lincoln's dogs, the inequality to determine how many additional dogs Kelli walks on Monday is written as:

x+5 ≤ 25

Take 5 away from both sides.

x + 5 - 5 ≤ 25 - 5

x ≤  20

Therefore, all potential values of x are represented by the inequality x≤20.

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Complete question:
Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?

The breakeven point after the adjustment in the expense function.

What is the revenue?

Revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production costs.

Revenue is the product of the number of units and the price per unit. It is given by:

Revenue = number of units * price per unit

Revenue = x * p(x)

Revenue = 8q Expense = 4.55q + 69,000

To find the breakeven point Revenue = Expense

8q = 4.55q + 69,000 3.3.45q = 69,000 q = 20,000

Equate both and find q

E = 4.55(20,000) + 69,000 = 160,000

E at q = 20,000

(20,000, 160,000)

Hence, the breakeven point after the adjustment in the expense function.

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Answer: x = -9 , y = -13

Step-by-step explanation:

Multiply the second equation by 5, then add the equations together.

(−5x+3y=6)

5(x−y=4)

Becomes:

−5x+3y=6

5x−5y=20

Add these equations to eliminate x:

−2y=26

Then solve −2y=26 for y:

−2y = 26

Divide both sides by -2

y= -13

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

−5x+3y=6

Substitute−13 for y in −5x+3y=6:

−5x+(3)(−13)=6

−5x−39=6 (Simplify both sides of the equation)

−5x−39+39=6+39 (Add 39 to both sides)

−5x=45

Divide both sides by -5

x = -9

hope it help

you can proof it in the first equation if you want

Answer:

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

From the series we can observe:

Use the nth term equation to find the value of n:

Apply this to the last term and solve for n:

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

Given

Infinite sequence:

It has:

Find the sum of terms:

Correct choice is D.

Answer: 2 miles

Step-by-step explanation:

Answer:

f(x) = 500+40m

Step-by-step explanation:

500 = initial

40m because she deposits 40 each month

Order of Sides from smallest to largest is AC, BC , AB.

Finding the Triangle's Angles and/or Sides in Order of Largest to Smallest

Step 1: As stated in the issue, sort the supplied angles or sides in the order of smallest to greatest or largest to smallest.

If the sides are supplied in the issue and we are requested to arrange the angles, step 2 is to find the angles that are opposite the given sides.

If the problem specifies the angles and asks us to arrange the sides, find the sides that are perpendicular to the provided angles.

The sides opposing the angles will be listed in the same sequence as step 1's first-identified sides. Therefore, the side across from the biggest angle will be the largest, and the side across from the smallest angle will be the smallest. The angles opposing the sides will also be in the same sequence as those found in step 1 for the angles. As a result, the angle opposite the side with the greatest length will be the largest, while the angle opposite the side with the lowest length will be the smallest.

angle B is smallest , so the smallest side is opposite side of angle B i.e AC.

Again angle C is largest so similarly AB is the largest.

Order of Sides from smallest to largest is AC, BC , AB

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The domain of the function described in the problem is given as the number of people living in the house. The correct option is (D).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

Suppose the number of rooms in the house be y.

And, the number of people is x.

As per the question, the function can be written as,

y = f(x)

From the definition of the function it is clear that all the possible values of x are domain and all values of y are range.

Thus, the domain of the function is number of people living in the house.

Hence, the domain of the function for the given case is the number of people living in house.

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The two numbers whose sum is 20 and sum of their squares is 218 are

13 and 7 respectively.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Let, The two numbers be a and b.

Given, The sum of two numbers is 20 which is, a + b = 20...(1) and the sum of their squares is 218 which is, a² + b² = 218...(2)

We know, (a + b)² = a² + 2ab + b².

Therefore, 20² = 218 + 2ab.

2ab = 400 - 218,

2ab = 182.

ab = 91...(3)

Now, (a - b)² = a² + b² - 2ab.

(a - b)² = 218 - 182.

(a - b)² = 36.

a - b = 6...(4).

Adding (1) and (4) we get,

2a = 26.

a = 13 and hence b = 7.

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