A rectangular gardan is surrounded by a walk of uniform width. The area of the garden is 200 square yards. If the dimensions of the garden plus the walkway are 18 yards by 26 yards, find the dimensions of the garden.

***NOTE*** This is a Quadratic Word Problem, so please use the Quadratic Method when solving and show all steps!!

The measurement pairs that could be the dimensions of rectangle B include:

A. 6cm by 1.5cm

D. 18cm by 4.5vm

F. 80cm by 20cm

From the information, Rectangle A measures 12 cm by 3cm. Therefore, it should be noted that the scale factor is:

= 12/3

= 4/1

Therefore, the options should also have that same constant of 4:1

In this case, 6cm by 1.5cm, 18cm by 4.5cm, and 80cm by 20cm all possess this. This illustrates the concept of equivalent dimensions since they all have a ratio of 4:1.

The complete question is written below.

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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

A. 6 cm by 1.5 cm

B.10 cm by 2 cm

C. 13 cm by 4 cm

D.18 cm by 4.5 cm

E.80 cm by 20 cm

Answer:

  x = 3⁴

Step-by-step explanation:

You want the exponential form of log₃(x) = 4.

It can be helpful to remember that a logarithm is an exponent of the base of the logarithm.

  log₃(x) = 4   ⇔   x = 3⁴

The exponential form is x = 3⁴.

The equation that relates M to R is M = 13 - R

From the question, we have the following parameters:

The total number of new magazines is the sum of the number of magazines read and the number of magazines left

This is represented as

Total number of new magazines = Number of magazines read + Number of magazines left

Substitute the known values in the above equation

13 = R +M

Make M the subject

M = 13 - R

Hence, the equation is M = 13 - R

See attachment for the graph

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The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.

A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.

The linear equations are given below.

y = -3x + 9        ...1

3y = -9x + 9     ...2

Divide the equation 2 by 3, then the equation will become.

y = -3x + 3

The slope of the lines is the same but the lines are separated by a distance.

The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

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All right angles are congruent which is determined by the definitions of a right angle and congruent angles.

Congruent angles are two or more angles that are identical to each other. As a result, the measurements of these angles are equivalent.

Given that ∠1 and ∠2 are right angles.

By the definition of right angles i.e. right angle is one that is exactly 90 degrees. It is precisely one-quarter of a circle. When a pie is divided into four equal pieces, the tip of each slice forms a straight angle.

⇒ m ∠1 =90° ; m ∠2 = 90°

By the substitution to get

⇒ m ∠1 = m ∠2

Therefore, ∠1 ≅ ∠2

Hence, all right angles are congruent which is determined by the definitions of a right angle and congruent angles.

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Data

Length = 15 ft

Width = 8 ft

Area

265 students at this college have taken a course in either calculus or discrete mathematics.

Let X = number of students who have taken a course in calculus

Y = number of students who have taken a course in discrete mathematics

To determine the number of students who have taken a course in calculus only, subtract 135 from 324.

Only X = X - X∩Y

Only X = 324 - 135

Only X = 189

To determine the number of students who have taken a course in discrete mathematics only, subtract 135 from 211.

Only Y = Y - X∩Y

Only Y = 211 - 135

Only Y = 76

To determine the number of students who have taken a course in either calculus or discrete mathematics, add 189 and 76.

either X or Y = only X + only Y

either X or Y = 189 + 76

either X or Y = 265

To better illustrate the X and Y, see the attached photo of the Venn Diagram.

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A proportion is an equation in which two ratios are set equal to each other. No option is satisfying the proportion

Ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

In the given question, rayon drove 320 miles in 5 hours to complete the first part of his trip. 12 hours to drive 768 miles.

we can write this

320miles/5 = 768 miles/12

320miles/768 miles=5/12

In option d the values are not given in a correct way. It doesnot hold for the proportion.

Hence no option is correct.

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Answer: You could assume that X=8 and y=0

Step-by-step explanation:

Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of intercepts of a graph.

Intercepts of a graph are namely the x-intercept and y-intercept.

x-intercept is when y = 0. Example: (3,0)

y-intercept is when x = 0. Example: (0,9)

We are given the equation: x + 4y = 8

To find x-intercept, we can substitute y = 0 into the equation to obtain the value of x.

x + 4(0) = 8

x + 0 = 8

x = 8

Coordinates: (8, 0)

To fins y-intercept, we can substitute x = 0 into the equation to obtain the value of y.

0 + 4y = 8

4y = 8

y = 8 ÷ 4

y = 2

Coordinates: (0, 2)

The expression for the sequence of operations is 2(t x 5).

Expression:

Expression consists of minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Here we have the phrase "multiply t by 5, then double the result"

Now we have to written the algebraic expression for it.

For the given phrase, we have to divide it into two part,

The first part is "multiply t by 5",

So, it can be written as

=> 5 x t

Now, we have to move on to the next part that is,

"double the result".

For that, we have to multiply the first part by 2,

It can be written as,

=> 2 x ( 5 x t)

Therefore, the resulting expression is 2(5t).

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A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

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<EOG =90° AS INDICATED IN THE DIAGRAM

<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)

[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]

<AOB =180°( STRAIGHT LINE )

<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)

[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]

[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]

ATTACHED IS THE SOLUTION

Given:

Total number of people surveyed = 205

a) Percentage of the survey respondents that do not like both hamburgers and burritos.

Number of people that do not like both = 54

To find the percentage of the respondents that do not like both, we have:

Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%

b) Marginal relative frequency of all customers that like hambugers.

Given:

Number of customers that like hamburgers = 110

To find the marginal relative frequency, we have:

The marginal relative frequency of all customers that like hambugers is 54%

c) Conditional relative frequencies:

i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:

ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:

The table that represents a linear function is Table 1. Thus, the correct option is A.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

We know that, slope m= (y2-y1)/(x2-x1)

Table 1:

Put (x1, y1)=(1, 5) and (x2, y2)=(2, 9) in slope formula

That is, (9-5)/(2-1)

= 4

Similarly, the slope between last two points is (9-5)/(4-1)

=4

Table 2:

Put (x1, y1)=(1, -5) and (x2, y2)=(2, 10) in slope formula

That is, (10+5)/(2-1)

= 15

Similarly, slope between last two points (20+15)/(4-3)

=35

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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Answer: (2, 5/2)

Step-by-step explanation:

CD=(2, 4),(2, 1)

((2+2)/2, (4+1)/2)=

(4/2, 5/2)=(2, 5/2)

4x^4-10x^3-15x^2+27x

(use foiling)

The equation which describes Riya's graph is:

a). C(t) = -3t + 24.

We can easily find out the equation by concentrating on the axes.

For example,

Just look from the graph the value of C when t = 0.

We can conclude that C should be equal to 24 when t is equal to 0.

Now, let us put this value of t ( which is 0) in the equations one by one:

a). C(t) = -3t + 24

=> C(0) = -3 (0) + 24

=> C(0) = 24.

So, equation a). satisfies the given criteria.

Similarly, b) also qualifies but c) and d) are not equal to 24 when t = 0.

So, remove them.

Now, let's look at the value of t when C=0.

We can see that t should be equal to 8.

Let's put this value in equations,

a). 0 = -3t + 24

=> 3t = 24

=> t = 8.

Now, we can see that equation a). satisfies all the given conditions for the graph.

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Answer:

37

Step-by-step explanation:

Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.

Answer:96

Step-by-step explanation: Answer is 96 because you can do 16 times 3 which is 48 so for the fifth seat to the end will be 96 ways.

Hope this helps! :)

The resulting value for the quotient of 21 and a equals 30 is 7/10.

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three.

Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b

Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;

21/a = 30

Cross multiply

30a = 21

Divide both sides by 30

30a/30 = 21/30

a = 21/30

a = 7/10

Hence the value of a from the equivalent expression is 7/10.

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Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

Answer:

9

Step-by-step explanation:

t < 13 - 4

t < 9

again as far as it goes

D

1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial

g (x)= (x+1) (x-2) (x+5)

g(x) =x³+4x²-7x-10

As the coefficient is positive, then we'll have

Examining the options, we have as the roots S={-5,-1,2} So the answer is D

The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3

The line is passing through the point = (-6,-3)

The slope of the line = 0

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

(y-(-3)) = 0×(x-(-6))

We have to convert this equation the slope intercept form

Slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

(y-(-3)) = 0×(x-(-6))

y+3 = 0×(x+6)

y+3 = 0

y = -3

Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.

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Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.

We want to find x such that:

We'll use the second right triangle to show what we want.

First, given a triangle:

We know that the hypotenuse will be:

But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.

and

Now look at the triangle we have:

We can easily check that:

So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!

Therefore, we have:

And the solution to x is:

The length of the guy wire to the nearest foot is 42 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 15

∅ = tan ⁻¹ 1 / 3

∅ = 18.4349488057

∅ = 18.43°

Therefore, let's find the length of the guy wire using the angle.

cos 18.43° =  adjacent / hypotenuse

0.94871060813 = 40 / h

h = 40 / 0.94871060813

h = 42.162488395

Therefore,

length of the guy wire = 42 feet

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a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].

b) Percentage of employees don't like either tea or coffee is 30.4%

c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.

Given Data

In a work survey, it was found that:

28 employees preferred tea

45 employees preferred coffee

32 didn't like either

a) Number of employees that prefer coffee

= 45

Fraction:

= [tex]\frac{45}{105}[/tex]

= [tex]\frac{3}{7}[/tex]

b) Percentage of employees don't like either tea or coffee

= [tex]\frac{32}{105}[/tex] × 100

= 30.4%

c) Number of employees that prefer tea.

= 28

= [tex]\frac{28}{105}[/tex]

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Answer: 14

Step-by-step explanation:

87.5% of 105 is 91.875 (91)

105-91=14