Joe walks over on a treadmill at constant rate the equation below describes the relationship between t the time he walks in hours and d the distance he walks in miles d=4t

Answer:

Therefore x = 1 is an extraneous solution.

Step-by-step explanation:

The solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction

[tex]\Rightarrow \frac{1}{x - 1} = \frac{x- 2}{2x^2-2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} 2x^2 - 2 = (x-1)(x-2)[/tex]

therefore [tex]2x^2 - 2 = x^2 - 3x + 2 \hspace{0.3cm} \Rightarrow \hspace{0.3cm} x^2 + 3x - 4 = 0[/tex]

therefore [tex]x^2 + 3x - 4 = 0 \hspace{0.3cm} \Rightarrow = \hspace{0.3cm} (x-1)(x+4) = 0 \\[/tex]

therefore x = 1 and x = -4 but we can see that if we place x = 1 in the original solution then [tex]\frac{1}{x-1} = \frac{1}{1-1} = \frac{1}{0}[/tex] which is indeterminate.

Therefore x = 1 is an extraneous solution.

Answer:

C. x = 1

Step-by-step explanation:

Which solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction is extraneous?

x = 1 and x = –4

neither x = 1 or x = –4

x = 1

x = –4

Answer:

It will take 3.6 hours to wax a car if they work together.

Step-by-step explanation:

Calvin one hour work = [tex]\frac{1}{3}[/tex]

Alvin one hour work = [tex]\frac{1}{5}[/tex]

To find out how much they can do together per hour,

We have to add [tex]\frac{1}{3}[/tex] and [tex]\frac{1}{5}[/tex]

= [tex]\frac{1}{3} + \frac{1}{5} = \frac{(5 + 3)}{15}[/tex]

= [tex]\frac{8}{15}[/tex]  --------------(1)

They can do [tex]\frac{8}{15}[/tex] of the job per hour.

If "t" is the time taken to finish the  job together, then one hour work

[tex]\frac{1}{t}[/tex] ------------------------(2)

Now we have to find the value of "t" by setting the expression (1) and (2) equal.

[tex]\frac{8}{15} = \frac{1}{t}[/tex]

It can solve by flipping the equation;

[tex]\frac{t}{1} = \frac{18}{5}[/tex]

t = 3.6 hours

It will take 3.6 hours to wax a car if they work together.

Answer:

Hello, I think your answer is d/24 = 18.4/6

Hope This helps

Answer:

The commission rate is 9%

Step-by-step explanation:

We are given;

We are required to determine the commission rate;

We need to know that;

Total earnings = Monthly salary + Commission

Therefore;

Commission = Total earnings - monthly salary

                     = $1182.60 - $315

                     = $867.6

Therefore, assuming the commission rat is x %

Then;

x/100 × $9640 = $867.6

x/100 = $867.6 ÷ $9640

x/100 = 0.09

 x = 9%

Therefore, the commission rate is 9%

Answer:

no

Step-by-step explanation:

the line has a value which is y=7

Answer: Zero slope

Step-by-step explanation: A common mistake made by many students is to confuse what no slope is and what zero slope.

If a line has a slope of zero, it means that the line is flat or horizontal.

No slope is a vertical line or straight up and down. No slope means that we cannot describe its slope using a number because its line is vertical and it's slope is undefined. This has to do with dividing a number by 0. When you do this, you should get an error message or it should say undefined.

So, this line would have zero slope because it's flat.

Answer:

The total number of fliers the volunteers gave out is 1,368

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of fliers the volunteers gave for a political campaign = 21/38

Remaining 612 were given out in another neighborhood

2. What is the total number of fliers they gave out?

x = Total of fliers

Let's solve for x, this way:

x - 21x/38 = 612

38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)

17x = 23,256

x = 23,256/17

x = 1,368

The total number of fliers the volunteers gave out is 1,368

The minimum value at -1 ⇒ D

Step-by-step explanation:

The completing square form of ax² + bx + c is a(x - h)² + k, where

∵ The expression is x² + 4x + 3

∴ a = 1 , b = 4 , c = 3

- Use the rule above to find h

∵ [tex]h=\frac{-4}{2(1)}[/tex]

∴ h = -2

- To find k substitute x by the value of h

∵ k = (-2)² + 4(-2) + 3 = 4 - 8 + 3

∴ k = -1

- Substitute h and k in the form of the completing square

∵ a(x - h)² + k = 1(x - -2)² + (-1)

∴ a(x - h)² + k = (x + 2)² - 1

∴ x² + 4x + 3 = (x + 2)² - 1

∵ The completing square is (x + 2)² - 1

∵ a = 1 ⇒ greater than zero

∴ The value is minimum

- The minimum value is the value of k

∵ k = -1

∴ The minimum value of the function is -1

The minimum value at -1

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Answer:

BF = 30

Step-by-step explanation:

[tex]BF=\frac{1}{2}*CE\\\\=\frac{1}{2}*60=30[/tex]

The line segment connecting the midpoint of two sides of a triangle is parallel to the third side and half the length of the that third side

Answer:

The numerator is 57 ⇒ B

The denominator is 78 ⇒ B

The value of the fraction is 73.1% ⇒ A

Step-by-step explanation:

Let us solve it step by step

∵ The loan is 12 month

∵ The numerator is after 6 month

- Put n = 1 in each bracket

∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}

∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}

∴ The numerator = {57}

The numerator is 57

∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}

- Do the same as the numerator put n = 1

∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}

∴ The denominator = {78}

The denominator is 78

Now find the value of the fraction

∵ The fraction = [tex]\frac{57}{78}[/tex]

∴ Its value = 0.730769230

- Multiply it by 100%

∴ Its value = 0.730769230 × 100% = 73.0769230%

- Round it to the nearest tenth

∴ Its value = 73.1%

The value of the fraction is 73.1%

Answer:

1: a prince can use violence to keep control.

2: the safest way is to destroy them.

Answer:

For those who need this:

Step-by-step explanation:

Which text structure does Machiavelli use in this passage?

✔ cause and effect

Which signal word or words help you identify this structure?

✔ “for this reason”

How does this text structure help the author convey his central idea?

✔ It explains why destroying a state is successful.

Answer:

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

1. Scale:

2. Proportion:

Naming x the model length:

Cross multiply:

Divide both sides by x:

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?​

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.

Answer:

x=0,3,-6,7

Step-by-step explanation:

set each factor equal to zero and then solve for x.

The zeroes of the polynomial are 0, 3, -6 and 7.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

We have the polynomial in form

x(x-3)(x+6)(x-7)=0

As, we can see the polynomial is of degree 4.

Also, the polynomial is in the form of factors.

Now, to find the zeros of the polynomial we compare each factor to 0.

x= 0

x -3 = 0

x= 3

and, x + 6= 0

x = -6

and, x -7 = 0

x = 7

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Equation of the line is y = 4x + 4

Step-by-step explanation:

⇒ m = (0 - 4)/(1 - 2) = -4/-1 = 4

⇒ b = 4

⇒ y = 4x + 4

Answer:

[tex]22 x^4y^3[/tex]

Step-by-step explanation:

[tex]11x^2y\times 2x^2y^2\\[/tex]

by multiplying

[tex]=11 \times 2 \times x^2 \timesx^2 \times y \times \times y^2\\=22 \times x^{2+2}y^{1+2}\\=22 x^4y^3[/tex]

Answer:

B and C

Step-by-step explanation:

7 would be B. m = 2

8 would be C m = -1/2

If a line is parallel, then the slop is the same. If it is perpendicular, the it will be the opposite sign and the reciprocal. So parallel would be 2 and perpendicular would be -1/2

Hope this helped! :)

Answer:

7. m= -2

8. m= -1/2

Step-by-step explanation:

picture is taken

b

Step-by-step explanation:

the pattern goes by 2s so you do 13 times 2 plus 4 which would be your 0th term because six is your first term so you add 4 and 26 you get 30 and it is not 33 because that is the 14th term

Answer:common difference is -2

Step-by-step explanation:

Answer:common difference is -2

Step-by-step explanation:

The sequence is arithmetic if the difference between consecutive terms is constant.

Answer:

x = 50

Step-by-step explanation:

140 = 85 + 1/2 x + 30

140 = 115 + 1/2x

25 = 1/2 x

x = 50

Answer:

can you elaborate?

Step-by-step explanation:

Answer: 0.15J

Step-by-step explanation:

Fom th question, we obtained the following information:

F = 60N

e = 5mm

We need to covert 5mm to m

1mm = 0.001m

5mm = 5 x 0.001 = 0.005m

We need to find the spring constant (K) for the spring. This is illustrated below:

K = F / e

K = 60 / 0.005 = 12000N/m

Now we can obtain the energy stored on the spring by the doing following:

Energy = 1/2 Ke^2

Energy = 1/2 x 12000 x (0.005)^2

Energy = 0.15J

Final answer:

Cole spent 7/12 hours on history homework after spending 5/12 hours on Spanish homework, with the total homework time being 1 hour.

Explanation:

The student asked: Cole spent some time working on his history homework. Then, he spent 5/12 hour working on his Spanish homework. Cole spent 1 hour on homework. What fraction of an hour did Cole spend on history? To find the time Cole spent on history homework, we subtract the time he spent on Spanish homework from the total homework time. Cole's total homework time is 1 hour, which is equivalent to 12/12 hours.

Therefore, the time spent on history homework is: 12/12 hours (total time) - 5/12 hours (Spanish homework) = 7/12 hours on history homework. So, the correct answer is C) 7/12.

Answer:

1

Step-by-step explanation:

The first thing to simplify is the Exponent

If The Exponent is a fraction than the denominator of the fraction will be the power of the root and the numerator will be the power of the expression

It will be in the form

[tex] \sqrt[a]{ {x}^{b} }[/tex]

Where a is the denominator and b is the numerator of the fraction

The first expression 216^1/3 will be

[tex] \sqrt[3]{{216}^{1} } [/tex]

6×6×6=216 so the expression = 6

The second expression 125^1/3 will be

[tex] \sqrt[3]{ {125}^{1} } [/tex]

5×5×5=125 so the expression =5

216^1/3 - 125^1/3

6 - 5

1

Answer:

Therefore side B= 11.18  and side A=2×11.18=22.36.

Step-by-step explanation:

Given,side A is twice as long as B and C is 25.

Let side B= x

Then side A = 2x

Using Pythagorean Theorem,

A²+B²=C²

⇔(2x)²+x²=25²

⇔4x²+x²=625

⇔5x²=625

⇔x²=125

⇔x=√125

⇔x =11.18

Therefore side B= 11.18  and side A=2×11.18=22.36.

Answer:

The length of side A is 22.4 and length of side B is 11.9.

Step-by-step explanation:

Given:

If side A is twice as long as B and C is 25.

Solve by using the Pythagorean Theorem.

Now, to get the lengths of side A and side B.

As side C = 25.

Let the side B be [tex]a.[/tex]

As, given A is twice as long as B.

So, the side A be [tex]2a.[/tex]

So, we solve by using Pythagorean Theorem:

A² + B² = C²

[tex](2a)^2+(a)^2=(25)^2[/tex]

[tex]4a^2+a^2=625[/tex]

[tex]5a^2=625[/tex]

Dividing both sides by 5 we get:

[tex]a^2=125[/tex]

So, using square root on both sides we get:

[tex]a=11.18.[/tex]

Rounding to the nearest tenth B =  11.9.

Now, to get A by putting the value of [tex]a[/tex]:

[tex]2a\\=2\times 11.18\\=22.36.[/tex]

Rounding to the nearest tenth A  =  22.4.

Therefore, the length of side A is 22.4 and length of side B is 11.9.

Answer:

The rest of the question:

Find Mean, Median, Mode, 25th Percentile, 75th Percentile, Maximum, Minimum, Range and IQR.

Let's begin by placing the data points in order from least to greatest:

32  55  66  72  72  76  77  84  88  89  89  94  97

n = 13

1) Mean sometimes called the average = the sum of the data over its number

Mean =( 32+55+66+72+72+76+77+84+88+89+89+94+97 )/13 =

         = 991/13 = 76.23 ≈ 76.2 (to the nearest tenth)

2) Median is the middle data point = 77

3) Mode is any number within a set that occurs the most often

Mode = 72 and 89

We will making a data in suitable form to find the remaining requirements:

(32  55  66  72  72  76) 77  (84  88  89  89  94  97)

4) 25th Percentile = Quartile 1 (Q1) which is the median of the first set of data

∴ 25th Percentile = (66+72)/2 = 138/2 = 69

5) 75th Percentile= Quartile 3 (Q3) which is the median of the second set of data

∴ 75th Percentile = (89+89)/2 = 89

6) Maximum = 97

7) Minimum = 32

8) Range = Maximum - Minimum = 97 - 32 = 65

9) IQR (interquartile range) = Q3 - Q1 = 89 - 69 = 20

Answer: 11.636 = 12 tickets to a whole figure

Step-by-step explanation:

Let the number of adult tickets be x and y represent children tickets.

From the question;

x + y = 28 ....... equation (i)

(7.25*x) + (y*4.50) = 158

7.25x + 4.50y = 158 ........ equation (ii)

From equation (i);

x + y = 28

y = 28 - x ...... equation (iii)

Put equation (iii) into equation (ii)

7.25x + 4.50(28 - x) = 158

7.25x + 126 - 4.50x = 158

Collect like terms and subtract

2.75x = 32

x = 11.636 approximately 12 to a round number.

Put x = 11.636 into equation (i)

11.636 + y = 28

y = 28 - 11.636

y = 16.364 approximately 16 to a whole number

Final answer:

To find the number of adult tickets purchased, we can set up two equations: C + A = 28, and 4.50C + 7.25A = 159. By solving the equations, we determine that 12 adult tickets were purchased for the carnival.

Explanation:

The question asks us to determine the number of adult tickets purchased for a carnival, given the cost of children's tickets, the cost of adult tickets, and the total amount paid for a group of tickets. Let's take the number of adult tickets as A and the number of children's tickets as C. According to the given information, the admission fee for children is $4.50 and for adults is $7.25. Also, we know that 28 tickets were purchased for a total of $159.

We can set up the following system of equations based on the information provided:

C + A = 28 (since the total number of tickets is 28)

4.50C + 7.25A = 159 (this represents the total cost of all tickets)

We can solve this system of equations using substitution or elimination method. If we rearrange the first equation to get C = 28 - A and substitute it into the second equation, we get:

4.50(28 - A) + 7.25A = 159

126 - 4.50A + 7.25A = 159

2.75A = 33

A = 33 / 2.75

A = 12

Hence, the number of adult tickets purchased is 12.

Answer:

(1,0)

Step-by-step explanation:

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0)

Answer:

B,C

(1,0)

F

Step-by-step explanation:

Answer:

PS = 28 units.

Step-by-step explanation:

See the attached diagram.

This is a figure of rectangle with length (3y + 3) and width 4y.

Now, the perimeter of the rectangle is 2[(3y + 3) + 4y] = 2(7y + 3)

The perimeter of the rectangle is given to be 104 units.

So, 2(7y + 3) = 104

⇒ 7y + 3 = 52

⇒ 7y = 49

⇒ y = 7

Therefore, PS = 4y = 4(7) = 28 units. (Answer)

Answer:

Step-by-step explanation:

-5 means the x coordinate

and 6 means the y coordinate

The solutions are [tex]x=15, x=-8[/tex] and [tex]x=9[/tex]

Explanation:

Part a: The equation is [tex]\frac{1}{3} (5x-9)=2(\frac{1}{3} x+6)[/tex]

Let us find the value of x.

Multiply the terms within the bracket, we get,

[tex]\frac{5}{3} x-3=\frac{2}{3} x+12[/tex]

Subtracting both sides by [tex]\frac{2}{3} x[/tex], we have,

[tex]\frac{3}{3} x-3=12[/tex]

Adding both sides by 3,

[tex]x=15[/tex]

Thus, the solution of the equation [tex]\frac{1}{3} (5x-9)=2(\frac{1}{3} x+6)[/tex] is [tex]x=15[/tex]

Part b: The equation is [tex]4(3x+5)-3=9x-7[/tex]

Multiply the terms within the bracket, we get,

[tex]12x+20-3=9x-7[/tex]

Subtracting both sides by 9x, we have,

[tex]3x+17=-7[/tex]

Subtracting both sides by 17,

[tex]3x=-24[/tex]

Dividing both sides by 3, we have,

[tex]x=-8[/tex]

Thus, the solution of the equation [tex]4(3x+5)-3=9x-7[/tex] is [tex]x=-8[/tex]

Part c: The equation is [tex]5(x+7)-3(x-4)=7x+2[/tex]

Multiply the terms within the bracket, we get,

[tex]5x+35-3x+12=7x+2[/tex]

Adding the like terms, we have,

[tex]2x+47=7x+2[/tex]

Subtracting both sides by 2 and 2x, we get,

[tex]45=5x[/tex]

Dividing both sides by 5, we have,

[tex]x=9[/tex]

Thus, the solution of the equation [tex]5(x+7)-3(x-4)=7x+2[/tex] is [tex]x=9[/tex]

This question requires understanding of mathematical equations and their solutions. The answer derives from equations wherein you first simplify inside parentheses, follow with multiplications or other operations, then isolate variables. The solutions to these equations can then be matched with each one.

The task here is drag the tiles to the correct boxes to complete the pairs and match each equation with the correct solution. This is a mathematical practice that requires algebraic methods. Let's solve the equations one by one:

Example 1: 5(3150 - 9) = 2(5x + 6)

First, perform the functions inside the parentheses, then distribute accordingly. Afterwards, isolate the variable to one side of the equation to find its value:

Example 2: 4(35 + 5) - 3 = 9.5 - 7

Follow the same steps as above to match this equation with its solution:

Example 3: 5(5 + 7) - 3(3 - 4) = 7x +:

Again, simplify inside the parentheses first, then distribute and isolate the variable. This process will provide solutions to match with each equation:

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Some number increased by two = b + 2

A variable decreased by two = x - 2

Product of an unknown value and two = 2z

Quotient of some number and two = [tex]a \div 2[/tex]

An unknown value squared = [tex]y^2[/tex]

Solution:

Some number increased by two

Let the number be "b"

Therefore, "b" is increased by two

Here, "increased" means added

Thus we get,

Some number increased by two = b + 2

A variable decreased by two

Let the number be "x"

Therefore, "x" is decreased by two

Decreased means reduced or subtraction

Thus we get,

A variable decreased by two = x - 2

Product of an unknown value and two

Let the unknown value be "z"

Product means "multiplication"

Therefore, product of "z" and 2

Product of an unknown value and two = 2z

Quotient of some number and two

Let the some number be "a"

Quotient means result of division

Quotient of some number and two = [tex]a \div 2[/tex]

An unknown value squared

Let the unknown value be "y"

Squared means multiplied by itself

An unknown value squared = [tex]y^2[/tex]

Answer

answer above is correct

Step-by-step explanation:

Answer:A

N=; 1% = 9.6; PV= -180; PMT 102.5; FV=0; P/Y=12, C/Y=12;PMT ;END

Final answer:

The correct TVM Solver setup for Troy's loan has a monthly interest rate of 0.8% and the rest of the parameters reflect the details of the loan and payment structure, making Option B the right choice.

Explanation:

To calculate the number of monthly payments Troy will have to make to pay off the loan for the television, we can use the Time Value of Money (TVM) formula where certain values will be plugged into the TVM Solver of a graphing calculator. Given the loan amount ($1850) and APR (9.6% annually, compounded monthly), we have to adjust the annual percentage rate to a monthly rate by dividing it by 12 months, resulting in a 0.8% monthly interest rate. Therefore, the values entered should reflect a monthly rate, not an annual rate.

The correct setup for the TVM Solver would be:

Therefore, the correct answer is Option B, where the monthly interest rate is accurately represented.