Question :
Jessica rode 9 miles farther than Roger rode. Let r represent the number of miles Roger rode . Write am expression for the number of miles jessica rode

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of [tex]t=0.6482[/tex]

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

[tex]h(t)=-16t^2 +v_{o}t+s[/tex]       Eqn(1).

Where:

[tex]h(t)[/tex] : is the height range as a function of time

[tex]v_{o}[/tex]   : is the initial velocity

[tex]s[/tex]     : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

[tex]h(t)=-16t^2 + v_{o}t + 40[/tex]        Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

Ben:

We know that [tex]v_{o}=60ft/s[/tex]

Thus Eqn. (2) becomes:

[tex]h(t)=-16t^2+60t+40[/tex]        Eqn.(3)

Josh:

We know that [tex]v_{o}=48ft/s[/tex]

Thus Eqn. (2) becomes:

[tex]h(t)=-16t^2+48t+40[/tex]       Eqn. (4).

Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at [tex]h(t)=0[/tex]. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.

Thus we have for Ben, Eqn. (3) gives:

[tex]h(t)=0<=>-16t^2+60t+40=0[/tex]

Using the quadratic expression to find the roots of the quadratic we have:

[tex]t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec[/tex]

Since time can only be positive we reject the [tex]t_{2}[/tex] solution and we keep that Ben's book took [tex]t=4.3276[/tex] seconds to reach the ground.

Similarly solving for Josh we obtain

[tex]t_{1}=3.6794sec\\t_{2}=-0.6794sec[/tex]

Thus again we reject the negative and keep the positive solution, so Josh's book took [tex]t=3.6794[/tex] seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

[tex]t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482[/tex]

So to answer the original question:

Whose textbook reaches the ground first and by how many seconds?

Answer:

A - 2B

Step-by-step explanation:

3x + 2y = A

5x + y = B

The first equation has 2y. The second equation has y.

If you multiply the second equation by 2, it will have 2y.

Then you subtract teh second equation from the first equation.

2y - 2y = 0, so you eliminate the y variable.

********

3x + 2y = A

2(5x + y) = 2B

********

3x + 2y = A

10x + 2y = 2B

********

Subtract the second equation from the first equation.

3x + 2y - (10x + 2y) = A - 2B

3x - 10x + 2y - 2y = A - 2B

-7x = A - 2B

Answer: A - 2B

Answer:

Step-by-step explanation:

Here, an equation of straight line is given.

The equation is [tex]y = -\frac{3x}{2}[/tex].

If you put x = 0, in the above equation, you will get y = 0.

Hence, the equation passes through (0, 0).

Again if we put, x = 1 in the above equation, we will get y = - 1.5.

It means the equation also passes through (1, -1.5).

Joining these two points, you can graph the straight line.

Answer:

B, D

Step-by-step explanation:

Solve all equations:

A.

[tex]x-3x=-2x+4\\ \\-2x=-2x+4\\ \\0=4[/tex]

This is false equality, so this equation has no solutions.

B.

[tex]x-\dfrac{1}{3}(3x)=0\\ \\x-x=0\\ \\0=0[/tex]

This equality is true for all values of x, so this equation has infinitely many solutions.

C.

[tex]\dfrac{1}{3}x-3=4+2x\\ \\x-9=12+6x\\ \\x-6x=12+9\\ \\-5x=21\\ \\x=-\dfrac{21}{5}[/tex]

This equation has the unique solution.

D.

[tex]3x+2-\dfrac{1}{3}(3x)=2+2x\\ \\9x+6-3x=6+6x\\ \\6x+6=6+6x\\ \\0=0[/tex]

This equality is true for all values of x, so this equation has infinitely many solutions.

E.

[tex]x-\dfrac{1}{3}x+2=0\\ \\3x-x+6=0\\ \\2x=-6\\ \\x=-3[/tex]

This equation has the unique solution.

Answer:

From Walter's steps we have that Step2: Reason 2 is incorrect.

The correct reason is Subtraction property of equality (we are using this property only not addition property of equality )

Step-by-step explanation:

Given equation is three halves times x plus ten equals forty

It can be written as below

[tex]\frac{3}{2}x+10=40[/tex]

To solve the given equation :

Step1 Reason1 : [tex]\frac{3}{2}x+10=40[/tex]

Step2 Reason2: Subtracting 10 on both sides of the above equation we get

[tex]\frac{3}{2}x+10-10=40-10[/tex] which is Subtraction property of equality

Step3 Reason3: [tex]\frac{3}{2}x=30[/tex]

Step4 Reason4: Multiply the above equation into [tex]\frac{2}{3}[/tex] on both sides we get

[tex]\frac{3}{2}x\times \frac{2}{3}=30\times \frac{2}{3}[/tex]

which is the Multiplication Property of Equality

Step5 Reason5: Simplify the above equation we get

 [tex]x= \frac{60}{3}[/tex]

Therefore x=20

From Walter's steps we have that Step2: Reason 2 is incorrect.

The correct reason is Subtraction property of equality (we are using this property only not addition property of equality )

Answer:

b

Step-by-step explanation:

[tex]\text{The sum of given polynomials is } 8x^2+x+14[/tex]

Solution:

Given given expression to calculate is:

[tex](x^2+x+9) + (7x^2+5)[/tex]

We have to add both the polynomials

Addition of two polynomials involves combining like terms present in the two polynomials

We have to add like terms

Like terms means "the terms having same variable and same exponent"

And we have to add the constants

[tex]\rightarrow (x^2+x+9) + (7x^2+5)\\\\\text{Remove the parenthesis and simplify }\\\\\rightarrow x^2 + x + 9 + 7x^2 + 5\\\\\text{Combine the like terms }\\\\\rightarrow x^2 + 7x^2 + x + 9 + 5\\\\\text{Add the coefficients of like terms }\\\\\rightarrow 8x^2 + x + 9 + 5\\\\\text{Add the constants 9 and 5 }\\\\\rightarrow 8x^2 + x + 14[/tex]

Thus the polynomials are added

Answer:

4.4 cubic inches

Step-by-step explanation:

From the question;

We are required to determine the volume of a cone;

Volume of a cone is given by the formula;

V=1/3πr²h

Therefore; taking π to be 3.142

Volume =1/3 × 3.142 × 1.2² × 2.9

             = 4.373664

             = 4.4 cubic inches (to the nearest tenth)

Thus, the volume of a cone is 4.4 cubic inches

Answer:

$681

Step-by-step explanation:

619.100 * 10% = 61.91

619.100 + 61.91 = 681.01

Rounding it down because it is not over 5. $681

Therefore your answer will be $681

Hope this helps!

Answer:

290 miles.

Step-by-step explanation:

To answer this, first multiply the hours by miles. 2 hours at 55 miles per hour means a total of 110 miles. 3 hours at 60 miles per hour means a total of 180 miles. Therefore, 110 + 180 = 290, so you drive 290 miles.

Answer:

Step-by-step explanation:

Answer:

Yes it can.

Step-by-step explanation:

We plot the data given on the graph and see whether there is any correlation.

The data is graphed in the figure attached. Looking at the graph we see that the points do seem to lie on a straight line which I have drawn as a dashed line.  

The dashed line represents the function

[tex]f(x)=-2x+40[/tex]

The function tells us that as Khaled gives more homework to his students, less students complete their homework.

Answer:

The pharmacy should give 3.0 mL solution to the patient

Step-by-step explanation:

Given,

750 mg of penicillin in 5 mL solutions

Hence, amount of penicillin in 1 mL of solution= [tex]\frac{750}{5}[/tex] = 150 mg/ mL

So, amount of solution for 450 mg of penicillin= [tex]\frac{450}{150}[/tex] = 3.0 mL

Answer:

{(3, 4), (4, 8), (6, 6), (7, 10)}

Step-by-step explanation:

Only the first one is a function because the others have repeated x values in some of the ordered pairs.

For example,  {-1, 4), (0, 3), (0, -2)}   has a repeated x = 0.

Probability is the calculation of = (desired outcomes/total outcomes)

therefore,10/107).

Answer:

Step-by-step explanation:

d = rt....and just so you know, speed is the same as rate

since we are looking for r, I am gonna change the equation

d = rt......r = d / t

d = 400

t = 10

now sub

r = d / t

r = 400/10

r = 40 ft per minute <=====

Answer: 40 per minute

Step-by-step explanation:

The resulting graph is valid as it uses the concept of area scaling, where the area of each square accurately represents the relative land sizes of the different countries.

Yes, the resulting graph is valid. This is because a proportional representation by different-sized squares aligns with the principle of area scaling. Area scaling is a mathematical concept where each length is scaled by a particular factor and the area will scale by the square of that factor. If the areas of the countries are correctly scaled to the squares, then the graph accurately represents the relative sizes of the land areas of the five largest countries.

For example, if country A is twice as big as country B, the square representing country A should have an area that is four times (2^2) the area of the square representing country B. Vice versa, if country C is half the size of country D, the square for country C should have an area that is a quarter of the square for country D. Therefore, through area scaling, each country will be proportionately represented on the graph.

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The probability of the sum of the numbers rolled on two dice being at least 4 is 25/36.

When rolling two dice, the total number of outcomes is 36 (each die has 6 possible outcomes). To find the probability of the sum being at least 4, we need to determine the number of favorable outcomes. The pairs that satisfy this condition are (1, 3), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6). Therefore, there are 25 favorable outcomes. So, the probability is 25/36.

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45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10

By finding common denominators, we can express the boat drawbridge opening times in terms of a shared timeframe, such as every 60 minutes or 30 minutes. The common denominator is the smallest number that the opening times can be equally divided into.

The question relates to the application of common denominators in the context of timekeeping. Without specific times for the opening of Colby and Wave drawbridge, I will give a hypothetical scenario as an example.

Let's say Colby drawbridge opens every 20 minutes and Wave drawbridge opens every 15 minutes. A common denominator of 20 and 15 is 60, as they both divide evenly into 60. So, you could rename the opening times in terms of 60 minutes: Colby drawbridge opens 3 times every 60 minutes (60/20) and Wave drawbridge opens 4 times every 60 minutes (60/15).

If we want to use another common denominator, you could use 30. Then Colby drawbridge opens 1.5 times every 30 minutes (30/20) and Wave drawbridge opens 2 times every 30 minutes (30/15).

The way to find common denominators involves looking for the smallest number that both of the numbers can divide equally into. In this case, 60 was an obvious choice since there are 60 minutes in an hour, but other common denominators like 30 can also be used.

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Answer: f(x)=1x can have any number as an input except for zero.

Step-by-step explanation:

Domain is all the possible x-values that can be plugged in and range is all the possible y-values that can be outputs. f(x)=1x can have any number as an input except for zero.

Final answer:

To determine Zoe's share from the 3:7 tip ratio when Hannah received £24, divide £24 by 7 to find the value of one part of the ratio, then multiply by 3 to find Zoe's share, resulting in £10.29.

Explanation:

When Zoe and Hannah share tips at a ratio of 3:7 and it is known that Hannah received £24, we can set up a proportion to find out how much Zoe received. Since Hannah's share of the tips corresponds to the 7 parts of the ratio, each part is worth £24 divided by 7 (which is Hannah's portion of the ratio). To find out Zoe's share, we multiply the value of each part by 3 (which is Zoe's portion of the ratio).

Calculate the value of one part of the ratio: £24 / 7 = £3.43 (rounded to two decimal places).

Calculate Zoe's share: £3.43 * 3 = £10.29 (rounded to two decimal places).

Therefore, Zoe's share of the tips would be £10.29.

Answer:

100

Step-by-step explanation:

We know that if we convert 1/4 into a decimal it becomes 0.25 so,

0.25

x

400

____________________

100

Hope this helps!

Answer:

84 cases

Step-by-step explanation:

The amount of money need to be raised = $ 500

Selling price of each ball = $2

1 Tennis case = 3 balls.

Earnings = Selling Price of each ball x Number of balls sold

Quantity sold = Earnings / Selling Price of each ball

Quantity sold = $ 500 / $ 2 = 250 balls

Using direct proportions

1 case = 3 balls

? cases = 250 balls

No.cases = 250 balls / 3 balls = 83.333

Note: Minimum number of cases required are 83.3333 to earn $ 500; however, we can not sell 0.3333 number of cases, hence, we will sell atleast 84 cases.

Answer:

Step-by-step explanation:

x + 3y = 24.....multiply by -1

5x + 3y = 36

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

-x - 3y = -24 (result of multiplying by -1)

5x + 3y = 36

------------------add

4x = 12

x = 12/4

x = 3 <=======

x + 3y = 24

3 + 3y = 24

3y = 24 - 3

3y = 21

y = 21/3

y = 7 <========

Final answer:

To solve the system of equations for the given word problem, define two variables and set up two equations. Use the substitution or elimination method to find the solution. The numbers are 3 and 7, and this solution is confirmed by substituting the values back into the original equations.

Explanation:

To solve the given word problem using a system of equations, we can define two variables for the two numbers we are looking for. Let's call the first number x and the second number y. Now we can formulate two equations based on the information provided:

One number added to three times another number is 24: x + 3y = 24

Five times the first number added to three times the other number is 36: 5x + 3y = 36

We can choose substitution or elimination method to solve these simultaneous linear equations. To use the substitution method, we start by solving the first equation for x (x = 24 - 3y) and then substitute this expression into the second equation:

Solve for x in the first equation: x = 24 - 3y

Substitute x into the second equation: 5(24 - 3y) + 3y = 36

Expand and simplify: 120 - 15y + 3y = 36

Solve for y: -12y = -84

Divide by -12: y = 7

Substitute y back into x = 24 - 3y to find x: x = 24 - 3(7)

Calculate x: x = 3

So the two numbers are 3 and 7.

As a check, we can substitute these values back into the original equations to verify that they lead to identities:

3 + 3(7) = 24, which simplifies to 24 = 24

5(3) + 3(7) = 36, which simplifies to 36 = 36

This confirms our solution is correct.

Answer:

when multiplying polynomials you want to times the coefficients but add the exponents

(-7a^4b^1c^3)(5a^1b^4c^2) (if there isn't an exponent then it is 1)

-7*5=-35

a^4*a^1=a^5

b^1*b^4=b^5

c^3*c^2=c^5

Your answer would be

-35a^5b^5c^5

Hope this helps ;)

Answer:

28.56

Step-by-step explanation:

Find the perimeter of the square:

4s

= 4×4

=16

Find the circumference of the circle and since it's half circle for both side it's going to be 1 circle:

3.14×d

= 3.14×4

=12.56

Add perimeter of square and circumference:

16+12.56

=28.56

It might help to think of this shape as a track for runners to run around, even though the scale is much too small for it.

The two semicircles on each end can be combined to form a full circle. This circle has radius r = 2, which is half of the diameter 4 (square's side length).

C = 2*pi*r

C = 2*pi*2

C = 4pi is the exact circumference

C = 4*3.14

C = 12.56 is the approximate circumference

This represents the distance around the curved portions of the track.

The straight portions are 4 each. We do not include the vertical sides as they are not on the outside, and the runners do not run along those vertical portions (they run around the curved parts instead). So we add on 4+4 = 8 to the previous value 12.56 to get 20.56 as our final answer.

Answer:

Option a=$6.37 is correct

The value of the variable is the solution of the given equation is a=$6.37

Step-by-step explanation:

Given equation is a+$5.92=$12.29

To find the value of the variable is the solution of the given equation :

a+$5.92=$12.29

Subracting the above equation by $12.29 on both sides we get

a+$5.92-$12.29=$12.29-$12.29 ( Subtraction property of equality)

a-$6.37=0

Now add $6.37 on both sides we get

a-$6.37+$6.37=0+$6.37 ( Addition property of equality)

a-0=$6.37

Therefore a=$6.37

Therefore option a=$6.37 is correct

Answer:

3rd answer is correct, $6.37

Step-by-step explanation:

Answer:

The complete answer is explained below.

Step-by-step explanation:

The problem is demanding to simply determine the number of years each color light would last.

We know the following information from the question:

Also the bulbs for each color are LED and are designed to last 100,000 hours. So, each light does last 100,000 hours.

lets make conversions

As

[tex]1\:day\:=\:24\:hours[/tex]  

[tex]1\:year\:=\:365\:days[/tex]

Dividing [tex]100,000[/tex] hours by [tex]24[/tex] hours would bring [tex]4166.67[/tex] days

Dividing [tex]4166.67[/tex] days by [tex]365[/tex] days would bring [tex]11.4[/tex] years, meaning 11 years and 4 months.

Keywords: light, conversion, day, hours

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Answer:

Amount in 4% account: $550

Step-by-step explanation:

Use simple interest formula [tex]I=P\cdot r\cdot t,[/tex] where

I = interest

P = principal

r = rate (as decimal)

t = time.

4% account:

[tex]P_1=x\\ \\r_1=0.04\\ \\t_1=1,[/tex]

then

[tex]I_1=x\cdot 0.04\cdot 1=0.04x[/tex]

5% account:

[tex]P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,[/tex]

then

[tex]I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)[/tex]

You have earned $69.50 in total, so

[tex]I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950[/tex]

Amount in 4% account: $550

Amount in 5% account: $950

Answer:

Step-by-step explanation:

[tex](\sqrt[3]{2} )^{5}=(2^{\frac{1}{3}})^{5}=2^{\frac{1}{3}*5}=2^{\frac{5}{3}}[/tex]

The linear equation that models the value of the automobile in terms of the year x is y = -1,110 x + 14,220

Step-by-step explanation:

The average value of a certain type of automobile was 14,220 in 1993 and depreciated to 9,780 in 1997

We need to write and graph a linear equation that models the value of the automobile in terms of the year x

The form of the linear equation is y = mx + b, where b is the initial value (value y at x = 0), and m is the rate of change

∵ The average value the of automobile was 14,220 in 1993

∵ x = 0 represents 1993

∴ The point which represent the data is (0 , 14,220)

- b is the value of y at x = 0

∴ b = 14,220

∵ The average automobile was 9,780 in 1997

- To find x subtract 1993 from 1997

∵ 1997 - 1993 = 4

∴ x = 4

∴ The point which represent the data is (4 , 9,780)

∵ m = Δy/Δx

∴ [tex]m=\frac{9780-14220}{4-0}[/tex]

∴ m = -1,110

- Substitute the values of m and b in the form of the equation

∴ y = -1,110 x + 14,220

The linear equation that models the value of the automobile in terms of the year x is y = -1,110 x + 14,220

The graph is attached below

Each square unit represents 1000 in the graph

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A linear function is a function that changes at a constant rate.

The equation of the linear function is [tex]y = -1110x + 14220[/tex]

The given parameters are:

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

This gives

[tex]m = \frac{9780 - 14220}{4- 0}[/tex]

Simplify

[tex]m = \frac{-4440}{4}[/tex]

This gives

[tex]m = -1110[/tex]

The equation is then calculated as:

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

This gives

[tex]y = -1110(x -0) + 14220[/tex]

Expand

[tex]y = -1110x + 14220[/tex]

Hence, the equation of the linear relationship is [tex]y = -1110x + 14220[/tex]

See attachment for the graph

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