Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycle? Round your answer to two decimal places, if needed.

Answers

Answer 1

Answer:

17 mph

Step-by-step explanation:

Miguel's speed = m, Raul's speed = rGivenm = 4rDistance = 68 milesTime difference = 3 hoursSolutiontime = distance/speed

Substitute values and solve for r the equation of the time difference:

68/m + 3 = 68/r68/4r + 3 = 68/r17/r + 3 = 68/r17 + 3r = 683r = 68 - 173r = 51r = 17

Raul's speed is 17 mph

Answer 2

Answer:

[tex] \huge \boxed{ \boxed{ \red{ \tt17 \: mph}}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:equationequation word problemsPEMDASgiven:Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycletips and formulas:t=d/sto findhow fast can Raul ride his bicyclelet's solve:

let's the speed of Raul be x

likewise

Miguel can drive 4 times as fast as Raul can ride his bicycle

therefore

4x

according to the question

[tex] \sf \frac{68}{4x}+3=\frac{68}{x}[/tex]

[tex] \implies \sf \frac{68 + 12x}{4x} = \frac{68}{x} [/tex]

[tex] \sf factor \: out \: 4 \: and \: reduce \: it : \\ \sf \implies \frac{4(17 + 3x)}{4x} = \frac{68}{x} \\ \\ \implies\sf \frac{17 + 3x}{x} = \frac{68}{x}[/tex]

[tex] \sf multipy \: both \: sides \: by \: x : \\ \sf \implies (\frac{17 +3 x}{x} )x = (\frac{68}{x} )x \\ \implies \sf 17 + 3x = 68[/tex]

[tex] \sf cancel \: 17 \: from \: both \: sides : \\ \implies \sf 17 - 17 + 3x = 68 - 17 \\ \implies \sf 3x = 51[/tex]

[tex] \sf divide \: both \: side s \: by \: 3 : \\ \sf \implies \frac{3x}{3} = \frac{51}{3} \\ \therefore x = 17[/tex]


Related Questions

Gina has one-third scale model of a three-dimensional solid, meaning that all lengths
of the model are 1/3 of the corresponding lengths in the full-size solid. If the volume of
Gina’s model is 20 cubic inches, what is the volume of the full-sized solid?

Answers

Answer:

volume is 540 inches^3

Step-by-step explanation:

The computation of the volume of the full sized solid is given below:

The length would be

[tex]\frac{a}{3}, \frac{b}{3}, \frac{c}{3}[/tex]

And, the volume is

[tex]\frac{a}{3} \times \frac{b}{3} \times \frac{c}{3}[/tex]

As the volume is given 20 cubic inches

So,

[tex]\frac{abc}{27} = 20\\\\abc = 540 inches^3[/tex]

hence, volume is 540 inches^3

what is this 3d shape called

Answers

Answer:

The name of the shape is Hexagonal Prism

PLEASE HELP!!!
what is the length of segment SR? units​

Answers

Answer:

Its 12

Step-by-step explanation:

Plot the x-intercepts and make a sign chart that represents the function shown below

Answers

Step-by-step explanation:

step 1. the x intercepts (called zeros) are where y = 0 or where the graph is on the x axis

step 2. the zeros are -3, 0, 2, 5.

step 3. therefore there are 5 intervals

step 4. ( ,-3) - f(x) = "-"

step 5. (-3, 0) - f(x) = "+"

step 6. (0, 2) - f(x) = "+"

step 7. (2, 5) - f(x) = "-"

step 8. (5, ) - f(x) = "+".

A function assigns the values. The x-intercept for the given function is -3, 0, 2, and 5.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The given function can be rewritten as,

f(x) = x²(x-5)(x+3)³(x-2)

f(x) = (x-0)² (x-5) (x+3)³ (x-2)

Now, the value of x in the given function, or the x-intercept can be found by substituting the value of the factors of function as 0.

0 = (x-0)² (x-5) (x+3)³ (x-2)

(x-0)² = 0

x = 0

x-5 = 0

x = 5

x+3 = 0

x = -3

x - 2 = 0

x = 2

x = -3, 0, 2, 5

Hence, the x-intercept for the given function is -3, 0, 2, and 5.

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final solution to the system of equations given below
x=-4
5x+4y=-10​

Answers

Answer:

(-4, 5/2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Coordinates (x, y)Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

x = -4

5x + 4y = -10

Step 2: Solve for y

Substitution

Substitute in x:                                                                                                5(-4) + 4y = -10Multiply:                                                                                                           -20 + 4y = -10[Addition Property of Equality] Add 20 on both sides:                               4y = 10[Division Property of Equality] Divide 4 on both sides:                                 y = 10/4Simplify:                                                                                                             y = 5/2

fen bilimleri sorusu limana yaklaşan bir geminin önce gövdesimi görünüyorduuuuu yoksa bacasımı ¿¿¿¿ ^-^​

Answers

Answer:

ilk önce en ön kısmı gözükür

bacası öndeyse bacası gözükür

şöyle düşün elinde bir top var ve bir gemi gemiyi topun altindan yukariya doğru götürüyorsun ve ilk en öndeki kısmı gözükür

Evaluate the expression: 16.2 x 2 + 1/2 x 8.5 x 12

Answers

83.4. Is the answer.

Answer:

83.4

Step-by-step explanation:

16.2 x 2

=

32.4 +

1/2 x 8.5 x 12  

=

51 + 32.4 = 83.4

Hope this helps!

Is (2, 1) a solution to this system of equations?
4x + 12y = 20
x + y = 3
yes
no

Answers

Answer:

yes

I hope to help you

my dear

Answer:

no

Step-by-step explanation:

4(2)+12(1)=20

8 + 12 =20

20 = 20

Which polynomial represents the sum below? (-x^3 + 3x^2 + 3) + (3x^2 + x + 4)

Answers

Answer:

Cddd

Step-by-step explanation:

Write the recurring decimal 0.1 as a fraction in its simplest form

Answers

The answer is going to be 1/9

Answer:

1/9

Step-by-step explanation:

lol

The bus driver has driven 49 miles this morning. His route is 123 miles. How much further must he drive to finish his route

Answers

Answer:

74 miles

Step-by-step explanation:

Answer:

74 miles

Step-by-step explanation:

123-49=74

(3.5 x 10^5) : (7x10^8)
What is the answer to this question?

: is divide

Answers

Answer:

5 • 10^-4 I evaluate this by using scientific notation.

The value of the ratio  (3.5 x 10⁵) : (7x10⁸)  is 0.0005.

What are expressions?

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

To solve (3.5 x 10⁵) : (7x10⁸), we can simplify the expression by dividing the numerical coefficients and dividing the exponents separately.

Dividing the numerical coefficients 3.5 and 7, we get:

3.5 ÷ 7 = 0.5

Dividing the exponents 5 and 8, we get:

10⁵ ÷ 10⁸ = 10⁵⁻⁸

              = 10⁻³

Therefore, the simplified expression is:

0.5 x 10⁻³

We can further simplify this expression by converting 10⁻³ to a decimal:

10⁻³ = 1/1000 = 0.001

So, the final answer is:

(3.5 x 10⁵) : (7x10⁸) = 0.5 x 10⁻³

                              = 0.5 x 0.001

                              = 0.0005

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Prior to the Academy Awards ceremony in 2009, the United Kingdom bookmaker Ladbrokes reported the following odds for winning an Oscar in the category of best actress (The Wall Street Journal, February 20, 2009).
Best Actress Movie Odds
Anne Hathaway Rachel Getting Married 2:11
Angelina Jolie Changeling 1:20
Melissa Leo Frozen River 1:33
Meryl Streep Doubt 3:10
Kate Winslet The Reader 5:2
a. Express the odds for each actress winning as a probability. (Round your answers to 3 decimal places.)
Best Actress Probability
Anne Hathaway
Angelina Jolie
Melissa Leo
Meryl Streep
Kate Winslet

Answers

Answer:

Anne Hathaway: 0.154 = 15.4%

Angelina Jolie: 0.048 = 4.8%

Melissa Leo: 0.029 = 2.9%

Meryl Streep: 0.231 = 23.1%

Kate Winslet: 0.714 = 71.4%

Step-by-step explanation:

Odds to probability:

Odds of a:b

The probability is given by:

[tex]p = \frac{a}{a+b}[/tex]

Anne Hathaway 2:11

So [tex]p = \frac{2}{2+11} = \frac{2}{13} = 0.154[/tex]

Angelina Jolie 1:20

So [tex]p = \frac{1}{1+20} = \frac{1}{21} = 0.048[/tex]

Melissa Leo 1:33

So [tex]p = \frac{1}{1+33} = \frac{1}{34} = 0.029[/tex]

Meryl Streep 3:10

So [tex]p = \frac{3}{3+10} = \frac{3}{13} = 0.231[/tex]

Kate Winslet 5:2

So [tex]p = \frac{5}{5+2} = \frac{5}{7} = 0.714[/tex]

Find angle picture below

Answers

Answer:

Angle C = 28°

Angle D = 59°

Angle DEC = 63°

I need help with this also

Answers

Answer:

Part A: $336.4

Part B:279.2645625

Step-by-step explanation:

$320+5.125% tax = 336.4

Part B:$279.2645625-5.125% tax = 279.2645625 bucks.

Thank you and good luck cheating


What is the GCF of 4 and 8? *

Answers

Answer:

i think it is for 4 it is 2 and for 8 it is 4 hope this helps

Step-by-step explanation:

Enter a phrase for the expression. 49s

Answers

I don’t get this explain it better

Matt E. Matic was applying for a job. To determine whether he could handle the job, the personnel manager sent him out to poll 100 people about their favorite types of TV shows. His data were as follows. 58 preferred comedies. 38 preferred variety shows. 44 preferred serious drama. 19 preferred comedies and variety programs. 14 preferred variety and serious drama. 15 preferred comedies and serious drama. 7 preferred all types. 5 did not like any of these TV show types. If you were the personnel manager, would you hire Matt on the basis of this survey

Answers

Answer: No, I wouldn't because he didn't do what he was told.

Step-by-step explanation: Using Matt's survey we draw a Venn Diagram.

Venn Diagram is a diagram used to show the logical relationship between two or more set of items.

The survey Matt did is represented below.

To construct the diagram:

1) Create 3 sets of data (represented by the circles) intersecting each other;

2) The space where the three intersect is the number of people surveyed that preferred all types. So, we write 7 in the space;

3) According to the research, 19 preferred comedies and variety. But there are already 7 in the intersect, so, 12 has those preferences;

4) Following the same logic, 14 preferred variety and drama. Then, 7 has those preferences;

5) And, 8 preferred comedy and drama;

6) Now, to determine how many of them has an exclusive preference, we take the data and subtract the already known values:

Comedy: 58 - 12 - 7 - 8 = 31;Variety: 38  - 12 - 7 - 7 =  12;Drama: 44 - 8 - 7 - 7 = 22;

7) 5 don't like any of the types, so it is represented outside the three circles;

After creating the Diagram, we can determine how many people answered the poll:

total = 31 + 12 + 12 + 8 + 7 + 7 + 22 + 5

total = 104

Therefore, as a personnel manager, I wouldn't hire Mr. Matic because he was supposed to poll 100 people but he polled 104 people.

4x -(9 - 3x) = 8x -1​

Answers

Answer:

x = -8

Step-by-step explanation:

4x - (9 - 3x) = 8x - 1

remove parenthesis

4x - 9 + 3x = 8x - 1

add 9 to both sides

4x + 3x = 8x + 8

subtract 8x from both sides

-x = 8

x = -8

The solution to the equation 4x - (9 - 3x) = 8x -1​ is x = -8

How to determine the solution to the equation

From the question, we have the following parameters that can be used in our computation:

4x - (9 - 3x) = 8x -1​

Open the brackets

So, we have

4x - 9 + 3x = 8x - 1

Evaluate the like terms

So, we have the following representation

7x - 9 = 8x - 1

Next, we have

8x - 7x = 1 - 9

So, we have

x = -8

Hence, the solution is x = -8

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(giving brainiest)

A bottle holds 2 pints. A carton holds 3 cups. What is the total the two containers hold in fluid ounces?

A. 6 fluid ounces
B. 32 fluid ounces
C. 56 fluid ounces
D. 66 fluid ounces

Answers

Answer:

your answer is c (56 fluid ounces)

Step-by-step explanation:

A. a scientist is studying the change in population for two species of fish in a lake. The table shows how the numbers of each species changed during a 4-year period.
YEAR: 1; 2; 3; 4
FISH A: 500; 520; 540; 560; 580
FISH B: 400; 430; 460; 490; 520
The scientist uses a linear model to predict future populations of both fish. Explain why, given the data in the table, population of fish A and the population of fish B can be modeled using linear equations.

Answers

Answer:

The data can be modeled using linear equatins, because there's the same amount of population for fish A (+20 per year) and fish B (+30 per year) every year.

Use structure: How is subtracting -4x from 9x similar to subtracting -4 from 9?

Answers

Answer:

It is the same thing except for subtracting -4x and 9x, you subtract -4 and 9 and just add x at the end

What is the slope of a line that is perpendicular to the line y = 1/6x + 4
The slope of the line is

Answers

Answer:

-1/6x

Step-by-step explanation:

for a slope to be perpindicular it has to be the opposite.

Hello there! :)

Perpendicular lines have slopes that are opposite reciprocals. It means that if we have a number, we flop it over and make it negative.

We have 1/6.

We flop it over:

6/1

Now, we make it negative:

-6/1

-6/1 simplifies to

-6

Hope it helps!

If you have any question, feel free to ask!

~An excited gal

[tex]MagicalNature[/tex] here to help :)

WILL GIVE BRAINLIEST FOR RIGHT ANSWER.

Answers

The answer is 35

g(1)= -3(1) = -3

f(g(-3)) = (-3)^2 - 8(-3) + 2 = 35

Russia bought 9 books for $3 each sold them making a profit of $18 for what price did she sell each book?​

Answers

Answer:

$45

Step-by-step explanation:

Profit= $18

Books = 9

Sold each at = $3

So, total CP (Cost Price)= 9*3 = $ 27

Also Profit = SP - CP

Therefore, SP = Profit + CP

= 18 + 27 = $45

A lumber mill needs one more tree cut down that is at least 29 feet long. The person cutting down the tree is 6 feet 2 inches tall. Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 32 inches. What is the length (to the nearest tenth of a foot) of the tree’s shadow that will allow the tree to be cut down?

Answers

Answer:

create a proportion 72/348 = 32/x

Step-by-step explanation:

x = 1682

1682 ÷ 12 = 140.1

The length of the tree’s shadow that will allow the tree to be cut down will be 150.5 inches.

What are ratio and proportion?

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

A lumber mill needs one more tree cut down that is at least 29 feet long. The person cutting down the tree is 6 feet 2 inches tall.

            29 feet = 348 inches

6 feet 2 inches = 74 inches

Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 32 inches.

Then the length of the tree’s shadow that will allow the tree to be cut down will be

Let x be the tree’s shadow. Then we have

x / 348 = 32 / 74

x = 150.486

x ≅ 150.5 inches

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Write an equivalent expression. 4x - x

Answers

Answer:

5x-2x

Step-by-step explanation:

4x-x = 3x

so,

5x-2x = 3x

The equivalent expression would be; 5x-2x

What are equivalent expressions?

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We are given that the expression as; 4x - x

We need to find an equivalent expression.

Therefore, solving further;

4x-x = 3x

Thus, we can also create one expression as;

5x-2x = 3x

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Please help me please ! Also the answer is not a

Answers

Answer:

The answer is c

Step-by-step explanation: Since both terms are perfect squares, factor using the difference of squares formula to get the answer i hope this helps

Hey there!

The answer is C.

To factor an expression, you take the root (same as exponent variable has) of the terms and put them into parantheses. We can also check the choices to see if they're correct by solving them.

A is incorrect, because if you solve it, you would have [tex]x^2-121[/tex]

B is incorrect, because if you solve it, you would have [tex]121x-x^2[/tex]

C is correct, because if you solve it, you would have [tex]121-x^2[/tex]

D is incorrect, because it CAN be factored.

Have a super awesome day! :)

plz help i have 9 min and i dont understand plz help worth 20 points

Answers

Answer:

no question

Step-by-step explanation:

. A un concierto asistieron 10000 personas , lo que representó un total de
$6600000 en ingresos por venta de boletos. Había boletos de dos precios
de acuerdo con la proximidad al escenario: general ($500) y preferente
($1300). ¿Cuántos boletos de cada tipo se vendieron?

Answers

Answer:

Número de boletos general = 8000

Número de boletos preferente = 2000

Step-by-step explanation:

Total de personas = 10000 personas

Venta total = $6600000

Ecuación para la venta total en terminos de boletos vendidos:

Número de boletos general = variable g

Número de boletos preferente = variable p

$500g + $1300p = $6600000

Simplifica la ecuación:

5g + 13p = 66000

Subsituye una de las variables usando la ecuación g + p = 10000:

g + p = 10000 => g = 10000 - p

5g + 13p = 66000 => 5(10000 - p) + 13p = 66000

Aislar la variable p:

5(10000 - p) + 13p = 66000

50000 - 5p + 13p = 66000

8p = 16000

p = 16000/8 = 2000

g = 10000 - p = 10000 - 2000 = 8000

Número de boletos general = 8000

Número de boletos preferente = 2000

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