Jacob took a taxi from his house to the airport. The taxi company charged a pick-upfee of $1.30 plus $5 per mile. The total fare was $16.30, not including the tip. Writeand solve an equation which can be used to determine , the number of miles in the

Answers

Answer 1

Let the total number of fare be f and total number of miles be m.

Therefore, the total fare f is given by:

[tex]f=1.30+5m[/tex]

Substitute f = 16.30 into the equation:

[tex]\begin{gathered} 16.30=1.30+5m \\ 16.30-1.30=5m \\ 15=5m \\ \frac{15}{5}=\frac{5m}{5} \\ 3=m \\ m=3 \end{gathered}[/tex]

Therefore, the required number of miles is 3.


Related Questions

suppose that you have a savings account with 8500 in it. it pays 7% interest compound as shown below. find the value for the next 4 years

Answers

We want find the compound interest annualy for 4 years, $8500, at 7%'

The formula for the compound amount over one year is;

[tex]A=P(1+\frac{r}{100})[/tex]

1st year:

[tex]\begin{gathered} A=8500(1+0.07) \\ A=\text{ \$9095} \end{gathered}[/tex]

2nd year:

[tex]\begin{gathered} A=9095(1.07) \\ A=\text{ \$9731.65} \end{gathered}[/tex]

3rd year:

[tex]\begin{gathered} A=9731.65(1.07) \\ A=\text{ \$10412.87} \end{gathered}[/tex]

4th year:

[tex]\begin{gathered} A=10412.87(1.07) \\ A=\text{ \$11141.77} \end{gathered}[/tex]

Put the following equation of a line into slope-intercept form, simplifying allfractions.2x + 8y = 24

Answers

[tex]\begin{gathered} y=mx+c \\ \text{where} \\ m=\text{ slope} \\ c=\text{intercept} \\ 2x+8y=24 \\ 8y=24-2x \\ \text{divide through by 8} \\ \frac{8y}{8}=\frac{24}{8}-\frac{2x}{8} \\ y=3-\frac{1}{4}x \\ y=-\frac{1}{4}x+3 \end{gathered}[/tex]

3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.Formulas:

Answers

A sequence is called arithmetic if the difference between two consecutives is a constant

In the first case we see a constant difference of 5

every two consecutives have difference of 5, for example 20-15, 30-25 and so on.

In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.

the constant in this case is 18/6 =3

lets return to the 1st case find the explicit

An = Ao +(n-1) d

An means the n term in the sucession

Ao means the first term

d means the constant

with that in mind we replace the values obtained

An= 5 + (n-1) •5

now for the recursive

a1= 5

An = An-1 + 5

Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula

so then

An = A1 •(3)^(n-1)

An = 2• (3)^(n-1)

Graph the line y=1/4x+3 then name the slope and y-intercept by looking at the graph. How do I graph this what are my points and what is m= as well as what is b=?

Answers

Make graph line using the slope and the y-intercept or the point.

m=1/4 and b=3

What is graph ?

graph is a mathematical representation of a networks and it describes that the  relationship between lines and points. A graph consists of some points and lines are  between them. The length of the lines and position of the points do not matter.

Sol-as per the given question y=1/4x+3

The slope-intercept form y=mx+b where m is the slope and b is the y intercept

y=mx+b

Reorder terms

y=1/4x +3

Use the slope-intercept form to find the slope and y-intercept

Slope=1/4

y-intercept :(0,3)

Any line can be graphed using two points is  Select two x

values, and plug them into the equation to find the corresponding Y values.

In record terms -y=1/4 x+3

The table of x and y values are-

X-0,4

Y-3,4

graph the line using the slope and the y-intercept, or the points.

Slope -1/4

y-intercept (0,3)

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Which equation is set up for direct use of the zero-factor property? A. 3x2 - 19x - 14 = 0 C.X2 + x = 42 B. (7x + 9)2 = 3 D. (3x - 2)(- 2) = 0

Answers

Explanation:

The zero-factor property states that if ab=0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more factors is zero.

From these options only B and D have factors, but B equals to 3. In D we have that (3x-2) = 0 or the other factor is zero (or both)

Answer:

The correct answer is option D

Help please!!!!!!!!!!!!!!!!!!!!!!!!!Which is the best buy?a. $18.09 for 9 bottles of juiceb. $22.33 for 11 bottles of juice

Answers

Answer:

The correct option is option a.

$18.08 for 9 bottles is the better buy.

Explanation:

The best buy is the item with the lesser price tag.

Let us chech which of the given items has the lesser price tag.

a. $18.08 for 9 bottles of juice

Let us find how much one bottle costs.

1 bottle = 18.08/9

= 2.01

1 bottle of juice costs $2.01 approximately

b. $22.23 for 11 bottles of juice

1 bottle = 22.23/11

= 2.03

1 bottle of juice costs $2.03 approximately.

Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.

What is the measure of the exterior angle of the triangle? A. 23°B. 149°C. 180°D. 31°

Answers

Solution

The diagram below will be of help

From the image above

We know that the sum of angle in a triangle is 180 degrees

That is

[tex]\begin{gathered} 63+86+y=180 \\ 149+y=180 \\ y=180-149 \\ y=31^{\circ} \end{gathered}[/tex]

Now, to find x

We also know that the sum of angle in a straight line is 180 degrees

That is

[tex]y+x=180[/tex]

We now solve for x

[tex]\begin{gathered} x=180-y \\ x=180-31 \\ x=149^{\circ} \end{gathered}[/tex]

Therefore, the value of x = 149 degrees

Option B

I really need help make sure that your answer is 7th grade appropriate

Answers

Examples:

1. Five increased by four times a number

[tex]5+4n[/tex]

where n is the number

2.The product of 4, and a number decreased by 7

[tex]4(n-7)[/tex]

Devon is 30 years old than his son, Milan. The sum of both their ages is 56. Using the variables d and m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.How old is Devon?

Answers

Let's set d as the age of Davon and m as the age of Milan.

Devon is 30 years old than his son Milan, it is represented by the equation:

[tex]d=m+30\text{ Equation (1)}[/tex]

The sum of both ages is 56, the equation that represents the situation is:

[tex]d+m=56\text{ Equation (2)}[/tex]

To find Devon's age, in equation 1, solve for m in terms of d:

[tex]m=d-30[/tex]

Now, replace in equation 2 and solve for d:

[tex]\begin{gathered} d+(d-30)=56 \\ 2d-30=56 \\ 2d=56+30 \\ 2d=86 \\ d=\frac{86}{2} \\ d=43 \end{gathered}[/tex]

Devon is 43 years old.

A $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.25% compounded daily find the value in dollars of the account after 2 years assume years have 365 days round your answer to the nearest cent

Answers

SOLUTION

From the question, we want to find the value in dollars of the account after 2 years.

We will usethe formula

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }\frac{4.25}{100}=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}[/tex]

Applying this, we have

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=40,000(1+\frac{0.0425}{365})^{365\times2} \\ A=40,000(1.000116438)^{730} \\ A=40,000\times1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}[/tex]

Hence the answer is 43,548.47 to the nearest cent

9×6 can u help me with this

Answers

You have to multiply the numbers:

9x6 =54

Multiply is the same as adding the number 6 times

9+9+9+9+9+9 =54

Animal is a bird Can fly Tiger Penguin ✓ ✓ Robin ✓ Snail Sparrow ✓ ✓ Pelican ✓ ✓ ✓ Bat Let event A = The animal is a bird. Let event B = The animal can fly. Which outcomes are in A and 8? O A. (robin, sparrow.pelican) B. (penguin, robin, sparrow, pelican) c. robin, sparrow, pelican, bat) D. (penguin, robin, sparrow. pelican, bat)

Answers

Outcome that are in A and B simply means both outcome must be achieved.

Therefore,

[tex]\begin{gathered} \text{Animal can fly and Animal is bird both exist in } \\ A\text{. }\mleft\lbrace\text{Robbin, sparrow, pelican}\mright\rbrace \end{gathered}[/tex]

Mr. Herman had $125, and Mr.Chandra had $80. After each of them had paid for a concert ticket, Mr. Herman had 6 times as much money as Mr. Chandra. how much money did Mr. Chandra have left?

Answers

We have

Let x = cost of the ticket

After paying for the tickets, Mr. Herman had 125 - x

and Mr Chandra had 80 - x

Then, the equation is:

[tex]125-x=6(80-x)[/tex]

So, solve for x:

[tex]\begin{gathered} 125-x=480-6x \\ 125-x+6x=480-6x+6x \\ 125+5x=480 \\ 125+5x-125=480-125 \\ 5x=355 \\ \frac{5x}{5}=\frac{355}{5} \\ x=71 \end{gathered}[/tex]

The concert ticket cost is $71

Therefore, Mr. Chandra have left:

[tex]80-71=9[/tex]

Answer: $9

If the correlation coefficient r is equal to 0.755, find the coefficient of determination and the coefficient of nondetermination.Question 10 options: The coefficient of determination is 0.430 and the coefficient of nondetermination is 0.570 The coefficient of determination is 0.869 and the coefficient of nondetermination is 0.131 The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430 The coefficient of determination is 0.131 and the coefficient of nondetermination is 0.869

Answers

Given the word problem, we can deduce the following information:

The correlation coefficient r is equal to 0.755.

To determine the coefficient of determination and the coefficient of nondetermination, we use the formulas below:

[tex]Coefficient\text{ }of\text{ }Determination=r^2[/tex][tex]Coefficient\text{ }of\text{ N}ondetermination=1-r^2[/tex]

Now, we first plug in r=0.755 to get the coefficient of determination:

[tex]Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ D}eterm\imaginaryI nat\imaginaryI on=r^2=(0.755)^2=0.57[/tex]

Next, we get the coefficient of nondetermination:

[tex]\begin{gathered} Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ N}ondeterm\imaginaryI nat\imaginaryI on=1-r^2=1-0.57=0.43 \\ \end{gathered}[/tex]

Therefore, the answer is:

The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430

Which ocean animal is closest to a depth of -0.7km?

Answers

Answer:

whales, walruses, porpoises, dolphins, seals, dugongs, manatees, and sea otters

Step-by-step explanation:

have good day

given: S is the midpoint of BT ; BO || AT prove:

Answers

"S is the midpoint of BT": this is given.

BO || AT: this is given.

SB = ST: definition of midpoint.

alternate interior

vertical

ΔBOS = ΔTAS: SAS or ASA (both are right).

find the zeros algebraically: f(x)=x^4-8x^3+5x^2+14x

Answers

The given equation is:

x^4-8x^3+5x^2+14x​

In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.

Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots

Therefore,

x^4-8x^3+5x^2+14x​ = 0

or

x(x^3-8x^2+5x+14​) = 0

=> x = 0 and x^3-8x^2+5x+14​ = 0

Therefore, the first root is x = 0.

Now,

x^3-8x^2+5x+14​ = 0

To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.

Let's start with (1):

For x = 1

(1)^3 - 8(1)^2 + 5(1) + 14 = 0

1 -8(1) + 5 + 14 = 0

-1 -8 +5 + 14 = 0

- 9 + 19 = 0

10 = 0

It is false, therefore, x = 1 is not the solution.

For x = -1

(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0

-1 -8(1) - 5 + 14 = 0

-1 -8 -5 + 14 = 0

- 14 + 14 = 0

0 = 0

hence, x = -1 is the second solution.

If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor

x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)

Now, let's find the roots of x^2 - 9x + 14

x^2 - 9x + 14 = 0

x^2 - 7x - 2x + 14 = 0

x(x - 7) - 2 (x - 7) = 0

(x - 7) (x - 2) = 0

or

x - 7 = 0. and x - 2 = 0

x = 7 and x = 2

Therefore, the zeros of the given equation are, 0, -1, 2 and 7.

Look at this graph: у 10 9 8 7 6 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?

Answers

EXPLANATION

As we can see in the graph, we can calculate the slope with the following equation:

[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

Let's consider any ordered pair, as (x1,y1)=(1,7) and (x2,y2)=(5,8), replacing this in the equation will give us:

[tex]\text{Slope}=\frac{(8-7)_{}}{(5-1)}=\frac{1}{4}[/tex]

Answer: the slope is equal to 1/4.

A dwarf seahorse swims 3/4 inch in a minute. How many minutes would take the seahorse to swim 1/3 inch?
A. 1/3 divided by 3/4= 4/9
B. 1/3 times 3/4= 1/4
C. 3/4 divided by 1/3= 9/4
D. 3/4 + 1/3= 13/12

Answers

Answer:

A

Step-by-step explanation:

we have 3/4 in / minute.

so, we divide this by 3/4 to get the time for 1 inch.

and then we multiply by 1/3 to get the time for 1/3 inch.

that combination, dividing by 3/4 and multiplying by 1/3, can be done in any sequence (commutative property of multiplication).

therefore, this can be expressed as 1/3 divided by 3/4. and A is the correct answer.

I
Three relationships are described below:
I. The amount of time needed to mow a yard increases as the size of the yard increases.
II. The amount of timeneeded to drive from city A to city B decreases as the speed you are driving increases.
III. The income of a worker who gets paid an hourly wage increases as the number of hours worked increases and
increases as the salary rate increases.
What type of variation describes each relationship?

Answers

The type of variation that describes each relationship include the following:

Direct variation: the amount of time needed to mow a yard increases as the size of the yard increases.Indirect variation: the amount of time needed to drive from city A to city B decreases as the speed you are driving increases.Joint variation: the income of a worker who gets paid an hourly wage increases as the number of hours worked increases and increases as the salary rate increases.

What is an indirect variation?

An indirect variation simply refers to a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other, which means as one variable increases, the other variable decreases and vice-versa.

What is direct variation?

Direct variation refers to a type of proportional relationship in which a variable is directly proportional to another variable. This ultimately implies that, a direct variation represents two variables that are directly proportional to each other, which means as one variable increases, the other variable also increases and vice-versa.

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Find the length of the missing side of the triangle using the Pythagorean theorem. (Type an integer or decimal rounded to the nearest tenth as needed.)

Answers

Pythagorean theorem

[tex]\begin{gathered} a^2=b^2+c^2,\text{ where a is the hypotenuse} \\ a^2=(6.5)^2+(4.9)^2 \\ a^2=42.25+24.01 \\ a^2=66.26 \\ a=\sqrt[]{66.26}=8.1^{\prime} \end{gathered}[/tex]

(Type an integer or decimal rounded to the nearest tenth as needed.)

Integer = 8'

decimal rounded to the nearest tenth as needed = 8.1'

What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?

Answers

y=(5/4)x-1

First you put the equation into y=mx+b form:
1. move the 4x to the other side
5y=-4x+25
2. divide by 5 on both sides
y=(-4/5)x+5

Next, since the line has to be perpendicular, you take the negative reciprocal of the slope (flip the fraction and put the opposite sign)
1. 5/4

Now, find the y intercept (the b)
1. set up the equation
-6=(5/4)(-4)+b
2. multiply the 5/4 and -4
-6=-5+b
3. move the -5 to the other side (add it)
-1=b

Now, put all the elements together
1. y=(5/4)x-1

What is the value of 10 1

Answers

10

10x1=10

Hope this helps

Let E be the event where the sum of two rolled dice is less than 9. List the outcomes in E^c

Answers

The Solution:

Let the outcomes when two dice are tossed be as summarized in the picture attached below:

Which steps show how to use the distributive property to evaluate 9 - 32? A. 9(32) = 9(30 + 2) = 9.30 + 9 - 2 = 270 + 18 = 288 0 B. 9(32) = 9(30 + 2) = 9 - 30 + 30 - 2 = 270 + 60 = 330 OC. 9(32) = 9(30 + 2) = 9.30 – 9.2 = 270 – 18 = 252 O D. 9(32) = 9(30 + 2) = 9.30 + 2 = 270 + 2 = 272

Answers

to find the distribution of

[tex]9\cdot32[/tex]

rewrite 32 as an addition

[tex]32=30+2[/tex]

rewrite the product

[tex]9\cdot(30+2)[/tex]

distribute the 9

[tex]\begin{gathered} 9\cdot30=270 \\ 9\cdot2=18 \\ \\ 9\cdot(30+2)=9\cdot30+9\cdot2 \\ 9\cdot(30+2)=270+18 \\ 9\cdot32=288 \end{gathered}[/tex]

Jo borrowed $3800 for 8 months from a bank at 5.5% a. how much interest did jo pay the bank for the us of it's money?b. how much did he pay total?

Answers

Let's begin by listing out the given information:

Loan (p) = $3,800

Time (t) = 8 months = 8/12 year

Interest rate (r) = 5.5%

a)

We calculate it thus:

[tex]\begin{gathered} I=\frac{p\times r\times t}{100} \\ I=\frac{3800\times5.5\times\frac{8}{12}}{100}=139.33 \\ I=\text{\$}139.33 \end{gathered}[/tex]

b)

The amount paid in total is:

[tex]\begin{gathered} A=p+I \\ A=3800+139.33=3939.33 \\ A=\text{\$}3939.33 \end{gathered}[/tex]

Write a SITUATION that can be represented with this graph. Not an equation.

Answers

We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.

I NEED HELP ASAP Which of these data sets could best be displayed on a dot plot?721, 722, 722, 723, 724, 724, 724, 725, 727, 728, 73016, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 971.3, 1.9, 2.5, 2.7, 2.7, 3.5, 4.8, 5.3, 7.9, 9.00.012, 0.078, 0.093, 0.147, 0.187

Answers

Take into account that dop plots are usefull for small or moderate sized data sets, and also they are suefull for data with big gaps.

Based on the previous description, you can conclude that the best option for a dot plot is:

16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97

in comparisson with the other data sets, the elements of the rest of data sets are closer to each other.

Explain how to find the point equidistant from all three vertices in the given triangle. Choose the correct answer below. A. Find the intersection of the perpendicular bisectors of each side of the triangle B. Find the intersection of all of the midsegments of the triangle, C. Find the intersection of the angle bisectors of each angle of the triangle, D. Find the midpoint of the line segment that bisects Angle B.

Answers

ANSWER:

The correct option is the following:

C. Find the intersection of the angle bisectors of each angle of the triangle,

EXPLANATION:

The point that equidistant is the point at which the three bisectors of the internal angles of the triangle intersect, and it is the center of the circumference inscribed in the triangle and equidistant from its three sides.

IMPORTANT NOTE:

Any point on the bisector of an angle of a triangle equidistant from the sides that define that angle.

Question 2 (2 points)Find the value of x. If needed, round your answer to the nearest tenth.50°X5Not drawn to scaleX =

Answers

Solution

Find the value of x in the triangle shown below:

Calculate the value of x

Opposite = 5

adjacet = x

[tex]tan\theta=\frac{opp}{adj}[/tex][tex]\begin{gathered} tan50=\frac{5}{x} \\ x=\frac{5}{tan50} \\ x=\frac{5}{1.19175} \\ x=4.1955 \\ x=4.2\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]

Therefore the correct value of x = 4.2

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