#4-#5 please
Find the equation of a line with given slope and \( y \)-intercept. Write the equation in slope-intercept form. slope 7 and \( y \)-intercept \( (0,9) \) Find the equation of a line containing the giv

The estimate of the cost to travel 455 miles as required in the task content is; $63.4.

It follows from the task content that the cost of travelling 455 miles is to be determined from the given information.

Hence, this is two-step problem.

First, since the car gets 28 miles per gallon, the amount of gas needed to travel 455 miles by proportion is;

455/28 = 16.25 gallons.

Also, since the cost per gallon as in the complete task content is; $3.899.

The cost of 16.25 gallons is; 16.25 × $3.899

= $63.4.

Remarks: Gas costs $3.899 per gallon.

Read more on ratios;

https://brainly.com/question/2914376

#SPJ1

Jameson earns more interest than Quincy.

The correct answer is D. Jameson will have about $2,367.58 more in his account than Quincy. This is because Jameson earns annual simple interest, while Quincy earns annual compound interest.

With simple interest, the interest earned each year is based only on the initial amount of money deposited, while with compound interest, the interest earned each year is based on the initial amount plus the accumulated interest from previous years. Therefore, over time, compound interest earns more money than simple interest.

In this case, after 60 months, Jameson will have earned $10,500 in simple interest, while Quincy will have earned $10,871.58 in compound interest. This means that Jameson will have a total of $17,500 in his account, while Quincy will have a total of $15,132.42 in his account. Therefore, Jameson will have $2,367.58 more than Quincy in his account.

Learn more about D. Jameson

brainly.com/question/29050743

#SPJ11

The total amount of Zach's paycheck was $174.

The fraction of the paycheck spent by Zach on the new video game is 2/6. The cost of the video game is $58. We need to find the total amount that Zach had in the paycheck.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

Let the total amount of the paycheck be "x". Using the information above, we can form an equation as given below :

(2/6)*x = 58

x = (6/2)*58

x = 174

To learn more about equations, visit :

brainly.com/question/10413253

#SPJ1

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

To learn more about division, click on below link:

https://brainly.com/question/11781269

#SPJ4

Answer:

Step-by-step explanation:

You want to know how much money Abby and Ben each have if when Abby gives $10 to Ben, then they will have the same mount of money. If Ben gives $20 to Abby, then she'll have four times as much as he has.

The transfers give rise to two equations:

  (A-10) = (B +10)

  (A +20) = 4(B -20)

Using the first equation, we can write an expression for A:

  A = B +20

This can be substituted into the second equation to give ...

  (B +20) +20 = 4(B -20)

  B +40 = 4B -80 . . . . simplify

  120 = 3B . . . . . . . . . . add 80-B

  40 = B . . . . . . . . . . . . divide by 3

  A = B +20 = 60 . . . . Abby's amount

Abby has $60; Ben has $40.

The player who goes first will win.

This is because the chocolate bar can be broken up into 6*8=48 squares, and the player who goes first can always ensure that the second player is left with one square on their turn (by breaking the bar into two pieces that leave one square for the second player to take). This means that the second player will always be the one who cannot make a break, and thus loses the game.

Therefore, The player who goes first will win.

To learn more about probability,

Visit; brainly.com/question/30034780

#SPJ4

The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

To learn more about number here:

https://brainly.com/question/32210789

#SPJ4

The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

Therefore, the missing number in the sequence is 21.

About fill in here:

https://brainly.com/question/182137

#SPJ11

Answer:

y = 1/2 x - 6

Step-by-step explanation:

y = mx + b

y = (1/2)x + b

-4 = (1/2) × 4 + b

-4 = 2 + b

b = -6

y = 1/2 x - 6

The answer is:

\(\rm{y=\dfrac{1}{2} x-6}\)

Work/explanation:

Given the slope and a point on the line, we can write the equation in point slope form, which is:

\(\rm{y-y_1=m(x-x_1)}\)

Where m is the slope and (x₁, y₁).

Plug the data in the formula:

\(\rm{y-(-4)=\dfrac{1}{2}(x-4)}\)

Simplify:

\(\rm{y+4=\dfrac{1}{2} (x-4)}\)

Now focus on the right side & simplify it :

\(\rm{y+4=\dfrac{1}{2}x-2}\)

Finally, subtract 4 on each side:

\(\rm{y=\dfrac{1}{2} x-2-4}\)

Simplify:

\(\rm{y=\dfrac{1}{2} x-6}\)

This is our equation in slope intercept form.

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

Step-by-step explanation:

The following system answer is no solution. Change one number to make the system an infinite solution and explain why it is now an infinite solution.

12y = 17 - 9x

-4y - 3x = 31

Based on the fact that it is a multiple of 36 and that all the digits are different, the 6-digit number is 492,768.

None of the numbers are to be the same which rules out the numbers:

= 4,2,7 and 8.

The product of the missing figures is a non zero number so 0 cannot be one of the numbers either.

The remaining numbers left that could be the missing figures would be:

= 1, 3, 5, 6, 9

A common trend in all multiples of 36 is that when the last number is 8, the number before it must be an even number. 6 is the only even number there so will then be the second missing number.

This leaves us with:

= 1, 3, 5, and 9

You can then slot these numbers into the missing place and try dividing by 36 to see which is a multiple of 36. Your answer will then be 492,768.

Find out more on multiples at https://brainly.com/question/13577664.

The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

x=0

Step-by-step explanation:

6x-18=4(2x-3)-(2x+6)

We move all terms to the left:

6x-18-(4(2x-3)-(2x+6))=0

We calculate terms in parentheses: -(4(2x-3)-(2x+6)), so:

4(2x-3)-(2x+6)

We multiply parentheses

8x-(2x+6)-12

We get rid of parentheses

8x-2x-6-12

We add all the numbers together, and all the variables

6x-18

Back to the equation:

-(6x-18)

We get rid of parentheses

6x-6x+18-18=0

We add all the numbers together, and all the variables

=0

x=0/1

x=0

The information about the distance as a function of time of given by the piecewise function include :

At 0 ≤ t < 2.5 ; D(t) = 300t + 125 ;

The starting distance at 0 hours is ;

D(0) = 300(0) + 125 = 125 miles  

At t = 2 hours

D(2) = 300(2) + 125 = 600 + 125 = 725 miles

At t = 2.5 hours ; At 2.5 ≤ t ≤ 3.5

D = 880 miles (Fixed)

At t = 3 hours ; 2.5 ≤ t ≤ 2.5

D = 880 miles

At t = 6 hours ; 3.5 < t ≤ 6

D = 75(6) + 612.5 = 450 + 612.5 = 1062.5 miles

Therefore, only statements, B, D and E are correct.

Learn more about functions on

https://brainly.com/question/10439235

#SPJ1

Complete question

The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.

D(t) = StartLayout enlarged left-brace 1st Row 1st column 300 t + 125 , 2nd column 0 less-than-or-equal-to t less-than 2.5 2nd Row 1st column 880, 2nd column 2.5 less-than-or-equal-to t less-than-or-equal-to 3.5 3rd Row 1st column 75 t + 612.5, 2nd column 3.5 less-than t less-than-or-equal-to 6 EndLayout

Which times and distances are represented by the function? Select three options.

The starting distance, at 0 hours, is 300 miles.

At 2 hours, the traveler is 725 miles from home.

At 2.5 hours, the traveler is 875 miles from home.

At 3 hours, the distance is constant, at 880 miles.

The total distance from home after 6 hours is 1,062.5 miles

The value of the functions 2f + 4g is {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)} and the value of 2g/h is (1,2.5)

In particular, a function maps each element of a set (called the domain) to a unique element of another set (called the range). In this context, we'll look at two functions, f and g, and explore how we can perform arithmetic operations with them.

We can think of these pairs as points on a Cartesian plane, where the x-coordinate represents the input and the y-coordinate represents the output.

Now, let's move on to the arithmetic operations with functions. The first operation we're asked to perform is 2f + 4g. To do this, we need to apply the following steps:

Multiply each ordered pair in f by 2, and multiply each ordered pair in g by 4. This means that the inputs stay the same, but the outputs are multiplied by their respective constants.

Simplify the resulting set by removing any duplicate ordered pairs.

Let's work through this process step by step for our given functions:

Multiplying f by 2 gives us: {(-2,4), (0,6), (2,10), (-2,6)}

Multiplying g by 4 gives us: {(-8,4), (0,12), (4,20), (-4,12), (12,0)}

Taking the union of these sets gives us: {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}

Simplifying this set by removing duplicates gives us: {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}

So, 2f + 4g is the function represented by the set {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}.

For the ordered pair (1,5) in g, the corresponding ordered pair in h is (5,4). So, we can compute 2g(1)/h(5) as follows:

2g(1) = 2 * 5 = 10

h(5) = 4

2g(1)/h(5) = 10/4 = 2.5

Therefore, the ordered pair (1,2.5) is in the result set.

To know more about function here

https://brainly.com/question/28193995

#SPJ4

Simplified it would be \(\frac{11}{10}\).

The graph of the function f(x) = [[3x]] + 3 is attached in the image.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

To graph the equation f(x) = [[3x]] + 3, where [[3x]] represents the greatest integer less than or equal to 3x, you can follow these steps:

Choose a set of values for x. For example, you could choose x = -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, etc.

Substitute each value of x into the equation to find the corresponding value of f(x). For example, if x = -2, then f(-2) = [[3(-2)]] + 3 = [[-6]] + 3 = -3 + 3 = 0.

Plot each point (x, f(x)) on a coordinate plane. For example, the point (-2, 0) would be plotted at x = -2 on the horizontal axis and f(x) = 0 on the vertical axis.

Connect the points with a line to create the graph of the equation.

Note that since [[3x]] is always an integer, the function f(x) will change in steps rather than smoothly.

For example, if x goes from -1.5 to -1.4, f(x) will not change until x reaches -1, at which point f(x) will increase by 3.

Hence, the graph of the function f(x) = [[3x]] + 3 is attached in the image.

To learn more about the linear function visit:

brainly.com/question/29612131

#SPJ1

Answer:

Step-by-step explanation:

Given system:

Solving by elimination

Multiply the first equation by 3 and add up equations, then solve for y:

Find the value of x:

The answer is: (2, -1)

Answer:

To solve this problem, first we need to calculate the total annual revenue from membership fees.

That is equal to 3.5 x 105 members multiplied by the annual membership fee per person.

Then we divide the total annual revenue by the total number of members to get the annual membership fee per person.

So the equation is: 4.2 x 107 dollars / (3.5 x 105 members) = 12 dollars per person per year.

The answer in standard form is $12.

For more information:

A chain of gyms has 3.5105 members throughout the U.S.

https://brainly.com/question/30458600

The length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

To determine the angles and length of sides, we use the sine rule

Given;

a = 2. 5cm

c = 3. 6cm

∠A = 43°

Let's find angle C

\(\frac{sin 43}{2. 5} =\frac{sin C}{3. 6}\)

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = \(sin^-^1 ( 0. 982)\)

C = 79°

To find length of b

\(b = \sqrt{c^2 - a^2}\)

substitute the values

b = \(\sqrt{3. 6^2 - 2. 5^2}\)

b = 2. 59 cm

b = 3cm

To find angle B, we have

\(\frac{sin 43}{2. 5} = \frac{sinB}{3}\)

cross multiply

0. 682 × 3= sin B × 2. 5

sin B = 0. 7065

B = \(sin^-^1(0. 7065)\)

B = 45°

Hence, the length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

Learn more about sine rule here:

https://brainly.com/question/12827625

#SPJ1

We have the next function

And we must find f(-2) and f(0.3)

To find f(-2) and f(0.3) we need to know that

We can see that we have a constant function because it has the next form

That means, for any value of x the function will always be equal to 4.

Using that, we obtain

ANSWER:

f(-2) = 4

f(0.3) = 4

The length of time the ball was in the air is 4 seconds.

To find the maximum height of the ball and the time at which it reaches this height, we need to first determine the vertex of the parabolic function h(t) = -16t² + 48t + 64.

The vertex of the parabola is given by the formula:

t = -b / (2a)

where a = -16 and b = 48 are the coefficients of the quadratic function. Substituting these values, we get:

t = -48 / (2(-16)) = 1.5

So the time at which the ball reaches its maximum height is t = 1.5 seconds. To find the maximum height, we substitute this value back into the function:

h(1.5) = -16(1.5)² + 48(1.5) + 64 = 112

Therefore, the maximum height of the ball is 112 feet, and this occurs at t = 1.5 seconds.

To find the length of time the ball was in the air, we need to find the times at which the ball hits the ground. The ball hits the ground when its height is zero, so we need to solve the equation h(t) = 0 for t:

-16t² + 48t + 64 = 0

Dividing by -16, we get:

t² - 3t - 4 = 0

Factoring, we get:

(t - 4)(t + 1) = 0

Therefore, the ball hits the ground at t = 4 seconds and t = -1 second. Since time cannot be negative,

we only consider the positive root t = 4. So the ball is in the air for the time between t = 0 and t = 4 seconds.

Learn more about function here:

https://brainly.com/question/29633660

#SPJ1

Answer: x = -1

Step-by-step explanation:

6x-2x+8 = x+5

4x+8 = x+5

3x = -3

x = -1

Answer:

4x + 8 = x + 5

4x - x = 5 - 8

3x = -3

x = -3/3

x = -1

Answer:

125 women

Step-by-step explanation:

Answer: 75 women

Step-by-step explanation:

4/5

60/4=15

15x5= 75

For the linear equation (x/y) ÷ (3a/b) = 3a/b to be true, x must equal 9a² × y/b² if a does not equal 0, b does not equal 0 and y does not equal 0.

To determine what must be true of x/y ÷ 3a/b = 3a/b, we can follow the order of operations, which is to perform the division before the multiplication.

First, we can simplify the left side of the equation by dividing x/y by 3a/b, which is equivalent to multiplying x/y by b/3a.

This gives us x / (y × (3a/b)) = 3a/b.

We can simplify further by multiplying both sides of the equation by y*(3a/b), which eliminates the denominators.

This gives us x = 3a × (y/b) × (3a/b).

Simplifying further, we get x = 9a² × y/b².

Learn more about linear equations at

https://brainly.com/question/11897796

#SPJ4

Answer:

1) f(-2) = -2 + 3

2) f(-2) = 1

Answer:

a. \(\frac{x+2}{x+6}\)

Step-by-step explanation:

\(\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}\)

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Learn more about parallelogram at: https://brainly.com/question/10744696

#SPJ1

Step-by-step explanation:

It is given that,

Speed of Anna is x miles/hour

Speed of Sara is 10 mi/h

We need to find an expression that represents the average of Anna's and Sara's speeds. Average of two objects is given by :

\(v=\dfrac{v_1+v_2}{2}\)

ATQ,

\(v=\dfrac{x+10}{2}\)

The above expression represents the average speed of Anna and Sara.