Dan is training for a bike race. He wants to bike 300 miles over the next couples of weeks. Dan biked 29 miles a day for 3 days. Then, he biked 32 miles a day for 4 days. How many more miles does he still have to bike to get to his goal of 300 miles?


A. Sara estimated that Dan would need to bike about 80 more miles to get to his goal of 300 miles. Is this a reasonable estimate? Why or why not?

B. Write an equation for this problem with a letter standing for the unknown quantity.

C. Solve the problem. Show your work.

Answer: decrease in the GDP by 2.5%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A:

Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:

y = velocity of the runner in km/h

x = time in hours

The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:

y - 5 = -2/3(x - 1)

Simplifying this equation, we get:

3y - 15 = -2x + 2

Rearranging to standard form, we get:

2x + 3y = 17

So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.

Part B:

To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.

Here are the values of y for different values of x:

x = 0, y = 17/3

x = 1, y = 5

x = 2, y = 13/3

x = 3, y = 3

x = 4, y = 7/3

x = 5, y = 1

Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:

|

6.0 -| .

| .

5.5 -| .

| .

5.0 -| .

|.

4.5 -|

|

4.0 -| .

| .

3.5 -| .

| .

3.0 -| .

|.

2.5 -|

|

2.0 -| .

| .

1.5 -| .

| .

1.0 -|.

|

0.5 -|

|

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

0 1 2 3 4 5

The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.

Answer: CLICK THANKS IF YOU LIKE MY ANSWER. HAVE A GOOD DAY SIR/MAAM #KEEPSAFE

Part A:

Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:

v = 5 when t = 1

v = 3 when t = 3

To find the equation in standard form, we can first use point-slope form:

v - 5 = m(t - 1) (using the point (1, 5))

v - 3 = m(t - 3) (using the point (3, 3))

Simplifying both equations:

v - 5 = m(t - 1)

v - 3 = m(t - 3)

v = mt + (5 - m)

v = mt + (3m - 3)

Setting the right-hand sides equal to each other:

mt + (5 - m) = mt + (3m - 3)

Simplifying and rearranging:

-m = -2

m = 2

Substituting m = 2 into one of the equations above:

v = 2t + 3

This is the equation in two variables in standard form that describes the velocity of the runner at different times.

Part B:

To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:

When t = 0, v = 3, so the point (0, 3) is on the line.

When t = 1, v = 5, so the point (1, 5) is on the line.

When t = 2, v = 7, so the point (2, 7) is on the line.

When t = 3, v = 9, so the point (3, 9) is on the line.

When t = 4, v = 11, so the point (4, 11) is on the line.

When t = 5, v = 13, so the point (5, 13) is on the line.

Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:

    |

 15 +-------*

    |       |

 13 +           *

    |           |

 11 +               *

    |               |

  9 +                   *

    |                   |

  7 +                       *

    |                       |

  5 +                           *

    |                           |

  3 +---------------*-----------*

    0   1   2   3   4   5   6   7

The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.

Step-by-step explanation:

Answer: LN = 15

Make a proportional relationship:

[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]

Insert the values:

[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]

cross multiply:

[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]

Simplify:

Answer:

Below

Step-by-step explanation:

Pick two convenient integer coordinate sets on the line

 like 0,0 and 10,4

find slope, m  = ( y1-y2) / (x1-x) = ( 4-0) / ( 10-0) =  4/10  = 2/5

b = y axis intercept = 0

Slope - intercept equation of a line is of the form : y = mx + b

  substitute in the m and b values found above to get

     y = 2/5 x + 0

or just   y = 2/5 x

Answer:

The formula for the population P, of the town as a function of year t, if the population increases by 60 people per year, is:

P(t) = 1900 + 60t

where t is the number of years elapsed since t=0.

The formula for the population P, of the town as a function of year t is

P = 1900 + 60t

We have,

If the population increases by 60 people per year, then we can use the following formula to find the population P as a function of time t (in years):

P = 1900 + 60t

Here, the initial population at t=0 is 1900 people, and the population increases by 60 people per year,

So we add 60t to the initial population to get the population at time t.

For example,

If we want to find the population after 5 years, we can substitute t=5 into the formula:

P = 1900 + 60(5) = 2200

So the population after 5 years would be 2200 people.

Thus,

The formula for the population P, of the town as a function of year t is

P = 1900 + 60t

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The value οf the variable y is 9 when k is -3 in the given question.

In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.

A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.

A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.

Given: y=k x

where, x= -3 and k= -3

we can find the value of y by multiplying k with x,

so, y=k x

now, putting values as follows:

we get, y = -3 × -3

               = 9

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Answer:

Step-by-step explanation:

Answer:

siuuuuuuuuuuuuuuuuuuuuuuuuuu

The area of the sector formed by angle DFE is approximately 3.29 square feet.

What is area of the sector?

To find the area of a sector of a circle, we need to know the central angle that defines the sector and the radius of the circle. We can then use the formula:

Area of sector = (central angle / 360 degrees) x π x (radius)²

In this case, we are given that the radius of the circle is 4 feet and the central angle that defines the sector is 75 degrees. Therefore, the area of the sector can be calculated as:

Area of sector = (75 / 360) x π x (4)²

= (0.2083) x π x 16

= 3.29 square feet (rounded to the nearest hundredth)

Therefore, the area of the sector formed by angle DFE is approximately 3.29 square feet.

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The fraction of learners who do not cycle to school is equal to 9/10.

Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;

40 - [12 +2(12)] = 4

The number of learners who do not cycle to school is;

12 + 2(12) = 36

fraction of learners who do not cycle to school = 36/40

by simplification;

fraction of learners who do not cycle to school = 9/10.

Therefore, the fraction of learners who do not cycle to school is equal to 9/10.

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Answer:

3/10 = 0.3

19/50 = 0.38

5/10 = 0.5

1/5 = 0.2

14/25 = 0.56

3/25 = 0.12

Answer:

1st one.-sin(X)+5e^5x

Answer: 11/9 or 1 2/9 or 11 over 9

Step-by-step explanation:

Firstly, you need to know what a fraction is.

A fraction is a segment (part of) a whole. To express a fraction, you write the numerator over the denominator. A numerator is the top part of the fraction, and it shows how much it is out of. The denominator shows how much it is out of.

Example: [tex]\frac{1}{3}[/tex]

That means it is 1 part out of 3 parts

Now you know what a fraction is, now let's add them.

Next, convert the word form into the number form:

2 over 3 is 2/3

plus is +

5 over 9 =is 5/9

Combine them:

2/3 + 5/9

Steps of the problem:

Firstly, you have to find the L.C.M (Lowest Common Multiple) of 3 and 9 because to add fractions, you need a common (same) denominator.

9 is the L.C.M of 3 and 9, as 9x1 = 9 and 3x3 = 9.

Mulitiply the numerator and denominator by 3:

2x3/3x3 = 6/9

Now, the equation is 6/9+5/9.

Add the numerators:

11/9

The answer is 11/9

If the question tells you to convert into a mixed number, then here's the following steps:

You have to find the highest number 11 goes into 9

It's 1.

Take the remainder (2) into the fraction:

2/9

Now, add 1 in front of it:

1 2/9

As a decimal, it is 1.2222222 (recurring).

If that helped you, please make me Brainliest!

Answer:

11 over 9 [tex](\frac{11}{9})[/tex]

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for [tex]\frac{2}{3} +\frac{5}{9}[/tex], we need to first convert these fractions so that they share a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

If a common denominator just refers to 2 fractions having the same denominator, we can simply multiply the numerator and denominator of the fraction [tex]\frac{2}{3}[/tex] by a number. To solve for that number, we can divide 9 by 3.

Now that we know that the number is 3, multiply both by 3.

Now the fraction looks like this: [tex]\frac{6}{9}[/tex].

We can now change the expression to this:

When adding fractions with the same denominator, we can just add the 2 numerators and keep the common denominator the same.

Now just insert 11 in as the numerator:

Therefore 2 over 5 plus 5 over 9 is 11 over 9.

Answer:

1/4

Step-by-step explanation:

First, Pick a point

A (-4, 8) → A' (-1, 2)

We see that to get from A to A' we time 1/4

So, the scale of dilation is 1/4

Answer:

21 feet by 15 feet

hope this helps

Answer:0.25

Step-by-step explanation:

[tex]f(-x)[/tex] is not equal to f(x), the function [tex]f(x) = 5x^3 + x[/tex] is neither even nor odd.

If a function meets the requirements for both odd and even, then the answer is yes. The function is both even and odd if  [tex]f(-x) = f(x)[/tex] and [tex]f(-x) = -f(x)[/tex] for every x in the domain of f.

These functions are known as the zero function or identically zero function because they imply that f(x) = 0 for all x in the domain of f.

The given function is [tex]f(x) = 5x³ + x.[/tex]

To know that a function f(x) is even if f(-x) = f(x) for all x in the domain of f.

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f.

Thus,

[tex]f(-x) = 5(-x)³ + (-x) = -5x³ - x[/tex]

[tex]f(x) = 5x³ + x[/tex]

Comparing f(-x) with f(x), we get:

[tex]f(-x) = -5x³ - x[/tex]

[tex]f(x) = 5x³ + x[/tex]

Since f(-x) is not equal to f(x), the function f(x) = 5x^3 + x is neither even nor odd.

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Answer:

Step-by-step explanation:

Let the amount invested by A, B, and C be denoted by a, b, and c respectively.

From the given information,

a + b + c = 60000 ---(1)

a + c = 2b ---(2)

a + b = 3c ---(3)

Multiplying equation (2) by 3 and equation (3) by 2, we get:

3a + 3c = 6b

2a + 2b = 6c

Adding these two equations, we get:

5a + 5b + 5c = 0

a + b + c = 0

This is not possible as the sum of the investments cannot be zero. Therefore, there must be an error in the problem statement.

Without further information or correction, it is not possible to find the share of B in the profit.

Step-by-step explanation:

given quadratic equation is

simplification,

by using,

[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0

\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\

[/tex]

[tex]square[/tex]

[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]

[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]

For the first equation, we can complete the square to find its vertex form. Here's how we do it:

0 = x^2 - 18x + 1

0 = (x - 9)^2 - 80

So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.

For the second equation, we can complete the square in a similar way:

x^2 + 26x + 167.5 = 0

x^2 + 26x = -167.5

x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2

(x + 13)^2 = 9.25

So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.

I hope that helps!

Answer:

subtract 20; 80, 60, 40

The pattern is to subtract 20 from the previous term.

Next three terms: 20, 0, -20.

Therefore, the sequence continues as follows:

80, 60, 40, 20, 0, -20.

Answer:

Veronica is correct

Step-by-step explanation:

On Monday, Veronica earns 3 walks * $5.25 per walk = $15.75.

On Tuesday, Veronica earns 2 walks * $5.25 per walk = $10.50.

So far, Veronica has earned a total of $15.75 + $10.50 = $26.25.

To reach her goal of $86, Veronica needs to earn an additional $86 - $26.25 = $59.75.

Since Veronica earns $5.25 per walk, she needs to complete $59.75 ÷ $5.25 per walk = 11.38 walks.

Since Veronica cannot complete a fraction of a walk, she will need to complete 12 more walks (rounded up from 11.38) by the end of the week.

Answer:

The function g(x) = (x + 2)³ − 6 is obtained by applying three transformations to the parent function f(x) = x³.

First, g(x) is shifted 2 units to the left by subtracting 2 from x inside the parentheses:

g(x) = (x + 2 - 2)³ − 6 = (x)³ − 6

This shows that option C, "g(x) is shifted 2 units to the left and 6 units down," is not correct.

Next, g(x) is shifted 6 units down by subtracting 6 from the entire function:

g(x) = (x + 2)³ − 6 - 6 = (x + 2)³ - 12

This shows that option A, "g(x) is shifted 2 units to the right and 6 units down," is correct.

Finally, g(x) is not shifted left or right by any additional units, but it is shifted 2 units up by adding 2 to the constant term:

g(x) = (x + 2)³ − 6 + 2 = (x + 2)³ - 4

This shows that option B, "g(x) is shifted 6 units to the right and 2 units up," is not correct.

Therefore, the correct answer is option A: g(x) is shifted 2 units to the right and 6 units down.

Answer:

7, 12, 17 which is the second choice

Step-by-step explanation:

The given sequence is expressed by the equation

[tex]a_n = 7 + (n - 1)5\\\\(n - 1)5 = 5n - 5\\\\a_n = 7 + (n - 1)5= 7 + 5n - 5\\\\= 2 + 5n\\\\a_n = 5 + 2n\\\\a_1 = 2 + 5(1) = 2 + 5 = 7\\\\a_2 = 2 + 5(2) = 2 + 10 = 12\\\\a_3 = 2 + 5(3) = 2 + 15 = 17\\\\[/tex]

So the first three terms are
7, 12, 17 which is the second choice

a.The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I.

b.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.

c.The lowest price of books that Lizzy will substitute for Milo is $6.

A budget line is a graphical representation of all possible combinations of two goods that can be purchased with a limited amount of income or resources. It shows the various combinations of two goods that a consumer can afford to buy with a given income and the prices of the two goods.

In the given question,

a. The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I

where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.

Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.

b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:

4M + 8B = I - 20(20)S - 20(40)J

B = (1/2)I - 40S - 40J - 2M

c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:

4M + P(2/3)B + 20(20)S + 20(40)J = I

To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:

4 = (2/3)P

P = (3/2) * 4

P = 6

Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.

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A.The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I.

B.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.

C.The lowest price of books that Lizzy will substitute for Milo is $6.

What is budget line?

A budget line is a graphical representation of the limits of a consumer's purchasing power, given their income and the prices of goods and services. It shows all the possible combinations of two goods that a consumer can purchase with a given income, while spending all of their available resources.

a. The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I

where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.

Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.

b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:

4M + 8B = I - 20(20)S - 20(40)J

B = (1/2)I - 40S - 40J - 2M

This equation shows that the maximum number of books that Lizzy can buy depends on her income (I), the prices of shoes (S) and jeans (J), and the number of tins of Milo (M) she buys. The slope of the budget line is -4, which means that for every 1 unit increase in the number of books, Lizzy has to give up 4 units of Milo.

To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph, where the x-axis represents the number of tins of Milo (M) and the y-axis represents the number of books (B). Then, we can draw a straight line connecting these points to represent Lizzy's budget line.

c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:

4M + P(2/3)B + 20(20)S + 20(40)J = I

To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:

4 = (2/3)P

P = (3/2) * 4

P = 6

Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.

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Answer:

1. 57/16 or 3.5625 ounces of water

8 : 4.75

1 : 19/32  -----> divide both by 8

19/32x6=57/16 = 3.56 ounces

2. 2.4375 ounces of other ingredients

6-3.5625=2.4375

Answer:

28 units

Step-by-step explanation:

The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.

Substituting l = 9 and w = 5, we get:

P = 2(9 + 5) = 2(14) = 28

Therefore, the perimeter of the rectangle is 28 units.

Answer:

Step-by-step explanation:

Let x be the original price of the television set.

The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.

So we can write an equation based on this information:

0.72x = 435.60

Solving for x, we get:

x = 435.60 / 0.72

x ≈ $605

Therefore, the original price of the television set was approximately $605.