Geri ran in a marathon race. It took her 3 hours and 28 minutes to run 26 miles. How many minutes did it take her to run 1 mile if she ran at the same rate for the whole race? (1 hour = 60 minutes)

The answer is F(t)=30-5t

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The temperature at the North Pole is 30°F and is expected to drop 5°F per hour for the next several hours.

let the time in hours be t and F(t) be the temperature after t hours then we have the following equation:

F(t)=30-5t

Hence, The answer is F(t)=30-5t

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Answer: So, to find velocity we take the first derivative of the equation.

just in case you do not know how to take a derivative or a polynomial

the derivative of axn  = naxn-1  where a is a coefficient and n is the exponent.

s' = 3t2 - 24t +36 this is your velocity in time t.

to solve for your velocity at t = 3 seconds we will plug 3 seconds into any t in the velocity equation.

s' = v this is just stating that s' is equal to your velocity

v = 3(3)2 - 24(3) + 36

v = 27 - 72 + 36

v = -9 m/s

to find when the particle is at rest we must consider the at rest velocity which is 0. An object at rest has no velocity(only applies to Newtonian mechanics)

so, we will change v to 0 and solve for t

0 = 3t2 - 24t + 36

to solve this we need to factor to quadratic equation.

to solve this we first will factor out 3 from the equation.

0 = 3(t2 - 8t + 12)

now we can factor. we need two numbers that when multiplied together give 12 but when added give -8. since the addition is negative and the multiplication is positive we know that we are dealing with two negative integers.

we end up with

0 = (t-2)(t-6)   the three was divided on both sides to eliminate it from the equation.

so, the particle is at 0 at t = 2 seconds and t = 6 seconds.

Now, just because the particle has 0 velocity does not mean it has no acceleration. However, I do not believe the acceleration is important for this problem.

To find when the particle is moving forward you must consider again when it is at 0. When it is at 0 a speed change is happening. So, to find out if velocity is positive or negative we will test a number before 2 after 2 but before 6 and after 6.

So, we can start with t = 0 for the before 2 number

v = 3(0) - 24(0) + 36

we get v = 36 which is positive. So, the particle was moving forward before 2 seconds.

now we have already used 3 seconds and we got a negative velocity. So, the particle is moving backwards at t = 3 seconds.

So the last one to check is after 6 seconds. We will choose 10 for this one because it is easy to multiply with.

v = 300 - 120 + 36 = a positive number. You do not actually need to know what number as long as you know it is positive. That means the particle was moving forward after 6 seconds.

to find the total distance traveled we must break up the distance equation by direction of travel. So, we must take the distance traveled by the particle in pieces using the original equation.

s = t3 -12t2 + 36t

first we will solve for the distance traveled in 2 seconds.

s = 8 - 48 + 72 = 32 meters

Now we will solve for 6 seconds and figure out the distance traveled from 32 meters in the opposite direction. Then we will add the two numbers together.

s =216 - 432 + 192 = -24 meters

To find the distance travelled between 2 and 6 seconds we add the absolute value of the values together.

We end up with distance traveled between 2 and 6 seconds was

56 meters

we then add this to the original 24 meters to get the distance traveled from 0 to 6 seconds of

88 meters

then we solve for the distance at 8 seconds

s = 512 - 768 + 288 = 32 meters

so, again we add the absolute values of the previous time interval with the one we just calculated for.

24 + 32 = 56 meters. So, the particle traveled back up at this point.

We add the new 56 with the current total of 88 meters to get

total distance traveled  = 144 meters

this shows us that the particle is moving in a wave pattern from 0 to 8 seconds. So, if you were to draw a graph you would have a particle start at s = 0 and t = 0, then the particle would move much like the graph of sine instead of stopping at 1 it would stop at s = 32 then drop down to s = -24 and rise up continuously after that.

Step-by-step explanation:

( 3x+8 ) ( 7x-2 )

= 21x² + 56x - 6x -16

= 21x² + 50x -16

HOPE IT HELPS :)

Answer:

1 1/2 or 1.5

As a simplified fraction

If this helped pls give brainlest.

Answer:

Miles or mi

Step-by-step explanation:

This is because measuring the distance from one street corner to the next requires miles. Yards would be too less and would be less convenient.

There is a possibility of converting miles to yards as well.

You just have to multiply the miles by 1760 to get the right units.

Answer:

[tex]x^2[/tex] + 9x + 8 = 0

Step-by-step explanation:

First, we have to simplify this quadratic equation:

(x+2)^2 + 5(x+2) - 6 = 0

x^2 + 4x + 4 + 5x + 10 - 6 = 0

x^2 + 9x + 8 = 0

Answer:

Yes, Chen is correct.

Step-by-step explanation:

Chen has 1/4 chance of getting a 4, whereas Megan has 1/5 chance of getting a 4.

1/4 = 0.25

1/5 = 0.20

Therefore, Chen is correct.

Answer:

It's 96

Step-by-step explanation:

-The left and right rectangles
5*4=20

(5*4)*2=40


-Triangle (front and back)
8*3/2=12

(8*3)/2*2=24


-Bottom Triangle (base)

8*4=32


-Area
=40+24+32
=96

Answer: 96 in^2

Step-by-step explanation: I took the quiz and got it right!! Hope this helps you, have a beautiful day!! :)

Step-by-step explanation:

(sinx/cosx - cosx/sinx) + sinxcosx

sin²x - cos²x = 1

I can't prove

I only know sin²x + cos²x = 1 : )

Answer:

Rational & integer

Step-by-step explanation:

Rational numbers are terminating. -7 is terminating.

All integers are rational numbers. Integers do not have decimals.

This is not whole because it is negative.

This is not irrational because... it's rational!

it is a rational and integer Hopefully you pass this assignment

Answer:

can you post the question I don't understand

Answer:

In geometry, the area of a two dimensional object is the amount of space an area takes up. A square unit is a square with sides of length one unit.

The new monthly salary will be $1,457.50.

You received a monthly salary of $1,375.00

Now by economy expansion, causing wages to increase by = 6%

Increment of the salary = 6% of 1,375.00

[tex]= \frac{6}{100} \times 1,375[/tex]

[tex]= 0.06 \times 1,375 =\$82.50[/tex]

Monthly Salary means Employee's monthly salary, before deductions.

Therefore our new monthly salary would be

[tex]= $1,375.00 + $82.50\\ = $1,457.50[/tex]

Therefore our new monthly salary will be $1457.50.

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Answer:

sample size is the number of individuals in the sample and the sample is 60 guests.

Step-by-step explanation:

She wants to find out the food preferences for the guests, so she surveys 60 guests and discover 45 of those guests prefer chicken and 15 prefer fish.

The sample is 60 guests.

Answer:

slope = [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, - 4) and (x₂, y₂ ) = (- 2, 4) ← 2 points on the line

m = [tex]\frac{4-(-4)}{-2-(-5)}[/tex] = [tex]\frac{4+4}{-2+5}[/tex] = [tex]\frac{8}{3}[/tex]

Answer:

Ted has 10 books and Omar has 15 books

Step-by-step explanation:

Hey there!

In order to find how many books each of the boys have, we can make a system of equations

First equation: O+T=25

Second equation: O=2T-5

After making the equations, you can use substitution by plugging in 2T-5 For O in the first equation:

2T-5+T=25

Simplify LHS

3T-5=25

Take 5 to the other side

3T=30

Divide by 3 on both sides to get T by itself

T=10

So this means that Ted has 10 books

Now we can plug this into the second equation

*note that you can plug 10 into the first equation too*

O=2(10)-5

Simplify RHS

O=20-5

Combine like terms

O=15

This means that Omar has 15 books

So, Ted has 10 books and Omar has 15 books

Answer:

x = 155°

Step-by-step explanation:

This is called a vertically opposite angle.

Answer:

as a percentage it is: 0.25 x 0.2 =0.05 or 5%
but as a common fraction it is: 5/100 or 1/20

Step-by-step explanation:

Let x be the cost of a box of apples and y be the cost of a box of oranges.

Danielle : 3x + 2y = 44.5

Esther: 5x + 4y = 81.5

3x + 2y = 44.5 --- 1

5x + 4y = 81.5 --- 2

6x + 4y = 89 --- 3

From 2 and 3, we have:

x = 7.5

Subsitute x = 7.5 into 1

3(7.5) + 2y = 44.5

2y = 22

y = 11

Therefore, a box of oranges costs 11 dollars

The equation C -7 - 3/4 = 0 is an algebraic equation

To solve the equation we (a) add 7 and 3/4 to both sides of the equation

The equation is given as:

C -7 - 3/4 = 0

Make C the subject of formula by adding 7 and 3/4 to both sides of equation

C = 7 + 3/4

Now, we can solve for C

Hence, to solve the equation we (a) add 7 and 3/4 to both sides of the equation

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Answer:

Answer D is correct

Step-by-step explanation:

Let us solve this now.

58

× 100

      000

      00

+   58

= 5800

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

Let us solve this sum in a different way.

If there's a number to multiply by 100 you can simply put 2 zeros to the other number like this.

58 × 100 = 5800

The total monthly salary earned by Ram in the month of April 2022 is an amount of 30000 AED before payments and donations.

Word problems are statements that embody a set of algebraic expressions that offers at least one solution. In this case, we have to read the statement, find the equivalent formula and solve for the resulting variable.

After a careful reading, the statement is equivalent to the following formula:

x = x / 3 + x / 4 + x / 20 + x / 10 + 5000 + 3000

4 · x / 15 = 8000    (1)

Where x is Ram's monthly salary.

The solution of (1) is x = 30000.

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Answer:

2 & 13

Step-by-step explanation:

The square of 2 plus the prime number 13 add up to 17

[tex]2^{2}+13=4+13 =17[/tex]

Hope this helps

Answer:

Square number = 4

Primer number = 13

Step-by-step explanation:

A square number is the result when a number has been multiplied by itself.

A prime number is a whole number greater than 1 that only has two factors, itself and 1.

List all the square numbers and prime numbers below 17:

Square numbers: 1, 4, 9, 16, ...

Prime numbers: 2, 3, 5, 7, 11, 13, ...

Therefore, the only combination of square number and prime number that sums to 17 is:  4 + 13 = 17

Solution

Square number = 4

Primer number = 13

Answer:

2nd and 4th option

Step-by-step explanation:

The equivalent expression is,

⇒ 4 (5 - 2d)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 20 - 8d

Now, We can simplify the expression as;

⇒ 20 - 8d

⇒ 4 x 5 - 4 x 2d

⇒ 4 (5 - 2d)

Thus, The equivalent expression is,

⇒ 4 (5 - 2d)

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Answer:

Below in bold.

Step-by-step explanation:

tan 150 = -tan 30

= -1/√3 = y/x    (1)

This is a unit circle so the hypotenuse = 1.

so sin 150 = y/1 = y

y = 1/2

So substituting in equation (1)

1/2 / x =  -1/√3

-x = √3/2

x = -√3/2.

The value of x in the unit circle is -√3/2.

Option B is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

Since the angle is 150 degrees, we know that it is in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.

Since the circle has a radius of 1, the y-coordinate is sin(150) = 1/2.

To find the x-coordinate, we can use the formula x = cos(θ), where θ is the angle in radians.

To convert 150 degrees to radians, we multiply by π/180:

150 degrees x π/180 = 5π/6 radians

So,

x = cos(5π/6) = -√3/2.

Therefore,

The value of x is -√3/2.

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Answer:

END OF EACH YEAR

-1 442.395

-2 449.91

-3 457.56

-4 465.34

-5 473.25

-6 481.29

-7 489.481

-8 497.80

-9 506.26

-10 514.87

however, how much INTEREST

514.87-435=

79.8

Answer:

x = 10^4 =  10000

Step-by-step explanation:

log(x) = 4

x = 10^4