Derrick and Mark are brothers who live in the same house. Mark is home, and Derrick is 5 mi from home. Both boys begin riding their bikes at the same time. Derrick rides directly home at a constant rate of 15 mph, and Mark rides away from home at a constant rate of 18 mph. Let d represent distance from home, and let t represent time in hours. Which system models this situation? A. d = 5 − 15t d = 18t B. d = 15 − 5t d = 18t C. d = 5 + 15t d = 18t D. d = 5 − 15t d = 5 + 18t

Answer:

Step-by-step explanation:

Given:

Length (l) = 12 cm

Width (w) = 4 cm

Perimeter of the rectangle = 2(l + w) units

P = 2(12 + 4)

P = 2 (16)

P = 32

Answer:

1/2 of his book

Step-by-step explanation:

1/3 of an hour = 1/6 of the book

3/3 of an hour = 3/6 or 1/2 of the book read

Answer:

y=1/2x+15

y=x/2+15

Step-by-step explanation:

Every y-value is the sum of one-half of x and 15.

y = 1/2 x+15

We can rewrite this as

x/2 +15

Answer:

The height of the Mantis is 145 feet

Step-by-step explanation:

There is a table with the roller coasters' heights at Cedar Point amusement park in the assignment that is missing from the post.

Looking up the info online, the Millennium Force is 310 feet tall.

The Mantis is 165 feet shorter than the Millennium Force.

So the height of the Mantis is 310 - 165 = 145 feet

To find the height of the Mantis roller coaster, subtract 165 feet from the height of the Millennium Force roller coaster.

The problem states that the Mantis is 165 feet shorter than the Millennium Force. To find the height of the Mantis, we need to subtract 165 feet from the height of the Millennium Force.

If we let x represent the height of the Millennium Force, then the height of the Mantis would be x - 165 feet.

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See the attachment for graphs.

The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).

You can get there a couple of ways:

Answer:

The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).

You can get there a couple of ways:

Replacing y by y-k shifts the graph up by k units. Here, k=-4, so the graph is shifted down 4 units.

Adding k to the function value shifts the graph vertically by k units. The equation y+4 = |x| can be rewritten to y = |x| -4, showing that -4 is added to the function value.

Step-by-step explanation:

Answer:

72.25 in^2

Step-by-step explanation:

Formula

Area = s^2 where s is the length of a side.

Given

s = 8.5 in

Solution

Area = s^2

Area = 8.5^2 = 8.5 * 8.5

Area = 72.25 in^2

1.50

Let h and f represent the cost of 1 hamburger and 1 order of fries, respectively. Then you can write two equations for the cost of the orders.

... 5h +3f = 9.90

... 3h +5f = 8.50

Using Cramer's rule, the cost of a hamburger can be found to be ...

... h = (3·8.50 -5·9.90)/(3·3 -5·5) = (25.50 -49.50)/(9 -25)

... = -24/-16

... h = 1.50

The cost of one hamburger is 1.50.

_____

Formulation of Cramer's Rule

For equations ...

... ax +by = c

... dx +ey = f

The rule tells you ...

... x = (bf -ec)/(bd -ea)

... y = (cd -fa)/(bd -ea)

_____

Note that we have chosen this method of solution because we only needed the value of one of the variables. It is effectively the same as substitution (or elimination), but does all the steps in one formula.

Using the matrix solution methods on a calculator is another fast way to solve a pair of equations like this.

Answer:

at least 43 1/4 minutes (or 44 rounded)

Step-by-step explanation:

I set up an equation:

175+6x=10x

Isolate x:

175=4x

x=43.25

is this a college question? (just curious)

The absolute value function that represents the parent function f(x) = |x| reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.

The absolute value function that represents the parent function f(x) = |x|, reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.

Reflecting over the x-axis involves multiplying the function by -1 to get -|x|. Translating 1 unit to the right involves substituting (x-1) for x within the absolute value to get -|x-1|.

Therefore, the transformation involves two steps:

The average rate of change of the function  (x) = (−2)x + 3 from x = 0 to x = 9 is calculated as  (9) -  (0) divided by 9 - 0, resulting in −2.

The average rate of change of a function over a given interval is calculated as the change in the function's value (((9)) -  (0)) divided by the change in the interval's value (9 - 0). For the function  (x) = (−2)x + 3, to find the average rate of change from x = 0 to x = 9, we must first evaluate the function at these points:

Now, subtract the value of the function at x = 0 from the value at x = 9 and divide by the change in x (9 - 0):

Average Rate of Change =  rac{(9) -  (0)}{9 - 0} =  rac{−15 - 3}{9} =  rac{−18}{9} = −2

Therefore, the average rate of change of the function over the interval from x = 0 to x = 9 is −2.

96,767,921

5 - 7 + 2 - 6 ÷ 2 + 24^3 * 7000 - 76 = 96,767,921

Exponentiation is performed first, followed by multiplication and division in their order of appearance.

= 5 - 7 + 2 - 6 ÷ 2 + 13,824 · 7000 -76

= 5 - 7 + 2 - 3 + 96,768,000 -76

Then addition and subtraction are peformed in the order of appearance. (The commutative and associative laws apply.)

= (5 -7 +2) +96,768,000 -3 -76

= 96,767,921

_____

A Google or Bing search box will evaluate an arithmetic expression strictly according to the order of operations. Your result is attached. The preferred symbols are * (asterisk) for "times" and / (slash) for "divided by". The usual ^ (caret) is used for "to the power of." If you intend grouping, parentheses are required.

Substituting the given expressions for bore and stroke and 8 cylinders, you have ...

... D = π((k/2)/2)^2 · h · 8

... D = (π/2)hk^2 . . . . simplified expression for 8 cylinders

_____

For bore = 4 in, stroke = 3.4 in, n = 4, the displacement is ...

... D = π(4 in/2)^2 · (3.4 in) · 4 = 54.4π in^3

... D ≈ 170.9 in^3

Answer:

[tex]85.4[/tex] cubic inch

Step-by-step explanation:

Given-

Displacement = [tex]\pi (\frac{bore}{2} )^2 * stroke * n[/tex]

Now,

bore is represented as [tex]\frac{k}{2}[/tex]

and stroke is represented as [tex]h[/tex]

and number of cylindres "n"[tex]= 8[/tex]

Substituting these values in above equation, we get -

Displacement [tex]= \pi (\frac{\frac{k}{2} }{2})^2*h*8\\= \pi \frac{k^2}{16} * h* 8\\= \frac{\pi* k^2*h}{2}[/tex]

Now substituting the given values, in above equation we get -

Displacement [tex]= \frac{\pi* 4^2*3.4 }{2}\\= \frac{\3.14* 16*3.4 }{2} \\ = 85.408\\= 85.41= 85.4[/tex]cubic inch

Answer:

D. 13

Step-by-step explanation:

Multiply the given equation by 39x/27:

... x = 9·39/27 = 39/3

... x = 13

______

The usual approach

You may have learned to "cross multiply" to eliminate fractions. That means you multiply by the product of the denominators, 39x:

... 9·39 = 27x

Now, you divide by the coefficient of x, which is 27.

... 9/27 · 39 = x = 39/3 = 13 . . . . . . in the end, the same as above

To find the unknown value in the given proportion, we can cross-multiply and solve for the variable.

To find the unknown value in the proportion 9/x = 27/39, we can cross-multiply. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and multiplying the denominator of the first fraction with the numerator of the second fraction. So, we have 9 * 39 = 27 * x.

Now, we can solve for x by dividing both sides of the equation by 27. So, x = (9 * 39) / 27. Simplifying further, we have x = 351 / 27 = 13.

Therefore, the unknown value in the proportion is 13. Hence, the correct option is D.

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Answer:

A, D, and E

Step-by-step explanation:

So the function 350-45t for t hours means that he reads 45 pages every hour. So, going from 11 AM to 1 PM is two hours. Since his reading pace doesn't change, we just have to look for an answer that has a difference of two answers. The only answers that have a difference of two hours are A, D, and E.

To find the time periods during which Marco reads the same number of pages as he reads between 11 a.m. and 1 p.m., we need to solve the equation P(t) = 350 - 45t for t using the value of 260 pages read between 11 a.m. and 1 p.m. The time periods are from 9 a.m. to 11 a.m., and from 1:30 p.m. to 3:30 p.m.

To find the time periods during which Marco reads the same number of pages as he reads between 11 a.m. and 1 p.m., we need to determine the values of t that make P(t) = 350 - 45t equal to the number of pages read between 11 a.m. and 1 p.m. which is 350 - 45(2) = 260 pages.

Substituting this value into the equation, we get:

P(t) = 350 - 45t = 260

Solving for t, we have:

t = (350 - 260) / 45 = 2

So, Marco reads the same number of pages during the time period from 9 a.m. to 11 a.m., and also during the time period from 1:30 p.m. to 3:30 p.m.

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Answer:

1: The diver is 8 feet below sea level.

2: -20

3: -20 + 20 = 0

Step-by-step explanation:

1: This is determined by adding 4 to negative 12. -12 +4 = -8

2: You get this by subtracting 12 from negative 8. -8 - 12 = -20

3: This is done by adding 20 to negative 20. -20 + 20 = 0

The diver's depth in relation to sea level is determined by subtracting the ascent from the initial descent and subsequent descents are added or subtracted accordingly. To reach sea level from a negative depth, the diver needs to ascend by swimming.

The depth of the diver in terms of sea level is -8 feet. This was determined by subtracting the ascent of 4 feet from the initial descent of 12 feet below sea level, resulting in -8 feet.

The new depth of the diver in terms of sea level is -20 feet. This was determined by adding the additional descent of 12 feet to the previous depth of -8 feet below sea level, resulting in -20 feet.

The diver will reach sea level from the position found in part B by swimming up 20 feet. This will bring the depth of the diver to 0 feet below sea level, which is equivalent to sea level.

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Answer:

D. 98:112

Step-by-step explanation:

We want to find Annette:Joaquin

49:56

Both of these numbers are divisible by 7. so we need to divide both of them by 7.

7: 8

Now multiply by each side by 14

7*14 : 8*14

98: 112

Answer:

negative $1.60 was the "interest" added to Vito's account

Step-by-step explanation:

new balance = old balance + deposits - withdrawals + interest

$9669.26 = $6955.01 + 2815.85 - 100.00 + interest . . . . fill in givens

$9669.26 = $9670.86 + interest . . . . . simplify

$9669.26 - 9670.86 = interest = -$1.60 . . . . . subtract 9670.86

_____

Comment on the problem

This result is "unexpected." Usually an interest amount will be positive. Please have your teacher work this problem for you and explain the result.

Vito Melvin started with $6,955.01 in his account, deposited $2,815.85, and withdrew $100. The expected balance was $9,670.86, but the actual balance was $9,669.26, meaning Vito earned $1.60 in interest.

This problem is about calculating interest earned on a bank account. Let's start by looking at Vito Melvin's actions with his bank account.

He began with a previous balance of $6,955.01. He then made a deposit of $2,815.85 and then withdrew $100. This means his new balance should be his previous balance plus his deposit minus his withdrawal. In calculation, (($6,955.01 + $2,815.85) - $100) = $9,670.86.

However, Vito's actual balance is $9,669.26. The difference between the expected balance ($9,670.86) and the actual balance ($9,669.26) is the interest he earned. So, subtract the actual balance from the expected balance to find the interest: $9,670.86 - $9,669.26 = $1.60.

Therefore, Vito Melvin earned $1.60 in interest.

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Answer:

86%

Wouldn't you just be finding the ratio of pennies to Canadian.

Step-by-step explanation:

The amount of pennies to Canadian pennies are 13/15

And the amount of Canadian pennies to pennies are 2/15

If you pick a random penny out of your pocket it would be a larger possibility to get the regular pennies.

So the ratio would be I think:

There would be an 86% more chance of grabbing a regular penny than the 13% chance of getting a Canadian penny.

The probability of not picking a Canadian penny from a total of 15 pennies, with 2 being Canadian, is 13/15 or approximately 86.7%.

To find the probability of not picking a Canadian penny (P(not Canadian)), we first consider the total number of non-Canadian pennies. Since there are 15 pennies in total and 2 of them are Canadian, there must be 15 - 2 = 13 non-Canadian pennies.

The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability of picking a non-Canadian penny is:

P(not Canadian) = Number of non-Canadian pennies / Total number of pennies

P(not Canadian) = 13 / 15

This simplifies to approximately 0.867, or 86.7% when expressed as a percentage.

Answer:Temperature of 10 degrees

Step-by-step explanation:

The others involve a decrease of 10 units, justifying use of a megative number.

The situation would not be represented by the integer -10 is Temperature of 10 degrees.

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Integers come in three types:

Given:

The representation of integer -10.

first, You owe $10

Owning is taken which can be represented as -10.

Temperature of 10 degrees have no clear idea of above or below 0 degree.

and, hole 10 feet deep can be represented as -10.

if we take ground at 0 then the above will positive integer and depth will be negative integer.

Lastly, 10 yard penalty can be represented as -10.

Penalty means deduction which can be shown as negative integer.

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Answer:

2b³ +2a -2c . . . . degree 3 polynomial

Step-by-step explanation:

The monomials are ...

... 4a . . . . degree 1 in a

... -5b·b² = -5b³ . . . . degree 3 in b

... -3c . . . . degree 1 in c

... 7b³ . . . . degee 3 in b (like term with -5b³)

... +c . . . . degree 1 in c (like term with -3c)

... -2a . . . . degree 1 in a (like term with 4a)

So, we have 3 pairs of like terms. The like terms can be combined by summing their coefficients.

The degree of the polynomial is that of the highest-degree term. (Here, the b³ term makes it a polynomial of degree 3.)

... 4a -2a = (4-2)a = 2a . . . . combining the "a" terms

... -5b³ +7b³ = (-5+7)b³ = 2b³ . . . . combining the b³ terms

... -3c +c = (-3 +1)c = -2c . . . . combining the "c" terms

In standard form, we write the highest-degree term first. Follwing terms are in order by decreasing degree. It is convenient, but perhaps not required, to then write the terms of the same degree in alphabetical order.

... = 2b³ +2a -2c . . . . a 3rd degree polynomial

Answer:

A. (0,0) is a solution to n=m and to n=4m.

Step-by-step explanation:

The solution to the system is the point where the lines intersect. The lines do intersect: they are distinct and not parallel.

(x, y) = (0, 0) is the point of intersection

The solution point (0,0) satisfies both the system of equations n=m and n=4m, making statement A correct. The other statements are incorrect since (0,0) exists on both lines, which are not equivalent and not parallel.

The system of equations n=m and n=4m indeed has the solution point (0,0). To verify if the provided solution is correct, we can substitute the values into both equations. Substituting into the first equation, we get 0=0, which is true. Substituting into the second equation, we also get 0=0, which is true as well.

Given this assessment, the correct statement is A. (0,0) is a solution to n=m and to n=4m. The other options can be disregarded as follows: B is incorrect because (0,0) exists on both lines; C is incorrect because the two equations are not equivalent; D is incorrect because the lines intersect, proving they are not parallel.

There are 7 work stations.

This is because:

7/8 divided by 1/6 divided by 2 =

7/8 times 16/1 times 1/2 = 7

Hope this helps :)

Workstations the teacher set up in each of the classrooms is is mathematically given as,

⇒ x = 7

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;

An art teacher has a total of 7/8 pound of clay.

And, The teacher puts 1/16 pound of clay at each workstation.

Since, The teacher sets up an equal number of workstations in each of 2 classrooms

Generally the equation for the workstations is mathematically given as,

1/16(x) = 7/8

x = 16 × 7/(8×2)

x = 7

Therefore, The workstations the teacher set up in each of the classrooms is, ⇒ x = 7

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Answer:

Step-by-step explanation:

First put the point slope form equation into slope intercept form.

y−2=0.5(x+3)

y - 2 = .5x + 1.5

y - 2 + 2 = .5x + 1.5 + 2

y = .5x + 3.5

With it in the slope intercept form we can see that the y intercept is at (0,3.5)

Find a graph that has this as the y intercept. Next we can graph it like the picture I have attached. You graph the equation by inserting numbers for x.

Answer:

Step-by-step explanation:

The given equation is y - 2 = 0.5(x + 3)

Since the equation is of a straight line so we further rewrite the equation in the form of intercept form.

y - 2 = 0.5x + 1.5

y = 0.5x + 1.5 + 2

y = 0.5x + 3.5

Now plot the graph for the points suitable for the equation

x     0       2        -2         4        -4

y     3.5    4.5     2.5      5.5     1.5

Now the graph which matches the graph plotted will be the graph of the equation.

$392.16 in interest saved

The payoff in 1 year costs a total of 12 × $366.72 = $4400.64.

The payoff in 2 years costs a total of 24 × $199.70 = $4792.80.

Paying off the balance in 1 year saves interest charges of ...

... 4792.80 -4400.64 = $392.16

Answer:

The greatest value is q-n

The smallest value is n-q

q is closest to 0

Step-by-step explanation:

The further to the left we go, the more negative it gets

n < q

from looking at the graph

n<q

Subtract q from each side

n-q < q-q

n-q < 0

This is less than 0

Now subtract n from each side

n<q

n-n < q-n

0 < q-n

This is greater than 0

Lets compare n-q  and q

n = -4

q = -1

n-q  = -4 --1 = -4 +1 = -3

-3 < -1

n-q < q

Lets look at q-n

-1 --4

-1 +4 = 3

q is closer to 0 than q-n

The greatest value is q-n

The smallest value is n-q

q is closest to 0

Answer:

58

Step-by-step explanation:

The midsegment has a length that is the average of the lengths of the parallel sides it is halfway between.

... LM = (38 +78)/2 = 116/2 = 58

C). The function is linear because it decreases at a constant rate.

y changes by -1 every time x changes by +2. When the rate of change is constant, the function is linear.

38 m/s

The formula tells you Rachael's distance to the exit decreases by 38 m for each passing second. Her speed is 38 m/s.

Answer:

38 m/ s

Step-by-step explanation:

We are given that Rachel is a stunt driver , and she escaping from a building .

D(t) models Rachel's remaining  distance ( in meters) a s  function of times t ( in seconds)

D(t)=-38 t+220

We have to find the speed of Rachel's

We know that speed is a absolute value of velocity

We are finding velocity

[tex]v=\frac{ds}{dt}[/tex]

[tex]v=\frac{d(-38t+220)}{dt}[/tex]

[tex]v=-38 m/s[/tex]

Speed=38 m/s

Hence, speed of Rachel's=38 m/s

about 0.04023

My probability calculator says that probability is about 0.04023.

Answer:

16

Step-by-step explanation:

We need to evaluate the expression 3x-2

Plugging in x=6, we get

3(6)-2

=18-2

=16

Answer:

16

Step-by-step explanation:

3x – 2 if x = 6

To solve this we substitute the x with 6.

3x – 2 = 3(6) - 2

           = (3×6) - 2

           = 18 - 2

            = 16