Mr. Roy was creating bundles for his classes. He had 20 pencils, 80 pens and 55 markers.
He wanted each bundle to contain the same number of pencils, pens and markers.
a) What is the largest number of bundles he could create without any left over?

Answer:

Step-by-step explanation:

Let the speed of the cars be x and y.

When moving in opposite directions, the speeds add up and when moving in the same direction the speeds subtracted.

Convert time from minutes to hour:

Add up the two equations and find the value of x:

Find y:

Answer: 4x10²

Step-by-step explanation:

According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,

To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:

According to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).

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The answer for the given function g(x) is  |x - 4|² - 2.

Given parent function is f(x) = |x|

Given vertex (h, k) = (-2, 4)

The simplest function in a family of functions, a parent function maintains the definition of the entire family.

The parent function that has vertex must be used to create the function of g, as shown below.

vertex form can be written as

a ( x - k )² + h

Here a = 1 , k = 4, h = -2

Now the function g(x) = | x -4 |² + ( -2)

                            g(x) = |x - 4|² - 2

Therefore, the function g(x) is found to be  |x - 4|² - 2.

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Answer:

Hayley will have 200 milliliters of paint left.

Step-by-step explanation:

1 liter=1000 milliliter

1000-800=200

Answer:

305

Step-by-step explanation:

There are 1,000 milliliters in 1 liter.solveYou need to find how many milliliters of blue paint Annie has left. But first, you need to know how many milliliters she started with.There are 1,000 milliliters in a liter, so multiply 0.5 liters by 1,000.0.5×1,000=500Annie started with 500 milliliters of blue paint.Now, add to find how much blue paint Annie used for her beach painting. She used 75 milliliters of blue paint for the sky and 120 milliliters for the ocean.75+120=195Annie used 195 milliliters of blue paint in all.Now, find how much blue paint Annie has left. She started with 500 milliliters. Subtract the 195 milliliters she used.500–195=305Annie has 305 milliliters of blue paint left.

If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.

An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of function f over the interval [-3, 0]:

a = -3; f(a) = -4.5

b = 0; f(b) = 0

Substituting the given parameters into the formula, we have;

Average rate of change = (0 - (-4.5))/(0 - (-3))

Average rate of change = 4.5/3

Average rate of change = 1.5.

Also, we would determine the average rate of change of function g over the interval [-3, 0]:

a = -3; f(a) = 5

b = 0; f(b) = 14

Substituting the given parameters into the formula, we have;

Average rate of change = (14 - 5)/(0 - (-3))

Average rate of change = 9/3

Average rate of change = 3.

In conclusion, the average rate of change of function f is less than the average rate of change of function g.

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Answer:

The average rate of change of f is less than the average rate of change of g.

Step-by-step explanation:

Plato/Edmentum

The dimensions of the bulletin board is 2 ft and 9 ft.

Let the width of board = x

Then, the length of board = 7+x

Area of board = 18 ft²

Area of rectangle = L×W

so, (7+x) × x = 18 ft²

7x + x² = 18 ft²

7x + x² + 18 = 0

x² + 9x -2x -18 = 0

x(x+9) -2(x+9) = 0

(x+9) (x-2) = 0

x+9 =0, x -2 = 0

Dimension can not be in negative number, so

x = 2, Width = 2 ft

Length = 2+7 = 9 ft

Hence, the dimensions of board will be:

The width of board = 2 ft

And, the length of bard = 9 ft.

The Janitor used 8/15 of the bottle

How to calculate the amount of the solution of the bottle used ?

The Janitor has 3/5 of a spray bottle solution

He uses 1/9 of the solution in a day

The amount of solution used can be calculated as follows

3/5 × 1/9

= 3/45

= 1/15

The initial amount  in the bottle is

3/5 - 1/15

= 8/15

Hence the amount of solution he has used is 8/15

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The -2/3 is an  integer and rational number.

It is required to choose the number.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

Given:

-2/3 is an integer and rational number.

The square root of 25 is 5 is an Natural numbers, whole number, integer, and rational number.

Natural numbers are positive whole numbers (1, 2, 3, 4, 5, ...)

Whole numbers are positive numbers start with  zero  (0, 1, 2, 3,...)

Integers are positive and negative whole numbers or zero (..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)

Rational numbers include all integers as well as positive or negative numbers that have fractional parts ( -2.0, -3/4, 0.25, 2.1, 5, etc.)

Irrational numbers are numbers that can not be written as a simple fraction.  Its decimal goes on forever without repeating (π = 3.14159....)

5 is a natural number, whole number, integer, and rational number.

Therefore, the -2/3 is an  integer and rational number.

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Answer:

10 days

Step-by-step explanation:

60/50×12 give u the number of days it will last them

Answer:

8 1/4 or 33/4

Step-by-step explanation:

How to muliply fractions: just multiply all the denominators together and the numerators together

However, if your mulitplying whole numbers, you have to change those into improper fractions using the formula: Whole number x denomiator + numerator

**Make sure to put the same numerator as you had before when you change to an improper fraction!!!

-4 1/2 = -9/2

-2 1/5 = -11/5

5      -9    -11        5 x -9 x -11        -45 x -11 (use a calculator)       495

--   x  -- x  ---   =   ---------------  =   -------------                              =  ------------

6       2     5         6 x 2 x 5           12 x 5                                         60

                      1         33

=  8.25 or  8  ---- =  --------

                       4         4

Answer:

Let Pip get = x

Fiona gets = x + 35

Ratio = 6:1

x+35/x = 6

x + 35 = 6x

5x = 35

x = 7

Total money = x + x + 35 = 14+ 35 = £49

Answer:

£49

Step-by-step explanation:

Fiona gets 35 more than Pip so 6-1 =5 and 5 portions = 35

so 1 portion = 7

7x6 = 42

7x1 =7

7+42 = 49

so they got £49

hope this works :)

Number of servings of Gerber mixed cereal for baby = 1

Number of servings of Gerber mango tropical fruit dessert for baby = 3

Given information about Gerber products are,

Gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.

Gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.

We have to find the number of servings of each to provide exactly 300 calories and 74 grams of Carbohydrates. So we need to find the appropriate combination of numbers 60 and 80 to make 300 and combinations of 11 and 21 to get 74.

Since 1 x 60 + 3 x 80 = 60 +240 = 300

and 1 x 11 + 3 x 21 = 11 + 63 = 74 ,

we can conclude that 1 serving of Gerber mixed cereal and 3 servings of Gerber mango tropical fruit dessert  will do.

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Answer:

21(10)

Step-by-step explanation:

youll have to do 21 times 10

Answer:

[tex]\frac{210.00}{10}[/tex] = x

Step-by-step explanation:

[tex]\frac{210.00}{10}[/tex] = x

Let x is the number that each person needs to pay.

Maria should leave home for the airport terminal at 14:30.

We all know that one hour equals sixty minutes.

As a result, 6 hours = (6 × 60) minutes = 360 minutes.

For, the given question;

The time at which Maria need to be at airport terminal is 16:15.

Time taken for the driving is 1 1/3 = 4/3 hours.

convert this in minutes;

= 4×60/3

= 80 minutes.

Now, extra 25 minutes is requires to park.

Total time = 80 minutes + 25 minutes

Or we can write 60 minutes + 45 minutes.

Total time = 1 hour + 45 minutes.

The time at which Maria has to reach = 16:15 - 1:45 = 14:30

Therefore, the time at which Maria must reach the airport is 14:30 in 24-hour clock.

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Answer:

See Explanation

Step-by-step explanation:

During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

Given the expression, a³ - b³ / 5, where:

a = 2

b = -3

Substitute the values into the expression

Step 1: (2)³ - (-3)³ / 5

Evaluate

Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)

Step 3: 8 + 27/5

Step 4: 35/5 [addition]

Simplify

Step 5: 35/5 = 5 [division]

Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

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The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.

An item or particle that is thrown toward the planet's surface and moves somewhere along a curved route only under the influence of gravity is said to be experiencing projectile motion.

Let u be the initial speed and θ be the angle at which the ball hits. Then the range of the call is given as,

R = (u² sin 2θ) / g

Where 'g' is the acceleration due to gravity.

A tennis player strikes the ball at a height of 1.8 feet with an initial speed of 55 feet per second and an angle of 17°.

R = [55² x sin (2 x 17°) ] / 9.81

R = [3025 x sin 34° ] / 9.81

R = 172.43 meters

The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.

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Answer:

61.988 feet

Step-by-step explanation:

I took the test and got it right :)

Answer:

2/15

Step-by-step explanation:

Slope: m=(y2-y1)/(x2-x1)

m = (3 - 7)/(-14 - 16) = (-4)/(-30) = 4/30 = 2/15

Answer:

0.24 ounces for 3 teabags.

Step-by-step explanation:

Since this is a 1 digit number, we should find out how much each teabag weighs. We can do this by dividing 8 by 100, which gives us 0.08.

Now we can multiply that by 3, which gives us 0.24, so 3 teabags are 0.24 ounces.

Answer:

5 x + 4 y = 4 b

Step-by-step explanation:

You haven't specified what form you need. Here is the Standard form, but you can also calculate the Slope intercept form points and the Point-Slope form.

Find the equation of the line in standard form with the properties:

slope: m = -5/4

At least two parameters must be provided to determine a line equation:

Since the line is incompletely determined, compute the equation assuming an arbitrary y-intercept b

Substitute the slope m = -5/4 into the slope-intercept equation y = m x + b:

y = -(5 x)/4 + b

Add (5 x)/4 to both sides:

(5 x)/4 + y = b

Multiply both sides by 4:

4 ((5 x)/4 + y) = 4 b

Distribute: 4 ((5 x)/4 + y) = 5 x + 4 y:

Answer: 5 x + 4 y = 4 b

The simplified result is :

[tex]4x/x^{2}[/tex] - 1

= 4/x -1

4-x / x.

Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.

An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.

In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.

To know more about "Factored Form"

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The price the machinery have initially cost rounded to the nearest dollar is $244,693

The formula for calculating depreciation is expressed according to the formula:

P(t) = P0e^-rt

Given the following parameters

P(t) = $100,000

rate = 12% = 0.12

time =7 years

Substitute

100,000 = P0e^-(0.12)(7)

100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693

Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693

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Answer:    Find the square roots and the multiply that by 4

Step-by-step explanation:

hope this helped

The values of the variables are:

a = -3

b = 2

c = -4

d = 6

e = -7

Given, the expressions are:

4a + 2 = -10

4a = -10-2

4a = -12

a = -3

substitute a value in the next expression.

a(2+b) = -12

-3(2+b) = -12

-6-3b = -12

-3b = -12+6

-3b = -6

b=6/3

b = 2

now substitute b value in the next expression.

-5c+b= 22

-5c+2 = 22

-5c = 22-2

-5c = 20

c = -20/5

c = -4

substitute c value in the next expression.

7(c+d) = 14

7(-4+d) = 14

-28+7d = 14

7d = 14+28

7d = 42

d=42/7

d=6

In the last expression substitute c and d values to find e.

d-c-e= 17

6-(-4)-e = 17

6+4-e = 17

10-e = 17

-e = 17-10

-e = 7

e = -7

hence we get the values of all the variables.

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