Can you please help me solve these math problems questions 49-62

Answer:

Step-by-step explanation:

y = x^3 + 3
y = (-1)^3 + 3
y = -1 + 3
y = 2

The simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12

Given the expression in question;

( (-2 + h)³ + 8 ) / h

First, we simplify the numerator.

Lets rewrite 8 as 2³

(-2 + h)³ + 2³

Now, we can use the sum of cubes formula to factorize since both terms are perfect cubes.

a³ + b³ = ( a + b )( a² - ab + b² )

(-2 + h)³ + 2³ = ( -2 + h + 2 )( (-2 + h)² - (-2 + h)2 + 2² )

(-2 + h)³ + 2³ = h( (-2 + h)² + 4 - 2h + 4 )

(-2 + h)³ + 2³ = h( (-2 + h)²- 2h + 8 )

(-2 + h)³ + 2³ = h( (h² - 4h + 4 )- 2h + 8 )

(-2 + h)³ + 2³ = h( h² - 4h + 4 - 2h + 8 )

(-2 + h)³ + 2³ = h( h² - 6h + 12 )

Now bring back the denominator.

( h( h² - 6h + 12 ) ) / h

Cancel the common factors h

h² - 6h + 12

Therefore, the simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12

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Answer:

375

Step-by-step explanation:

Let the number of hamburgers sold be x. Then, x-66 cheeseburgers were sold.

[tex]x+x-66=684 \\ \\ 2x=750 \\ \\ x=375[/tex]

The mathematical expression of the statement is x - 15 <= 5

The statement is given as:

Hourly wage of $15 differs from the average by less than or equal to $5

Let the average hourly wage be x

So, we have:

Hourly wage of $15 differs from the average = x - 15

less than or equal to $5 => <=5

So, the expression is

x - 15 <= 5

Hence, the mathematical expression of the statement is x - 15 <= 5

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Answer:

The answer to your problem is -1/3

Step-by-step explanation:

Let me know if you need the steps. Thanks

The one cup holds 7 ounces of juice.

According to the statement

We have to find that the How many ounces does a cup hold.

So, For this purpose, we know that the

A quantity is a property of some object or collection of objects that is measurable.

From the given information:

A large juice jug holds the equivalent of 10 drinking cups: 4 jugs hold 189 ounces more than 13 drinking cups.

Let the amount held by a cup be y ounces.

So the large jug holds 10y ounces.

4 jugs hold 189 ounces more than 13 cups

4*10y=189+13y

40y-13y=189

27y=189

y=7

A cup holds 7 ounces.

So, The one cup holds 7 ounces of juice.

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Answer:

She will need to buy 589 kilograms.

Step-by-step explanation:

First of all we know about the Estimation.

What is the Estimation?

To estimate the result of multiplication (product), round the numbers to some close numbers that can easily multiply . One method of estimation is to round all factors to the biggest digit (place value) they have.

General rule for rounding:

1 ) If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2 ) If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So the last digit of number is 44 which is less then 50 so the number is down to its 10's.

thats the reason why when we estimate the product of 416x9 =3,744 is 3,600.

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The solution set of the given inequality i.e.{x ; 2<x≤7} is (2,7].

Given that a inequality y={x ; 2<x≤7} and asked to find the solution set for the given inequality and plot graph according to that

⇒ y={x ; 2<x≤7} i.e domain=(2,7].

⇒y=x ∀ x ∈ (2,7]

The solution of the given inequality is x ∈ (2,7].

Therefore,The solution set of the given inequality i.e.{x ; 2<x≤7} is (2,7].

Graph: image attached

y=x  ∀ x ∈ (2,7] is plotted {open at (2,0) and close at (7,0)}              

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Answer: x > 75

Step-by-step explanation:

(85+84+69+82+x)/5 > 79

85+84+69+82+x > 395

x > 75

Answer is  f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

vertical asymptote, the denominator must be contained (x−5)

and for zeros the numerator must be contained (x−2)

then we get,

So far f(x)= f(x)= [tex]\frac{ (x - 2)}{x - 5}[/tex]

​

For slant asymptote, quotient of numerator divided by denominator must be (x+4)

Therefore:

f(x)= [tex]\frac{(x + 4) (x - 2)}{x - 5}[/tex]

after solving this equation we get,

So f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

​A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.

In Mathematics, a slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.

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Answer:

He can buy 2 full sets

Step-by-step explanation:

$25 divided by $9 per set is 2.8 sets.  Assuming sets are only sold as whole packages that would be 2 full sets.

The function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -

(y - 4) - |x - 3| = 0

The modulus function can be written as follows -

|x| =  x  [for x ≥ 0]  

|x| = - x [for x < 0]

Given that a function f(x) = |x| which is shifted down by 4 units and right by 3 units. Therefore, we can write -

y = f(x) = |x|

Change in y - coordinate = y + 4.

Change in x - coordinate = x - 3.

We will plot the graph of h(x) after the doing the given changes in the coordinates.

Now, we have -

y = |x|

y - |x| = 0

Change in y - coordinate can be written as -

(y + 4) - |x| = 0

Change in x - coordinate can be written as -

(y - 4) - |x - 3| = 0

Now, the graph of both f(x) and and h(x) is attached at the end.

Therefore, the function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -

(y - 4) - |x - 3| = 0

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Answer:

y = 6x + 760

Step-by-step explanation:

In the problem you are given two pairs of numbers. These are both a pair of inputs and outputs, (x, y):

(390, 3100) also,

(490, 3700)

Write an equation by finding and filling in m and b in the following equation:

y = mx + b

To find m, which is the slope of the line, subtract y-y and put that on top. Then subtract x-x and put that on the bottom. See image.

Next, find b by use EITHER pair of numbers to find b.

I used (390, 3100).

see image.

m = 6 and b = 760

Fill these into

y= mx + b

y = 6x + 760

In case they ask, this means each calculator takes $6 to make and it costs $760 to set up your operation even before you have made any calculators.

Answer:

321,800 cm. (Rounded)

Step-by-step explanation:

2 × 160,900 = 321,800

There are 160,900 centimeters in one mile, so you must multiply that by 2 and round.

Answer:

-3

Step-by-step explanation:

Hope this helps!

Answer:

-3

Step-by-step explanation:

if its negative then it will continue to be unless 7 is added into -6. So, adding 3 to that would make it -3

Answer:

11

Step-by-step explanation:

2x-3=19

2x=22

x=11

The maximum number of performers in each row so that all the rows are equal in length is 8.

From the information, the marching band needs to create rows for its performance. there are 24 instruments and 16 flag bearers.

Therefore, we will find the highest common factor for both numbers. This will be:

24 = 1 2 3 4 ,6 8 12 24

16 = 1 2 4 16

Therefore the highest factor is 8

The maximum number of performers in each row so that all the rows are equal in length is 8.

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(A) The expression to represent the elevation level of city D, in feet will be :  [tex]D = \frac{1}{4} * [C][/tex]    
(B) The elevation of city D will be -6 feet. The negative here shows that city D is below sea level.

In the question, it is given that city A is 96 feet below sea level, city C is 24 feet below sea level, and the elevation of city D is 1 over 4th of the elevation of C. Since, City A & C are both below sea level their elevation will be negative. So, by these we get elevations:

For City A,  A = -96

      City C,  C = -24

      City D,  [tex]D = \frac{1}{4} *[C][/tex]      ----> Equation (1)

By Equation (1) we get the representation of elevation for City D.

Now, Calculating the elevation of city D, we will put the value of city C in equation (1).

        =>   [tex]D = \frac{1}{4} *[-24][/tex]

        =>   [tex]D = -6\\[/tex]

The negative sign here shows that the elevation is below sea level for city D.

Hence, the expression representing the elevation of city D will be [tex]D = \frac{1}{4} * [C][/tex] and, the elevation of city D will be -6.

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We get the equation in terms of n as n = s / 4 - v.

Equation:

An equation is an expression with an equal sign.

For example:

3 x + 4 y = 5

2 x + 5 y = 9 etc.

We are given an equation:

s = 4 n + 4 v

We have to solve this for n.

First we will subtract 4 v from both sides:

s - 4 v = 4 n + 4 v - 4 v

s - 4 v = 4 n

4 n = s - 4 v

Now divide both the sides by 4:

4 n / 4 = (s - 4 v) / 4

n = s / 4 - v

Therefore, we get the equation in terms of n as n = s / 4 - v.

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The height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.

The time of motion of an object is the time taken for an object to travel from point of projection to the projection plane or it can be said as the time a projected object spent in air.

The time taken for an object dropped from a certain height is calculated as follows;

h = vt + ¹/₂gt²

where;

when the object is dropped from rest, v = 0

h =  ¹/₂gt²

t = √(2h/g)

Thus, the height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.

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Answer: 59.5

Step-by-step explanation: 29 3/4 times 2

I think

Answer: $52 is your new balance

Step-by-step explanation: -12+60=52

The expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width is 6x + 18.

Let the width of the rectangle be x units.

According to the given question.

The length of a rectangle is nine more than twice the width.

⇒ Length of the rectangle = 9 + 2x

As we know that, the perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width.

Therefore, the expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width

= 2[x + (9 + 2x)]

= 2[ x + 2x + 9]

= 2[ 3x + 9]

= 6x + 18

Hence, the expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width is 6x + 18.

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Answer:

down below

Step-by-step explanation:

Brooke's team won 55%. 9 out word of 17 is 52.94% and 7 out of 13 is 53.85%. Now, we compare the numbers. 55% is more so, Brooke's team had the best winning percentage.

Hope this helps! :)

hsksebhssv hnshsnsjdndj ldgehsiw c 3072729 lvwjaiwn sj. +a iwiwirbfhx ska hamd +675196 = $ 20000 solved

Answer:

1.37037037 or 1 10/27

Step-by-step explanation:

What's there to explain?

27/27 + 10/27 = 1 10/27

What is the Fibonacci sequence?

The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.

The Fibonacci sequence begins with the following 14 integers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...

Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.

The sequence can theoretically continue to infinity, using the same formula for each new number. Some resources show the Fibonacci sequence starting with a one instead of a zero, but this is fairly uncommon.

Example 1: Starting with 0 and 1, write the first 5 Fibonacci numbers.

Solution: The formula for the Fibonacci sequence is Fn= Fn-1+Fn-2

The first and second terms are 0 and 1, respectively.

F0 = 0 and F1 = 1.

F2 = F0 + F1 = 0+1 = 1 is the third term.

F3 = F2+F1 = 1 + 1 = 2 is the fourth term.

F4 = F3+F2 = 1+2 = 3 is the fifth term.

The Fibonacci sequence’s first five terms are 0,1,1,2,3.

Example 2: Find the Fibonacci series’ next term: 0, 1, 1, 2, 3, 5…

Solution: The preceding two Fibonacci terms are the next term in the series.

As a result, the word that must be used is – 3 + 5 = 8

Example 3: What is the significance of Fibonacci numbers?

Solution: In financial statement analysis, Fibonacci numbers are pretty helpful. In addition, the Fibonacci number series may be utilized to provide valuable proportions or ratios for business people.

Example 4: Find the 12th term of the Fibonacci sequence if the 10th and 11th terms are 34 and 55, respectively.

Solution: Using the Fibonacci Sequence recursive formula, we can say that the 12th term is the sum of the 10th term and the 11th term

12th term = 10th term + 11th term

= 34 + 55

= 89

The 12th term of the Fibonacci sequence is 89.

Example 5: The 14th term in the sequence is 377. Find the next term.

Solution: We know that the 15th term = the 14th term × the golden ratio.

F15 = 377 × 1.618034

≈ 609.99 = 610

The 15th term in the Fibonacci sequence is 610.

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