50 yards of tape is needed to pack and ship 100 packages. You have a roll of tape that is 2000 inches long. About how many yards do you have? A) 28 yards B) 50 yards C) 56 yards D) 67 yards

answer is inverse operations are used

Answer:

The variable needs to be isolated and inverse operations are used.

Remark

You can use a formula to get the right answer. Otherwise you will use a lot of paper adding 100 numbers together.

Givens

A = 1

L = 100

n = 100 numbers to be added together. There are 100 numbers between 1 and 100 numbers inclusive.

Formula

Sum = (A + L)*n/2

Solution

Sum = (1 + 100)*100/2     Substitute in the givens. Add what is inside the brackets

Sum = (101) * 100 / 2       Divide by 2

Sum = 101* 50                  Multiply

Sum = 5050                     Answer

The sum of the numbers from 1 to 100 is 5050

The sum of the numbers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers where the difference between two consecutive terms is constant. In this case, the difference between successive numbers is 1.

The formula for an arithmetic series's sum (S) is S = n/2 (a + l), where n is the number of terms, a is the first term, and l is the last term.

Here, n = 100 (because we're adding the numbers from 1 to 100), a = 1 (the first number) and l = 100 (the last number). Substituting these values into the formula gives us S = 100/2 * (1 + 100) = 50 * 101 = 5050.

So the sum of the numbers from 1 to 100 is 5050.

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It's the third answer. This is because since there is no middle term where both variables are combined, that would lead to the signs of the 2 factors to be different. However, that still leaves 2 answers, 3 and 2. If we were to square i, you would get -1. This is because √-1 is equal to i. i^2 would be -1. Since the sign in the unfactored expression is positive and not negative, that would mean that the i in the factoring turned it around. that leads us to believe that answer 3 is the correct answer.

The length of the first piece is 4 the second piece is 8 and the third piece is 27.  Your Welcome

The problem can be solved by setting up an equation where x represents the length of the first piece. Solving for x, we find that the lengths of the three pieces are 4 inches, 8 inches, and 27 inches.

To solve this question, you can define the length of the first piece as 'x'. According to the problem, the second piece is twice as long as the first one, so it can be represented as '2x'. And the third piece is three inches more than six times the first one, which can be represented as '6x+3'.

Because the total length of the steel is 39 inches, you can setup an equation to solve for 'x':

x + 2x + 6x + 3 = 39

This simplifies to:

9x + 3 = 39

Subtracting 3 from both sides:

9x = 36

Finally, divide each side by 9:

x = 4

Therefore, the lengths of the three pieces of steel are:

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Answer:

A.-12x^2-5x-102

Step-by-step explanation:

We are given a polynomial of degree 2 where terms are not grouped and simplified.

We have

-21x^2+22x^2-13x^2-10x+5x-102

To get this in proper form we have to group the like terms first

x^2 term = -21x^2+22x^2-13x^2 = x^2 (-21+22-13)

= x^2(-34+22) = -12x^2

x terms are -10x+5x = x(-10+5) = -5x

Constant term is only one = -102

Hence the polynomial in simplified form is

-12x^2-5x-102

Answer:

28  dvds were given if 455 people visit the store.

Step-by-step explanation:

4 out of every 65 people who visited the store will receive a free dvd.

Suppose,  [tex]x[/tex]  dvds were given if 455 people visit the store.

Now, according to the ratio of "people who got dvd"  to "total number of people" , the equation will be.........

[tex]\frac{4}{65}=\frac{x}{455}\\ \\ 65x= 455*4=1820\\ \\ x=\frac{1820}{65}=28[/tex]

So, the number of dvds given is 28.

Answer:

28

Step-by-step explanation:

Given that there is a store contest.  Out of 65 people who visit the store only 4 will be receiving a free dividend.

Remaining 61 will not receive.

There were 455 people who visited the stores.

Of these 455/65 times 4 persons would be given dividends.

i.e. Since 4 out of 65 would be given

no of visitors who received dividend= 455(4)/65 = 7(4) = 28

Hence answer is 28 persons would receive dividend.

Answer:

56

Step-by-step explanation:

Given that Lydia is painting flower vases.

Paint required for painting one flower case = 3/16 quart

total paint available with Lydia = 21/2 quart

We have to find the no of flower cases that can be painted.

This is a problem of direct variation since when no of flower cases increase paint required also increases.

3/16 quart for 1 flower case

Hence 21/2 quart for 21/2 divided by 3/16

= 21*16/(3*2)  (by rule for fraction division)

= 7(8)

= 56

Solution: We are given that the Jennifer's grandmother bought 28 kg of carrot.

Also we are given that 28 kg of carrot are to be divided into 4 persons.

Therefore, the number of kilograms of carrots that Jennifer will get is:

[tex]\frac{28}{4}[/tex]

[tex]7[/tex] kg

[tex]\therefore[/tex] Jennifer gets 7 kilograms of carrot.

We are given that

a and b are integers and 71 < ab < 76

We will check each options

option-A:

b=18

we can plug it

[tex]71<a(18)<76[/tex]

we can divide both sides by 18

[tex]\frac{71}{18} <b<\frac{76}{18}[/tex]

now, we can simplify it

[tex]3.944<a<4.222[/tex]

Since, 'a' is a integer

so, a=4 lies on interval

so, this interval is true

so, this is FALSE

option-B:

b=8

we can plug it

[tex]71<a(8)<76[/tex]

we can divide both sides by 8

[tex]\frac{71}{8} <b<\frac{76}{8}[/tex]

now, we can simplify it

[tex]8.875<a<9.5[/tex]

Since, 'a' is a integer

so, a=9 lies on interval

so, this interval is true

so, this is FALSE

option-C:

b=12

we can plug it

[tex]71<a(8)<76[/tex]

we can divide both sides by 12

[tex]\frac{71}{12} <b<\frac{76}{12}[/tex]

now, we can simplify it

[tex]5.9166<a<6.333[/tex]

Since, 'a' is a integer

so, a=6 lies on interval

so, this interval is true

so, this is FALSE

option-D:

b=7

we can plug it

[tex]71<a(5)<76[/tex]

we can divide both sides by 7

[tex]\frac{71}{7} <b<\frac{76}{7}[/tex]

now, we can simplify it

[tex]10.14285<a<10.857[/tex]

Since, 'a' is a integer

so, no integer lies on this interval

so, this interval is false

so, this is TRUE

option-E:

b=5

we can plug it

[tex]71<a(5)<76[/tex]

we can divide both sides by 5

[tex]\frac{71}{5} <b<\frac{76}{5}[/tex]

now, we can simplify it

[tex]14.2<a<15.2[/tex]

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE

Apples = X

Pears = Y

3x+2y = 0.60

pears cost 2X-0.05 replace Y with this:

3X +2(2x-0.05) = 0.60

Simplify:

3X + 4X-0.10 = 0.60

Simplify:

7X -0.10 = 0.60

Add 0.70 to each side:

7X = 0.70

Divide both sides by 7:

X = 0.70 / 7

X = 0.10

Apples cost 0.10 each.

Pears cost 2x-0.05 = 2(0.10) - 0.05 = 0.20 - 0.05 = 0.15 each

Here we are given the expression:

[tex](b-2ya^{2})(3b-3ya^{2})[/tex]

We will use foil method to solve this expression.

The word FOIL is an acronym for the four terms of the product:

First ("first" terms of each binomial are multiplied together)

Outer ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second)

Inner ("inside" terms are multiplied—second term of the first binomial and first term of the second)

Last ("last" terms of each binomial are multiplied)

Using this method let us simplify our expression.

[tex](b-2ya^{2})(3b-3ya^{2})[/tex]

=[tex]3b^{2}-3bya^{2}-6bya^{2}+6y^{2}a^{4}[/tex]

Now combining like terms we have:

=[tex]3b^{2}-9bya^{2}+6y^{2}a^{4}[/tex]

Answer: [tex](b-2ya^{2})(3b-3ya^{2})[/tex] simplifies to [tex]3b^{2}-9bya^{2}+6y^{2}a^{4}[/tex]

Answer:

The answer is 3b² - 9bya² - 6y²a².

Explanation:

(b - 2ya²)(3b-3ya²)

3b² - 3bya²-6bya²-6ya²

3b² - 9bya² - 6y²a².

Answer would be 3b² - 9bya² - 6y²a².

Answer:

Option B

Step-by-step explanation:

Given that f(x) = 3x+5 and g(x) = 3x^2-x-10

Hence the function f/g = (3x+5)/(3x^2-x-10)

Since denominator cannot be 0 we have

3x^2-x-10 cannot be 0

i.e. x should not take values where 3x^2-x-10 =0

Solving (3x+5)(x-2) =0

x cannot take value as 2 or -5/3

So we can cancel 3x+5 and write

f/g =1/ x-2

Hence x cannot take values as 2

Option B

Option: B is the correct answer.

The function is:  [tex](\dfrac{f}{g})(x)=\dfrac{1}{x-2}[/tex]

and the domain is:  The set of all real numbers except 2

We are given a function f(x) and g(x) in terms of variable x by:

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

and

[tex]g(x)=3x^2-x-10[/tex]

Now, the function

[tex](\dfrac{f}{g})(x)[/tex] is given by:

[tex](\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}[/tex]

i.e.

[tex](\dfrac{f}{g})(x)=\dfrac{3x+5}{3x^2-x-10}[/tex]

[tex]3x^2-x-10=3x^2-6x+5x-10\\\\i.e.\\\\3x^2-x-10=3x(x-2)+5(x-2)\\\\i.e.\\\\3x^2-x-10=(3x+5)(x-2)[/tex]

i.e.

[tex](\dfrac{f}{g})(x)=\dfrac{3x+5}{(3x+5)(x-2)}\\\\i.e.\\\\(\dfrac{f}{g})(x)=\dfrac{1}{x-2}[/tex]

Also, the domain of the function is the set of all the real values except where the denominator is equal to zero.

The denominator is equal to zero when x=2.

Hence, the domain is the set of all the real values except 2.

The given information suggests that the sequence is a geometric sequence. The common ratio is 2, and the common difference is 2. The next term of the sequence can be found using the coordinates (5, 64) and (5, -64).

The given information about the sequence suggests that it is a geometric sequence.

If the common ratio is 2, it means that each term is obtained by multiplying the previous term by 2.

If the next term is represented by the point (5, 64), it means that the 5th term of the sequence is 64. Using the formula for a geometric sequence, we can find the first term: a * (2^(5-1)) = 64, where a is the first term of the sequence.

Similarly, if the next term is represented by the point (5, -64), it means that the 5th term of the sequence is -64. Using the formula for a geometric sequence, the first term is -8.

To find the new price of an item that has been reduced by a certain percentage, multiply the original price by the percentage (converted to decimal form) to find the discount. Subtract this discount from the original price to get the new price. Therefore, the new price of the item originally priced at $39 and reduced by 85% is $5.85.

This is a basic percentage problem in mathematics. The phrase 'reduced by 85%' implies that we are subtracting 85% of the original price from the original price itself. To find the discount, we multiply the original price by the reduction rate (in decimal form). Then, to get the final price, we subtract the discount from the original price. So, if the original price is $39 and the item has been reduced by 85%, then the discount would be $39. The calculation would look like this:

So, the new price of the item is $5.85.

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First you need to distribute

2x-10=6x-x+8

Add like terms

2x-10=5x+8

Subtract 8 from each side

2x-18=5x

Subtract 2x from each side

-18=3x

Divide each side by 3

X=-6

2x-10=6x-x+8

2x-10=5x+8

add 10 to both sides

2x=5x+18

subtract 5x from both sides

-3x=18

divide each side by -3

x=-6

Technically you should use "substitution" in place of "transitive property of equality", though they are very closely related ideas. If I were your teacher, then I would accept that answer as valid nonetheless.

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

Substitution says that if a = b and c = b, then a = c. We replace the 'b' in a = b with 'c'. Think of your substitute teacher who replaces your current teacher for a temporary basis. This is how to remember the term "substitution.

On the other hand, the transitive property of equality says that if a = b and b = c, then a = c. The equations chain together and can simplify into one single equation.

We already got

f(x)= a(x-2)(x-3)(x-5)

We got [tex]a=\frac{1}{6}[/tex]

first we multiply the parenthesis in f(x)

f(x)= a(x-2)(x-3)(x-5)

[tex]f(x)= a(x^2-5x+6)(x-5)[/tex]

[tex]f(x) = a(x^3 - 10 x^2 + 31 x - 30)[/tex]

Replace the value of 'a'

[tex]f(x) = \frac{1}{6}(x^3 - 10 x^2 + 31 x - 30)[/tex]

Multiply 1/16 inside the parenthesis

[tex]f(x) = \frac{1}{6}x^3 - \frac{5}{3} x^2 + \frac{31}{6} x - 5[/tex]

Marshall retires from the partnership of? Marshall, Mark, and Dennis. Marshall had a capital balance of? $25,000. If Marshall received? $25,000 as final? settlement, how will this transaction affect the balance sheet?  The answer is equities will decrease.

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the [tex] x^2 [/tex] coefficient is 1, i.e. the equation is written like [tex] x^2+bx+c=0 [/tex], then you can say the following about the coefficients b and c:

So, for example, if we want an equation whose roots are 4 and -2, we have:

So, the equation is [tex] x^2-2x-8=0 [/tex]

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

And so the equation is

[tex] x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0 [/tex]

In order to have integer coefficients, you can multiply both sides of the equation by 8:

[tex] 8x^2 - 10 + 3 = 0 [/tex]

Answer:

c.

Alexa is earning quite a bit more money than she was previously. This would be a good time for her to re-evaluate her budget. Part of the extra money she is making could be put in her savings account.

Step-by-step explanation:

Alexa's increased income has allowed her to increase her expenses in various categories, while still maintaining a balanced budget.

Alexa's increased income will have an impact on her budget. Let's compare her previous budget and her current budget:

As we can see, her expenses have increased in line with her increased income. Rent, utilities, groceries, and savings have all increased, while the cost of the bus pass remains the same.

Coordinates of the triangle ABC:

A(-2,2).

B(2,1)

C(-1,-2).

And the coordinates of the dilated triangle A'B'C':

A'(-4,4)

B'(4,2)

C'(-2,-4).

We can clearly see that each x and y-coordinate of triangle ABC is being multiplied by 2 to get the coordinates of triangle A'B'C'.

Therefore, triangle ABC is being dilated by a scale factor of 2.

The formula of a distance between A and B = |B - A|.

We have -3 and 4. Substitute:

|4 - (-3)| = |4 + 3| = |7| = 7

So I always go to this site for grade calculations

https:// rogerhub. com   /final-grade-calculator/

So go down to "I already took my final" or something like that

So with you having a 99, then got a 45% on a project that's worth 50% of your grade, your grade unfortunately drops 72%.

Keri walks approximately 4.29 kilometers in one week.

Keri walks her dog every morning. On weekdays, the length of the walk is 0.55 km. On weekends, the walk is 1.4 times as long as a walk on a weekday. To find out how many kilometers Keri walks in one week, we need to calculate the total distance she walks on weekdays and weekends.

Distance walked on weekdays = 0.55 km per day

Distance walked on weekends = 1.4 * 0.55 km per day = 0.77 km per day

Total distance walked in one week = (distance on weekdays * number of weekdays) + (distance on weekends * number of weekends)

Since there are 5 weekdays and 2 weekend days in a week, we can calculate the total distance:

Total distance walked in one week = (0.55 km * 5) + (0.77 km * 2) = 2.75 km + 1.54 km = 4.29 km

Keri walks approximately 4.29 kilometers in one week.

Answer: C

Step-by-step explanation:

Add like terms

    -1 + 6i

+   -4 + 2i

    -5 + 8i