Eli needs to order some new supplies for the restaurant where he works. The restaurant needs
at least 546 knives. There are currently 312 knives. If each set on sale contains 10 knives, write
and solve an equation or inequality which can be used to determine x, the number of sets of
knives Eli could buy for the restaurant to have enough knives.
Write the equation or inequality

The required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

The statement is three times the smaller of three consecutive even integers is four less than twice the larger

According to given question we have

Let the even integers be x and x + 2 .

Here, x is the smaller integer

(x + 2) the bigger integer.

By the equation is

3x =2(x + 2)-4

compare the like terms we get

x=4-4

x=0

The smaller integer=0

The bigger integer= 0+2=2

Therefore, the required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.

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1.

[tex] 2x {}^{2} + 17x + 35 \\ = 2x {}^{2} + 10x + 7x + 35 \\ = 2x(x + 5) + 7(x + 5) \\ = (2x + 7)(x + 5)[/tex]

2.

[tex]2y {}^{2} - 5y - 3 \\ = 2y {}^{2} -6y + y - 3 \\ = 2y(y - 3) + 1(y - 3) \\ = (2y + 1)(y - 3)[/tex]

3.

[tex]3x {}^{2} - 8x + 4 \\ = 3x {}^{2} - 6x - 2x + 4 \\ = 3x(x - 2)( - 2)(x - 2) \\ = (3x - 2)(x - 2)[/tex]

The radius of the new parking area is 82 meters

The radius of the old parking area is given as

Radius, R = 123 meters

From the question, we understand that:

The parking area must be temporarily reduced to 1/3 of its original area

This means that

New Radius = Old radius - Old radius * 1/3

So, we have

New Radius = 123 meters - 123 meters * 1/3

Evaluate the product

So, we have

New Radius = 123 meters - 41 meters

Evaluate the difference

New Radius = 82 meters

Hence, the radius of the new parking area is 82 meters

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Answer:

-41.1 feet

Step-by-step explanation:

-32.5-8.6=-41.1

1/2=0.5

3/5=6/10=0.6

The solution of system of equations is (1,-1).

Given that the system of equations is x+5y=-4, x+6y=-5.

The system of equations can be written in matrix form as

x+5y=-4

x+6y=-5

[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]

Write the matrix on the left as the product of coefficients and variables.

[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]

Firstly, find the inverse of the coefficient matrix.  

The inverse of [tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right][/tex] is

[tex]\begin{aligned}\left[\begin{array}{ll}1& 5\\ 1&6\end{array}\right]&=\frac{1}{6(1)-5(1)}\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right] \\ &=\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right]\end{aligned}[/tex]

Next, multiply each side of the matrix equation by the inverse matrix .  Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.

[tex]\begin{aligned}\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{l}-4\\ -5\end{array}\right]\\ \left[\begin{array}{ll}1&0\\ 0&1\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{l}1\\ -1\end{array}\right]\end{aligned}[/tex]

The identity matrix on the left verifies that the inverse matrix was calculated correctly.

[tex]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}1\\ -1\end{array}\right][/tex]

The solution is (1,-1).

Hence, the solution of the system of equtions using matrix is x+5y=-4, x+6y=-5 is (1,-1).

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The total amount did he earn this month is $3125.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Dave earns his salary by making a 12.5% commission.

sales= $25000 this month.

According to given question we have

The basic formula is

Sales × Commission Percent/100 = Commission

$25000  ×12.5/100= Commission

Commission=$3125

Therefore, the total amount did he earn this month is $3125.

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Answer:

Q= (1, -1), R = (7,-1), S = (7,-10), P =. (1,-10)

Step-by-step explanation:

Look at the coordinate grind then look at the coordinates (x) vertically, then look at the coordinates(y) horizontally.

then plot it as (x, y)

Relation r is not a function and Inverse function because a single

input gives several outputs.

1. Identity Relation: In an identity relation, every element is related to itself. Its notation is I = (a, a), A.

2. Empty relation: In an empty relation, there will be no connection between the set's components. This is a subset of.

3. Reflexive relation: Each element is mapped to itself in a reflexive relation. If (a, a) R for all aR, a relation R in a set A is automatic.

4. An irreflexive relation exists when two elements are not related to one another.

5. Inverse relation: An inverse relation exists when a set contains elements that are inverse pairs of those in another set. For instance, R-1 = (q,p), (s,r) if A = (p,q), (r,s), etc.

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Answer:

100 + 35x = 240

240 - 100 = 140 = 35x

140/35 = 4

Step-by-step explanation:

4 hours, not a bad pay o.o

Answer:

4 Hours

Step-by-step explanation:

Let y=money

Let x= Hours

y=mx+b

240=35x+100

minus 100

140=35x

divide 35

4=x

APR include: Interest on the loan

What does APR mean?

The APR which means annual percentage rate, is the interest rate on the loan, it is expressed in annual terms which is normally compounded monthly, by monthly compounding I mean the interest is computed on monthly basis.

APR has does not have anything to do with the principle and term of the loan since the principle is the loan amount and the term is the number of periods that the borrower is allowed to make repayments until the loan is fully repaid

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Answer:

so your first number in your plotted points is the x value and the next is the y value as shown here (x,y) so if it needs to go up 2 and right 1 what we do is increase the -1 to a 0 because you are moving right on the graph which makes it become a positive. now if you were to move up 2 that is your y coordinate because y controls up and down movement while x controls left and right movement so you would increase the 8 to 10 so you'll find no coordinates would end up being (0,10)

Answer:times  5 and 5 =25  7 and 7=49 add answers 74

Step-by-step explanation:

your ans

Step-by-step explanation:

the value of x is 6

The value of x will be 6 for the given triangle.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that in the right-angle triangle, the hypotenuse is 10, the base is 8 and the perpendicular is x.

The value of x will be calculated as:-

x² = 10² - 8²

x² = 100  - 64

x² = 64

x = √36

x = 6

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Prime numbers are those numbers that are divisible only by the number itself and by 1. Such numbers are 2, 3, 5, and 7 etc.

Factorization is when we write a given mathematical term in product of its various factors. Suppose we are provided with a mathematical expression of:

x^2 + 3x + 2

We will undergo its Factorization and write the expression in its possible factors:

( x + 1 ) ( x + 2)

By multiplying these factors, we will get the actual expression x^2 + 3x + 2.

Prime Factorization is a method of identifying which prime numbers multiply together to give the original value/expression.

Suppose we have a number 60, then the prime factors of it will be:

60

6  x  10

2 x 3    2 x 5

In the problem statement above, we are provided with some popular dog breeds, and we are expected to find the prime factors of each of the given weights of the breed.

The weights that have a prime factorization of exactly three number are as follows:

Prime factors of 20 (Cocker Spaniel)

= 2 x 2 x 5

Prime factors of 50 (Siberian Husky)

= 2 x 5 x 5

Prime factors of 70 (Golden Retriever)

= 2 x 5 x 7

Weights that have the same number in their prime factorization are:

Prime factors of 81 (German Shepherd)

= 3 x 3 x 3 x 3

Prime factors of 25 (Beagle)

= 5 x 5

So, the prime factorization of the weights of the dog breeds are being found. While Labrador Retriever 67 is a prime number itself.

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The correct argument in support of the team that should be awarded the prize is; Team A because their distribution of total call times is skewed to the right, which shows the majority of total call times are less than the mean.

A skewed distribution is a distribution which is non-symmetric and also it has no mirror-imaging.

One common characteristic of skewed distributions, is that one tail of the distribution will be quite longer or drawn out relative to the other tail.

A distribution is said to be skewed right when one of the tail is on the right side.

A distribution is said to be skewed left when one of the tail is on the left side.

Now, we want to find the correct argument in support of the team that should be awarded the prize.

Looking at the two graphs of team A and B, we see that team A has a distribution that is skewed to the right which means majority of total call times are less than the mean.

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The image of the triangle at point L is L' = (-8, 4)

The vertices of the triangle are given as:

L(4, 8), M(4, 3), and N(8, 8)

The transformation rule is given as

270 degrees rotation

The rule of 270 degrees rotation is

(x,y) = (-y , x)

When the above rule is applied to the vertices of the triangle, we have:

L' = (-8, 4)

Hence, the image of the triangle at point L is L' = (-8, 4)

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Answer: 110 degrees

Step-by-step explanation:

We know that all the angles of a triangle add to 180 degrees. Notice how there are already 60 and 50 degrees on the triangle. In order to find the last angle, we subtract 110 (60+5) from 180 to get 70.

Now, we know that the angle of a straight line is 180.

So, in order to find <BCD, take 70 and subtract it from 180.

Doing this, we find that m<BCD is 110 degrees

Answer:

the third option I think it says (-1,4)

Step-by-step explanation:

So the directions are basically asking to turn in the paper 3 times ending up in the 1st quadrant. Because 90*3 equals 270 degrees. There would be only one point in the negative and there are 2 options. So, we would immediately know that the first option or the last option is wrong. I don't really know how to explain this without drawing so if you could try turning your paper 3 times then you'll see what I mean. Comment if you need any more help. Or if you have any questions. My explanation is pretty bad I apologize.

Answer:

x=0

Step-by-step explanation:

12 = -4(-6x-3)

12 = 24x+12

-12         -12

0 = 24x

/       /

24   24

0 = x

Check

12 = -4(-6(0)-3)

12 = -4(0-3)

12 = 0 + 12

12 = 12

The amount of change that Melvin would receive from a $20 bill is equal to: C. $11.78.

In order to determine the amount of change that Melvin would receive from a $20 bill, we would first of all calculate the total cost before tax.

For the cinnamon roll, we have:

Cinnamon roll's cost = $2.59.

For three (3) doughnuts, we have:

Doughnut's cost = 0.95 × 3

Doughnut's cost = $2.85.

For two (2) dozen doughnut holes, we have:

Doughnut hole's cost = 1.75 × 2

Doughnut hole's cost = $3.5.

Total cost = $2.59 + $2.85 + $3.5

Total cost = $8.94

Next, we would determine the new cost after applying sales tax:

New cost = 8.94 - 0.72

New cost = $8.22.

Now, we can determine Melvin's change:

Change = Dollar bill - New cost

Change = $20 - $8.22.

Change = $11.78.

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Answer:

4 C$11.78

Step-by-step explanation:

1st - 3

2nd-1

3rd-4

5th-2

The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.

Let Jackie wants to make x necklace and y bracelets.

Now, Since it take her half an hour to make a necklace and one hour to make a bracelet.

Also since she has fewer than 20 h total to work on the jewelry. So we have

0.5x + 1y < 20

=> 0.5x + y < 20

and she want at least twice as many bracelets as necklace, so we have

y ≥ 2x

also the number of necklace should be greater than 0. So x > 0

So the required inequalities are:

0.5x + 1y < 20

y ≥ 2x

and x > 0

Hence, The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.

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The the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 is 7x + y + 8 = 0.

A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

The equation of a line parallel to a given line will have the same slope as the given.

The equation of a line having a slope m and passing through the point (x', y') is written as

y - y' = m (x - x').

This is called point - slope equation of a straight line.

In the given equation,

14x+2y=6

⇒ 2y = -14x + 6

⇒ y = -7x + 3

Comparing it with standard equation of a straight line; y = m x + c, the slope m of the given line = -7

Therefore equation of the line parallel to the given line and passing through point (x', y') = (2, -10) would be:

y - (-10) = -7x + 2

⇒ y + 10 = -7x + 2

⇒ 7x + y + 8 = 0

Hence the required equation of line 7x + y + 8 = 0

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The wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.

We are given that the area of the pond = 22,000 square feet

Area = 22,000 feet²

π r² = 22,000

22 / 7 r² = 22,000

r² = 22000 × 7 / 22

r² = 7000

r = √ 7000

r = 10 √70

r = 83.76 feet

Also, since the wave travels 16 feet per second,

Time taken to cover the entire area = 83.76 / 16 = 5.23 seconds

The diameter of the lake = 83.76 + 83.76

d = 167.52 feet

Therefore, we get that the wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.

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Answer:

True

Step-by-step explanation:

After evaluating the logarithm log ₇ 49, we get the result as 2.

The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.

For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output.  The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.

We need to evaluate log ₇ 49

x = log₇ 49

We can also write it as:

7ˣ = 49

7ˣ = 7²

Comparing the bases, we get that:

x = 2

Therefore, after evaluating the logarithm log ₇ 49, we get the result as 2.

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