A baker orders 162 eggs. Each carton contains 18 eggs. Determine the number c of cartons.

Answer:

(-7) (-10x - 3y = -18)

(10) (-7x - 8x = 11)

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

70x + 21y = 126

+ -70 - 80x = 110

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

-59x = 236

x = -4

Answer

[tex] \huge{ \boxed{ \text{(3 \:, - 4)}}}[/tex]

✑ [tex] \underline{ \underline{ \text{First ,\: let's \: know \: about \: elimination \: method}}}[/tex] :

☇ In this method , we add or subtract the given equations to eliminate one of the two variables by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.

☯ [tex] \underline{ \underline{ \text{Let's \: solve}}} : [/tex]

[tex] \underline{ \text{Original \: system}} : [/tex]

[tex] \text{ - 10x - 3y = - 18 - - - - Equation\: (i)}[/tex]

[tex] \text{ - 7x - 8y = 11 - - - - Equation \: (ii)}[/tex]

[tex] \text{Step \: 1} : [/tex] Take L.C.M ( Lowest Common Multiple ) of 10 and 7. For this , find the prime factors of each number. Then, take out the common prime factors and other remaining prime factors and multiply them.

L.C.M = Common factors × Remaining Factors

= 1 × 2 × 5 × 7

= 70

[tex] \text{Step \: 2} : [/tex] Multiply equation ( i ) by 7

[tex] \text{7( - 10x - 3y ) = - 18  * 7}[/tex]

⇢ [tex] \text{ - 70x - 21y = - 126 - - - - equation \: (iii)}[/tex]

[tex] \text{Step \: 3} : [/tex]Multiply equation ( ii ) by 10

[tex] \text{10( - 7x - 8y) = 11 \: * \: 10}[/tex]

⇢ [tex] \text{ - 70x - 80y = 110 - - - - equation \: (iv)}[/tex]

[tex] \text{Step \: 4} : [/tex] Subtract equation ( iv ) from equation ( iii ) :

Also Remember that while subtracting , sign of each term of the second equation changes. Here , we are eliminating x . So to make the coefficient of y same , equation ( i ) is multiplied by 7 and equation ( ii ) is multiplied by 10.⇩

[tex] \text{ - 70x - 21y = - 126}[/tex]

[tex]\text{+70x + 80y = - 110}[/tex]

___________________

[tex] \text{ \: \: \: \: \: \: 59y = - 236}[/tex]

Solve :

⇢ [tex] \text{59y/59 = - 236/59}[/tex]

⇢ [tex] \boxed{ \bold{ \text{y = - 4}}}[/tex]

[tex] \text{Step \: 5} : [/tex]

Substitute the value of y into equation ( iii ) , we get :

[tex] \text{ - 70x - 21y = - 126}[/tex]

➳ [tex] \text{ - 70x - 21( - 4) = - 126} [/tex]

➳ [tex] \text{ - 70x - ( - 84) = - 126} [/tex]

➳ [tex] \text{ - 70x + 84 = - 126}[/tex]

➳ [tex] \text{ - 70x = - 126 - 84}[/tex]

➳ [tex] \text{ - 70x = - 210}[/tex]

➳ [tex] \text{ - 70x/  - 70 = - 210/  - 70}[/tex]

➳ [tex] \boxed{ \bold{ \text{x = 3}}}[/tex]

[tex] \bold{ \underline{ \text{Hence ,\: x = 3 \: and \: y = - 4}}}[/tex]

Hope I helped!

♡ Have a wonderful day / night ツ

~ [tex] \sf{TheAnimeGirl} [/tex] ♪

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

3

Step-by-step explanation:

-3 is 3

Answer:

1.75qt

Step-by-step explanation:

Answer:

The basketball travels in a parabolic route in order to engage in the passage through the net.

Step-by-step explanation:

Answer:

quiz let or brainy helps me just look up the chapter question and you will get the answer

Step-by-step explanation:

hope this helps

f(x) can be considered as a linear function because of the following conclusions -

1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.

2 → The slope of the function is constant.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is the following statement representing a function - f(x), that models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute.

Assume that we represent the depth of the water rate by [y] and the time in minutes by [m]. We can write the function f(x) as -

y = f(x) = 11m

This is a linear relation and its graph will be a straight line passing through origin.

From this equation, we can make the following conclusions -

1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.

2 → The slope of the function is constant.

Therefore, f(x) can be considered as a linear function because of the following conclusions -

1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.

2 → The slope of the function is constant.

To solve more questions on straight line graphs, visit the link below-

brainly.com/question/2954112

#SPJ6

Answer:

246.00

Step-by-step explanation:

58.75+23.25=82 then 82*3

Answer:

246.000

Step-by-step explanation:

Well If you take it and Line it up like this,

(A)Amy; 58.75

(J)Jeremy; A+23.25

(O)Oscar; A+23.25= ?x3

This is an easy way to find out what it is you need to do, So A+23.25 is 58.75+23.2 which should give you the value of 82, which brings you to the next step of A+23.25= ?x3 which in this you only wanna focus on the ?x3, we now know ?= 82 so this brings it to 82 times 3 which gives you a value of 246. Thus giving you your answer.

  Hope this helps.

Answer:

1. Steve's age is 18 and Anne's age is 8.

2. Max's age is 17 and Bert's age is 11.

3. Sury's age is 19 and Billy's age is 9.

4. The man's age is 30 and his son's age is 10.

Step-by-step explanation:

1. Let us assume that:

S = Steve's age now

A = Anne's age now

Therefore, in four years, we have:

S + 4 = (A + 4)2 - 2

S + 4 = 2A + 8 - 2

S + 4 = 2A + 6 .................. (1)

Three years ago, we have:

S - 3 = (A - 3)3

S - 3 = 3A - 9 ................................ (2)

From equation (2), we have:

S = 3A - 9 + 3

S = 3A – 6 …………. (3)

Substitute S from equation (3) into equation (1) and solve for A, we have:

3A – 6 + 4 = 2A + 6

3A – 2A = 6 + 6 – 4

A = 8

Substitute A = 8 into equation (3), we have:

S = (3 * 8) – 6

S = 24 – 6

S = 18

Therefore, Steve's age is 18 while Anne's age is 8.

2. Let us assume that:

M = Max's age now

B = Bert's age now

Therefore, five years ago, we have:

M - 5 = (B - 5)2

M - 5 = 2B - 10 .......................... (4)

A year from now, we have:

(M + 1) + (B + 1) = 30

M + 1 + B + 1 = 30

M + B + 2 = 30 .......................... (5)

From equation (5), we have:

M = 30 – 2 – B

M = 28 – B …………………… (6)

Substitute M from equation (6) into equation (4) and solve for B, we have:

28 – B – 5 = 2B – 10

28 – 5 + 10 = 2B + B

33 = 3B

B = 33 / 3

B = 11

Substituting B = 11 into equation (6), we have:

M = 28 – 11

M = 17

Therefore, Max's age is 17 while Bert's age is 11.

3. Let us assume that:

S = Sury's age now

B = Billy's age now

Therefore, now, we have:

S = B + 10 ................................ (7)

Next year, we have:

S + 1 = (B + 1)2

S + 1 = 2B + 2 .......................... (8)

Substituting S from equation (7) into equation (8) and solve for B, we have:

B + 10 + 1 = 2B + 2

10 + 1 – 2 = 2B – B

B = 9

Substituting B = 9 into equation (7), we have:

S = 9 + 10

S = 19

Therefore, Sury's age is 19 while Billy's age is 9.

4. Let us assume that:

M = The man's age now

S = His son's age now

Therefore, now, we have:

M = 3S ................................... (9)

Five years ago, we have:

M - 5 = (S - 5)5

M - 5 = 5S - 25 ................ (10)

Substituting M from equation (9) into equation (10) and solve for S, we have:

3S - 5 = 5S – 25

3S – 5S = - 25 + 5

-2S = - 20

S = -20 / -2

S = 10

Substituting S = 10 into equation (9), we have:

M = 3 * 10

M = 30

Therefore, the man's age is 30 and his son's age is 10.

Answer:

D

Step-by-step explanation:

18 - 3 = 15

Answer:

7x + 6 = 55; x=7

Step-by-step explanation:

"six more than" -> +6

"product of seven and a number" -> 7x

7x + 6 = 55

7x = 55 - 6

7x = 49

x=7

Answer:

6+7x=55, x=7

Step-by-step explanation:

7x=55-6

7x=49

x=7

Answer:

The lines will not intersect, because this system has no solutions

Step-by-step explanation:

Answer:

They will not intersect!

Step-by-step explanation:

A-P-E-X

Answer:

-9.

The product of -9 and -8 is 72.

Step-by-step explanation:

Product means the answer of a multiplication, so we're given 72 and -8.

We can solve this by using inverse operations.

The inverse operation of multiplication is division, so we divide 72÷ -8

This will give us -9.

Answer:

Step-by-step explanation:

x      y

-2     6

-1       2

0       -2

1          -6

2         -10

Answer: The slope of the line = 4.

Step-by-step explanation:

We know that ,

Slope of a line passes through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]  = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Here , the line passes through points (2,18) and (8,42).

Then the slope of the given line = [tex]\dfrac{42-18}{8-2}[/tex]

[tex]=\dfrac{24}{6}=4[/tex]

Hence, the slope of the line = 4.

Answer:

4

Step-by-step explanation:

i took the test and got it right

Answer:

you mean 2.5?????? in two quart????

Answer:

Line A is x = -3

Line B is y = 2.5

Step-by-step explanation:

Answer:

$13.99

Step-by-step explanation:

20% of $69.99 is $13.998

We get this by taking 69.99 X .2 = 13.998

Technically she would save $14 if we rounded up. But most stores will round down in order to save more money.

Answer:

Elena scored 22 points.

Step-by-step explanation:

Mai scored 5 points, and Noah scored three times as many. This means Noah scored 15 points and if Tyler scored four points fewer, he scored 11 points. If Elena scored twice as many as Tyler, she scored 22.

Answer:

Step-by-step explanation:

-14 - 73 i

Answer:

-28i^2-73i-42

Step-by-step explanation:

(−7)(6)+(−7)(7i)+(−4x)(6)+(−4i)(7i)

= −42−49i−24i−28i^2

= -28i^2-73i-42

Answer:

the answer is 5 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

First of all, we will sort the data.

185 227 234 245 278 278 279 281 281 291 299

Mean:

Mean is defined as the sum of values divided by the number of values.

n = 11

[tex]Mean = \frac{sum}{n}\\= \frac{185+227 +234+ 245+ 278+ 278+ 279+ 281+ 281+ 291+ 299}{11}\\=\frac{2878}{11}\\=261.63\ pounds[/tex]

Median:

As the number of values is odd,

The median will be:

[tex]Median = (\frac{n+1}{2})th\ value\\= \frac{11+1}{2}\\=\frac{12}{2}\\=6th\ value[/tex]

The 6th value is 278

Median = 278

Mode:

Mode is the most frequent value in a data set.

In the given dataset,

278 and 281 are modes as both are repeated twice

Mid-range:

Mid-range is the average of maximum and minimum value

So,

Min = 185

Max = 299

So,

[tex]Mid-range = \frac{Max+Min}{2}\\= \frac{185+299}{2}\\= \frac{484}{2}\\= 242[/tex]

Hence,

Answer:

5.15 hope this help!!!

Step-by-step explanation:

give this brainlieast so other people can know its not 20.60

Answer:

-5k - 10

Step-by-step explanation:

-k + 2 (-2k - 5)

-k - 4k - 10

-5k - 10

Answer:

-K+2(-2K-5)

-K-2K-10

-3K=10

K= 10÷(-3)

K=-3.333333

Answer:

..

Step-by-step explanation:

Answer:

The equation of the circle having centre (-5,-9) and radius r=3  is

x² + 10 x +y² + 14 y + 65 = 0

Step-by-step explanation:

Explanation:-

From graph  The centre of the circle  C( -5 , -7)

The radius of the circle r = 3cm from the centre of the given circle

The equation of the circle



From graph the centre ( h, k) = ( -5,-7) and r = 3cm

                 [tex](x-(-5))^2+(y-(-7))^2 = 3^2[/tex]

                x² + 10 x +25 +y² + 14 y + 49 =9

              x² + 10 x +25 +y² + 14 y + 49 -9=0

 The equation of the circle

                x² + 10 x  +y² + 14 y + 65 = 0  



====================================================

Explanation:

Let's say we have the following code names for each shape

We have 4! = 4*3*2*1 = 24 ways to arrange them without any restrictions

Some permutations have C and S together, while others do not.

Example of them together: CSTP

Example of them separated: CTSP

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

Let's say Amanda used a rubberband or glue to connect the circle to the square. This way the two shapes would always be together. They combine to form a new shape of sorts.

Let's call this new shape "polygon" and define it as

L = polygon

The codename L is just a placeholder for CS or SC.

So instead of the set of these codenames {C,S,T,P}, we have this reduced set {L,T,P}

No matter how we arrange the items in {L,T,P}, the circle and square are always going to be together. Again, anywhere you see an L, you replace it with CS or SC.

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

There are 3 letters in {L,T,P} so there are 3! = 3*2*1 = 6 ways to arrange those 3 letters. There are 2 ways to arrange S and C within any of those 6 arrangements mentioned earlier.

So there are 2*6 = 12 different ways to arrange the four shapes such that S and C are together somehow.

Recall earlier we found 24 ways total to arrange the shapes without restriction. This must mean there are 24 - 12 = 12 permutations such that S and C are not together. This is the final answer we're after.

Answer:

x = 8

Step-by-step explanation:

2x + 5 = 21

      -5    -5

      2x = 16

     2x/2 = 16/2 ( divided 2 on both sides)

     you get x= 8

to check your work, replace x with 8 in the equation

                            2 x 8 + 5 = 21    ( don't forget PEMDAS!!)

                               16 + 5 = 21  

Answer:

the top one and bottom one

Step-by-step explanation:

Answer:

first and sixth

Step-by-step explanation:

they match

Answer:

-5

Step-by-step explanation:

You can count backwards from -1.

-1, -2, -3, -4, and then -5 is the blue dot.

The left side of 0 is the negative side. The right side is the positive side.

Hope this helps!

Answer:

-5

Step-by-step explanation:

If you're going backward on the number line then you are in the negative zone because of -1

Answer: 3 x 7^4

Because there's one 3 & four 7's .

Step-by-step explanation: