Yesterday a chef used 36 eggs to make 8 chocolate souffles and 3 lemon meringue pie. The day before, he made 2 chocolate souffles and 2 lemon meringue pies, which used 14 eggs. How many eggs does each dessert require?

Write the system. Define your variables.
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The number is 11. 63

Algebraic expressions are mathematical expressions comprised of constants and variables.

These expressions combines numbers, symbols, variables and mathematical operators such as addition, subtraction, multiplication, etc

From the information, let the number be x

2( x + (-6)) = x - 3/ 8

expand the bracket

2x - 12 =  8x - 3 /8

cross multiply

8 ( 2x - 12) = 8x - 3

expand the bracket

16x - 96 = 8x - 3

collect like terms

16x - 8x = -3 + 96

8x = 93

Make 'x' the subject

x = 93/ 8

x = 11. 63

The number is 11. 63

Thus, the number is 11. 63

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Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

Let's analyze each system of equations and classify them based on the number of solutions they have:

1) y = 11 − 2x

  4x − y = 7

This system of equations represents two lines. The first equation is in slope-intercept form, and the second equation is in standard form. Since the equations have different slopes and different y-intercepts, they intersect at a single point. Thus, the system has a single solution.

2) x = 12 − 3y

  3x + 9y = 24

The first equation represents a line, and the second equation is a linear equation. Since the first equation can be rewritten as 3y = 12 - x or y = 4 - (1/3)x, it indicates that the slope-intercept form can't be satisfied. Both equations are equivalent and represent the same line. Therefore, the system has infinitely many solutions.

3) 2x + y = 7

  -4x = 2y + 14

The first equation represents a line, and the second equation is also a linear equation. If we simplify the second equation, we get y = -2x - 7, which is equivalent to the first equation. Thus, the system has infinitely many solutions.

4) x + y = 15

  2x − y = 15

Both equations are in standard form. By adding the equations, we eliminate y and get 3x = 30, which simplifies to x = 10. Substituting x = 10 into either equation, we find y = 5. Therefore, the system has a single solution.

5) x + 4y = 6

  2x = 12 − 8y

The first equation represents a line, and the second equation is a linear equation. By simplifying the second equation, we get x = 6 - 8y, which is equivalent to the first equation. Therefore, the system has infinitely many solutions.

To summarize:

- System 1: Single solution.

- System 2: Infinitely many solutions.

- System 3: Infinitely many solutions.

- System 4: Single solution.

- System 5: Infinitely many solutions.

Answer:

I believe the answer is c. g(x)=2x-18

You can plug each multiple choice answer into a graphing calculator, or an online graphing program, to check the transitions against the parent function.

Answer:

A. g(x)= 2[x-6] - 3

Step-by-step explanation:

I took the quiz on Ed

Answer:

centroid = (3, 2)

Step-by-step explanation:

The centroid of a triangle is the point of intersection of the medians.  

Given that S (3, 1) is the middle point of QR, this indicates that triangle PQR is an isoceles triangle with sides QP = PR and base QR.  Therefore, the x-coordinate of the centroir will be x = 3.

Vertical distance between S and P = 3 units

Therefore, centroid will be 1/3 of SP.  1/3 of 3 = 1.

Therefore, y-coordinate of centroid = 1 + 1 = 2.

Answer:

\((a^6b^1^2)^\frac{1}{3}\) = \(a^2b^4\)

\(\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}\) = \(a^3b^2\)

\((\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}\) = \(a^2b\)

\((\frac{a^3}{ab^-^6})^\frac{1}{2}\) = \(ab^3\)

Step-by-step explanation:

Simplify each of the expressions:

1

\((a^6b^1^2)^\frac{1}{3}\)

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

\((a^6b^1^2)^\frac{1}{3}\)

\(a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}\)

Simplify,

\(a^2b^4\)

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

\(\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}\)

Rewrite as square roots:

\(\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}\)

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

\(\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}\)

Simplify,

\(\sqrt{a^5b^3}*\sqrt{ab}\)

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

\(\sqrt{a^5b^3*ab}\)

Simplify,

\(\sqrt{a^6b^4}\)

Since this operation is taking the square root, divide the exponents in half to do this operation:

\(a^3b^2\)

3

\((\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}\)

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

\((\frac{a^8}{b^-^4})^\frac{1}{4}\)

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

\((a^8b^4)^\frac{1}{4}\)

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

\(\sqrt[4]{a^8b^4}\)

SImplify, divide the exponents by (4) to simulate taking the quartic root,

\(a^2b\)

4

\((\frac{a^3}{ab^-^6})^\frac{1}{2}\)

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

\((a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}\)

\((a^2b^6)^\frac{1}{2}\)

Rewrite to the half-power as a square root,

\(\sqrt{a^2b^6}\)

Simplify, divide all of the exponents by (2),

\(ab^3\)

After solving the equations, we know that a total of 25 ladies attended the party.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, take dudes as x and ladies as y.

Now, form the required 2 equations as follows:
2x + y = 45 ...(1)

x + y = 35 ...(2)

Work on equation (2):

x + y = 35

x = 35 - y

Now, substitute x = 35 - y in equation (1):

2x + y = 45

2(35-y) + y = 45

70 - 2y + y = 45

-y = -25

y = 25

Since ladies were charged $1 for each ticket, then 25 ladies attended the party.

Therefore, after solving the equations, we know that a total of 25 ladies attended the party.

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The annual equivalent cost (AEC) for the pickup truck is $4,308. We found the equivalent uniform annual cost (EUAC) first.

To calculate the AEC, we need to first find the equivalent uniform annual cost (EUAC) which includes both the initial cost and the present value of the maintenance and operation costs.

Find the present value of maintenance costs over five years using the gradient formula:

where A = $135, i = 12%, g = 0, n = 5

PV maintenance = $501.21

Find the present value of operating costs over five years using the present value formula:

where C = $0.2/mile * 344 miles/month * 12 months/year = $827.52/year, i = 12%, n = 5

PV operation = $3,322.08

Find the EUAC using the formula:

where A/P = [(1+i)^n * i] / [(1+i)^n - 1]

Finally, convert the EUAC to AEC by adding the present value of the salvage value and multiplying by the interest rate:

where PV salvage = $3,580 / \((1+i)^5\)

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Answer:

250 hamburgers were sold on Sunday

Step-by-step explanation:

Let there are x hamburgers and y cheeseburgers sold on Sunday.

ATQ,

x + y = 553 .....(1)

There were 53 more cheeseburgers sold than hamburgers.

y = 53 + x ....(2)

Put the value of y from equation (2) in equation (1).

x + (53 + x) = 553

2x+53 = 553

2x = 500

x = 250

Put the value of x in equation (2).

y = 53 + 250

y = 303

Hence, 250 hamburgers were sold on Sunday

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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Answer:

D because you have to cos

Answer:

B and D

Step-by-step explanation:

sin(15)=0.25

cos(65)=0.42

Answer:54

Step-by-step explanation:66-12=54

Answer:

shrek

Step-by-step explanation:

1+1=2

For the triangle is right, the Pythagorean theorem holds; namely,

Now, we need to remember the formula for the square of a sum:

Then, the first equality becomes

Now, we need to calculate the roots of the polynomial on the left. Let's use the general formula:

Note that x_2 is negative. It doesn't work for negative lengths makes no sense. Then,

Answer:

48/7

Step-by-step explanation:

= 3 1 × 2 1

5. 7

= 16 × 15

5. 7

= 240 , if we divide both numbers by 5 we get;

35

= 48

7

Answer:

2.06 is smallest ans 2.9 is largest

Answer:

2,320,000

Step-by-step explanation:

10,000,000

                   -

7,680,000

__________

2,320,000

Answer:

2,320,000

Step-by-step explanation:

You have to subtract the 10,000,000 by the amount that has already been sold in order to find out the difference on how many copies are left in order to receive an award.  

10,000,000 - 7,680,000 = 2,320,000

Answer:

131072

Step-by-step explanation:

Let's put it into expression form and simplify as much as possible :

\(\frac{(2)(4)(8)(16)(32)(64)}{2^{4} }\) =

\(\frac{2097152}{16}\) =

131072

Hope this helped and have a good day

Answer: 131,072

Step-by-step explanation:

2 x 4=8

8 x 8=64

64 x 16=1024

1024 x 32=32768

32768 x 64=2097152

\(2^{4}\)=16

2097152/16= 131072

Answer:

the answer is 3√3

Step-by-step explanation:

Answer:

The quantity that depends on the other quantity is called the dependent variable, and the quantity it depends on is called the independent variable.

Hope this helps!

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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hopefully this is correct..

it's either e = 1/3 or 3

Answer:

1/3 or 3^-1

Step-by-step explanation:

please mark me as brainlest

Answer:

Option B is correct one

B. 25 square centimeters

If you are helped with my answer pls tag me brianliest I really want it... Plzz

THANK you...

The area of the rectangle to the nearest square centimeter will be 15 square centimeters. Then the correct option is E.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

A golden rectangle has a length of 5 cm. Then the width of the rectangle is given as,

W = 5 - 2

W = 3 cm

Then the area of the rectangle will be given as,

A = 5 x 3

A = 15 square centimeters

The area of the rectangle to the nearest square centimeter will be 15 square centimeters. Then the correct option is E.

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Answer:

(x, y) = (4,-3)

Step-by-step explanation:

...............

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