Helen has to buy all the butter she needs to make 60 biscuits.

She buys the butter in 250 g packs.

What is the exact amount of butter she needs?

Answer:

  (a)  A(x) = (12 -2x)√(3x -9)

Step-by-step explanation:

You want a formula for the area (a(x)) of an isosceles triangle with congruent sides of length x and perimeter 12. You also want its maximum value, and a graph and the maximum value of z = 2a(3x+3)+1.

Heron's formula for the area of a triangle with side lengths a, b, c is ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

Given a perimeter of 12, and two sides x, this becomes ...

  A(x) = √(6(6 -x)(6 -x)(6 -(12-2x))) = √(6(6 -x)²(2x -6))

  A(x) = 2(6 -x)√(3(x -3)) . . . . . . factor out perfect squares

  A(x) = (12 -2x)√(3x -9) . . . . . . domain: 3 ≤ x ≤ 6

The domain is such that the radical and the area are non-negative.

The derivative of the area function is ...

  [tex]A'(x)=-2\sqrt{3x-9}+\dfrac{3(6-x)}{\sqrt{3x-9}}=\dfrac{-2(3x-9)+3(6-x)}{\sqrt{3x-9}}\\\\A'(x)=\dfrac{-9x+36}{\sqrt{3x-9}}[/tex]

The derivative is zero at the maximum, so ...

  -9x +36 = 0   ⇒   x = 4 . . . . . . . an equilateral triangle

The maximum area is ...

  A(4) = (12 -2·4)√(3·4 -9) = 4√3

The maximum area is 4√3.

Since the maximum of A(x) is 4√3 at x=4, the maximum of 2A(3x+3) +1 will be ...

  2(4√3) +1 = 8√3 +1 . . . . . . . where 3x+3 = 4  ⇒  x = 1/3

The maximum of 2A(3x+3)+1 is 8√3 +1 at x = 1/3.

The function ...

  z = 2A(3x+3) +1 = 2A(3(x+1)) +1

Compare this to ...

  z = p·A(q(x -r)) +s

which is vertically expanded by p, horizontally compressed by q, then translated right r and up s.

We see that the parent function A(x) is vertically expanded by a factor of 2, compressed horizontally by a factor of 3, then translated left 1 and up 1.

Applying these transformations to the original A(x) domain and range, we find the domain is ...

  1/3[3, 6] -1 = [0, 1] . . . . . domain of z

And the range is ...

  2[0, 4√3] +1 = [1, 8√3 +1] . . . . . range of z

If a player who is off the field of play to receive medical treatment trips a player who is on the field of play , then (c) the referee cautions the player and the play is restarted with a indirect free kick.

On the field of play of football , the medical treatment of any player is not permitted under any circumstances.

When the player is bleeding, the player is required to leave the field immediately.

When the play has been restarted, only time the injured player is allowed to return to field of play is after game has started again.

It is exclusive responsibility of match referee to decide whether or not an injured player may return to the game.

The given question is incomplete , the complete question is

A player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?

(a) A. The referee shows a red card and sends off the player. Play is restarted with an indirect free kick.

(b) The referee shows a yellow card and cautions the player. Play is restarted with an indirect free kick.

(c) The referee cautions the player and Play is restarted with an direct free kick.

(d) The referee cautions the player and restarts with a dropped ball.

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The area of each box would be proportional to the salaries of each group. Option C.

The use of models to represent data in mathematics is well known. In the case of the data we have, the salaries of the college graduates and the high school graduates have been shown by the use of squares.

We can see that the sizes of the squares respectively show the magnitudes of the salries of the high school graduate and that of the college graduate. The area of the boxes would be proportional to the salaries.

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The length of BC in simplest radical form is 2√19

The Pythagorean theorem states that the square of the hypotenuse side of a right angled triangle is equal to the square of the other sides.

It is represented mathematically as;

a² = b² + c²

Given that the parameters;

From the information given, we have that;

Hypotenuse side, a = 20

Adjacent side = 18

Substitute the values

20² = 18² + b²

Find the squares

400 =324 + b²

collect like terms

b² = 400 - 324

b² = 76

Make 'b' the subject of formula

b = 2√19

Hence, the value is 2√19

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Answer:

A quadratic equation of the form ax^2 + bx + c = 0 has solutions (or roots) that are either real or complex. The solutions of the equation vanish (or become equal to zero) when the equation is equal to zero.

For the equation x^2 (2p-4)x-(3q5)=0 to have a solution that vanishes, the discriminant (b^2 - 4ac) must be equal to zero.

Therefore, the roots of the quadratic equation x^2 (2p-4)x-(3q5)=0 vanish when p = 4 and q = 0

The  inequality shown on the graph is x > -2 and x < 5 or -2 < x < 5

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

If you examine the graph, you will notice that there is one circle on -2 and another circle on 5. These give you the range of values. Also, notice that circles are not shaded. Thus, this can be written as:

x > -2 and x < 5 or  -2 < x and x < 5

Which can then be combined as:

-2 < x < 5

Note: The reason we did not use ≤ is because the circles are not shaded.

Thus, the inequality is x > -2 and x < 5 or -2 < x < 5

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Answer: 8/12

Step-by-step explanation:

First you multiply 1/6 with 1/2 that would give us 1/12

Then you add 1/12 with 7/12

Our answer would be 8/12

Answer:

2/3 or in Decimal its 0.6

Step-by-step explanation:

1/6x+7/12 when x= 1/2.

1/6(1/2)+7/12

Answer:

Shown Below

Step-by-step explanation:

The difference between the two polynomials 3x^2-4x-5 and 2x^2-7x-3 is the result of subtracting the second polynomial from the first one.

3x^2 - 4x - 5 (first polynomial)

(subtraction operator)

2x^2 - 7x - 3 (second polynomial)

= x^2 - 3x - 2 (difference)

So the difference between 3x^2-4x-5 and 2x^2-7x-3 is x^2 - 3x - 2

This is a polynomial with a degree of 2 (quadratic) and the coefficient of x^2 is 1, x is -3 and the constant is -2.

There is a 0.81 Probability that the breakdown entails a gas leak. Given that there is a gas leak, there is a 0.63 percent chance that there is evidence of electrical failure. Given that there is evidence of an electrical failure, the likelihood of a gas leak is 0.77.

A)

Total number of  units

= 55 + 32 + 17 + 3

= 107

Hence the Probability that  failure involves a gas leak

= ( 55 + 32 ) / 107

= 0.8131

B) Probability that there is  a evidence of electrical failure given that there is a gas leak

P ( A / B ) = P( A∩B ) = 55/107 = 0.5140

P ( B ) = ( 55 + 32 ) / 107 = 0.8131

Hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322

A = failure due to electrical

B = failure due to gas leak

C)  Probability of a gas leak given that there is evidence of electrical failure

P ( B / A ) =  P ( B ∩ A ) = 0.5140

P( A ) = ( 55 + 17 ) / 107  = 0.6729

Hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639

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For the graph with points (-2, 2) and (2,0), the slope, linear equation and y-intercept is m = -1/2, y = -1/2x + 1 and y = 1 respectively.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first graph shows the points (-2, 2) and (2,0).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[0 - 2]/[2 - (-2)]

(-2)/(2 + 2)

-2/4

-1/2

So, the slope point is obtained as m = -1/2.

The equation becomes - y = -1/2x + b

To find the value of b substitute the values of x and y in the equation -

2 = -1/2(-2) + b

2 = 1 + b

b = 2 - 1

b = 1

So, the value for b is 1.

Now, the equation becomes -

y = -1/2x + 1

To find the y-intercept substitute the value of x = 0 in the equation -

y = -1/2(0) + 1

y = 0 + 1

y = 1

Therefore, the slope is 1, equation is y = -1/2x + 1 and y-intercept is y = 1.

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The value of x  when y = 10 and Z = 16, in the given joint variation is: 1120.

If X varies jointly with Y and Z, then we can use the formula X = k * Y * Z, where k is the constant of proportionality.

Using the given information, we can find k by plugging in the values of Y, Z, and X and solving for k:

14 = k * 2 * 4

k = 14 / (2 * 4)

k = 7/2

Now that we know the value of k, we can use it to find the value of X when Y = 10 and Z = 16:

X = k * Y * Z

X = (7/2) * 10 * 16

X = 70 * 16

X = 1120

So the value of X when Y = 10 and Z = 16 is 1120.

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Answer:

Step-by-step explanation:

0-2-0

1-11-11

2-28-56

3-18-54

4-11-44

5-15-75

6-10-60

7-2-14

8-3-24

total number of tickets won - 100

mean number - 336 divided by 100 = 3.36

Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.

Common denominators are used to describe fractions with the same denominators. Take a look at the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 The fractions' denominators are both common, making it simple to calculate the variable result in both situations.

Here,

Given :

=>29 + 151/20

=> 580 + 151/20

=> 731/20

=> 36.55

As a zero denominator would result in an infinite fraction, a finite fraction can never have a denominator of 0.

Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.

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Answer: I believe your x-intercept is (-7,0) and your y-intercept is (0,2)

Step-by-step explanation: I hope this helps! (It's kind of sad how this is the only bit of math I'm good at)

By simplifying  45y/30y (7x+49)  this  we get 3 / 2(7x + 49).

45y/30y (7x+49)

45y / 30y(7x +49) : 3 / 2(7x + 49)

45y / 30y(7x + 49)

45y / 30(7x + 49)

Factor the number :45 = 15 . 3

=15.3 / 30(7x + 49)

Factor the Number : 30 = 15 . 2

15.3 / 15.2(7x + 49)

Cancel the common factor : 15

= 3 / 2(7x + 49).

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Answer:

1:2.42

Step-by-step explanation:

145/60 = 2.42

Answer: 1 : 29/12

Step-by-step explanation:

60/60 = 1
145/60 = 29/12 in simplest form
therefore 1 : 29/12

Table (D) represents a linear function which the graph has been attached below.

A linear function is defined as an equation in which the highest exponent of the variable is always one. In mathematics, independent and dependent variables are values that vary in relation to one another.

The table is given in the question, as an option (D)

x:  −2  −1   0    1    2

y:    3    1  −1  −3  −5

According to the above table, we plot the graph through the points then we can see that the graph of a function looks linear.

Thus, this table represents a linear function.

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The correct statement is : The probability of landing on purple is equal to the probability of landing on yellow.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given here: A spinner with four different colors purple, yellow, blue and orange.

Now Section 1&8 = Blue

Section 2&3 = yellow

Section 4,5,6 = blue

Section 7 = orange

Total=8

Thus probability for each section are as follows

P(purple)=2/8

           =1/4

P(yellow)=2/8

              1/4

P(Blue)=3/8

P(orange)=1/8

∴ The probability of landing on purple is equal to the probability of landing on yellow.

Hence, The probabilities of all the individual sections are 1/4,1/4,3/8,1/8 for purple, yellow, blue and orange respectively.

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Answer: b) ? · 2 5= 4

d) 4 ÷ 2 5= ?

e) ? ÷ 2 5= 4

The equations that represent the situation are b) ? · 2 5= 4 , d) 4 ÷ 2 5= ?, e) ? ÷ 2 5= 4

The question is asking for an unknown quantity and it is asking to find it by using the 4 and 25, so the equations that represent the situation are the ones that have 4 and 25 in them and have the unknown quantity on one side of the equation and the known quantity 4 on the other side.

a) 4 · 2 5= ? is not a valid equation as it is asking to multiply 4 and 25, which is known and doesn't have any unknown quantity.

c) 2 5÷ 4 = ? is also not a valid equation as it is asking to divide 25 by 4 and doesn't have any unknown quantity.

Step-by-step explanation:

Steps to remove the quarter 1 data series from Dana's column chart in Microsoft Excel are given below.

You might need to add an additional data series to the chart after it has been created. A data series, such as a list of quarterly corporate profits, is a row or column of figures that are input in a worksheet and plotted in your chart.

To remove the quarter 1 data series from Dana's column chart in Microsoft Excel:

Note: The steps may vary slightly depending on the version of Excel you are using.

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Answer:

3x = 42

Step-by-step explanation:

The correct equation is

3x = 42

However, because your formatting has been scrambled, I cannot tell you which choice it is

Compare this equation with your original question and see which is the correct choice

3x = 42 means

each kite = 42/3 = $14
but the question is only asking for the equation not the solution

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The area of the base of the parcel box is given by the expression A=2x²+8x+6. The dimensions (length and width) are determined from this expression as (2x+2) and (x+3).

In general, the volume of a rectangular box is calculated by the product of the height, width, and length of the box. From the given hint, we can write the volume of the parcel box as a product of the height and the area of the base. This is written as,

[tex]\begin{aligned}V&=A\times h\\6x^2+24x+18&=A\times 3\\A&=\frac{1}{3}(6x^2+24x+18)\\A&=2x^2+8x+6\end{aligned}[/tex]

The above equation gives the area of the base

Now solving the above quadratic equation to find dimensions, we get,

[tex]\begin{aligned}A&=2x^2+8x+6\\&=2x^2+6x+2x+6\\&=2x(x+3)+2(x+3)\\&=(2x+2)(x+3)\end{aligned}[/tex]

The dimensions are (2x+2) and (x+3).

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The measure of the angle m∠ABD is 100°.

What is the measure of angle?

In mathematics, an angle is defined as the amount of rotation between two lines or planes that share a common point. The measure of an angle is typically given in degrees or radians. A full rotation is equal to 360 degrees or 2π radians, and the size of an angle can range from 0 degrees (no rotation) to 360 degrees (a full rotation).

In the given figure, m∠ABC = 130° and m∠DBC = 30° is given.

And we have to find the m∠ABD

so

m∠ABC = m∠ABD + m∠DBC

130° = m∠ABD +  30°

m∠ABD =  130° -  30°

m∠ABD = 100°

Hence, the measure of the angle m∠ABD is 100°.

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The coordinates of point A are given as follows:

A(19, 23).

The coordinates of point A are obtained applying the proportions in the context of this problem.

The segment AB is represented as follows:

AB = B - A.

Hence the segment 5AB is given as follows:

5AB = 5(B - A) = 5B - 5A.

Then the x-coordinate of A is obtained as follows:

5(16) - 5A = -15

5A = 95

A = 19.

The y-coordinate of A is obtained as follows:

5(30) - 5A = 35

5A = 115

A = 23.

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Answer: 1

Step-by-step explanation:

Anything to the power of 0 is 1

A plate of spring roll is price of $7.5.

What is Linear System?

A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties.

Let n, b, and c represent the cost per plate of spring roll, chicken tenders , and pretzel dipper, respectively.

One party spends $23 and purchases two plates of chicken tenders and one plate of pretzel dipper.

i.e. 2b + 1c = 23

     2b + c = 23                                        --------------------- 1

Three plates of  spring roll and a plate of chicken tenders are purchased by another group for $30.75.

That is

          3n + 1b = 30.75

          3n + b = 30.75                                          ---------------------- 2

A third party spends $22.25 and purchases one of each appetizer.

That is

             n + b + c  = 22.25                                    --------------------- 3

On solving;

eqn2 - eqn3

            2n - c = 8.5                                           --------------------- 4

on solving;

eqn 1 + eqn 4

             2b+ 2n = 31.5

             b + n = 15.75                                           --------------------- 5

On solving;

eqn 3 - eqn 5

              c = 6.5

Substituting in eqn 4

           2n - 6.5 = 8.5

              n = 7.5

Substituting in eqn 3

           7.5 + b + 6.5  = 22.25

               b = 8.25

Price of spring roll n = $7.5 .

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Each bag of lemons costs $3.99

Let m represents the cost of eggs and n represents the cost of each bag of lemons.

He buys 6 bags of lemons that each cost the same amount.

so, the cost of six bags of lemons would be 6n

He pays a total of $29. 33

so, we get an equation,

m + 6n = 29. 33               ............(1)

Levi pays a total of $5. 39 for the eggs

So, m = 5.39

We need to find the value of n.

substitute above value of m in equation (1)

m + 6n = 29. 33

5.39 + 6n = 29. 33

6n = 23.94

n = 23.94 / 6

n = 3.99

Thus, the cost of each bag of lemon = 3.99 dollars

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