A recipe for pastry has flour, butter and water mixed in the ratio 24 : 8 : 3 if fiona follows the recipe and uses 3 cups of flour, how many cups of butter should she use?

Answer:

[tex]cos(180\°)=-1[/tex]

[tex]sin(180\°)=0[/tex]

Step-by-step explanation:

we know that

In the unit circle the coordinates of the point belong to the x-axis for an angle equal to [tex]180\°[/tex] is [tex](-1,0)[/tex]

we have

[tex]x=1\ units, y=0\ units[/tex]

Applying Pythagoras theorem

[tex]H=\sqrt{1^{2}+0^{2}} =1[/tex]

so

[tex]cos(180\°)=x/H[/tex]

substitute

[tex]cos(180\°)=-1/1=-1[/tex]

[tex]sin(180\°)=y/H[/tex]

substitute

[tex]sin(180\°)=0/1=0[/tex]

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

We have been an equation [tex]x^2-3x-4=x^2-5x+6[/tex]. We are asked to find the solution of our given equation.

[tex]x^2-x^2-3x-4=x^2-x^2-5x+6[/tex]

[tex]-3x-4=-5x+6[/tex]

Adding 5x on both sides of our equation we will get,

[tex]-3x+5x-4=-5x+5x+6[/tex]

[tex]2x-4= 6[/tex]

Upon adding 4 on both sides of our equation we will get,

[tex]2x-4+4= 6+4[/tex]

[tex]2x=10[/tex]

Now, we will divide both sides of our equation by 2.

[tex]\frac{2x}{2}=\frac{10}{2}[/tex]

[tex]x=5[/tex]

Therefore, the solution of our given equation is [tex]x=5[/tex].

The value of x from the expression is 5

Given the equation x²-3x-4 = x²-5x+6

Collect the like terms

x² - x² -3x +5x -4 -6 = 0

Simplify the result

2x - 10 = 0

Add 10 to both sides

2x - 10 + 10 = 10

2x = 10

x = 5

Hence the value of x from the expression is 5

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The resale value of the laptop after 3 years will be $949.22

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.

The formula for the exponential decay is

[tex]y = a(1-b)^{x}[/tex]

Where,

y is the final amount

a is the original amount

b is the decay factor

x is the amount of time that has passed

According to the given question.

The initial price of the laptop, a = $2250.

decay factor, b = [tex]\frac{25}{100} = \frac{1}{4}[/tex]

Therefore,

The resale value of the laptop after 3 years

= [tex]2250(1-\frac{1}{4} )^{3}[/tex]

[tex]= 2250(\frac{4-1}{4} )^{3}[/tex]

[tex]= 2250(\frac{3}{4} )^{3}[/tex]

[tex]= 2250\times \frac{27}{64}[/tex]

[tex]= 35.156 \times 27\\=\$ 949.22[/tex]

Hence, the resale value of the laptop after 3 years will be $949.22

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Answer: $16

Step-by-step explanation:

Let x represents the cost of one subway ticket and y represents the cost of one express ticket.

According to the question, we have the following equations :-

[tex]6x+4y=24.........................(1)\\\\3x+7y=27..................(2)[/tex]

Multiply equation (2) with 2 on both sides , we get

[tex]6x+14y=54....................(3)[/tex]

Subtract equation (1) from equation (3) , we get

[tex]10y=30\\\\\Rightarrow y=\dfrac{30}{10}=3[/tex]

Put the value of y in (2), we get

[tex]3x+7(3)=27\\\\\Rightarrow\ 3x+21=27\\\\\Rightarrow\ 2x=6\\\\\Rightarrow\ x=2[/tex]

Thus, the cost of a subway ticket = $2

The cost of a express ticket = $3

Now, the cost of 5 subway tickets and 2 express tickets will be :-

[tex]5(2)+2(3)=\$16[/tex]

A polynomial expression can be factored by grouping when it has at least four terms. To factor by grouping, group the terms into pairs, factor out the greatest common factor from each pair, apply the distributive property to factor out the common binomial factor, and simplify.

A polynomial expression can be factored by grouping when it has at least four terms. To factor by grouping, follow these steps:

For example, let's consider the polynomial expression 3x^3 - 3x^2 + 2x - 2. We can group the terms as (3x^3 - 3x^2) + (2x - 2). Factor out the greatest common factor from each pair of terms, which gives us 3x^2(x - 1) + 2(x - 1). Applying the distributive property, we can factor out the common binomial factor (x - 1), resulting in (x - 1)(3x^2 + 2). This is the factored form of the original polynomial.

A polynomial expression that can be factored by grouping typically has four terms that are grouped into pairs, with each pair having a common factor. After factoring out the common factors from each pair, if the resulting binomials are identical, the expression can then be factored into the product of two binomials.

The structure of a polynomial expression that can be factored by grouping typically involves four terms with the possibility of factoring pairs of terms separately. To use this method, you would look for common factors in the first two terms and in the last two terms. If a common factor is found in both pairs, you can then factor out these common factors and check if the resulting binomials are identical. If so, you can factor out the binomial, leaving you with a product of two binomials as the factored form of the polynomial.

Here is a step-by-step example:

Thus, you've factored the original polynomial by grouping.

g(x)  = 12(2)x - 1

 h(x)  = 3x  

 We are looking for this :

 g(6) * h(6)     ....so we have....

 12(2)6-1  * 36   =

 12(2)5  * 729  =

 12*32 * 729   =  279,936 points

On the hardest setting of level 6, a player will need 729 points.

The student is asking how many points they will need on the hardest setting of level 6 in a video game according to the function that sets the point requirement.

The function given in the question is [tex]g(x) = 12(2)^x - 1[/tex] and the function for the hardest setting is [tex]h(x) = 3^x.[/tex]

To find the number of points required on the hardest setting for level 6, we plug in x = 6 into the hardest setting function: [tex]h(6) = 3^6.[/tex]

Calculating this gives us h(6) = 729.

Therefore, a player will need 729 points on the hardest setting of level 6.

The weight of Anna is: 115 pounds

and the weight of Janet is: 135 pounds.

It is given that:

Janet weighs 20 pounds more than Anna.

This means if the weight of Anna is: x pounds

Then the age of Janet is: (x+20) pounds.

Also,

The sum of their weights is 250 pounds.

i.e.

x+x+20=250

i.e.

2x+20=250

On subtracting both side by 20 we have:

2x=250-20

i.e.

2x=230

On dividing both side by 2 we have:

x=115

Hence, the weight of Anna is:115 pounds.

and the weight of Janet is: 115+20=135 pounds.

Answer:

1.24 acres or 54,000 feet

by-step explanation:

54000=1.2396694

300*180=54000

Then round up 1.2396694 and u get 1.24

19/7 = 114/x

= 114*7 = 798

798/19 = 42

answer is 42

For the table, y = 9x.

 so the price of a short cake is $9


For the graph, y = 4x
so the price of a sweet bread is $4

9-4 = 5

 the short cake is $5 more than the sweet bread

Answer:

If you look at the pictures the question gives you. 5 shortcakes = 45$

5 sweetbreads = 20$.

So you would divide 45 by 5, which gives u 9

Then you would divide 20 by 5, which gives you 4.

Then after you would subtract 9 by 4, which gives you 5$

So your answer for this question would be 5$.

A. Sigma notation

The formula for finding the nth value of the geometric series is given as:

an = a1 * r^n

Where,

an = nth value of the series

a1 = 1st value in the geometric series = 940

r = common ratio = 1/5

n = nth order

The sigma notation for the sum of this infinite geometric series is therefore,

                     (see attached photo)

B. Sum of the infinite geometric series

The formula for calculating the sum of an infinite geometric series is given as:

S = a1  / (1 – r)

Substituting the given values:

S = 940 / (1 – 1/5)

S = 1,175

To write the equation in point-slope form, plug in the given values of the point and slope into the formula and simplify.

To write an equation in point-slope form for a line, we use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the given point is (8, -3) and the slope is -1/4. Plugging in these values into the formula, we get:

y - (-3) = (-1/4)(x - 8)

Simplifying the equation, we have:

y + 3 = (-1/4)x + 2

Therefore, the equation in point-slope form for the line through the point (8, -3) with slope -1/4 is y + 3 = (-1/4)x + 2.

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The correct answer is X=-3+or-rad33/6

The roots of the quadratic equation 3x^2+3x-2=0 as provided by the quadratic formula are x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6.

The quadratic equation in question is 3x^2+3x-2=0. Here, a=3, b=3, and c=-2. We can solve this equation using the quadratic formula, which, in general terms, is given as: x = [-b ± sqrt(b² - 4ac)] / 2a.

Plugging the coefficients into the quadratic formula, we get:

x = [-3 ± sqrt((3)² - 4*3*(-2))] / 2*3

= [-3 ± sqrt(9 + 24)] / 6

= [-3 ± sqrt(33)] / 6

That gives us two roots: x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6. These are the solutions for the quadratic equation given.

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78 / 3 3/4 =

78/1 / 15/4 =

78/1 x 4 /15 = 312/15 = 20.8

 20 pieces 3 3/4 inches long can be cut

The solution to the system of linear equations graphed is (-2.5, -2). So, the correct answer is option D.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The ordered pair that is a solution to both equations is the system's solution. We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.

In the given graph, the intersection point is (-2.5, -2).

Therefore, option D is the correct answer.

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Answer:

A

Step-by-step explanation:

1) LN=LN reflexive property of congruence

2) KN=MN, given

3) <MLN=<KLN, bisected angles are congruent

4) Triangle MNL=Triangle KNL by the HL theorem

Answer:

The solution is x = 2 or x = 3  

Step-by-step explanation:

we have to find the solution of the equation

[tex] x=2+\sqrt{(x-2)}[/tex]

[tex]x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3[/tex]

Hence, correct option is x = 2 or x = 3

Answer:

C) x = 2 or x = 3

Step-by-step explanation:

Edge 2021

Answer:

Dilation by a scale factor of 2 followed by reflection about the x-axis

Step-by-step explanation:

To answer it and view it properly let's do it by parts.

1) A closer look at the Triangle ABC shows us the coordinate points A(-2,-1) B(0,0) and C(1,-3).

2) Reflection across the x-axis gives us this triangle: A'(-2,1) B'(0,0) and C'(1,3). Notice that all y-coordinates have an opposite sign. This is a natural characteristic of a Reflection: an opposed sign of one Coordinate.

3) Finally, To Dilate a Triangle is to transform it so that it gets bigger than its original size.

If we compare the triangle with points  A''(-4,2) B"(0,0) and C"(2,6) to A'(-2,1) B'(0,0) C'(1,3). Each coordinate is multiplied by 2.

Dilation by a scale factor of 2 followed by reflection about the x-axis

Given the constraints, the total number of ways Mr. Smith can distribute pets to his children is calculated as 216 ways. This involves the concept of combinations and permutations from combinatorics in mathematics.

The problem posed is a typical combinatorics or probability question found in mathematics. Given the constraints, the number of ways Mr. Smith can distribute pets is calculated as follows:

Since these scenarios are independent, we multiply these results. Hence, the total number of ways Mr. Smith can distribute pets to his children is 6 x 6 x 6 = 216.

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Considering the preferences of each child, there are 2160 different possible ways Mr. Smith can distribute the 7 pets to his 7 children.

The question posed is a classic problem of combinatorics. We have Anna, Betty, Charlie, Danny, and three other unnamed children who will be receiving pets. Anna and Betty do not want the goldfish, and Charlie and Danny want only cats. Therefore, options for Anna and Betty include the 4 cats and 2 dogs (6 choices total). For each choice Anna makes, Betty has one less choice (5). We can multiply these together, which will give us 30 possible assignments for Anna and Betty. For Charlie and Danny, who just want cats, there are 4 available. Charlie can have one of 4, then Danny can have one of the remaining 3, yielding 12 possibilities.

With Anna, Betty, Charlie, and Danny assigned pets, there are 3 children and 3 pets (2 dogs and 1 goldfish) remaining. Three children can be given 3 pets in 3! = 3*2*1 = 6 ways.

Finally, multiplying these together gives us 30 * 12 * 6 = 2160 possible ways Mr. Smith can distribute the pets among his children.

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