Form linear equations in two variables using suitable variables for the unknowns.

The perimeter of a rectangle is 98 cm. [Take length as x and breadth as y.]

well, let's take a peek at the graph, hmmm it has a straight line from the origin to (5,10), and then another straight line from (5,10) to (10,5) and then another one from there up to (20,5).

well, let's simply get the equations for each of those lines then

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{0})\implies \boxed{y = 2x} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{5}}} \implies \cfrac{ -5 }{ 5 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-1}(x-\stackrel{x_1}{5}) \\\\\\ y-10=-x+5\implies \boxed{y=-x+15} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{20}-\underset{x_1}{10}}} \implies \cfrac{ 0 }{ 10 }\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{0}(x-\stackrel{x_1}{10})\implies y-5=0\implies \boxed{y=5}[/tex]

so then hmmm let's use those, we know how f(x) is moving now, so

[tex]\stackrel{y}{f(x)}= \begin{cases} 2x&x\geqslant 0\\\\ -x+15&x\leqslant 10\\\\ 5&x\leqslant 20 \end{cases}[/tex]

We need to find out unit price per minute and the unit price is $0.4 per minute.

According to the question we have been given that

                 12 mile taxi rides takes = 18 minutes

                   cost of 12 mile taxi ride = $7.20

Thus we need to find the mile and the cost covered in 33 minutes which will be find out by unitary method.

Thus,

               18 minutes taxi ride will cover = 12 mile

               33 minutes taxi ride will cover = 12/18*33

                                                                 =  22 miles

                  cost of  12 mile taxi ride = $7.20

   then,       cost of 22 miles taxi ride = 7.20/12 * 22

                                                          = $ 13.2

Now we need to find out the unit price which is unit price per minute.

Thus unit price is = $13.2/33

                            = $ 0.4

Hence we need to find out unit price per minute and the unit price is $0.4 per minute.

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0.58 or more than half of sugar is sprinkled by rose on the brownies.

Given,

Rose has 1 3/4 cups of powdered sugar.

1/3 of the sugar sprinkled on lemon cookies

Therefore'

1 3/4 = (4*1+3) / 4

= 7/4

1/3 of the sugar sprinkled on lemon cookies

= 1/3 (7/4)

= 7/12

= 0.58 or more than half of sugar is sprinkled by rose on the brownies.

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Answer: 3

Step-by-step explanation:

A/B

30/10 = 3

(a) True, x is an element of the set {x}

(b) True, the set {x} is a subset of itself.

(c) False, x is an element of {x}, but the set {x} is not an element of {x}.

(d) True, the set {x} is an element of the set {{x}}.

The numbers 1, 2, 3, and 4 are the elements of set A, as indicated by the formula A=1,2,3,4. Subsets of A are collections of components from A, like 1, and 2. Sets may also function as elements.

Consider the set B=1,2,3,4 as an example. B's constituent parts are not 1, 2, 3, or 4. Instead, there are just three components of B: the numbers 1 and 2, as well as the set "3, 4."

A set's components can be anything. For instance, the set "C=red, blue, green" contains the colors red, green, and blue as its constituents.

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Answer:

Step-by-step explanation:

A. L+W= 2 in. x 2 in. = 4 in.

Below are some things to help you with perimeter and area(just type it into whatever browser you use, copy and paste)

https://youtu.be/LoaBd-sPzkU

https://th.bing.com/th/id/OIP.Q5D_8qbK_9XGQLj1s0tpbwHaJ3?w=186&h=248&c=7&r=0&o=5&dpr=1.65&pid=1.7

Answer:

A. 3005

B. 3110

C. 1016.67

Step-by-step explanation:

A. Inital means occuring at the beginning. So the month they got the account, the value is around 3005. Every tick mark on the y-axis represents 30.

B. Like I said, every tick mark represents 30, so on the x-axis, the line between 6 and 8 is 7. go up towards where the line is, and that equals 3110.

C. I really haven't learned about rate of interest yet, but I tried my best to figure it out. I found out that for every month, you get 1016.67 value of interest.

Answer:

[tex] \sf \large \: h = \frac{v}{lw} [/tex]

Step-by-step explanation:

Let's solve for h.

v=lwh

Step 1: Flip the equation.

hlw=v

Step 2: Divide both sides by lw.

hlw/lw = v/lw

h= v/lw

The Cost of jacket before tax is 74.73.

According to the statement

We have to find that the cost of jacket.

So, For this purpose, we know that the

The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.

From the given information:

the sales tax is 6%. The total cost is $79.49.

Then the real cost is :

Real cost = 6% of the $79.49

Then

solve it

tax amount applied on the jacket = 6/100*79.49

tax amount applied on the jacket = 0.06*79.49

tax amount applied on the jacket = 6/100*79.49

tax amount applied on the jacket = 4.76

Then

Cost of jacket before tax = 79.49 -4.76

Cost of jacket before tax = 74.73.

So, The Cost of jacket before tax is 74.73.

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Answer:

b 2 2/9

Step-by-step explanation:

As we know

6×2/3 = {6×3+2}/3

=> 20/3

20/3 is the walk for 3 days

by unitary method

Walk of one day should be

20/3×3

20/9 = 2×2/9 miles per day

Answer:

2 2/9 miles per day

Step-by-step explanation:

If she walked 6 2/3 miles in 3 days, then she walked 1/3 of 6 2/3 miles in 1 days.

We need to find 1/3 of 6 2/3 miles.

1/3 of 6 2/3 =

= 1/3 × 6 2/3

= 1/3 × (6 + 2/3)

= 1/3 × 6 + 1/3 × 2/3

= 2 + 2/9

= 2 2/9

the subsets in this case are:

Remember that for two sets A and B, we say that A is a subset of B if and only if all the elements of A also are elements of B.

In this case, we have 3 sets:

We can rewrite these ones as:

Here we can see that all the elements in C also belong in B and also belong in A, and all the elements in B also belong to A, then the subsets are:

C ⊆ B

C ⊆ A

B ⊆ A

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Answer:

7m-8

Step-by-step explanation:

distribute 4 through the parentheses

4m-8+3m

collect like terms

7m-8

Answer:

7m-8

Step-by-step explanation:

So to simplify this expression, you would need to do distributive property.

4(m-2)

(4*m) + (4*-2)

4m-8+3m

7m-8

So your simplification is 7m-8

Answer:

9 inches

Step-by-step explanation:

To find the volume of a cube, you could cube the side length, simplified as x³.

x³ = 729

x = 9

9 inches

Hope this helps! :)

The number of green beads left over = 15

Walter:

Number of green beads = 476

Number of red beads = 32

Agnes:

Number of green beads = 104

Number of red beads = 16

Holly:

Number of green beads = 281

Number of red beads = 80

Total number of red beads = 32+16+80 = 128 beads

Number of red beads required for making one lizard = 16

Since 128/16 = 8 , there will be no red beads left after making 8 lizards.

Total number of green beads = 476+104+281 = 861 beads

Number of green beads required for making one lizard = 94

Now 861/94 = [tex]9\frac{15}{94}[/tex]

That is , 15 is the remainder when 861 is divided by 94

So there will be 15 green beads left after making 9 lizards.

Therefore, the number of green beads left over = 15

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Dave and Tanvir each think of a number, where Dave's number is larger,

The difference between their numbers is 5. Dave's number plus twice Tanvir's number is 26. By forming simultaneous equations, determine each bloke's number. The numbers are 12 and 7.

The number of Dave is 12 and the number of Tanvir is 7.

Given that

Dave and Tanvir each think of a number, where Dave's number is larger.

The difference between their numbers is 5.

Dave's number plus twice Tanvir's number is 26.

To find

By forming simultaneous equations, determine each bloke's number.

So, according to the question

Let's assume that numbers are x and y.

So, we can say that

      x - y = 5 ------------(1)  and

   x + 2y = 26 ------------(2)

We have to solve that equations by using forming simultaneous equations.

For forming simultaneous equations, we have multiply equation(1) by 2, then add eq(2) with result.

So, we will get

      2x - 2y = 10

  (+)  x + 2y = 26

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

       3x +0 = 36

            3x = 36

             x = 36/3

            x = 12

Putting the value of x in equation (1),

We will get,

        x - y = 5 ------------(1)

        12 - y = 5

            - y = 5 - 12

            - y = -7

              y = 7

The numbers are 12 and 7.

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Equations for the set of the plane through the point [tex](x_0,y_0,z_0)[/tex] and parallel to:

a. xy-plane is [tex]z=z_0[/tex]   b. yz-plane is [tex]x=x_0[/tex] c. xz-plane is [tex]y=y_0[/tex]

The given set is the plane through the point  [tex](x_0,y_0,z_0)[/tex] parallel to:

a. xy-plane   b. yz-plane  c. xz-plane

Equation of the plane parallel to a plane containing a vector [tex]\vec r[/tex] through the point [tex](x_0,y_0,z_0)[/tex] is [tex](\vec r-(x_0,y_0,z_0)) .\vec n=0[/tex] ,where [tex]\vec n[/tex] is the normal to the plane and [tex]\vec r =x\vec i +y\vec j +z\vec k[/tex].

a. Plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to the xy-plane is,

    [tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec k[/tex] = 0

⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec k=0[/tex]

⇒ [tex]z-z_0 =0[/tex]

⇒ [tex]z=z_0[/tex] is the equation of the plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to xy-plane.

b. Plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to the yz-plane is,

    [tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec i[/tex] = 0

⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec i=0[/tex]

⇒ [tex]x-x_0 =0[/tex]

⇒ [tex]x=x_0[/tex] is the equation of the plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to yz-plane.

c.  Plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to the xz-plane is,

    [tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec j[/tex] = 0

⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec j=0[/tex]

⇒ [tex]y-y_0 =0[/tex]

⇒ [tex]y=y_0[/tex] is the equation of the plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to xz-plane.

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The expression for the total number of miles Pablo drove in the two weeks is (115+k) miles.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given that Last week, Pablo drove 115 miles. This week, he drove k miles. Therefore, the total number of miles for which Pablo drove can be written as,

Total number of miles = Number of miles last week + Number of miles this week

                                    = 115 miles + k miles

                                    = (115 + k) miles

Hence, the expression for the total number of miles Pablo drove in the two weeks is (115+k) miles.

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Answer:

236

See the picture below for the work.

Step-by-step explanation:

The area of the rectangle as a function of its width is  a=3b-2.

[tex]s=(3b-2)b\\=3b^{2}-2b[/tex]

[tex]a=3b-2[/tex]

What is the advantages of area ?

Area is significant in contemporary mathematics. Aside from its obvious significance in geometry and calculus, area is also a fundamental characteristic of surfaces in differential geometry and is connected to the definition of determinants in linear algebra. The amount of space within a form is measured by its area.

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If [tex]X,Y[/tex] are independent, we have the properties for expectation and variance,

[tex]\Bbb E[aX + bY] = a\,\Bbb E[X] + b\,\Bbb E[Y][/tex]

[tex]\Bbb V[aX + bY] = a^2\,\Bbb V[X] + b^2\,\Bbb V[Y][/tex]

where [tex]a,b\in\Bbb R[/tex] are fixed.

Then

[tex]\Bbb E[R - S] = \Bbb E[R] - \Bbb E[S] = 10 - 7 = \boxed{3}[/tex]

and

[tex]\Bbb V[R - S] = \Bbb V[R] + (-1)^2\, \Bbb V[S] = 4^2 + 3^2 = \boxed{5}\,{}^2 = 25[/tex]

(recall that standard deviation = √(variance))

Answer: a. 21 terms

b. 798

Step-by-step explanation:

a. 68-8=60 ==> difference between 1st and last term

60/3=20 ==> number of terms after the first term

20+1=21 terms ==> total number of terms

b. Find the mean of the terms first:

(68+8)/2=    ==> the mean of all terms in a sequence is equal to the mean of the first and last term

76/2=38

38*21=798   ==> add the mean 21 times to get the total sum since there are 21 terms in the sequence.

Answer:

y is about equal to -4.692

Step-by-step explanation:

The algebraic properties used in the steps are the distribution property, the associative property, the identity property, and the distribution property

The first step in the equation is given as:

t + 5(t + 1) = t + (5t + 5)

The distribution property states that

a(b + c) = ab + ac

So, the property used in t + 5(t + 1) = t + (5t + 5) is the distribution property

Next, we have:

t + 5(t + 1) = (t + 5t) + 5

The associative property states that

a + (b + c) = (a + b) + c

So, the property used in t + 5(t + 1) = (t + 5t) + 5 is the associative property

Next, we have:

t + 5(t + 1) = (1t + 5t) + 5

The identity property states that

a * 1  = a

So, the property used in t + 5(t + 1) = (1t + 5t) + 5 is the identity property

Next, we have:

t + 5(t + 1) = (1 + 5)t + 5

The distribution property states that

a(b + c) = ab + ac

So, the property used in t + 5(t + 1) = (1 + 5)t + 5 is the distribution property

Lastly, we have the solution

(6t + 5)

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If a cartoon of 2 dozen eggs includes 3 with cracks, then the number of eggs without cracks in 6 dozen eggs can be expected to be 63.

A dozen abbreviated as doz is a batch of 12. So in this situation, one dozen refers to 12 eggs. Therefore the number of eggs in 2 dozen will be equal to,

1 dozen = 12 eggs

2 dozen = 12x2= 24 eggs.

Therefore, a cartoon of 24 eggs includes 3 with cracks.

Similarly, 6 dozen is equal to,

1 dozen = 12 eggs

6 dozen = 12 x 6 = 72 eggs

We can determine the number of eggs with cracks by using an algebraic expression,

24 eggs include 3 eggs with cracks

72 eggs include: x eggs with cracks

x = 72×3 ÷ 24

x = 216 ÷  24 = 9 eggs with cracks.

Therefore the number of eggs without cracks can be calculated by the subtraction of total eggs from the eggs with cracks.

Eggs without cracks= 72 - 9 = 63 eggs.

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Answer: 0.29

Step-by-step explanation:

= 0.288

8>5

= 0.29

19 miles the average number of miles Lori ran.

Miles Lori ran on Monday = 5 ½ = 11/2

Miles Lori ran on Tuesday = 6 ¼  = 25/4

Miles Lori ran on Wednesday = 4½ = 9/2

Miles Lori ran on Thursday = 2¾ = 11/4

Total miles she ran = sum of 4 days runs

= 11/2 + 25/4 + 9/2 + 11/4

= 22/4 + 25/4  + 18/4 + 11/4

= [tex]\frac{22 +25+18+11}{4}[/tex]

= 76/4 miles or 19 miles

By combining a set of integers and then dividing by their count, the average number—also known as the arithmetic mean—is created. For instance, the sum of 2, 3, 3, 5, 7, and 10 is equal to 30 divided by 6, which equals 5.

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Answer:

If you want it graphed the answer is

andb=7

The formula wights are

mass of  1 1  mole of  9 a − a b + 5 b i f a = 2 = 0 g

Step-by-step explanation:

Number of boys = a - b

Number of children in the class = a

Number of girls in the class = b

Number of boys = Total - Girls

                              a - b