9. The sum of two numbers is 130 and their difference is 34. Let x be the first number and y be the second
number. Set up a system of equations and use the elimination method to find the numbers. You must
show your work.

One bag of cat food costs $6 and one bag of dog food costs $9.

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.

Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.

Therefore, the equation becomes,

6c + 9d = 117         ..(1)

This week she paid $87 for 4 bags of cat food and 7 bags of dog food.

Therefore, the equation becomes,

4c + 7d = 87         ..(2)

Now to solve the system of equations

To solve the first equation for c.

6c + 9d = 117

6c = 117 - 9d

[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]

Plug value of c in equation (2).

[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]

Plug d = 9 in equation (1)

6c + 9(d) = 117

6c + 9(9) = 117

6c + 81 = 117

6c = 117 - 81

6c = 36

c = 6

Hence, one bag of cat food costs $6 and one bag of dog food costs $9.

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The equation of the line that passes through (3, 1) and (1,2) in slope intercept form is y = - 2 / 2 x + 5 / 2.

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Therefore, let's write the equation of a line that passes through (3, 1) and (1, 2).

using slope intercept form,

y = mx + b

where

Therefore, let's find slope

m = 2 - 1 / 1 - 3

m = 1 / - 2

m = - 1 / 2

Let's find y-intercept using (1, 2)

2 = - 1 / 2(1) + b

b = 2 + 1 / 2

b = 5 / 2

Therefore, the equation is y = - 2 / 2 x + 5 / 2

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The area of given figure is 93mm².

Answer: 0.5

Step-by-step explanation:

1.45*0.34 = 0.493

Rounded to the tenth place is 0.5

The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).

How to determine the midpoint of the line joining two points (a,b) and (p,q)?

To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.

To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.

so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.

Hence ans will be ,(-5/2,-11/2)

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The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways

The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:

nCr = n!/(r!(n - r)!)

The total number of cards that we have in a deck of cards = 52.

There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways

After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).

Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:

Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card

Plugging in the relevant values gives;

Number of ways = (13 × 6) × 48 × 44 × 40

= 6,589,440 ways

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Answer:

13.9375

Step-by-step explanation:

this is your answer 1234

The expression without the summation notation is Sₙ = 4(n² - 1)/n²

Summation notation is used to write a very long sum (of elements) in a very concise manner. It is also called Sigma notation

Given:

[tex]\displaystyle \sum\limits_{i = 1}^n \frac{12k(k-1)}{n^{3} }[/tex]

Below are the useful summation formulas you will need in order to rewrite the expression without the summation notation:

[tex]\displaystyle \sum\limits_{i = 1}^n i = \frac{{n\left( {n + 1} \right)}}{2}[/tex]

[tex]\displaystyle \sum\limits_{i = 1}^n {{i^2}} = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}[/tex]

Where i is a variable

Since 12 and n are constants, we can rewrite the given equation as follows:

[tex]\displaystyle \sum\limits_{i = 1}^n \frac{12k(k-1)}{n^{3} } = \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n k(k-1)[/tex]

                       [tex]= \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n k(k-1)[/tex]

                     [tex]= \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n (k^{2}-k)[/tex]

                    [tex]= \displaystyle \frac{12}{n^{3} } ( \displaystyle\sum\limits_{i = 1}^n k^{2} - \displaystyle\sum\limits_{i = 1}^n k )[/tex]

Using the formula, we have:

                   = 12/n³ ( n(n+1)(2n+1)/6 - n(n+1)/2 )      Factorise n(n+1) out

                   = 12n(n+1)/n³ ( (2n+1)/6 - 1/2 )

                   = 12(n+1)/n² ( (2n+1-3)/2 )

                   = 12(n+1)/n² ( (2n-2/6) )

                   = 2(n+1)/n² (2n-2)

                  =  ( (2n+2)(2n-2) )/n²

                 = (4n² - 4)/n²

                 = 4(n² - 1)/n²

Therefore, using summation formulas to rewrite the expression without the summation notation gives Sₙ = 4(n² - 1)/n²

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Answer:

45

Step-by-step explanation:

the pattern adds 3 if you look at it care fully

The value of the variables in the right triangle are as follows;

A right triangle is a triangle that has one of its angles as 90 degrees.

The side of a right triangle can be found by using trigonometric ratios.

Therefore, let's find the variable length of the right triangle as follows;

sin 30 = opposite / hypotenuse

sin 30 = v / 3√2

1 / 2 = v / 3√2

cross multiply

3√2 = 2v

divide both sides by 2

v = 3√2 / 2

Let's find the variable w.

cos 30 = adjacent  / hypotenuse

cos 30 = w  / 3√2

√3 / 2 = w  / 3√2

cross multiply

√3 × 3√2 = 2w

3√6 = 2w

divide both sides by 2

w = 3√6 / 2

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The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = [tex]96t - 16t^{2}[/tex]

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]

⇒ [tex]t = 3[/tex]

So, time taken to reach its max height is 3 seconds.

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The answer to the questions from 4 through 12 are below:

4. z³ + 5z + 3z² + 1 - 4 - 2z²

= z³ + 5z² + 5z + - 3

5. Perimeter of the square = Addition of all the sides

= (2d - 3) + (3c) + (2d - 3) + (3c)

= 2d - 3 + 3c + 2d - 3 + 3c

= 4d + 6c - 6

6. Perimeter of the triangle = Addition of all the sides

= (4a - 2b) + (9a - 4) + (7a + 3)

= 4a - 2b + 9a - 4 + 7a + 3

= 20a - 2b - 1

7. Perimeter of a square = 4 × side length

= 4 × 10x

= 40x

8. Perimeter of a rectangle = 2(length + width)

= 2{(2x + 7) + (3x + 8y)}

= 2(2x + 7 + 3x + 8y)

= 2(5x + 8y + 7)

= 10x + 16y + 14

Simplify the following

9. 3a + a² + 5(a - 2)

= 3a + a² + 5a - 10

= a² + 8a - 10

10. 8(v + w) + 7(v + 2w)

= 8v + 8w + 7v + 14w

= 15v + 22w

11. 4c² + 6(c + c²) - 2c

= 4c² + 6c + 6c² - 2c

= 10c² + 4c

12. z³ + 5(z + 3) + 4(2 - 2z²)

= z³ + 5z + 15 + 8 - 8z²

= z³ - 8z² + 5z + 23

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Answer:

3 units left 7 units down

Step-by-step explanation:

if the sign is inside the bracket opposite sign

if the sign is outside the bracket leave it as it is

so (x+3)=0 which means x= -3 so 3 units left since it is on x axis. 7 is on y axis and since it is negative so 7 units down.

4.8 × 10^4

There are 284 number of students and 152 number of adults.

Two or more expressions with an Equal sign is called as Equation.

Given,

The ratio of teachers to students on a field trip is 2:13

Let x be the number of adults

If there are 132 more students than adults on the field trip, then 132+x

To find the number of adults and number of students formulate a equation as below

2/13=(x+132)/x

Apply cross multiplication

2x=13(x+132)

Apply distributive law on RHS

2x=13x+1716

11x=1716

Divide both sides by 11

x=152

x+132=152+132=284

Hence there are 284 number of students and 152 number of adults.

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The solution for (18x45) divided by 8 = 101.25

Simplify (18x45) divided by 8

Step 1: Rewrite the equation in mathematical terms

we have:

[tex]\frac{18 x 45}{8}[/tex]= [tex]\frac{810}{8}[/tex]

= 101.25

Therefore, the solution for (18x45) divided by 8 = 101.25

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Answer:

x = √10,-√10

explanation:

5x2 + 1 = 51

you would carry the +1 to the other side making it

5x2=51-1

which is 5x2=50

this equation above can then be turned into

x2=50÷5

which goes on to form the equation

x2=10

this can then be turned into x=the square root of ten

and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer

but yeah I'm not smart or whatever but I hope this helps

not too sure it's correct though

The cost of plastering the rectangle walls at rate of Rs.15/[tex]m^2[/tex] is Rs.5565.

What is rectangle?

  With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.

Given,

Length of room =12m

Breadth of room =10m

Height of room =6m

So, Area of four walls =2(l+b)×h

=>area of four wall=2(12+10)×6=264[tex]m^2[/tex]

Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)

=> area of 2 doors and 3 windows = 13[tex]m^2[/tex]

Area of ceiling =l×b=12×10=120 [tex]m^2[/tex]

Thus, total area for plastering =(264−13+120)= 371[tex]m^2[/tex]

Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.

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Answer:

$12,312

Step-by-step explanation:

$2,052 * 6 = $12,312

Answer:

The Number is -5

Step-by-step explanation:

We will form the Equation and solve for the Number

Let the Number be x

Product of 30 and a Number = 30x

75 less than the Product of 30 and a Number = 30x - 75

75 less than the Product of 30 and a Number is -225

Then 30x - 75 = -225

Now solve for x (the Number)

add 75 for both sides

30x = -225 + 75 = -150

Divide both sides by 30

x = -150 / 30 = -5

Glad to Help

The volume of the crate if there is no extra space in the crate is 36m³.

From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.

In this case, the volume will be:

= Length × Width × Height

= 2 × 1 × 1

= 2m³

Since there are 18 crates, the total volume will be:

= 2m³ × 18

= 36m³

The volume is 36m³.

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Complete question

A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?

Answer: [tex]\frac{3}{5}[/tex]of the class like blue

Step-by-step explanation:

There are : 40 - 12 - 4 = 24 ( students like blue )

[tex]\frac{24}{40}[/tex]= [tex]\frac{3}{5}[/tex]

The age of the three brothers, based on the relationship between the ages of Frankenstein, Pugsley, Gomez, is:

Frankenstein is older than Pugsley and so is not the youngest. Pugsley is not the youngest according to the question so Gomez must be the youngest.

Assuming Gomez's age is x, the relationship between their ages is:

Gomez age + Pugsley age + Frankenstein age = 34
x + x + 5 + x + 8 = 34

3x + 13 = 34

x = (34 - 13) / 3

x = 7 years

Pugsley's age is:

= x + 5

= 7 + 5

= 12 years

Frankenstein's age is:
= x + 8

= 7 + 8

= 15 years

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[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{-1 +2}{2} \implies \cfrac{ 1 }{ 2 }[/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}{(-2)}=\stackrel{m}{ \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{5}) \implies y +2 = \cfrac{1 }{ 2 } ( x -5) \\\\\\ y+2=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }\implies y=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }-2\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 2 }x-\cfrac{9}{2} \end{array}}[/tex]

Answer:

y=1/2x-9/2

Step-by-step explanation:

First you want to find the slope by doing -2-(-1)/5-7

Therefore the slope is 1/2

Next you want to add in any set of points, either (5, -2) or (7, -1)

Substitute the x- point in place of x and the y in place of y in y=1/2x+b

Once you do this you should get -2=1/2(5)+b

You should get -2=2 1/2+b

Then subtract 2 1/2 from -2

You should get -4 1/2

Once you have the slope and y- intercept you can put together your problem

y=1/2x-4 1/2

don't forget to convert, y=1/2x-9/2

Hope this helps  

If a man is 6 feet 2 inches tall, his z-score is equal to 1.82.

If a woman is 5 feet 10 inches tall, her z-score is equal to 2.92.

The 5 feet 10 inches American woman is relatively taller.

In a normal distribution, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Next, we would convert the height in feet to inches as follows:

American man = 6 × 12 + 2 = 74 inches.

American woman = 5 × 12 + 10 = 70 inches.

For the American man's z-score, we have:

Z-score = (74 - 69.2)/2.64

Z-score = 4.8/2.64

Z-score = 1.82

For the American woman's z-score, we have:

Z-score = (70 - 64.2)/2.53

Z-score = 5.8/2.53

Z-score = 2.92

Therefore, the 5 feet 10 inches American woman is relatively taller because she has a higher z-score (2.92 > 1.82).

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Complete Question:

The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.53 inches.

a) If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)?

b) If a woman is 5 feet 10 inches tall, what is her z-score (to two decimal places)?

c) Who is relatively taller?

The 6 feet 2 inches American man

The 5 feet 10 inches American woman

The statements about lines that is true are

A. Line 11y = 55 is vertical.

C. For both lines, all points on the line have an x and a y-coordinate.

D. For either line, one of the coordinates of all of the points is always the same value.

Lines given to us are

1. 7x = -21

x = -3

2. 11y = 55

y = 5

Now let us check the statements.

A. Line 11y = 55 is vertical.

Yes, it is absolutely true as y = 5 will be a straight vertical line from origin of the graph (0 , 0) to (0 , 5)

B. Line 7x= -21 is vertical.

No, this statement is not true as this will be a horizontal line from (0 , 0) to (-3 , 0)

C. For both lines, all points on the line have an x- and a y-coordinate.

Yes, for both the lines there will be both x and y coordinate as every point on graph has x and y coordinates to represent them.

D. For either line, one of the coordinates of all of the points is always the same value.

Yes, this statement is true as for first line x coordinate is a constant value of 0 and for second line y is a constant value of 0.

Therefore the statements about lines that is true are A, C and D.

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Trey, Raina, and Deandre have $21,$31, and $93 in their wallets respectively.

From the question the sum of the money in their wallets is:

Raina  +  Trey +Deandre=$145

      R   +    T    +       D      =$145................(i)

Raina has $10 more than Trey= ($10 + T)

Deandre has 3 times more Raina =3($10 + T)

substituting the values of Raina and Deandre in Eqn (i) we have

R   +    T    +       D      =$145

($10 + T) +  T  +{3$(10 + T)}=$145

$10 +T   +T+  $30   + 3T    =$145

                     5T   +$40    =  $145

                                5T   =   $145   -  $40

                                 5T     =    $105

                                    T      = $105/5

                                     T     =   $21

i.e  Trey   =  $21

Raina has $10 more than Trey= ($10 + T)

i.e                                               = ($10 + $21)    

                                      Raina  =$31    

Deandre has 3 times more Raina =3($10 + T)

                                                        =3($10 + $21)

                                                        =$30   +$63

                                       Deandre  =$93

Therefore the total sum of money in thier wallet is:

        Raina  +  Trey +Deandre=$145

             $31  + $21   +  $93=    $145

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Answer:

a. 17 - 2 × 3 - 8 = 3

b. 33 ÷ 3 - 2 × 5 = 1

Step-by-step explanation:

a. 17 - 2 × 3 - 8 = 3

b. 33 ÷ 3 - 2 × 5 = 1

y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The given equation is y = -4(x - 3)² + 6.

We need to write this equation as standard form of parabola.

the equation of a parabola in  standard form is.

y=ax² +bx+c

The given equation should be expanded y = -4(x - 3)² + 6.

y = -4(x²+9-6x)+6

Now apply distributive property

y = -4x²-36+24x+6

y = -4x²+24x+6-36

y = -4x²+24x-30

Hence y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

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