Please help with problem 10

The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + y = -6     (equation 1)

2x - y = 3     (equation 2)

Express y in terms of x in one of the equations,

x + y = -6     (equation 1)

y = -x - 6

and then substitute it in the 2nd equation.

2x - y = 3     (equation 2)

2x - (-x - 6) = 3

2x + x + 6 = 3

3x = 3 - 6

3x = -3

x = -1

Substituting the value of x in the equation of y,

y = -x - 6

y = -(-1) - 6

y = 1 - 6

y = -5

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The rate of change will be 0.074 grams per year.

The change in hydrocarbon will be:

= 3.4 - 0.8

= 2.6

The number of years will be:

= 2007 - 1972

= 35

Therefore, the rate will be:

= Change in hydrocarbon / Years

= 2.6 / 35

= 0.074 grams per year.

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There are 715 ways to select 9 players for the starting lineup.

Permutation is used whenever there is arrangement or where order is important . denoted by [tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]

n= no of item  , r = no of items to be arranged.

Combination is used when there is selection . denoted by[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

n=no of item  , r= no of item to be selected.

Part (a)

In the given question

we have to select 9 players out of 13 player , combination will be used

[tex]C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}[/tex]=715 ways.

Part(b)

In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.

Since the batting order is important , permutation will be used.

[tex]P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5[/tex]

=259459200 ways.

Part(c)

In this part we have to do selection of  3 left-handed outfielders and have all other 6 positions occupied by right-handed players.

Since order is not important Combination  will be used.

To select 3 left handers from total 6 left handers = C(6,3)

& to select 6 positions of left handers from remaining 7 right handers=C(7,6)

No of ways of selection = C(6,3)*C(7,6)

[tex]=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\[/tex]

On solving further we get

[tex]= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways[/tex]

Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.

(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .

(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.

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The first step is to move -x to RHS and second step is to solve to get the value of x. The solutions will be x = -2 , 0 , 2.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , subtraction , division , etc.

The equation given is [tex]4x^{1/3}[/tex]- x = 0

We need to solve it stepwise.

The first step will be to to move -x to RHS.

[tex]4x^{1/3}[/tex]- x = 0

or

[tex]4x^{1/3}[/tex] = x

The second step is to solve to get the values of x.

4x = x³

4x - x³ = 0

x (4 - x²) = 0

So , this will give us two equations which are ,

x = 0

and

4 - x² = 0

or

x² = 4

x = ± 2

So , solving the equation for x initially yields two equations which are x = 0 and 4 - x² = 0 and the solution we get is x = 0 , 2 , - 2.

Thus , the solutions will be x = -2, 0, 2.

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Step-by-step explanation:

In this exercise we have to use the knowledge of quadrilaterals to calculate the measures of each side of the square, in this way we can say that it will be valid:

Given in the exercise that each the value of:

WT=3

The diagonals  of a square are congruent, and bisect each other, that will help to find:

As the degrees of freedom (DF) increase, the t distribution approaches the normal distribution. Therefore, the correct answer option is: C. normal distribution.

The degrees of freedom (DF) in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses because they are the maximum number of logically independent numerical values (data points) in the final calculation of a statistical problem.

A normal distribution is sometimes referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data that are far from the mean.

In this context, we can reasonably infer and logically deduce that the t-distribution generally approaches the normal distribution as the degrees of freedom (DF) increase.

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Using compound interest, it is found that the annual rate of increase was of 3.10%.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are given as follows:

t = 9, A(t) = 6, A(0) = 4.5, n = 12.

Hence we solve for r to find the interest rate as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]6 = 4.5\left(1 + \frac{r}{12}\right)^{12 \times 9}[/tex]

[tex]1 + \frac{r}{12}\right)^{108} = 1.33[/tex]

[tex]\sqrt[108]{1 + \frac{r}{12}\right)^{108}} = \sqrt[108]{1.33}[/tex]

[tex]1 + \frac{r}{12} = (1.33)^{\frac{1}{108}}[/tex]

1 + r/12 = 1.0026.

r/12 = 0.0026

r = 12 x 0.0026

r = 0.031.

The annual rate of increase was of 3.10%.

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Answer: (Likely) y = -2x

Step-by-step explanation:

1. We know the line y = 2x + 4, it intersects 4 and it's rate of change is 2. We also know the point it is passing, (-4,-1).

2. With this info, It is best to confirm the slope is likely -2, since it is likely that lines when perpendicular are likely to be congruent.

3. So, how about the y intercept? Well, it's simple as well, we will substitute x for 0, and 2 times 0 equals 0, and y = 0, so the perpendicular line is y = -2x

Answer:

9.5>6      41.8>0

Step-by-step explanation:

Answer: Hope it helps!!

I believe it is B. as well

Desmos Graphing calculator is great for problems as well!

Answer:y=-3, x=6

Step-by-step explanation:

Answer:

x=6 y=-3

Step-by-step explanation:

Answer:

No solution the lines are parallel

Step-by-step explanation:

see picture for reference.

∠1 and ∠2 will have the values 33° and 147° respectively when they form a Linear Pair.

In the question, It is given that ∠1 and ∠2 form a Linear Pair.

So, ∠1 and ∠2 = 180°, Also it is stated that ∠1 is 18° lesser than 5 times ∠2.

Taking ∠2 = x we get ∠1 = 5x-18

Now for Linear Pair, we have ∠1 + ∠2 = 180°

putting values of ∠1 and ∠2  we get :  (5x-18) + x = 180

Solving the equation  => (5x-18) + x = 180   =>   6x = 198

=>  x = 33

Putting the value of x in both ∠1 and ∠2  we get :

∠2 = 33°  and ∠1  = 5(33) - 18 =>  ∠1  = 147°

Hence, we get ∠1 and ∠2  measures 147° and 33° respectively.

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The height to the top of the nth story of the building is  ( 24 + 18(n-1) ).

Height of first story of a building = 24 feet

Height of each additional story = 18 feet

Total number of stories in a building = n

The Height of first story of a building is fixed to be 24 feet and Height of each additional story is 18 feet. We first need to calculate total number of additional stories to write an equation.

The total number of additional stories =  ( total number of stories in a building - 1) = (n-1)

The height of total additional stories = 18 (n-1)

Total height of the building = (Height of first story of a building + height of total additional stories) = ( 24 + 18(n-1) ).

The height to the top of the nth story of the building is  ( 24 + 18(n-1) ).

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If he makes the cubes as large as possible, the maximum number of cubes is equal to 900 cubes.

In order to determine the number of cubes that would be produced by Richard when the rectangular prism is cut into congruent cubes without any part of the rectangular prism leftover, we would make the edges of the cube 100 times larger and then evaluate:

Note: The greatest common factor (GCF) of the dimensions above is 75.

Next, we would divide each of the dimension by 75:

Length of cube = = 450/75 = 6 feet.

Breadth of cube = 750/75 = 10 feet.

Height of cube = 1125/75 = 15 feet.

Therefore, the maximum number of cubes is given by:

Maximum number of cubes = 6 × 10 × 15

Maximum number of cubes = 900 cubes.

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Complete Question:

Richard cuts a 4 1/2 ft × 7 1/2 ft × 11 1/4 ft rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?

The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.

In this question we have a geometric system generated by three lines, where two lines pass through the first lines and four angles are generated on each intersection. The measures of the missing angles can be found by the following concepts:

The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.

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Answer: The first one is correct.

Step-by-step explanation:

x = 3
y = -2
So: 2 x 3 + 2 x (-2) = 6 + (-12) = -6

Answer:

adding them together, x+2x−6=180 . this can be solved algebraically. the smaller angle is 62∘ . the supplement to that, 2x−6 , is (124−6)∘ , which is 118∘ .

Answer:

I think it’s (4,1)

The table shows relationship between the number of targets a person

hits in a game of laser tag and that score of that person. The table shows is a continuous graph.

As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil. In calculus, learning about a function's continuity is crucial since without it, a function cannot be differentiated.

If a function's graph is a continuous curve without any holes, gaps, or breaks, it is said to be continuous.

Now,

x-axis on the graph show "Target hit" and y-axis shows "Score"

Graph the points using a graphing calculator.

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The complete question is:

"The table shows the relationship between the number of targets a person

hits in a game of laser tag and that person's score.

Target hit  0   1    2     3     4     5    6

Score        0   8   16  24   32   40   48"

Answer:

b , d

Step-by-step explanation:

Answer:

Step-by-step explanation:

function notation

1) -13

2) -4

3) 7

4) 23

5) 13

6) -4

7) 14

8) -1

9) 15

10) 0

function operations

1) -3x^2 + 11x -4

2) 6x - 12

3) 3x^2 - 2x + 5

4) x^2 - 4x + 5

5) 27x^2 - 32x

6) 2x^5 + 4x^4 - 5x^3 - 10x^2

7) -6x^4 + 8x^3 + 15x^2 - 20x

8) 3x^4 - 2x^3 - 16x^2

[tex]f(x) = (3 {x}^{4} + 1) {}^{2} \\ f(x) = 0 \\ (3 {x}^{4} + 1) {}^{2} = 0 \\ 3x {}^{4} + 1 = 0 \\ 3x {}^{4} = -1 \\ x {}^{4} = \frac{ - 1}{3} [/tex]

[tex]f(x) \: admits \: no \: real \: roots[/tex]

Based on the calculations, the sample standard deviation is equal to 4.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

[tex]Z=\frac{\bar x\;-\;u}{\delta}[/tex]

Where:

In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:

Note: Variance, δ² = 16

Taking the square root of the variance, we have:

Standard deviation, δ = √16

Standard deviation, δ = 4.

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Complete Question:

A sample of n=225 scores has [tex]\bar x[/tex] = 103 and δ² = 16. What is the sample standard deviation?

The quotient of the problem given are 49/12, -1/25, -20 and 13/10 respectively

These are the simple problems of fractions

A) 7/12 ÷ 1/7

   7/12×7/1

    49/12

B) -0.05 ÷(5/8 ÷ 1/2)

 - 5/100 ÷ ( 5/8 ×2/1)

  -5/100÷ (5/4)

  -5/100 ×4/5

   -1/25

C) 6 1/4 ÷(-5/16)

   25/4 × (-16/5)

  -20

D) -1 ÷(-10/13)

   -1 ×(-13/10)

    13/10

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Answer: Total cost for the two services of hours = $6.

Step-by-step explanation:

Given data,

Nate is looking for a repair service for general household maintenance.

First service charges = $75

First service charge per hour = $30 per hour

Another service charges = $15

Another service charge per hour = $40 per hour

Total cost of hours of service is = x

So,

We can write,

                          75 + 30x = 15 + 40x

Rearrange variables to the left side of the equation,

                          30x - 40x = 15 - 75

Combine like terms,

                                  -10x = 15 - 75

Calculate the sum or difference,

                                    -10x = -60

Divide both sides of the equation by the coefficient variable,

                                      x = -60/-10

Determine the sign for multiplication or division,

                                      x = 60/10

Cross out the common factor,

                                       x = 6

Therefore,

Total cost for the two services of hours = $6.

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Answer:

Step-by-step explanation:

2 pounds / 5 people

x pounds / 13 people

2/5 pounds per person so 2/5 * 13 = 26/5

5 1/5 i think

sorry if its wrong

Answer: The answer of the question is 2 and 3/5.

Step-by-step explanation: Every pound of meat serves one person, because 10 divided by 2 people is 5. Then, there are 3 pieces of meat left over, and since every person eats 5/5, or 1 whole, then there are 3/5 pieces left over. You then add 2 and 3/5 together, getting your answer 2 3/5.

Answer:

18,6,2

Step-by-step explanation:

To get from the first term to the second term we divide by 3 .

To get from the second term to the third term we divide by 3 .

So we continue this pattern to find the next 3 terms :

So 54 ÷ 3 = 18

18 ÷ 3 = 6

6 ÷ 3 = 2

Hope this helped and have a good day

Answer:

9/16

Step-by-step explanation: