Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or
simplified fractions.
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1

Answer: 8÷2 or 8/2 and also just in case, the answer is 4

Step-by-step explanation: Ok, 8 markers split equally between 2 students, this means that for each marker that student one takes, student two also takes one. they repeat this until there are no more markers left. This ends up with the two students each having four markers. Now, what is 8 divided by 2? Why yes, the answer is 4, just like the word problems answer. So the word problem "Two students share 8 markers equally" translates to 8÷2.

Hope this helps!

These lines y = 12x + 1 and y = 2x + 4 intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given are two equations y = 12x + 1 and y = 2x + 4.

Now by graphing we conclude that these lines intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.

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The simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

What is a radical expression?

An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.

We have,

k² = 17

The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.

[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]

[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]

[tex]k= 17^{\frac{1}{2} }[/tex]

[tex]k = -17^{\frac{1}{2} }[/tex]

Hence, the simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

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Answer:

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

Step-by-step explanation:

Knowing the x-intercepts, we can set up the equation:

y = (x + 4)(x - 3)

However, we are unaware of whether there is a dilation applied to it, so we input a point on the parabola. "a = dilation"

-12 = a(2 + 4)(2 - 3)

-12 = a(6)(-1)

-12 = -6a

2 = a

Now, we can write the equation for the parabola:

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

Answer:

It looks just fine! Well done!

It looks just fine! Well done!A bit more simply,

It looks just fine! Well done!A bit more simply,(A+C)(AD+AD)+AC+C=(A+C)AD+AC+C=AAD+CAD+AC+C=AD+(AD+A+1)C=AD+C

Step-by-step explanation:

Hope this helped

In given order puzzle Aya's bag is the heaviest bag .

What is order puzzle?

 A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.

Here the given statements ,

=> Alex bag > Hisham bag

And Hisham bag < Aya bag and Irene bag

Now ,

=> Aya bag > Alex bag and Irene bag

Then combine the given ,

=> Aya bag> Alex bag>Irene bag>Hisham bag.

Therefore Aya's bag is the heaviest bag.

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The difference in the cost of all 30 pens between two shops is,

£1.05

Given, Eve is going to buy 30 pens from either shop A or shop B.

Shop A: pack of 10 pens for £2

Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.

So, the cost of 30 pens from the shop A is,

as, a pack of 10 pens is of £2

1 pen = 2/10

30 pens = £6

Now, the cost of 30 pens from the shop B is,

as, a pack of 5 for £1.10

1 pen = 1.10/5 = £0.22

also buy 1 and get 1 at half price.

So, 2 pens = 0.22 + 0.11 = £0.33

Therefore, 30 pens = £4.95

So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.

Hence, the difference in the cost of all 30 pens between two shops is,

£1.05

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When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.

For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.

I hope this helps!

The standard score (z-score) of the given sample is -20.

Given,

[tex]u[/tex] = 35

[tex]o[/tex] = 9

n = 60

x = 32

To calculate standard score (z-score) use formula,

[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]

Thus, the standard score(z-score) of given sample mean is -20.

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Answer:

  28 mph

Step-by-step explanation:

Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.

The speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.

  7/9 × 36 mph = 28 mph

The speed of the car is 28 mph for the 9-hour trip.

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In the given equation we get the following values:

M = 2

C = 5

Given, we have the equation:

Y = 2x + 5

we are asked to determine the following values of m and c.

The given equation is in the form of slope intercept form.

slope intercept form is given as:

y = mx+c

hence :

M = 2 and

C = 5

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:

hence we get the required values.

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Check the picture below.

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{16}}\implies cos(\theta )=\cfrac{1}{4}\implies \theta =cos^{-1}\left( \cfrac{1}{4} \right)\implies \theta \approx 75.5^o[/tex]

Make sure your calculator is in Degree mode.

The slope equation form is :

m = - 7/5

Slope Solution

To calculate the slope use the slope formula.

m = (y2- y1)/(x2- x1)

Where (x1,y1) and (x2,y2) are 2 coordinate points.

Here the 2 points are (0,-3) and (-5,4)

let (x1,y1) = (0,-3) and (x2,y2) = (-5,4)

m = (4 - (-3))/((-5) - 0)

m = 7/((-5) )

m = - 7/5

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If a 40-foot rope is cut into 2 pieces.  the length of the longer rope piece x  is 23ft.

Seven less than 4 times = 4x-7

4x-7=5(40-x)

4x-7=200-5x

Collect like terms

9x=207

Divide both side by 9x

x = 207 /9

x=23 ft  (longer part of the rope)

Shorter part of the rope

40-x where x is 23

40 -23

= 17ft

Therefore the longer part is 23ft.

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Answer:

6x + 3y

Step-by-step explanation:

=3x + (3)(x) + (3)(y)

=3x + 3x + 3y

=3x + 3x +3y

=(3x + 3x) + (3y)

=6x + 3y

Answer:

I do not see the choices.  There could be more than one right answer

6x + 3y

Step-by-step explanation:

3x + 3(x+y)

3x + 3x + 3y

6x + 3y

The expressions which have only one constant are:

A. 18+5r³

B. 90(h-4)

Given: we have a set of equations.

an equation is  a combination of variables and constants.

In the given set of equations we have a single variable with a single constant.

those are:

→ 18+5r³

→  90(h-4)

In the other equations we don't have constants.

A constant is defined as an object whose value is fixed regardless of changes in its usage.

Even after the expression is changed, these values stay the same.

Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.

A variable is a thing whose value changes depending on how it's used and isn't fixed.

Hence we get the required answer.

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Answer:

Step-by-step explanation:

a.

f(d)=11(1.01^d

d=6.97 days

b.

t

f(c) represents the size of algae after c days

c.

f(2)=11(1.01)^2

f(7)=11(1.01)^7

[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]

Using the multiplication, 192 unique keys will result from the distribution.

In the given question we have to find the number of unique keys will result from the distribution.

As given that a package contains 12 electrical locks, each with a unique key.  A package is delivered to 16 job site superintendents.

So 1 package have 12 electrical locks with a unique key.

Package delivered to 16 job site.

We can find the total number of unique keys y multiplying the total number of electrical locks with a unique key in a pckage to the total number of site of package delivery.

So total keys=12×16

Total keys=192

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Answer:

162

Step-by-step explanation:

12²+6² ÷ 2

= 144 + 36 ÷ 2

= 144 + 18

= 162

The correct statement will be  "Neither ordered pair is a solution".

What are ordered pairs?

Given equation is:  6x = 14

For ordered pair (-9, 3) ,  the values of x=-9 and y=3

Plugging these values into the given equation

6(-9) = 14

-54 = 14 (False)

Now for ordered pair (2, -4) ,  the values of x=2 and y=-4

Plugging these values into the given equation

6(2) = 14

12 = 14 (False)

The correct statement will be  "Neither ordered pair is a solution".

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The values of the variables a, b and c are; a = 5/19, b = -160/19, c = 960/19

We are given the quadratic function formula as;

p(t) = at² + bt + c

Thus, the equation is now;

p(t) = at² + bt + 0

p(t) = at² + bt

From the graph, we see that when x = 8, y = 0. Thus;

p(8) = a(8²) + 8b + c = 0

64a + 8b + c = 0   ------(1)

From the graph, we know that the axis of symmetry is;

x = -b/2a

Thus;

16 = -b/2a

b = -32a  -----(2)

From the graph, we see that when x = 5, y = 15. Thus;

p(8) = a(5²) + 5b + c = 0

25a + 5b + c = 15   ------(3)

Put -32a for b in eq 1 and 3 to get;

64a + 8(-32a) + c = 0  

-192a + c = 0   ------(4)

25a + 5(-32a) + c = 15

-135a + c = 15   ------(5)

Subtract eq 4 from eq 5 to get;

192a - 135a = 15

57a = 15

a = 15/57

a = 5/19

Thus;

b = -32(5/19) = -160/19

-135(5/19) + c = 15

15 + (675/19) = c

c = 960/19

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The general form of a linear equation is slope m and y-intercept c is given as y = mx + c thus the slope of the line y = -2x + 4 is -2 so option (C) is correct.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given line,

y = -2x + 4

The general form of a linear equation is the slope(m) and y-intercept (c) is given as

y = mx + c

Compare,

m = -2 and c = 4

Slope = -2 and y-intercept = 4

Hence "The slope of the line y = -2x + 4 is -2 and y-intercept is 4".

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5x - 3x = 2x

2x = 40

x = 20

x * 8 = 160

After 5 years, Offer A will offer a higher total salary.

The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

Given

a)  that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:

b) Offer A -> Arithmetic

=>55000 x 1.05 ^ 5 = X

=>55000 x 1.2762 = X

70,195.48 = X

Offer B -> Geometric

=>56000 + (5 x 2000) = X

=>56000 + 10000 = X

66,000 = X

c) Hence comparing the above 2, Offer A will provide a greater total income after 5 years.

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Answer:

It is not a solution

Step-by-step explanation:

put in (-9,-5) in for x and y

9(-9)+4(-5)=10

-81-20=10

-101=10

This is false so (-9,-5) is not a solution to the equation 9x+4y=10

The probability of getting a total that is a factor of 21 is 2/9

Tom rolls 2 fair dice and adds the results from each

Total number of outcomes = 6 × 6

= 36

The probability = Number  of favorable outcomes / Total number of outcomes

The factors of 21 = 1, 3, 7, 21

The possible outcomes = {(1,2), (2,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Number of possible outcomes = 8

The probability = Number  of favorable outcomes / Total number of outcomes

Substitute the values in the equation

= 8 / 36

= 2/9

Hence, the probability of getting a total that is a factor of 21 is 2/9

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According to the growth function, the population be in 2050 will be 10,635

Growth function:

The growth function refers the pattern of data that shows greater  increases with passing time, creating the curve of an exponential  function.

Given,

In 1965, the population of a certain town was 2010. In 1995, the population was 3620.

Here we need to find the population in 2050.

While we looking into the given problem, let us consider,

P refers the final population

A refers the the starting population, and

x refers the time passed

Now,  we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.

Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.

And the value of x is 30

So, it can be written as,

=> 3620 = 2010eⁿˣ³⁰

=> 3620/2010  = e³⁰ⁿ

=> 362/201 = e³⁰ⁿ

Here by applying ln to both sides of the equation:

⇒ln(362/201) = ln(e³⁰ⁿ)

By, using the laws of logarithms:

=> 30n = ln(362) - ln(201)

=> n = [ln(362) - ln(201)] / 30

=> n = 0.0196

Here we have to use this information to determine P in 2050.

Here the value of A will still be 2010, but x will be 85 years.

Here we have to apply these values then we get,

=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵

=> P = 2010e¹°⁶⁶⁶

=> P = 2010 x 5.2909

=> P = 10635

Therefore, there are 10635 in 2050.

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Answer:

1170 teenagers would have corrective devices

Step-by-step explanation:

hope this helps :)