write each system of equations as a matrix

Considering the definition of perpendicular line, the equation of perpendicular line is y= -1/10x + 11/5.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 10x -8.

The line has a slope of  10. If you multiply the slopes of two perpendicular lines, you get –1:

10× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 10

slope perpendicular line= -1/10

The perpendicular line has a form of: y= -1/10x + b

The line passes through the point (2, 2). Then:

2= -1/10× (2) + b

2= -1/5+ b

2+ 1/5= b

11/5= b

Finally, the perpendicular line is y= -1/10x + 11/5.

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Giving every student in the experiment the same final exam is an example of A. Randomization.

The process of conducting research in an objective and controlled manner in order to maximize precision and draw specific conclusions about a hypothesis statement is known as experimental design.

The process in which participants in clinical trials are randomly assigned to separate groups that receive different treatments or other interventions. Neither the researcher nor the participant has any say in which treatment or intervention the participant receives.

A random process is a sequence of random variables that describe a process whose outcomes follow an evolution described by probability distributions. This was illustrated in the examination.

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Complete options

A. Randomization

B. Blocking

C. Direct control

D. Replication

The one time joining fee found from the linear relationship between total cost and the number of months of membership is $250

A linear relationship is a relationship between two variables that has a straight line when graphed.

The total cost of the gym membership = C

The number of months of membership = t

The table in the question is presented as follows;

t (Time in months)     [tex]{}[/tex]                 C (Total cost)

2      [tex]{}[/tex]                                            200

4     [tex]{}[/tex]                                             250

9     [tex]{}[/tex]                                             375

The linear equation that represents the value in the table is found as follows;

Slope of the line, m = (375 - 250)/(9 - 4) = 25

The equation of the line in point and slope form is therefore;

(C - 375) = 25·(t - 9)

C = 25·(t - 9) + 375

C = 25·t - 225 + 375 = 25·t + 250

C = 25·t + 250

The joining fee is the amount paid at the start when t = 0, therefore;

Joining fee = 25 × 0 + 250 = 250

The one time joining fee is $250

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The markup price on the table would be $32.

So, we have:

Now, calculate the makeup price:

Mark-up price = Discount * Selling Price

Mark-up price = (28/100) * 114

Mark-up price  = 31.92

Mark-up price ≈ 32.

Hence, the markup price on the table would be $32.

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The statement that shows the correct relationship between production cost and the number of golf balls produced is that the minimum production cost of 17.5 occurs when 35 golf balls are produced.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Then the minimum is represented by the formula;

c - b² / 4a

We have given equation C(x) = 0.1x² - 7x + 140

a = 0.1

b = -7

c = 140

Now plugging in values to c - b² / 2a

= 140 - 7² / (4 * 0.1)

=  17.5

The minimum production cost will be; 17.5

Now plugging 35 into the given equation;

C(x) = 0.1x² - 7x + 140

C(x) = 0.1 ( 35)² - 7 (35) + 140

C(x) = 17.5

Therefore, 35 golf balls produce the minimum cost.

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Answer:

that the minimum production cost of 17.5 occurs when 35 golf balls are produced.

Step-by-step explanation:

Answer:

a) 1/11

b) 2/11

c) 0/11

d) 4/11

e) 9/11

Step-by-step explanation:

'MATHEMATICS' has 11 letters.

a) there is only one H out of the 11 letters meaning the probability is 1/11

b) there are two M s out of the 11 letters meaning the probability is 2/11

c) there is no B in the word meaning the probability is 0/11

d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11

e) there two A s in the word and 11-2=9 meaning the probability is 9/11

Hope this helps :)

Answer: 15√11z

Step-by-step explanation:

Answer:

density = 1.43 × 10⁻³ g/cm³

Step-by-step explanation:

We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.

To do this we have to first convert the mass, which is given in kg, to g:

mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]

                          = 2230 g

Next, we can find the density of the gas using the following formula:

[tex]\boxed{density = \frac{mass}{volume}}[/tex]

⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]

                 = 1.43 × 10⁻³ g/cm³

Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.

Answer:

Step-by-step explanation:

A is a point

AB is a line

ABC is a plane

Therefore,  ABC is a plane.

__________________

Hope this helps!

Have a great day!

Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.

In the given question,

Manuel wishes to purchase 25 cent and 30 cent stamps.

He decides to buy 10 fewer 30 cent stamps.

We have to find how many of each can he buy for no more than $19.00.

Let he buy x stamps of 25 cent.

He want to buy 10 fewer 30 cent stamps.

So he buy x−10 stamps of 30 cent.

But he have to buy total stamps of $19.

So the equation is

x+x−10 = 19

Simplifying

2x−10=19

Add 10 on both side

2x−10+10=19+10

2x=29

Divide by 2 on both side

2/2 x =29/2

x=14.5

x≈15

Hence, he buy 15 stamps of 25 cent.

Now finding the number of 30 cent.

he buy x−10 stamps of 30 cent.

So 15−10=5.

So he buy 5 stamps of 30 cent.

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Use the distributive property to multiply 2 times 4−2w.

Subtract 8 from 8 to get 0.

Divide both sides by −4.

Divide −4 by −4 to get 1.

Answer:

w = 1

Step-by-step explanation:

2(4 - 2w) - 8 = -4

(2*4 + 2*-2w) - 8 = -4

(8 - 4w) - 8 = -4

-4w + 8 - 8 = -4

-4w = -4

w = -4/-4

w = 1

Check:

2(4 - 2*1) - 8 = -4

2(4-2) -8 = -4

2(2) - 8 = -4

4 - 8 = -4

The required consecutive even integers are 66, 68, 70, and 72.

We have four integers. The integers are consecutive, that means the integers are one after the other. The integers are even, which means they are all divisible by two. The sum of these four even integers is 276.

Let the first even integer be represented by the variable "n". The next three consecutive integers are (n + 2), (n + 4), and (n + 6). Let the sum be denoted by "S".

S = n + (n + 2) + (n + 4) + (n + 6)

276 = 4n + 12

4n = 264

n = 66

Hence, the required integers are 66, 68, 70, and 72.

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By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let Warren has drawn 5x pictures of animals and 2x pictures of people

Warren has drawn 18 more pictures of animals than people in his notepad

By the problem,

5x - 2x = 18

3x = 18

x = [tex]\frac{18}{3}[/tex]

x = 6

Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]

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Considering the triangle given the variables are calculated to be

x = (5√6)/3

y = (10√6) / 3

Information given in the question

right angle triangle

The unknown variables is calculated using SOH CAH TOA

Definition of variables for the  right angle triangle

hypotenuse = y

opposite = 5√2

adjacent = x

The variable x is solved using tan, TOA, the angle is 60

tan 60 = Opposite / Adjacent

tan 60 = (5√2) / x

x = (5√2) / tan 60

x = (5√6)/3

The variable y is solved using sin, SOH, the angle is 60

sin 60 = Opposite / Hypotenuse

sin 60 = (5√2) / y

y = (5√2) / sin 60

y = (10√6) / 3

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Potential rational solution(s) to the above polynomial equation is ±1, ±2.

Actual rational solution are ±1, +2.

What is  polynomial equation?

Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.

Main Body:

Given:

x³ - 2x² - x +2 = 0

We will use the Rational Root Theorem:

If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.

So, if the constant therm is 2 and the leading factor is 1, candidates for roots are:

±1,±2

Dividing x³ - 2x² - x +2 = 0 by x-1, we get

x²-x-2 as quotient.

Splitting the middle term ,

⇒x² - 2x + x - 2

⇒x(x- 2) + 1(x-2)

⇒(x+1)(x-2)

so x= -1 , 2

Hence the rational solution to the equation are ±1, 2.

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Derek's hourly rate is $10 and Charlie's hourly rate is $10.45, Charlie's earns $0.45 more per hour than Derek.

A unit rate means a rate for one of something.

Given that, a graph which shows Derek's earning hourly, and Charlie earns $52.25 in 5 hours of work,

Derek's earns $10 for an hour

Charlie's earning for an hour = 52.25/ 5 = $10.45

Hence, Charlie's hourly rate is $10.45, and he earns $0.45 more per hour than Derek.

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The equation of the line is y = x -3. The graph of the line is attached below.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

Given that the slope of the line is 1.

Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.

Putting m = 1 in y = mx +c:

y = 1 × x +c

y = x +c

Since the line passes through the point (-2, -5), thus the point satisfies  the given equation of line.

Putting x = -2 and y = -5 in y = x +c

-5 = -2 + c

c = -3

The equation of line is y = x - 3.

The points on the line are

(-2, -5), (0, -3), (3, 0).

Plot the points and join them:

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The ratio of the areas of the similar figures is given as follows:

225/16.

Similar figures are figures that share these two features:

The ratio of the side lengths of the similar figures can be represented as follows:

(b/a).

The side length is measured in units, while the area is measured in units squared, hence the ratio of the areas of the similar figures is represented as follows:

(b/a)² = b²/a².

From the image of the right triangle shown at the end of the answer, the ratio of the side lengths is:

15/4.

Hence the ratio of the areas of the figures is given as follows:

(15/4)² = 225/16.

The figures are given by the image at the end of the answer.

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For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.

As given in the question,

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( -9, 5 )

( -9 , 5 ) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = -9

Altitude = 5

Using Pythagoras theorem,

Hypotenuse² = (-9)² + (5)²

⇒ Hypotenuse = √106

cos ∅ = -9 / √106

sec ∅ = 1/ cos ∅

         = - √106/9 ( simplest radical form )

Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of

sec∅= ( - √106/ 9 )  in simplest radical form.

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The equation formed when x is the subject of the function f(x) = x² - 9, has two values of output for each input value to the function, therefore;

f(x) = x² - 9 does not have an inverse.

An inverse of a function is an anti function that reverses the values in the output into the input values thereby undoing the operations performed by the function.

A function f has an inverse if and only if it is bijective, such that there is a one to one correspondence between the set of the input elements and the set of the output elements

A function that has an inverse is said to be a bijective or invertible function or a function with one-to-one correspondence

The function in the question f(x) = x² - 9

Making x the subject of the function to verify if it has an inverse gives;

x² = f(x) + 9

[tex]x = \pm\sqrt{f(x) +9}[/tex]

Putting x = f⁻¹(x) gives;

[tex]f^{-1}(x) = \pm\sqrt{x +9}[/tex]

Therefore, each value of x gives two values of f⁻¹(x), such that the set of the output of inverse function, f⁻¹(x) does not have a one-to-one correspondence with the set of values of x.

The function f(x) = x² - 9 is not invertible and therefore does not have an inverse function.

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Simon bought a $48 table on sale. The price of the table can be estimated by $50.

The sale propose 30% off, then an estimate for the discount can be calculated using proportion:

$50 -- 100%,

$x -- 30%

that is mathematically

Find x:

Answer: correct choice is B

The coordinates M along the directed line segment is (-12, -2)

The points are given as:

K  = (-16, 10)

L = (-9, -11)

The ratio on the segment can be represented as;

KM : LM, m : n = 4 : 3

So, we have the coordinates of the point M that lies along the directed line segment to be

M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

So, we have:

M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)

Evaluate

M = 1/7 * (-84, -14)

Evaluate

M = (-12, -2)

Hence, the coordinates of the point M is (-12, -2)

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Here is what i did

I used a graphing calculator

The ball was in the air for 1.5 seconds. The answer is true.

The equation of the form ax² + bx +c is known as a quadratic equation.

The given equation is h(t) = -16t² + 20t + 6.

To find the time for which the ball was in the air, substitute h(t) =0.

0 = -16t² + 20t + 6

Use the quadratic formula to solve the equation:

[tex]t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}[/tex]

t = (-20 + 28)/(-32) or t = (-20-28)/(-32)

t = -0.25 or t = 1.5

Since time cannot be negative, discard the negative value.

Hence, the ball was in the air for 1.5 seconds. The answer is true.

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The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.

AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.

In the given figure FE║GE means FE is parallel to GE.

so ∠EFS = ∠HGS

and ∠FES = ∠GHS

also ∠S is common for both.

If two triangles are similar then ratio of corresponding sides are also same.

So, by applying this

[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]

54/24 = FE/20

( 54*20 ) / 24 = FE

FE = 45m.

Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.

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Answer:

5

Step-by-step explanation:

:)

Answer:5

Step-by-step explanation:|-10|-|-5|

                                             10-5

                                              5

Answer:

Just add the 3 sides together

Step-by-step explanation:

if a triangle has the side values of 3, 4, 6. Then you would simply add them together!

3+4+6=13

therefor that triangles perimeter is 13

hope this helps!

Answer: $323,050

Step-by-step explanation:

355,000 over 1 x 9 over 100 = 3195000 over 100 (31950)

355,000- 31,950 = 323,050 which is your answer, hope this helped <3