Write an expression to represent the perimeter of the figure below.

Using the Cramer's Rule, the solution of the given system of equation is (-17/11, 48/11)

The given system of equations are

10x+4y=2

-6x+2y=18

Solving the equations by using Cramer's rule.

We know that, the solution of a system of linear equations in two unknowns

a(1)x+b(1)y = c(1)

a(2)x+b(2)y = c(2)

is given by ∆x=∆1, and ∆y=∆2.

where,

[tex]\Delta=\text{det}\left [ \begin{matrix} a(1)&b(1) \\ a(2) & b(2)\end{matrix} \right ], \Delta(1)=\text{det}\left [ \begin{matrix} c(1)&b(1) \\ c(2) & b(2)\end{matrix} \right ]\text{ and }\Delta(2)=\text{det}\left [ \begin{matrix} a(1)&c(1) \\ a(2) & c(2)\end{matrix} \right ][/tex]

Since the given equations are;

10x+4y=2

-6x+2y=18

Now,

[tex]\Delta=\text{det}\left [ \begin{matrix} 10&4 \\ -6 & 2\end{matrix} \right ][/tex]

∆ = [(10×2)-(-6×4)]

∆ = 20+24

∆ = 44

[tex]\Delta(1)=\text{det}\left [ \begin{matrix} 2&4 \\ 18 & 2\end{matrix} \right ][/tex]

∆(1) = [(2×2)-(18×4)]

∆(1) = 4-72

∆(1) = -68

[tex]\Delta(2)=\text{det}\left [ \begin{matrix} 10&2 \\ -6 & 18\end{matrix} \right ][/tex]

∆(2) = [(10×18)-(-6×2)]

∆(2) = 180+12

∆(2) = 192

By Cramer's Rule,

∆x = ∆(1)

44 × x = -68

x = -68/44

x = -17/11

Now,

∆y = ∆(2)

44 × y = 192

y = 192/44

y = 48/11

Hence, the solution of the given system of equation is (-17/11, 48/11).

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The right question is:

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.

10x+4y=2

-6x+2y=18

The improper fraction 7/8 has no value in the options given

To do this, we must divide the dividend by the divisor in order to change an improper fraction to a mixed number. After division, the acquired quotient becomes the whole numerals, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.

To convert 7/8 into decimal number;

7/8 = 0.875

2 1/2 = 2.5

1 5/8 = 1.625

4% = 0.04

5 5/8 = 5.625

In the given options, none of them has a value of 7/8

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Triangle ABC is similar to triangle A prime B prime C prime, because Triangle A prime B prime C prime is obtained by dilating Triangle ABC. By a scale factor of 1 over 4 and then rotating it about the origin by 180 degrees. The correct answer is B.

Dilation is a transformation that is used while resizing an object. The structures can be made longer or shorter via dilation. This transformation produces a picture that retains the original shape. There is, however, a significant fluctuation in the form. During a dilatation, the starting shape should be elongated or compressed.

All the coordinates of A'B'C' are -1/4 times those of ABC.

The dilation factor is 1/4, and rotation by 180° is indicated.

A'(-1, -1) = (-1/4) × A(4, -4)

            = A(4x-1/4, -4x-1/4)

            =  (-1, -1)

B'(-3, 1) = (-1/4) × B(12, -4)

            = B(12x-1/4, -4x-1/4)

            = (-3, 1)

C'(-2, 3) = (-1/4) × C(8, -12)

             =  C(8x-1/4, -12x-1/4)

             =  (-2, 3)

Both coordinates are invalidated by a 180° rotation. In either sequence, it is the same as reflection across the x-axis and reflection across the y-axis.

Therefore, triangle A′B′C′ is obtained by dilating Triangle ABC by a scale factor of 1 over 4 and then rotating it about the origin by 180°.

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The complete question is:

Triangle ABC is transformed to obtain triangle A′B′C′:

A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.

Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees

The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.

If the one-way ANOVA test rejects the null hypothesis, it means that there is a significant difference in the mean time kept awake among the four treatments. This means that at least one of the treatments is more effective in keeping you awake than the others. It is important to note that the alternative hypothesis does not specify which of the treatments is more effective, only that at least one is different from the others. To determine which treatment is more effective, you would need to conduct additional tests, such as post-hoc tests.

The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.

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The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.

An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.

An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"

2x + y = 4

now, putting the values in the equation (6,-8)

2(6) + (-8) = 4

or, 12 - 8 = 4

or, 4 ≡ 4

This equation, point IS a solution to the system.

x + 3y = - 20

or, 6 + 3(-8) = -20

or, 6 - 24 = -20

or, - 18 ≠ - 20

So, for this equation the result is not identity.

Thus, option A is the correct answer.

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The total pressure experienced by a diver working 15m below surface of sea is 150000 Pa.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

We need to find the total pressure experienced by a diver working 15m below surface of sea.

P = h·ρ·g

P = pressure

h = depth = 15 m

ρ = density = 1g/cm³=1000kg/m³

g = acceleration due to gravity = 10 m/s²

Substitute the values in the formula of total pressure.

P=1000×15×10

P=150000Pa

Hence, 150000Pa is the total pressure experienced by a diver working 15m below surface of sea.

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The vertex (0,2) of the parabola's vertex shape, which can expand upward or downward, equals (x - 0)² + 2.

What is parabola?

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.

What is a vertex form of an equation?

An equation's conventional vertex form is written as:

f(x) = (x-h)² + k where;

(h, k) is the vertex

Vertex (0,2) should be replaced in the equation's vertex form.

f(x) = (x - 0)² + 2

As a result, vertex (0,2) of the parabola with an opening up or down is equal to (x - 0)² + 2.

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The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.

Given is the equation -

3y = 2x + 6

The given equation is -

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2

Slope of the line -

m = 2/3.

We know slope is also given by -

m = tan(θ)

So -

tan(θ) = 2/3

(θ) = tan⁻¹(2/3)

(θ) = 33°69'

Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.

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The function after the reflection and translation will be h(x) = - (x + 4).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = x

The line is reflected over the x-axis. Then replace x with negative x, then the function is written as,

g(x) = -x

The function is translated by 4 units to the left. Then x is replaced with (x + 4). Then the function is given as,

h(x) = - (x + 4)

The capability after the reflection and interpretation will be h(x) = - (x + 4).

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Answer:

4.) a.) 2.01 b.) 404.01

6.) a.) 152.17 b.) 18412.17 c.) 153.14 d.) 18565.60

Step-by-step explanation:

To solve, use the exponential growth formula [tex]A_t=A_0(1+\frac{r}{p})^t[/tex] where

[tex]A_t[/tex] = Amount as a function of time

[tex]A_0[/tex] = Original amount

[tex]r[/tex] = rate

[tex]p[/tex] = period

[tex]t[/tex] = time

For question 4, let

[tex]A_0=400\\r=0.06\\p=12\\t=2[/tex]

So,

[tex]A_t=400(1+\frac{0.06}{12})^2\\A_t=400(\frac{201}{200})^2\\A_t=400(1.01)\\A_t=404.01[/tex]

So, the second-period interest would be 404.01-402=2.01

Question 6 can be solved using the same formula, but let

[tex]A_0=18260\\r=0.025\\p=\frac{12}{4}=3\\t_1=1\\t_2=2[/tex]

So,

[tex]A_t=18260(1+\frac{0.025}{3})^1\\A_t=18260(\frac{121}{120})^1\\A_t=18412.17[/tex]

The first-period interest would be 18412.17-18260=152.17

For the second-period, use [tex]t_2[/tex]:

[tex]A_t=18260(1+\frac{0.025}{3})^2\\A_t=18260(\frac{121}{120})^2\\A_t=18260(1.02)\\A_t=18565.60[/tex]

The second-period interest would be 18565.60-18412.17=153.43

Answer:

B

Step-by-step explanation:

Determine the equation of the line given by the table and compare with given options.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (7, 19) ← 2 ordered pairs from the table

m = [tex]\frac{19-9}{7-2}[/tex] = [tex]\frac{10}{5}[/tex] = 2 , then

y = 2x + c ← is the partial equation of the line

to find c substitute any ordered pair from the table into the partial equation.

using (6, 17 ), that is x = 6, y = 17 , then

17 = 12 + c ⇒ c = 17 - 12 = 5

y = 2x + 5 ← equation of line from table, with y- intercept c = 5

thus the function with a y- intercept greater than the table line is B

It is true that the objective function and the restrictions in a linear programming problem must be linear functions of the choice variables.

The method of choosing the best result from a linear function is known as linear programming. Making a few straightforward assumptions is the easiest way to accomplish linear optimization. As the goal function, the linear function is referred to. Real-life relationships can be quite challenging. However, such interactions can be represented using linear programming, which facilitates analysis of such relationships.

When the need of a mathematical model are represented by linear relationships as, the optimal result can also be obtained using a technique known as the linear programming (LP), sometimes known as linear optimization. A particular type of mathematical programming is linear programming.

Formally speaking, linear programming is the method for optimizing a linear objective function under the restrictions of the linear equality and linear inequality. Convex polytopes, a set defined as the total intersection of a finite number of half spaces, each of which is determined by the linear inequality, make up viable region.

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Theres no point 'Z', so i'm gussing you want the angle of <KLJ?

<K and <M are the same, therefore <M = 130

<J + <K + <M + <L = 360

130 + 130 = 260,  360 - 260 = 100

<J and <L are the same

<MJK = 50 and <KLM = 50

<KLM/2 = <KLJ

50/2 = 25

Answer:

75% of 600 is 450

The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

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The system of equations is:

3a + 2r + 7b = 21

2a + 6r + b = 29

a + 4r + 5b = 23

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

a = price of apples

r = price of oranges (I used r instead of letter o since o can be confused with zero)

b = price of bananas

Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21.

3a + 2r + 7b = 21

Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29.

2a + 6r + b = 29

Heather bought 1 lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23.

a + 4r + 5b = 23

The system of equations is:

3a + 2r + 7b = 21

2a + 6r + b = 29

a + 4r + 5b = 23

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To get a number point 1 is impossible for any of the team to reach at the end of the described tournament.

As given in the question,

Total number of footballs teams = 3

Each team plays once with other team

Let three teams are Team1, Team2, and Team3

Team1 plays with Team2 and Team3

Team2 will play with Team3

Winning points = 3

Losing team points = 0

Withdraw teams points = 1

To reach in finals suppose Team1 plays with Team2 and Team3 and win

Points of team1 = 3 + 3

                         = 6points

As team plays once with other team , Team1 is out of the game.

Team2 and Team3 play with each other

To reach at the end of the tournament one team has to win let it be Team2

Points of Team2 = 3

Points of Team3 = 0

No withdraw game is possible to reach into finale.

Therefore, point 1 is impossible for any team to reach at the end of the tournament.

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The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²

You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box

The quadratic function reads

A= πr²

Where A= Area of circle,

π = 22/7

and r= radius of the circle

A= (22/7)*6

Width of the box is 12

Therefore 12/2 = r=6

A= (22*6*6)/7

A=113.1 in²

In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²

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A. x= 4

Step-by-step explanation:

|x|-7 = -3

x = -3 +7

|x|= 4

x= 4

x=-4

Percent decrease from 100 to 82 is 18% decrease.

Calculating the % decrease from 100 to 82,

[tex]\frac{82-100}{100}[/tex]×100%

[tex]\frac{-18}{100}[/tex]×100%

on simplifying we get,

-18%

here, negative sign indicates that there is a decrease of percentage.

Hence, we get 18% decrease from 100 to 82.

How to calculate Percent decrease?

Do the % growth and reduction calculations. By dividing the new number by the initial value, the percentage is computed.

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If an original conditional statement is true, the option that will always be true as

well is B. Contrapositive.

A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences. P is referred to as the hypothesis and Q is referred to as the conclusion for this conditional statement. If P then Q logically implies that Q must be true whenever P is true.

A conditional statement is present. In the event of rain, we will not play. Let's say A: It's raining and B: We're not going to play. If A is true—that is, if it is raining—and B is false—that is, if we played—then A implies that B is untrue.

Therefore, based on the information, the correct option is B.

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Answer: x=19

Step-by-step explanation:

x+45=64

Subtract 45 from both sides.

x=64−45

Subtract 45 from 64 to get 19

x=19

answer

X=19

Step-by-step explanation:

because 64-45= 19 and 19+45=64

Answer:

See attached image

Step-by-step explanation:

You can graph lines on a website called desmos graphing calculator!

Answer:

Step-by-step explanation:

you replace x with anything you want I will do 0. Then the the first point is (0,-4). Now I am gonna replace x with something else like 4. The second point is (4,8), now connect the two points and you got a line.

Explanation of why Priya's conclusion is correct.

What is a function?

An association between a number of inputs and outputs is called a function. Exactly one output is connected to each input in a function, which is an association of inputs. Every function has a range, co-domain, and domain.

Given the functions;

Simplifying,

f(x)=10x² and

g(x)=6x

The coefficient of variable x :

10 and 6,

where 10> 6.

And the value of x:

x² > x, for all x.

As x continues to grow, the values of f will be greater than the values of g.

Therefore, Priya's conclusion is correct.

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Step-by-step explanation:

SWT + TWU =180º therefore SWU must be a line. Aka SWU is linear. So SWT and TWU must be a linear pair.

SWT + SWT = 180º therefore 2SWT=180º deviding both sies by 2 we get SWT = 90º Therefore SWT is replacing TWU. SWT is substituted into TWU. So substitution.

SU | TV basically means the line that passes through both points S and U is perpendicular to the line that passes through both points T and V. Therefore it is the Defenition of perpendicular lines.

If this helped please rate the answer.

Answer: 8

Step-by-step explanation:

8 times 8 is 64

Output for the givin input for function f(x)=-5x+1, f (3) is -14.

What is  function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

f(x)=-5x+1

Then, f(3)=-5*3+1

f(3)= -15+1

f(3)=-14

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