Match the reason to the statements in the proof.

Given:
1 m<1+<5=189
m<1+m<4=180

Prove:
—> | | —>
YZ UV

The required area model is shown in the figure, as per the given expression.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Area model of the expression x² + x - 56 is formed as,
factorize the given expression
x² + x -56= (x + 8)(x - 7)

Thus, the required area model is shown in the figure, as per the given expression.

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The solution for the given problem is X= -4, Y= -5.

First we will substitute into one of the equations: 2(3x-1)-6x=4

Then reduce the greatest common factor on both sides:3x-1-3x=2(i.e divide the above equation by 2)

The sum of two opposites equals 0: -1 =2

Rearrange unknown terms to the left side of the equation:

                                   2y+x=6

                                   4y+2x=12

Reorder the equation: x+2y=6

                                    4y+2x =12

Again reorder the equation by taking x variable first : x+2y = 6, 2x+4y= 12

Reduce the greatest common factor on both sides of the equation:

Subtract the two equations:2y-(x+2y)=6-6

Remove parentheses:

Cancel one variable:0=6-6

The sum of two opposites equals 0:0=0

The system of equations has: infinte solutions

Substitute into one of the equations: :x+2x+3=-9

Rearrange unknown terms to the left side of the equation:

Combine like terms:3x=-9-3

Calculate the sum or difference:

Divide both sides of the equation by the coefficient of variable:x=-12/3

Cross out the common factor:x=-4

Substitute into one of the equations:-4+y=-9

Rearrange unknown terms to the left side of the equation: y=-9+4

Calculate the sum or difference: y=-5

Therefore, the solution of the given problem is x=-4, y=-5.

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Note that for WKST to be a parallelogram, y must be equal to 8 and m∠S must be equal to 126°. Thus the correct option is (Option C).

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.

To justify the above answer, note that:

Since Opposite angles of a parallelogram are congruent, we have

∠W = ∠T

That is:

 3x -18 = 2x +6

Collecting like terms over the equation sign, we have:

3x - 2x = 6 + 18

x = 24

Substituting x into the equation for ∠W = ∠T, we have:

3x -18 = 2x +6

3(24)-18 = 2(24) +6 =54

72-18 = 48 +6 = 54

Thus, the above expression is True. That is:

3x -18 = 54°; and

2x +6 = 54°.

Since The adjacent angle, W is supplementary to either of these, it means that:
∠W = 180° -∠E

⇒ 15y +6 = 180 -54

⇒ 15y = 120

y = 8

Thus, it is correct to state that the value of y and m∠S required to classify WKST as a parallelogram are:

y-8; ∠126° (Option C)

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Full Question:

See the attached image.

a)The given expression is; x + 9/2

b) The smallest number is  0.104

A mathematical expression is a combination of numbers, variables, and operations that represents a mathematical relationship or equation. We are asked to renter the expression as shown into the box that have been given.

If we arrange the numbers in order, we can see that the decreasing order of the numbers would take the form;

104 > 10.4 > 1.04 > 0.104

Thus we can see that the number that is smallest is  0.104.

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The volume of the drinking glass in cubic centimeters is 442.4189 cm^3 .

The cylinder is a three-dimensional shape having a circular base.

A cylinder can be seen as a set of circular disks that are stacked on one another.

The volume of a three-dimensional shape is equal to the amount of space occupied by that shape.

Now, think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cylindrical box.

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

Therefore, the cylinder’s volume of base radius ‘r’, and height ‘h’ = (area of base) × height of the cylinder

Since the  base is the circle, it can be written as

Volume =  πr^2 × h

Therefore, the volume of a cylinder = πr^2h cubic units.

diameter of 2.5 in

r = 2.5/2 in.

r = 1.25 in

r = 3.175 cm

cylindrical drinking glass 5.5 in. tall

h = 5.5 in.

h = 13.97cm

volume of the drinking glass

Volume =  πr^2 × h

              =   π ( 3.175)^2 ×  13.97  cm^3

              = 442.4189 cm^3

The volume of the drinking glass in cubic centimeters is 442.4189 cm^3 .

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The rate of change is -2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the table,

(0, 42), (1, 40) and (2, 38)

Rate of change of drone A.

= (40 - 42) / (1 - 0)

= -2/1

= -2

Thus,

-2 is the rate of change.

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Functional continuity and derivative continuity (slope smoothness) between the device saturated and device active segments is the value of V12, VOL and Vhr, Vih and Get the NM2 & NmH

What is Functions?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Suppose the threshold vintage of N- mas is VTO

(i) Vin < VTO – Cat of f

(ii) VTO < Vin < V out – Saturation

(iii) Vin > V out + VTO – Liniar

When N-Nos is in Liniar

IR = Kn/2 { 2.(Vin-VTO). V out – V2out }

Cat calculation of VOH,

V out = V Do – RL- IR

When Vin is Low, i.p. Vin <Vto, the M mess is Off Home ID = IR = O

Calculation of VOL,

Let us assume Vin = VoH

= VDo

Since Vin – VTO > V Out, the Transitar is in Lininers,

IR= VDo – V out

Off have IO = IR = o

Calculation of VOL,

Let us assume Vin = VOH = VDO

Since Vin – VTO > V out, the Transifar is in Linears,

IR= VDO – V Out / R2

Using KCL – IR = IO

VDO – VOL / R2 = Kn/2 { 2(VOD  - VTo ) . Vo2 – VOL2}

Vol2 – 2 .{ VOD – VTO + 1/KnR2 } VOL + 2/KnRL . VDD = 0

On Solving for VOL,

VOL = VDD = VTO + 1/KnRL - /- ( VDD – VTO + 1/KNR2 ) 2 – 2VDD/KnR2

D Vot/DVin = 1

For VOCD > Vin – VTO; The N-Mas in Saturation

VDD – V Out /R2 = Kn/2 ( Vin – VTO ) 2

-1/R2 . D V out / D Vin = Kn( Vin – Vto )     put Vin = Vin

-1/RL ( -1) = Kn( Vin – Vto )

Calculation of Visit :-

Put D V out / D Vin = -1

When V Out  < Vin – Vto: M- mas Linier

Vdd – V out / RL = Kn/2 { 2- ( Vin –Vto ) Vout – V2 out }

Differtatyboth side  by d Vin:

-1/RL – D Vout/D Vin = kn/2 { 2.( Vin – Vto) D v out /d Vin

= 2 vat . Dat/dxt

Vdd – V out /R2 = Kn/2 { 2. ( Vin – VTO) V out – V2 Out }

Diffent Both side by D Vin .

-1/RL. DV out/DVin = Kn/2 {2. (Vin – Vto) Dv out / D vin + 2 vat .dat/Dithal      ------- ( i)

Put  dV out/D vin = -1

                                         Put Vin = VTT

-1/RL (-1) = Kn{( Vin – Vto ) – (-1) +2 V out }

VTH = Vto +2 V out -1 / Kn RL ----------(II)

Now Put the Value of Vin From ( II ) in ( I) in the Place of Vin.

Then

Vin = Vto + 8/3 VDo/KnRL – 1/knRL

Now ,Nasie Margin :-

NM2 = V12 – Vol

NMH = Vas – Vin

Substitute the value of V12, VOL and Vhr, Vih and Get the NM2 & NmH.

The value of V12, VOL and Vhr, Vih and Get the NM2 & NmH between the device saturated and device active segments is functional continuity and derivative continuity (slope smoothness).

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Answer:none of the above

Step-by-step explanation:

The maximum Z is 1800 and the value of X₁ and X₂ at the optimal solution : X₁ = 5 and X₂ = 3.

The constraints for the linear programming problem:

30X₁ + 70X₂ ≤ 210

20X₁ + 10X₂ ≤ 100

X₁, X₂ ≥ 0

First we draw the graph for equations 30X₁ + 70X₂ = 210 and 20X₁ + 10X₂ = 100

Consider equation 30X₁ + 70X₂ = 210

For X₁ = 0,

70X₂ = 210

X₂ = 3

For  X₂ = 0,

30X₁ = 210

X₁ = 7

This means, the line 30X₁ + 70X₂ = 210 passes through (0, 3) and (7, 0) as shown in the following graph.

So, 30X₁ + 70X₂ ≤ 210  includes the region below the line.

Consider equation 20X₁ + 10X₂ = 100

For X₁ = 0,

10X₂ = 100

X₂ = 10

For  X₂ = 0,

20X₁ = 100

X₁ = 5

This means, the line 20X₁ + 10X₂ = 100 passes through points (0, 10) and (5, 0) as shown in the following graph.

so, an inequality 20X₁ + 10X₂ ≤ 100 includes the region below the line.

From the figure, (0, 3) and (5,0) are feasible corner points.

Thus the optimal solution is:  X₁ = 5 and X₂ = 3

For X₁ = 5 and X₂ = 3,

Z = 300X₁ + 100X₂

Z = 300(5) + 100(3)

Z = 1500 + 300

Z = 1800

Therefore, the maximum value of Z is 1800

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The most important details in this question are the three simultaneous equations: 5x + 3y = 136, 8x + 9y = 268, and the difference in price between a candle and a bath bomb. These equations can be solved by adding the equations together: 13x + 12y = 404, subtracting 5x and 8x from both sides of the equation:-3x/12 + y = 404/12, and substituting the values of x and y into the equation: Sx - Sy = -26.472.

A simultaneous equation is a collection of two or more equations with two or more variables. Because they share variables, these equations must be solved together. In other words, the variables' values must fulfil all of the equations simultaneously.

(a) 5x + 3y = 136

Substitute the values given in the equation:

5(25) + 3(15) = 136

125 + 45 = 136

Simplify:

170 = 136

This equation is not true.

(b) 8x + 9y = 268

Substitute the values given in the equation:

8(16) + 9(18) = 268

128 + 162 = 268

Simplify:

290 = 268

This equation is not true.

(c) Solve these simultaneous equations.

5x + 3y = 136

8x + 9y = 268

Add the equations together:

13x + 12y = 404

Subtract 5x and 8x from both sides of the equation:

-3x + 12y = 404

Divide both sides of the equation by 12:

-3x/12 + y = 404/12

Simplify:

-1/4x + y = 33.67

Substitute this equation into the original equation:

5x + 3y = 136

5x + 3(33.67) = 136

Simplify:

5x + 100.01 = 136

Subtract 100.01 from both sides of the equation:

5x = 35.99

Divide both sides of the equation by 5:

x = 7.198

Substitute this value into one of the original equations:

5(7.198) + 3y = 136

Simplify:

35.99 + 3y = 136

Subtract 35.99 from both sides of the equation:

3y = 100.01

Divide both sides of the equation by 3:

y = 33.67

(d) Calculate the difference in price between a candle and a bath bomb.

Substitute the values of x and y into the equation:

Sx - Sy = 7.198 - 33.67

Simplify:

Sx - Sy = -26.472

Therefore, the difference in price between a candle and a bath bomb is Sx - Sy = -26.472.

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About two minutes long after shaking begins during the tangshan earthquake does it take the last building collapses.

At 3:42 am, an earthquake of magnitude 7.8 to 8.2 struck Tangshan, a Chinese industrial city of about one million people. The quake was particularly costly in terms of human life because most people slept in beds rather than outside the relatively safe streets. occurred along an unknown fault in the Cangdong fault system near the confluence of the The Tangshan fault is a north-northeast-trending strike-slip fault. An estimated 242,000 people died in Tangshan and surrounding areas, making the earthquake one of the deadliest in recorded history, with 300,000 killed in the Calcutta earthquake of 1737, believed dead in 1556. Shaanxi Province, where 830,000 people died of Chinese nationality. It lasted 23 seconds and destroyed 90% of Tangshan's buildings. At least 250,000 killed and 160,000 injured

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Answer:

576π cm³

Step-by-step explanation:

Find volume of 1 sphere:

V = 4/3πr³ = 4/3π(6)³ = 288π

Volume occupied by 4 spheres = 4(288π) = 1152π

Find volume of cylinder:

V = πr²h

h = 4(12) = 48     (4 spheres stacked inside the cylinder)

V = π(6)²(48) = 1728π

Empty space = (Volume-cylinder) - (Volume-4 spheres) = 1728π - 1152π = 576π

The required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,

Maximum and minimum points of the function y = 2 sin 2(x + π) + 3. can be determined by drawing the graph of the function, from the graph maximum of point of the function is (-3π/4, 5) and the minimum point is (-π/4, 1).

Thus, the required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

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When the length of 2 section combined is 18 in

width is 12 in

When the length of 2 section combined is 24 in

width is 9 in  

A quadrilateral with four right angles is a rectangle. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Rectangles have the following basic characteristics:

The length of the poster is 24 in

The width of the poster is 18 in

The area of the poster = 24*18 = 432 in²

The area of each section of the poster is 432/4 = 108 in².

Length of each section is 24/2 = 12 in

Width of each section is 18/2 = 9 in

The total length when 2 sections are combined is 9 + 9 = 18 in

or, 12 + 12 = 24 in

When the length of 2 section combined is 18 in

width is (108*2)/18 = 12 in

When the length of 2 section combined is 24 in

width is (108*2)/24 = 9 in  

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The five values which are required to graphed a box plot are as follow:

Option 1. Minimum , Quartile 1, Median, Quartile 3 , Maximum

The five values required to represent on the graph of box plot are :

Therefore, the five values used to graphed on a box plot are:

Option 1. Minimum , Quartile 1, Median, Quartile 3 , Maximum

The above question is incomplete , the complete question is :

Which five values are graphed on a boxplot?

1.  Min, Quartile 1, Median, Quartile 3. Max

2.  Min. Quartile 1, Mean Quartile 3, Max

3. Min. Quintile 1, Median, Quintile 3. Max

4. Min. Quintile 1. Mean, Quintile 3, Max

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Step-by-step explanation:

what do you not understand here ?

you got the formula, the numbers for the formula.

since you should use 3 for pi, this is a very simple calculation :

3×15² = 3×225 = 675 ft²

that's it.

Note that according to the areas of the circles in square units, the circles ordered from the least to the greatest is:

To determine the correct order, we need to solve for the areas of all the circles given the various factors provided.

A) a circle with an area of 1,040.09 square units. (Area given)

B) a circle with a radius of 27 units

Area where radius is given is computed using:

A = πr²

A = π * 27²

A [tex]\approx[/tex] 2290.22

C) a circle with a circumference of 87.92 units

Since Circumference is given:

A = C²/4π

Where C = Circumference

Thus A = 87.92²/*4*π)

A [tex]\approx[/tex] 615.13

D) a circle with a diameter of 19 units.

Area, where the diameter is given, is:
A = 1/4 πd²

A = 1/4 * π * 19²

A [tex]\approx[/tex] 283.53

Thus, it is correct to state that the order of the Areas of the Circles given from least to greatest is:
Area of a circle with a Diameter of 19

a circle with a radius of 27 units.

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Full Question:

Place the circles in order from the circle with the smallest area to the circle with the largest area

* a circle with a area of 1,040.09 square units.

* a circle with a radius of 27 units

*a circle with a circumference of 87.92 units

*a circle with a diameter of 19 units.

Answer:

0.12698412698

Step-by-step explanation:

Answer:

Step-by-step explanation:

10

20 divide by 2=10

The mean absolute deviation of the number in the list is 8.8

Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. The formula for MAD is:

MAD =∑|x-m|/n

∑ is known as Sigma and means to sum up

| | are vertical bars that mean absolute value

x is each value

m is the mean

n is the total number of data points in your data set

Given: 35,47,52,40,21

n = 5

m = (35 + 47 + 52 + 40 + 21) /5 = 195/5 = 39

∑|x-m| = |35-39| + |47-39| + |52-39| + |40-39| + |21-39|

          = 4 + 8 + 13 +  1 + 18 = 44

MAD =∑|x-m|/n = 44/5 = 8.8

Therefore, the mean absolute deviation of the number in the list is 8.8

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The values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

sin 45° = √2/2 and cos 45° = √2/2

considering the right triangle;

sin 45° = x/6 {opposite/hypotenuse}

√2/2 = x/6

x = 6 × √2/2

x = 3√2

cos 45° = y/6 {adjacent/hypotenuse}

√2/2 = y/6

y = 6 × √2/2

y = 3√2

Therefore, the values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45.

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The amount that Amir's car will be worth in 5 years is £9, 645. 09

From the information given, we have that;

For the first year, we have;

= £11985 × 4.25/100

= £509. 36

For the second year

= £ 11475 × 0. 0425

= £487. 71

For the third year

= £10, 987. 28 × 0. 0425

= £466. 96

For the fourth year

= £10, 520.32 × 0. 0425

= £447. 1136

For the fifth year

= £ 10. 073. 20 × 0. 0425

= £428. 111

Hence, the value is £9, 645. 09

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The missing side, which is 8.2 (rounded to the closest tenth), is indicated by the provided statement.

The leading edge that connects two vertices of a form or two-dimensional object is referred to as a side in geometry. To put it another way, in mathematics, a side is the vector that joins two points on a form. Here, the term "shape" refers to a two-dimensional (flat) form, such as a triangle, rectangle, or square.

Your hypotenuse is present. You require the inverse.

Sin = x/Hypotenuse

Sin27° = x/18

x = Sin27° * 18

x = 0.45 * 18

x = 8.17

x ≈ 8.2

As a result, side 8.2 is missing.

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Answer:

Without rounding $24.58 alternately $24.95 would be a comparable price as well and would also fit the parameters.

Step-by-step explanation:

50 ÷ 6 =  8.33

$ 2.95 × 8.33 = $24.58

Answer:

Below

Step-by-step explanation:

Company 1 charges 9.25 for 2.5 pounds and 14.50 for 6 pounds

      so  (6-2.5) pounds costs (14.50 - 9.25)

                3.5 pounds cost an increase of 5.25  

                       5.25 dollars / 3.5 pounds = 1.50 per pound

Company 2 's rate is the slope of the line =   (7.25-6.50)/ 1 = .75 dollar per pound   ( found by looking at the cost of 1 pound and the cost of 2 pounds)

Fixed cost for company 2 is the value where x = 0......the y-axis intercept = $ 5.75

Answer:

Step-by-step explanation:

Company 1:  find constant rate =  Δy/Δx, from any two (x,y) pairs on the data table

Constant rate = (14.50 - 9.25) / (9.25 - 2.5) = 1.5

Company 2 constant rate = $1.50/lb

Find the fixed fee for Company 1 by finding the y-intercept.

y - y1 = m(x - x1)     Choose any (x,y) from the data table

y - 9.25 = 1.50(x - 2.5)     Now put the equation in slope-intercept form.

y = 1.50x - 3.75 + 9.25

y = 1.50x + 5.50

Company 1 fixed fee = $5.50

Company 2:  find the slope of the line to get the constant rate, pick any 2 points on the line.

m = Δy/Δx = (7.25 - 5.75) /(2 - 0) = 0.75

Company 2 constant rate = $0.75/lb

Find the fixed fee by finding the y-intercept on the graph (where the line intersects the y axis at x = 0)

Company 2 fixed fee = $5.75

Answer:

2 green

Step-by-step explanation:

The ratio of blue to green is 4 to 1  <===== there is 1/4th asmany green as blue.... so if there are 8 blue, there are only   2 green

Therefore , the solution of the given problem of fraction comes out to be  the rainfall continues to fall at a rate of 50mm.

Any number of equal amounts or fractions can be used to represent a whole. In standard English, the quantity of a certain size is stated as a fraction. 8, 3/4. Wholes also include fractions. Numbers are represented in mathematics by the fraction to numerator ratio. These are all straightforward integer fractions. There is a fraction in the denominator of a difficult fraction. because the calculations, numerators, and numerators of actual fractions vary.

Here,

the amount of rainfall in Miami over s two hour period. If the rain continues to fall at this rate,

=> Radius

=>  fraction = 127/2 =63.5 mm

=> 2 hours rainfall

Per hour rainfall = 10 mm

=> After 5 hours

=> 50 mm

So,

the rainfall continues to fall at a rate of 50mm.

Therefore , the solution of the given problem of fraction comes out to be  the rainfall continues to fall at a rate of 50mm.

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Answer:

1 point

Step-by-step explanation:

if each question is worth twice as much as the question before it , then the question before each question is half the value, then

5th question = 16

4th question = 16 ÷ 2 = 8

3rd question = 8 ÷ 2 = 4

2nd question = 4 ÷ 2 = 2

1st question = 2 ÷ 2 = 1

the first question is worth 1 point

In total, there are 5 non-congruent triangles with integer sides that have a perimeter of 12.

The number of such non-congruent triangles can be found by considering all possible combinations of sides that add up to 12.

We can start by finding all possible combinations of two sides, and then adding the third side to make the perimeter equal to 12.

For example, for the two sides with lengths 1 and 11, the third side must be equal to 0, which is not allowed in a triangle.

The combinations of two sides are:

(1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6).

For the combination (1, 11), the third side cannot be greater than 10, so it is not a valid triangle.

For the combination (2, 10), the third side can have lengths 0, 1, or 2, but none of these values result in a valid triangle.

For the combination (3, 9), the third side can have length 0, 1, 2, or 3. The only value that results in a valid triangle is 3, so there is 1 such triangle.

For the combination (4, 8), the third side can have length 0, 1, 2, or 4. The only value that results in a valid triangle is 4, so there is 1 such triangle.

For the combination (5, 7), the third side can have length 0, 1, 2, 3, or 5. The only value that results in a valid triangle is 5, so there is 1 such triangle.

For the combination (6, 6), the third side can have length 0 or 6. The only value that results in a valid triangle is 6, so there is 1 such triangle.

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