What are we missing in the triangle in the picture?

The required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.

Given that,
To arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p²​.

The algebraic expression consists of constant and variable. eg x, y, z, etc.

Here,
(a)
= 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
= 7x⁵ - 7x⁴  - 4x⁴+ 2x³ + 11x³– x
=  7x⁵ + 13³ - 11x⁴ - x,

(b)
=  -2p - 3p² +  1 - 5p + 8p²
= 1  -2p - 5p -3p² + 8p²
=  1 - 5p + 8p²​

Thus, the required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.

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The required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵  – x and - 7p + 5p²​+ 1.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.

The polynomials are given in the question :

2x³ - 7x⁴ + 7x⁵, and 11x³ - 4x⁴ – x

-2p - 3p² and,1 - 5p + 8p²​

According to the question,

⇒ 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x

Rearrange the terms and apply the arithmetic operation,

⇒ 2x³ + 11x³- 7x⁴- 4x⁴ + 7x⁵  – x

⇒ 13x³- 11x⁴+ 7x⁵  – x

⇒ -2p - 3p² + 1 - 5p + 8p²​

Rearrange the terms and apply the arithmetic operation,

⇒ -2p - 5p - 3p²  + 8p²​+ 1

⇒ - 7p + 5p²​+ 1

Thus, the required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵  – x and - 7p + 5p²​+ 1.

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There are 54% of the participants are female.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage

Given:
There are 104 males and 121 females

participating in a marathon.

So, the total number of participants are,

104 + 121 = 225.

There are 225 total number of participants.

So, the percent of the female are,

[tex]\frac{121}{225} (100) = 53.78[/tex]

Therefore, the percent of the participants of female are 54%.

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The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624, or 96.24%.

We must comprehend the central limit theorem and the normal probability distribution in order to answer this query.

Distribution of Normal Probabilities

The z-score formula can be used to address problems with normal distributions.

The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.

Imagine that 9% of a huge shipment of televisions were defective.

As a result, the sample size has a p value of 0.09

As a result, n=393

Standard deviation and the mean

u=p= 0.09

s= sqrt(p(1-p)/n)

s=sqrt(0.09*0.91/393)= 0.0144

What is the likelihood that the sample percentage and population proportion will deviate by less than 3%?

The ratio of 0.09 - 0.03 = 0.06 to 0.09 + 0.03 = 0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p-value of Z when X = 0.06.

X = 0.12

By the Central Limit Theorem

Z= x-u/s

Z=2.08  has a p-value of 0.9812

X = 0.06

Z= x-u/s

Z=-2.08 has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.

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Answer:

Step-by-step explanation:

The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624.

Distribution of Normal Probabilities

The z-score formula can be used to address problems with normal distributions.

The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p- value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.

Imagine that 9% of a huge shipment of televisions were defective.

As a result, the sample size has a p value of 0.09

As a result, n=393

Standard deviation and the mean u=p=0.09 s= sqrt(p(1-p)/n)

s=sqrt(0.09*0.91/393)=0.0144

The ratio of 0.09 -0.03=0.06 to 0.09 + 0.03 =0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p- value of Z when X = 0.06.

X = 0.12

By the Central Limit Theorem

Z=x-u/s

Z-2.08 has a p-value of 0.9812

X = 0.06

Z=x-u/s

Z=-2.08 has a p-value of 0.0188

0.9812 -0.0188=0.9624

Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.

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Inequality involving the sum of the angles of a triangle i.e,

[tex]\alpha +\beta +y > \pi[/tex]

The area of a spherical triangle ABC with angles a, B, Y are

AABC = ([tex]\alpha[/tex] + [tex]\beta[/tex]+ Y- [tex]\pi[/tex] ) [tex]R^{2}[/tex]

The AA'B'C' = AABC (by sss) as we discuss move.

We just need to demonstrate that IACI = IAC' and C'L IBCI = 1BC '1 will proceed similarly.

since AC & ATC resulted in the same.

the middle.

We now have external proof that the surface and their mon- are real. As of (ABCA) and LA'B'C) cover. A overlapping sphere with appropriate angles for each letter of the alphabet Las offered my first figure of $ segments that are completely separate from one another, so we may write -

( AABC A ) + ( A A'B'C' )A + ( An -x ) + ( Ax-B ) + ( An-V ) = [tex]4\pi R^{2}[/tex]

2 ( A ABC A ) =[tex]4\pi R^{2}[/tex] - 2 ( [tex]\pi -\alpha[/tex] ) [tex]R^{2}[/tex]- 2 ( [tex]\pi -\beta[/tex])[tex]R^{2}[/tex]-2([tex]\pi -Y[/tex])[tex]R^{2}[/tex]

AABCA = [tex](\alpha +\beta +Y-\pi )R^{2}[/tex]

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The acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.

Differentiation is a process to find the instantaneous rate of change in function based on one of its variables.

The hypotenuse of a right triangle is growing at a constant rate of a centimeters per second

[tex]\frac{dH}{dt} = a[/tex]

One leg is decreasing at a constant rate of b centimeters per second

[tex]\frac{dy}{dt} = -b[/tex]

From the right triangle

sin θ = [tex]\frac{y}{H}[/tex]           (y is the perpendicular and H is the hypotenuse)

Differentiate both sides with respect to t

cos θ*dθ/dt = (H*dy/dt - y*dH/dt) / H²

cos θ*dθ/dt =  [H(−b)−y(a)] / H²........................(1)

If the both legs are 1 cm.

∴ H= [tex]\sqrt{ 2[/tex],cosθ=sinθ=1/[tex]\sqrt{2}[/tex]

Thus , Equation (1)

cos θ*dθ/dt =  [H(−b)−y(a)] / H²

1/√2*dθ/dt = [√2 (−b)−(a)] / 2

dθ/dt = √2  [(√2 (−b)−(a)) / 2]

Therefore, we can conclude that the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.

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Answer:

Step-by-step explanation:

Item 1

<RSL is not ≅ < XYM

Item 2

< LST and < QRX are not supplementary (they are congruent)

Item 3

m < LST = 120 - there is no evidence for this.

Item 4

< JRS = <LST

so, If < LST =  120, then this can't be 195

Answer:

The translation rule is;

Explanation:

Given the graph attached;

Let us pick a corresponding edge(point) on the preimage and image respectively;

The change on the x and y axis is;

Therefore, the translation rule is;

It is called the slope of the regression line.

The slope of the regression line including the intercept displays the linear relationship between 2 variables and can also be used in estimating an average change rate.

The slope of a regression line depicts the rate of change in the dependent variable as the independent variable alters because the dependent variable y is dependent on the independent variable x.

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6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given three vertices are D(1, 1), E(3, −1), and F(4, 4)

we need to find the area of triangle

Area of triangle=1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

x₁=1, x₂=3, x₃=4, y₁=1, y₂=-1, y₃=4

put in the formula

Area of triangle=1/2|1(-1-4)+3(4-1)+4(1-(-1))|

=1/2|-5+9+8)|

=1/2 |12|

=6 square units.

Hence 6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)

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The perpendicular linear equation that passes through (8, 2) is:

y = x - 6

A general linear equation is of the form:

y = m*x + b

Where m is the slope.

Two lines are perpendicular only if the product between the slopes is equal to -1.

Here we start with the line:

y = -x

So the slope is -1.

Then the slope of the perpendicular line m must be:

-1*m = -1

m = -1/-1 = 1

Then the perpendicular line is something like:

y = x + b

And we want this to pass through (8, 2), replacing these values we get:

2 = 8 + b

2 - 8 = b

-6  =b

The linear equation is:

y = x - 6

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The spaces with inputs; 5 has an output of 16 × 4 + 6 × 25, 100 has an output of 16 × 99 + 6 × 10000, and p has an output of 16 × (p-1)+ 6 × p².

Following the given three examples of the outputs from inputs 1, 3 and 7, we will discover a pattern of subtracting 1 from an input, multiply the result by 16, and then add the square of the input multiplied by 6 to it.

We will derive the missing outputs as follows;

For input 5:

5 - 1= 4

16 × 4

16 × 4 + 6 × 5²

16 × 4 + 6 × 25

For input 100:

100 - 1 = 99

16 × 99

16 × 99 + 6 × 100²

16 × 99 + 6 × 10000

For input p:

p - 1

16 × (p - 1)

16 × (p - 1) + 6 × p²

Hence, the input 5 gives an output 16 × 4 + 6 × 25, input 100 gives an output 16 × 99 + 6 × 10000 and input p gives an output of 16 × (p - 1) + 6 × p² from the reasoned pattern.

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The coordinates of the dresser

i.e A(-1,-1), B(2,-1), C(2,1), D(-1,1)

after rotating the dresser 180 degrees about the origin, translating 2 units left and 3 units up becomes

A(3, 2), B(0, 2), C(0,0), D(3, 0)

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The coordinates of the vertices of the dresser.

A(-1,-1), B(2,-1), C(2,1), D(-1,1).

Now,

Rotating 180 degrees the coordinates become,

A(2, 1), B(-1, 1), C(-1, -1), D(2, -1)

Translating 2 units left.

The coordinates become:

A(2-2, 1-2), B(-1-2, 1-2), C(-1-2, -1-2), D(2-2, -1-2)

A(0, -1), B(-3, -1), C(-3, -3), D(0, -3)

Translating 3 units up.

The coordinates become:

A(0+3, -1+3), B(-3+3, -1+3), C(-3+3, -3+3), D(0+3, -3+3)

A(3, 2), B(0, 2), C(0,0), D(3, 0)

Thus,

The coordinates of the dresser

i.e A(-1,-1), B(2,-1), C(2,1), D(-1,1)

after rotating the dresser 180 degrees about the origin, translating 2 units left and 3 units up becomes

A(3, 2), B(0, 2), C(0,0), D(3, 0)

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Answer:

G

Step-by-step explanation:

the domain is the interval or set of all valid x values.

we see x starts at -3 and goes up to +1.

but x = 1 has the be excluded (the hollow point tells us that, a filled point says "include").

therefore, the -3 <= x < 1 answer is correct

The equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)

From the question, we have the following parameters:

Roots = -4 and 2

Point = (1, -5)

Rewrite the given parameters as

Roots: x = -4 and x = 2

Point: (x, y) = (1, -5)

Recall that:

x = -4 and x = 2

This gives

x + 4 = 0 and x - 2 = 0

Multiply the equations

So, we have

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

When (x, y) = (1, -5), we have

-5 = a(1 + 4)(1 - 2)

This gives

a = 1

Substitute a = 1 in y = a(x + 4)(x - 2)

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

Hence, the equation of f(x) = (x + 4)(x - 2)

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Answer:

f(x) = (x − 2)(x + 4)

Hope this helps you

The three sigma control limits range from 0 to 8.20 for this size inspection limit and The probability of a type I error is 0.0038.

The inspection unit calculator in this case is 2

1.5 non-conformities on average per machine

Consequently, we would typically discover 2 * 1.5 = 3 non-conformities.

Here, C equals 3.

Lower Limit = C - 3 * c, which equals 3 - 3 * sqrt (3), which results in -2.19 (impossible), therefore 0

Reduced Limit = 0

Upper Limit: 8.20 when C + 3 * с + 3 + 3 * sqrt(3)

In this case, the three sigma control limits range from 0 to 8.20 for this size inspection limit.

(b) Type I errors happen when non confirmations go above the acceptable range.

This is a POISSON (3)

P(c > 8.20) = -1 POISSON (8, 3, true)

=1 - 0.9962

= 0.0038

In this case, the probability of a type I error is 0.0038.

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37 inches total, but 35 with just December, January, and February (depending on the definition of winter)

Part A

[tex]D(1,0) \longrightarrow D'(1-8, 0-3)=D'(-7, -3)\\\\E(7,2) \longrightarrow E'(7-8, 2-3)=E'(-1, -1)\\\\F(8,-1) \longrightarrow F'(8-8, -1-3)=F'(0, -4)\\\\G(2,-3) \longrightarrow G'(2-8, -3-3)=G'(-6, -6)[/tex]

Part B

Reflecting over the x axis means [tex](x, y) \longrightarrow (x, -y)[/tex].

[tex]D'(-7, -3) \longrightarrow D''(-7, 3)\\\\E'(-1, -1) \longrightarrow E''(-1, 1)\\\\F'(0, -4) \longrightarrow F''(0, 4)\\\\G'(-6, -6) \longrightarrow G''(-6, 6)[/tex]

Answer:

y = 54

Step-by-step explanation:

a) Multiply both sides by 9/(-7).

(9/-7) * (-7/9 y) = (9/-7) * (-42)

y = 54

Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.

Remember the relation:

Speed*time = distance.

Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.

Here we know that:

Kadeem drives at a constant speed of 50mi/h

Quinn drives at a constant speed of 75 mi/h.

Replacing that in the equation:

Kadeem's case:

(50 mi/h)*t = 25mi

t = (25 mi)/(50 mi/h) = 0.5 hours.

Quinn's case:

t = (25mi)/(75 mi/h) = 0.33 hours.

So Kadeem takes longer.

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Answer:

b = 18

The mortar is 17 times ( 3 / 8 ) tall.

The brick height is equal to 18 times ( 2 + ( 1 / 4 ) ).

I don't know the options, so you have to use those values.

Step-by-step explanation:

The question uses imperial units which are generally bad.

12 inches = 1 feet;

The height of the wall should be written in inches for convenience.

4 feet = 4 * 12 inches;

4 feet = 48 inches;

The wall is short 1 + ( 1 / 8 ) inches short of 4 feet.

48 inches - ( 1 + ( 1 / 8 ) inches ) = 46 + ( 7 / 8 ) inches;

Now that the wall is done let's do the bricks. The height of the bricks is 2 + ( 1 / 4 ) inches and the mortar is ( 3 / 8 ) inches tall. The amount of mortar is the number of bricks - 1 because nobody puts extra mortar on the top of the wall.

let b;

46 + ( 7 / 8 ) = b( 2 + ( 1 / 4 ) ) + ( b - 1 )( 3 / 8 );

375 / 8 = b( 9 / 4 ) + ( 3 / 8 )b - ( 3 / 8 );

375 / 8 = ( ( 9 / 4 ) + ( 3 / 8 ) )b - ( 3 / 8 );

375 / 8 = ( ( 18 / 8 ) + ( 3 / 8 ) )b - ( 3 / 8 );

375 / 8 = ( 21 / 8 )b - ( 3 / 8 );

Multiply both sides by 8 to get rid of those annoying fractions.

375 = 21b - 3;

Add 3 to both sides.

378 = 21b;

Divide both sides by 21.

18 = b;

The polar form of the rectangular form - 9 - i 9√3 is 18 · [cos (4π / 3) + i sin (4π / 3)]. (Correct choice: A)

Herein we find a complex number in rectangular form, that is, a complex number of the form a + i b, whose polar form has to be found. Complex numbers in polar form are defined by the following expression:

z = r · (cos θ + i sin θ)

r = √(a² + b²)

θ = tan⁻¹ (b / a)

Where:

If we know that a = - 9 and b = - 9√3, then the complex number in polar form is:

r = √[(- 9)² + (- 9√3)²]

r = 18

θ = tan⁻¹ √3

θ = 4π / 3

The polar form is 18 · [cos (4π / 3) + i sin (4π / 3)].

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Answer: 529.3 downloads

Explanation:

Standard version size = 2.1 MB

High quality version = 4.7 MB

The high-quality version was downloaded twice as often as the standard version

H = 2 S

The total size downloaded for the two versions = 3335 MB

H + S = 3335

We have the system:

H = 2 S (a)

H + S = 3335 (b)

Put A into B

(2S ) + S = 3335

3S = 3335

S= 3335/3

S= 1,111.67 MB

Divide the total MB of standard versions by the size of each standard version.

1,111.67 / 2.1 = 529.3 downloads

1) Area of patio = 1/2 base x height

Height = 3.1ft

base = 7 + 10 =17 ft

Area = 1/2 x 3.1 x 17

Area of patio = 26.35 square ft

1 yard = 3 ft

1 square yard = 9 square ft

so the area of the patio in yard is

26.35/9 = 2.927777778 square yard

2) Cost of concrete = $10/square yard poured 1/9 yard deep+ $60 delivery fee

for 2.9277777778 square yard it will cost 1/9($10 x 2.9277777778) + $60 =$

3)

Using a piecewise function, it is found that:

a. The rule is:

b. C(75) = 36.25.

c. C(100) = 27.

d. A practical domain for the function is integer values of w ≥ 0

e. A practical range the function is C(w) ≥ 0.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For 0 to 50 wristbands, which is the first definition of the function, the cost is of $0.75 per each wristband, hence the definition is:

C(w) = 0.75w, 0 ≤ w ≤ 50.

From 51 to 75 wristbands, which is the second defition of the function, the cost is of $0.35 per each wristband plus the $10 shipping fee, hence:

C(w) = 0.35w + 10, 51 ≤ w ≤ 75.

For more than 75 wristbands, which is the third definition of the function, the cost is of $0.2 per wristband plus the $7 shipping fee, hence:

C(w) = 0.2w + 7, w > 75.

The numeric values are as follows:

The domain and the range of the function are as follows:

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Answer

A) f(w) = 80w + 30

B) w represents the number of weeks and f(w) the number of flowers that bloomed

C) 2830 flowers

Step-by-step explanation

A) To find the function f, which represents the number of flowers that bloomed, as a function of w, the number of weeks, we have to evaluate f(s) with s = s(w) = 40w, as follows:

B) w represents the number of weeks and f(w) the number of flowers that bloomed, like before.

C) Substituting w = 35 weeks into f(w), we get:

The transformation that relates the two functions:

f(x) = y = -√(-4x)

g(x) = y = √(-4x)

Is a reflection across the x-axis.

We define a reflection across the x-axis as a transformation that does a "vertical reflection" along the line y = 0 (which is the x-axis).

For a function f(x), a reflection across the x-axis generaste the new function g(x) that can be written as:

g(x) = -f(x).

In this case the original function is:

f(x) = y = -√(-4x)

And the transformed function is:

g(x) = y = √(-4x)

You can see that the only difference is the sign, such that we can write:

g(x) = -f(x) = -(-√(-4x)) = √(-4x)

So we conclude that the transformation is a reflection across the x-axis.

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The diagonals of a rectangle are congruent, so RT = SU, that is

3x + 8 = 6x - 4 (subtract 4x from both sides)

3x + 8 = 6x - 4

Subtract 8 from both sides 3x + 8 - 8 = 6x - 4 - 8

Simplifying the above equation, we get

3x = 6x-12

Subtract 6x from both sides 3x - 6x = 6x - 12 - 6x

Simplifying the above equation, we get

-3x = -12

Divide both sides by -3

[tex]$\frac{-3 x}{-3}=\frac{-12}{-3}[/tex]

x = 4

Then, R T= 3x + 8 = 3(4) + 8 = 20

The diagonals bisect each other, then

RV = 0.5 × 20 = 10

∠ RVU = ∠ SVT = 54° ( vertical angles)

RV = UV ( diagonals are congruent and bisect each other)

Then Δ RVU is isosceles with base angles congruent, then

∠ VUR =[tex]$\frac{180-48}{2}[/tex] = 66°.

In the rectangle, RV = 3x+8, SV = 6x-4, and ∠ VRS = 54° then the value of x is 4 and ∠ VUR is 66°.

The diagonals of a rectangle are congruent, so RT = SU, that is

3x + 8 = 6x - 4 (subtract 4x from both sides)

3x + 8 = 6x - 4

Subtract 8 from both sides 3x + 8 - 8 = 6x - 4 - 8

Simplifying the above equation, we get

3x = 6x-12

Subtract 6x from both sides 3x - 6x = 6x - 12 - 6x

Simplifying the above equation, we get

-3x = -12

Divide both sides by -3

[tex]$\frac{-3 x}{-3}=\frac{-12}{-3}[/tex]

x = 4

Then, R T= 3x + 8 = 3(4) + 8 = 20

The diagonals bisect each other, then

RV = 0.5 × 20 = 10

∠ RVU = ∠ SVT = 54° ( vertical angles)

RV = UV ( diagonals are congruent and bisect each other)

Then Δ RVU is isosceles with base angles congruent, then

∠ VUR =[tex]$\frac{180-48}{2}[/tex] = 66°.

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