Brenda is placing tile on her
bathroom floor. The area of the
floor is 15x2-8x - 7 ft². The area
of one tile is x² - 2x + 1ft². To find
the number of tiles needed,
simplify the rational expression:
15x²-8x-7
x²–2x+1

$50 is the constant charge used for each minute.

We must put up two variables in order to fix this issue. In this instance

F = constant Fee

R = rate used per minute.

So the cost for the month of January is calculated like this:

F+250R= 70

And the cost for February is calculated like this:

F+275R= 72

So no we have a system of equations we can solve simultaneously. This can be solved using different methods, elimination, substitution, graphically, or by using matrices. I will solve this by substitution.

So let's solve the first equation for R:

[tex]R = \frac{70-F}{250}[/tex]

And let's substitute this first equation into the second equation:

[tex]F+275(\frac{70-F}{250})= 72[/tex]

And now we can solve this for F:

[tex]F+275(\frac{70-F}{250})= 72\\F+11(\frac{70-F}{10})= 72\\F+(\frac{770-11F}{10})= 72.....eq(1)\\[/tex]

We can multiply both sides by 10 so we get:

[tex]10*F+10(\frac{770-11F}{10})= 10*72\\\\10F+770-11F= 720\\\\770-720 = 11F - 10F\\50 = F[/tex]

Therefore, $50 is the constant charge used for each minute.

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Answer: 26

Step-by-step explanation:

Since we are given the value of y, all we need to do is plug it into the equation and solve it. Make sure if you plug this into a calculator that you put the substituted number in parenthesis that way it squares the number correctly without a negative sign.

(-3)²-5(-3)+2

9 - 5(-3) +2

9 - -15 + 2

9 + 15 + 2

24 + 2

26

Hope this helps!

[tex](3x+2)(3x^{2} +4)[/tex]

This equation can be solved using the distributive is by multiplying each term by the other term.

First, multiply [tex]3x[/tex] by [tex]3x^{2} +4[/tex]

[tex]3x(3x^{2} +4)=(3x*3x^{2} )+(3x*4)[/tex]

Then, multiply [tex]2[/tex] by [tex]3x^{2} +4[/tex]

[tex]2(3x^{2} +4)=(2*3x^{2} )+(2*4)[/tex]

Summary the two equations

[tex](3x*3x^{2} )+(3x*4)+(2*3x^{2} )+(2*4)[/tex]

The correct expansion of [tex](3x+2)(3x^{2} +4)=(3x*3x^{2} )+(3x*4)+(2*3x^{2} )+(2*4)[/tex] (C)

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The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14)  of the graph x is 9/2.

The turning point's x-coordinate will be "9/2."

The answer to the query is

y = [tex]x^{2}[/tex] + bx + c

curving goes by.

(2 , 0)

and,

(0 , 14)

Putting (0, 14) results in

→ 14 = 0 +  0 + c

c = 14

then,

→ y = [tex]x^{2}[/tex] + bx + 14.

Putting in (2, 0) gives us

→0 = 4 + 2b + 14

-2b = 18

b =  - 18 /2

= -9

then,

→ y = [tex]x^{2}[/tex] - 9x + 14.

the discovery of

→ dy / dx = 0

dy/dx = 2x - 9

turning point

→ dy / dx = 0

2x - 9 = 0

x = 9/2.

The curve intersects

The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14)  of the graph x is 9/2.

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6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.

6! = 720

6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

So the answer is 720 ways.

There are 720 ways in which a multiple-choice question on an online quiz with six answer choices can be displayed. This is calculated by multiplying all the integers from 1 to 6, which is referred to as 6 factorial, or 6!. 6! is calculated by multiplying 6 x 5 x 4 x 3 x 2 x 1, which equals 720. This means that there are 720 possible combinations of answer order that can be shown to each student when they take the quiz. With such a wide variety of possible answers, students can focus on the content of the question rather than on the order of the answers, which can help to reduce bias and ensure the validity of the quiz.

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Students that ran faster than Amy are Chris and Ethan.

Speed is the ratio between distance and time. The formula for speed

v = d ÷ t

Amy's speed

Brian's speed

Chris's speed

Ethan's speed

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The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.

Given data :

calculate a 95% two-sided confidence interval on the mean for women and men separately :

A) The confidence interval for women: [1711.70] <u< [1894.10]

Women = [tex]\frac{1674+ 1622 + 1637 + 1838 + 1964 + 1836 + 1728 +1913 + 1885 + 1932}{10}[/tex] = 1802.9

B) B) The confidence interval for men: [2096.50] <u< [2513.80]  

Men =   [tex]\frac{1852 + 2403 + 2383 + 2336 + 2597 + 2581 + 2169 + 2120}{8}[/tex] =  2305.125

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The cosecant of angle U is csc(U) = 1 / sin(U) = √55 / 4

To find the cosecant of angle U in triangle UTV, we need to find the sine of angle U. To do this, we can use the sides of the triangle that are opposite and adjacent to angle U. In a right triangle, the sine of an angle is equal to the opposite side divided by the hypotenuse.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]VT^2 + UT^2 = UV^2[/tex]

4^2 + (√39)^2 = UV^2

16 + 39 = UV^2

55 = UV^2

UV = √55

So, the length of the hypotenuse is √55. To find the sine of angle U, we can use the ratio of the opposite side (UT) to the hypotenuse:

sin(U) = UT / UV = 4 / √55

The cosecant of angle U is then:

csc(U) = 1 / sin(U) = √55 / 4.

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If Brick San Antonio playing a game of counters Rick has some counters Selma. the number of count as Tony has = 1: P work out the value of paid is 1.5.

Let x represent the number of counter brick

Let 2x counter represent  Selma

Let 2x -6 counter  represent Tony

Hence,

x+2x+2x -6 =54

5x -6 =54

5x =60

x =60/5

x =12

So Brick has 12

Tony has 2×12 -6

= 24 -6

=18

Thus

12:18 = 1: 18/12

=1:1.5

Hence,

P =1.5

Therefore the number of count as Tony has = 1: P work out the value of paid is 1.5.

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The credit term 3/15, n/45 states that the buyer will receive a 3% discount if the payment is made within 15 days. Otherwise, full payment is expected within 45 days from the invoice date.

This term can be expressed as a formula and calculation as follows:

Discount = 3% of Invoice Total

Payment due within 15 days = Invoice Total - Discount

Payment due within 45 days = Invoice Total

For example, if the invoice total is $500, then the buyer will receive a 3% discount (Discount = 3% x $500 = $15) if the payment is made within 15 days. The payment due within 15 days is then equal to the invoice total minus the discount ($500 -$15 = $485). On the other hand, if the payment is not made within 15 days, the buyer is expected to pay the full invoice total within 45 days ($500).

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The area of the octagon is 40 + 40√(2) in simplest radical form.

What is the area of the octagon?

The area of a regular octagon can be calculated using the formula:

Area = (2 + 4 * √2) * s^2

where s is the length of one of the sides.

An equiangular octagon is an octagon in which all of the angles are congruent. In addition, all the side lengths are also congruent. However, in the case of the side lengths of the octagon are given as 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order.

To find the area of the octagon, we can use the following formula:

Area = 2(1 + 2 + 3 + 4)(4) * (1 + √(2))/4

Area = 2(10)(4) * (1 + √(2))/4

Area = 80 * (1 + √(2))/2

Area = 40 + 40*√(2)

Hence, the area of the octagon is 40 + 40√(2) in simplest radical form.

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Answer:

transformed function, g (x) =1/7x+5

Step-by-step explanation:

The standard deviation of the Age variable is 8.2195 years. 95% of the data observations fall between 18.8 and 31.1.

1) The standard deviation of the Age variable is 8.2195 years.

2) Between 18.8 and 31.1.

1) To calculate the standard deviation of the Age variable, first calculate the mean of the variable. To do this, add up all of the values and divide by the total number of observations (in this case, 12). The mean is then 24.75. To calculate the standard deviation, subtract the mean from each observation, square the result, and sum the squared differences. Divide the sum by 11 (the total number of observations minus 1), then take the square root of the result. The standard deviation of the Age variable is 8.2195 years.

2) To find the values between which 95% of the data observations fall, calculate the standard deviation multiplied by 1.96. This will give the range for the 95% of the data observations. To find the lower value, subtract the standard deviation multiplied by 1.96 from the mean. For the upper value, add the standard deviation multiplied by 1.96 to the mean. In this case, the lower value is 18.8 and the upper value is 31.1.

The standard deviation of the Age variable is 8.2195 years. 95% of the data observations fall between 18.8 and 31.1.

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Answer:

-1/2

Step-by-step explanation:

first u would label ur x and ys 2,6 would be x1, y1 then u would put 8,4 would be x2 and y2 . You would put 4-6 as y2 - y1  and 8-2 as x2 - x1 to get -2 divided by 4 to get your -1/2

The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.

Given an eight-sided die,

to find the sample space,

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.

when eight sides die is tossed there will be 8 sample spaces that are,

1, 2, 3, 4, 5, 6, 7, 8,

so S = {1, 2, 3, 4, 5, 6, 7, 8}

Hence option D is correct.

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In this sample, the events "bride" and "groom"  are not mutually exclusive.

In logic and probability theory, mutually exclusive events are events that do not take place at the same time.  This means that any such two or more events are not going to happen together but will take place at different times. For example - when a die is rolled, we might get any of the six numbers but they don't appear at the same time together.

In the given problem we see that the randomly selected person can either be the groom's friend or the bride's friend or they can be a friend of both of them. This means that both events can take place together at the same time. And, hence, these are not mutually exclusive events.

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Therefore ,as a result, the total surface area is 64 + 16 = 80 square units.

The amount of space it occupies on the surface is a decent indication of its overall size. The complete surroundings is taken into account when calculating the area of a tri shape. Something's total size is determined by its surface area. The volume of water inside a cuboid is equal to the total of the volumes on each and every six of its rectangular sides. To calculate the box's measurements, use the formula below: In 2lh, 2lw, and 2hw, the region is identical (SA). The surface area of the multipurpose shape represents the region.

Here,

Imagine a line running from 8m to 4m at the intersection. As a result, a rectangle and a triangle are formed.

Simple

=> is the square's area

=> 8 *8  = 64 square units.

Use the formula

=> (1/2)b*h to determine the triangle's area 

We need to enter the hieght, which is already known to be 4, and the base, which is already known to be 8, into the equation.

=> Triangle area unit = 1/2 * 8 * 4

Therefore ,as a result, the total area is 64 + 16 = 80 square units.

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Answer:

x=-1

Step-by-step explanation:

3x^2+6x=-3

factor:

3x(x+2)=-3

Here, its obvious what x has to be: -1, just solve to confirm:

(3*-1)(-1+2)=-3

(-3)(1)=-3

-3=-3

Hope this helps.

The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

Let us suppose the width of the rectangular metal = w.

Then the length of the rectangular metal is = 20 + w

Given that squares of 4in are cut from the four corners, then the new width and length will be:

width = w - 8

length = 20 + w - 8

The height of the rectangular metal when the flaps are folded are 4 in.

The volume of the rectangular prism is:

V = (l)(w)(h)

Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:

1716 = (w - 8)(20 + w - 8)(4)

1716 = 80w + 4w^2 - 32w - 640 - 32w + 256

1716 = 4w^2 + 16 w - 384

4w^2 + 16w -384 - 1716 = 0

4w^2 + 16w - 2100 = 0

w^2 + 4w - 525 = 0

w^2 + 25w - 21w - 525 = 0

w(w + 25) - 21 (w + 25) = 0

(w - 21) (w + 25) = 0

w = 21

w = -25

The dimensions of the box cannot be negative hence, the width is 21.

length = 20 + 21

length = 41

The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.

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The Ordinary integral of the Line integral [tex]\int _c {(y-z)} \, ds[/tex] where C is the helix ⟨7cos t, 7sin t, t⟩ is [tex]\int\limits^0 _{-2\pi} \sqrt{50}{(7sin\ t -t)} \, dt[/tex] and its value in the range -2π ≤ t ≤ 0 is 10√2 π²

We have x = 7cos t, y = sin t and z = t.

We also need ds =[tex]\sqrt{(\frac{dx}{dt})^{2} +(\frac{dy}{dt})^{2} +(\frac{dy}{dt})^{2} }dt[/tex]

     ds  = [tex]\sqrt{(-7sin\ t)^{2} +(7cost\ t)^{2} +(1)^{2} }dt[/tex]

           = [tex]\sqrt{49sin^{2}t +49cos^{2}t+1 }dt[/tex]

           = [tex]\sqrt{49(sin^{2}t +cos^{2}t)+1 }dt[/tex]

     ds  = [tex]\sqrt{50}dt[/tex]

Now,  [tex]\int _c {(y-z)} \, ds[/tex] =  [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]

Evaluating the integral [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]

[tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]   =  [tex]\sqrt{50}\ {[-7cos\ t -\frac{t^{2} }{2} ]}\limits^0 _{-2\pi}[/tex]

                                     =  [tex]\sqrt{50}\ {[-7+7+2\pi ^{2}]}[/tex]

                                     =  [tex]10\sqrt{2}\pi ^{2}}[/tex]

The question is incomplete, the complete question is

" Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.[tex]\int _c {(y-z)} \, ds[/tex] ; C is the helix ⟨7cos t, 7sin t, t⟩, for -2π ≤ t ≤ 0 "

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The area of ∆PQR is 42 [tex]cm^{2}[/tex]

We can use Heron's Formula to find the area of a triangle when we have the length of its three sides. Heron's Formula states that the area of a triangle with sides p, q, and r is:

Heron's Formula :

Area =[tex]\sqrt(s(s-p)(s-q)(s-r))[/tex]

where s is the semi-perimeter of the triangle (half of the perimeter).

In this case, we know that the perimeter of the triangle is 24 cm and p+q = 18 cm, and q+r = 14 cm. We can use these equations to find the length of the third side, r.

p+q+r = 24 cm

r = 24 - (p+q) = 24 - 18 = 6 cm

Now we can use this information to find the semi-perimeter of the triangle:

s = (24 cm) / 2 = 12 cm

Now we can substitute the values of p, q, r, and s into Heron's formula to find the area of the triangle:

Area = √(12 x (12-18) x (12-14) x (12-6))

Area = √(12 x (-6) x (-2) x 6)

Area = √(12 x (-12) x (-12))

Area = √(12 x 144)

Area = √(1728) = 42 [tex]cm^{2}[/tex]

Therefore, the area of ∆PQR is  42[tex]cm^{2}[/tex]

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B) In a right triangle where a=1 and b=1, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 1^2 + 1^2 = 1+1 =2, so c = √2

C) In a right triangle where a=5 and b=6, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 5^2 + 6^2 = 25+36 =61, so c = √61

The equation as a single logarithm is log(4x)^3)/(4y)^2

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]

Log with base e = 2.71828... is written as

[tex]\ln(x)[/tex]

Log with base 10 is written as

[tex]\log(x)[/tex]

Given;

Equation=3log4x-2log4y

=log(4x)^3-log(4y)^2

=log(4x)^3)/(4y)^2

Therefore, the answer of logarithm will be log(4x)^3)/(4y)^2

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The required correct way of division has been shown, as per the long division.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
The questions seem to be incomplete, so we assume the number 729 that Allie divides it by the number 9.
According to the question,
Long division,

9 ] 729  [8 1
   - 72
---------------
       0 9
        - 9
---------------
          0

Thus, the required correct way of division has been shown, as per the long division.

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Three standard deviations contain a portion of the data equal to 88.9%.

According to Chebyshev's theorem, you can use the equation to roughly estimate the fraction of the data that lies within k standard deviations of the mean given a normal distribution.

Portion of data[tex]$=\left(1-1 / k^2\right)$[/tex]

The answer is, per Chebyshev's theorem, the range of of prices in which [tex]$88.9 \%$[/tex] of data lies is [tex]$[\$ 3.62, \$ 4.28]$[/tex].

The equation for Chebyshev's theorem is:

Portion of data [tex]$=\left(1-1 / k^2\right)$[/tex]

Where:

- k is the number of standard deviations a value is from the mean.

In this case the portion of data interest is [tex]$88.9 \%$[/tex]

Solve the equation for k

[tex]& 0.889=\left(1-1 / k^2\right. \\[/tex]

[tex]& -0.111=-1 / k^2 \\[/tex]

[tex]& k^2=1 / 0.111 \\[/tex]

[tex]& k^2=9.0 \\[/tex]

[tex]& k=3.0[/tex]

Three standard deviations contain a portion of the data equal to[tex]$88.9 \%$[/tex].

That is 3 times [tex]$\$ 0.11=\$ 0.33$[/tex]

Range is [tex]$\$ 3.95 \pm \$ .33$[/tex].

The complete question is,

Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.95 with a standard deviation of $0.11. Using Chebyshev's Theorem, state the range in which at least 88.9% of the data will reside.

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The value of x makes that makes the parallelogram a rectangle is D. 5

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. The interior opposite angles of it are equal. Additionally, the angles on the same side of the transversal are complementary to one another or add up to 180 degrees.

This will be:

2x + 4 = 14

Collect the like terms

2x = 14 - 4.

2x = 10

Divide

x = 10 / 2

x = 5

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The expression in terms of xx that represents the total amount that Elizabeth paid is - xx + 0.07xx + 0.2(xx + 0.07xx) = 1.47xx

This question uses the concepts of percentages and algebraic expressions.

The expression that is used to calculate the total amount that Elizabeth paid is an example of an algebraic expression.

It uses the percentage tax rate of 7% and the percentage tip rate of 20%, which are both represented by decimal numbers.

Step 1: Calculate the tax by multiplying the subtotal (xx) by the tax rate (0.07): 0.07xx

Step 2: Calculate the tip by multiplying the subtotal (xx) plus the tax (0.07xx) by the tip rate (0.2): 0.2(xx + 0.07xx)

Step 3: Calculate the total by adding the subtotal (xx), the tax (0.07xx), and the tip (0.2(xx + 0.07xx)): xx + 0.07xx + 0.2(xx + 0.07xx)

Step 4: Simplify the expression to 1.47xx.

xx + 0.07xx + 0.2(xx + 0.07xx) = 1.47xx

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In order to get another number, a number must be raised to a certain power, which is known as a logarithm.

calculation is attached below :

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The angles for the triangle are 42°, 68° and 70° and x=21.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As sum of all angles of a triangle is 180°

2x+3x+5+4x-14=180

x=21

hence,

         The angles for the triangle are 42°, 68° and 70° and x=21.

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Right question:-

Angles in the question are 2x°,(3x+5)° and (4x-14)° of a triangle.