Find the value of Theta in these diagrams (a and b)​

In accordance with the Ferrari's method, all the roots of the quartic polynomial are complex numbers.

By fundamental theorem of algebra quartic polynomials have four roots. Based on characteristics of the quadratic formula, use for the solution of quadratic polynomials, there are three possible sets of roots:

There are several methods to solve quartic polynomials. In this case, we decide to use the Ferrari's method to determine all roots of the polynomial:

[tex]x_{1} = \frac{1 + i \sqrt{3}}{2}[/tex], [tex]x_{2} = \frac{1 - i\,\sqrt{3}}{2}[/tex], [tex]x_{3} = - \frac{5}{3} + i\,0.471[/tex], [tex]x_{4} = -\frac{5}{3} - i\,0.471[/tex]

All the roots of the quartic polynomial are complex numbers.

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The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).

Given:  (a + 1)² - 4b²

Apply Perfect Square Formula, and we get

(a + b)² = a² + 2 a b + b²

(a + 1)² = a² + 2a1+1²

= a² + 2a1 + 1² - 4 b²

simplifying the equation, we get

a² + 2a1 + 1² = a² + 2a + 1

= a² + 2a + 1 - 4b²

Factor, a² + 2a + 1 = (a + 1)²

= (a + 1)² - 4 b²

Simplify 4 b² = (2 b)²

= (a + 1)² - (2b)²

Apply the Difference of Two Squares Formula, and we get

x² - y² = (x + y)(x - y)

(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)

simplifying the equation, we get

= ((a + 1) + 2b)(a + 1) - 2 b)

= (a + 1 + 2b)(a + 1 - 2b)

Therefore, the correct answer is (a+1+2b)(a+1-2b).

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Answer:

Step-by-step explanation:

The steps to constructing either circle start with finding the relevant center and radius. The required construction techniques are ...

The incenter (center of the inscribed circle) is located at the coincidence of the angle bisectors. The radius is the perpendicular distance to any side, so will lie on the line through the incenter and perpendicular to one side.

Reference the first attachment. We have elected to bisect the largest two angles of triangle ABC. In each case, we used these steps:

After this process is repeated for another angle, the point of intersection of the two angle bisectors is the incenter (R).

Finding the radius requires finding the perpendicular distance to one side of the triangle. That is done by constructing a perpendicular to the side through the incenter.

The inscribed circle is centered at R and has radius RX.

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The circumcenter (center of the circumscribed circle) is located at the coincidence of the bisectors of the sides of the triangle. The radius is the distance from the circumcenter to any vertex.

Reference the second attachment. We have elected to bisect the longest and shortest of the triangle's sides. The purpose of this choice is to make the perpendicular bisectors intersect at a large angle, so the point is as accurately located as possible.

Repeat this process for another side (BC to create bisector JK). The intersection of the two bisectors (L) is the circumcenter.

The circumscribed circle is centered at L and has radius LA.

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Additional comments

In general, arcs that are required to intersect each other will be drawn with the same radius. An arc that is required to intersect two lines, or one line in two places, may have any convenient radius.

As with any geometric construction, the tools required are a marking tool, a compass, and a straightedge. Usually, the preferred marking tool is a sharp pencil.

If the triangle is obtuse, the circumcenter will be outside the triangle (adjacent to the long side). If the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse.

Answer:0.333

Step-by-step explanation:4+8=12 so there is only 4 chances it can be male so 4/12=0.333

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

probability (P) is calculated as

P = (desired result ) ÷ ( number of possible results )

here desired result is choosing a male from 4 males

number of possible results = 4 + 8 = 12 , then

P( male) = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]

a) The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).

b) The quadrilateral MATH is a rectangle.

Quadrilaterals are figures with four sides and whose internal angles sums a total of 360 degrees. A quadrilateral is a rectangle when each pair of opposite sides are parallel and have the same length to each others, each of the four angles are right angles and each pair of perpendicular sides.

a) Vectorially speaking, we can construct a rectangle by using the following definitions:

M(x, y) = (a, b), A(x, y) = (c, d), T(x, y) = (a, d), H(x, y) = (c, b)

If we know that a = 2, b = - 4, c = 5, d = - 2, then the points T and H are described below:

T(x, y) = (2, - 2), H(x, y) = (5, - 4)

The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).

b) To prove that quadrilateral MATH, we need to prove that:

MT = HA      

(2, - 2) - (2, - 4) = (5, - 2) - (5, - 4)

(0, 2) = (0, 2)

TA = MH

(5, - 2) - (2, - 2) = (5, - 4) - (2, - 4)

(3, 0) = (3, 0)

MT • TA = 0

(0, 2) • (3, 0) = 0 · 3 + 2 · 0 = 0

MH • HA = 0

(3, 0) • (0, 2) = 3 · 0 + 0 · 2 = 0

Therefore, the quadrilateral MATH is a rectangle.

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Answer:  $200  (choice B)

Explanation:

Notice that 100/4 = 25 which matches with the fact the cost is $25 per hour.

Therefore, 8 hours will yield a total cost of 8*25 = 200 dollars

The cost for Susan to rent a truck for her entire 8-hour work day is $200. Therefore, option B is the correct answer.

Given that, if it costs Susan $25 to rent a truck for 1 hour and $100 to rent a truck for 4 hours.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Cost of rent of truck for 8 hours = 1 hour rent × Number of hours

= 25 × 8

= $200

The cost for Susan to rent a truck for her entire 8-hour work day is $200. Therefore, option B is the correct answer.

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The volume of the right prism is 1280 cm³

The volume of a right prism is calculated using the formula

Volume = length × width × height

Where

height = 20cm

width = 8cm

length = 8cm

Substitute into the formula

Volume = 20 × 8 × 8

Volume = 1280 cm³

Thus, the volume of the right prism is 1280 cm³

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Answer:

now we know that

book is 120page

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Answer:

○ 1 hour 41 minutes or more

Step-by-step explanation:

We can make two equations that represent the total amount each plumber charges.

If [tex]x[/tex] represents the number of hours they work, then:

•Total charged by Plumber A = [tex]35 + 15x[/tex]

• Total charged by Plumber B = [tex]40+12x[/tex]

Now, if Plumber A is more expensive than Plumber B, then:

Total charged by Plumber A > Total charged by Plumber B

∴ [tex]35 + 15x[/tex] > [tex]40+12x[/tex]

Now all we have to do is solve for [tex]x[/tex]:

[tex]35 + 15x[/tex] > [tex]40+12x[/tex]

⇒ [tex]35 + 15x -12x > 40[/tex]

⇒ [tex]35 + 3x > 40[/tex]

⇒ [tex]3x > 5[/tex]

⇒ [tex]x > \bf \frac{5}{3} \space\ \mathrm{h}[/tex]

[tex]\frac{5}{3} \space\ \mathrm h[/tex]  is equivalent to  [tex]\frac{5}{3} \times 60 \space\ \mathrm {min}[/tex] = 100 minutes, which is the same as 1h 40min.

This means if Plumber A works more than 1h 40min, they become more expensive than Plumber B.

More than 1h 40min is equivalent to '1 hour 41 minutes or more', therefore the first option is correct.

Answer:

  x = 22

  BD = 20 units

Step-by-step explanation:

The formula for the area of a rhombus can be used with the given values to write an equation that can be solved for x and for BD.

The formula is ..

  A = 1/2(d1)(d2) . . . . where d1 and d2 are the lengths of the diagonals.

Using the given values, we have ...

  120 = 1/2(12)(x-2)

Dividing by 6, we find ...

  20 = x -2 = BD

  22 = x . . . . . . . . add 2

The value of x is 22.

The length of BD is 20.

Answer:

x=12

BD=10

Step-by-step explanation:

The exact value of cos(c+d) is (D) [tex]cos(c+d) = \frac{21+24\sqrt{7} }{100}[/tex].

To find the exact value of cos(c+d):

In the second quadrant:

In the third quadrant:

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

[tex]\frac{21+24\sqrt{7} }{100}[/tex] ≈ [tex]0.84498[/tex]

To prove: Perhaps you want to work this out using the trignometric identities.

cos(c) = -√(1 -sin(c)²) = -7/25

sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is: cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

Therefore, the exact value of cos(c+d) is (D) [tex]cos(c+d) = \frac{21+24\sqrt{7} }{100}[/tex].

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The complete question is given below:

What is the exact value of cos(c+d), given sine c = start fraction 24 over 25 end fraction for c in quadrant ii and cosine d = negative three-fourths for d in quadrant iii?

(A) Negative StartFraction 47 Over 100 EndFraction

(B) Negative 1 and StartFraction 3 Over 100 EndFraction

(C) StartFraction 21 minus 24 StartRoot 7 EndRoot Over 100 EndFraction

(D) StartFraction 21 + 24 StartRoot 7 EndRoot Over 100 EndFraction

Answer:

1. e

Step-by-step explanation:

18/3 +2(12-5)

=6+2(7)

=6+14

=20

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]

Divide 18 by 3 to get 6.

Therefore, the correct option is "E".

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]

It seems that none of the options is correct.

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the expression:

[tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\\ \\Simplifying:\\\\=\frac{\sqrt[4]{3x^2}}{2y}[/tex]

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

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Answer:

The answer is D

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12

7x3=21

[tex]\frac{12}{21} = \frac{4}{7}[/tex]

Answer:

.....................................

The real statement is that the closer you get to the center of the vortex, the closer the current speed approaches infinity. option C is correct.

Given the speed s of the flow in a given vortex is modeled by x=300/d, where d is the distance to the center of the vortex.

speed is defined as the rate of change of an object's position in any direction. Speed ​​is measured as the ratio of distance traveled to time traveled.

As d approaches 0, you are approaching the center of the vortex.

[tex]\begin{aligned}S&=\lim_{d\rightarrow 0}\frac{300}{d}\\ &=\frac{300}{0}\\ &=\infty\end[/tex]

Thus, if the flow in a given vortex is modeled by x = 300/d, as one approaches the center of the vortex, the speed of the flow tends to infinity.

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Answer: C- As you move closer to the center of the whirlpool, the speed of the current approaches infinity.

If the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.

Given that two trains are moving towards each other on the same railroad track. From this track there's an offshot peice of railroad- the length of whice is shorter than the length of the train but longer than the length of one train car.

We are required to find how the trains pass each other.

Two cases are there:

For each car in the shorter train

We assume that cars can be decoupled at any point in the train,so that any required order of cars can be preserved.We further assume that train can move any one of the A's car in addition to all of them.

The total number of cars lengths that must pass the off shoot is the product of the number of cars in both the trains.So,it does not seems to matter which train makes use of the offshoot.

Hence if the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.

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The value of the missing probability is:

P(A) = 1/5

So the correct option is D.

First, we know that:

P(A∩B) = probability that events A and B are true = 3/100

And we also know that:

P(B|A) = probability that event B is true given that event A is true = 3/20

Here we have the rule:

P(A∩B) = P(B|A)*P(A)

Replacing the first two:

3/100 = (3/20)*P(A)

Solving for P(A), we get:

(3/100)*(20/3) = 1/5 = P(A).

So we conclude that the correct option for the missing probability is the one in option D.

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[tex]\textit{sum of all interior angles in a polygon}\\\\ S =180(n-2) \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ S =1620 \end{cases}\implies 1620=180(n-2) \\\\\\ \cfrac{1620}{180}=n-2\implies 9=n-2\implies \underline{11=n} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{sum of all exterior angles in a regular polygon}\\\\ n\theta = 360 \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{angle~in}{degrees}\\[-0.5em] \hrulefill\\ \underline{n=11} \end{cases}\implies 11\theta =360\implies \theta =\cfrac{360}{11}\implies \theta \approx 32.7^o[/tex]

A regular polygon is a figure in which all the sides have the same length that is, they are equal and all the interior angles are of the same measure.

This regular polygon is a hendecagon.

A hendecagon is a polygon that has 9 equal sides.

( n - 2 ) 180° = 1620

As a second step, we divide by 180:

We divide

We change the direction, as the sign is negative, in the change of direction it starts to add.

We add both numbers.

Answer: the measure of the exterior angle of the regular polygon (hendecagon) is 11. ✅

Answer:

   [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

mean: (22+12+14+14+13+9)=14

|22-14| + |12-14| + ... + |9-14| =16

MAD = 16/6 = [tex]\frac{8}{3}[/tex]

The y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought. Therefore, option B is the correct answer.

Given that, Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint.

The average is (15 + 3x)/(3+x) per pint.

We need to find what quantity will be represented by the y-intercept of the graph.

Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

Now, the graph of y=(15 + 3x)/(3+x)is given below.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (−5,0)

y-intercept(s): (0,5)

So, the y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought.

Therefore, option B is the correct answer.

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Answer:

the answer to your question is 2

Step-by-step explanation:

using distance formula

√(-1-(-3))^2+(-2-(-2))^2

Answer:

2

Step-by-step explanation:

since the y- coordinates are equal, both - 2

then the distance between the points is the absolute value of the difference of the x- coordinates, that is

d = | - 1 - (- 3) | = | - 1 + 3 | = | 2 | = 2

or

d = | - 3 - (- 1) | = | - 3 + 1 | = | - 2 | = 2

Answer:

x = 7

Step-by-step explanation:

since the points all lie on the same line then the slopes of adjacent points will have the same slope.

calculate the slope using R and S then equate to slope using R and T or S and T

calculate slope using slope formula

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

with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = S (- 1, - 1 )

[tex]m_{RS}[/tex] = [tex]\frac{-1-(-3)}{-1-(-5)}[/tex] = [tex]\frac{-1+3}{-1+5}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = T (x, 3 )

[tex]m_{RT}[/tex] = [tex]\frac{3-(-3)}{x-(-5)}[/tex] = [tex]\frac{3+3}{x+5}[/tex] = [tex]\frac{6}{x+5 }[/tex]

equating [tex]m_{RS}[/tex] and [tex]m_{RT}[/tex]

[tex]\frac{6}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

x + 5 = 12 ( subtract 5 from both sides )

x = 7

If adding only twelve, you must leave out three of the fifteen, and the number of ways is = 15! / (3! * 12!).

1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12∗13∗14∗15 over

(1∗2∗3)∗(1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12) =

13∗14∗15 over

(1∗2∗3)

27306 = 455

Answer: If all toppings are distinct, then you have C 4 15 combinations. If there are three distinct toppings, you have 3 ⋅ C 3 15 combinations (because we have C 3 15 choices for toppings and then 3 choices for which of those three toppings is doubled).

Step-by-step explanation:

Answer:

-2.25

Step-by-step explanation:

The volume of box B is (A) 864 cubic meters.

To find the volume of box B:

= 864 cubic meters.

Therefore, the volume of box B is (A) 864 cubic meters.

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The complete question is given below:

Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B?

a. 864 m3.

b. 288 m3.

c. 96 m3.

d. 32 m3

The x-intercept is when y=0, but since [tex]\log_{3}(x-4) \neq 0 \text{ } \forall x[/tex], there is no x-intercept.

The asymptote is when the argument equals 0, which is at x=4.

The Surface area of the triangular prism is: 318 km³.

A triangular prism is a solid that has two triangular bases and three rectangular faces.

The surface area of a triangular prism is the sum of the areas of its two triangular bases and three rectangular faces.

The formula for the surface area of a triangular prism = (S1 +S2 + S3)L + bh, where:

Perimeter of the base  = S1 + S2 + S3

Length of the prism = L

2 × Base Area = bh

Given the following:

s1 + s2 + s3 = 7 + 9 + 8 = 24 km

L = 11 km

bh = (9)(6) = 54 km²

Plug in the values

Surface area of the triangular prism = (24)11 + 54

Surface area of the triangular prism = 264 + 54

Surface area of the triangular prism = 318 km³

Thus, the Surface area of the given triangular prism in the diagram above is: 318 km³.

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Michael took the return trip at a velocity 33.75 miles per hour.

Let suppose that Michael drove in straight line road and at constant velocity. Therefore, the speed of the vehicle (v), in miles per hour, can be defined as distance traveled by the vehicle (d), in miles, divided by travel time (t), in hours.

First trip

45 = s / 3     (1)

Second trip

v = s / 4       (2)

By (1) and (2):

45 · 3 = 4 · v

v = 33.75 mi / h

Michael took the return trip at a velocity 33.75 miles per hour.

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