Find the value of x in the triangle shown below.

Answer:

[tex]2+i[/tex]

Step-by-step explanation:

Given the expression:

[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}[/tex]

To find:

The expression of above complex number in standard form [tex]a+bi[/tex].

Solution:

First of all, learn the concept of [tex]i[/tex] (pronounced as iota) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by [tex]i[/tex].

Value of [tex]i =\sqrt{-1}[/tex].

Now, let us consider the given expression:

[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i[/tex]

So, the given expression in standard form is [tex]2+i[/tex].

Let us compare with standard form [tex]a+bi[/tex] so we get [tex]a =2, b =1[/tex].

[tex]\therefore[/tex] The standard form of

[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}[/tex]

is: [tex]\bold{2+i}[/tex]

Answer:

D. 1.3

Step-by-step explanation:

Perimeter (square) = 4*side

4 = 4*side

side = 1

We have triangle QVR. QV is a hypotenuse.

If we look at the triangle QTR, QT is a hypotenuse.

QV should be less than QT.

Let's find QT using Pythagorean theorem.

c² = a² + b²

QT² = QR² + RT² = 1² + 1² = 2

QT = √2 ≈ 1.4

QV < QT

QV < 1.4

We have 1.3 and 1 that are less than 1.4, but 1 is a length of a leg of the triangle, so 1 is impossible.

Answer D. 1.3

Answer:

(1/2)x + (1/4)y <= 200

Step-by-step explanation:

If

x = # of lbs of House blend he makes/sells a day

y = # of lbs of Exotic blend he makes/sells a day

then constraints are

(1/2)x + (1/4)y <= 200  ....................(1)

x+y <= 530  .....................................(2)

The exact answer choices are not very clear from the question, but either (or both) (1) or (2) must be one of them.  If not, please edit question or add a comment to show the answer choices.

Answer:

The true answers:

A

B

C

Step-by-step explanation:

A P E X

Answer:53 dresses

Step-by-step explanation:

First of all..if one kid required 2 1/4m of cloth,what about 119 1/4m of cloth?

So u take 119 1/4m of cloth and divide it by 2 1/4m of cloth.

Then change the mixed numbers into improper fractions.

So the question will be 477/4 m divided by 9/4 m.

The second improper fraction (9/4)m will be reciprocated to be (4/9)m.

Afterwards,take 477/4 m and multiply it by 4/9 m.

The result will be 53 dresses.

Answer:

-6x + 8(-x+6) = 6

Step-by-step explanation:

x+y = 6 => y = 6-x  ..............(1)

Substitute y (1) in

-6x+8y = 6 .......................(2)

to get

-6x + 8(6-x) = 6

or equivalently

-6x + 8(-x+6) = 6

Answer:

- (x - 3y)(3x + y)

Step-by-step explanation:

Given

(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL

= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute

= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms

= - 3x² + 8xy + 3y² ← factor out - 1 from each term

= - 1(3x² - 8xy - 3y²) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.

product = 3 × - 3 = - 9 and sum = - 8

The factors are - 9 and + 1

Use these factors to split the xy- term

3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )

= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term

= (x - 3y)(3x + y)

Thus

(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)

Answer:

Step-by-step explanation:

Due to the '+1', the graoph of x^2 is shifted 1 unit to the left.  The '+9' results in the entire graph being shifted downward 9 units.

Answer:

1800cm^3

Step-by-step explanation:

l=10cm

w=10cm

h=18cm

V=l.w.h

V=10cmx10cmx18cm

V=100cm^2x18cm

V=1800cm^3

Hope this helps. ❤❤❤

Answer:

600 cm³

Step-by-step explanation:

Volume of a square-based pyramid = a² × h/3

a = 10

h = 18

10² × 18/3

100 × 6

= 600

How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.

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Extra info:

Answer:

8

Step-by-step explanation:

Let's denote the number of members ordered chicken a, the number of members ordered beef b.

We have:

a + b = 12 (total number of members is 12)

10a + 14b = 136 (the chicken costs 10$, the beef costs 14$)

a + b = 12 => a = 12 - b

Substitute a into second equation, we have:

10(12 - b) + 14b = 136

=> 120 - 10b + 14b = 136

=> 4b = 16

=> b = 4

=> a = 12 - b = 12 - 4 = 8

=> Number of members ordered chicken: a = 8

Answer:

2x-11

Step-by-step explanation:

2 x X = 2x + 11

Answer:

0 represents ground level.

Step-by-step explanation:

0 on the number line represents ground level. Based on the photo, the 0 is in between the underground and the space above. The answer cannot be one of the negative numbers because those are all shown to be underground in the photo.

Answer:

Step-by-step explanation:

To find the sales tax on a purchased or sold item, first convert the sales tax percentage into the equivalent decimal fraction.  If the sales tax rate is 5.5%, then the desired decimal fraction is 0.055.  Next, multiply the selling price of the purchased or sold item by this decimal fraction.  If, for example, the selling  price is $100, the sales tax is 0.055($100) = $5.50

rational numbers are numbers which can be expressed in fraction form whereas irrational is just opposite

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by .  

Answer:

I guess that you want to know the transformations:

We start with:

f(x) = y = 4*x + 3

a)the transformed function is:

f(x) = y = -4*x - 3

So the sign changed.

This means that we go from (x, y) to (x, - y)

This is a reflection over the x-axis which changes the sin of the y component.

b) Now we go to f(x) = 4*x + 3

So the coefficient in the leading term changed.

This is a horizontal contraction:

A horizontal contraction of factor K for the function g(x) is: g(K*x)

In our case, we have:

f(K*x) = 4*(k*x) + 3 = x + 3

4*k*x = x

4*k = 1

k = 1/4

Then the transformation is an horizontal contraction of scale factor 1/4.

Answer: Price of rice per gram =  $ 0.006  per gram or 0.6 cents per gram .

Step-by-step explanation:

Given: David wants to make 10 servings, where each serving has 75 grams of rice.

Total quantity of rice required = 10 x 75 = 750 grams

Overall, David spends 4.50 dollars on rice.

i.e. cost of 750 grams of rice = 4.50 dollars

Price of rice per gram =(cost of 750 grams of rice ) ÷ 750

= (4.50 dollars )  ÷ 750

=  $  0.006  per gram.

Price of rice per gram =  $ 0.006  per gram.

Answer:

0.006

Step-by-step explanation:

ehgfdcgmkmvnnrebsbhbnjrfjgnjkae

Answer: A

Step-by-step explanation:

They have one solution because as you look at the lines they have different slopes and different y intercepts which means it has one solution.It is not parallel to each other to have no solutions. They seems to be going to one direction and eventually they will intersect.

Answer:

49453757

Step-by-step explanation:

Answer:

49453757

Step-by-step explanation:

Dont forget to rate and thanks!

Answer:

Degree 5

Step-by-step explanation:

Given

Degree of f(x) = 3

Degree of g(x) = 5

Required

Degree of 2f(x) + 4g(x)

2f(x) means 2 * f(x)

Since 2 is a constant

Multiplying f(x) by 2 will result in a polynomial with a degree of 3

Hence 2f(x) has a degree of 3

4g(x) means 4 * g(x)

Since 4 is also a constant

Multiplying g(x) by 4 will result in a polynomial with a degree of 5

Hence 4g(x) has a degree of 5

Having said that;

When 2 polynomials of different degrees are added together, the degree of the result will be the higher degree of both polynomials;

This means that;

Adding a polynomial of degree 3 and another of degree 5 will result in a polynomial of degree 5

Answer:  20.8 cm

Step-by-step explanation:

Notice that the corners of the squares form a line.

Set the x-axis to time and the y-axis to length of a side (not perimeter) to create coordinates.

At 0 seconds the side length is 1 --> (0, 1)

At 2.5 seconds the perimeter is 32 (side length is 32/4 = 8) --> (2.5, 8)

First, find the slope between the coordinates using    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Let (x₁, y₁) = (0, 1) and (x₂, y₂) = (2.5, 8)

[tex]m=\dfrac{8-1}{2.5-0}\quad =\dfrac{7}{2.5}\quad =\dfrac{7}{\frac{5}{2}}\quad =\dfrac{14}{5}\quad =2.8[/tex]

Next, use the Point-Slope formula to find the equation of the line:

[tex]y-y_1=m(x-x_1)\\\\y-1=2.8(x-0)\\\\y=2.8x+1[/tex]

Lastly, find the side length (y) when x = 1.5

y = 2.8(1.5)x + 1

  = 4.2 + 1

  = 5.2

Perimeter of a square = 4 times the side length

P = 4(5.2)

  = 20.8

Answer: no I cannot it hasn't been working since this late afternoon I believe

Step-by-step explanation:

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

[tex]S=b^2+\frac{1}{2}ps[/tex]           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]

Thus, you replace the values of b, p and s in the equation (1):

[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

Answer:

Hey there!

We can write this equation:

cosine xyz=6/15, or 0.4

arc cosine 0.4= 66.4

Thus, angle xyz is 66.4 degrees

Hope this helps :)

24 and 16

Step-by-step explanation:

let's assume two part be x and (40 - x)

According to Question,

[tex] x\dfrac{1}{4} = (40 - x) \dfrac{3}{8} [/tex]

[tex] x= \dfrac{3(40 - x)}{2} [/tex]

[tex]2 \times x = 120 - 3x [/tex]

[tex]2x + 3x = 120[/tex]

[tex]5x = 120[/tex]

[tex] \cancel{5}x= \cancel{120}[/tex]

[tex]x = 24[/tex]

Hence one part is 24 and other is (40 - 24) = 16 .

Answer: 24 and 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \mathrm{9 \div \frac{2}{3} }[/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \mathrm{ = 9 \times \frac{2}{3} }[/tex]

Calculate the product

[tex] \mathrm{ = \frac{27}{2} }[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\boxed{13\frac{1}{2} }[/tex]

Step-by-step explanation:

[tex]9 / \frac{2}{3}[/tex]

Changing "division" into "multiplication" and inverting the term after it:

[tex]9 * \frac{3}{2}[/tex]

[tex]\frac{9*3}{2}[/tex]

[tex]\frac{27}{2}[/tex]

=> [tex]13\frac{1}{2}[/tex]

Answer:

22

Step-by-step explanation:

Given

From Juan's calculation,

Difference of two positive integers = 2

From Maria's calculation,

Product of same integers = 120

Required

Find the sum of the two numbers

Let the two integers be represented by a and b

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

a * b = 120 ------- (2)

Make a the subject of formula in (1)

a = 2 + b

Substitute 2 + b for a in (2)

(2 + b) * b = 120

Open bracket

2 * b + b * b = 120

2b + b² = 120

Rearrange

b² + 2b = 120

Subtract 120 from both sides

b² + 2b - 120 = 120 - 120

b² + 2b - 120 = 0

At this point, we have a quadratic equation.

We start by expanding the expression

b² + 12b - 10b - 120 = 0

Factorize

b(b + 12) - 10(b + 12) = 0

(b - 10)(b + 12) = 0

This implies that

b - 10 = 0 or b + 12 = 0

Make b the subject of formula in both cases

b = 10 or b = -12

From the question, we understand that both numbers are positive.

This means that

b = -12 will be discarded.

Hence, b = 10

Recall that a = 2 + b

Substitute 10 for b

a = 2 + 10

a = 12

This implies that the two numbers are 12 and 10.

Their sum = 12 + 10

Sum = 22

The correct answer is 22

Answer:

D. 19

Step-by-step explanation:

because they are parallel bases you can compare

63/57 = 21/x

x = 19

Answer: D. 19

Let x by the length of CG. Since the two bases are parallel, we can create the following equation using proportions:

[tex]\dfrac{63}{21}=\dfrac{57}{x}[/tex]

Simplify left side of equation

[tex]3=\dfrac{57}{x}[/tex]

Multiply both sides by x

[tex]3x=57[/tex]

Divide both sides by 3

[tex]x=19[/tex]

Let me know if you need any clarifications, thanks!

Answer:

14%

Step-by-step explanation:

If the percentage of boys wearing polo shirts were boys, then the rest has to be girls. So 100%-80%=20%. However, we are not done here.

We have only figured out the percentage of girls out of the total number of people wearing polo shirts. We want to find the percentage of girls wearing polo shirts out of the whole school. To do that, we multiply 20% by 70%, since 20% of the polo shirt wearers were girls, and 70% of the entire student body is wearing a polo shirt.

Multiplying those two together gets you 14%.

Answer:

14%

Step-by-step explanation:

Answer:

The first and last answer.

Step-by-step explanation:

If you look closely at the triangles you can tell which ones are the same and which differ.

Hope this helps!! <3