x:20 = 5:x

Calculate the positive value of x

Answer:

The answer is

[tex]2 \cos(100) + i \sin(100) [/tex]

Step-by-step explanation:

This is a complex number,

[tex]a + bi[/tex]

First, convert this to de movire form.

[tex]r( \cos( \alpha ) + i \sin( \alpha ) [/tex]

where

[tex]r = \sqrt{ {a}^{2} + {b}^{2} } [/tex]

and

[tex] \alpha = \tan {}^{ - 1} ( \frac{b}{a} ) [/tex]

[tex]a = 4[/tex]

[tex]b = - 4 \sqrt{ 3} i[/tex]

[tex]r = \sqrt{ {4}^{2} + ( - 4 \sqrt{3}) {}^{2} } [/tex]

[tex]r = \sqrt{16 + 48} [/tex]

[tex]r = \sqrt{64} = 8[/tex]

and

[tex] \alpha = \tan {}^{ - 1} ( \frac{ - 4 \sqrt{3} }{4} ) [/tex]

[tex] \alpha = \tan {}^{ - 1} ( - \sqrt{3} ) [/tex]

Here, our a is positive and b is negative so our angle in degrees must lie in the fourth quadrant, that angle is 300 degrees.

So

[tex] \alpha = 300[/tex]

So our initially form is

[tex]8( \cos(300) + i \sin(300) )[/tex]

Now, we use the roots of unity formula. To do this, we first take the cube root of the modulus, 8,

[tex] \sqrt[3]{8} = 2[/tex]

Next, since cos and sin have a period of 360 we add 360 to each degree then we divide it by 3.

[tex] \sqrt[3]{8} ( \cos( \frac{300 + 360n}{3} ) + \sin( \frac{300 + 360n}{3} ) [/tex]

[tex]2 \cos(100 + 120n) + i \sin(100 + 120n) [/tex]

Since 100 is in the second quadrant, we let n=0,

[tex]2 \cos(100) + i \sin(100) [/tex]

The coordinates of the image after a dilation with respect to the origin is A'' (2,10), B" (0,4), C" (4,2) .

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due to the involvement of coordinates, it involves a center of a dilation, which is like a pinned point that stays at the same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

The vertices of a triangle are A(2,5), B(1, 2), and C(3, 1).

A' = 2(2.5) = (4,10)

B' = 2(1,2) = (2,4)

C' = 2(3,1) = (6,2)

Translation of 2 units left means change in x

A'' = (4-2,10) = (2,10)

B" = (2-2,4) = (0,4)

C" = (6-2,2) = (4,2)

Translation of 1 units up means change in y

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Answer:

A.

Step-by-step explanation:

It says he scored five points less than twice the number of points he scored last week.

2x-5=25

the 2x represents the number of points last week.

the -5 represents the five points less.

the number 25 is the points this week.

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

Here in the given figure b and 30° are alternate to each other so it can be name as alternative angle....

b = 30°

Now...

a + 30° = 180° ( being supplementary angle )

a = 180° - 30°

a = 150°

Now the value of c will be 150° being corresponding

angle with a

c = 150°

z = 60° ( being alternative angle )

Now let's find the value of x.....

here ,

60° + 50° + x = 180° ( the sum of interior angle of triangle is 180°

x = 180° - 110°

x = 70°

Now...

y = 70° ( alternative angle )

[tex]....[/tex]

Jack and Jills' speed in miles per hour is 4

The given parameters are:

Jack speed = x^2-11x-22

Jill distance = x^2-3x-54 and time = x + 6

Speed is calculated as:

Speed = Distance/time

So, we have:

Jill speed = x^2-3x-54/x + 6

Factorize the numerator

Jill speed = (x + 6)(x - 9)/x + 6

Cancel the common factor

Jill speed = x - 9

Both speeds are equal.

So, we have:

x^2-11x-22 = x - 9

Collect like terms

x^2-11x - x -22 + 9 = 0

Evaluate

x^2 - 12x - 13 = 0

Factorize the expression

(x + 1)(x - 13) = 0

Solve for x

x = -1 or x = 13

x cannot be negative.

So, we have:

x =13

Substitute x =13 in Jill speed = x - 9

Jill speed = 13 - 9

Evaluate

Jill speed = 4

Hence, their speed in miles per hour is 4

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Answer:

2√3

Step-by-step explanation:

The shown triangle is a 30-60-90 special right triangle due to the right angle and the thirty degree angle(the other angle has to be 60 degrees).

The hypotenuse of a 30-60-90 triangle is twice the leg opposite the 30 angle. The leg opposite the 30 degree angle is √3, so x would be 2√3.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve for x ~

We can apply Trigonometric ratios here, since the given triangle is a right angled triangle

so,

[tex]\qquad \sf  \dashrightarrow \: \sin(30) = \dfrac{ \sqrt{3} }{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{2} = \dfrac{ \sqrt{3} }{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 2 \times \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 2 \sqrt{3} [/tex]

i hope you you understood

The area of the parallelogram of height 9 in and base 13 in will be 117in².

The area of a parallelogram is the product of the base and the height of the figure.

The area of a parallelogram = Base x Height

WE have given a parallelogram of height 9 in and base 13 in.

So,

The area of a parallelogram = Base x Height

A = Base x Height

A = 13 × 9

A = 117in²

Hence, the area of the parallelogram will be 117in².

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The expression with a single rational exponent as follows

Exponents are often known as powers or indices. In simple terms, power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

1) The expression ⁴√x³ can be expressed as;

[tex]x^{\frac{3}{4} }[/tex]

2)The expression ¹/x⁻¹.

This is expressed as a single rational exponent as x

3) The given expression as a single rational exponent.

The expression is; ¹⁰√(x⁵ · x⁴ · x²)

¹⁰√(x¹¹) = [tex]x^{(11/10)}[/tex]

4) [tex]x^{(1/3)} * x^{(1/3)} * x^{(1/3)}[/tex]

x¹ = x

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Answer:

The expression with a single rational exponent as follows

What is exponents and powers?

Exponents are often known as powers or indices. In simple terms, power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

1) The expression ⁴√x³ can be expressed as;

x^{\frac{3}{4} }x

4

3

2)The expression ¹/x⁻¹.

This is expressed as a single rational exponent as x

3) The given expression as a single rational exponent.

The expression is; ¹⁰√(x⁵ · x⁴ · x²)

¹⁰√(x¹¹) = x^{(11/10)}x

(11/10)

4) x^{(1/3)} * x^{(1/3)} * x^{(1/3)}x

(1/3)

∗x

(1/3)

∗x

(1/3)

x¹ =11

Answer:

(0,6), (0,4), (0,-10)

Step-by-step explanation:

#x

#y

#z

Answer:

(x+3)^2 + (y-12)^2 =root 5

Step-by-step explanation:

Assumming you meant equation of the circle with center ()

Answer:

3$

Step-by-step explanation:

if the sale is 50% you multiply the 6$ original price by the 50% discount to get 3$

[tex]\left( \dfrac 49 \right) \div \left( \dfrac{18} 3 \right)\\\\\\=\dfrac 49 \div6\\\\\\=\dfrac 49 \times \dfrac 16\\\\\\=\dfrac{2}{9\times 3}\\\\\\=\dfrac{2}{27}[/tex]

Answer:

length • width = area

expression:

area • height = (result) • 1/3 = volume

Example:

x (area) • 6 (height) = 6x

6x • 1/3 = 2x(inches)³ or 6x ÷ 3 = 2x(inches)³

Answer:

[tex]y = - 2 |x - 2| + 4[/tex]

Step-by-step explanation:

as the function moved to the right 2 steps, and up 4 steps

Answer:

-1 feet

Step-by-step explanation:

below means that your answer will be a negative because sea level is at 0 how many feet below 1 so your answer is -1

Answer:

First option.

Step-by-step explanation:

Look at the position of letters, you don't really need to look at the picture.

BQRT ~ XZGJ means figure BQRT is similar to figure XZGJ and congruent angles are written in same order.

So first letter of BQRT is B and first letter of XZGJ is X.

That means that angle B is congruent to angle X.

You can write that as: ∠B ≅ ∠X

Second letter of BQRT is Q and second letter of XZGJ is Z.

Angle Q is congruent to angle Z.

∠Q ≅ ∠Z

And same for last two pairs of angles.

Final answer:

∡B ≅ ∡X, ∡Q ≅ ∡Z, ∡R ≅ ∡G, ∡T ≅ ∡J

Step-by-step explanation:

[tex]( {x - 2)}^{2} + 2 = 38 \\ {x }^{2} + 4 - 2 {x}^{2} + 2 = 38 \\ x = 38 - 2 - 4 \\ x = 32[/tex]

Answer: 36

Step-by-step explanation:

By the triangle midsegment theorem, CE=16, CD=10, and ED=10.

So, the perimeter of triangle CDE is 10+10+16=36

For 1st row

For 3 Rd row

For last row

Answer:

The only complete ordered pair in the given table is:

5 months → $60 saved

Therefore, to determine the relationship between the variables, divide the amount saved by the number of months:

[tex]\implies \sf \dfrac{Amount\:saved}{Number\:of\:months}=\dfrac{\$60}{5}=\$12[/tex]

So we can assume that $12 is saved each month.

To complete the table:

⇒ 3 × $12 = $36

⇒ $72 ÷ $12 = 6

⇒ 10 × $12 = $120

Completed table:

[tex]\large\begin{array}{| c | c |}\cline{1-2} \sf Times\:(month) & \sf Amount\:Saved\: (\$) \\\cline{1-2} 3 & 36 \\\cline{1-2} 5 & 60 \\\cline{1-2} 6 & 72 \\\cline{1-2} 10 & 120 \\\cline{1-2} \end{array}[/tex]

The number that the digit 1 has a value that is ten times as great as the value of the digit 1 in the number 215,784 is 2.

Place value can be defined as the value that's represented by a digit on the basis of the position of the digit.

It should be noted that the value of the digit 1 in 215784 is 10000. On the other hand, the value of 2 is 200000. It's in hundred of thousands. Therefore, it's 10 × (10000).

Therefore the digit is 2.

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Answer:

it is 103,748

Step-by-step explanation:

because it was wrong when I pressed 15,839

Answer:

Because Rhomboids have adjacent sides that makes it equal, and also both sides have the same meeting point which is M.

Step-by-step explanation:

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of the legs XY and YZ is equal to 39 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°. An isosceles triangle has two sides out of three equal.

A.) The value of n can be found by equating XY and XZ together,

XY = XZ

9n + 12 = 15n - 6

12 + 6 = 15n - 9n

18 = 6n

n = 3

Hence, the value of n is 3.

The length of different legs of the triangle is,

B.) XY = 9n + 12 = 9(3) + 12 = 27 + 12 = 39

C.) YZ = 15n - 6 = 15(3) - 6 = 45 - 6 = 39

Hence, the length of the legs XY and YZ is equal to 39 units.

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Answer:

Step-by-step explanation:

3

39

39

Using proportions, considering the amount she received from each person, it is found that Annie had 30 sweets originally.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

The final amount was of 63, hence:

1.4 x 1.5 x n = 63

n = 63/(1.4 x 1.5)

n = 30.

Annie had 30 sweets originally.

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