<6 and <7 can be classified as?
a. vertical angles
b. alternate interior angles
c. same side interior angles
d. alternate exterior angles

Answer:

Distributive property

Step-by-step explanation:

The rule being shown here is the distributive property, because the first binomial is taken apart and separately multiplied with the other binomial.

Answer:

The product of 16 and 26 would be 16 * 26

Step-by-step explanation:

This is because "the product of" means multiplication so *. Making it 16 * 26.

Answer:

The first option is the right one.

Step-by-step explanation:

7/2. Rate is rise/run

7 is your rise

and 2 is your run

therefore, the answer is 7/2

Answer: 63.64 cm² (rounded to the hundredth place)

Step-by-step explanation:

Concept:

Here, we need to understand how to find the area of a circle.

The general formula is: A = πr²

π = 3.14 (or any constants that equals to this value)

r = radius = (1/2) diameter

Solve:

π = 22/7

r = d/2 = 9 / 4 = 4.5

A = πr²

A = (22/7) (4.5)²

A = (22/7) (4.5)²

A = 63.64 cm² (rounded to the hundredthe place)

Hope this helps!! :)

Please let me know if you have any question

Answer:

63.64 cm²

Step-by-step explanation:

r = d/2 = 9 / 4 = 4.5

A = πr²

A = (22/7) (4.5)²

A = (22/7) (4.5)²

A = 63.64 cm² (rounded to the hundredth place)

Answer:

The value for C is 2.3

in this case we know of x to be 4.85

therefore subtract the summation of both X+C from the value of x.

Hence we will have the equation X - X+C =2.3

Answer:

hello,

Step-by-step explanation:

12²=(x-16)*16

9=x-16

x=25

Relation metric in a right triangle

Answer:

See Below (Boxed Solutions).

Step-by-step explanation:

We are given the two complex numbers:

[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]

First, convert z to polar form. Recall that polar form of a complex number is:

[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]

We will first find its modulus r, which is given by:

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

In this case, a = √3 and b = -1. Thus, the modulus is:

[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]

Next, find the argument θ in [0, 2π). Recall that:

[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]

Therefore:

[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]

Evaluate:

[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]

Since z must be in QIV, using reference angles, the argument will be:

[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]

Therefore, z in polar form is:

[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]

Part A)

Recall that when multiplying two complex numbers z and w:

[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]

To find the complex form, evaluate:

[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]

Part B)

Recall that when raising a complex number to an exponent n:

[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]

Therefore:

[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]

Substitute:

[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]

Simplify:

Simplify using coterminal angles. Thus, the polar form is:

[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]

And the complex form is:

[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]

Part C)

Recall that:

[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]

And the complex form is:

[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]

Part D)

Let a be a cube root of z. Then by definition:

[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

From the property in Part B, we know that:

[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]

Therefore:

[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:

[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]

The first equation can be easily solved:

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

For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:

[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]

Solve for the argument:

[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]

There are three distinct solutions within [0, 2π):

[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]

Hence, the three roots are:

[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]

Or, approximately:

[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]

Answer:

[tex]ST = 6cm[/tex]

Step-by-step explanation:

Given

[tex]RS =2x[/tex]

[tex]ST = 3x[/tex]

[tex]RT = 10[/tex]

Required

Find ST

From the question, we understand that S is between R and T.

So:

[tex]RS + ST = RT[/tex]

Substitute known values

[tex]2x + 3x = 10[/tex]

[tex]5x =10[/tex]

Divide both sides by 5

[tex]x =2[/tex]

Given that:

[tex]ST = 3x[/tex]

[tex]ST = 3 * 2[/tex]

[tex]ST = 6cm[/tex]

Answer:

C or 6 centimeters

Step-by-step explanation:

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.  

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios

Sin θ Opposite Side to θ/Hypotenuse

Cos θ Adjacent Side to θ/Hypotenuse

Tan θ Opposite Side/Adjacent Side & Sin θ/Cos θ

Cot θ Adjacent Side/Opposite Side & 1/tan θ

Sec θ Hypotenuse/Adjacent Side & 1/cos θ

Cosec θ Hypotenuse/Opposite Side & 1/sin θ

Note: Opposite side is the perpendicular side and the adjacent side is the base of the right-triangle. Also, check out trigonometric functions to learn about each of these ratios or functions in detail.Trigonometric Identities

Definition

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The three sides of the right triangle are:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

Answer:

510°

Step-by-step explanation:

Total Time from 8:10pm to 9:35pm is 1hour 25mins= 85mins

Movement of the minute hand from one point around the clock and back to the same point gives a complete rotation of 360°

if 60mins = 360°

85mins=

[tex] \frac{85}{60} \times 360[/tex]

= 510 degrees

Answer:

b

Step-by-step explanation:

Answer:

10m

Step-by-step explanation:

area of a square =s^2

therefore s^2=100

s= under root 100

= 10

First we need to assume that the sum of the angles is also 180°. if one is less than 90°, the other will be more. we can do this because in a plane 4-sided polygon the sum of the inner angles will always be 360°, and we already know the two angles on the right side

so we can say that:

3x + 20 + x = 180

Since we got only one variable in this equation, we can already solve for x.

4x + 20 = 180

4x = 160

x = 40

the lower left angle is just 40°

the upper left is three times that plus 20, so it's 160°

hope this helps you to get the method

Answer:

x = 16.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 66 = 15/x

x sin 66 = 15

x = 15/sin 66

x=16.41954

Rounding to the nearest tenth

x = 16.4

Answer:

20.4

Step-by-step explanation:

cos(74) = x/74

x = 74×cos(74)

x = 20.4

Answered by GAUTHMATH

Answer:

600

Step-by-step explanation:

Volume=l*b*h=5*12*10=600

Answer:

The answer is (0,2)

Step-by-step explanation:

The second quadrant or Quadrant II has coordinates that are ALL positive.

(my favorite quadrant)

The coordinates would look like (4, 5) or (19, 69) and so on.

Answer:

the batteries are 74 cents and oranges are 5.10

Step-by-step explanation:

for the first one just divide 5.92 by 8 to get the unit price

and for the second multiply 2.7 by 1.89

Answer:

b

Step-by-step explanation:

(-x+2 ) +5 -(x - 2)  [tex]\geq[/tex] 0

-2x+ 9[tex]\geq[/tex]0

x [tex]\leq[/tex]9/2

Answer:

BC=22

Step-by-step explanation:

Hi there!

We are given an isosceles triangle (notice the markings on m<C and m<B), the length of the sides AB and AC as x-2 and 2x-24 respectively, and we want to find the length of BC (given as x)

In an isosceles triangle, the sides known as the legs (in this case, AC and AB), are congruent to each other

As they both contain x in their side lengths (remember that x=BC), let's set them equal to each other to find the value of x

2x-24=x-2

Add 24 to both sides

2x=x+22

Subtract x from both sides

x=22

So the length of BC is 22

Hope this helps!

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

If you want to read more about triangle rectangles, you can see:

https://brainly.com/question/16893462

Answer:

x = 0

Step-by-step explanation:

-2(2 − 2x) = 4 − 8(1 − x)

Apply the distributive property:

−2(2 − 2x) = 4 − 8(1 − x)

(−2)(2) + (−2)(−2x) = 4 + (−8)(1) + (−8)(−x)

−4 + 4x = 4 + (−8) + 8x

Combine like terms:

4x − 4 = (8x) + (4+−8)

4x − 4 = 8x + (−4)

4x − 4 = 8x − 4

Subtract 8x from both sides:

4x − 4 − 8x = 8x − 4 − 8x

−4x − 4 = −4

Add 4 to both sides:

−4x − 4 + 4= −4 + 4

−4x = 0

Divide both sides by -4:

-4x/-4 = 0/-4

x = 0

Answer: 0

Step-by-step explanation:

Answer:

x=400 m is the correct answer

Step-by-step explanation:

9 a = soln

3:9 = 6:n

or, 3/9 = 6/n

or, 3n = 54

or, n = 54/3

so, n = 18

b = soln

n/10 = 6/15

or, 15n = 60

or, n = 60/15

so, n= 4

10) a = 15% of 450

= 15/100 * 450

= 15/10 * 45

or, 15/2 * 9

or,  135/2

= 67.5 g

b= 125% of 60

= 125/100 * 60

= 5/4 * 60

= 5*15

= $75

Answer:

S = 35 + 20w

Step-by-step explanation:

Amount Samantha has in her account = $35

Additional savings per week = $20

Let

S =Totai savings in Samantha's account at the end of the week

w = number of weeks

The equation:

Totai savings in Samantha's account at the end of the week = Amount Samantha has in her account + (Additional savings per week * number of weeks)

S = 35 + 20w

Answer:

s=35+20w

Step-by-step explanation:

Answer:

(x-7)²+(y+24)² = 625

Step-by-step explanation:

A circle with center (h, k) and radius r can be represented as

(x-h)²+(y-k)² = r²

We know the center and one point, and need to find the radius. The radius is equal to the distance from the center to any point on the circle. Therefore, we need to find the distance from the center to the point on the circle (in this case, the origin) to obtain the radius.

The distance formula for points (x₁, y₁) and (x₂, y₂) is √((x₁-x₂)²+(y₁-y₂)²). Note that x₁ and x₂ (as well as y₁ and y₂) are interchangeable but x₁ and y₁ or x₂ and y₂ are not.

Our distance between (7, -24) and the origin is

√((x₁-x₂)²+(y₁-y₂)²) = √((7-0)²+(-24-0)²)

= √625

= 25

Therefore, the radius is 25 and our equation is

(x-7)²+(y-(-24))² = (x-7)²+(y+24)² = 25² = 625

Answer: reduction

Step-by-step explanation:

ABCD-> 'ABCD

its bc 'ABCD got smaller compared to ABCD

Answer:

It is a reduction.

Step-by-step explanation:

Hope this helped.

Answer:

its c 120in

Step-by-step explanation:

The perimeter of the triangle is,

⇒ 138 in.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The hypotenuse of a right triangle is 52 in.

And, One leg of the triangle is 8 in. more than twice the length of the other.

Hence, We get;

Lengths of legs are,

⇒ x

And, ⇒ 8 + 2x

Hence, We can formulate;

⇒ 52² = x² + (2x + 8)²

⇒ 2704 = x² + 4x² + 64 + 24x

⇒ 5x² + 24x - 2640 = 0

⇒ x = 20 and x = - 132/5

For perimeter;

Take x = 20

Hence, The perimeter of the triangle is,

⇒ 52 + x + (2x + 8)

⇒ 52 + 20 + (2 × 20 + 8)

⇒ 52 + 20 + 48

⇒ 138 in.

Thus, The perimeter of the triangle is,

⇒ 138 in.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ7

Answer:

[tex]x = 0[/tex] or [tex]x = 1[/tex].

Step-by-step explanation:

Start by adding [tex]1[/tex] to both sides of this equation:

[tex](x - 1) + 1 = (\sqrt{x} - 1) + 1[/tex].

[tex]x = \sqrt{x}[/tex].

If two numbers are equal, their square should also be equal. Therefore, since[tex]x = \sqrt{x}[/tex], it must be true that [tex]x^{2} = (\sqrt{x})^{2}[/tex]. That is: [tex]x^{2} = x[/tex].

Notice that since [tex]x[/tex] is under a square root, the result must ensure that [tex]x \ge 0[/tex].

Subtract [tex]x[/tex] from both sides of the equation:

[tex]x^{2} - x = x - x[/tex].

[tex]x^{2} - x = 0[/tex].

Factor [tex]x[/tex] out:

[tex]x\, (x - 1) = 0[/tex].

Hence, by the Factor Theorem, [tex]x = 0[/tex] and [tex]x = 1[/tex] would satisfy this rearranged equation. Because of the square root in the original equation, these two value must be non-negative ([tex]x \ge 0[/tex]) to qualify as actual roots of that equation.

In this example, both [tex]x = 0[/tex] and [tex]x = 1[/tex] qualify as roots of that equation.

x-1 = \sqrt{x} -1

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