is zero a rational number?​

Answer:

[tex](x^2+y^2)^3 = 16x^2y^2[/tex]

Step-by-step explanation:

We want to convert the polar equation:

[tex]\displaystyle r = 2 \sin 2\theta[/tex]

To rectangular form.

Recall the double-angle identity for sine:

[tex]\displaystyle \sin 2\theta = 2\sin\theta\cos\theta[/tex]

Hence:

[tex]\displaystyle r = 4\sin\theta\cos\theta[/tex]

Since x = rcosθ and y = rsinθ:

[tex]\displaystyle r = 4\left(\frac{x}{r}\right)\left(\frac{y}{r}\right)[/tex]

Multiply:

[tex]\displaystyle r = \frac{4xy}{r^2}[/tex]

Recall that x² + y² = r². Hence:

[tex]\displaystyle r = \frac{4xy}{x^2 + y^2}[/tex]

By squaring both sides:

[tex]\displaystyle r^2 = \frac{16x^2y^2}{(x^2+y^2)^2}[/tex]

Substitute:

[tex]\displaystyle x^2+y^2 = \frac{16x^2y^2}{(x^2+y^2)^2}[/tex]

And multiply. Therefore:

[tex](x^2+y^2)^3 = 16x^2y^2[/tex]

Answer:

x<3

Step-by-step explanation:

We divide equation by 3. So we get x<3. You can think of it with logic, too.

Answer:

x<3

Step-by-step explanation:

3x< 9

Divide each side by 3

3x/3 <9/3

x < 3

There is an open circle at 3 and a line going to the left

Answer:

B .62.5 m

Step-by-step explanation:

convert Kmh-1 in to ms-1

30 Kmh-1 = (30×1000) ÷3600 = 8.3ms-1

60 Kmh-1 = (60×1000) ÷3600 = 16.6 ms-1

acceleration = (16.6 - 8.3) ÷ 5 = 1.66 ms-2

V^2 = U^2 +2aS

(16.6)^2 = (8.3)^2 + 2×1.66 ×S

S = 62.5 m

Answer: [tex]\dfrac{11}{12}[/tex]

Step-by-step explanation:

Given

The odds against winning in a chess tournament are 1 to 11.

Odds is defined as the ratio of the probability of occurrence to the non-occurrence of event.

[tex]\therefore \text{Probability that event will occur is P'=}\dfrac{1}{1+11}\\\\\Rightarrow P'=\dfrac{1}{12}[/tex]

Probability of non-occurrence i.e. she wins the first prize is

[tex]\Rightarrow P=1-\dfrac{1}{12}\\\\\Rightarrow P=\dfrac{11}{12}[/tex]

Answer:

At least 7 girls: 0.5^7 OR 0.0078125

At least 8 girls: 0.5^8 OR 0.00390625

Answer: 2, acute equilateral

Step-by-step explanation:

the image shows a triangle with all 3 sides congruent and 3 acute angles

Answer:

13x^2 - xy

Step-by-step explanation:

4x^2-3xy+2xy+9x^2

=13x^2-xy

p = 6/11.

So we have a bag that contains 6 red marbles and 6 green marbles.

Then the total number of marbles that are in that bag is:

6 + 6  = 12

There are 12 marbles in the bag, and we assume that all marbles have the same probability of being randomly drawn.

Now we draw two marbles, we want to find the probability that one is red and the other is green.

The first marble that we draw does not matter, as we just want the second marble to be of the other color.

So, suppose we draw a green one in the first attempt.

Then in the second draw, we need to get a red one.

The probability of drawing a red one will be equal to the quotient between the red marbles in the bag (6) and the total number of marbles in the bag (12 - 1 = 11, because one green marble was drawn already)

Then the probability is:

p = 6/11.

Notice that would be the exact same case if the first marble was red.

Then we can conclude that the probability of getting two marbles of different colors is:

p = 6/11.

Answer:

b i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

The modal group is 10-20, as it has the greatest frequency of 27.

Estimated mode is calculated by formula:

where

Substitute values to get:

Answer:

C

Step-by-step explanation:

you are adding

-3√18=

-27

√16=4

-27+4=-23

Answer:

3 a + 4 b

Step-by-step explanation:

Biểu thức đại số biểu thị bạn Cúc mua  3  ly trà sữa và  4  ly kem là:

3 a + 4 b

Answer:

The answer is a translation

Step-by-step explanation:

In Math, translation is the displacement of a shape or object from one place to another.

Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.

Answer:

y - intercept = 2.25

Step-by-step explanation:

y = mx + c

Where,

y = Total cost

x = additional cost

m = slope

c = y - intercept

y = 0.25x + 2.25

Relating with the above equation,

y - intercept = 2.25

Slope, m = 0.25

Answer:

X1=6

X2=7

y1= -1

y2= 3

now,

slope = y2-y1/x2-x1

= 3+1/7-6

=4/1

=1

hence slope= 1

Answer:

Step-by-step explanation:

a) x=6 (x= 8-2)

b) x=4 ( 4x=21-5=16 -> x=4

c) x=7 (3x=34-13=21 -> x=7)

9514 1404 393

Answer:

  18a +42ax +24az

Step-by-step explanation:

6a(3 +7x +4z) = 18a +42ax +24az

__

Additional comment

In order for 6a to be the GCF, the terms inside parentheses cannot have any common factors.

Let the perimeter be 100cm

Then value of x = 100/4

x = 25cm

Answered by Gauthmath must click thanks and mark brainliest

Answer:

B. SAS

[tex] \frac{sm}{dl} = \frac{27}{9} = 3 \\ \frac{am}{el} = \frac{15}{5} = 3 \\ angle \: m= angle \: l[/tex]

Brainliest please~

By SAS similarity, ΔASM is similar to ΔDLE. Thus, option C is correct.

The SAS theorem is also known as the side-angle-side theorem, also known as a statement in Euclidean geometry that states two triangles are congruent if their corresponding sides are both the same length and their included angles are both of the same measures.

According to the given figure,

SM=27

DL=9

MA=15

LE=5,

∠M=∠L=31°

It is required to determine the similarity postulate that applies. Therefore,

From the ΔASM and ΔDLE, we have

[tex]\frac{SM}{DL}=\frac{27}{9} \\=3\\\frac{ML}{LE}=\frac{15}{5}\\ =3\\ Hence, \frac{SM}{DL}= \frac{ML}{LE}[/tex]

∠M=∠L=31°

Hence, by SAS similarity, ΔASM is similar to ΔDLE.

Therefore, it can be concluded that option C is correct.

Learn more about the SAS theorem here:

https://brainly.com/question/31243316

#SPJ7

Answer:

£510

Step-by-step explanation:

5% of 3400 is 170. SInce she gets that much money every year, after 3 years she'll have 3*170 = £510.

Answer: Simple Interest = PRT

P= 3400

R = 5% = 5/100

T = 3

=> 3400 × 5/100 × 3 = 510

=》3400 + 510 = 3910

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.

Calculate slope m using the slope formula

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

with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)

m = [tex]\frac{13-1}{9-(-7)}[/tex] = [tex]\frac{12}{9+7}[/tex] = [tex]\frac{12}{16}[/tex] = [tex]\frac{3}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] ←  slope of perpendicular bisector

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then

midpoint = ( [tex]\frac{-7+9}{2}[/tex], [tex]\frac{1+13}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex], [tex]\frac{14}{2}[/tex] ) = (1, 7 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{4}{3}[/tex] , then

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute the midpoint (1, 7) into the partial equation

7 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{21}{3}[/tex] + [tex]\frac{4}{3}[/tex] = [tex]\frac{25}{3}[/tex]

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{25}{3}[/tex] ← equation of perpendicular bisector

Answer:

x ≈ 28.2

Step-by-step explanation:

Δ CAB ≅ Δ CDE then corresponding sides are in proportion, that is

[tex]\frac{CA}{CD}[/tex] = [tex]\frac{CB}{CE}[/tex] , substitute values

[tex]\frac{14+x}{x}[/tex] = [tex]\frac{18.7+9.3}{18.7}[/tex] = [tex]\frac{28}{18.7}[/tex] ( cross- multiply )

28x = 18.7(14 + x) ← distribute

28x = 261.8 + 18.7x ( subtract 18.7x from both sides )

9.3x = 261.8 ( divide both sides by 9.3 )

x ≈ 28.2 (to the nearest tenth )

Answer:

The answer is 97!

Step-by-step explanation:

The formula for Pythagorean Theorem is a^2+b^2=c^2. (65)^2 + (72)^2 is 9409, which has a square root of 97. Hope this helped! :)

Answer:

5

Step-by-step explanation:

We know that a^2+b^2=c^2 from the Pythagorean theorem   where a and b are the legs and c is the hypotenuse

4^2+3^2 = c^2

16+9 = c^2

25 = c^2

Taking the square root of each side

sqrt(25) = sqrt(c^2)

5 =c

Answer:

d = 5 m

Step-by-step explanation:

The diagonal divides the rectangle into 2 right triangles with legs 3 and 4 and hypotenuse h

Using Pythagoras' identity in one of the right triangles, then

d² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

d = [tex]\sqrt{25}[/tex] = 5

Answer:

You need to use sohcahtoa to find your answer.

first you gotta identify what sides of the triangle you have.

You're missing the hypotenuse, and you have the value of the adjacent.

since you have the adjacent and need the hypotenuse, you're going to use cosine to find x

cos(65) = 16/x

x = 37.859

Answer:

x = 37.85

this is a standard "trig" question

it requires two pieces  of insight.

First that a triangle has 180° interior angles.

from that you can determine that the third angle is 25° because

90 + 65 + β = 180

the red symbol lets you know that it is 90°

the second think that will help is SOHCAHTOA

that is if you have a "right triangle" (one with a 90° angle)

in this problem (in your mind rotate the triangle so the 65° is at the bottom left and the two long sides are pointing up

in this case you have the 16 on the bottom (adjacent to the angle) and

the x is on the hypotenuse...

you have the A& H that is COS

thus you have cos(65) = [tex]\frac{16}{x}[/tex]

x = 37.85

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Step-by-step explanation:

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Answer:

The third option, (-30,10)

Step-by-step explanation:

A proportional relationship is when you multiply one number in the coordinate/pair to get the other number, and that number that you multiply with is consistent. For example, in (60,-20) you multiply the x coordinate 60 by -1/3 to get 20. Next, you have to check if the other answer choices follow the same pattern. For (-30,10), you multiply -30 by -1/3 and get 10! So it works.