Can a rational number be subtracted by a irrational number an equal a rational number?

Answer:

C. 150

Step-by-step explanation:

x° + 30° = 180°...(sum of interior angles)

x° = 180° -30°

x°= 150°

x= 150

The value of x° in the given diagram is 150°. This is obtained by using the pair of interior angles formed along a transverse when passing through parallel lines.

The verticle angles are opposite to each other when two lines are intersected at a point. Those angles are the same in size.

It is given that line AB is parallel to line CD and transverse is making angles with these lines.

The angles are x° and 30°.

The angle of 30° is at the exterior side of these lines at the point of intersection of line CD and the transverse line. So, it forms a verticle pair of angles with the angle opposite to it.

Thus, the angle opposite to it also becomes 30°. This opposite angle lies inside the parallel lines. So it forms a pair of interior angles with a given angle x.

Since we know that sum of pair of interior angles = 180°, we get

x° + 30° = 180°

⇒ x° = 180° - 30°

⇒ x° = 150°

∴ x = 150°

Thus, the angle x = 150°. So, option C is correct.

Learn more about interior angles here:

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Answer:

Step-by-step explanation:

We can find half of a side of the pentagon with the expression

[tex]tan(36\°)=\frac{s_{half} }{11}[/tex]

Because, as a regular polygon, all its sectors have the same central angle, and the apothem divides equally each sector in two equal parts.

[tex]s_{half} \approx 8[/tex]

Therefore, half of a side is 8 units long, which means each side measures 16 units.

Now, the area of a penthagon is defined by

[tex]A=\frac{p \times a}{2}[/tex]

Where [tex]p[/tex] is the perimeter and [tex]a[/tex] is the apothem. Where the perimeter is the sum of all sides, which is 80 units.

[tex]A= \frac{80 \times 11}{2} =440 \ u^{2}[/tex]

Therefore, the right answer is the second choice.

Answer:

Time, t = 2 seconds

Step-by-step explanation:

The height of a flare fired from a 32-foot high platform can be modeled by the function :

[tex]h= -16t^2 + 16t + 32[/tex]

Here, h is the height in feet above the ground and t is the time in seconds.

It is required to find the time taken by the flare to reach the ground. When its reaches ground, height covered by it equals 0 such that,

h = 0

[tex]-16t^2 + 16t + 32=0\\\\t=\dfrac{-16+\sqrt{16^2-4\times (-16)(32)} }{2(-16)}, \dfrac{-16-\sqrt{16^2-4\times (-16)(32)} }{2(-16)}\\\\t=-1\ s, 2\ s[/tex]

Neglecting t = -1 seconds, the time taken by the flare to reach the ground is 2 seconds.

Answer:

Step-by-step explanation:

its 5, 12 and 13

its the most common pythagorean triplet ever known.

The right answer is (5,12,13)

look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

hi! id say your answer should be B. DF/FB=EG/GC

Step-by-step explanation:

Your question was if FB is parallel to BC, what must be true? A. and C. are not necessarily connected to FB and BC and do not prove that those two lines are parallel. while B. DF/FB = EG/GC does prove that they are parallel because the lines mentioned in the question, FG and BC, are attatched by the lines that are provided by answer B. I hope this helps!

The necessary equation which is true for the  given triangle is:

[tex]\frac{AD}{AB} = \frac{AE}{AC}[/tex]

Similar triangles are those with the same form but different sizes. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two triangles that are comparable have corresponding sides that are proportionately equal and corresponding angles that are congruent. The symbol "≈" above illustrates how the triangle looks similar.

Given that,

A right triangle ABC,

which contains two segments DE & FG

So according to properties of similar triangles, the ratio of length of the sides of the triangle is equal,

AB/AC  = AD/AE

it can be further simplified as

AB/AD = AC/AE

Therefore, the equation is AB/AD = AC/AE

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Answer:

a. 2

Step-by-step explanation:

Plugging in 9 for x and 2 for y we get: 2=2/3(9)-4

2/3 times 9 = 6

6-4 is 2

When solved we get 2=2 this is true.

I believe the answer is b= -5

Answer:

b=-5

Step-by-step explanation:

3b+2-6b=32+5b-2b(first you should collect like terms on each side.) so

3b-6b+2=32+5b-2b (lessen thing by both sides.)

-3b+2=32+3b (then you collect terms to one side)

-3b-3b=32-2

-6b=30 (you divide both sides by 6)

-b=5 (since b cannot be a negative u divide both sides by -1)

so..b=-5

Answer:diameter to circumference

Answer:

Circumference to diameter

Step-by-step explanation:

Answer:

This puts Brandon at a net worth of $12,679. So, your answer is option A.

Step-by-step explanation:

Answer:

The answer is A) x=5

Step-by-step explanation:

Sq root of 156 is about 22,so that doesnt work, 313 is bigger, and 1 is too small

Answer:

#1: 1) Buying a pack of 3

#2: 2) Jim

#3: 2) 65

#4: 1) $0.04 per fluid ounce

Step-by-step explanation:

#1:

5 shirts for $26.25; divide $26.25 by 5 to get the individual shirt which is $5.25

3 shirts for $14.25; divide $14.25 by 3 to get the individual shirt which is $4.75

10 shirts for $52.25; divide $52.25 by 10 to get the individual shirt which is $5.225 ($5.23).

The cheapest individual shirt is the 3 shirt package.

#2:

Dwight: 3 tickets for $191; divide $191 by 3 to get the individual ticket cost which is $63.67 (Rounded to the nearest hundredth)

Jim: 5 tickets for $309; divide $309 by 5 to get the individual ticket cost which is $61.80

Pam: 7 tickets for $435; divide $435 by 7 to get the individual ticket cost which is $62.14 ( Rounded to the nearest hundredth

Andy: 4 tickets for $256; divide $256 by 4 to get the individual ticket cost which is $64.00

The one who paid the lowest price per ticket is Jim.

#3:

91 portraits in 7 weeks

? portraits in 5 weeks

By cross multiplying, we get 455 portraits in 7weeks*?

To find the unknown, we divide 7 by both sides, leaving the unknown by itself.

[tex]\frac{455}{7}[/tex] = ?

? = 65 portraits

#4:

2-quart bottle for $2.56

1 quart is equal to 32 ounces

Since we know that the bottle cost $2.56, we can divide the cost with the amount of ounces it needs, like the following: $2.56 divided by 64 ounces.

Why 64? The bottle of juice is 2-quarts, so we multiply 32 ounces by 2 to get 64 ounces.

The answer should be $0.04 per fluid ounce.

Answer:

3) 53 degrees

4) 38 degrees

Step-by-step explanation:

Similarly to the previous question, the value of b in both of these examples can be found because you know that they are complementary with their adjacent angle.

3)

b+37=90

b=90-37

b=53 degrees

4)

b+52=90

b=90-52

b=38 degrees

Hope this helps!

Answer:

I don't think x is in there. But, I could be wrong.

Step-by-step explanation:

Answer:

0%

Step-by-step explanation:

The first thing you need to do, is add the total of all of the marbles together.

9 + 8 + 11 + 12 = 40.

Knowing this, you can take the amount of white marbles, (0) and put this against the 40 total marbles.

Since there are 0 white marbles in the jar, you know that it is impossible to pull one out of the jar.

0%

Answer: The answer is 0, because there is 0 white marbles in the jar to begin with.

Answer:

144

Step-by-step explanation:

32+112=144

Answer:

352

Step-by-step explanatioThe shape as you can see is a trapezoid. To find the area of the trapezoid is base 1 + base 2 x height. I multiplied 26 and 16 which made the whole shape 416. Now, we need to take away the white triangle which will show in the end the area of the shaded figure. To find the area of the triangle, you need to do 8x16 then divide by 2. 8 x 16= 128 feet. Then we divide that number by two which equals 64. The area of the unshaded triangle is 64 feet. Finally, we take 416 and subtact 64, which equals 352.

Answer:

In this discussion, they both got  the same answer, so they're both right. However, when Jackson said Lena was wrong, he was incorrect, because Lena's way was also correct. So, they were both right in this discussion when it comes to the answers, but Jackson was wrong when he said lena was wrong. (I hope this helped).

Step-by-step explanation:

Lena: 14(8 + 12)

14(20)

280

Jackson: 14 x 8 = 112

14 x 12 = 168

168 + 112 = 280

Answer:

a b d

Step-by-step explanation:

is all that apply

Answer:a c e

Step-by-step explanation:just took it. Those are all that apply.

Answer:

c-24

a-156

Step-by-step explanation:

a=180-24( angles on s straight line)=156

c= 24 opposite angles

Answer:

C

Step-by-step explanation:

To solve this problem, we need to first find the ratio of numbers less than four to total numbers.

There are 3 numbers on the wheel less than 4 (1, 2, and 3). There are 8 total numbers, meaning the ratio of numbers less than 4 to total numbers is 3:8.

Now, we need to find the probability of spinning a white number. There are 3 white numbers on the wheel (3, 5, 8). However, one of these numbers (3) is less than 4, so it is already accounted for in the previous ratio. There are 2 numbers left, meaning the ratio of remaining white numbers to total numbers is 2:8.

Adding this to the original equation, we get 5:8. As a fraction, 5:8 = 5/8. The answer that correctly highlights this is C.

Answer:

40 meters

Step-by-step explanation:

Answer:

[tex]16^{3x}= 32^{2(x+2)}[/tex]exponential equation represents this situation

Step-by-step explanation:

Let the number be x

Raising 16 to a power that is 3 times some number=[tex]16^{3x}[/tex]

Raising 32 to twice the sum of the number and 2 =[tex]32^{2(x+2)}[/tex]

We are given that Raising 16 to a power that is 3 times some number is the same as raising 32 to twice the sum of the number and 2.

Equation:[tex]16^{3x}= 32^{2(x+2)}[/tex]

So, The required equation is[tex]16^{3x}= 32^{2(x+2)}[/tex]

Hence  [tex]16^{3x}= 32^{2(x+2)}[/tex]exponential equation represents this situation

Answer:

y = 3x + 2

Step-by-step explanation:

So we can use the point-slope equation to help us figure out our y = mx +b equation

First we need to choose two points on the graph so we can calculate our slope

I personally like to choose point that intersects two numbers perfectly on the line rather than a point that is maybe half way between two numbers

So we can use the point (0,2) and the point (2,8)

Our (0,2) will represent (x₁, y₁) and our (2,8) will represent (x₂,y₂)

The equation to find the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex], so plugging in our values, we get [tex]m=\frac{8-2}{2-0} =\frac{6}{2} =3[/tex]

We have found our slope, 3, and now we can use the point-slope equation: y - y₁ = m(x - x₁) to figure out the remainder of the equation.

Plugging in our values we get: y - (2) = (3)(x - (0)) which simplifies to y - 2 = 3x which then simplifies to y = 3x + 2

Answer:

Step-by-step explanation:

200% of x = 105% of 90

(200/100) * x = (105/100) * 90

2 * x = 1.05 * 90

[tex]x = \frac{1.05*90}{2}\\\\x=1.05*45\\\\[/tex]

x = 47.25

Answer:

47.25 or 47 1/4

Step-by-step explanation:

Answer:

(-30, 10)

multiply -20/60 by -0.5 each and you get 10/-30

this is the only pair achievable by proportion.

Answer:D

Step-by-step explanation:180 degrees counterclockwise rotation about the origin and translation 2 units down

Answer:

C.

Step-by-step explanation:

x^2+20^2=25^2

x^2+400=625

x^2=225

x=15

Answer:

15ft

Step-by-step explanation:

Because the Pythagorean theorem stats [tex]A^{2}+B^{2}=C^{2}[/tex] the first leg, the unknown leg would be A. The leg that is the side of the house would be substituted in for B. The length of the ladder would be C. Thus [tex]x^{2}+20^{2}=25^{2}[/tex], then you would simplify it to [tex]x^2+400=625[/tex] then you would subtract 400 from both sides. Then that would equal [tex]x^{2}=225\\[/tex]. Then you would square root both sides giving you [tex]x=15\\[/tex].

Answer: true...

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

In a standard 90°- 60°- 30° triangle

with legs 1 and [tex]\sqrt{3}[/tex] and hypotenuse 2

cos60° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] ← True

Answer: 3456 cubic metres

Step-by-step explanation:

32 * 18 * 6 is the volume of which can be held in the pool

Answer: 3456 cubic feet

Step-by-step explanation:

Multiply the length times width times depth.

32 × 18 × 6 = 3456

Then multiply the unit measure.

Feet × feet = square feet. Ft^2

Feet × feet × feet = cubic feet. Ft^3

Answer:

9.3361

Step-by-step explanation:

simplify each term

subtract 3.51 from 6.2