Which pair of undefined terms is used to define the term parallel lines?
point and line
plane and line
point and ray
ray and line

Answer:

Geetha is 32.5 years old

her daughter is 11.5 years old

Step-by-step explanation:

sum of their ages is 44 years

G + D = 44

in two years, Geetha's age is 3 times her daughters age. (to find present age, subtract 2)

G = 3D - 2

substitute

(3D - 2) + D = 44

combine like terms

4D - 2 = 46

4D = 46

D = 11.5

plug in D to either equation

G + (11.5) = 44

G = 32.5

G = 3(11.5) - 2

G = 32.5

Answer:

Step-by-step explanation:

R = 12 in

360°:30° = 12

so the area of the slice is ¹/₁₂ of whole pizza

A = ¹/₁₂•πR² = ¹/₁₂•π•12•12 = 12π in² ≈ 37.7 in²

Crust is the perimeter of pizza so crust of the slice is ¹/₁₂ of the perimeter:

L = ¹/₁₂•2πR = ¹/₁₂•2π•12 = 2π in ≈ 6.28 in

Answer:

Orthogonal.

Step-by-step explanation:

Given:

u = <10, 0>

v = <0, -9>

In unit vector notation, the above vectors can be re-written as:

u = 10i + 0j

v = 0i - 9j

Now, note the following:

(i) two vectors, u and v, are parallel to each other if one is a scalar multiple of the other. i.e

u = kv

or

v = ku

for some nonzero value of a scalar k.

(ii) two vectors are orthogonal if their dot product gives zero. i.e

u . v = 0

Let's use the explanations above to determine whether the given vectors are parallel or orthogonal.

(a) If parallel

u = k v

10i + 0j = k (0i - 9j)   ?

When k = 1, the above equation becomes

10i + 0j  ≠  0i - 9j

When k = 2,

10i + 0j ≠ 2(0i - 9j)

10i + 0j ≠ 0i - 18j

Since we cannot find any value of k for which u = kv or v = ku, then the two vectors are not parallel to each other.

(b) If Orthogonal

u.v = (10i + 0j) . (0i - 9j)  

[multiply the i components together, and add the result to the multiplication of the j components]

u.v = (10i * 0i) + (0j * 9j)

u.v = (0) + (0)

u.v = 0

Since the dot product of the two vectors gave zero, then the two vectors are orthogonal.

Greetings from Brasil...

We have 2 conditions:

1 - angles opposed by the vertex - the angles are equal

2 - supplementary angles - the sum of the two angles results in 180

2:

(4X + 15) and (5X + 30) are supplementary angles, so:

(4X + 15) + (5X + 30) = 180

9X = 180 - 15 - 30

9X = 135

1:

(3Y + 15) and (5X + 30) are angles opposed by the vertex, so they are equal

3Y + 15 = 5X + 30

3Y = 5X + 30 - 15

3Y = 5X + 15   above we have already calculated the value of X

3Y = 5.(15) + 15

3Y = 75 + 15

3Y = 90

Y = 90/3

Answer:

on her first quiz

Step-by-step explanation:

27/30=

27÷30=

0.9=

09×100/100=

0.9×100%=

(0.9×100)% =

90%

Answer:

first quiz

Step-by-step explanation:

100 divided by 30 times 27<92%

Answer:

b.  $1215.00

Step-by-step explanation:

The area of the room can be figured any of several ways. One easy way is to figure the area of the enclosing 8 ft by 12 ft rectangle, then subtract area of the 3 ft by 5 ft cutout at upper left.

  A = (8 ft)(12 ft) - (3 ft)(5 ft) = (96 -15) ft^2 = 81 ft^2

At a cost of $15 for each square foot, the installed flooring will cost ...

  ($15 /ft^2)(81 ft^2) = $(15·81) = $1215

The value of the gauge car after 4 years will be $18195.25.

Compound interest is applicable when there will be a change in principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given,

Principle amount (P)  = $29000

Rate of decrement (R) = 11%

Time period(T) = 4 years

Percentage decrement over T time period is given by

Final amount = P[tex][1 - R/100]^{T}[/tex]

Final amount = 29000[tex][1 - 11/100]^{4}[/tex]

Final amount = 29000(0.89)⁴

Final amount = $18195.25.

Hence, The value of the gauge car after 4 years will be $18195.25.

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The value of the car after 4 years is $18195.24989.

Given,

Gage bought a new car for $29000 to use while he is away at college.

The car decreases in value by 11% annually.

We need to find what would the cars value after 4 years.

we have,

Cost of the car = $29000

The car decreases annually by = 11%

1st-year decrease.

$29000 x 11/100 = $3190

The cost of the car after 1st year = $29000 - $3190 = $25810

2nd-year decrease.

$25810 x 11/100 = $2839.1
The cost of the car after 2nd year = $25810 -  $2839.1 = $22970.9

3rd-year decrease.

$22970.9 x 11/100 = $2526.799

The cost of the car after 3rd year = $22970.9 - $2526.799 = $20444.101

4th-year decrease.

$20444.101 x 11/100 = $2248.85111

The cost of the car after 4th year = $20444.101 - $2248.85111 = $18195.24

Thus the value of the car after 4 years is $18195.24989.

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Answer:

y = 8

Step-by-step explanation:

[tex] \frac{y}{4} = \frac{5 + 5}{5} \\ \\ \frac{y}{4} = \frac{10}{5} \\ \frac{y}{4} = 2 \\ y = 4 \times 2 \\ y = 8[/tex]

Answer:  10 yards

Step-by-step explanation:

Covert 30  feet into yards to find how many yards he should buy.

[tex]\frac{30}{3} = \frac{x}{1}[/tex]     Solve by cross product

3x = 30  

x = 10  

Answer:

is repeating rational

Answer:

20

Step-by-step explanation:

[tex] \frac{9}{g} + 2h + 5 \\ = \frac{9}{3} + 2 \times 6 + 5 \\ = 3 + 12 + 5 \\ = 20[/tex]

Answer:

11/6

Step-by-step explanation:

To find the improper fraction

Take the denominator times the whole number

6*1 = 6

Add the numerator

6+5 =11

Put this over the denominator

11/6

Answer:

[tex]\frac{11}{6}[/tex]

Step-by-step explanation:

What is 1 5/6 as an improper fraction?

If you wanna make 1 5/6 as a improper fraction, you must take the 5 from 1 5/6 and add it 6.

[tex]6+5=11[/tex]

[tex]\frac{11}{}[/tex]

Since the denominator is 6, you will put it down.

[tex]\frac{11}{6}[/tex]

So now you got your answer!

Hope this Helps!

Answer:

Option (A)

Step-by-step explanation:

One side of the given triangle is a diameter of the semicircle given.

Measure of the diameter = 10 units

Total area of the semicircle = [tex]\frac{1}{2}\pi (r^{2})[/tex]

                                              = [tex]\frac{1}{2}\pi (5)^2[/tex]

                                              = 39.27 square units

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}(6)(8)[/tex]

                                         = 24 square units

Area of the shaded region = Area of the semicircle - Area of the right triangle

                                            = 39.27 - 24

                                            = 15.27 square units

                                            ≈ 15 square units

Therefore, option (A) will be the answer.

Answer:

[tex] \frac{1}{5} ( - m - 4)[/tex]

Step-by-step explanation:

But method 1 best suits the question

Answer:

[tex] - \frac{1}{5} m - \frac{4}{5} [/tex]

Answer:

-1/5m    -4/5

Step-by-step explanation:

2/5 m -4/5 - 3/5 m

Combine like terms

2/5m - 3/5m    -4/5

-1/5m    -4/5

Step-by-step explanation:

First factor out the negative sign from the expression and reorder the terms

That's

[tex] \frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) } [/tex]

Using trigonometric identities

That's

Rewrite the expression

That's

[tex]\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } } [/tex]

We have

Rewrite the second fraction

That's

Since they have the same denominator we can write the fraction as

[tex] - \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]

Using the identity

Rewrite the expression

We have

Using the trigonometric identity

Rewrite the expression

That's

Which is

Using the trigonometric identity

Rewrite the expression

That's

Simplify the expression using symmetry of trigonometric functions

That's

Remove the parenthesis

We have the final answer as

As proven

Hope this helps you

Answer:   see proof below

Step-by-step explanation:

Use the following identities:

[tex]\cot\alpha=\dfrac{1}{\tan\alpha}\\\\\\\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\cdot \tan\beta}{\tan\alpha-\tan\beta}[/tex]

Proof  LHS →  RHS

Given:                  [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\cot 6A-\cot 2A}[/tex]

Cot Identity:        [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}-\dfrac{1}{\tan 2A}}[/tex]

Simplify:              [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}\bigg(\dfrac{\tan 2A}{\tan 2A}\bigg)-\dfrac{1}{\tan 2A}\bigg({\dfrac{\tan 6A}{\tan 6A}\bigg)}}[/tex]

                         [tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{\tan 2A-\tan 6A}{\tan 6A\cdot \tan 2A}}[/tex]

                         [tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}[/tex]

                         [tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}\bigg(\dfrac{-1}{-1}\bigg)[/tex]

                        [tex]= \dfrac{1}{\tan 6A-\tan 2A}+\dfrac{\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]

                        [tex]= \dfrac{1+\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]

Sum Difference Identity:    cot(6A - 2A)

Simplify:                               cot 4A

cot 4A = cot 4A   [tex]\checkmark[/tex]

Answer:

A. Trapezoid

B. Isoclese triangle

c. Equilateral triangle

d. Kite

Answer:

A, Parallelogram (more specifically a trapezoid)

B. Isosceles Triangle

C. Equilateral Triangle

D. Kite

Answer:

The measures are 108 deg and 72 deg.

Step-by-step explanation:

The larger angle has measure x.

The smaller angle has measure (2/3)x.

They are supplementary, so the sum of their measures is 180 degrees.

x + (2/3)x = 180

(3/3)x + (2/3)x = 180

(5/3)x = 180

(3/5) * (5/3)x = (3/5) * 180

x = 108

(2/3)x = 2/3 * 108 = 72

Answer: The measures are 108 deg and 72 deg.

Answer:

The value of the 8 in the front is 800,000 and the value of the second is 80,000. The front value is ten times as big as the second value.

Step-by-step explanation:

Answer:

8(20 + 6)

8(20) +8(6)

208

Step-by-step explanation:

Got it right EDGE 2021

The value of 8(26) after using the distributive property will be 208.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

As per the given, 8(26)

8(26) = 8(20 + 6)

By using the distributive property of multiplication,

8(26) = 8 × 20 + 8 × 6

⇒ 160 + 48

⇒ 208

Hence "The value of 8(26) after using the distributive property will be 208".

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Answer:

10x²+3xy+6x-y²+3y

Step-by-step explanation:

(2x+y)(5x-y+3)  steps

2x(5x-y+3)=10x²-2xy+6x

y(5x-y+3)= 5xy-y²+3y

add: 10x²-2xy+6x+5xy-y²+3y

10x²+3xy+6x-y²+3y

Answer:

Always

Step-by-step explanation:

Coplanar lines are lines that intersect making intersecting lines always coplanar.

Answer:

Slope-Intercept form: y=3x+7

Standard form: 3x-y=-7

Point-slope form: y-1=3(x+2)

Step-by-step explanation:

Slope-Intercept form:

First, find the slope, using the formula: [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).

So let's write those in our equation to find slope:

[tex]m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3[/tex]

Therefore, our slope is 3.

Now let's write our linear equation with what we have already in slope-intercept form:

y=3x+b

Well, we still need to find the y-intercept, or "b".

Plug in one of your points for the x and y values of the equation.  We'll use the point (-2,1)

[tex]y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b[/tex]

This means our y-intercept is 7.  Now we can write our equation in slope-intercept form completely:

y=3x+7

Standard form:

Now, let's find this equation is standard form.

Take your equation in slope-intercept form and write it out again:

[tex]y=3x+7[/tex]

Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:

[tex]y-3x=3x-3x+7\\-3x+y=7[/tex]

The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:

[tex]\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7[/tex]

Therefore, your equation in standad form is:

3x-y=-7

Point-Slope form:

The formula for point-slope form is y-y₁=m(x-x₁).  We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.

x₁ is -2 and y₁ is 1 and m is 3, so:

y-1=3(x-(-2)) or y-1=3(x+2)

That means our equation in point-slope form is:

y-1=3(x+2)

Answer:

58 feet

Step-by-step explanation:

Find the difference by subtracting 23 from 81.

81 - 23

= 58 feet

Answer: Because division is the inverse of multiplication.

Step-by-step explanation:

By multiplying the equation 2x=20 by 1/2  you will be able to eliminate the x variable,

For example,

1/2 * 2x = 20*1/2  

 x=  10  

The same way if  you divide both sides of the equation 2x=20 by 2 you will be able to to eliminate the x variable.

For example

2x = 20  Divide both sides by 2

x= 10  

As you can see 2 is the division inverse of 1/2.

Answer:

4.8%

Step-by-step explanation:

21% of 18

following the BODMAS rule, OF means multiplication

and also this sign% always means 100

so,it will be  21/100 * 18/1

this a laptop so i cant put it in a fraction way.....okay

this is how it shows...21/100 * 18/1

lets divide....

21/100 * 18/1

we will use 2 to divide

2 in 100=50

2 in 18=9

so it will be 21/50 * 9/1

nothing can divide so we will multiply

21*9/50*1

189/50=3.78≈4.8%

Answer:

If you meant the area was 255 in²:

Perimeter is [tex]4\sqrt{255}[/tex], or around 63.89 in.

If you meant that the area was 225 in²:

Perimeter is 60 in

Step-by-step explanation:

If you meant the area was 255 in²:

If we have a square with an area of 255 in², then it's side length will be [tex]\sqrt{255}[/tex] inches long, since the area of a square is [tex]l^2[/tex], where l is the length.

Since [tex]\sqrt{255}[/tex] doesn't return a rational number, we'll leave it as [tex]\sqrt{255}[/tex].

Now that we know the side length, the perimeter of a square is represented as [tex]4l[/tex], where l is the length.

We know the length is [tex]\sqrt{255}[/tex], so we can multiply this by 4.

[tex]4\sqrt{255}[/tex]. This is the simplest it gets.

If you meant the area was 225 in²:

Following the same concept as again:

Length: [tex]\sqrt{225} = 15[/tex]

Perimeter: [tex]4\cdot15=60[/tex] in

Hope this helped!

Answer:

P = 63.87 in

Step-by-step explanation:

area of a square window = 255 in²

find perimeter of the window.

A = s²

255 = s²

s = 15.97 in.

perimeter = 4 * s

P = 4 (15.97)

P = 63.87 in

Answer:

Width = 40ft

Step-by-step explanation:

Area of a rectangle = Length x Width

=> 1600 = 40 x W

=> 1600 = 40W

=> 1600/40 = 40W/40

=> 40 = W

So, the width is 40 ft

Answer:

40 ft  is the correct answer

Answer:

[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]

Step-by-step explanation:

Given

[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]

Required

Find an equivalent expression

[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]

Apply the following law of indices;

[tex]\frac{a^m}{a^n} a^{m-n}[/tex]

The expression becomes

[tex]125^{2-\frac{4}{3}}[/tex]

Solve the exponents

[tex]125^{\frac{6-4}{3}}[/tex]

[tex]125^{\frac{2}{3}}[/tex]

Express 125 as 5³

[tex]5^{3^*\frac{2}{3}}[/tex]

Solve the exponents

[tex]5^2[/tex]

[tex]25[/tex]

Hence;

[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]

Answer:

d

Step-by-step explanation:

i just took it! edgen

Answer:

x = - [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Given

5x - 2 = 25x + 14 ( subtract 25x from both sides )

- 20x - 2 = 14 ( add 2 to both sides )

- 20x = 16 ( divide both sides by - 20 )

x = [tex]\frac{16}{-20}[/tex] = - [tex]\frac{4}{5}[/tex]

Answer:

X = 2000 / (75 + 150)

Step-by-step explanation:

Given the following :

Christine's typing rate = 75 words per minute

Paula's speed = 2 times Christine's speed

If 2000 words needs to be transcribed. The time taken in minute 'x' will be :

From the relation :

Time = distance / speed

Distance here is the number of words in the document

Christine's speed = 75 words per minute

Paula's speed = 150 words per minute

Combined speed per minute = 150 + 75 = 225 words per minute

Time taken (x) = 2000 / 225

X = 2000 / (75 + 150)