Martin drew a pair of perpendicular lines and a pair of parallel lines.

Which of these statements best compares the pairs of perpendicular and parallel lines?

Perpendicular and parallel lines have their lines extending in one direction only.
Perpendicular and parallel lines always have a common endpoint.
Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.
Perpendicular lines have only one point lying on them, and parallel lines have no points lying on them.

For this case we have the following equations:

[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x[/tex]

We must find [tex](f_ {o} g) (x):[/tex]

By definition of composition of functions we have to:

[tex](f_ {o} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {o} g) (x) = \frac {1} {x ^ 2-3x}[/tex]

We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.

[tex]x ^ 2-3x = 0\\x (x-3) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = 3[/tex]

The domain is given by all real numbers except 0 and 3.

Answer:

x other than 0 and 3

ANSWER

0 and 3

EXPLANATION

The given functions are

[tex]f(x) = \frac{1}{x} [/tex]

and

[tex]g(x) = {x}^{2} - 3x[/tex]

[tex]( f \circ g)(x) = f(g(x))[/tex]

[tex]( f \circ g)(x) = f( {x}^{2} -x )[/tex]

[tex]( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x} [/tex]

Factor the numerator:

[tex]( f \circ g)(x) = \frac{1}{ x(x - 3)} [/tex]

The function will be undefined if the denominator is zero.

[tex]x(x - 3) \ne0[/tex]

[tex]x \ne0 \: and \: x \ne3[/tex]

Therefore 0 and not in the domain of the composed function.

Answer:

No

Step-by-step explanation:

0.26*16 + 12.25 = 16.41

16.41 < 16.50

Answer:

No, Vicky should not switch.

Step-by-step explanation:

Vicky's checking account charges a monthly service fee = $12.25

Account also charges per-check fee = $0.26

Vicky writes checks per month = 16

His total monthly charges = 12.25+( 16 ×0.26 )

                                           = 12.25 + 4.16

                                           = $16.41

Another account that charges a $16.50 monthly service fee and no per-check fee.

Comparison between account = 16.50 > 16.41

So Vicky should not switch to another account because it charges more than her current account.

Answer:

11.2

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = B(4, 7) and (x₂, y₂ ) = C(2, - 4)

d = [tex]\sqrt{(2-4)^2+(-4-7)^2}[/tex]

   = [tex]\sqrt{(-2)^2+(-11)^2}[/tex]

   = [tex]\sqrt{4+121}[/tex]

   = [tex]\sqrt{125}[/tex] ≈ 11.2

Answer:

AA similarity theorem

Step-by-step explanation:

we know that

AA (Angle-Angle) Similarity states that  In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar

In this problem we have that

∠BCA=∠ECD ----> by vertical angles

∠BAC=∠DEC ---> because AB is parallel to ED (alternate interior angles)

therefore

Triangles ABC and EDC are similar by AA similarity theorem

Answer:

0.98x24=23.52+35.95=59.47     hope im right

Step-by-step explanation:

The total cost of renting the truck for one day if you drive 24 miles is $58.47.

The function notation for the total cost of renting the truck for one day if you drive 24 miles is C(24). The total rental cost can be calculated by multiplying the cost per mile ($0.98) by the number of miles driven (24) and adding the base cost ($35.95). So, the total rental cost would be $35.95 + ($0.98 x 24) = $58.47.

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Answer:

I'm guessing you need this now, So I'm just going to give the answer without the explanation

Step-by-step explanation:

52.5

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

(look at the picture).

We have 2a = 20. Therefore a = y = 20 : 2 = 10 and a√3 = x = 10√3

For this case we have the following expression:

(63 + 9) ÷ 3 (2)

To find the value of the expression we must first solve the terms associated with parentheses, that is:

[tex](63 + 9) = 72\\3 (2) = 6[/tex]

So:

72 ÷ 6 =

12

So, the correct option is 12.

Answer:

(63 + 9) ÷ 3 (2) = 12

Option B

First add the numbers inside the parentheses, then divide the result by 3, and finally multiply that result by 2. The final answer is 48, matching option C.

Therefore, the answer to (63 + 9) ÷ 3(2) is 48, which corresponds to option C.

Answer:

8 in

Step-by-step explanation:

Area of a square is given by

A = s^2 where s is the side length

64 in^2 = s^2

Taking the square root of each side

sqrt(64 in^2) = sqrt(s^2)

8 in =s

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side length

We have the area

[tex]A=64\ in^2[/tex]

Substitute:

[tex]s^2=64\to s=\sqrt{64}\\\\s=8\ in[/tex]

[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]

Answer:

The interior angles are 70°,65°,80°,155° and 170°

Step-by-step explanation:

step 1

Find the sum of the interior angles of the pentagon

The sum is equal to

S=(n-2)*180°

where

n is the number of sides of polygon

n=5 (pentagon)

substitute

S=(5-2)*180°=540°

step 2

Find the value of x

Sum the given angles and equate to 540

x+(x-5)+(x+10)+(2x+15)+(2x+30)=540°

7x+50=540°

7x=490°

x=70°

step 3

Find all the angles

x=70°

(x-5)=(70-5)=65°

(x+10)=(70+10)=80°

(2x+15)=(2*70+15)=155°

(2x+30)=(2*70+30)=170°

Answer:

Step-by-step explanation:

I think its 823 ppm?

I'm not sure

Answer:

Step-by-step explanation:

C.35%

If you divide the number of hearts drawn by the number of total draws you get your answer.

14/20=0.35

C. 5 and seventy-six hundredths sorry If I'm wrong, but I'm pretty sure I'm right

please rate my answer

Answer:

Five and seventy six hundredths

Your Welcome :3

Answer:

Point Q is (3 , 4)

Step-by-step explanation:

* Lets revise the rule of the point which divides of a line segment in

 a ratio

- If point (x , y) divides the line segment AB, where A is (x1 , y1) and

 B is (x2 , y2) in the ratio m1 : m2

∴ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ y = [m2(y1) + m1(y2)]/(m1 + m2)

* Now lets solve the problem

- Point Q divides ST in the ratio 5 : 2 where S (-2 , -6) and T (5 , 8)

- To find the coordinates of point Q use the same rule above

# Q is (x , y)

# S is (x1 , y1) and T is (x2 , y2)

# m1 : m2 is 5 : 2

∵ x1 = -2 and y1 = -6

∵ x2 = 5 and y2 = 8

∵ m1 = 5 and m2 = 2

- Substitute these values in the rule

∵ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ x = [2(-2) + 5(5)]/(5 + 2) ⇒ multiply the numbers

∴ x = [-4 + 25]/7 ⇒ add

∴ x = [21]/7 ⇒ Divide

∴ x = 3

* The x-coordinate of Q is 3

∵ y = [m2(y1) + m1(y2)]/(m1 + m2)

∴ y = [2(-6) + 5(8)]/(5 + 2) ⇒ multiply the numbers

∴ y = [-12 + 40]/7 ⇒ add

∴ y = [28]/7 ⇒ Divide

∴ y = 4

* The y-coordinate of point Q is 4

∴ Point Q is (3 , 4)

Answer:

1/9

Step-by-step explanation:

Of the 36 possible sums, 4 of them are 9. The probability is 4/36 = 1/9.

_____

Comment on these dice

Interestingly, the probability of any given sum is the same as it is with "normal" dice.

Answer:

What you have to do is add all of the sums up and put 2 over it. it is 2/20 which is 1/10.

Step-by-step explanation:

in a percent it is 0.1

Can I get brainiest

The probability that Alina selects 2 cans of lemonade is

How to calculate probability?

The given question has concept of conditional probability.

Conditional probability is applied when we have to find the possibility of an event given the another event already occurred.

Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Here, the first event is selecting the lemonade can and second event is also selecting lemonade can given one lemonade is already selected.

The probability to select 1st lemonade= 7/20

The probability to select 2nd lemonade=6/19

Multiplying them we get:

Probability:7*6/20*19=21/190

Therefore, the probability to select two lemonades is 21/190.

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Answer:

A) P(stars) = 1/3

B) P(odd)= 4/7

C)P(solid grays or stars or striped)= 1

D)P(1,4 or 7)= 3/7

E)P(not striped)= 2/3

Step-by-step explanation:

Given:

sample set contains 1-7 solid gray, 1-7 stars and 1-7 striped cards

Let solid gray be x

stars be y

striped be z

then sample set be

1x,2x,3x,4x,5x,6x,7x,

1y,2y,3y,4y,5y,6y,7y,

1z,2z,3z,4z,5z,6z,7z

total number of cards in sample set =21

Now

a)Finding probability of stars

Number of star cards in above sample set = 7

P(stars)= 7/21

     P(y)=1/3

b)Finding probability of odd

Number of odd cards in above sample set = 12

P(odd)= 12/21

          =4/7

c)Finding probability of solid grays or stars or striped

P(solid grays or stars or striped) = P(x or y or z)

                                                      =P(x U y U z)

As the events are mutually exclusive

P(x U y U z)= P(x)+P(y)+P(z)

now P(x)= 1/3

P(y)=1/3

P(z)=1/3

P(x U y U z) = 1/3 + 1/3 + 1/3

                   = 3/3

                   =1

d)Finding probability of 1,4 or 7

Number of 1,4 or 7 cards in above sample set = 9

P(1,4 or 7) = P(1 U 4 U 7)

As the events are mutually exclusive

P(1,4 or 7) = P(1) + P(4) + P(7)

P(1)= 3/21

     =1/7

P(4)= 3/21

     =1/7

P(7)= 3/21

     =1/7

P(1,4 or 7)= 1/7 + 1/7 + 1/7

               =3/7

e)Finding probability of not striped

Number of not striped cards in above sample set = 14

P(not striped)= 14/21

                      = 2/3 !

The scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].

The scale factor between two similar triangles is the ratio of the corresponding side lengths. In this case, we can find the scale factor by comparing the corresponding sides of triangles FGH and MNO.

Let's denote the scale factor as [tex]\( k \)[/tex]:

[tex]\[ k = \frac{MN}{FG} \][/tex]

Given that NO = 15 units and FG = 6 units, and MN is denoted as [tex]\( x \)[/tex], we can substitute these values into the formula and solve for [tex]\( x \)[/tex]:

[tex]\[ k = \frac{x}{6} \][/tex]

Since [tex]\( k = \frac{NO}{FG} \)[/tex] we can set up the equation:

[tex]\[ \frac{x}{6} = \frac{15}{9} \][/tex]

Now, solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{15}{9} \times 6 \][/tex]

[tex]\[ x = 10 \][/tex]

So, the scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].

The scale factor of the given figures is 5 : 3.

The value of x is 10

What is the scale factor?

Scale factor is calculated by finding the ratio of the dimensions of the new shape to the dimensions of the original shape.

15 : 9 = x : 6

15/9 = x/6

Cross product

15 × 6 = 9 × x

90 = 9x

Divide both sides by 9

x = 90/9

x = 10

Therefore, the scale factor 15 : 9

= 15/9

= 5/3

= 5 : 3

Answer:

The missing angle has a measure of 2 degrees.

Step-by-step explanation:

Every triangle's inner angles can be added and will always equal 180. Therefore, use subtraction to find any missing angle. In this case,

180 - 91 = 89

89 - 87 = 2

So, your answer is 2.

If the two angles of the triangle are 91° and 87°. Then the measure of the third angle of the triangle will be 2°.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The two angles of the triangle are 91° and 87°.

Then the measure of the third angle of the triangle will be

Let x be the third angle. Then we have

91° + 87° + x = 180

                 x = 180° - 87° - 91°

                 x = 2°

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Answer:

17.872, 8

Step-by-step explanation:

Chords that pass through the center are the diameter, and lines that are tangent to the circle are perpendicular to the diameter at that point.

Therefore, what we are looking at are right triangles, and we can find the distance using Pythagorean theorem.

c² = a² + b²

(19.5)² = (7.8)² + b²

b ≈ 17.872

c² = a² + b²

(10)² = (6)² + b²

b = 8

Answer:

A) f(x) = -3x+7

Step-by-step explanation:

f(x) is interchangeable with y when writing a function, so the functions are the same.

The function that corresponds to the equation -3x + 7 = y is f(x) = -3x + 7, which maintains the same relationship between x and y as the given equation.

The equation -3x + 7 = y can be rewritten in function notation, which typically uses the format f(x) = some expression involving x. The correct corresponding function is one that maintains the relationship between x and y as displayed in the original equation. Therefore, among the options provided:

The correct answer indicates that the function of x (f(x)) is given by the linear equation -3x + 7.

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Answer:

the answer is 1. the trick here is to divide the exponent to 4.

Step-by-step explanation:

i^32 32÷4=8

i

-1

-i

1

Answer:  The required value of the given power of i is 1.

Step-by-step explanation:  We are given to simplify the following power of i :

[tex]P=i^{32}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the value of the imaginary number i(iota) is given by

[tex]i=\sqrt{-1}~~~~~\Rightarrow i^2=-1.[/tex]

From expression (i), we get

[tex]P\\\\=i^{32}\\\\=(i^2)^{16}\\\\=(-1)^{16}\\\\=(1)^8\\\\=1.[/tex]

Thus, the required value of the given power of i is 1.

Answer:

x = 30.

Step-by-step explanation:

The angle next to the 60 degree angle = 180 - 60 = 120 degrees (adjacent angles are supplementary).

Let the angle  just above 3x be y.  The sum of 3x and y = 120 degrees (as opposite angles of a parallelogram are equal).

We have the following equations.

3x + y = 120............(1)

2x + 90 + y = 180

2x + y = 90.............(2)

Subtracting, (1) - (2):

x = 30.

Answer:

[tex]5y^{6}\sqrt{2}[/tex]

Step-by-step explanation:

We want to  simplify:

[tex]\sqrt{50y^{12}}[/tex]

We rewrite as:

[tex]\sqrt{2\times25 \times (y^{6})^2}[/tex]

We split the radical sign to obtain:

[tex]\sqrt{25} \times \sqrt{(y^{6})^2} \times \sqrt{2}[/tex]

Simplify the square root for the perfect squares to get:

[tex]5y^{6}\sqrt{2}[/tex]

Therefore the simplified form is: [tex]5y^{6}\sqrt{2}[/tex]

Answer:

its 0.4

Step-by-step explanation:

Answer:

The answer is C) 0.4

Answer:

t x 2.5 =m

Step-by-step explanation:

[tex]\bf (\stackrel{x}{1}~~,~~\stackrel{y}{7.5})\implies 7.5=ab^1\implies \boxed{7.5=ab} \\\\\\ (\stackrel{x}{3}~~,~~\stackrel{y}{16.875})\implies 16.875=ab^3\implies 16.875=ab^{1+2}\implies 16.875=abb^2 \\\\\\ 16.875=\boxed{7.5}b^2\implies \cfrac{16.875}{7.5}=b^2\implies 2.25=b^2 \\\\\\ \sqrt{2.25}=b\implies \blacktriangleright 1.5=b \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 7.5=ab\implies \cfrac{7.5}{b}=a\implies \cfrac{7.5}{1.5}=a\implies \blacktriangleright 5=a \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=5(1.5)^x~\hfill[/tex]

Answer: First option.

Step-by-step explanation:

Given the function f(x):

 [tex]f(x)=2x-7[/tex]

And the function g(x):

[tex]g(x)=-6x-3[/tex]

You need to add them to get [tex]f(x)+g(x)[/tex]. Then:

 [tex]f(x)+g(x)=(2x-7)+(-6x-3)[/tex]

Therefore, when you add the like terms you get that [tex]f(x)+g(x)[/tex] is:

[tex]f(x)+g(x)=2x-7-6x-3[/tex]

[tex]f(x)+g(x)=-4x-10[/tex]

Since it is a linear function, the Domain is: All real numbers.

You can observe that the result obtained matches witht the first option.

The correct statement about the function represented by the table is:

  D.  It is a linear function because the y-value increase by an equal difference over equal intervals of x-values.

The table of values are given as follows:

            x                    y

            1                    26

            2                   44

            3                   62

            4                   80

            5                    98

Here with the x-value is increasing by each 1.

Hence, we will check whether the difference in y-value is equal or not.

( Since, the rate of change is the ratio of the change in y-value to the change in x-value)

Hence,

44-26=18

62-44=18

80-62=18

and 98-80=18

Hence, we get that the change in y-value is equal .

Hence, we get that the slope or rate of change of the function is constant.

Hence, the function is linear.