Use the data in the table to complete the sentence.
х
-2
-1

0
1

y
7
6
5
4

The function has an average rate of change of ______.

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Explanation:

It helps to add point labels. Let's place point A at the very top point of the triangle. Then point B will be at the 90 degree angle. Point C is the far left point. Lastly, point D is on segment BC such that DC = 3.

Since BC = 8 and CA = 17, we can use the pythagorean theorem to get...

(AB)^2 + (BC)^2 = (AC)^2

(AB)^2 + (8)^2 = (17)^2

(AB)^2 + 64 = 289

(AB)^2 = 289-64

(AB)^2 = 225

AB = sqrt(225)

AB = 15

Now focus on triangle ABD and apply the pythagorean theorem again to find side AD

(AB)^2 + (BD)^2 = (AD)^2

AD = sqrt(  (AB)^2 + (BD)^2  )

AD = sqrt(  (AB)^2 + (BC-CD)^2  )

AD = sqrt( (15)^2 + (8-3)^2 )

AD = sqrt(250)

AD = sqrt(25*10)

AD = sqrt(25)*sqrt(10)

AD = 5*sqrt(10) .... answer is choice B

Answer:

A

Step-by-step explanation:

Firstly x cannot be -5 because the expression on th left would be undefined so it's only between choices a and c.

Create a number line with makes the expression on left 0 and undefined...so at 6 and -5 this happens.

-------(-5)--------(6)---------

Let's test the 3 intervals by choosing a value from that interval to see if all numbers from that interval will make the expression on left less than 0.

Number before -5 is -6:

(-6-6)/(-6+5)=-12/-1=12 >0 so this interval is not a part of our solution.

Number between -5 and 6 is 0:

(0-6)/(0+5)=-6/5<0 so this interval is a part of our solution

Number after 6 like 7:

(7-6)/(7+5)=1/12>0 so this interval is not a part of our solution.

The winner is everything between-5 and 6 so answer is A.

Answer:

oi ngl levi is hawt I like your pfp ^^

Step-by-step explanation:

my name is Riley

Answer:

B (x+7, y-6)

Step-by-step explanation:

It goes right 7 and down 6

Answer:

(x,y) --> (x+7, y-6)

Step-by-step explanation:

Good luck with your exam! :DD

Answer:

i dont know man

Step-by-step explanation:

i dont know

Answer:

Just want the points

Step-by-step explanation:

========================================================

Explanation:

The two points mentioned in bold are midpoints of segments AB and AC respectively.

To find the coordinates of a midpoint, you add up the x coordinates and divide by 2. Do the same with the y coordinates.

For example, points A and B are at (7,6) and (1,-2)

If we add up the x coordinates and divide by 2, then we get (7+1)/2 = 4. Do the same for the y coordinates to get (6+(-2))/2 = 2. So that's how (4,2) is the midpoint of segment AB. You'll use similar logic to find that (8,2) is the midpoint of segment AC.

A slight alternative is that once you find one midpoint is (4,2), you can draw a horizontal line until you reach (8,2). We're using the idea that the midsegment is parallel to BC which is also horizontal.

Answer:

B

Step-by-step explanation:

A x - 36 <42 is wrong because its saying how many can be added

B x +36 < 42 this one is most likely correct because its displays x as how many can be added

C x - 36 > 42 this is wrong because the bus has less than 42 seats

D x + 36 >57 like i said cant be over 42

The inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. Inequality is used most often to compare two numbers on the number line by their size. There is always a definite equation to represent it.

Let x be the number of passengers that can be added to the bus.

It is given that the bus has less than 42 seats and 36 seats are already occupied.

The sum of the remaining seats which are to be filled by the passenger and the 36 seats which are filled, must be less than the total seats that is 42.

Therefore the inequality equation becomes,

x + 36 < 42.

Thus, the inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.

To learn more about inequality equation, refer -

https://brainly.com/question/17448505

#SPJ2

Answer:

4

Step-by-step explanation:

y = kx

Use point (3, 12).

12 = k * 3

k = 12/3 = 4

y = 4x

Answer: 4

Divide y by x:

12/3 = 4

36 / 9 = 4

The constant of variation is 4

The mark price of the pen is 120 rs

The first step is to write out the parameters given the question

Discount= 15%

Gain= rs 10

Discount= 15%

loss= rs

When a pen is sold at a discount of 15% there is a gain of rs 10

When the pen is sold at 25% discount there is a loss of rs 2

The mark price of the pen can be calculated as follows

15% = c.p + 10 rs

25 % = c.p - 2 rs

25%-15% = 10 rs +2 rs

10% = 12 rs

10/100 = 12 rs

0.1= 12 rs

12/0.1

= 120 rs

Hence the mark price of the pen is 120 rs

Please see the link below for more information

https://brainly.com/question/17109020?referrer=searchResults

Mark Price: RS. 120

The Gain Function is the difference between Resulting Price, which is the Mark Price including Discount Rate, and the Reference Price, where positive result represents Net Gain, as negative result represents Net Loss. Gain Function is described below:

[tex]G = \left(1-\frac{r_{D}}{100} \right)\cdot P_{M}-P_{R}[/tex] (1)

Where:

[tex]G[/tex] - Gain function, in monetary units.

[tex]r_{D}[/tex] - Discount rate, in percentage.

[tex]P_{M}[/tex] - Mark price, in monetary units.

[tex]P_{R}[/tex] - Reference price, in monetary units.

The Mark Price of the pen is the price shown on the label of the product, whereas the Reference Price is the purchase cost of the product from provider.

Based on what it is written on statement we have the following system of linear equations:

1) When a pen is sold at a discount of 15 %. There is a gain of RS. 10: ([tex]G = 10[/tex], [tex]r_{D} = 15[/tex])

[tex]\left(1-\frac{15}{100} \right)\cdot P_{M} - P_{R} = 10[/tex] (2)

2) But if it is sold at 25 % discount there is a loss of RS. 2: ([tex]G = -2[/tex], [tex]r_{D} = 25[/tex])

[tex]\left(1-\frac{25}{100} \right)\cdot P_{M} - P_{R} = -2[/tex] (3)

The solution of the resulting system of linear equations is:

[tex]P_{M} = 120[/tex], [tex]P_{R} = 92[/tex]

The mark price of the pen is RP. 120.

Answer:

D

Step-by-step explanation:

As the counter clockwise rule is A(x,y) becomes A'(-y,x).

So (1, -6) becomes (6, 1)

Hope it helps you

Initial value is your y intercept, and to find that you just need to substitute 0 for x. Anything to the power of 0 is just 1. So you get 34.2(1), which means that your initial value is 34.2.

Answer:

81/16

Step-by-step explanation:

(⅔)-⁴

81/16

= 5.0625

Answer:

9

Step-by-step explanation:

Using the rules of logarithms

log[tex]x^{n}[/tex] = nlogx

[tex]log_{b}[/tex] b = 1

Then

[tex]log_{x}[/tex] [tex]x^{9}[/tex]

= 9[tex]log_{x}[/tex] x

= 9

Answer:

112

Step-by-step explanation:

The volume is given by l*b*h=4*4*7=112

Answer:

Yes, the function is symmetric about y-axis.

Step-by-step explanation:

To check whether the function is symmetric with respect to y-axis, replace each x as -x and simplify.

If h(x) = h(-x) then it is symmetric about y-axis.

Let's find h(-x) now.

h(-x)= [tex](-x)^4} -5(-x)^{2} +3[/tex]

Let's simplify it

h(-x)=[tex]x^{4}-5x^{2} +3[/tex]

Here, h(x) = h(-x). The function is symmetric about y-axis.

Answer:

Question 16 = 22

Question 17 = 20 cm²

Step-by-step explanation:

Concepts:

Area of Square = s²

Area of Triangle = bh/2

Diagonals of the square are congruent and bisect each other, which forms a right angle with 90°

Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Question # 16

Step One: Find the total area of two squares

Large square: 5 × 5 = 25

Small square: 2 × 2 = 4

25 + 4 = 29

Step Two: Find the area of the blank triangle

b = 5 + 2 = 7

h = 2

A = bh / 2

A = (7) (2) / 2

A = 14 / 2

A = 7

Step Three: Subtract the area of the blank triangle from the total area

Total area = 29

Area of Square = 7

29 - 7 = 22

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Question # 17

Step One: Find the length of PT

Given:

PT = PR + RT [Segment addition postulate]

PT = (4) + (6)

PT = 10 cm

Step Two: Find the length of S to PT perpendicularly

According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

Step Three: Find the area of ΔPST

b = PT = 10 cm

h = S to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

Step Four: Find the length of Q to PT perpendicularly

Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

Step Five: Find the area of ΔPQT

b = PT = 10 cm

h = Q to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

Step Six: Combine area of two triangles to find the total area

Area of ΔPST = 10 cm²

Area of ΔPQT = 10 cm²

10 + 10 = 20 cm²

Hope this helps!! :)

Please let me know if you have any questions

Answer:

it should be the second one I hope this help

Answer:

x <= -4 or x >= 2

Step-by-step explanation:

so, it actually says

|x+1| >= 3

so, then, this is valid for all x >= 2 (then x+1 is 3 or higher), and for all x <= -4 (then x+1 is -3 or lower, and |x+1| is still 3 or higher)

Answer:

n = 9

Step-by-step explanation:

20.75 = 1.75n + 5

20.75 - 5 = 1.75n

15.75 = 1.75n

-------     -------

1.75       1.75

  9    =     n

The conversion rate US dollars to Euros is represented with the function:

E(n)=0.72n

n- number of dollars

E(n) - Euros as a function of US dollars

The conversion rate Euros to Dirhams is :

D(x)=5.10x

x- number of Euros

D(x)- Dirhams as a function of Euros

We are trying to find D(x) in terms of n.

D(x) = 5.10x

x can be rewritten as E(n)

D(x) = 5.10(E(n))

D(x) = 5.10(E(n))

D(x) = 5.10(0.72n)

D(x) = 3.672n

According to this the following statement is true:

A) (D x E)(n) = 5.10(0.72n)

Answer:

Yes, she will be able to retrieve the item

Step-by-step explanation:

The information with regards to the research historian interest in finding a sunken treasure are;

The depth from which the equipment can recover items = 5,000 m

The speed of sound through water, v = 1,530 m/s

The time it takes the echo from the item to return to the sonar detector, t = 6.2 s

Let d, represent the depth at which the item is located

Given that an echo travels from the sonar detector to the item and back to the sonar detector, the distance traveled by the sound wave which is received as an echo by the sonar detector = 2 × d

Velocity, v = Distance/time

∴ Distance = Velocity × Time

The distance traveled by the echo = 2 × d = v × t

2 × d = v × t

∴ 2 × d = 1,530 m/s × 6.2 s

d = (1,530 m/s × 6.2 s)/2 = 4,743 m

The depth at which the item is located, d = 4,743 m is less than the maximum depth the equipment can recover items, therefore, she will be able to retrieve the item.

Answer:

x=10

Step-by-step explanation:

I hope this will help you

Answer:

3/4 more hours

Step-by-step explanation:

Hours taken to clean bedroom = 5/4

Hours taken to clean den = 1/2

How much more = 5/4 - 1/2

5-2/4 (common denominator)

3/4 more hours (It's a propper fraction, so we can't write it as a mixed number)

Answer from Gauthmath

Answers:

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Explanation:

Refer to the diagram below.

The segment AB is the player's height of 6 ft.

The segment CD is the hoop's height, which is 10 ft.

There is a point E on CD such that rectangle BACE forms. This will help us form ED later.

Angle EBD is what we're after, which I'll call x.

Since the free throw line is 15 ft from the basket, this means segments EB and AC are 15 ft each.

In rectangle BACE, the side EC is opposite AB. So both of those sides are 6 ft each.

Since CD = 10 and EC = 6, this must mean ED = CD-EC = 10-6 = 4.

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To summarize, we found that ED = 4 and EB = 15.

We'll focus our attention entirely on triangle EBD

We have two known legs of the triangle, specifically the opposite and adjacent sides.

So we'll use the tangent ratio.

tan(angle) = opposite/adjacent

tan(B) = ED/EB

tan(x) = 4/15 .... is the equation to solve

x = arctan(4/15) .... same as inverse tangent or [tex]\tan^{-1}[/tex]

x = 14.931417 ..... make sure to be in degree mode

x = 15 ..... rounding to the nearest whole degree

So that unknown angle in the diagram is approximately 15 degrees

Answer:

x=-2

sorry i messed up coord val :/

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

a parabola  is symmetric (has a mirror image)

a parabola has ONE vertex (a highest or lowest point).

thus a line that goes through the vertex is it's axis of symmetry.

x = 5 , x=99, x=102 are vertical lines that intersect the x axis no matter what the y value is....

your axis of symmetry is a line that looks like  X= SOMETHING

the "something" is the X value of the vertex, which is (-2,3)

this the equation x = -2 is the answer ... see the image

Answer:

18

Step-by-step explanation:

The interior and exterior angle of a polygon is supplementary

let interior be I

let exterior be E

I + E = 180

Since the interior angle is 8 times that of an exterior angle,

8E + E = 180          [replacing I with 8E]  

9E = 180                

E = 20                      

The exterior angle is 20 degrees

I + E = 180          

I + 20 = 180      

I = 160              

The interior angle is 160 degrees.

The equation to find the interior angle of a polygon with 'n' number of sides is:

I = ( (n − 2) × 180 ) ⁄ n

We know the interior angle, so plug it in and solve for n:

160 = ( (n − 2) × 180 ) ⁄ n      

160n = (n − 2) × 180            

160n = 180n − 360                  

-20n = -360                            

n = 18                                  

6√5 + 3√6 = 6√5 + 3√6 [cannot be simplified]

; roots do not contain any perfect squares, and the roots are not similar.

6√5(3√6) = 18√30 [can be simplified]

; although roots do not contain any perfect squares, the product rule can be applied to create a singular expression.