A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 10 mm halfway across a horizontal distance of 80 mm.

Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)

Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)

Answer:

C) 1

Step-by-step explanation:

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Answer:

Step-by-step explanation:

h(3) means that x = 3. That's the right side of the x axis. At that point, h(3) has a y value of 1.

Answer: [tex]\frac{17}{4}[/tex]

Step-by-step explanation:

Simply convert 3/1 into 12/4, then add it to 5/4, to get 17/4.

Hope it helps :) and let me know if you want me to elaborate.

Answer:

Slope of the perpendicular line

m2=-5/2

Step-by-step explanation:

Answer:

(- 7, - 2 ) , (9.5, 0.75 )

Step-by-step explanation:

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex] = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

(- 7, - 2 ) and  (9.5, 0.75 ) are the solutions.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Here, we have,

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y =  = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

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Answer:

(ii) 1 dollar

Step-by-step explanation:

each pencil costs 17 cents

- thus 3 pencils x 17c is 51c

1.00 dollars minus 0.51 is 49

- 5 pencils x 17c is equal to 85

1.00 dollars minus 0.85 is 15 c

Answer:

a)2 * 2 = 4

b)2 * 3/2 = 3

c) 20 * 3/2 = 30

d) 100 * 8/5 = 160

e)473*1/100=4.73

f)111*1/100=1.11

Answer:

answers are written

Step-by-step explanation:

Answers:

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

Work Shown:

Original set = {5, 2, 5, 3, 1, 6, 2, 2, 3, 4, 2, 1, 2, 2, 4, 3, 2, 2, 2, 3}

Sorted set = {1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6}

Do not toss out the duplicates.

The most occurring or most frequent value is 2, so this is the mode.

---------------------------

To find the median, we divide the n = 20 item set into two parts

n/2 = 10

So we'll count to the 10th slot to get to the number "2", which is the second to last "2" in the sorted list shown above.

The number just after this is also "2" in the 11th slot. Average these two values to get (2+2)/2 = 4/2 = 2

The median is 2.

----------------------------

To find the mean, we need to first add up all the data values.

1+1+2+2+2+2+2+2+2+2+2+3+3+3+3+4+4+5+5+6 = 56

Then divide this over n = 20 to get 56/20 = 2.8

The mean is 2.8

The mean being larger than the median tells us we have an outlier that is larger than the main cluster. Those outliers are 5 and 6.

Answer:

y=4x+3

=)4x=y-3

=)x=(y-3)/4

Answer:

[tex]\frac{y - 3}{4}[/tex]

Step-by-step explanation:

To make x the subject, first, subtract 3 from both sides:

y = 4x + 3 → y - 3 = 4x

Next, divide both sides by 4 to get x on its own:

y - 3 = 4x → (y - 3)/4 = x

Hope this helps

Answer:

About 1205.12352941 people per square mile in 2010

About 1329.36306853 people per square mile in 2015

Explanation:

take population and divide by land area

for 2015 pop do total pop divided by 9.7 plus total pop

Answer:

it could be 34 , 34 and 82

or 34 , 73 and 37

Step-by-step explanation:

angles in a triangle add up to 180. in and isosceles triangle two angles are always the same so there will be 2 possible outcomes.

pls mark brainalist

Answer:

1: 155

2: 222

3: 44

4: 132

5: 163

6: i dont know

7: 202

8:?

9: ?

hope this helped!

Step-by-step explanation:

1.)155

2.)222

3.)44

4.)132

5.)163

6.)93.92857142857142

7.)202

8.)112.9032258064516

9.)76.66666666666666

Sana po makatulong( ˘ ³˘)♥︎

Answer:

The answer is = (x',y')=(-x,-y)

Step-by-step explanation:

= (x',y')=(-x,-y)

Rectangle PQRS is rotated 180 degrees clockwise about the origin to create triangle P'Q'R. Complete the rule that describes the coordinates of triangle P'Q'R after the rotation has occurred.

Rule of 180° Rotation

If the point (x,y) is rotating about the origin in a 180-degree clockwise direction, then the new position of the point becomes (-x,-y).

Please check the attached file for a detailed answer.

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Answer: b

Step-by-step explanation:

Answer:

1) 1085 ÷ 7

7 )1085(155

- 7

38

- 35

× 35

- 35

0

1085 ÷ 7 = 155

2) 7104 ÷ 32

32 )7104(222

- 64

× 70

- 64

×64

- 64

××

7104 ÷ 32 = 222

3) 2244 ÷ 51

51)2244(44

- 204

×244

- 244

×××

2244 ÷ 51 = 33

4) 1584 ÷ 12

12)1584(132

- 12

×38

- 36

×24

- 24

××

1584 ÷ 12 = 132

5) 1467 ÷ 9

9)1467(163

- 9

56

- 54

27

- 27

××

1467 ÷ 9 = 163

6) 2830 ÷ 28

28)2830(101

- 28

××3

- 0

30

- 28

×2

2830 ÷ 28 = 101 with the remainder 2

7) 9090 ÷ 45

45)9090(202

- 90

××9

- 0

90

- 90

××

9090 ÷ 45 = 202

8) 7000 ÷ 62

62)7000(112

- 62

×80

- 62

180

- 125

×55

7000 ÷ 62 = 112 with the remainder 55

9) 1150 ÷ 15

15)1150(76

- 105

×100

- 90

10

1150 ÷ 15 = 76 with the remainder 10

Hope that my answer is right and helpful to you

Answer:

the 1. is y = (5/4)x + 6 and 2 . is y = 20x+10, so you are right, both of them correct

Answer:

P = 5M + 10

Step-by-step explanation:

15 pages/month * M months + 10 pages = P pages

5 Months = 5*15 + 10 = 85 pages

Answer:

= -8

(hope this helps) :)

Answer:

simplify of 15.8 is 16

Step-by-step explanation:

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Answer:

15 4/5

Step-by-step explanation:

Answer:

the answer is one whole or one out of one

Answer:

1) 5.28 x 10^4 g

2)2.556 x 10^2 m

3)4.109 × 10^-2cm

Have a nice day!!!!!

Answer:

52,800 in scientific notation is [tex]5.28[/tex] × [tex]10^4[/tex].

255.6 in scientific notation is [tex]2.556[/tex] × [tex]10^2[/tex].

0.04109 in scientific notation is [tex]4.109[/tex] × [tex]10^{-2}[/tex].

Replace x with √7/5

5/√7/5 = p √7

Divide both sides by √7

P = 5/√7/5 /√7

P = 25/7

Answer: p = 25/7

The average amount earned based on the information given is $5.31 per product.

Number of farm products = 293

Total amount earned = $1557

Therefore, the average amount will be gotten by dividing the total amount by the number of farm products and this will be:

= $1557/293

= $5.31

In conclusion, the average will be $5.31.

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Answer:

A= 2

B= 3

D=2

maka

A x B ÷C

2 x 3 ÷ 2

=6 ÷ 2

=3

Answer:

A= 2

B= 3

D=2

maka

A x B ÷C

2 x 3 ÷ 2

=6 ÷ 2

=3

Step-by-step explanation:

follow the above attachment.

hope this helps you.

Answer:

the y intercept is 5 because the line passes through 5 on the y axis. Now to find the slope, pick two points where the line hits directly on the corner of the grid squares. pIck 2 of those and count the squares up till you are lined up with your other point then count over and get another number. Put the number going up over the number going down like x/y and you'll have your answer. ( simplify it if you can.(-2,3) and (0,5) are a good place to start. The answer should be 2/3. Hope this helped and God bless!

Answer:

Factor the numerator and denominator and cancel the common factors.

x/4+3/2 or 32/4  or Reduce the expression, if possible, by cancelling the common factors. 8 is your final answer

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

First, you substitute.

x + 6 / 4

26 + 6 / 4

Then, you add.

26 + 6 = 32

Finally, you divide.

32 / 4 = 8

Answer: 8

Answer:To write a linear expression in standard form, rearrange the terms in alphabetical order.

7384000000

Step-by-step explanation:

Answer:

738400000.0

Step-by-step explanation:

738400000.0*10^10