I hope you can see my question, if you have a phone look at the top for my question. Thank you.

The spider's movement is an illustration of a parabola.

(a) The equation

The spider passes through the origin.

So, we have:

[tex]\mathbf{(x,y) = (0,0)}[/tex]

The spider jumps to a maximum height of 20mm, midway 160mm.

So, the vertex is:

[tex]\mathbf{(h,k) = (80,20)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

So, we have:

[tex]\mathbf{0 = a(0 - 80)^2 + 20}[/tex]

[tex]\mathbf{0 = 6400a + 20}[/tex]

Subtract 20 from both sides

[tex]\mathbf{6400a =- 20}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{320}}[/tex]

Substitute [tex]\mathbf{a =- \frac{1}{320}}[/tex] and [tex]\mathbf{(h,k) = (80,20)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]

(b) The focus, directrix and the axis of symmetry

The focus of a parabola is:

[tex]\mathbf{Focus = (h,k+p)}[/tex]

Where:

[tex]\mathbf{p = \frac{1}{4a}}[/tex]

So, we have:

[tex]\mathbf{p = \frac{1}{4\times -1/320}}[/tex]

[tex]\mathbf{p = -\frac{320}{4}}[/tex]

[tex]\mathbf{p = -80}[/tex]

So, we have:

[tex]\mathbf{Focus = (80 , 20-80)}[/tex]

[tex]\mathbf{Focus = (80 ,-60)}[/tex]

The axis of symmetry is:

[tex]\mathbf{x = h}[/tex]

So, we have:

[tex]\mathbf{x = 80}[/tex]

The directrix is:

[tex]\mathbf{y = k - p}\\[/tex]

So, we have:

[tex]\mathbf{y = 20+80}[/tex]

[tex]\mathbf{y = 100}[/tex]

Read more about parabolas at:

https://brainly.com/question/5430838

Answer:

1 hour

Step-by-step explanation:

am i right

Answer:

17.92

Step-by-step explanation:

Answer:

1 3/5

Step-by-step explanation:

if you multiply 1/5 x 8, you get the decimal 1.6, and 1.6 as a mixed fraction is 1 3/5

Answer: (8,1)

Step-by-step explanation:

The line that connects (-4,5) and (2,3) has a slope of (-2/6) or -1/3. The y-intercept is calculated from one of the points: 3 = -(1/3)*(2) + b

b = 3 2/3

The equation for the line is y = -(1/3)x + 3 2/3

The reflection covers a distance of x of (2 - (-4)) = 6. Add 6 to the x value of (2,3) and calculate the resulting y. (8,y): y = -(1/3)(8) + 3 2/3, y = -8/3 + 11/3 = 3/3 or 1

The point is (8,1)

Answer:

The answer would be 36/7 and that would be 5.14285714286

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=36/7

Answer:10 & 12

Step-by-step explanation:

Answer:

The 5th step will need 32 blocks, and the 6th step will need 64 blocks.

Step-by-step explanation:

Each step requires the blocks to be doubled. The first step has two, 2x2 is 4. There are 4 blocks in the next step. 4x2 is 8. There are 8 blocks in the next step, and so on and so forth. Just multiply by 2. Hope this helped!

Answer:

3rd option

Step-by-step explanation:

a point (0, y ) lies on the y- axis

a point (x, 0 ) lies on the x- axis

a point (x, y ) lies in I quadrant

a point (- x, y ) lies in II quadrant

a point (- x, - y ) lies in III quadrant

a point (x, - y ) lies in IV quadrant

Then

point (2, - 5 ) lies in IV quadrant

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

We require 2 equations with the repeating digit 7 placed after the decimal point.

let x = 0.427777... ( multiply both sides by 100 and 1000 )

100x = 42.777..... (1)

1000x = 427.777.... (2)

Subtract (1) from (2), thus eliminating the repeating digits

900x = 385 ( divide both sides by 900 )

x = [tex]\frac{385}{900}[/tex] = [tex]\frac{77}{180}[/tex]

Answer:

5x - y = 21  

Step-by-step explanation:

Given the linear equation in point-slope form, y + 6 = 5(x - 3):

In order to transform the given equation into its standard form, Ax + By = C, start by distributing 5 into the parenthesis:

y + 6 = 5(x - 3)

y + 6 = 5x - 15

Subtract 5x from both sides:

- 5x + y + 6 = 5x - 5x - 15

- 5x + y + 6 = - 15

Subtract 6 from both sides:

- 5x + y + 6  - 6 = - 15 - 6

- 5x + y = - 21

Divide both sides by -1:

[tex]\frac{-5x + y}{-1} = \frac{-21}{-1}[/tex]

5x - y = 21    

Answer:

you have to do it look up how to chart coordinates

Step-by-step explanation:

Answer:

ok brain less and point alr bet I will do this feal quick

Step-by-step explanation:

ok so the anser r very ez

first multiply and do tibi top in botton out dived the factor and thete for u will get *** and ****** **** *** for the first anser

Answer:

y = 3x + 5

Step-by-step explanation:

y = total cost

x =  basket of apples

5 = admission fee

y =  cost per basket  + admission fee  

y =  3x + 5

Answer:

1. B. 12

2. D. 6

3. A. 12

4. C. 64

5. D. 1[tex]\frac{17}{18}[/tex]

6. B. 16

Step-by-step explanation:

Answer:

$40,000 + $300x

Step-by-step explanation:

If the machine salesperson sold 5 machines, his commission would be $300 × 5 so if he sold x machines his commissions would be $300x. This value is added on to his base salary of $40,000.

Answer: $40,000 + $300x

Using the probability concept, it is found that there is a [tex]\frac{1}{55}[/tex] probability that Luella will pull out a Reese's  Cup, eat it, and then pull out another Reese's Cup.

A probability is the number of desired outcomes divided by the number of total outcomes.

The probability of both events is the multiplication of the probabilities of each event, thus:

[tex]p = \frac{2}{11} \times \frac{1}{10} = \frac{2}{110} = \frac{1}{55}[/tex]

[tex]\frac{1}{55}[/tex] probability that Luella will pull out a Reese's  Cup, eat it, and then pull out another Reese's Cup.

A similar problem is given at https://brainly.com/question/15536019

Using the data given, the 95% confidence interval of the true mean is (205.20 ; 230.20)

Given the data :

The confidence interval is defined as :

Since, sample size ls less than 30 we use a t-distribution table :

[tex] C.I = \bar{x} ± t_{α/2, n-1} \frac{s}{\sqrt{n}}[/tex]

Using a calculator :

Lower boundary = [tex] 217.7 - 2.26(\frac{17.49}{\sqrt{10}}) = 205.20[/tex]

Lower boundary = [tex] 217.7 + 2.26(\frac{17.49}{\sqrt{10}}) = 230.20[/tex]

Therefore, the confidence interval is (205.20 ; 230.20)

Learn more :https://brainly.com/question/25173276

The confidence interval is simply a range that contains the true mean of the population

The 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]

The given parameter is:

[tex]\mathbf{n = 10}[/tex]

Start by calculating the degree of freedom

[tex]\mathbf{df = n - 1}[/tex]

[tex]\mathbf{df = 10 - 1}[/tex]

[tex]\mathbf{df = 9}[/tex]

Next, calculate the mean

[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]

[tex]\mathbf{\bar x = \frac{225 + 240 + 215 + 206 + 211 + 210 + 193 +250 + 225 + 202}{10}}[/tex]

[tex]\mathbf{\bar x = \frac{2177}{10}}[/tex]

[tex]\mathbf{\bar x = 217.7}[/tex]

Calculate the standard deviation

[tex]\mathbf{\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]

[tex]\mathbf{\sigma = \sqrt{\frac{(225 -217.7)^2+ (240 -217.7)^2+..........+ (202 -217.7)^2}{10-1}}}[/tex]

[tex]\mathbf{\sigma = \sqrt{\frac{2752.1}{9}}}[/tex]

[tex]\mathbf{\sigma = 17.49}[/tex]

Calculate the standard error

[tex]\mathbf{SE = \frac{\sigma}{\sqrt n}}[/tex]

[tex]\mathbf{SE = \frac{17.49}{\sqrt {10}}}[/tex]

[tex]\mathbf{SE = 5.53}[/tex]

At 95%, df = 9. the t-value is:

[tex]\mathbf{t= 2.262}[/tex]

So, the confidence interval is:

[tex]\mathbf{CI = \bar x \pm t \times SE}[/tex]

So, we have:

[tex]\mathbf{CI = 217.7 \pm 2.262 \times 5.53}[/tex]

Split

[tex]\mathbf{CI = (217.7 - 2.262 \times 5.53, 217.7+ 2.262 \times 5.53)}[/tex]

[tex]\mathbf{CI = (205,19, 230.20)}[/tex]

Hence, the 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]

Read more about confidence intervals at:

https://brainly.com/question/2396419

Step-by-step explanation:

2x + 9 = 35

→ 2x = 35 - 9 = 26

→ x = 26/2 = 13

→ x = 13

therefore, option A is correct

4 + | 7 - m | = 5

→ | -m + 7 | = 5 - 4

→ - m + 7 = 1 ( however or (only) m < 7 )

→ ( -m + 7 ) ( however or only m ≥ 7 )

→ m = 6 and m = 8

therefore, Option B is correct.

3t + 3/5 = 6

→ 3t + 3 = 6 × 5 = 30

→ 3t = 30 - 3 = 27

→ t = 27/3 = 9

→ t = 9

6(d + 1) - 2d = 54

→ 6d + 6 - 2d = 54

→ 4d + 6 = 54

→ 4d = 54 - 6 = 48

→ d = 48/4 = 12

→ d = 12

-110 = 13 + 3(4h - 6)

→ -110 = 13 + 12h - 18

→ -12h = 13 - 18 + 110

→ -12h = 105

→ h = 105/12

→ h = 8.75

hope this answer helps you dear!..

Answer:

The blur of the photo I do not understand sorry

Step-by-step explanation:

ty for the points

Answer:

The car has traveled 405 miles if it has 2.5 gallons of gas left in the tank.

Step-by-step explanation:

16 - 2.5 = 13.5  ( The amount of gas the car has already used )

30 * 13.5 = 405  ( How far the car traveled with 13.5 gallons of gas )

Hope this helps!

Answer:

its 40

Step-by-step explanation:

180-100=80

80/2= 40

Answer:

25 percent the answer is 25 percent I'm pretty sure. cause it's just 112.5/450

3.2128 is a rational number because you can not make it into a fraction/ratio

Answer: Yes

Step-by-step explanation:

2:3 is the same as (2/3) and 4:6 is the same as (4/6). (4/6) can be reduced by dividing both sides by 1/22: (4/6)*(1/2)/(1/2) = 2/3, They are the same.

Answer:

25%

Step-by-step explanation:

(original value - new value / original value) x 100

So

4 - 3 = 1

1/4 = 0.25

0.25 x 100 = 25

So there was a 25% decrease in the number of apples bought.

Hope it helps :)

Answer:

42 miles

Step-by-step explanation:

180/3=6 6x7=42

Answer:

420 miles in 7 hours

Step-by-step explanation:

You divide 180 by 3 to get how much the van is traveling per hour. When you get the answer 60 multiply it by 7 then you have 420 miles in 7 hours.

Answer:

148 cm2

Step-by-step explanation:

5 * 4 * 2 = 40

6 * 5 * 2 = 60

6 * 4 * 2 = 48

40 + 60 + 48 = 148

Answer:

Step-by-step explanation:

T.S.A (TOTAL SURFACE AREA) OF CUBOID :

→ 2(lb + bh + lh)

( l = length, b = breadth , h = height )

→ Given :

• Length (l) = 6cm

• Breadth (b) or width = 4cm

• Height (h) = 5cm

Total Surface area of cuboid :

• 2( 6×4+ 4×5+ 5×6) cm²

• 2 ( 24 + 20 + 30 ) cm²

• 2 ( 74 ) cm²

• 148 cm²

Answer:

[tex]y=\frac{3}{8}x-\frac{17}{8}[/tex]

Step-by-step explanation:

The slope: m= 3/8

hope this helps.

Answer:

82.96 people/km^2

Step-by-step explanation:

people / square km

3.70 x 10^9        

----------------- =    

4.46 x 10^7      

3.70 x 10^2

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

 4.46

0.8295... x 100 = 82.959641 or rounded 82.96

Answer:

Step-by-step explanation:

sum of angles of a triangle=180°

9x-2+3x-19+3x+6=180

15x-15=180

15x=180+15=195

x=195/15=13

m∠G=9x-2=9×13-2=117-2=115°

Answer:

it would be 15 or 14 that only came up when I did it

Step-by-step explanation:

Answer:

30* or A

Step-by-step explanation:

If the triangles are congruent, corresponding angles and sides are equal.

So angle c is 60* because it is opposite of side x.

angle b is 180-90-60 because all angles add up to 180 in a triangle.