ANYBODY WHO ANSWERS THIS QUESTION CORRECTLY WILL GET 40 POINTS. THE ONES IN GREY ARE THE ANSWER OPTIONS.

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 10mm, midway 80mm.

So, the vertex is:

[tex]\mathbf{(h,k) = (40,10)}[/tex]

The equation of a parabola is:

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

So, we have:

[tex]\mathbf{0 = a(0 - 40)^2 + 10}[/tex]

Subtract 10 from both sides

[tex]\mathbf{a(0 - 40)^2 =- 10}[/tex]

[tex]\mathbf{1600a =- 10}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{160}}[/tex]

Substitute [tex]\mathbf{a =- \frac{1}{160}}[/tex] and [tex]\mathbf{(h,k) = (40,10)}[/tex] in [tex]\mathbf{(h,k) = (40,10)}[/tex]

[tex]\mathbf{y = -\frac{1}{160}(x - 40) + 10}[/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 -1/160}}[/tex]

[tex]\mathbf{p = -\frac{160}{4}}[/tex]

[tex]\mathbf{p = -40}[/tex]

So, we have:

[tex]\mathbf{Focus = (40,10-40)}[/tex]

[tex]\mathbf{Focus = (40,-30)}[/tex]

The axis of symmetry is:

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

So, we have:

[tex]\mathbf{x = 40}[/tex]

The directrix is:

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

[tex]\mathbf{y = 10 + 40}[/tex]

[tex]\mathbf{y = 50}[/tex]

Read more about parabolas at:

https://brainly.com/question/25237745

Answer:

here's your answer

hope it helps

(look at attachment)

Answer:

97

Step-by-step explanation:

[tex] {4}^{2} + 3(37 - (2 \times 5)) \\ {4}^{2} + 3(37 - 10) \\ {4}^{2} + 3(27) \\ {4}^{2} + 81 \\ 16 + 81 \\ 97[/tex]

Hope this helps! Brainliest would be really appreciated!

Answer:

that's what can I give

Step-by-step explanation:

hope it helps

Answer:(0,4)

Step-by-step explanation:

Answer:

1. 10

2. 4, and the bottom row is 21

3. divide the bottom by 4. you get 8

4. top row is 15 and bottom row is missing 6

Answer:

Step-by-step explanation:

The slope is - 2/3 and the point on the line is (-3, -1).

Find the y-intercept:

The line is:

Correct choice is D

Equation in point slope form

Option D

Answer:

1. 2.6

2. 29.1

3. 2490

4 3.4

Step-by-step explanation:

Answer:

to find the scale factor for a dilation, we would find the center point of dilation and measure the distance from this center point to a point on the shape from before (preimage) and also the distance from the center point to a point on the shape.

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Explanation:

The best case scenario is that you get 3 of the same color in a row on the first three attempts. The lower bound is 3.

However, we have to consider the worst case scenario when we want to guarantee something like this, without looking at the candies we selected.

Consider the case of something like this sequence:

As you can see above, I've listed the colors in the order presented by your teacher. I pick one candy at a time. Once I reach yellow, I restart the cycle. In slots 1, 7 and 13, we have a black candy selected. This example shows that we must make 13 selections to guarantee that we get at least 3 candies of the same color (that color being black). The order of the candies selected doesn't matter. We could easily use any other color except yellow to do this example. The black candy just happened to be the first listed, so I went with that.

Note how we have 6 unique colors in the set {black, white, green, red, blue, yellow}. If we pick 2 candies of each color, then we've selected 6*2 = 12 candies so far. That 13th candy (some color other than yellow) is guaranteed to be a color we already selected; therefore, we'll be guaranteed to have 3 of the same color. We won't know what color it is but we will know we have a match like this.

For more information, check out the Pigeonhole Principle.

Answer:

Step-by-step explanation:

For obects already in motion, the distance travelled, s, is:

s = vi*t + (1/2)at^2

where vi is the initial velocity, a is the acceleration, and t is the time in seconds.

We want the time, t, to reach 1000 meters.

1000 m = (3 m/s)*t + (1/2)*(0.1m/s^2)*(t^2)

(1/2)*(0.1m/s^2)*(t^2) = 0.05t^2

0.05t^2 + 3t -1000 = 0

Solve quadratic equation:

t = 114.6 seconds

Answer:

4/3

Step-by-step explanation:

Answer:

The answer is 4/3.

Answer:

1. 4a+5b

2. 6p+4r

3.  -20y-3x

Answer:

1.   4a + 5b;   2.  6p + 4r;    3.  -22y - 3x

Step-by-step explanation:

1. (4a + 5b) + (2a - 6b) - 2(a - 3b)

  (4a + 5b) + (2a - 6b)  + (- 2a + 6b)         Distributive

 (4a + 2a -2a) + (5b - 6b + 6b)                 Combine like terms

  4a + 5b

 2.  2(5p - q + 2r) - (p + 4q + 3r) - 3(p -2q - r)  

       10p - 2q + 4r - p - 4q - 3r - 3p + 6q + 3r

       (10p - p -3p) + (-2q - 4q + 6q ) + ( 4r - 3r + 3r)

         6p + 0 + 4r

          6p + 4r

3.    - (9y + x) + 2(x - 6y) - (4x + y)

         -9y - x  + 2x - 12y - 4x - y

        (-9y -12y -y) + (-x + 2x - 4x)

           -22y - 3x

El área del paralelogramo con base de 13 centímetros y altura de 8 centímetros es 104 centímetros cuadrados.

El área del paralelogramo, en centímetros cuadrados, es igual al producto de su base por su altura, ambos en centímetros. En consecuencia, el área de la figura geométrica es la siguiente:

[tex]A = (13\,cm)\cdot (8\,cm)[/tex]

[tex]A = 104\,cm^{2}[/tex]

El área del paralelogramo con base de 13 centímetros y altura de 8 centímetros es 104 centímetros cuadrados.

Invitamos cordialmente a ver esta pregunta sobre paralelogramos: https://brainly.com/question/17205536

Answer:

ik this

Step-by-step explanation:

i believe its 180

Answer: B) 115

Step-by-step explanation: i hop this help if not sorry :(

Answer:

1. The area is 72 ft².

2. No, one can of paint will not be enough.

3. The width of his property is 90 ft.

4. The width of the park is 19 miles.

5. The length of a side is 7.

Step-by-step explanation:

We will use the formula Area = length x width to answer the questions.

1. 9 x 8 = 72

2. 48 x 9 = 432, 432 > 400

3. 43560/484 = 90

4. 323/17 = 19

5. √49 = 7

Hope this helps!

Answer:

1. The area is 72 ft².

2. No, one can of paint will not be enough.

3. The width of his property is 90 ft.

4. The width of the park is 19 miles.

5. The length of a side is 7.

Step-by-step explanation:

I hope you find this useful, Mark as Brainliest please, it's very much appreciated.

Explanation:

In one minute, Diego can type 35 words;140÷4

At this rate, it will take him 11 minutes to type 385 words;385÷35

Therefore, he can type 525 words in 15 minutes; 35×15

Answer:

Hope this helps.

Step-by-step explanation:

1. 385 x 4 = 1540/140

    =11

2. 15/4 = 3.74 x 140

    =525

Answer:

1.She has 115 dimes because 0.10*115=11.5 0.25*4=1.00 11.5+1.00=12.5

2.She has 100 dimes because 0.10*100=10.00 and 0.25*10= 2.5 10+2.5=12.5

3.I think they don’t function because quarters are worth more than a dime.

4.he has 40 quarters because 0.25*40=10.00 0.10*25=2.5 10.00+2.5=12.5.

5.She has 38quarters because 0.25*38=9.5 0.10*30=3 9.5+3=12.5

6.Yes they can function because q=dx-12.5

The Questions:

Question 1 - 1 pts

If Jada has 4 quarters, how many dimes does she have?

Question 2 - 1 pts

If Jada has 10 quarters, how many dimes does she have?

Question 3 - 1 pts

Is the number of dimes a function of the number of quarters? If yes, write a rule (that starts with d =...) that you can use to determine the output, d, from a given input, q. If no, explain why not.

Question 4 - 1 pts

If Jada has 25 dimes, how many quarters does she have?

Question 5 - 1 pts

If Jada has 30 dimes, how many quarters does she have?

Question 6 - 1 pts

Is the number of quarters a function of the number of dimes? If yes, write a rule (that starts with q =...) that you can use to determine the output, q, from a given input, d. If no, explain why not.

Answer:

x=3.3333333333333333333333333333333

Answer:

If the REGULAR price of the t-shirt is $18, the SALE price with a 20% discount is $14.40. Hope this helps!

Step-by-step explanation:

Answer:

1.  y > -3/5 and y < 7/5        Direction to  graph 1 below.

2. r > 1 and r < 13/3              Direction to  graph 2 below

Step-by-step explanation:

|5y - 2| + 5 > 0

Case 1    Positive ||                                 Case 2  Negative ||

5y - 2 + 5 > 0                                       -(5y - 2) + 5 > 0

5y +3 > 0                                             -5y + 2 +5 > 0

5y > -3                                                  -5y + 7 > 0

y .> -3/5                                               -5y > -7

                                                             -y > -7/5

                                                             y < 7/5   y value negative, change sign

The graph 1: open circle at -3/5;  close circle at 7/5; shade between these two numbers.  

2.    |8-3r|< 5

       Case I                                           Case II

8 - 3r < 5                                                   -(8-3r) < 5

-3r < 5 - 8                                                   -8 + 3r < 5

-3r < -3                                                         3r < 5 + 8  

-r < -3/3                                                        3r <  13

r >1       r is negative, change                        r < 13/3

            the direction of the sign

Graph 2: Open circle at 1; open circle at 13/3;  shade between the two numbers.                    

Answer:

1/3 chance

Step-by-step explanation:

hoped this helped you!

Answer:

maybe 34 ? or 180-34 =146

Step-by-step explanation:

Answer:

x=34

Step-by-step explanation:

The two angles are congruent so x would be the same.

Jesus Loves You!

Answer:

B

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] + 4 = 1 ( subtract 4 from both sides )

[tex]\frac{x}{5}[/tex] = - 3 ( multiply both sides by 5 to clear the fraction )

x = 5 × - 3 = - 15 → B

Answer:

10

Step-by-step explanation:

1. Any number has a denominator of 1 so you have 6/1 and 8/2.

2. To add you need to make the denominators the same so multiply the 2 to the numerator and denominator of 6/1 which makes 12/2.

3. 12/2+8/2 is 20/2.

4. Simplify 20/2 by dividing the top and bottom by 2 to get 10/1.

Answer: 10

Answer:

b(x)=2x+4

Factor out 2.

2(x+2)

EVALUATE

2(x+2)

Step-by-step explanation:

Answer:

1.3

2.6

3.24

Step-by-step explanation:

Hope it helps

Answer:

1: First, keep the first number (known as the minuend) 2 .Second, change the operation from subtraction to addition

2. Third, get the opposite sign of the second number (known as the subtrahend)

4: finally, proceed with the regular addition of integers

Step-by-step explanation:

Example: 1: (6-(-4)

6+4=10

(10)

2: (-1-(-9)

-1+9=8

(8)