F(x)=6x+2
g(x)=2x+4/5

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:

I think that the answer is 50

Answer: 5/8 of a teaspoon of salt

Step-by-step explanation:

half of 1 is 1/2 or 4/8

half of 1/4 is 1/8

4/8 + 1/8 = 5/8

Answer:

Step-by-step explanation:

Well, in order to find the unit rate we simply do the following steps:

4,581 ÷ 9 = 509

So to answer the question, each week Robin earns $509.

Hope this helps! : )

Answer:

they earn 509 a week

Step-by-step explanation:4581 divided by 9

Answer:

Step-by-step explanation:

Number of students = 120

Number of those prefer hamburgers:

Number of hamburgers ordered:

Step-by-step explanation:

[tex]\boxed{\begin{array}{c|c|c} \boxed{\bf hamburgers } & \boxed{\bf hot \ dogs } &\boxed{\bf Students } \\ 65\%& (100-65)=35\% & 120 p \\ \end {array }}[/tex]

Each person is given 2 burgers or 2 hot dogs

Then :

120*2*0,65=156  hamburgers

Step-by-step explanation:

20-17+3=6

18+1-5=14

7-8+6=5

20-18+7=9

17+1-8=10

3-5+6=4

Answer:

24

Step-by-step explanation:

all 3 corners of any triangle adds to 180

the big triangle gives you 94 and 41 which equals 135. even though there's a line cutting off the last corner it still counts towards the 180 of the big triangle

180 - 135 = 45

now you know 2 corners of the smaller triangle

111+45 = 156

156+x= 180

x= 24

Answer:

Answer:(h) =***************************

(l)=***************

HOPE IT HELPS YOU

CAN YOU BRAINLEST ME

Jake's guesses are illustrations of probabilities.

The probability that Jake's guesses are correct is 1/720

The sample size is:

[tex]\mathbf{n = 10}[/tex] --- 10 different numbers

The probability that Jake's guesses are correct is as follows:

So, the required probability is:

[tex]\mathbf{Pr = \frac{1}{10} \times \frac 19 \times \frac 18}[/tex]

[tex]\mathbf{Pr = \frac{1}{720} }[/tex]

Hence, the probability that Jake's guesses are correct is 1/720

Read more about probabilities at:

https://brainly.com/question/11234923

Answer:

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

to find slope

m=(vertical distance)/(horizontal distance)

m=8/24

m=1/3

Answer:

Mya is 12

Step-by-step explanation:

EEstaban is 11 years older so Estaban was 22 and Mya was 11

so now Maya is 12

Hope this helps! :)

Answer: 12 years old

Step-by-step explanation:

Let x be Esteban's age, and let y be Mya's age.

x = y + 11

x-1 = 2(y-1)

Substitute

y + 11 - 1 = 2 (y - 1)

Solve

y + 10 = 2y - 2

12 = y

Hope it helps :)

Answer:

845

Step-by-step explanation:

I think that's what it's asking??

Answer:

845

Step-by-step explanation:

We are looking for a new number which is 120 less than 965.

We will get the new number by subtracting 120 from 965.

We write it down as:

965-120=845

And finally the solution for: What number is 120 less than 965?

is 845

Have a good day :)

Please check this out #TeamSeas

Answer:

5x−13=4x−14

Subtract 4x from both sides.

5x−13−4x=4x−14−4x

x−13=−14

Add 13 to both sides.

x−13+13=−14+13

x=−1

Answer:

x=1

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

115.6/340 = 0.34 x 100 = 34 percent

13. M=4/3

14. m=-6

Step-by-step explanation:

Step-by-step explanation:

The positive factors of -3 are 3 and 1

There is also -3 and -1

Answer:

Step-by-step explanation:

si...  yono  em usho de cmopu preo sloo estoy usand una jjssjsjsj jsjsj  c

Answer:

your answer is 38 with a remainder of 1

Step-by-step explanation:

Nominator

191

Denominator

5

38.2= 38 Remainder 1

The result of 191/5 is a terminating decimal with 1 digit to the right of the decimal point.

191 divided by 5 in decimal = 38.2

191 divided by 5 in fraction = 191/5

191 divided by 5 in percentage = 3820%

On dividing 191 by 5, the remainder is 1.

The divisor is the integer that divides a given number. The resultant number is sometimes referred to as the quotient. The residual is the number that the divisor leaves after partially dividing the original integer.

Dividend = Divisor x Quotient + Remainder

On dividing 191 by 5

Step 1: Divide 191 into 5 parts: 191/5 = 38(integer part only)

Step 2: Divide the quotient you just calculated by the divisor (5).

38 × 5 = 190

Step 3: Subtract the result from the initial dividend from step 2 (191) (191):

191 - 190 = 1

Step 4: The remainder is the outcome of step 3:

1 is the result of dividing 191 by 5.

Therefore, the remainder after dividing 191 by 5 is 1.

Learn more about the mathematical operation, here:

https://brainly.com/question/29635854

#SPJ6

Answer:

y = 2x+1

Step-by-step explanation:

Given, the slope of a line is 2 and y-intercept is 5.

Here, m=2 and c=1.

The equation of the line in slope-intercept form is given by

              y=mx+c

∴             y=2x+1 is a required equation.

Not sure if it correct or not.

Answer:

hiiii how r u

Step-by-step explanation:

brainiest pleasee

Answer:

x= -19/8

Step-by-step explanation:

Answer:

59049

Step-by-step explanation:

nine times negative 3 8 times

Answer:

a₉ = 59049

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 9 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-27}{9}[/tex] = - 3 , then

a₉ = 9 × [tex](-3)^{8}[/tex] = 9 × 6561 = 59049

Answer:

b

Step-by-step explanation:

Since it intercepts y at 4, and x at 2, we use y=ax+b and rearrange to get the equation from y=2x+4 to 2x-y=-4

Answer:

b) 2x - y = -4

Step-by-step explanation:

The y-intercept is the y-coordinate of the point (0, b) where the graph crosses the y-axis. It is also the value of y when x = 0.

The crosses the y-axis at point (0, 4). Therefore, the y-intercept, b = 4.

Next, we need to determine which of the given options matches the graph.  It helps to transform each of them into their slope-intercept form, y = mx +b:

2x - 2x + y = - 2x + 4

y = -2x + 4  (This is not the correct answer because the slope, m = -2. The given graph has a positive slope).

2x - 2x - y = - 2x - 4

-y = -2x - 4

Divide both sides by -1:

[tex]\frac{-y}{-1} = \frac{-2x - 4}{-1}[/tex]

y = 2x + 4 This is the correct answer because it matches the y-intercept (0, 4), and has a positive slope of 2.

We could easily disregard the last two options because both of their y-intercept is 0.

Therefore, the correct answer is Option b) 2x - y = - 4

Answer:

120?

Step-by-step explanation:

Might be incorrect. -_-

Answer: question 1, all you had to do was divide the shpaes up by simply finding the missing numbers and separating the two shapes.

The rectangle has a area of  96

The square has a area of 16.                 if we add this up we get a area of 112

so the area is 112cm^2

Happy To Help :)

Question 2.  8 x 2 is 16

2 x 10 is 20..      add that up we get 36m

Answer: 79798

Step-by-step explanation:

139101 - 59303

= 79798

please give me a brainliest answer

Answer:

79798

Step-by-step explanation:

  69632

+ 69469

=  139101

-   59303

=  79798

Hope this helps :)

Answer:

527 is your answer

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

n=1/24

Step-by-step explanation:

8/n=1/3

n=1/3÷8

=1/3×1/8

=1/24