how do i solve this

An equation that models the path of Johnny’s ball is [tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]

The maximum height is given as:

[tex]h_{max}= 10ft[/tex]

And the time spent is:

[tex]t = 3s[/tex]

So, the vertex of the ball would be:

[tex]Vertex = (t/2,h_{max})[/tex]

This gives

[tex]Vertex = (3/2,10)[/tex]

[tex]Vertex = (1.5,10)[/tex]

Rewrite properly as:

[tex](h,k) = (1.5,10)[/tex]

The ball is on the floor after 3 seconds.

So, another point on the graph is:

[tex](x,y) = (3,0)[/tex]

A quadratic equation is represented as:

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

Substitute [tex](x,y) = (3,0)[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]

[tex]0=a(3 - 1.5)^2 + 10[/tex]

[tex]0=a(1.5)^2 + 10[/tex]

Evaluate the exponent

[tex]0=2.25a + 10[/tex]

Subtract 10 from both sides

[tex]2.25a =- 10[/tex]

Divide both sides by 2.25

[tex]a = -\frac{10}{2.25}[/tex]

Multiply by 4/4

[tex]a = -\frac{40}{9}[/tex]

Substitute [tex]a = -\frac{40}{9}[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]

[tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]

See attachment for the graph that models the path

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Answer:

  a) 47.7%

  b) 87.2%

Step-by-step explanation:

Find the ratio of interest, and convert it to a percentage.

  (messy right-handed writers)/(right-handed writers)

  = 31/65 = 31/65 × 100% ≈ 47.7%

__

  (neat right-handed writers)/(neat writers)

  = 34/39 = 34/39 × 100% ≈ 87.2%

[tex]\sqrt{x^2 -\dfrac nm} = \dfrac{a^2}b\\\\\implies x^2 - \dfrac nm = \dfrac{a^4}{b^2}\\\\\implies x^2 = \dfrac{a^4}{b^2} + \dfrac nm}\\\\\implies x = \pm \sqrt{ \dfrac{a^4}{b^2} + \dfrac nm}}[/tex]

Answer:

2nd option

Step-by-step explanation:

Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

g(x) = f(x + 4)

Is the graph of f(x) shifted 4 units to the left

Answer:

75 seconds

Step-by-step explanation:

The graph intersects the x axis at 75 seconds.  That means y = 0, and y is the amount remaining (in ml).

After 75 seconds the amount of slushy left in the cup becomes zero the answer is 75 seconds.

A line graph is a type of graph where the data points are connected by segments of straight lines.

We have a line graph shown in the picture.

Sean is drinking a slushy as fast as he can. The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed.

As we can see the amount of slushy left in the cup is decreasing as the time increases.

At time = 75 seconds

The amount of slushy left in the cup = 0

Thus, after 75 seconds the amount of slushy left in the cup becomes zero the answer is 75 seconds.

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Answer:

The answer is t^-1 (r)=120r/120-r

i hope this is right sry if im wrong have a good day :)

The inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .

Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω).

According to the question

Janine is building a circuit that contains two lightbulbs in parallel.

One of the lightbulbs has a resistance of 120 ohms.

R = 120ohms

r = resistance of the second lightbulb

t = total resistance in the circuit  

[tex]t = \frac{120r}{r+120}[/tex]

Now,

The inverse of Janine's equation in which we will make r independent

[tex]t = \frac{120r}{r+120}[/tex]

[tex]t(r+120) = 120r[/tex]

[tex]tr + 120t = 120r[/tex]

[tex]120t = 120r - tr[/tex]

[tex]120t = r(120-t)[/tex]

[tex]r = \frac{120t}{120-t}[/tex]

Hence, the inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .

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The number of kilometers she will have left to run to finish the race is 0.9 km.

Given the following data:

To determine the number of kilometers she will have left to run to finish the race:

First of all, we would calculate the distance she has covered by using this formula;

[tex]Distance = speed \times time\\\\Distance = 8\frac{2}{5} \times 1.5\\\\Distance = \frac{42}{5} \times \frac{3}{2} \\\\Distance = \frac{63}{5}[/tex]

Distance = 12.6 meters.

For the distance left:

[tex]Distance\;left = Total\;distance - Distance\;covered\\\\Distance\;left =13.5 -12.6[/tex]

Distance left = 0.9 km.

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[tex]\mathfrak{7x(-4)} [/tex]

[tex]\mathfrak{=7x*-4} [/tex]

[tex]\boxed{\mathfrak{=-28x}} [/tex]

[tex]\mathbb{MIREU} [/tex]

A) -3

B) 5

C) -2

D)-6

i have to write 20 characters so sisiasskklsa

Answer:

a) -3

b)5

c)-2

d)-6

Step-by-step explanation:

4 - 7 =-3

4 is positive and 7 is negative

a positive minus a negative is equal to a negative

3 is negative and 8 is positive, but 8 is bigger than 3, so take the sign of the bigger number which is 8.

c) is the same as question b

same signs rule

a negative + a negative is = to negative

positive and a positive is = to a positive

a negative +/_ a positive = a negative

Answer:

GCF 4, LCM 80

Step-by-step explanation:

Since both 16 and 20 have two 2s as factor, their greatest common factor is 4.

The LCM is found by multiplying all of the remaining factors by the LCM:

16 still has (2 x 2), 20 still has (5), times the GCF (4)  so 2 x 2 x 5 x 4 = 80.

Answer:

  432 characters

Step-by-step explanation:

There are 36 inches in a yard, so there will be 36 times 12 characters:

  (36 in/yd)(12 char/in) = 432 char/yd

432 characters can be expected per yard of text.

The product of given binomial and trinomial is given by below polynomial:

[tex]x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4[/tex]

The expression formed by the sum of sub expressions which are product of constant integers with variables raised to some exponent is called polynomial.

Their product is given by:

[tex](x^3 + 3x^2 - x + 2) \times (x^2 + 6x -2)\\= x^5 + 6x^4 - 2x^3 + 3x^4 + 18x^3 - 6x^2 -x^3 -6x^2 + 2x +2x^2 + 12x - 4\\= x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4[/tex]

Thus the product of given binomial and trinomial is given by below polynomial:

[tex]x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4[/tex]

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Answer:

11 weeks

Step-by-step explanation:

If we multiply 50 by 11 we get 550 with a remainder of 100, if we're to take out another 50 for another week we would have 50 dollars remanding but the question says that we need to have at least 75 remaining so this will not be possible. Therefor 11 weeks is our answer.

I hope this helps have a great day :)

Step-by-step explanation:

the slower plane travels x km in 3 hours.

the faster plane travels x + 3×68 = x + 204 km in 3 hours.

x + x + 204 = 5052 km

2x = 4848 km

x = 2424 km (in 3 hours).

so, the slower plane's speed is 808 km/h.

the faster plane's speed is 808 + 68 = 876 km/h.

Answer:

1/8 + 1/4 = 3/8

Step-by-step explanation:

Answer:

The weight of permit fish 140 pounds

The weight of Tarpon fish 14 pounds

Step-by-step explanation:

Let the weight of Tarpon fish ve 'x' Then by question weight of permit fish be '10x'

Now by question

x+10x=154 pounds

or,11x=154 pound

or,x=154pound/11

Therefore, x = 14 pounds

Again by question weight of permit fish

for 10x

by substituting value of x we have,

=10×14 pounds

=140 pounds

Answer:

16, and 16.3

Step-by-step explanation:

Answer:

1. 16     2.16.3

Step-by-step explanation:

2.16.281 is 16.28 which is near 16.3 so you round. Also anything above 5 you round and anything below 5 you round down.

Answer:

x=[tex]\frac{3c-q^2}{5p}[/tex]

Step-by-step explanation:

5px+q^2=3c

subtract q^2 from both sides

5px=(3c)-q^2

divide by 5p from both sides

x=[tex]\frac{3c-q^2}{5p}[/tex]

Using the permutation and the combination formula, we have that:

a) The first three finishers can be awarded medals in 504 ways.

b) They can be arranged in 252 ways.

c) In how many ways can 4 students form a team from a set of 8.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Permutation formula:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Item a:

Order is important, as the finishers are ranked, hence:

[tex]P_{(9,3)} = \frac{9!}{6!} = 504[/tex]

The first three finishers can be awarded medals in 504 ways.

Item b:

The order is not important, hence:

[tex]C_{10,5} = \frac{10!}{5!5!} = 252[/tex]

They can be arranged in 252 ways.

Item c:

Situation in which the order is not important, hence, for example, in how many ways can 4 students form a team from a set of 8.

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Answer:

Assuming the 2 in 3x2 is an exponent, then it is binomial.

Step-by-step explanation:

A binomial is an expression with two terms, in this case those two terms are 3x^2 and 5

Answer:

2.binomial

Step-by-step explanation:

3x2=1

5=2

so its a binomial

The quadratic equation is given by y = -2x² + 4x + 1

The standard form of a quadratic equation is given by:

y = ax² + bx + c

At point (1, 3):

3 = a(1)² + b(1) + c

a + b + c = 3      (1)

At point (2, 1):

1 = a(2)² + b(2) + c

4a + 2b + c = 1      (2)

At point (-2, -15):

-15 = a(-2)² + b(-2) + c

4a - 2b + c = -15      (3)

Solving equations 1, 2 and 3 simultaneously gives:

a = -2, b = 4, c = 1

The quadratic equation is given by y = -2x² + 4x + 1

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Answer:

IP information is attached to each packet, and this information helps routers to send packets to the right place. Every device or domain that connects to the Internet is assigned an IP address, and as packets are directed to the IP address attached to them, data arrives where it is needed.

Step-by-step explanation:

hope i helped!

Answer: I think it's 6

Step-by-step explanation:

The value of k to the nearest integer is 21

If the number of international tourist arrivals in Russia in 2012 was 13.5% greater than in 2011 will be expressed as:

k = 24.7 - (13% of 24.7)

k = 24.7 - (0.135 * 24.7)

k = 24.7 - 3.3345

k = 21.3655

Hence the value of k to the nearest integer is 21

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[tex]\text{Consider the slope - intercept form} ~y = mx +c,\\\\ \text{where m is the slope and and c is the y-intercept.}\\\\(a) \\\\y = -\dfrac 12 x +8 \\\\\text{This is in a form of y = mx +c, so}\\\\\text{Slope, m =}-\dfrac 12 ~ \text{and}~ \text{y - intercept , c =8}\\\\(b)\\\\y = 9x -2 \\\\\text{This is in a form of y = mx +c, so}\\\\\text{Slope, m =9}~ \text{and}~ \text{y - intercept ,}~ c =-2\\\\[/tex]

Answer:

4

Step-by-step explanation:

firstly you separate y

y=-x-1

which means that the slope is equal to -1

then you flip the slope so -1 over -1 which is equal 1

Answer:

Solved: w = 2  

Step-by-step explanation:

Combine like terms

5w+4w = 9w

Isolate or make w alone

9w= 18 so divide both sides by 9 to make w alone

9w ÷ 9 = w

18 ÷ 9 = 2

w = 2

Answer:

you just add 5w and 4w and taht is 9w

[tex]9x = 18 \\ w = 18 \div 9 \\ w = 2[/tex]

Given :-

To find :-

Solution :-

According to the Question ,

[tex]\dashrightarrow[/tex] Passing marks = 40% .

[tex]\dashrightarrow[/tex] Seema's marks = 130 .

Let us take the maximum marks be x . Then ,

[tex]\dashrightarrow[/tex] Passing marks = 130 + 2

[tex]\dashrightarrow[/tex] Passing marks = 132

And , by question ,

[tex]\dashrightarrow[/tex] 40x/100 = 132

[tex]\dashrightarrow[/tex] x = 132 * 100/40

[tex]\dashrightarrow[/tex] x = 330

Hence the maximum marks for the exam is 330.

Given :

So, Let us assume the maximum marks as x .

Also,

Passing marks = 132 [ ∵ Seema got 130 marks and she failed by 2 marks ]

According to the question :

[tex] \\ \tt : \implies\dfrac{40x}{100} = 132 \\ \\ \tt : \implies\dfrac{4 \cancel{0}x}{10 \cancel{0}} = 132 \\ \\ \: \: \: \tt \: : \implies 4x = 132 \times 10 \\ \\ \tt : \implies \: 4x = 1320 \\ \\ \tt : \implies \: x = \frac{1320}{4} \\ \\ \tt : \implies \: x = 330 \: \: \\ [/tex]

Hence, The total marks is 330 .