Please answer circle theorem question.
Many thx.

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:

x=9,-7

Step-by-step explanation:

(x+3)(x-5)=48

x^2-2x-15-48=0

x^2-2x-63=0

(x-9)(x+7)=0

x=9,-7

dont use the negative number becuase it would not make sense in this scenario

width = 12

length=4

Answer:b

Step-by-step explanation:

Answer:

$11.55

Step-by-step explanation:

If we convert the percentage to 1.05 and multiply it by 11, it's 11.55.

Answer:

B

D

C

Glad I coild help you out.

Answer:

B,C and D

Step-by-step explanation:

They all expand back to 16x + 20.

The inequality [tex]2x + y >4[/tex] has a slope of -2, and the y-intercept of 4

The inequality is represented as:

[tex]2x + y >4[/tex]

Subtract 2x from both sides

[tex]y >4 - 2x[/tex]

Rewrite the inequality as:

[tex]y >- 2x+4[/tex]

The linear inequality is represented as:

[tex]y >mx+c[/tex]

Where:

So, by comparison:

[tex]m = -2[/tex]

[tex]c = 4[/tex]

This means that the inequality [tex]2x + y >4[/tex] has a slope of -2, and the y-intercept of 4

See attachment for the graph of the inequality

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Answer:

B and E

Step-by-step explanation:

I think the choice is wrong. choice B maybe 15a+20b...

5(3a+4b) = 15a+20b (B)

(E) : 10a + 5a + 15b + 5b = 15a+20b

fighting! ✌✌

Answer:

e. 5(3a+4b) = 15a+ 20b = 10a+5a+15b+5b

Answer:

HOPE THIS HELPS

Step-by-step explanation:

[tex]x^{2}[/tex]-14x-32 =(X+2)(X-16)

A=1

B=2

C=1

D=-16

Answer:

See below

Step-by-step explanation:

The population is all American households

The sample is 2,541 of those American households

Answer:

0.1 percent

Step-by-step explanation:

26 green apples

if you do 0.4 * 65 you get 26 which is 40% of 65

hope this helps!

Answer:

V= (2/3) π r³

hope this helps :>

Answer:

3:15 pm

Step-by-step explanation:

You can imagine that they go in a circle (we can do whatever we want in theoretical math and physics). By doing so we know we can obtain a cosinusoidal wave by projecting the motion on a plane. Each one of the buses has a period (minimum time after what they're in the same point again). For the first one it's 15 minutes, for the second one it's 20 minutes. We have to take the least common multiple of the periods, that is 75 minutes. So They'll meet every 75 minutes. Add 75 minutes (1h and 15 minutes) to 2pm and there you go.

the only one i could figure out was that q= 24 and i think r=48

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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Answer:

Step-by-step explanation:

Binomial Probability

P(x) =  n!/(n-x)!x! * p^x q^(n-x)

P(x) = probability there will be x required outcomes (here x is 3)

n = number of trials (here it is 10)

p = probability of 1 required outcome (getting a 4) on a single roll ( = 1/6).

q = probability of required outcome not occurring on a single roll.

p = 1/6

q = 1 -1/6 = 5/6

n = 10

x = 3

So the required probability

= 10!/ 7!3! (1/6)^3 (5/6)^7

= 0.155.

Answer:

what are you asking?

Step-by-step explanation:

[tex]x + y = 7~~~.....(i)\\\\xy=-30~~~~......(ii)\\\\\\\text{From (ii):}\\\\y= -\dfrac{30}x~~~~....(iii)\\\\\\\text{Substitute equation (iii) in equation (i):}\\\\\\x- \dfrac{30}x = 7\\\\\implies x^2 -30 = 7x\\\\\implies x^2 -7x -30 =0\\\\\implies x^2 -10x +3x -30 =0\\\\\implies x(x-10) +3(x-10) =0\\\\\implies (x+3)(x-10)=0\\\\\implies x = -3 ~~\text{or}~~ x=10\\\\\text{Substitute x = 10 in equation (iii):}\\\\\\y= -\dfrac{30}{10} =-3\\\\[/tex]

[tex]\text{Substitute x = -3 in equation (iii):}\\\\y = \dfrac{-30}{-3} =10\\\\\\\text{So, (x,y) =(10,-3) and (x,y)=(-3,10)}\\\\\\\text{Hence, the two numbers are}~ 10~ \text{and}~ -3.[/tex]

Answer:

Answer in the image

Step-by-step explanation:

Answer:

y=4/3x

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-0)/(3-0)

m=4/3

y-y1=m(x-x1)

y-0=4/3(x-0)

y=4/3(x)

y=4/3x

Answer:

$6.70

Step-by-step explanation:

Adrian purchases a book for 4.86 and a poster for 3.44

The total amount he owes would be 4.86 + 3.44 = $8.30

If she gives the cashier 15 dollars she should receive 15 - 8.30 = $6.70 back.

Answer:

D

Step-by-step explanation:

Same X, but different Y value, it is five apart in D

Answer:

0.321233-cups, 0.321233-tablespoon, 0.321233-teaspoon

Step-by-step explanation:

the next 2 questions I can't convert because I don't have grams

Answer:

76ml= 0.321233 cups

76ml = 5.13973 tablespoons

76ml = 15.4192 teaspoons

38g = 0.139 cups

38g = 2.224 tablespoons

38g = 6.672 teaspoons

78g = 0.349 cups

78g = 5.584 tablespoons

78g = 16.752 teaspoons

Step-by-step explanation:

I think thats right

Answer: The first option.

Explanation: 376/93 = 4 4/94, while 376/93.01 = 4.04257606709....., which is less than 4 4/94, therefore the first option has the greatest quotient.

Answer:

|x-480|<=40

Step-by-step explanation:

The absolute distance on the number-line from x to 480 has to be 40.

|x-val| <= error-margin

|x-480| <= 40

-7/40

/////

I honestly didn't know how to do this one. But thats the correct answer.

The solution of the mathematical expressions will be 0.175.

What is Number system?

A system of writing to express the number is called number system.

Given that;

The mathematical expressions are,

⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

Now,

Solve the mathematical expression as;

⇒  [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

Using the BODMAS rule to solve the expressions as;

⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

⇒ [ 2 - | - 1/4 + 6/5 | ÷ -6

⇒ [ 2 - 19/20 ] ÷ -6

⇒  [ 21/20] ÷ -6

⇒ 21/20 x 1/-6

⇒ - 7 / 40

Therefore,

The solution of the mathematical expressions will be 0.175.

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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:

x = 29

Step-by-step explanation:

(x + 3) + (x - 1) + (x + 1) = 90

3x + 3 = 90

3x = 87

x = 29

Answer:

x = 29

Step-by-step explanation:

(x+3)+(x-1)+(x+1) = 90

90 = 3x +3

3x = 87

x = 29

Answer:

1) The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.

2) The 6 in 54.162 has a smaller value than the 6 in 5,416.2.

Step-by-step explanation:

1) 0.06 times 100 equals 6

2) 0.06 < 6