You want to decorate a party hall with a total of least 40 red and yellow baloons. You want a minimum of 25 yellow baloons. Write and graph

Answers

Answer 1

Answer: there is 75 balls and thats the answer

Answer 2

Answer: 40-25=15 red balloons.

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Jonas is jogging from the Park to the school. He has jogged 0.424 miles so far. He has 0.384 mile left to jog. How far is the park located away from the school?

Answers

Answer:the park is located 0.808 miles away from the school

Step-by-step explanation:

Jonas is jogging from the Park to the school. The total number of miles that Jonas has jogged so far is 0.424.

He has 0.384 mile left to jog. This means that the distance of the park from the school would be the sum of the distance that he has jogged so far and the distance that he has left to jog. It becomes

0.424 + 0.384 = 0.808 miles

The height y of a ball (in feet) is given by the function and x is the horizontal distance traveled by the ball.a)How high is the ball when it leaves the child’s hand?
"b) How high is the ball at its maximum heigh
c) Explain in words the method you used in part b.
d) What is the horizontal distance traveled by the ball when it hits the ground?
e) Explain in words what you did to find your answer for part d.

Answers

Given: The height y of a ball (in feet) is given by the function y=-1/12x^2+2x+4 and x is the horizontal distance traveled by the ball.

Part A: How high is the ball when it leaves the child's hand?

Right after the ball leaves the child's hand, it has travelled 0 feet horizontally. Horizontal distance is represented by x, so we could say that x = 0.
Plug in 0 for our equation and solve for y, the height.

$y=-(1)/(12)x^2+2x+4\n\ny=(1)/(12)\cdot0^2+2\cdot0+4\n\ny=0+0+4\n\n\boxed{y=4}$

Part B & C: How high is the ball at its maximum height?

What we basically want to do is find the vertex of the function.
There are multiple ways to do this. You could graph it or make a table, but this method is not efficient.
The method I am going to go over right now is putting the equation in vertex form.

$y=-(1)/(12)x^2+2x+4$

Move the constant to the left side.

$y-4=-(1)/(12)x^2+2x$

Factor out the x² coefficient.

$y-4=-(1)/(12)(x^2-24x)$

Find out which number to add to create a perfect square trinomial.
(Half of 24 is 12, 12 squared is 144. We have to add 144/-12 (which is -12) to each side so that we end up with 144 inside the parentheses on the right side)

$y-4-12=-(1)/(12)(x^2-24x+144)$

Factor the perfect square trinomial and simplify the right side.

$y-16=-(1)/(12)(x-12)^2$

Isolate y on the left side.

$y=-(1)/(12)(x+12)^2+16$

And now we are in vertex form.
Vertex form is defined as y = a(x-h)² + k with vertex (h, k).
In this case, our vertex is (12, 16).

You could've also taken the shortcut that for any quadratic f(x) = ax² + bx + c, the vertex (h, k) is (-b/2a, f(h)). That's basically a summation of this method which you can use if your teacher has taught it to you.

Part D & E: What is the horizontal distance travelled by the ball when it hits the ground?
When the ball hits the ground, y is going to be 0, since y is the ball's height.
There are many ways to solve a quadratic...split the middle, complete the square, and the quadratic formula.

$-(1)/(12)x^2+2x+4=0$

Solving by splitting the midlde
If your quadratic has fractions, this is not a good option.

Solving by completing the square
Move the constant over the right side.

$y=-(1)/(12)x^2+2x=-4$

Divide by the x² coefficient.
(Dividing by -1/12 is the same as multiplying by its reciprocal, -12.)

$x^2-24x=-4*-12$

Simplify the right side.

$x^2-24x=48$

Halve the x coefficient, square it, and then add it to each side.
(Half of -24 is -12, and -12 squared is 144.)

$x^2-24x+144=192$

Factor the perfect square trinomial.

$(x-12)^2=192$

Take the square root of each side.

$x-12=\pm√(192)$

192 = 8 × 8 × 3, so we can simplify √192 to 8√3.
Add 12 to each side and we get our answer.

$x=12\pm8√(3)$

Our function does not apply when x or y is less than 0, of course.
12-8√3 is negative, so this cannot be our answer.
So, the ball had travelled 12+8√3 feet at the time when it hit the ground.

Solving with the quadratic formula
For any equation ax² + bx + c = 0, the solution for x is $(-b\pm√(b^2-4ac))/(2a)$ .

Our equation, y=-1/12x^2+2x+4, has a = -1/12, b=2, and c=4.
Let's plug these values into the quadratic formula.

$\frac{-2\pm\sqrt{2^2-4\cdot(-1)/(12)\cdot4}}{2\cdot(-1)/(12)}=\frac{-2\pm\sqrt{4-\frac{-4}3}}{\frac{-1}6}=\frac{-2\pm\sqrt{(16)/(3)}}{\frac{-1}6}=\frac{-2\pm(4)/(√(3))}{\frac{-1}6}$

Dividing by a fraction is the same as multiplying by its reciprocal...

$-6(-2\pm(4)/(√(3)))=12\pm(-24)/(√(3))=12\pm(24)/(√(3))=12\pm\frac{24√(3)}3=\boxed{12\pm8√(3)}$

Of course, we only want the positive value, 12+8√3.

Revisiting Part B & C:
Since parabolae are symmetrical, if you know two values of x for some value of y (like the x-intercepts we just found in part B) then you can find the average between them to find what the x value of the vertex is, then plug that in to find the y value of the vertex (the height we want)

The average between 12+8√3 and 12-8√3 is 12. Plug that in and we get 16!

the student council is organizing a trip to a rock concert. all proceeds from ticket sales will be donated to a charity. tickets to the concert cost $31.25 per person if a minimum of 104 people attend. for every 8 extra people that attend, the price will decrease by $1.25 per person.a). how many tickets need to be sold to maximize the donation to charity?b). what is the price of each ticket that maximizes the donation?c). what is the maximum donation?

Answers

I got the maximum donation $152

Final answer:

To maximize the donation to charity, a total of 117 tickets need to be sold. The price per ticket that maximizes the donation is $29.0625. The maximum donation is $3,400.3125.

Explanation:

To maximize the donation to charity, we need to determine the number of tickets that need to be sold and the price per ticket that will result in the maximum donation.

a) To find the number of tickets, we can start with the minimum attendance requirement of 104 people. For every 8 extra people that attend, the price decreases by $1.25. So the number of extra people is calculated by dividing the total increase in price ($31.25 - $30) by the decrease per person ($1.25), which is 8. Therefore, the number of extra people is 13. To find the total number of tickets, we add the minimum attendance of 104 people and the number of extra people of 13. So the total number of tickets that need to be sold to maximize the donation to charity is 117.

b) To find the price per ticket, we start with the price of $31.25 and take into account the decrease of $1.25 for every 8 extra people. We can calculate the price decrease per person by dividing $1.25 by 8, which is $0.15625. To find the price per ticket, we subtract the decrease per person from the initial price, multiplied by the number of extra people. So the price per ticket that maximizes the donation is $31.25 - ($0.15625 × 13) = $29.0625.

c) To find the maximum donation, we multiply the price per ticket by the total number of tickets sold. So the maximum donation is $29.0625 × 117 = $3,400.3125.

Learn more about Maximizing donation to charity here:

brainly.com/question/31888282

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Combine the like terms to create an equivalent expression:
\large{-2k-(-5)+1}−2k−(−5)+1

Answers

Answer:

The answer is

$- 2x + 5 + 1 - 2x + 5 + 1 = \n - 4x + 12 = \n - 4(x - 3)$

Which of the following scenarios exhibits a function relation? Take the first set listed to be the domain of the relation.the set of tree heights and the set of trees in a forest
the set of car make and models and the set of people in a certain town
the set of birthdays and the set of students in a class
the set of people with Social Security cards and the set of Social Security numbers

Answers

Answer:

The scenario that exhibits a function relation is:

The set of people with Social Security cards and the set of Social Security numbers.

Step-by-step explanation:

We know that a function is a relation in which each element of first set has one image i.e. an element can't be mapped to two distinct elements of the other set.

The set of tree heights and the set of trees in a forest.

This relation is not a function.

Since, two trees may have a same height.

The set of car make and models and the set of people in a certain town.

This relation is also not a function.

Since, two people may have a car of same model.

The set of birthdays and the set of students in a class

This relation is not a function since two students may share same birthday.

The set of people with Social Security cards and the set of Social Security numbers.

This relation is a function.

Since, the security card number has a unique number on each car.

This means that each person has a unique card number.

The set of people with social security cards and the set of social cecurity numbers

50 is 6.25% of what number?

Answers

Answer:

800

Step-by-step explanation:

Answer:

i think its 800

Step-by-step explanation:

taking the test

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