Mathematics High School

The function H(t) = −16t2 + 60t + 95 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 20 + 38.7t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points) (10 points)

Answers

Answer 1

We are given the functions:

h(t) = -16t^2 + 60t + 95

g(t) = 20 + 38.7t

Part A. All we have to do is to plug in the value of t = 1 to 4 on the two functions

t h(t) g(t)

1 139 58.7

2 151 97.4

3 131 136.1

4 79 174.8

Looking at the table, we can say that the time when h(t)=g(t) must be between t=2 and t= 3 seconds
At t=2 seconds h(t) is above g(t), and at t = 3 seconds h(t) is below g(t). Therefore the two functions must be at the same height in between.

Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that h(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.

Related Questions

Which relationship is always true for the angles x, y, and z of triangle MNP?
A. x + z = y
B. y + z = x
C. x + y + z = 180 degrees
D. x + y + z = 90 degree

Answers

It's C. The triangle angle sum theorem tells us that the angles of any triangle will always add up to 180 degrees.

-the answer would be C: "x+y+z= 180 degrees"

-and here is proof so you know you won't get the answer wrong

- hope you do good on your test, have a good day :)

literal equations, please help! this one is confusing to me.

Answers

What is asked here is that you isolate y so that the equation takes the form of y = ..., where ... will be something that contains a, b and c but not y. So how do we get there? By applying some standard permutations to equations like so:

aby - b = c

First, we bring the -b term to the right hand side by adding b left and right:

aby -b+b = c+b

The -b and +b cancel out, so we get:

aby = c + b

Then, we divide left and right hand side by ab:

aby/ab = (c+b)/ab

Again, the ab/ab on the left cancels out (it is 1), so we get:

y = (c+b)/ab

And we're done!

So you have to know that it is allowed to add or subtract something (anything) to/from the left and right hand side of an equation. Likewise, you have to know that it is allowed to multiply or divide by something, as long as it isn't 0.

the discriminant of a quadratic equation is negative. one solution is 2+3i. what is the other solution?

Answers

negative means it has 2 non-real roots

we assume that the coefients of the equation are real so therefor

if a+bi is a root then a-bi is also a root

if 2+3i is a root then 2-3i is also a root (solution)

the other solution is 2-3i

Answer:

2-3i

Step-by-step explanation:

Select the inequality that corresponds to the given graph. graph of an inequality with a dashed line through the points negative 3 comma 0 and 0 comma 4 and shading below the line

A. 4x-3y>-12
B. x+4y>4
C. 4x-2y<-8
D. 2x+4y=>-16

Answers

The first thing I did was plot the given two points: (3,0) and (0,4). I connected the two hollow dots and created a line. Then, I shaded the region below the line as mentioned in the problem. The result is show in the picture.

The detail about dashed line is important because it expresses an equality with a symbol < or >. The data points that coincide with that line is not part of the solution but just stand as a boundary, hence, I used dashed line and hollow points. If it were ≥ or ≤, then we use solid lines and dots. With that, we can already eliminate choice D.

Next, we test the inequality. Let's choose a point within the shaded region. Suppose the point is (1,0) denoted by the red dot. If it is part of the solution, then the inequality will be proven true.

A. 4x-3y>-12
4(1) - 3(0) > -12
4 > -12, this is true
B. x+4y>4
1 + 4(0) > 4
1 > 4, this is not true
C. 4x-2y<-8
4(1) -2(0) < -8
4 <-8, this is not true

∴The answer is A.

Answer:

Step-by-step explanation:

i took the test

Factor out the greatest common factor of 5ab^2+10ab

Answers

5ab^2 + 10ab

GCF is : 5ab

Answer: 5ab

Step-by-step explanation:

The given polynomial : [tex]5ab^2+10ab[/tex]

The prime factorization of [tex]5ab^2= 5\times a\times b\times b[/tex]

The prime factorization of [tex]10ab= 5\times2\times a\times b[/tex]

We can see that the greatest common factor of [tex]5ab^2\text{ and }10ab[/tex] is [tex]5\times a\times b[/tex]

Hence, the greatest common factor of [tex]5ab^2+10ab[/tex] = 5ab

Factor the following.

Answers

x^2 - 10x + 25
(x + 5)(x - 5)

The answer is B (x-5) (x+5)

Hope this helps :)
Please give brainliest

This is square of a binomial.

x² is the square of x and 25 is the square of -5

-10x is given by 2(x*-5)

Your final answer is (x-5)²

In a computer game, when choosing a character there are 5 choices for hair style, 3 choices for eye color, and 7 choices for outfits. How many different characters are possible if you were to choose 1 hair style, 1 eye color, and 1 outfit?
105
140
22
15

Answers

Hey there!

If there are 5 choices for a hairstyle, that means that there are 5 options per 1 eye color. This totals out to 15 options (3 × 5) total for eye color and hairstyle combinations.

For each of those combinations, there are an additional 7 options for an outfit. That means that there is a total of 105 options (7 × 15) available to choose from.

Hope this helped you out! :-)

7x1,000,000+
3x100,000+
5x10,000+
6x1.00+
2x100+3x10+7+1

Answers

When wording your problem, parenthesis would have helped to make sure that the problem was solved in the correct order of operations as it was intended to, but here is your answer from the way I solved it:
7350244

8700316.1 that your answer

The perimeter of a rectangular field is 376 yards. if the width of the field is 89 yards, what is its length?

Answers

The length of the field will be calculated as:
P=2(L+W)
P=376
W=89
thus substituting the values in the equation we get;
376=2(L+89)
376/2=(L+89)
solving for L;
188=L+89
L=188-89
L=99 yards
therefore the length is 99 yards

Answer:

Step-by-step explanation:

The length of the field will be calculated as:

P=2(L+W)

P=376

W=89

thus substituting the values in the equation we get;

376=2(L+89)

376/2=(L+89)

solving for L;

188=L+89

L=188-89

L=99 yards

therefore the length is 99 yards

About 15% of the population of a large country is allergic to pollenallergic to pollen. if two people are randomly selected, what is the probability both are allergic to pollen? what is the probability at least one is allergic to pollenallergic to pollen?

Answers

P(allergic) = 0.15

P(both are allergic to pollen) = (0.15)² = 0.0225 (you can use the binomial probability also)

Q(NOT allergic to pollen) = 1 - 0.0225 = 0.9775
Binomial probability

Probability of NEITHER is allergic
ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ
²C₀(0.15)⁰(0.9775)² = 0.9555

P(at LEAST ONE is allergic) = 1- 0.9555 = 0.0444

Answer:

(a) 0.0225

(b) 0.225

Step-by-step explanation:

It is given that 15% of total population is allergic to pollenallergic to pollen.

Thus, Probability of an individual s/he has allergy is 0.15

Thus, The probability that two person is selected and both has allergy is 0.15 × 0.15 = 0.0225

And the Probability that at least one person is suffered from allergy from that two person = P(allergic and non-allergic) + P(non-allergic and allergic)

⇒ 0.15 × (1 - 0.15) + (1 - 0.15) × 0.15

⇒ 0.15 × 0.85 + 0.85 × 0.15 = 0.225

By the empirical rule, what percentage of the area under the normal curve lies to the left of mu, the average? put your answer as a percentage.

Answers

The normal curve is a bell shaped curve which is symmetric about μ (the population mean), as shown below.
When the curve is plotted against the normalized coordinate z, the curve is symmetric about z=0, which coincides with μ.

Because the total area under the curve is 1, each half of the curve about the line of symmetry has an area of 0.5.
Ths means that 50% of the normal curve lies to the left of μ.

Answer: 50%

You are getting a line-up ready for a school kickball game. you have 55 girls and 55 boys. the rules state each child must kick the same number of times and alternate girl-boy or boy-girl. how many ways can a line-up be made for one round of kicking

Answers

To solve this problem, we must first imagine out that the sequence of the children is either
GBGBGB.... or BGBGBG....

So there are 2 possible sequence all in all. Now to solve for the total arrangements per sequence, the girls can be arranged in n! ways in their alloted spots, and so can the boys n! in their alternate spots, therefore:
Total arrangements = 2 * n! * n!

If n = 55

Total arrangements = 2 * 55! * 55!

Total arrangements = (The answer is very big ~almost infinite)

If n = 5

Total arrangements = 2 * 5! * 5!

Total arrangements = 28,800

So I believe the correct given is 5 boys and 5 girls and there are a total of 28,800 arrangements.

Rationalize the denominator.

10/√24x

write it in simplest form

Answers

[tex] \frac{10}{ \sqrt{24x} } =\frac{10}{ \sqrt{24x} } * \frac{ \sqrt{24x} }{\sqrt{24x}} [/tex] because
[tex]\frac{ \sqrt{24x} }{\sqrt{24x}} =1[/tex] and the expression has the same value when multiplied by 1.
Multiply the terms:
[tex]\frac{10}{ \sqrt{24x} } * \frac{ \sqrt{24x} }{\sqrt{24x}} =\frac{ 10\sqrt{24x} }{24x}[/tex]
Simplify to get the final answer:
[tex]\frac{ 10\sqrt{24x} }{24x}=\frac{ 5\sqrt{24x} }{12x}[/tex]

Gina mixed paint to make her favorite shade of purple. She filled up one third of the container with red paint. Then she filled the remaining space with 4 Liters of blue paint.How many milliliters of paint did Gina mix

Answers

If the red is one third full, and it takes 4 more liters of blue, than there are 6 liters total to make the paint purple. Because if 4 liters is 2/3 then that makes the amount of red 2 liters.

Which function below has the following domain and range?
Domain:
{−9,−5,2,6,10}
Range:
{−2,0,8}
Select one:
a.
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
b.
{(−9,10),(−2,8)}
{(−9,10),(−2,8)}

c.
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}

d.
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}

Answers

domain (ur x values) are { -9,-5,2,6,10)
range (ur y values) are { -2,0,8}

ur answer is : D

Answer:

The correct option is d.

Step-by-step explanation:

Domain is the set of all possible inputs or the values of x and the range is value of output or y.

In option a,

The given function is

{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}

Domain = {-2,0,8}

Range = {-9,-5,2,6,10}

Therefore option a is incorrect.

In option b,

The given function is

{(−9,10),(−2,8)}

Domain = {-9,-2}

Range = {8,10}

Therefore option b is incorrect.

In option c,

The given function is

{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}

Domain = {-9,-5,2,6,10}

Range = {-2,0,5,8,9}

Therefore option c is incorrect.

In option d,

The given function is

{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}

Domain = {-9,-5,2,6,10}

Range = {-2,0,8}

Therefore option d is correct.

Bret is starting a business selling handmade necklaces. He has decided to invest and initial amount of $387 for advertising and materials cost seven dollars for each necklace he makes. Bret can sell his creations for $10 per necklace.once he makes and sells a certain number of necklaces he will break even with identical expenses and sales. How many necklaces would that take? What would the total expenses and sales be then?

Answers

alrighty

each necklace costs him 7 dollars but he gets 10 dollars from selling them
so his profit per necklace=10-7=3 per necklace

so we want to find how many necklaces he needs to make and sell to cover the initial investment

the cost is 387
divide it by the profit per necklace
387/3=129
needs to make 129 necklaces
the total expenses would be equal to the total sales
ok, the sales are 10 dollars and 129 necklaces so total sales is 1290 dollars and so then the expenses are 1290 dollars

129 necklaces
total expensese is $1290
total sales is $1290

Final answer:

To break even, Bret would need to make and sell 40 necklaces, with a total expense of $15,760 and total sales of $400.

Explanation:

To determine the number of necklaces Bret needs to make and sell to break even, we need to consider his initial investment and the expenses and sales associated with each necklace.

First, let's calculate the total expenses for each necklace: $7 (materials cost) + $387 (initial investment) = $394.

Next, let's calculate the total sales for each necklace: $10 (selling price).

To break even, the total expenses and total sales need to be equal.

Let n represent the number of necklaces:

Total expenses = $394 * n

Total sales = $10 * n

Setting the two equations equal to each other, we have: $394 * n = $10 * n.

Now, let's solve for n:

$394 * n = $10 * n

$394 = $10

n = 394 / 10

n = 39.4

Since we cannot sell a fraction of a necklace, Bret would need to make and sell 40 necklaces to break even.

The total expenses for 40 necklaces would be $394 * 40 = $15,760, and the total sales would be $10 * 40 = $400.

The process of moving a figure to a different location is called:
mapping.
transformation.
isometry.
None of the choices are correct.

Answers

The process of moving a figure to a different location is called TRANSFORMATION.

The population of a town is decreasing at a rate of 1.1% each year. If there are 3,000 people in the town right now, how many people will be living in the town in 10 years? Round your answer to the nearest whole number.

Answers

total = 3000*(1-0.011)^10

1-0.011 = 0.989

total = 3000*(0.989)^10

0.989^10 = 0.895288314

3000* 0.895288314 = 2685.86

rounded to nearest whole number = 2686

there will be 2686 people

The formula is
P=Ae^-rt
P ?
A 3000
R 0.011
T 10 years
P=3,000×e^(−0.011×10)
P=2,687.5 round your answer to get
P=2688

Help please! In the figure line a and line b are parallel based on the figure match each given angle with its congruent angles

Answers

∠3, ∠7, ∠6: angles congruent to ∠2
∠2 and ∠3 are vertical angles, ∠3 and ∠7 are corresponding angles, and ∠7 and ∠6 are vertical angles.

∠3, ∠7, ∠2: angles congruent to ∠6
∠2 and ∠3 are vertical angles, ∠3 and ∠7 are corresponding angles, ∠7 and ∠6 are vertical angles.

∠4, ∠8, ∠5: angles congruent to ∠1
∠1 and ∠4 are vertical angles, ∠4 and ∠8 are corresponding angles, ∠8 and ∠5 are vertical angles.

Answer: copy the guy on top of me but the last one for PLATO users is <3,<6,<2 is angles congruent to <7

Step-by-step explanation: bec I said so

If an eagle and a bumblebee are traveling at 8 km/hr, which has more momentum explain

Answers

The eagle would have more momentum because it has a larger mass.

f(x)=5x^2 + 9x-4 g(x)= -8x^2-3x-4 find (f+g)(x)

Answers

It's -3x^2+6x-8 since you just add like terms that they both have

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters. A second prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism? 576 cubic centimeters 768 cubic centimeters 784 cubic centimeters 1,344 cubic centimeters

Answers

1st Prism = 8*14 = 112

672/112 = 6

2nd prism = 8*12=96

96*6 = 576 cubic cm

answer is 576 cubic centimeters

Answer:

The correct option is 1.

Step-by-step explanation:

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant.

Let the height of both rectangular prism be h cm.

The volume of a prism is

[tex]V=l\times b\times h[/tex]

Where, l is length, b is breadth or width and h is height.

The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters.

[tex]672=8\times 14\times h[/tex]

[tex]672=112h[/tex]

Divide both sides by 112.

[tex]\frac{672}{112}=h[/tex]

[tex]6=h[/tex]

The value of h is 6 cm. It means the height of both prism is 6 cm.

A second prism has a length of 12 centimeters and a width of 8 centimeters. So, the volume of second prism is

[tex]V=12 \times 8\times 6[/tex]

[tex]V=576[/tex]

The volume of second prism is 576 cubic centimeters. Therefore the correct option is 1.

Need help fast!
The table shows the relationship between the number of drops of food color added to different number of cups of cake frosting. Look at the first picture.

Which point below shows an equivalent ratio in this situation? Look at the second picture.

A. Point B, because if cups of frosting are 50, then drops of food coloring will be 200
B. Point B, because if drops of food coloring are 50, then cups of frosting will be 200
C. Point J, because if cups of frosting are 40, then drops of food coloring will be 10
D. Point J, because if drops of food coloring are 40, then cups of frosting will be 10

Answers

Answer: A) Point B, because if cups of frosting are 50, then drops of food coloring will be 200.

This is because the proportion of frosting to food coloring is 1:4, and if the answer to A is simplified (50:200), the ratio would be the same.

Answer:

Option A. will be the answer.

Step-by-step explanation:

From the given table we will find the relation first and the we will try to find the point with the same relation in the graph.

From the given table ratio of Cups of frosting and Drops of food color is = [tex]\frac{\text{Cups of frosting}}{\text{Drops of food color}}[/tex]

= [tex]\frac{2}{8}[/tex]

= [tex]\frac{1}{4}[/tex]

Or 1 : 4

Now the point B shows the ratio between food color and frosting = [tex]\frac{\text{Cups of frosting}}{\text{Drops of food color}}[/tex]

= [tex]\frac{\text{x-coordinates}}{\text{y-coordinates}}[/tex]

= [tex]\frac{50}{200}[/tex]

= [tex]\frac{1}{4}[/tex]

The same ratio 1 : 4

Option A. will be the answer.

The speed of light is about nine hundred eighty million feet per second. What is that speed in scientific notation?

Answers

Nine hundred eighty million is 9.8 x 10^8, which is the bottom left option.

I hope you are satisfied with my answer.

Answer:

The answer is 9.8*10^8

i think

Step-by-step explanation:

Evaluate the function rule to find the range of each function for the domain {-3, 0, 5}. f(x) = x² − 6x + 4
A. {-5, -4, -1}
B. {-5, -1, 4}
C. {-1, 4, 31}
D. {4, 31, 59}

Please I beg of you!

Answers

The range is the set of images; so, as you have the domain set and the function rule, you just have to calculate the value of the function for each value of the domain:

Domain        image, f(x) =x^2 - 6x + 4

-3                (-3)^2 - 6(-3) + 4 = 9 + 18 + 4 = 31

0                 (0)^2 - 6(0) + 4 = 0 - 0 + 4 = 4

5                  (5)^2 - 6(5) + 4 = 25 - 30 + 4 = - 1

So, we got the images -1, 4, and 31 and that is that is the range {-1, 4, 31}

Answer: option C. {-1, 4 , 31}

When positive integer x is divided by 11, the quotient is y and the remainder is 4. when 2x is divided by 8, the quotient is 3y and the remainder is 2. what is the value of 13y – x ?

Answers

[tex]\dfrac x{11}=y+\dfrac4{11}\iff x=11y+4[/tex]
[tex]\dfrac{2x}8=3y+\dfrac28\iff2x=24y+2[/tex]

[tex]\implies 2x-x=(24y+2)-(11y+4)[/tex]
[tex]\implies x=13y-2[/tex]
[tex]\implies 13y-x=2[/tex]

the answers are
A. 15
B. 14
C. 16
D. 19

Answers

Your answer is A. 15

6a+10 = 3a+ 55

6(15) + 10 = 3(15) + 55

6x 15 = 90 + 10 = 100
3 x 15 = 45 + 55 = 100

hope this helps

What is the range of the function y=2sin x

Answers

Answer:

Range: [-2, 2] {y | -2 ≤ y ≤ 2}

Step-by-step explanation:

The given function is y = 2sinx

We have to find the range of the given function.

Since at y-axis sine function has the variance between -1 to 1 so range of y = sinx is [-1, 1]

and if the amplitude of sine function is 2 then sine function will vary from -2 to 2 which implies that range of y = 2 sinx will be [-2, 2]

So range of y = 2sinx is [-2, 2]

The range of the function y=2sin x is mathematically given as

dy=(-2,2)

What is the range of the function y=2sin x?

Question Parameter(s):

function y=2sin x

Generally, the equation for the wave is mathematically given as

[tex]y(x,t)=Asin(kx−wt+\phi)[/tex]

Therefore, Comparing both equations

y(x,t)=Asin(kx−wt+\phi)

y=2sin x

We have

A=2

In conclusion, The range of a function y=2sin x is simply defined as the probable outcomes, with x values as independent factors.

Hence, with sinx having min and max values at (-1,1)

The y value range will be

dy=(2(-1),2(1))

dy=(-2,2)

Answers

It should be axaxa +10. Or a to the third plus 10

Given the parent function of f(x) = x3, what is the value of k in the translated graph of f(x − h) + k?

Answers

we have

[tex]f(x)=x^{3}[/tex]

we know that

The point [tex](0,0)[/tex] in the graph of f(x) is the point [tex](3,2)[/tex] in the translated graph

The rule of the translation is

[tex](x,y)----> (x+3,y+2)[/tex]

That means

The translation is [tex]3[/tex] units to the right and [tex]2[/tex] units up

The equation of the translated graph is equal to

[tex]f(x)=(x-3)^{3}+2[/tex]

therefore

The answer is

the value of k is equal to

[tex]k=2[/tex]

see the attached figure to better understand the problem

Answer:

k=2

Step-by-step explanation:

I just did the assignment

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