The rocket splashes down after 43 seconds.
The rocket peaks at 2400. meters above sea-level.
Step-by-step explanation: For the time taken before the splashStep 1
We realise that the rocket will hit the ground when our function [tex]h(t)=0[/tex] , i.e [tex]-4.9t^2+202t+318=0.[/tex]
Step 2
Use the quadratic formula to solve for the time. For the general quadratic equation [tex]at^2+bt+c=0[/tex], the general solution to the equation is
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} .[/tex]
In our case, the quadratic equation [tex]h(t)=-4.9t^2+202t+318=0[/tex] has a solution
[tex]t=\frac{-202\pm\sqrt{202^2-4((-4.9)(318))}}{2(-4.9)} \\t=-1.52,t=42.74.[/tex]
Step 3
In this step we pick the value of [tex]t[/tex] that makes physical sense. Since the NASA team launced the rocket at [tex]t=0[/tex], the rocket reaches the bottom when [tex]t=42.74[/tex]. This can be rounded up to [tex]43[/tex] seconds.
For the maximum height of the rocket above sea levelStep 1
The first step is to realist that since the coefficient of the quadratic term is negative, the graph of this function will face downwards. From this we can gather that the maximum value of this function occurs at the vertex.
Step 2
In this step we calculate the t coordinate of the of the vertex of this function. For any quadratic equation [tex]h(t)=at^2+bt+c[/tex] , the vertex occurs when ,
[tex]t=-\frac{b}{2a}.[/tex]
For the equation [tex]h(t)=-4.9t^2+202t+318[/tex] , the vertex occurs when ,
[tex]t=-\frac{202}{2(-4.9)}=20.61.[/tex]
Step 3
We substitute the value of [tex]t[/tex] from step 2 above into [tex]h(t)[/tex] to get the maximum value of this function. This calculation is shown below,
[tex]h(20.61)=-4.9(20.61)^2+202(20.61)+318=2399.84m.[/tex]
This can be rounded up to 2400m.
Beanbag chairs that normally sell for 36.50 are on sale for 32.12 find the precent of discount round your answer to the nearest tenth of a precent
Answer: 12.0 %
Step-by-step explanation:
Since according to the question,
The initial price of the chair ( Marked price) = 36.50
And, After the discount the price of the chair = 32.12
Thus, the discount on the price = 36.50 - 32.12 = 4.38
Therefore the discount percentage = [tex]\frac{discount}{marked price} \times 100[/tex]
= [tex]\frac{4.38}{36.50} \times 100[/tex]
= [tex]\frac{438}{36.50}[/tex]
= 12 %
Thus, the percentage of discount = 12.0 %
What’s the area of PQSU? ______sq mi
Answer:
35 mi^2
Step-by-step explanation:
Area of parallelogram = base x height
7 x 5 = 35
Answer:
Area = 35 mi^2
Step-by-step explanation:
Area = b*h
The base is 7 mi
The height is 5 mi
Area = 7*5
Area = 35 mi^2
A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is 4.3 MB. Yesterday, there were 1290 downloads of the song, for a total download size of 4403 MB. How many downloads of the high-quality version were there?
Answer:
770 high-quality songs were downloaded
Step-by-step explanation:
A web music store offerst two versions:
Standard Version = 2.1 MBHigh-Quality Version = 4.3MBThere were 1290 for a total download size of 4403MB.
According to the information above, we have the following system of equations:
A + B =1290
2.1A + 4.3B = 4403
Where 'A' referst to the number of Standard songs and 'B' refers to the number of High Quality songs.
Solving the sistem of equations we get that:
A + B =1290 ⇒ A = 1290 - B
2.1A + 4.3B = 4403 ⇒ 2.1(1290 - B) + 4.3B = 4403
⇒ 2709 - 2.1B + 4.3B = 4403 ⇒ 2.2B = 1694 ⇒ B=770
Now, let's find the value of 'A':
A + B =1290 ⇒ A = 1290 - 770 ⇒ A = 520.
Therefore, 770 high-quality songs were downloaded.
what is the perimeter of a rectangle with a length of 3x + 3 and a width of x - 1
Answer:
P = 8x+4
Step-by-step explanation:
The perimeter of a rectangle is found by using the formula
P = 2(l+w)
We know l = 3x+3 and
w = x-1
Substitute these values in
P =2(3x+3 + x-1)
Combine like terms
P = 2(4x+2)
Distribute the 2
P = 8x+4
Evaluate the summation
Answer:
114
Step-by-step explanation:
The first term (a1) = 1 + 3 = 4 (substituting 1 for i)
The last term (L) = 12 + 3 = 15
So the sum of the 12 terms = (n/2)(a1 + L)
= (12/2) (4 + 15)
= 6 * 19
= 114 (answer)
The value of the summation of arithmetic progression is 114
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the number of terms n = 12
Let the first term a = i + 3
when i = 1
a = 4
So , the first term of the arithmetic progression is a = 4
The second term a₁ = i + 3
when i = 2
a = 5
Now , the common difference d = second term - first term
Common difference d of the arithmetic progression = 5 - 4 =1
So , d = 1
Now , the sum of n terms of an AP is given by
Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Substituting the values in the formula , we get
Sₙ = ( 12/2 ) [ ( 2 x 4 ) + ( 12 - 1 ) x 1 )
Sₙ = 6 [ 8 + 11 ]
Sₙ = 6 x 19
Sₙ = 114
Therefore , the value of Sₙ is 114
Hence , The value of the summation of arithmetic progression is 114
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This year the paradas had 127 floats . That was 34 fewer floats than last year how many floats were in the parade last year
Answer:
161
Step-by-step explanation:
We will use the math operation addition to find last year's number of floats. We know this year was 127 and was fewer than 34. So 127+34=last year's floats.
127+34=161
Rectangle R was dilated to form rectangle R' Which is the scale factor of the dilation? 5/4 , 2/1 5/2 5/1
Answer:
I'm not sure if those are the answer choices but your answer should be 5/2
Hope this helps
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
PLEASE HELP ME!!! and if you could give me an explanation that would be good but if you can’t at least give me the answer please :(
Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C
=============================
Explanation:
Given roots: -2, 4, 4, 3
Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)
x = -2 leads to x+2 = 0, so (x+2) is one factor
x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor
x = 3 leads to x-3 = 0 so (x-3) is the last factor
Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)
Use the distributive property to expand everything out
g(x) = (x+2)(x-4)(x-4)(x-3)
g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )
g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )
g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )
g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96
g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96
which shows how I got choice C as the answer
Victoria's spends 5/9 of her money on a flan and two chicken pies each chicken pie cost 1/6 as much as the fly Victoria has $24 left how much does Victoria spend and how much does a flan cost
Answer:
She spend $30
A flan cost $22.5
Step-by-step explanation:
Let's call x her initial money
After she bought the flan and two chicken pies she has $24.
She spend (5/9)*x in the flan and two chicken, then
x - (5/9)*x = 24
(4/9)*x = 24
x = 24*(9/4)
x = $54
She spend (5/9)*54 = $30
Let's call f the flan cost
Each chicken pie cost 1/6 as much as the flan, then:
30 = f + (1/6)*f + (1/6)*f
30 = (4/3)*f
f = 30*(3/4)
f = $22.5
Victoria had $54 in total. She spent $30 on the flan and two chicken pies altogether. The cost of the flan is $22.50.
The problem presents a situation where Victoria spends a fraction of her money on a flan and two chicken pies. Victoria has $24 left after these purchases. To solve this, we must first calculate the total amount of money Victoria had before making her purchases. Given that 5/9 of her money was spent on the flan and two chicken pies, and she has $24 remaining, we can set up the following equation where x represents the total amount of money:
x - (5/9)x = $24
This simplifies to:
(4/9)x = $24
By multiplying both sides of the equation by (9/4), we find the total amount of money Victoria had:
x = $24 \times (9/4)
x = $54
Victoria spent 5/9 of $54 on the flan and two chicken pies, which is:
(5/9) \times $54 = $30
If each chicken pie costs 1/6 the cost of the flan, we can let f represent the cost of the flan and (1/6)f the cost of each chicken pie. We have 2 chicken pies, so the equation would be:
f + 2 \times (1/6)f = $30
This simplifies to:
f + (1/3)f = $30
Combining like terms, we get (4/3)f = $30 which leads to:
f = $30 \times (3/4)
f = $22.50
So the cost of the flan is $22.50.
A salesperson had $240,000 in sales last year, which is 60% of the sales she had this year. Which equation could be used to determine x, the salesperson's total amount in sales, in dollars, for this year?
Answer:
$400,000
Step-by-step explanation:
We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other.
[tex]\frac{60}{100}=\frac{240000}{x}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
60x=100(240,000)
60x=24,000,000
y=400,000
Answer:
$400,000
Step-by-step explanation:
800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6
Paul's MP3 player has a total of 852 songs. He has 4 different groups of songs. If he puts and equal number of songs in each group, how many songs will be in each group?
Answer:
213
Step-by-step explanation:
You have to divide the 852 songs into the 4 categories.
852/4=
213
What store has the best deal? Tae Store:4 cans for $2.48, Be Cool Store:5 cans for $3.00 or Not Today Store:59 cents per can?
Two trains begin in Milford and end in Pinkerton, which is 300 miles away. Train A leaves Milford at 10:00 a.M. And travels at a rate of 90 miles per hour. Train B leaves Milford at 8:00 a.M. And travels at 70 miles per hour. Which train(s) will arrive in Pinkerton before 1:00 p.M.?
Answer:
Step-by-step explanation:
Alright, lets get started.
For train A:
Distance from Milford and Pinkerton is 300miles.
Speed of train A is 90 miles per hour.
So, time taken to complete this distance = [tex]\frac{distance}{speed}[/tex]
So, time taken to complete this distance =[tex]\frac{300}{90}=3.333[/tex]
Means train A will take 3.33 hours or say 3 hrs and 19.8 minutes to reach Pinkerton.
So,if it starts at 10:00 AM, then it will reach at 01 hrs 19.8 minutes PM (01:19.8 PM).
For train B:
Speed of train B is 70 miles per hour.
Train B will take time =[tex]\frac{300}{70}=4.29[/tex]
Means 4 hrs and 17.4 minutes.
So, if it starts at 8:00 Am, then it will reach at 12 hrs 17.4 minutes PM(12:17.4 PM).
So, train B will be reaching Pinkerton before 1:00 PM : Answer
Hope it will help :)
Answer:
train B will be reaching Pinkerton before 1:00 PM
Step-by-step explanation:
Geometry: The rectangle shown has a perimeter of 34cm and the given area. Its length is 5 more than twice it's width. Write and solve a system of equations to find the dimension of the rectangle
w - width
2w + 5 - length
w + w + (2w + 5) + (2w + 5) = 6w + 10 - perimeter
34 cm - perimeter
The equation:
6w + 10 = 34 subtract 10 from both sides
6w = 24 divide both sides by 6
w = 4 cm
2w + 5 = 2(4) + 5 = 8 + 5 = 13 cm
Answer: Width = 4cm, Length = 13cmThe length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answer:
Width of rectangular storage room= 5 feet.
Step-by-step explanation:
Let x be the width of storage room.
We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.
We are also given that the area of the room is 40 square feet.
Since the area of a rectangle is length times width.
[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]
Let us substitute our given values in area formula.
[tex]40=x*(x+3)[/tex]
Upon distributing x we will get,
[tex]40=x^2+3x[/tex]
[tex]x^2+3x-40=0[/tex]
Now let us factor out our quadratic equation using splitting the middle term.
[tex]x^2+8x-5x-40=0[/tex]
[tex]x(x+8)-5(x+8)=0[/tex]
[tex](x+8)(x-5)=0[/tex]
[tex]x+8=0[/tex] or [tex]x-5=0[/tex]
[tex]x=-8[/tex] or [tex]x=5[/tex]
Since width can not be negative, therefore, the width of rectangle will be 5 feet.
Let us verify our answer.
Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.
Given: Area=40 square feet.
5*8=40.
Hence, width of rectangular storage room is 5 feet.
The width of the rectangular storage room, considering it is 3 feet shorter than the length and the area is 40 square feet, is 5 feet.
Explanation:The subject of this question is Mathematics and it is typically taught in Middle School. The problem describes a rectangle where the length is 3 feet longer than the width and the area is 40 square feet. The width is x and the length is x + 3 (since it is 3 feet longer). The area of a rectangle is defined as length times width, which can be expressed as 40 = x(x + 3), or x² + 3x - 40 = 0. This can be solved as a quadratic equation. The solutions of this equation are x = 5 and x = -8. But, since dimensions cannot be negative, the width of the room is 5 feet.
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?Write the equation in standard form. Then factor the left side of the equation.? 2x2 = 28 – x A.) (2x + 7)(x – 4) = 0 B.) (2x – 7)(x + 4) = 0 C.) (2x + 4)(x + 7) = 0 D.) (2x – 4)(x + 7) = 0
2x² = 28 - x
2x²+x-28=0
2x²+8x-7x-28=0
2x(x+4)-7(x+4)=0
(x+4)(2x-7)=0
(2x-7)(x+4)=0
B.) (2x - 7)(x + 4) = 0
A bag contains 56 marbles 7 red , 8 green , 11 yellow , 17 brown and 13 blues if a marble is chosen at random what is the probability that the marble is green
Answer:
The probability is 1/7 or 14.29%
Step-by-step explanation:
In order to find this, divide the number of marbles that are green by the total number.
8/56 = 1/7 = 14.29%
Which term applies when using the method shown to determine if two ratios are proportions
Answer:
I think that there is a part of your question that is missing maybe? What is the method shown?
Step-by-step explanation:
Decide whether the rates are equivalent. 126 points every 3 games 210 points every 5 games. What is the answer?
Step-by-step explanation:
To find whether the rates are equivalent or not, we will use proportions.
[tex]\frac{126\text{ points}}{3\text{ games}}=\frac{210\text{ points}}{5\text{ games}}[/tex]
Let us simplify our fractions.
[tex]42\frac{\text{ points}}{\text{game}}=42\frac{\text{ points}}{\text{game}}[/tex]
We can see that both unit rates are same, therefore, the rates are equivalent and equal to 42 points per game.
Will someone please help me solve this? A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?
Answer:
104 boxes109 boxes218 boxesStep-by-step explanation:
Let b represent the number of boxes of cookies sold the first week. Then b+5 boxes were sold the second week, and 2(b+5) boxes were sold the third week. The total sold was ...
b +(b+5) +2(b+5) = 431
4b +15 = 431 . . . . . . simplify
b = (431 -15)/4 = 104 . . . . . subtract 15, divide by the coefficient of b
First week: b = 104
Second week: b+5 = 109
Third week: 2(b+5) = 218
PLEASE I NEED HELP WITH THIS ONE...I THINK IT IS EITHER A. OR D.
Which of the following is a step in constructing a circle inscribed in a triangle?
A. Construct the perpendicular bisectors of each side.
B. Use a compass to locate the midpoint of each side.
C. Construct the angle bisectors of each side.
D. Use a compass to locate the altitude of each side.
Answer:
Step-by-step explanation:
i'm saying A is the correct answer
Please help!!!
Which best explains the relationship between the two triangles below?
Answer:
1. [tex]\Delta ADC\sim \Delta RTS[/tex] because [tex]\angle A\cong \angle R[/tex], [tex]\angle C\cong \angle S[/tex] and [tex]\angle D\cong \angle T[/tex]
Step-by-step explanation:
We have been given two triangles [tex]\Delta ADC[/tex] and [tex]\Delta RTS[/tex]. We are asked to find the relationship between these triangles.
By angle sum property let us find measure of angle C of triangle ADC.
[tex]m\angle C+m\angle D+m\angle A=180^{o}[/tex]
[tex]m\angle C+51.2^{o}+96.5^{o}=180^{o}[/tex]
[tex]m\angle C+147.7^{o}=180^{o}[/tex]
[tex]m\angle C=180^{o}-147.7^{o}[/tex]
[tex]m\angle C=32.3^{o}[/tex]
Let us find measure of angle T of triangle RTS.
[tex]m\angle T+m\angle R+m\angle S=180^{o}[/tex]
[tex]m\angle T+96.5^{o}+32.3^{o}=180^{o}[/tex]
[tex]m\angle T+128.8^{o}=180^{o}[/tex]
[tex]m\angle T=180^{o}-128.8^{o}[/tex]
[tex]m\angle T=51.2^{o}[/tex]
We can see that [tex]m\angle C=m\angle S[/tex], [tex]m\angle A=m\angle R[/tex] and [tex]m\angle D=m\angle T[/tex]. Therefore, [tex]\Delta ADC\sim \Delta RTS[/tex] and 1st option is the correct choice.
How do you solve this problem?
What is the length of a radius of the circle represented by the equation x^2+y^2-4x+4y=0 ?
Will award brainliest for best explanation.
so, if you checked the link above, you know what we'll be doing, lemme run through it without much fuss.
[tex]\bf \stackrel{\textit{firstly some grouping}}{(x^2-4x)+(y^2+4y)=0}\implies (x^2-4x+\boxed{a}^2)+(y^2+4y+\boxed{b}^2)=0 \\\\[-0.35em] ~\dotfill\\\\ 2\cdot x\cdot \boxed{a}=4x\implies \boxed{a}=\cfrac{4x}{2x}\implies \boxed{a}=2 \\\\\\ 2\cdot y\cdot \boxed{b}=4y\implies \boxed{b}=\cfrac{4y}{2y}\implies \boxed{b}=2[/tex]
now, let's recall, we're simply borrowing from our very good friend Mr Zero, 0, so if we add whatever, we also have to subtract whatever.
[tex]\bf (x^2-4x+2^2-2^2)+(y^2+4y+2^2-2^2)=0 \\\\\\ (x^2-4x+2^2)+(y^2+4y+2^2)-4-4=0 \\\\\\ (x-2)^2+(y+2)^2-8=0\implies (x-2)^2+(y+2)^2=8 \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-2)^2+(y+2)^2=(\sqrt{8})^2\qquad \impliedby radius=\sqrt{8}[/tex]
A set of cards includes 24 yellow cards, 18green cards, and 18 blue cards. What is the probability that a card chosen at random is not green ?
Answer: 70%
Step-by-step explanation:
Quadrilateral MATH is a square. If MA = 2x – 5 and AT = x + 10, find the perimeter of the square.
Answer:
Perimeter of the square MATH = 100.
Step-by-step explanation:
Given that MATH is a square, it means all sides would be equal to each other.
Given MA = 2x - 5 and AT = x + 10.
we know all sides are equal, so MA = AT.
2x - 5 = x + 10
2x = x + 10 + 5
2x = x + 15
2x - x = 15
x = 15
So, AT = x + 10 = 15 + 10 = 25.
Now the perimeter would be (MA + AT + TH + HM) = 4*AT = 4*25 = 100.
Hence, option D is the correct answer i.e. 100.
Answer:
100
Step-by-step explanation:
Sides of a square are congruent.
2x – 5 = x + 10
x = 15
Sides = 2(15) – 5 = 25
Perimeter = 25 + 25 + 25 + 25 = 100
Lola rode her bike for 7/10 of an hour on Saturday and 3/5 of an hour on Sunday.How much longer did she ride her bike on Saturday than Sunday?
Answer:
1/10 of an hour
Step-by-step explanation:
3/5 in a decimal is 6/10 and 7/10 - 6/10 is 1/10 of an hour
5a + 5b + 5c + 5d
Which expression is another way to write the expression shown here?
A) 5abcd
B) 5a + bcd
C) 5(a + b + c + d)
D) (5a)(5b)(5c)(5d) what the answer
Answer:
c
Step-by-step explanation:
Linnea's company's revenue in 20172017 is \dfrac{36}{25} 25 36 ? of its revenue in 20162016. What is Linnea's company's revenue in 20172017 as a percent of its revenue in 20162016 ?
Answer:
144%
Step-by-step explanation:
We are told that Linnea's company's revenue in 2017 is 36/25 of its revenue in 2016..
To find the Linnea's company's revenue in 2017 as a percent of its revenue in 2016, we will have to figure out 36 is what percent of 25.
[tex]\text{Percent}=\frac{36}{25}\times 100[/tex]
[tex]\text{Percent}=36\times 4[/tex]
[tex]\text{Percent}=144[/tex]
Therefore, Linnea's company's revenue in 2017 is 144% of its revenue in 2017.
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Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together. Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.
Answer:
t = 6 4/25 hours
Step-by-step explanation:
The formula to find out how long it takes them to do the job is
1/m + 1/ a = 1 /t
where m is the time for Matthew to do the job
a is the time for Arianna to do the job
and t is the time for them to do the job together
m = 14 hours
a = 11 hours
Substituting what we know
1/14 + 1/11 = 1/t
Multiplying by 154t (14*11*t) so we can clear the fractions
154t*(1/14 + 1/11) = 1/t* 154t
11t + 14t = 154
Combine like terms
25t = 154
Divide by 25
t = 154/25
t = 6 4/25 hours