Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y=-7x2 + 26x + 6 and
y=-6x2 + 25x + 4 where y represents the height in meters and x represents the time in seconds after the launch. What is the time in seconds that the balloons
collided at the highest point?
O 1.75 seconds
O 20 seconds
O2 25 seconds
O 2.5 seconds
The time in seconds that the balloons collided at the highest point is; B: 2.0 seconds
What are quadratic equations?We are told that the water balloons were modeled by the quadratic functions:
y = -7x² + 26x + 6 and y = -6x² + 25x + 4
where;
y = the height in meters
x = the time in seconds after the launch
The time at which they will collide has to be at the same height.
Thus;
-7x² + 26x + 6 = -6x² + 25x + 4
Rearranging this gives;
x² - x - 2 = 0
Using online quadratic equation solver gives us x = 2 or -1. We will take the positive one as x = 2.0 seconds
Read more about quadratic equations at; https://brainly.com/question/1214333
Answer:
the answer is 2.0 seconds
Step-by-step explanation:
I just took the test:)
The price of an item yesterday was $140 today the price is $343 what’s the percentage increase
Answer:
145% increase
Step-by-step explanation:
1) 343 - 140 = 203
2) 203/140 = 1.45
3) 1.45 x 100 = 145
After all tryouts are completed, the school will be hosting a party for all the new athletes. At the party, hot dogs and hamburgers will be provided to all athletes and their guests, if they choose to bring a guest. The ratio of hot dogs purchased to number of guests is 1:0.8. Determine how many hot dogs you would need if 150 people attend the party. Explain how you found your answer.
120 hotdogs would be served if 150 people attend the party.
RatioA ratio is the quantitative relationship between two value, showing how many times one number contains another.
The ratio of hot dogs purchased to number of guests is 1:0.8. For 150 people:
Number of hotdogs = 150 * 0.8/1 = 120 hotdogs
Therefore 120 hotdogs would be served if 150 people attend the party.
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Can you help with this problem?
Find the area.
Answer:
132 sq cm
Step-by-step explanation:
There is a rectangle on top of your shape and a trapezoid below.
Area of a rectangle:
A = length•width
A = 7•4
A = 28sq cm
Area of a trapezoid:
A= 1/2(b_1 + b_2)•h
A=1/2(19 + 7)•8
=1/2(26)•8
=13•8
=104 sq cm
Area of total:
A_rect + A_trapzd
=28 + 104
= 132 sq cm
Use the four-step definition of the derivative to find f'(x) if f(x)= -3x^3 + 10.
Please help me, A candle is in the shape of a frustum (a cone with the top cut off). Calculate the volume of the candle to the nearest tenth of a cubic centimetre.
Answer:
Height = 8 cm
You will need this formula (see attached):
Volume = [PI * 8 * (2² + 2*4 + 4²)] / 3
Volume = [3.14159265 * 8 * (4 + 8 + 16)] / 3
Volume = 234.57 cubic centimeters
Source: http://www.1728.org/volcone.htm
Step-by-step explanation:
John and Jane are two brands of shoes. John sells for R7, 20 for 8 pairs while Jane sells for R7, 76 for 9 pairs. Which brand is the cheapest?
Answer:
Jane
Step-by-step explanation:
because she sells 9 pairs for 7,76
F(x)x^2-x+3 find f(x+2)
Answer: =7
Step-by-step explanation:
A circular garden is enlarged so that the new diameter is twice the old diameter. What is the ratio of the original area to the enlarged area? Express your answer as a common fraction.
I do not understand WHY the answer is 1/4 I do not understand why it is k^2 and all that. HELP I am giving LOTS of points
Answer:
Explained briefly below.Step-by-step explanation:
For old circular garden:
take the radius as r.
then use the formula to find area of circle: πr² ......this is old garden area.
For new enlarged garden:
the radius is twice the old radius so, radius = 2 * r = 2r ......enlarged radius
now find area for this new garden: π(2r)² → 4πr²
In common fractions: (old garden)/(new garden)
: ( πr² ) / ( 4πr² )
: 1/4
Answer:
1/4Step-by-step explanation:
Original diameter is d and new diameter is D and:
D = 2dArea of original circle:
A₁ = πd²/4Area of enlarged circle:
A₂ = πD²/4 = π(2d)²/4 = πd²The ratio of areas:
A₁ / A₂ =πd²/4 ÷ πd² = 1/4 ÷ 1 = 1/4a
triangle
The measure of the First angle of
is 25 degree less than the measure of the
Second angle. The measure of the third angle
of the triangle is triple the measure of the
second angle.
Alright, lets say the measure of the 3rd angle (the smallest one) is x degree, then measure of the 1st angle will be (x + 25) degree, and 2nd one: 3x degree. The sum of all the angles in any triangles is 180 degrees.
(x + 25) + 3x + x = 180
5x + 25 = 180 ---> 5x = 180 - 25 ---> 5x = 155 ---> x = 155/5 ---> x = 31o (third angle)
31 + 25 = 56o (first angle)
3 × 31 = 93o (second angle)
56 + 93 + 31 = 180
Use one-variable equations and inequalities to fill in the graphic organizer
Answer:
when you dont know what to do what do you do? Do you just stand there and act like nothing is happening when something is actually happening dont do that just stand still and wait for it to come to you its your chance dont be left out you go this dont be scared you go this go go go go go go go go go gog og go go ogg og og og og og og og og o
Step-by-step explanation:
9. Which is the quadratic equation the
best fits the scatterplot?
A. f(x) = x² – 8x + 22
B. f(x)=-X2 – 8x-10
C. f(x)=-x? + 8x - 32
D. f(x)=-x? + 8x-10
Answer:
c
Step-by-step explanation:
3
Suppose that a very la: Enter your search term
cameras and that of them are defective. A sample of 2 cameras is
8
selected at random. Define the random variable X as the number of defective cameras in the sample.
a. Write the probability distribution for X. Round to two decimal places.
X
P(X)
b. What is the expected value of X? Round to two decimal places.
Preview
Answer:
you were present when a senor student bullied a junior one. describe what happened to the teacher on duty
Ann wants to set up chairs in rows of 8. If she sets 14 rows, how many seats will she have?
Answer:
112
Step-by-step explanation:
8×14 if each row has 8 chairs, and there's 14 rows that means 8×14 which equals 112 :)
Answer:
14 x 8=112
8 chairs are row multiply by the of rows
If one cubic foot of water weighs 62 1/2 pounds how much do 3 1/5 cubic feet of water weighs?
Answer:
3 1/5 cubic feet of water weighs 200 pounds
Step-by-step explanation:
1. Take 62 1/2 into decimal form: 62 1/2 = 62.5
2. Take 3 1/5 into decimal form: 3 1/5 = 3.2
3. Multiple 62.5 by 3.2: 62.5 x 3.2 = 200
The answer is 200 pounds.
What is 48(2)+1=
Please answer
Answer:
97
Step-by-step explanation:
48 ( 2 )
= 48 x 2
= 96
48 ( 2 ) + 1
= 96 + 1
= 97
Answer:
97
Step-by-step explanation:
Given the following question:
[tex]48(2)+1[/tex]
In order to find the answer, we apply the rule where 48(2) = 48 × 2
[tex]48(2)+1[/tex]
[tex]48(2)=48\times2[/tex]
[tex]48\times2=96[/tex]
[tex]96+1[/tex]
[tex]96+1=97[/tex]
[tex]=97[/tex]
Hope this helps.
Match the simplified version of the number given. Note: You do not need to find the opposite for the number, just the simplified number. Use the following clues:
The opposite of a positive number is a negative number and vice versa.
The opposite of the opposite of a positive number is a positive number.
The opposite of the opposite of a negative number is a negative number.
1. -(-75)
-20
2. -(87)
-75
3. -(20)
75
4. -(-20)
-12
5. -(12)
12
6. -(-12)
20
7. -(75)
-87
8. -(-(87)
87
The matching forms of the numbers are as represented below upon evaluation;
-(-75) = 75-(87) = -87-(20) = -20-(-20) = 20-(12) = -12-(-12) = 12-(75) = -75-(-87) = 87Opening up parenthesisThe given numbers can be simplified by opening up the parenthesis as indicated above in which case,
The product of 2 negatives equals a positive signThe product of ,a negative and positive equals negative.Read more on parenthesis;
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What is the solution to the system of equations?
-1/2x+1/2y=-1
x-y=2
a. There is no solution.
b. There are infinitely many solutions.
c. There is only one solution, (3, 1).
d. There is only one solution, (–6, –8).
Answer:
b. infinite solutions
Step-by-step explanation:
[tex]-\frac{1}{2}x+\frac{1}{2}y=-1\\\\\textsf{subtract} \ -\frac{1}{2}y \ \textsf{from both sides:}\\\\\implies -\frac{1}{2}x=-1-\frac{1}{2}y\\\\\textsf{mulitply both sides by -2:}\\\\\implies x=2+y\\\\\textsf{subtract} \ y \ \textsf{from both sides:} \ x-y=2[/tex]
Therefore, the graphs are the same.
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.
Answer:
There's one solution (2,0)
Hope this helps!
can you please solve this question please
Answer:
false
Step-by-step explanation:
x=1
4+24= 24
28=24
flase
PLEASE HELP ASAP!!!!( 50 POINTS)
Chef Alfredo invested $4800 at a simple interest rate of 5% and can now afford a $6,000 state-of-the-art pizza
oven. How many years ago did he make this investment? Show all your work and answer in a complete sentence.
Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. she buys 2 more cans. how many tennis balls does she now have?
Answer: 12 tennis balls
Step-by-step explanation: 4 cans of 3 tennis balls. 4 times 3 is 12.
It's actually 12.
He e is. Dis is vedy gude ansed.
On Monday, Janelle earned $21 for 7 hours of babysitting. Getting paid the
same rate, she earned $48 for babysitting on Saturday. How many hours
did Janelle babysit on Saturday? *
Answer:
16
$21 ÷ 7 = 3
which means she get $3 each hour she babysit
$48 ÷ 3 =16
Step-by-step explanation:
hope it helps
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3. Choose the single logarithmic expression that is equivalent to the one shown.
log; 4 - log2
log 2
O
log 4
O
log, 2
log, 3
Answer:
log, 2
Step-by-step explanation:
the answer is log, 2 or c
The solution of the single logarithmic expression that is equivalent to the one shown is,
⇒ log₃ 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ log₃4 - log₃2
Now, We can simplify as;
⇒ log₃4 - log₃2
⇒ log₃4/2
⇒ log₃ 2
Thus, The solution of the single logarithmic expression that is equivalent to the one shown is,
⇒ log₃ 2
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In rectangle KLMN, KM = 9x+26 and LN = 84.5. Find the value of x.
Answer:
x = 6.5
Step-by-step explanation:
square is rectangle
9x+26 = 84.5
84.5 - 26 = 58.5
9x = 58.5
x = 58.5 divided by 9
x = 6.5
this one too please help me learn math
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
equation of a circle: [tex](x - h)^2+(y-k)^2=r^2[/tex]
where (h, k) = center and r = radius
From inspection, we can see that the center of the circle = (0, 0)
and the radius = 1
[tex]\implies (x - 0)^2+(y-0)^2=1^2[/tex]
[tex]\implies x^2+y^2=1[/tex]
Substitute [tex]y=\frac{\sqrt{3}}{2}[/tex] into [tex]x^2+y^2=1[/tex] and solve for [tex]x[/tex]:
[tex]\implies x^2+(\frac{\sqrt{3}}{2})^2=1[/tex]
[tex]\implies x^2+\frac{3}{4}=1[/tex]
[tex]\implies x^2=\frac{1}{4}[/tex]
[tex]\implies x=\pm \sqrt{\frac{1}{4}}[/tex]
[tex]\implies x=\pm\frac{1}{2}[/tex]
As point P is in quadrant 1, [tex]x[/tex] is negative, so [tex]x=\frac{1}{2}[/tex]
Layla is baking a Double Chocolate Chocolate Chip cake. For this recipe, she will need one bag of flour and a number of bags of chocolate chips. At the grocery store, she sees that a bag of flour costs $3.59 and each bag of chocolate chips, c, costs $2.75. Write an algebraic expression to represent the total amount she will spend at the store.
Answer:
2.75c +3.59
Step-by-step explanation:
She only needs one bag of flour so it is a constant 3.59. She needs multiple bags of chocolate chips which is unknown so that will be c times the 2.75 for each bag
*will give brainliest for best answer*
The measure of an angle is 3°. What is the measure of its complementary angle?
Answer:
87
Step-by-step explanation:
3+87=90, whatever angle adds up to 90 is complimentary
Write 1,386 as the product of its prime factors.
Answer:
. A prime factor of x is a prime number that divides x correctly (so that the rest is equal to 0). 1386 = 2*3*3*7*11 in our situation. This result can be obtained by dividing the number (1386) by 2, 3, 5, 7, 11, and so on. You utilise the result you get every time you successfully divide it by a prime number (beginning with 2) and try to divide it using the same approach. When you can no longer divide a number by a prime number, you go on to the next prime number and try to divide it by that number. Finally, you multiply the prime numbers by which you were able to divide your number.
Step-by-step explanation:
Answer: We know the prime factorization of a number is the representation of a number in terms of multiples of its factors. Now to simplify the above factorization by applying the exponent rule to make the prime factorization simplest. So, the correct answer is “ $ \ 1386 = 2 \times {3^2} \times 7 \times 11 $ ”.
Step-by-step explanation:
Hope it helped you<3
How many is x - 87 = 13 just answer pls
Answer:
100
Step-by-step explanation:
I hope this helps you
?????????? WHAT ??????????
Answer:
Side of the square (a) = 3½ = 7/2 m
Area of the square
= a²
= (7/2)²
= 49/4
= 12.25 m²
Hope it helps ⚜