Answer:
14.43 years
Step-by-step explanation:
FV = PV (1+i)^n
FV = future value = 15100 PV = present value = 6000
i = period interest in decimal = .065/2 = =.0325
n = periods = the question
15100 = 6000(1+.0325)^n
solve for n = 28.86 periods or 14.43 years (each period is 6 mos)
The height of an object launched into the air can be modeled by the graph shown.
Enter your answer as a number, like this: 42
The maximum height reached by the object is 12.5 feet.
Describe Parabola?The vertex of a parabola is the point where the curve changes direction, and is located at the minimum or maximum point of the quadratic equation. If the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents a minimum value. If the coefficient is negative, the parabola opens downwards and the vertex represents a maximum value.
To find the maximum height reached by the object, we need to find the vertex of the parabola.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of the x² term, and b is the coefficient of the x term in the quadratic equation that represents the parabola.
In this case, the equation is of the form y = ax² + bx + c, where y is the height and x is the time. Using the given coordinates, we can set up a system of equations to solve for a, b, and c:
0 = a(1)² + b(1) + c
16 = a(5)² + b(5) + c
0 = a(9)² + b(9) + c
Simplifying each equation, we get:
a + b + c = 0
25a + 5b + c = 16
81a + 9b + c = 0
Solving for c in the first equation, we get c = -a - b. Substituting this into the other two equations, we get:
25a + 5b - a - b = 16
81a + 9b - a - b = 0
Simplifying these equations, we get:
24a + 4b = 16
80a + 8b = 0
Solving for b in the second equation, we get b = -10a. Substituting this into the first equation, we get:
24a + 4(-10a) = 16
4a = 2
a = 1/2
Substituting this value of a into the equation b = -10a, we get b = -5. Finally, substituting a, b, and c = -a - b into the equation for the x-coordinate of the vertex, we get:
x = -b/2a = 5
So the maximum height is achieved at time x = 5, which corresponds to a height of:
y = ax² + bx + c = (1/2)(5)² - 5(5) = -12.5
However, we are looking for the maximum height, so we take the absolute value of this result, which gives:
|y| = 12.5
Therefore, the maximum height reached by the object is 12.5 feet.
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simplify this expression
6x -8y -5x + 3y
Answer:
x-5y
Step-by-step explanation:
combine the X's and Y's
10 in
12 in
6 in
8 in
Surface Area =
I need the surface area
Answer: the answer is 312in
Find the two square roots of 121.
Answer:
11 and -11
Step-by-step explanation:
This problem can really only be solved either by way of a calculator or simple memorization. In this case, the product (121) is a perfect square root, meaning it has a whole number answer. One square root of 121 is 11. The second square root of 121 is -11.
[tex]\sqrt{121} = 11[/tex]
[tex]\sqrt{121} = -11[/tex]
You can check your work by squaring your answer and seeing whether it equals the product. Remember, a negative number times another negative number results in a positive answer.
[tex]11^{2} = 121[/tex]
[tex]-11^{2} = 121[/tex]
The two square roots of the number 121 are 11 and -11.
The square root of a number is a value that, when multiplied by itself, gives the original number.
In the case of 121, the square root represents the number that, when multiplied by itself, equals 121.
The two square roots of 121 are 11 and -11 because both 11 and -11, when squared, result in 121.
When we calculate 11 × 11, we get 121.
So, 11 is one of the square roots of 121.
Similarly, when we calculate (-11) × (-11), we also get 121. So, -11 is also a square root of 121.
Therefore, the two square roots of 121 are 11 and -11.
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the price of a video game was reduced from 65 to 45.50. by what percent was the price of the video games reduced
Bill gets a raise of 10% in his salary find the original salary if his salary after the raise is 4510
Bobby has a party while his parents are away for the weekend. Bobby estimated that if his 9 friends hep him to clean the house, they will finish in time if they start 8 hours before his parents return. But after only two hours of cleaning, Bobby's parents call and say they are just two hours from home. How many more friends does Bobby need to call to help finish cleaning in time.
Using an inverse rule of three, it is found that Bobby needs to call 18 more people.
What will be the number of friends?This question is solved by proportions, applying a rule of three.The number of people working and the time needed to complete the work are inversely proportional, as more people means less time, thus, instead of cross multiplication, we multiply the lines, which is an inverse rule of three.When Bobby's parents call, with 9 people, they will need 6 hours to finish the job. How many people are needed to finish the job in 2 hours?
The rule of three is:
9 people - 6 hours
x people - 2 hours.
Multiplying by line:
2x = 6 x 9
x = 3 x 9
x = 27
Already has 9 people, in total needs 97, so he needs to call 27 - 9 = 18 more people.
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Which type of function is shown in the table below?
Answer:
Exponential
Mark brainliest :)
four plastic bottles, each with a radius of 2 inches, are packed into a cardboard box. The glasses touch each other and the sides of the box. What is the area of the bottom of the box? (The area of a circle is equal to pi times radius squared)
The area of a 2D form is the amount of space within its perimeter. The area of the bottom of the box is 64 square inches.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or other quadrilateral, multiply its length by its width.
Given the radius of the base of the plastic bottle is 2 inches, and there are four bottles arranged as shown below, therefore, the area of the bottom of the box is,
[tex]\rm \text{Area of the bottom of the box} = 8 \times 8 = 64\ in^2[/tex]
Hence, the area of the bottom of the box is 64 square inches.
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1. Reflect triangle A across the line x = 2.
2. Write a single rule that reflects triangle A across the line x = 2.
PLEASE HELP
I only have till tomorrow midnight to turn this in
Draw a perpendicular at x=2
Now reflect each coordinates across there
(2,2)
Will remain same as x=2 is on Q1 positive side(8,4)
x coordinate=2-8=-6y coordinate=4(same)New coordinate (-6,4)
(6,8)
x coordinate=2-6=-4 y coordinate is sameNew coordinate
(-4,8)Answer:
Rule: Reflect the figure across the y-axis then translate the reflected figure 4 units to the right.
Step-by-step explanation:
Part 1Points of Figure A:
(2, 2)
(8, 4)
(6, 8)
Draw a line at x = 2, then reflect each point across the line
(2, 2) → (2, 2)
(8, 4) → (-4, 4)
(6, 8) → (-2, 8)
Part 2Reflection in the y-axis: (x, y) → (-x, y)
As the y-values of our two figures have not changed, the first part of the rule is: reflect across the y-axis
If we reflect the figure across the y-axis, the points of the reflected figure are:
(-2, 2)
(-8, 4)
(-6, 8)
To bring the reflected figure back to where we want it (reflection in x = 2) we need to translate the figure 4 units to the right:
(-2 + 4, 2) = (2, 2)
(-8 + 4, 4) = (-4, 2)
(-6 + 4, 8) = (-2, 8)
So the final rule is:
Reflect the figure across the y-axis then translate the reflected figure 4 units to the right.
2.
You draw five cards from a standard deck of 52 cards. P(heart) =
5
of probability is illustrated and why?
(1 point)
What type
Step-by-step explanation:
Prob. of at least one heart when drawing 5 cards from a full deck
= 1 - prob(no hearts at all)
= 1 - C(39,5) / C(52,5)
= .7785
hhhhhhhhhhhhhhhhhhhhh
Answer:it should be b!
Step-by-step explanation:
I’m pretty sure I had the question before
Write 1/2 as a percent.use repeating decimals when necessary.
Answer:
50%
Step-by-step explanation:
1 / 2 = 0.5
to turn a decimal to a percent you multiply it by 100
0.5 x 100 = 50%
Item 5
What is the correct classification for ∠JML?
obtuse
straight
right
acute
Ray M J and Ray M L are connected at point P, forming angle J M L. A ray M K sharing the same point forms a bisector. A ray M H also sharing the same point from the diagonally down from the right. The angle J M K measure 41 degrees and angle L M H measure 132 degrees.
∠JML is a right angle. The correct option is your third option- right
Determine the types of anglesThere are different types of angles which include
Acute: An acute angle is less than 90°Obtuse: An obtuse an angle is greater than 90° but less than 180° Straight: A straight angle equals 180° Right: A right angle equals 90°In the given diagram, we can observe that ∠JML equals 90°
Hence, ∠JML is a right angle. The correct option is your third option- right
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What is the value of c? Round to the nearest tenth.
Answer:
30%
Step-by-step explanation:
If [tex]f(x)=[[x+2]][/tex] find [tex]f(1.5)[/tex]
Please Explain Answer Please. Thank you!
Answer:
f ( 1.5 ) = 1.5 + 2 = 3.5
If in the case you need any other help , let me know. [ You need to pay me] :) Thanks!
Answer: ⇒ 3.5
Step-by-step explanation:
⇒ f(1.5) = 1.5 + 2
⇒ f(1.5) = 3.5
help me with this algebra equation
Answer:
it's D
Step-by-step explanation:
it's d because i guessed it was
PLease Help me its a math question Is the function represented by the following table linear, quadratic or exponential?
Answer:
Exponential
Step-by-step explanation:
From the table :
3⁰ = 13¹ = 33² = 93³ = 273⁴ = 81Hence, the function is :
y = 3ˣAs the x-value is an exponential value, the function is exponential
Is the function represented by the following table linear, quadratic or exponential?
Linear
Quadratic
ExponentialExplanation:
HEEEEEEEEEEEEEEEEEEEEEEEEEEELP!
Answer: It's a 180 degree angle.
Step-by-step explanation:
Help pls i cant get bad grades!!!!!!!!!
Answer:
bread
Step-by-step explanation:
If you get bad grades study :v
The cost of 4 sweatshirts and 10 pairs of shorts is $188. The cost of 9 sweatshirts and 12 pairs of shorts is $276.
Enter the cost of one sweatshirt and one pair of shorts in the response boxes
Answer: The cost of one sweatshirt is $12 and the cost of one short is $14
Step-by-step explanation:
x= sweat shirt cost
y= shorts cost
4x + 10y = 188
9x+2y=276
x= 12, y=14
when the number in pattern H is 48 what is the corresponding term in pattern G
Answer:
explain it better please
Toni bought these items for
an art project. The sales tax
is 8.5%. What is the total cost including tax, rounded to the nearest cent?
Answer: D, 43.38
Step-by-step explanation:
add all of the items up and then divide by sales tax percent. then add up the original number by the sales tax amount
6 Three of the ten people in the Latin club are chosen at random to represent the club at a tournament. What is the probability that Joseph, Heidi, and Katy are chosen?
The probability that Joseph, Heidi, and Katy are chosen is 1/40 if three of the ten people in the Latin club are chosen at random to represent the club at a tournament option (G) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Total ways of choosing 3 out of 10 = C(10, 3) = 120
Total outcomes = 120
Total favorable outcomes = 3(Joseph, Heidi, and Katy)
Probability = 3/120 = 1/40
Thus, the probability that Joseph, Heidi, and Katy are chosen is 1/40 if three of the ten people in the Latin club are chosen at random to represent the club at a tournament option (G) is correct.
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What can be said about the velocities of two cars that are both going 60 mph heading in opposite directions?
Answer:
0
Step-by-step explanation:
because they are heading in the same direction
Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
Share what you already know about third grade math.
Answer:
6×6=36
Step-by-step explanation:
2×3=5
6×10=60
50×10=50
Mixed Applications
Write an equation using the variable n. Then solve and check the solution.
42) If a number, n, divided by 8 equals 2.5, what is n?
43) The sum of a number, n, and 6.05 is 12.4. What is n?
44) Stacy is one-fourth as old as her mother. If Stacy's mother is
36, how old is Stacy?
45) One-third of a painting job takes 24 hours. How long will it take to finish the entire job?
Number Sense: Estimation
Use compatible numbers to estimate the solution.
46) 6b = 110
47) 4n = 159
48) 14/x = 5
The solution to the given question will be:-
A) If a number, n, divided by 8 equals 2.5, what is n: n = 20
B) The sum of a number, n, and 6.05 is 12.4. What is n: n = 6.35
C) Stacy is one-fourth as old as her mother. If Stacy's mother is
36, how old is Stacy: 9 years
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
A) If a number, n, divided by 8 equals 2.5, what is n?
n / 8 = 2.5
n = 8 x 2.5 = 20
B) The sum of a number, n, and 6.05 is 12.4. What is n?
n + 6.05 = 12.4
n = 12.4 - 6.05 = 6.35
C) Stacy is one-fourth as old as her mother. If Stacy's mother is
36, how old is Stacy?
(1 / 4) M[tex]_{age}[/tex] = S[tex]_{age}[/tex]
S[tex]_{age}[/tex] = ( 36 / 4)
S[tex]_{age}[/tex] = 9 years
Therfore the answers are n = 20 ,n = 6.35, S[tex]_{age}[/tex] = 9 years
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Find a factor pair of 80 that has a sum of 21.
Answer:
16 and 5
Step-by-step explanation:
Hope that helps! :)
What is the area of a square with sides of length 2 1/2 cm?
The area of the square with the sides 2 1/2 cm will be A=6.25 square cm.
What is the area?The space covered by the square in the two-dimensional plane will be the area of the square. Square actually covers the area with four equal sides.
The formula for the area of the square will be given as:-
A=Side x Side
A= 2 1/2 x2 1/2
A=5/2x5/2
A=2.5x2.5
A= 6.25 square cm
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