If f(x) = 2/3x^2 +8 , what is the value of f(6)?
Answer:
f(6) = 32
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 2/3x² + 8
f(6) is x = 6
Step 2: Evaluate
Substitute in x: f(6) = 2/3(6)² + 8Exponents: f(6) = 2/3(36) + 8Multiply: f(6) = 24 + 8Add: f(6) = 32Answer:
f(6)= 72
Step-by-step explanation:
f(6)= 72
to evaluate:
substitute x = 6 into
f(x)f(6)= 23 × (6) 2 + (8×6)×x = 231 × 3612+ 48
For what values of is the quadratic
function f (c)=22 – 20 – 24
positivie
Answer:
5485/45
Step-by-step explanation:
Approximate the correlation of the data shown below?
a. 1
b. 0
c. -0.5
d. -1
Answer:
Step-by-step explanation:
The required correlation of the data is given by -0.5. Option C is correct.
Given that,
To determine the approximate correlation of the data shown,
A statistical measure known as correlation expresses how closely two variables are related linearly.
here,
Draw a constant line from the first point to the last point,
Which shows a decreasing slope of -0.5. So it is the approximate correlation of the data given.
Thus, the required correlation of the data is given by -0.5. Option C is correct.
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midpoint between 10,0
Answer:
The correct answer is 5
Step-by-step explanation:
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Elijah started a college fund of $25,000 for a term of five years.The interest rate is 2.9 percent annually.How much interest will he have earned at the end of the term?
Answer:
Interest = Principal x rate x time
I = 25000(.029)(5) = $3,625
Step-by-step explanation:
Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?
Grayson is drawing a two dimensional shape and its dilation in a coordinate plane. Which attribute of this
shape will remain unchanged?
Answer:
area
Step-by-step explanation:
_____ is 1/10 of 0.07?
I have no idea what the blank is...help me. :(
How many solutions does 5(x+9)=5x+45 have
Answer:
Simplifying
5(x + 9) = 5x + 45
Reorder the terms:
5(9 + x) = 5x + 45
(9 * 5 + x * 5) = 5x + 45
(45 + 5x) = 5x + 45
Reorder the terms:
45 + 5x = 45 + 5x
Add '-45' to each side of the equation.
45 + -45 + 5x = 45 + -45 + 5x
Combine like terms: 45 + -45 = 0
0 + 5x = 45 + -45 + 5x
5x = 45 + -45 + 5x
Combine like terms: 45 + -45 = 0
5x = 0 + 5x
5x = 5x
Add '-5x' to each side of the equation.
5x + -5x = 5x + -5x
Combine like terms: 5x + -5x = 0
0 = 5x + -5x
Combine like terms: 5x + -5x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions
Step-by-step explanation:
What is the area?
Please help
The 3 x 5 matrix shows the number of sandwiches sold over five days at the school canteen. What does the number tell you which is: (06 Marks) (a) in the second row and the third column (b) in the third row and the fourth column (c) in the first row and the fifth column M T W T F Cheese 50 45 52 47 39 Salad 61 44 48 38 51 Chicken 53 46 39 42 52
Answer:
a. 48 salads were bought on Wednesday
b. 42 chickens were bought on Thursday
c. 39 cheese were bought on Friday
Step-by-step explanation:
Given
[tex]------- M -- T - W -- T -- F[/tex]
Cheese ----- 50 -- 45 - 52 - 47 --39
Salad -------- 61 -- 44 - - 48 - 38 -- 51
Chicken ---- 53 -- 46 - - 39 - 42 -- 52
First, it should be noted that the horizontal data represent the row while the vertical data represent the column.
Having said that, the solution is as follows:
Solving (a): Second Row, Third column
The data at the second row are:
[tex]------- M -- T - W -- T -- F[/tex]
Salad -------- 61 -- 44 - - 48 - 38 -- 51
The data at the third column is then limited to:
------------------W
Salad -------- 48
So the number at this position implies that: 48 salads were bought on Wednesday
Solving (b): Third Row, Fourth column
The data at the second row are:
[tex]------- M -- T - W -- T -- F[/tex]
Chicken ---- 53 -- 46 - - 39 - 42 -- 52
The data at the fourth column is then limited to:
------------------- T
Chicken ---- 42
So the number at this position implies that: 42 chickens were bought on Thursday
Solving (c): First Row, Fifth column
The data at the first row are:
[tex]------- M -- T - W -- T -- F[/tex]
Cheese ----- 50 -- 45 - 52 - 47 --39
The data at the fifth column is then limited to:
------------------F
Cheese ----- 39
So the number at this position implies that: 39 cheese were bought on Friday
Harry was assigned 75 problems for math homework. Harry did 1/5 of them correctly. How many problems did he get correct?
Answer:
15
Step-by-step explanation:
75 divided by 5
Answer:
15 problems
Step-by-step explanation:
To find how many problems were correct, find 1/5 of 75:
Divide 75 by 5:
75/5
= 15
So, Harry got 15 problems correct.
Write an expression in simplest form the perimeter of the figure ?
Answer:
4+11a+8b
Step-by-step explanation:
1) 4+3a+2b+6b+5a+3a
2) 3a+3a+5a=11a. 2b+6b=8b
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For the past ten years, Michelle has been tracking the average annual rainfall in Boynton Beach, Florida by recording her data in the given table. She has concluded that the relationship can be modeled by a linear function.
Year. Average Rainfall(in inches)
2004. 62.33
2005 61.8
2006 61.27
2007 60.74
2008 60.21
2009 59.68
2010 59.15
2011 58.62
2012 58.09
2013. 57.56
Use the values provided in the table to create a linear graph of the data. On the graph, let x=0 represent the year 2004. Be sure to include all proper labels on the graph.
Answer:
it is decreasing
Step-by-step explanation:
Answer:
Its obviously decreasing
Step-by-step explanation:
Water runs from a pump at a rate of 0.5 gallons per minute. At this rate, how long would it take to fill a tub with a 150-gallon capacity?
Answer:
300 min or 5 hours
Step-by-step explanation:
so if it pumps 0.5 gallons per minute than in 2 minutes it would pump 1 whole gallon so with that we know 1gallon=2 minutes.
so with that we multipy both sides by 150 which will be 150 galons=300 minutes or 5 hours
1. Given the production function: Q = A L½ K½ What returns to scale, does this function exhibit? Why?
Answer:
a. This function therefore exhibits a constant return to scale.
b. The reason is that the sum of the exponents of the multiplicative factor a is equal to 1.
Step-by-step explanation:
The given production function is first correctly stated as follows:
Q = A L^½ K^½ .......................... (1)
In order to know the returns to scale this function exhibits, the input K and L are scaled by the multiplicative factor a which is included in equation (1) as follows:
Q = A (aL)^½ (aK)^½
Q = A a^½L^½ a^½K^½
Q = A a^½ a^½ L^½ K^½
Q = A a^(½+½) L^½ K^½
Q = A a^1 L^½ K^½ ......................... (2)
Based on the equation (2), we now answer the following questions:
a. What returns to scale, does this function exhibit?
This function therefore exhibits a constant return to scale.
b. Why?
The reason is that the sum of the exponents of the multiplicative factor a in equation (2) is equal to 1.
A ball is dropped from a height of 1m. The ball bounces and rebounds, losing 14% of its previous height and then falls again. If the ball continues to rebound and fall in this manner, find the total vertical distance the ball travels until it hits the ground for the 6th time.
9514 1404 393
Answer:
7.51 m
Step-by-step explanation:
The distance traveled to the first floor hit is 1 m. The next hit has a height that is 14% less, so is 100% -14% = 86% = 0.86 times this height. The travel up and down to/from that height is added to the total.
The distance traveled to the second floor hit is 1 m + 2×(0.86×1 m).
The distance traveled to the third floor hit is 1 m + 0.86×2 m + 0.86²×2 m.
Then the distance traveled to the n-th floor hit is ...
-1 m + Sum(0.86^k × 2 m) for k = 0 to n-1
The sum can be found from the formula for the sum of a geometric series:
Sn = a1×(r^n -1)/(r-1) . . . . . where a1 is the first term and r is the common ratio.
For r = 0.86, n = 6, and a1 = (2m), the total distance is ...
vertical distance = -1 m + (2 m)(0.86^6 -1)/(0.86 -1)
= -1 m + (2 m)(-0.5954)/(-0.14) ≈ 7.5062 m
The total distance traveled to the 6th floor hit is about 7.51 meters.
_____
Alternate solution
Another way to answer the question is to add up the distances for each bounce. Attached is a spreadsheet that does that.
If 3/5vof a cup of water fills 3/4 of a plastic container, how much water, in cups, is needed to fill one whole container?
Answer:
3/5 3/4
3/5*4/3=12/15=4/5
4/5 cups of water
because 4/3 is the reciprocal of 3/4 and so 3/4*4/3=1
What is the composition of the translations (T ∘ T ) (x, y) as one translation
Answer:
Step-by-step explanation:
Which function represents the graph below?
1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15
Answer:
[tex]\frac{4+16a^3+23a^3}{a^2}[/tex]
Step-by-step explanation:
Given
[tex]1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15[/tex]
Required
Simplify
[tex]1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15[/tex]
Collect Like Terms
[tex]1/a^2 + 1/a^2 + 2/a^2-3a-5a-8a+2+6+15[/tex]
[tex]1/a^2 + 1/a^2 + 2/a^2-16a+23[/tex]
Add Fractions:
[tex]\frac{1+1+2}{a^2} + 16a + 23[/tex]
[tex]\frac{4}{a^2} + 16a + 23[/tex]
This can be further expressed as:
[tex]\frac{4+16a^3+23a^3}{a^2}[/tex]
Name a fourth point in plane TUW
Answer: Z
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Jeff is lining up children and adults bicycle at bike shop where he work the children bicycle is nine less three times the number of adult bicycle there are 42adult bicycle how many child
ren bike are there
Answer:
Number of children bicycles = 117
Step-by-step explanation:
Given that:
Number of adult bicycles = a = 42
Let,
x represent the number of children bicycle
According to given statement;
The number of children bicycle is nine less three times the number of adult bicycles.
x = 3a - 9
Putting a=42
x = 3(42)-9
x = 126-9
x = 117
Hence,
Number of children bicycles = 117
Ben saved 172 coins. He saved nickels and dimes only. If he had $14, how many nickels did he have?
Answer:
64 Nickels
Step-by-step explanation:
172 coins equal $14.00
It took time to figure this out, I just used a calculator to shimmy down the gap of possibilities, starting here;
100d = $10.00
72n = $3.60
I got closer here;
110d = $11.00
62n =$3.10
I subtracted 2 dimes and added 2 nickels from the previous to get the answer.
108d = $10.80
64n = $3.20
$10.80 + $3.20 = $14.00
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Answer:
20
Step-by-step explanation:
20 may be answer for this may be
How many different squares can be formed by using four of the evenly spaced dots shown as vertices of the square?
Plz quickly!!
Answer:
I Believe Its Eight Squares
There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.
What is equilateral triangle?An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.
here, we have,
Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.
Here, we will use the combination rule to find out the possible triangles,
Thus, the total number of possible triangles = 15C3 = (15.14.13) / (1.2.3) = 455
Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.
For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.
And 12/3 = 4 dots would be between any two connecting dots.
Taking 1st connecting dot, the second connecting dot would be
1 + 4 + 1 = 6th
Similarly, the third connecting dot would be 6 + 4 + 1 = 11th
So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);
After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:
So, there are 455 - 5 = 450 triangles that are not equilateral triangles.
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Complete question;
fifteen dots are evenly spaced on the circumference of a circle. how many combinations of three dots can we pick from these 15 that do not form an equilateral triangle?
Which of the points below does not belong?
(0, -3)
(0, 0)
(4, -3)
(4,0)
Answer:
c
Step-by-step explanation:
Use the Distributive Property to solve the equation 4x - 2(x - 2) = - 7+ 4x + 3 The solution of the equation is
Answer:
The answer is x = 4
Step-by-step explanation:
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Answer:
x= 56 x= 89
Step-by-step explanation: