The vertex of a parabola is at (p, q). As for the axis of symmetry, the p value is 8, and in this function the q value is 3. So the vertex is at (8,3).
Find the volume of a rectangle box given the length of x, width of (x-2) and height of (3x+5)
Answer:
3x^3 − x^2 − 10x
Step-by-step explanation:
V= l*w*h
V= x * (x-2) * (3x+5)
V= (x(x−2)) (3x+5)
= (x(x−2)) (3x) + (x(x−2)) (5)
= 3x^3 − 6x^2 + 5x^2 − 10x
=3x^3 − x^2 − 10x
Dalyn has been asked to consider the following functions:
f (x) = 6x² - 12x + 11
g (x) = 6(x - 1)² + k
Dalyn would like to find a value of a k such that both f(x) and g(x) model the same graph. Help Dalyn solve for the value of k so both functions will represent the same graph.
Answer:
In order that both functions to represents the same (one) graph then the value of k is 5
Step-by-step explanation:
The given functions are;
f(x) = 6·x² - 12·x + 11
g(x) = 6·(x - 1)² + k
Expanding the function g(x) gives;
6·(x - 1)² + k = 6 × (x² - 2·x + 1) + k = 6·x² - 12·x + 6 + k
∴ 6·(x - 1)² + k = 6·x² - 12·x + 6 + k
Comparing with the function for f(x), we have;
f(x) = 6·x² - 12·x + 11
g(x) = 6·(x - 1)² + k = 6·x² - 12·x + 6 + k
The difference between the two functions is the constant term, which are;
Constant term for f(x) = 11
Constant term for g(x) = 6 + k
For the two terms to describe exactly the same graph, the constant term should also be equal
We will then have, 11 = 6 + k
∴ k = 11 - 6 = 5
k = 5
For both functions to represent the same graph the value of k = 5.
how much more can you simplify this
Nadya has 19 1/4 yards of ribbbon she cuts ribbon into peices that measure 1 3/4 how many pieces of ribbon doe Nadya have?
Answer:
11
Step-by-step explanation:
Well basically i took 19 1/4 and divided it by 1 3/4 and there for i got 11. YOUR WELCOME.
There are 11 pieces of ribbon doe Nadya have.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Nadya has 19 1/4 yards of ribbon she cuts ribbon into pieces that measure 1 3/4.
Now, We can find the number of pieces as;
⇒ 19 1/4 ÷ 1 3/4
⇒ 77/4 ÷ 7/4
⇒ 77/4 × 4/7
⇒ 77/7
⇒ 11
Therefore, There are 11 pieces of ribbon doe Nadya have.
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II. Let f(x) = 9 – x , g(x) = x2 + x, and h(x) = x – 2. Compute the following:
9. H(g(x)) and h(g(f(x)))
Answer:
[tex]h(g(x))=x^2+x-2[/tex]
[tex]h(g(f(x))= x^2-19x+88[/tex]
Step-by-step explanation:
Composite Function
Suppose f(x) and g(x) are real functions, the composite function named [tex](f\circ g)(x)[/tex] is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]
The composite function can be found by substituting g into f.
We are given these functions:
[tex]f(x)=9-x[/tex]
[tex]g(x)=x^2+x[/tex]
[tex]h(x)=x-2[/tex]
Find:
a) h(g(x))
Substituting g into h:
[tex]h(g(x))=x^2+x-2[/tex]
b) h(g(f(x))
First we find g(f(x)):
[tex]g(f(x))=(9-x)^2+(9-x)[/tex]
Operating:
[tex]g(f(x))=81-18x+x^2+9-x[/tex]
Simplifying:
[tex]g(f(x))=90-19x+x^2[/tex]
Now find h(g(f(x)) replacing the above equation into h:
[tex]h(g(f(x))= 90-19x+x^2-2[/tex]
Simplifying and rearranging:
[tex]h(g(f(x))= 88-19x+x^2[/tex]
[tex]h(g(f(x))= x^2-19x+88[/tex]
even integers from 11 and 111
Answer:
Please see below :)
Step-by-step explanation:
Integers - Whole numbers (no fractions or decimals!)
11 to 111
12, 14, 16, 18, 20
22, 24, 26, 28, 30
32, 34, 36, 38, 40
42, 44, 46, 48, 50
52, 54, 56, 58, 60
62, 64, 66, 68, 70
72, 74, 76, 78, 80
82, 84, 86, 88, 90
92, 94, 96, 98, 100
102, 104, 106, 108, 110
Hope this helped!
Which one of these show the multiplication property of equality? I know what is it I just don’t see it on here, 5 and 9 both look like the substitution property but I don’t know.
Answer:
5 is c 9 is f
Jennifer's bank account is modeled by the following equation where x equals the number of weeks and f(x) equals the total balance. f(x) = 12x + 45 William's bank account balances after weekly deposits are showing in the following table. How much money was in Jennifer’s account when it was opened?
Answer:
30
Step-by-step explanation:
The money that was in Jennifer’s account when it was opened should be 30.
Calculation of the money:Since
Jennifer's bank account is modeled by the following equation
where x equals the number of weeks and f(x) equals the total balance.
And, the equation is f(x) = 12x + 45.
So here as per the attached graph, so the money should be 30.
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Record the length of this line shown in centimeters.
Answer:
12
Step-by-step explanation:
the ruler measured 12
Physics students were modeling the height of a ball once it was dropped from the top of a 10 foot ladder. The
students found that the height, in feet, h, of the ball above the ground as a function of the number of seconds, t, since
it wasdropped was given by h(t) = 10 - 2t^2
1. Determine an appropriate domain for the given scenario. Record your domain in both interval and set builder
notation.
Interval:
Set-Builder:
Justify your reasoning for choosing the above boundaries on your domain using the context of the problem.
How would the domain for this function differ if we were looking at it outside of the context of this problem?
Answer:
Interval notation: [0, 2.236]
Set Builder notation: [tex]\{t\ |\ 0\le t\le 2.236\}[/tex]
Step-by-step explanation:
Given that:
Equation of height of the ball dropped from a height of 10 foot, as:
[tex]h(t) = 10 - 2t^2[/tex]
Where [tex]t[/tex] is the time since the ball was dropped.
To find:
The domain of the function in Interval and set builder notation.
Solution:
Domain of a function is defined as the set of valid input values that can be given to the function for which the function is defined.
Here, input is time.
We can not have negative values for time.
Therefore, starting value for time will be 0 seconds.
And the value of height can not be lesser than that of 0 ft.
[tex]0= 10 - 2t^2\\\Rightarrow 2t^2=10\\\Rightarrow t^2=5\\\Rightarrow t =2.236\ seconds[/tex]
Maximum value for time can be 2.236 seconds.
Therefore the domain is:
Interval notation: [0, 2.236]
Set Builder notation: [tex]\{t\ |\ 0\le t\le 2.236\}[/tex]
(w-2) (w+5)
I need help I don't understand ...
===============================================
Work Shown:
Let x = w-2
This will allow us to replace the (w-2) with x to get...
(w-2)(w+5)
x(w+5)
x*w + x*5 ... distribute
w(x) + 5(x)
Now replace x with w-2 and distribute again
w(x) + 5(x)
w(w-2) + 5(w-2)
w*w + w*(-2) + 5*w + 5*(-2)
w^2 - 2w + 5w - 10
w^2 + 3w - 10
please i need help!!! Beth enlarged the triangle below by a scale of 5.
A triangle with a base of 4 centimeters and height of 3.5 centimeters.
She found the area of the enlarged triangle. Her work is shown below.
One-half (4) (3.5) (5) = 35 centimeters squared
Answer:
Your answer is: There is a mistake in Beth's answer the mistake was that she multiplied the area of the original triangle by the scale factor.
Step-by-step explanation:
Hope this helped : )
HELP PLEASE WHATS NOT A FUNCTION
Mike had some candy to give to his four
children. He first took two pieces for
himself and then evenly divided the rest
among his children. Each child received
two pieces. With how many pieces did he
start?
$1995 at 6.5% for 10 years.
answer:
10 times 6 is 60 plus 5 is 65 carry the 5 you've got
1995
+
565
=
2560
step-by-step explanation:
and that's on periodt
PLEASE HELP ME ASAP!
Divide.
(2x^3 - 5x^2 + 7) divided by (x - 2)
Answer:
2x^2 -x - 2 + (3/x-2)
Step-by-step explanation:
Translate (-2, -3) up 2 units.
Then reflect the result over the x-axis.
What are the coordinates of the final point?
Answer:
0,1
Step-by-step explanation:
i believe that’s the answer sorry if it’s incorrect
Half note times a whole note plus 2 quarter notes minus 3 half notes
equals...?
A. 2
B. 4
C. 6
D. 8
Alberto uses the steps below to solve the equation One-half x minus 3 equals 7. Step 1: One-half x minus 3 plus 3 equals 7 plus 3 Step 2: One-half x plus 0 equals 10 Step 3: One-half x equals 0 Step 4: 2 (one-half) x equals 2 (10) Step 5: 1 x equals 20 Step 6: x equals 20 Which justifies Step 6 of his work?
Answer:
Identity property of multiplication
Step-by-step explanation:
From step 5:
[tex] 1x = 20 [/tex]
Here, to solve for x so that the variable x stands alone, Alberto uses the identity property of multiplication, which justifies what he has in step 6.
Step 6:
[tex] x = 20 [/tex]
According to the identity property of multiplication, any value you multiply by 1 gives you that same value.
Therefore, 1x = 1 × x = x.
The variable x multiplied by 1 will give you x.
Which is the simplified form of r Superscript negative 7 Baseline + s Superscript negative 12?
Answer:1/r7+1 over 8 and 12
Step-by-step explanation:
The simplified form of expression r Superscript negative 7 Baseline + s Superscript negative 12 is,
⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]
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.
Given that;
The expression is,
r Superscript negative 7 Baseline + s Superscript negative 12
⇒ r ⁻⁷ + s ⁻¹²
Now, We can simplify the expression as;
⇒ r ⁻⁷ + s ⁻¹²
⇒ 1 / r⁷ + 1 / s ¹²
⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]
Thus, The simplified form of expression r Superscript negative 7 Baseline + s Superscript negative 12 is,
⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]
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whats the answer to 6/2(1+2)=
Answer:
the answer is 9
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
6/[2(1+2)]
Using PEMDAS
parentheses first
6/[2 (3)]
6/6
1
HELP PLZ DUE IN 30 MINUTES The Multiplication of Polynomials
Answer:
(x-1)(x^3+4x^3-1)=(x-1)(5x^3-1)
Step-by-step explanation:
The masses of two objects are compared during Mrs. Mobley’s Science experiment. It is determined that object A has a mass of 3 × 10^−2 grams and object B has a mass of 2 × 10^−3 grams. Mrs. Mobley offers extra credit to the first team that can determine how many times larger is the mass of object A than the mass of object B?
Answer:
15 times larger than b
Step-by-step explanation:
=3×10^-2/2×10^-3
=15×10^-1×10^+1
=15
The relationship between the number of pounds (lb) of trail mix and the price in dollars is shown in the graph. What is the unit price of trail mix? 40 32 Price (dollars) 24 16 2 3 Weight (pounds) 116 3
Answer: b - $8/1 lb
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I got it right :)
does anyone know it i think ik it but im not sure so i need help
Answer:
The "if" part is the hypothesis.
The "then" part is the conclusion.
Hypothesis: an animal is a poodle
Conclusion: it is a dog
solve the system of equations by the addition method
5x + 2y = 6
4x - 3y = 14
Answer: x=2, y=-2
Step-by-step explanation:
1) I will find x first, so make the amount of Ys same
3(5x+2y=6)
2(4x-3y=14)
2) 15x+6y=18
8x-6y=28
3) combine them together so Ys are all cancelled and 23x=46
4) x=2
5) for solving y, you can just plug in the x to any of that 2 equations, then 4(2)-3y=14
6) 8-3y=14
7) -3y=6
8) y=-2
I need help (please explain the answer and how you got it)
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Ok! So you want to find slope! First, you will need two points which you already have. Next, you will want to plot those two points on a graph. Once, you have that you can draw a straight line between the two points and until the end of the graph. After that, you want to find the rise/run or rise over run. Rise meaning up or down and run meaning left or right. Sometimes your problem will want you to keep the rise/run format and sometimes your problem will ask for a who number in which case you will divide your rise/run (rise ÷ run). How to find the rise over run you ask, simple! Draw a line-up or down from your first (or second) point whichever works, until you reach the y-value of your second (or first) point one your two points are connected, count the rise (up or down) and then the run (left or right). If your run goes left its a negative, right a positive. If your rise goes up its a positive, down a negative.
Boom! You know how to find slope!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
35% of the students in Mr. Simmons’ math class liked last nights’ homework. If there were 49 students who liked last nights’ homework, how many total students does Mr. Simmons teach?
Answer:
the answer should be 140
Step-by-step explanation:
Help me solve this problem please
Answer:
h(3) = 2
Step-by-step explanation:
The absolute value function always gives a positive value, that is
| - a | = | a | = a
To find h(3) substitute x = 3 into h(x), that is
h(3) = | 5(3) - 17 | = | 15 - 17 | = | - 2 | = 2
The aspect ratio of a rectangular shape is its length (L) divided by its width (W). It is expressed as L:W or L/W. If the aspect ratio of a chalkboard is 12:7 and the length is 36 in, what is the width of the chalkboard?
Answer:21
Step-by-step explanation:12 times three is 36 and 7 times 3 is 21