Answers:
Roots of g(x) are: -1, -6, 1, -4
Y intercept of g(x) is: 24
==============================================
Explanation:
Part 1) Finding the roots of g(x)
To do this, we need the roots of f(x). Plug in f(x) = 0 and solve for x using the zero product property.
f(x) = (x-2)(x+3)(x-4)(x+1)
0 = (x-2)(x+3)(x-4)(x+1)
(x-2)(x+3)(x-4)(x+1) = 0
x-2 = 0 or x+3 = 0 or x-4 = 0 or x+1 = 0
x = 2 or x = -3 or x = 4 or x = -1
Those four x values are the roots of f(x). Plugging any of those values into f(x) leads to f(x) = 0.
Now onto g(x). We see that g(x) = -f(x+3). The x+3 indicates the xy axis has been shifted by 3 units to the right. This gives the illusion the f(x) curve is shifted 3 units to the left. This will move each root 3 units to the left as well.
The root x = 2 on f(x) moves to x = -1 on g(x). We subtract 3 from the first x value to get the second x value.The root x = -3 on f(x) moves to x = -6 on g(x). Same idea as above.The root x = 4 on f(x) moves to x = 1 on g(x).The root x = -1 on f(x) moves to x = -4 on g(x).The four roots of g(x) are: -1, -6, 1, -4
------------------------------------------------
Part 2) The y intercept of g(x)
Let's plug x = 0 into g(x) to see what happens
g(x) = -f(x+3)
g(0) = -f(0+3) ... replace every x with 0
g(0) = -f(3)
We don't know f(3) yet, but we can plug x = 3 into f(x) to find out
f(x) = (x-2)(x+3)(x-4)(x+1)
f(3) = (3-2)(3+3)(3-4)(3+1)
f(3) = (1)(6)(-1)(4)
f(3) = -24
Therefore,
g(0) = -f(3)
g(0) = -(-24)
g(0) = 24
The y intercept of g(x) is 24.
You have 480 grams of radioactive kind of carbon. How much will be left after 60 minutes if it's half-life is 20 minutes?
Answer:
60 grams
Step-by-step explanation:
480/8 = 60
1. So far, Marta has correctly predicted the winner of 6 out of 13 football games. She wants to know how many consecutive games she would have to predict correctly to raise the percent of correct predictions to 65%. (a) Write an equation to represent this situation. (3 points) (b) Solve the equation. Show all steps. (5 points) (c) Answer the question. How many consecutive games must she predict correctly to raise her percent to 65%? (1 point)
Answer:
[(6 + x) / 13+x] = 0.65
7
Step-by-step explanation:
Given that:
Total number of games = 13
Number of correct prediction = 6
Number of correct predictions needed to raise prediction % to 65%
(Number of correct predictions) / (total number of games) = 0.65
Let x = number of additional consecutive correct predictions
[(6 + x) / 13+x] = 0.65
Where x = number of consecutive predictions required
6 + x = (13 + x) * 0.65
6 + x = 8.45 + 0.65x
x - 0.65x = 8.45 - 6
0.35x = 2.45
x = 2.45 / 0.35
x = 7
7 consecutive correct predictions
K
KL = 7, JL = 24, and JK = 25. Find tan J.
Answer:
Tan J = 0.2917
Step-by-step explanation:
Here, we want to find the value of tan J
Firstly, we need to understand that the numbers 24, 25 and 7 are a Pythagorean triple and as such the three measures represent the values of length of the sides of a right angled triangle
The tangent of an angle= measure of the opposite/measure of the adjacent
In the question, the opposite to point J measures 7 while the adjacent measures 24
So ;
tan J = 7/24
= 0.2917
Johnny says that 600 cm is not enough moulding for the baseboards that measure 5642 mm. Is he right in his statement? Explain
Answer:
Johnny is wrong.
Step-by-step explanation:
To compare two quantities, they must both be written in the same units. In this case, both must be in centimeters or millimeters. So, we must convert 600cm to millimeters or vice versa.
If we choose to use milimeters, we have
600cm=600cm [tex]\frac{10mm}{1cm}[/tex]
600cm = (600)(10) mm
600cm = 6000 mm
Now, we must compare 6000 mm with 5642 mm. We can see that 6000mm is greater than 5642 mm. hence, it is enough moulding for the baseboards.
In fact, 6000-5642 mm =358 mm would remain.
Which is equivalent to 180x11 after it has been simplified completely?
O 3x10 /5x
O 3x55x
O 6x10,5x
O 6x5/5x
Answer:
O 6x5/5x
Step-by-step explanation:
Answer:
It should be D. I'm not 100% sure though. But D is what I chose.
10. Reka Rahim is employed at a restaurant. She has family medical coverage through the company's group
medical plan. The annual cost of Reka's family coverage is $3,700.00. The company pays 35% of the cost. How
much does Reka pay annually for medical insurance?
$3,700.00
$1,295.00
$2,405.00
$4,050.00
Describe the series of rigid transformations that maps pqs onto p’’’q ’’’s ’’’ .explain.
learning task 1 identify if the if the given equation is a polynomial equation or not
Answer:
In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
Step-by-step explanation:
Consider the graph of z3. Which lettered point represents z?
Answer:B is correct for this specific question(5 of 11. C is correct for the other (4 of 11). Make sure to look at the picture of the graph before you answer.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
edg 2023
What is the value of Negative 5 Superscript 6? –15,625 –30 30 15,625
Answer:
D
Step-by-step explanation:
The value of the expression (-5)⁶ is, 15,625. So option D is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression (-5)⁶
In mathematical terms, this means that the expression
⇒ (-5) x (-5) x (-5) x (-5) x (-5) x (-5)
⇒ 15625
So, the value of the expression (-5)⁶ is 15625.
To know more about Expressions check:
brainly.com/question/16804733
#SPJ6
Classify the following triangle. Check all that apply.
how to find a 90 degree angle
Answer:
See explanation
Step-by-step explanation:
See if there's a right angle. A right angle will have a little box.
A lollipop costs $0.90. A candy necklace costs $0.31. How much more does a lollipop cost
than a candy necklace?
I really need help !!!!!! Gibing 89 points
Answer:
$0.59 more than the candy necklace
Step-by-step explanation:
you subtract .90 from .31
When angles are complementary, the sum of their measures is 90 degrees. Two complementary angles have the measures of 2x - 10 degrees and 3x - 10 degrees. Find the measures of each angle
Answer:
2x - 10 = 34 degrees
3x - 10 = 56 degrees
Step-by-step explanation:
Since they're complementary, they'd equal 90-degrees.
Solve for x:
2x - 10 + 3x - 10 = 90
5x -20 = 90
5x = 110
x = 22
2(22)-10 = 34
3(22)-10 = 56
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
y = 2x – 2
y = 2x + 2
y = x + 2
y = x – 2
Answer:
C
Step-by-step explanation:
We know that line CD passes through the two points (0, 2) and (4, 6).
First and foremost, let’s find the slope of the line. We can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are our two points.
So, let’s let (0, 2) be (x₁, y₁) and (4, 6) be (x₂, y₂). Substitute appropriately:
[tex]\displaystyle m=\frac{6-2}{4-0}[/tex]
Evaluate:
[tex]\displaystyle m=\frac{4}{4}=1[/tex]
Hence, our slope is 1.
Now, we can use the slope-intercept form:
[tex]\displaystyle y=mx+b[/tex]
Where m is our slope and b is our y-intercept.
Notice from our given points that we are given (0, 2).
So, our y-intercept is 2.
Therefore, we will substitute 1 for m and 2 for b. This yields:
[tex]\displaystyle y=(1)x+(2)[/tex]
Simplify:
[tex]\displaystyle y=x+2[/tex]
Hence, our answer is C.
If f(x) = 3x2 - 2 and g(x) = 2x + 4, find (f - g)(x).
Answer:
(f - g)(x) = 3x² - 2x - 6
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra
Combining like termsStandard Form: ax² + bx + c = 0Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 2
g(x) = 2x + 4
(f - g)(x) is f(x) - g(x)
Step 2: Find
Substitute: (f - g)(x) = 3x² - 2 - (2x + 4)Distribute -1: (f - g)(x) = 3x² - 2 - 2x - 4Combine like terms: (f - g)(x) = 3x² - 2x - 6Which point has coordinates (4, StartFraction 3 pi Over 4 EndFraction)
A
B
C
D
Answer:
B
Step-by-step explanation:
Answer:
It's C
Step-by-step explanation: I got it right.
9) Select the best method to solve the system.
4x+4y=16
2x-2y=6
*elimination
*substitution
Answer:
elimination
Step-by-step explanation:
multiply 2nd eqn by 2 and take eqn 1 - eqn 2 and you'll get rid of x term, leaving only the y term and a constant, where you can then easily solve for y and sub to get x
Topic: simultaneous eqn
If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!
Jina and her husband are each starting a saving plan. Jina will initially set aside $650 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function =A+135N650, where N is the number of months she has been saving. Her husband will not set an initial amount aside but will add $585 to the savings every month. The amount B (in dollars) saved using this plan is given by the function =B585N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Step-by-step explanation:
If A=650+135N; and B=585N,
then A+B= 650+135N+585N=650+620N
T=720N+650
A function assigns values to each element. An equation relating T to N can be represented by T=650+720N.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function which tells the amount that is been saved by Jina is given by the function A=650+135N, while the function which tells the amount that will be saved by her husband is B=585N.
Since the total saving amount is represented by T which is the sum of the two functions A and B. Therefore, the function of T can be written as,
[tex]\rm T=A+B\\\\T = (650+135N)+585N\\\\T = 650+135N+585N\\\\T = 650+720N[/tex]
Thus, an equation relating T to N can be represented by T=650+720N.
Learn more about Function:
https://brainly.com/question/5245372
5x2 + 4x = 3(2 - x)
help me :p
Answer:
Step-by-step explanation:
5x^2+4x=3(2-x)
5x^2+4x=6-3x
5x^2+4x+3x-6=0
5x^2+7x-6
(5x^2-3x)+(10x-6)
x(5x-3)+2(5x-3)
(5x-3)(x+2)
x=3/5,-2
When x = 1/2, what is the value of 8x-3/x ?
Help help help pls now
Give answer in cm squared
Answer:
13×11=143cm[tex]{2}[/tex]Step-by-step explanation:
you do base times height
Answer:
110.5 cm²
Step-by-step explanation:
The figure is composed of a rectangle with a triangle on top.
Area of rectangle = 13 × 6 = 78 cm²
Area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 13 and h = 11 - 6 = 5 cm , then
A = [tex]\frac{1}{2}[/tex] × 13 × 5 = 32.5 cm°
Thus
total area = 78 + 32.5 = 110.5 cm²
Which quadratic equation has real solutions?
A. 4x^2 -5 = -7
B. 2/3x^2 +7 = 11
C. 3x^2 -1 = 8x^2+9
Answer:
B. 2/3x^2 +7 = 11
Step-by-step explanation:
Composite numbers have less than two factors. more than two factors. exactly two factors. greater than or equal to two factors.
Answer:
More than two factors
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
more than 2 answers
Stay safe,wear a mask,stay at home <3
When writing the coordinates does it matter if we put x or y first?
Answer:
hii
Step-by-step explanation:
yes it does matter the The x-coordinate always comes first, followed by the y-coordinate.
Answer:To locate (2,5), move 2 units to the right on the x-axis and 5 units up on the y-axis. The order in which you write x- and y-coordinates in an ordered pair is very important. The x-coordinate always comes first, followed by the y-coordinate.
Step-by-step explanation: hope that this helps you! :)
Using compatible numbers to estimate, which expression has a quotient of about 70?
A. 3,424÷49
B. 5,358÷89
C. 6,409÷79
D. 5,238÷89
Answer:
A: 3,424/49
Step-by-step explanation: so its pretty simple if you ask me, if you do long division it is a lot more understandable. if you don't know how to do that then just use a calculator -_-
find an equation of the line that has a y-intercept of -1 that is parallel to the graph of the line x - 3y = 6
Answer:
y = [tex]\frac{1}{3}[/tex] x - 1
Step-by-step explanation:
x - 3y = 6 ⇔ y = [tex]\frac{1}{3}[/tex] x - 2
y = [tex]\frac{1}{3}[/tex] x - 1
x-4y=8 in slope-intercept form
Answer:
y= 1 over 4 x -2
Step-by-step explanation:
hope you understand that
Answer:
y = [tex]\frac{1}{4}[/tex] x - 2
Step-by-step explanation:
y = mx + b is slope-intercept form of linear equation.
Solve x - 4y = 8 for "y"
- 4y = - x + 8
y = [tex]\frac{1}{4}[/tex] x - 2
Rameez borrowed Rs. 20,000 from a bank at the rate 5% p.a compounded annually. What amount will he pay at the end of three years to clear the loan?
Answer:
23000
Step-by-step explanation:
If you multiply 20,000 * 0.05 (the percentage of the rate) you get 1000
This means that for 3 years he will pay an interest of 3000, plus the original loan 20000 which means he will pay 23000 :D
need help quick its my GCSE what is 1 +1 if you cant do it its okay LOL
THE ANSWER IS 2
PLS GIVE BRAINLIEST
Answer:
1 + 1 = 2
Step-by-step explanation:
I don't know why but I have been seeing a lot of questions like this lol