Answer:
See explanations below
Step-by-step explanation:
Given the functions f(x)=2x+3 and g(x)=x^2-1
a. Find f(g(x))
f(g(x)) = f(x^2-1)
f(g(x)) = 2(x^2-1)+3
f(g(x))= 2x^2-2+3
f(g(x)) = 2x^2+1
Hence the composite function f(g(x)) is 2x^2+1
b) g(f(x)) = g(2x+3)
g(f(x) = (2x+3)^2-1
g(f(x)) = 4x^2+12x+9-1
g(f(x)) = 4x^2+12x+8
factorise 3abc+6a²b pleaze with step too
Answer:
3ab(c+2a)
Step-by-step explanation:
Given data
3abc+6a²b
we can see that 3, a, and b are common between the two terms
so let us factor them out
3ab(c+2a)
Hence the factored form is
3ab(c+2a)
The hypotenuse of a right triangle measures 20 cm and one of its
legs measures 10 cm. Find the measure of the other leg. If
necessary, round to the nearest tenth.
I’m pretty sure 17.3 because of you do a^2+b^2=c^2 you get a^2= 10 square root 3 and that in a decimal is 17.3205
Answer:
8
Step-by-step explanation:
If you have $32 and you want to see how many bulbs of elephant garlic you want to buy if four bulbs costs $8 , you first need to see how many $8 can fit into $32 . Thus, divide 32 by 8 . Now that you know $8 can fit into $32 four times, multiply 4 by 4bulbs , since there are four bulbs per $8 .
Answer:
What's the question it awnsers itself?
Step-by-step explanation:
HELP ASAP PLZ
Write the next three terms of the arithmetic sequence.
-12, 0, 12, 24, _, _, _
Write the next three terms of the arithmetic sequence.
0.2, 0.6, 1, 0.4, __, __,__
Write the next three terms of the arithmetic sequence.
4, 3 3/4, 3 1/2, 3 1/4 ,__, __, __
Answer:
the next three for the first one are 36 48 60
Main Task 1 (Core):_Identify the type of angle: acute, right, obtuse, straight, reflex?
90°
Right angle
180°
4°
230°
127°
159°
116°
309
Answer:
Right angle
Step-by-step explanation:
90 degrees is a Right angle
The area of a parallelogram is 8x^2+2x-6 and it's height is 2x+2. What is the base of the parallelogram?
Answer:
4x - 6
Step-by-step explanation:
Remember the formula for finding the area of a parallelogram;[tex](base)*(height)=(area)[/tex]
Manipulate the equation such that it is solved for the base;
[tex](base)=\frac{(area)}{(height)}[/tex]
So the equation that needs to be solved is;
[tex]\frac{(8x^{2} + 2x - 6 )}{(2x + 2)}[/tex]
Set up the division problem and solve;
_____4x - 6___
[tex]2x + 2[/tex] | [tex]8x^{2} + 2x - 6[/tex]
[tex]-(8x^{2}+8x)[/tex]
________
-6x - 6
[tex]+ (6x + 6 )[/tex]
________
0
Solve and show your work: |4x − 1| = 13
PLEASE HELP ME
Answer: x=7/2, x=-3
Step-by-step explanation:
First lets do look at it without the absolute value marks
4x-1=13
4x=14
x=7/2
Now lets do the same but assume 13 is negative,
4x-1=-13
4x=-12
x=-3
6
Divide 2m in the ratio 9-1
Answer:
Step-by-step explanation:
First, add up the two numbers in the ratio to get 8. Next divide the total amount by 8, i.e. divide £40 by 8 to get £5. £5 is the amount of each 'unit' in the ratio.
To calculate the ratio of an amount we divide the amount by the total number of parts in the ratio and then multiply this answer by the original ratio. We want to work out $20 shared in the ratio of 1:3.
A sprinkler can water between 1 and 130 square yards of a lawn. The length L in inches of rotating pipe needed to water A square yards is given by the function L=119.75 square root of A. How much area can be watered if the length of the pipe is 600, 900, or 1,000 inches long?
Answer:
[tex]25.1\ \text{inches}^2[/tex]
[tex]56.5\ \text{inches}^2[/tex]
[tex]69.7\ \text{inches}^2[/tex]
Step-by-step explanation:
The length of the pipe is given by the function
[tex]L=119.75\sqrt{A}[/tex]
where A is the area
[tex]A=(\dfrac{L}{119.75})^2[/tex]
For [tex]L=600\ \text{in}[/tex]
[tex]A=(\dfrac{600}{119.75})^2\\\Rightarrow A=25.1\ \text{inches}^2[/tex]
Area watered when L = 600 inches is [tex]25.1\ \text{inches}^2[/tex]
For [tex]L=900\ \text{in}[/tex]
[tex]A=(\dfrac{900}{119.75})^2\\\Rightarrow A=56.5\ \text{inches}^2[/tex]
Area watered when L = 900 inches is [tex]56.5\ \text{inches}^2[/tex]
For [tex]L=1000\ \text{in}[/tex]
[tex]A=(\dfrac{1000}{119.75})^2\\\Rightarrow A=69.7\ \text{inches}^2[/tex]
Area watered when L = 1000 inches is [tex]69.7\ \text{inches}^2[/tex]
the algebraic expression for 24a+27
Answer:
3(8a+9) correct me if i'm wrong.
Step-by-step explanation:
If 19 erasers cost $3
The average length of the dragon used in the performance is 12 feet. The dragon is divided into 9 sections. How long is each sections
Answer:
do it urself sorry i letterely dont know
Step-by-step explanation:
please answer my question
A triangle has one angle that measure 75% and one that measure 19% what is the measure of the third angle
Answer:
86%
Step-by-step explanation:
angles in the triangle add up to 180
so we add 75% and 19%
to get 94%
then we subtract 180 by 94%
to get 86%
help me plzzzzzzzzzzzzzzzz
Answer:
Step-by-step explanation:
f(8)=-3(8)²-6(8)+1
=-192-48+1
= -239
Andrew was working on a project for Science class. He began working on the project at 10:32 a.m. When he finally
finished, the clock read 2:15 p.m. How long did it take Andrew to complete the project?
Answer:
3 hours 43 minutes
Answer:
3 hours and 43 minutes = 223 minutes
Step-by-step explanation:
write each number using words 6,240,018,000 and 900,019
Answer:
This will help you
Step-by-step explanation:
Which group of numbers could be the measures of the sides of a right
triangle?
Can someone help me with these definitions?
Answer:
Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000. So 4000 can be written as 4 × 10³. This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form.
Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph ). Converting a quadratic function to factored form is called factoring.
The y -intercept of a graph is the point where the graph crosses the y -axis. (Because a function must pass the vertical line test , a function can have at most one y -intercept . ) The y -intercept is often referred to with just the y -value.
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. and vertex is
In geometry, a vertex (in plural form: vertices or vertexes), often denoted by letters such as, is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.
Step-by-step explanation:
hope this helps have a good rest of your night :) ❤
Alex can climb 8 feet in 30 seconds and can run 112 feet in 20 seconds. When you combine his climbing and running, how many inches would that be?
Answer:
129024
Step-by-step explanation:
hope this help:)
Answer:
1440
Step-by-step explanation:
You add 8 + 112 then divide that by inches
Can someone help me with this question please.
I’ll mark as a brainliest.
Answer:
A
Step-by-step explanation:
a²+ b² = c²
(3 ft)² + (9 ft)² = (H)²
Answer:
A
Step-by-step explanation:
in a right triangle, the longest side (across from the right angle) is the hypotenuse (denoted as 'c')
the legs are denoted as 'a' and 'b'
the Pythagorean Theorem allows you to find the missing side using this formula:
a² + b² = c²
What is the center of the circle for this equation:
x² + (y - 9)² = 25
Answer:x=√−y2+18y−56 or x=−√−y2+18y−56
Step-by-step explanation:
x2+(y−9)2=25
Step 1: Add -y^2 to both sides.
x2+y2−18y+81+−y2=25+−y2
x2−18y+81=−y2+25
Step 2: Add 18y to both sides.
x2−18y+81+18y=−y2+25+18y
x2+81=−y2+18y+25
Step 3: Add -81 to both sides.
x2+81+−81=−y2+18y+25+−81
x2=−y2+18y−56
Step 4: Take square root.
x=√−y2+18y−56 or x=−√−y2+18y−56
Answer:
x=√−y2+18y−56 or x=−√−y2+18y−56
20 POINTS / I need this ASAP Solve the Problem
Answer:
n= 7.5
Step-by-step explanation:
So to get the answer to this equation, we have to create different equivalent equations, in the base equation so that in the end all bases are equivalent to solve for n.
Exact Form:
7/2
Decimal Form:
3.5
Mixed Number Form:
3 1/2
Hope this was helpful! Have a great day! :)
Answer:
n = 4
Step-by-step explanation:
Properties of Exponents
We are required to solve the following equation:
[tex]\displaystyle 7^7\cdot 7^5=\frac{(7^n)^4}{7^4}[/tex]
Operating:
[tex]\displaystyle 7^{7+5}=\frac{7^{4n}}{7^4}[/tex]
[tex]\displaystyle 7^{12}=7^{4n-4}[/tex]
Equating the exponents:
4n - 4 = 12
Adding 4:
4n = 16
Dividing by 4:
n = 4
Write a rational function for the given scenario. There may be more than one correct answer.
Question 1. X-intercept: none
Vertical Asymptote: X = -3
Horizontal Asymptote: y = 0
Question 2. X-intercept: none
Vertical Asymptote X=2 & x= -2
Horizontal Asymptote: y = 0
Question 3 x-intercept: (3,0) & (-3,0) Vertical Asymptote: X=-1 & x= -4
Horizontal Asymptote: y = 1
Question 4. X-intercept: (-2, 0)
Vertical Asymptote: X = 4 & x=-5 Horizontal Asymptote: y=0
Need to make a rational function for each question.
Answer:
Q1: [tex]\frac{1}{x+3}[/tex]
Q2: [tex]\frac{1}{(x-2)(x+2)}[/tex]
Q3: [tex]\frac{(x-3)(x+3)}{(x+1)(x+4)}[/tex]
Q4: [tex]\frac{x(x+2)}{(x-4)^{2}(x+5) }[/tex]
Step-by-step explanation:
If there is a vertical asymptote at x=k, then the denominator must contain a term (x-k) or (x-k) raised to a positive integer power.
If there is an x intercept at k, then the numerator must contain a term (x-k) or (x-k) raised to a positive integer power.
If there is a horizontal asymptote of 0, then the highest power of x in the denominator must exceed the highest power of x in the numerator.
If thee is a horizontal asymptote of k, then the highest power of x in the numerator and denominator must be the same and the ratio of their coefficients (numerator to denominator) must be k.
f(x) = 3x^2-x
Find f(10)
Answer:
f(x)=3x^2-x
Minimum = ( 1/12, -1/24)
if you graph.
Step-by-step explanation:
HEEEEEEEEEEELLLLLLLLPPPPPPPPPPP. PPPPPPLLLLLLEEEEEEAAAAASSSSSEE When Laura started her career at the age of 24, she deposited $800 into a savings account that earns 8.75% interest compounded semiannually. If she makes no other deposits or withdrawals, find the total amount in the account when she retires at the age of 65.
Answer:
she mad 52,000
Step-by-step explanation:
she made 52,000 by working by her job
What is this can you help
Answer:
yes
Step-by-step explanation:
Find the greatest common factor of 28 and 44.
Answer:
The GCF is 4
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
look at a Multiplication chart find all factors and find the highest number for 28 and 44
Lori bought 6,000 grams of cayenne pepper and 2 kilograms of black pepper. How many grams of pepper did she buy all together?
Answer:
2000
Step-by-step explanation:
1 kilogram = 1000 grams
2*1000=2000
Plsss help plssssssss
Answer:
x = 2
y = 6
Step-by-step explanation:
We have a system of equations and are asked to solve for x and y.
y = -2x + 10
y = 3x
Since both equations start with y, we can subtitute.
3x = -2x + 10
Solve for x :
Add 2x to both sides :
5x = 10
Divide 5 from both sides :
x = 2
Now substitute x in the second equation because it's more easier :
y = 3(2)
3(2)
6
y = 6