Answer:
3rd option
Step-by-step explanation:
[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] ( factorise numerator and denominator )
3x² - 3 ← factor out 3 from each term
= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 1
= x² - 1²
= (x - 1)(x + 1) , then
3x² - 3 = 3²(x - 1)(x + 1) ← in factored form
--------------------------------
x² - 5x + 4
consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)
the factors are - 1 and - 4 , since
- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then
x² - 5x + 4 = (x - 1)(x - 4)
then
[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] = [tex]\frac{3(x-1)(x+1)}{(x-1)(x-4)}[/tex] ← in factored form
Find dy/dx (the derivative ) of f(x) = 4x
2
using
limits definition of the derivitive (of limit of the
DQ when h> 0
Formulas needed
a) Equation of a line in slopeyintercept form y = f(x) = mx + b
b) Equation of a line slopepoint y y1 = m (x x1)
Derivative are used to determine the nature of a function. The derivative of the function f(x) = 4x^2 is 8x
Derivative of a functionThe formula for finding the derivative of a function is expressed as:
f'(x) = nax^n-1
Given the function expressed as:
f(x) = 4x^2
We are to find its derivative as shown:
f'(x) = 2(4)x^2-1
f'(x) = 8x^1 = 8x
Hence the derivative of the function f(x) = 4x^2 is 8x
Learn more on derivative here: https://brainly.com/question/416343
Can I? I really need your help, b'coz, I can't understand how to solve it.
Answer:
See below ~
Step-by-step explanation:
1. D. cylinder
2. A. pyramid
3. E. rectangular prism
4. C. cone
5. F. cube
find the surface area of each shipping package. Which package has the greater surface area? Does the same package have a greater volume?
package A: 14 x 12 x 3
package B: 11 x 6 x 8
Answer:
greater area: Ano, B has the greater volumeStep-by-step explanation:
The relevant area and volume formulas are ...
A = 2(LW +H(L +W))
V = LWH
When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.
Figure A has the larger area.
Figure B has the larger volume.
__
Additional comment
The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)
Ben spent 1/6 of his money on a burger, fries, and a drink. Then he spent half of the money he had left: $5 on a magazine, $8.25 on a bookmark, and $10.50 on a book. How much money did he have to begin with?
Please answer asap and please explain your answer.
The amount of money Ben had to begin with after spending 1/6 and 1/2 of it is 57 dollars.
How to find the how much money he had with an equation?let
x = amount he had to begin with
He spent 1/6 of his money on a burger, fries, and a drink. Therefore,
amount spent on burger, fries, and a drink = 1 / 6 x
Hence,
amount he had left = x - 1 / 6 x =6x - x /6 = 5 / 6 x
Then he spent half of the money he had left.
1 / 2(5 /6 x) = 5 + 8.25 + 10.50
5 / 12 x = 23.75
cross multiply
5x = 23.75 × 12
5x = 285
divide both sides by 5
x = 285 / 5
x = 57
Therefore, the amount of money he have to begin with is $57.
learn more on equation here: https://brainly.com/question/5718696
Answer:
$57
Step-by-step explanation:
10.50 - 7.50 = 3
3 x 19 =57
$57
I NEED THIS ANSWER ASAP
base twelve needs 12 digits so we use "t" for ten and "e" for eleven and our usual ten digits.* what base ten number does 1t5e represent?
Answer:
65
Step-by-step explanation:
t = 10
e = 11
10 + (11*5)
65
Find the equation of a line parallel to y=4x+2 that contains the point (−2,−3). Write the equation in slope-intercept form.
Answer:
y = 4x + 5
Step-by-step explanation:
Use point-slope formula to plug in the known point and slope.
Identify and correct the error. B 50° A 50
Answer:
30 degrees
this is a guess but an educated one because the total angle adds up to 180 deg so one i assume is around 100 plus 50 plus 30 makes sense
Use appropriate property and find -1/6×4/7+1/2-3/7×1/6
Answer:
1/3
Step-by-step explanation:
Multiply left to right, so you start with -1/6*4/7=-2/21
Then you apply the fraction rule so -1/6*4
and 4 can be expressed by 4/1 so -1/6*4/1=-2/3
Then after solving you will get -4/6
then you factor 4=2*2 what will be -2*2/6
Then you cancel the common factors what are 2
so you bring back the 7 so -2/3/7 and 7 can be expressed as 7/1 and then you apply the fraction rule and flip it to 1/7 what will be solved as -2/21
so then it will be -2/21+1/2-1/14-3/7*1/6
Then you will have to solve -3/7*1/6 what is 1/14
so -2/21+1/2-1/14=1/3 final equation
Answer:
⅓Step-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧Find the area and circumference of each shaded sector. Use 3.14 for . Round to the
nearest tenth.
Answer:
Area = 226.1 ft^2
and circumference = 61.7 ft.
Both to the nearest tenth.
Step-by-step explanation:
The area of shaded part
= 1/2 *3.14 r^2
= 1/2 * 3.14 * 12^2 = 226.1 ft^2.
Circumferences of the shaded part = diameter + length of the semicircle
= 2 *r + 3.14 * r
= 2*12 + 3.14 * 12
= 61.68 ft.
Write the algebraic expression that matches each graph.
Answer:
f(x) = |x - 2| - 2
Step-by-step explanation:
Based on the shape of the graph, it's an absolute value function.
so the template for it is f(x) = |x|
From there, you can make some additions to show how much the graph has shifted from the template equation
since the graph went over to the left by 2 units and down by 2 units, this is added into the equation as follows:
f(x) = |x - 2| - 2
Which table shows a data o for an antenna that revolves at exactly twice the rate of the antenna described in the graph?
The table shows a data for an antenna that revolves at exactly twice the rate of the antenna described in the graph is Table D.
How to illustrate the rate?The formula to calculate the rate will be:
= Change in revolution/Change in time
The rate of the given antenna will be:
= (60 - 30)/(4 - 2)
= 30/2
= 15
Also, the rate of antenna 1 is 23, antenna 2 is 25, antenna 3 is 2. The rate for antenna 4 will be:
= (720 - 660)/(24 - 22)
= 60/2
= 30
It can be seen that 30 is double of 15.
Therefore, table D revolves at exactly twice the rate of the antenna.
Learn more about rate on:
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Solve for the missing components
Which unit could be used to measure the capacity of a kitchen pot? O a) kilograms b) quarts c) pounds
Answer:
a
Step-by-step explanation:
pounds because all will measure with it only even shop keepers........................................
PLEASE HELP NOW
HURRY
Answer:
13
Step-by-step explanation:
we us the pythagorean theorem
sqrt( 144 + 25) = 13
A boat travels 1/5 of a mile on 7/9 gallon of gas. How many miles can the boat travel on 1 gallon of gas
Answer:Since we know the boat uses 25 gallons of gas per 64 miles, we can divide 64 miles by 25 gallons to get the rate of gallons per hour.
64 ÷ 25 = 2.56 gallons of gas every hour.
Using this information, we can multiply the amount of gas used for one hour, 2.56 gallons, by the 125 gallons of gas that the problem suggests, 125, to find the number of miles the boat can travel on the amount of gas.
2.56 x 125 = 320 miles
Answer: The boat can travel 320 miles on 125 gallons of gas.
CAN SOMEONE PLEASE HELP ME WITH THIS
Answer:
7a is not a factor because it doesnt divide into anything.
7a is not a term because it is not only the variable.
3 is a constant because it is a number in the expression.
7a is not a coefficient because it is not just the number.
8b and 5b are like terms because they have the same variables.
None of these are true Thats false because some of the answers are right
can you help me to solve this problem
g ( t ) = | t | - 3 ; find g ( 3 ) , g ( -5 ) , and g ( 0 )
Answer:
g(3) = 0. g(-5) = 2. g(0) = -3
Step-by-step explanation:
simply put whatever is inside the brackets, into where t is in the equation
e.g:
|t| - 3 for g(3) is: |3| - 3 = 0
the two lines around t just mean that whatever is inside you should always turn positive. so |-1| = 1 and |-3 + 1| = 2
22points) what’s 1+1?
A=1
B=2
C=-2
D=11
E=21
F=77
G=I don’t know
Step-by-step explanation:
1 plus 1 equals 2
It's addition so u just add
1 + 1 = 2
Pls mark me brainiest
What is the value of the expression.
20 + 12 ÷ 1/4 x 3
Answer:
164
Step-by-step explanation:
[tex]20 + 12 \div \frac{1}{4} \times 3 \\ \\ = 20 + 12 \times 4 \times 3 \\ \\ = 20 + 144 \\ \\ = 164[/tex]
You are designing a triangular pennant for your school. If you have only 117 square inches of fabric and you want the pennant, when suspended from its base, to hang down 18 inches, what must the length of the
base be?
Answer:
13 inches
Step-by-step explanation:
Area of fabric : 117 square inchesHeight : 18 inchesBase x Height x 1/2 = Area (Fabric)Base x 18 x 1/2 = 117Base x 9 = 117Base = 13 inchesAnswer:
The base must be 13 inches
Step-by-step explanation:
Step 1: Determine the length of the base
[tex]A = 1/2 * b * h[/tex]
[tex]117\ in^2 = 1/2 * b * 18\ in[/tex]
[tex]117\ in^2 = 9\ in * b[/tex]
[tex]\frac{117\ in^2}{9\ in} = \frac{9\ in * b}{9\ in}[/tex]
[tex]13\ in = b[/tex]
Answer: The base must be 13 inches
In which type of circuit can you find total resistance by adding all of the individual resistances?
Answer:
Series Circuit
Step-by-step explanation:
In a series circuit, the total resistance is equal to the sum of all resistances. Hope this helps u out!
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answer:
<1= 68 degree
<2= 112 degree
<3= 68 degree
<4= 112 degree
<5= 68 degree
<6= 112 degree
<7= 68 degree
<8= 112 degree
Step-by-step explanation:
steps in the image-
Solve for t. Please help asap!
Answer:
The answer is B.
[tex]t=+\sqrt{\frac{d-3}{a} } , -\sqrt{\frac{d-3}{a}[/tex]
Step-by-step explanation:
[tex]d=3+at^2\\\\d-3=at^2\\\\\frac{d-3}{a}=t^2\\\\ t=+\sqrt{\frac{d-3}{a} } , -\sqrt{\frac{d-3}{a} }[/tex]
2x - 8 + 3x + 2 = 4x + 10 + 3x - 6
Answer:
x = 10/-6 or 5/-3
Step-by-step explanation:
2x - 8 + 3x + 2 = 4x + 10 + 3x - 6
x - 6 = 7x + 4
+6 +6
---------------------
x = 7x + 10
-7x -7x
---------------------
-6x = 10
x = 10/-6 or 5/-3
I hope this helps!
Use a net to find the surface area of the prism.
A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. (a) What is the probability that both grapes are green? (b) What is the probability that Henry eats a red grape then a green grape?
Answer:
A. 28/253
B. 60/253
Step-by-step explanation
A. first step is to add all the grapes up which = 23
then you would put the
green grapes/ the total which would be 8/23
since henry ate one grape you would subtract 8-1 and then 23-1 and you would get 7 and 22
then you would put 7/22 and multiply 8/23 which gets you 28/253
B. first you put red grapes over total grapes which are 15/23
then,
you would do the green grapes which are 8/22
you would multiply 15/23 and 8/22 which = 60/253
What is the value of 14 × 10,000?
140
1,400
14,000
140,000
Answer:
140000
Step-by-step explanation:
Hewo Yuri-san here Allow me to help! :3
Answer:
-140,000
Step-by-step explanation:
Here's a trick I learned in 5th grade.
You see all the zero's behind the number 10,000 just add them onto the back of the number you're mutliplying with and it gives you the answer.
In this case, we have the number 10,000 with 4 zero's and we're going to add that to the back of 14 which gives us the answer 140,000 And they both have 4 zero's. :)
Therefore, the answer is 140,000
Hope this Helps!
Have a great day!
-Yuri-san
I log 25 - 2log 3 2 - 2log3 + log 18 10
Step-by-step explanation:
1 log 5² - 2 log 2⁵ - 2log3 + log 18 10
= 2log 5 - 10log2 - 2log3 + log 18 10
A factory’s production is modeled by function f(x) where f(x) is the number of parts produced per hour and x is the number of people working during production choose the ordered pair that represents a posible domain and range of the function
Answer:
5,10
Step-by-step explanation:
this is the answer
A doughnut shop made 32 chocolate doughnuts one morning. The chocolate
doughnuts were 40% of the total number of doughnuts made that morning. How
many doughnuts were made, in all?
3
80 donuts were made
i hope this helps !