Answer:3.13/1
Step-by-step explanation:
Which of the following fraction below is an IMPROPER FRACTION?
a. 1/3
b. 16/5
c. 2/3
d. 4/27
Identify the factors of the following numbers 1. 40- 2. 54- 3 63 - 4.70 - 6. 85 -
Does this graph represent a function? Why or why not?
Answer:
yes
Step-by-step explanation:
you can use the vertical line test
Which logarithmic equation is equivalent to the exponential equation below?
e^4x = 5
Step-by-step explanation:
e^4x = 5
x = 1/4 × ln(5)
x ÷ 1/4 = ln(5)
x.4 = ln(5)
4x = ln(5)
ln(5) = 4x
Option → D
If it takes 2.5 gallons of milk to make 2 pounds of cheese. How many pounds of cheese can John make with 50 gallons of milk?
Answer:
21 pounds
tell me if it helped :P
Step-by-step explanation:
Help this is due today!!!!!!!
y<_ - 1/2 + 4
y> - x
Answer:
1.4.5
2.idont know the answer for that question because I am grade 6
Write the equation of the line passing through the points (-7, 5) and (7, 1)
Answer:
y = -2/7(x) + 3
Step-by-step explanation:
The equation of a line can be stated as y = mx + b, where m is the slope and b is the y-intercept (the value of the function when x = 0). To find the equation of the line, we'll start by finding the slope.
The slope can be expressed as [tex]\frac{y_{2} - y_{1}}{x_{2}-{x_1}}[/tex]
Substituting in our coordinates, we have:
[tex]m = \frac{1 - 5}{7 - (-7)} = \frac{-4}{7 + 7} = \frac{-4}{14}[/tex], which can be simplified to [tex]-\frac{2}{7}[/tex]
Plugging that back into our equation, we have y = [tex]-\frac{2}{7}[/tex]x + b
Now, to find b, we substitute in one of our sets of coordinates. Let's use (-7, 5)
x = -7 and y = 5, which gives us:
[tex]5 = -\frac{2}{7} (-7) + b[/tex]
[tex]-\frac{2}{7} (-7) = 2[/tex], which gives us:
5 = 2 + b
Subtracting 2 from both sides, we get:
3 = b
Plugging that back into our equation, we have [tex]y = -\frac{2}{7} x + 3[/tex]
2x² - x + 6 is subtracted from x² + 3x - 2, the result is
Answer:
-x² + 4x - 8
Step-by-step explanation:
Given: 2x² - x + 6 is subtracted from x² + 3x - 2
Rewriting: (x² + 3x - 2) - (2x² - x + 6)
Distrubte negative: x² + 3x - 2 - 2x² + x - 6
Combine like terms: -x² + 4x - 8
Answer: -x² + 4x - 8
Hope this helps, have a nice day :D
What is 5/8÷1 and 1/3
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{8}\div 1\frac{1}{3}\implies \cfrac{5}{8}\div \cfrac{4}{3}\implies \cfrac{5}{8}\cdot \cfrac{3}{4}\implies \cfrac{15}{32}[/tex]
Marcus works at a clothing store and gets an employee discount. The price
he pays can be modeled by the function d(c) = C -0.10c, where c is the original price
of the item. Find d(32) and describe what this means in the context of the problem.
(please answer i need asap)
9514 1404 393
Answer:
d(32) = 28.80
the price Marcus pays on an item with an original price of 32
Step-by-step explanation:
d(32) = 32 -0.1(32)
d(32) = 28.8
The problem statement tells you d(32) is the price Marcus pays when the original price is 32.
3.
Which of the following is the graph of y = 5x2 + 2?
Answer:
Graph A
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: ( 0 , 2 )
Focus:
( 0 , 41 /20 )
Axis of Symmetry: x = 0
Directrix: y = 39 /20
x y
− 2 22
− 1 7
0 2
1 7
2 22
Juanita has saved 10% of the money that she needs to buy a new bicycle.
If she has saved $22, how much money does the bicycle cost?
A swimming club is conducting a vote to choose a mascot. There are 164 club members who want a dolphin for their mascot. These members represent 82% of the total number of club members. How many club members are there?
Group of answer choices
134
200
136
2,000
Step-by-step explanation:
82÷100= 0.82
0.82×164= 134.48 /134
perpendicular to 8x - 2y = 5.
Step-by-step explanation:
First consider the given line 8x = 2y - 5. This can be rewritten as
2y = 8x + 5
y = (8x + 5)/2 = 4x + 2.5
The line is y = 4x + 2.5. This is of the form y = mx + b.
On comparing, we see that the slope of the given line is m = 4
Now, we require to find the slope of a line perpendicular to this. Let its slope be m'.
We know that for two lines to be perpendicular, the product of the slopes = -1
So, m * m' = -1
4 * m' = -1
m' = -1/4
Answer: Slope of the perpendicular line is -1/4.
In one jar, I have two balls labelled 1 and 2 respectively. In a second jar, I have three balls labelled 0, 1 and 2 respectively. I draw one ball from each jar, multiply the numbers on the two balls together, and then calculate three to the power of that product, e.g. if I draw 1 and 2, I calculate 3^2=9. Let’s call this number X. What is the probability that the number 1,024 is an exact multiple of X?
Step-by-step explanation:
this is a kind of trick question, actually.
with whatever we draw, we produce X values as power of 3.
to be precise, we can have only
3⁰ = 1
3¹ = 3
3² = 9
3⁴ = 81
due to the possible combinations of drawn numbers (e.g. 3 cannot be created by a multiplication of 0s, 1s and 2s).
so, mostly, these results cannot be exact factors of 1024.
1024 cannot be divided by 3, nor by 9 nor by 81.
but 1024 is a multiple of 1 (as is every number).
so, we are looking at the probability to get 0 as multiplication result of the numbers on the 2 drawn balls.
the only possibilities are
1 and 0
2 and 0
out of in total 6 (2×3) different outcomes
1 and 0
1 and 1
1 and 2
2 and 0
2 and 1
2 and 2
the probability of this "0" event is again
number of desired outcomes / number of possible outcomes = 2/6 = 1/3
Suppose a poll is taken that shows that 530 out of 1000 randomly selected, independent people believe the rich should pay more taxes than they do. Test the hypothesis that a majority
(more than 50%) believe the rich should pay more taxes than they do. Use a significance level of 0.06.
State the null and alternative hypotheses.
please help me thank you
Answer:
3
Step-by-step explanation:
The slope is 3. It's the correct answer.
Slope of 4/5 on line graph
Answer:
0
Step-by-step explanation:
Because it is a line parallel to x-axis.
Does anyone know this?
Answers:
A. b=4/3, c=12
B. b=4/3, c=2/3
C. b=8/3, c=16/3
D. b=8/3, c=16
Answer:
the answer will be choice D
as we can see that the triangle have angles measuring 30 60 and 90 so we will use the 30-60-90 rule
you can look up the explantion about the rule online
There were 5 7/10 of water in a bucket. Mollie spilled some of the water. Then she added an additional 1 5/10 liters of water to the bucket. After that, there was 6 4/10 liters of water in the bucket. How much did Mollie spill?
Answer:
8/10
Step-by-step explanation:
57/10 add 15/10=72/1072/10 subtract 64/10=8/10Which of the following expressions are equivalent?
Answer:
all of the expressions are equivalent
Step-by-step explanation:
if you simplify each expression, you get the same answer for all of them
HELP I NEED HELP ON THIS QUESTION ITS TIMED
Answer:
The answer is A
Step-by-step explanation:
When you reflect something over the x-axis all of the negative y coordinates become positive.
someone please help me due in an hour
Answer:
9 players rushed 20 or more yards this season
Step-by-step explanation:
How to find the GCF 2x-4y+6z
Answer:
inding the Greatest Common Factor (GCF): To find the GCF of two expressions:
Factor each coefficient into primes. Write all variables with exponents in expanded form.
List all factors—matching common factors in a column. ...
Bring down the common factors that all expressions share.
Multiply the factors
Answer:
Step-by-step explanation:
2x = 2*x
4y = 2 *2 *y
6z = 2* 3 * z
GCF = 2
GCF is the greatest common factor. Here 2 is common factor
2x - 4y + 6z = 2*(x - 2y + 3z)
Solve the equation 6m + 10n = 12 for m.
-IO
Answer:
N=7.2
Step-by-step explanation:
6x-10= -60
10x7.2= 72
72+-60=12
So N=7.2
I need help with this one and don't understand what it is trying to say!
Answer:
A
Step-by-step explanation:
Each colored box cost 0.01
Answer:
A
Step-by-step explanation:
Each colored box cost 0.01
Bob needs 496 inches of border to put around his kitchen walls. if each roll contains 10 ft of border, how many rolls will Bob need?
Identify the focus, directrix, an axis of symmetry of (f)x=1/16^2
Answer:
Focus is (0,64)
Step-by-step explanation:
Directrix is y = -64
Axis of Symmetry is x = 0
(d). Use an appropriate technique to find the derivative of the following functions:
(i) y = √4+3x²/ (x² +1)¹/³ . Pie^x
(ii) xy^3/1+ sec y= e^xy
[Verify your answer by MATHEMATICA and attach the printout of the commands and output]
(i) I would first suggest writing this function as a product of the functions,
[tex]\displaystyle y = fgh = (4+3x^2)^{1/2} (x^2+1)^{-1/3} \pi^x[/tex]
then apply the product rule. Hopefully it's clear which function each of f, g, and h refer to.
We then have, using the power and chain rules,
[tex]\displaystyle \frac{df}{dx} = \frac12 (4+3x^2)^{-1/2} \cdot 6x = \frac{3x}{(4+3x^2)^{1/2}}[/tex]
[tex]\displaystyle \frac{dg}{dx} = -\frac13 (x^2+1)^{-4/3} \cdot 2x = -\frac{2x}{3(x^2+1)^{4/3}}[/tex]
For the third function, we first rewrite in terms of the logarithmic and the exponential functions,
[tex]h = \pi^x = e^{\ln(\pi^x)} = e^{\ln(\pi)x}[/tex]
Then by the chain rule,
[tex]\displaystyle \frac{dh}{dx} = e^{\ln(\pi)x} \cdot \ln(\pi) = \ln(\pi) \pi^x[/tex]
By the product rule, we have
[tex]\displaystyle \frac{dy}{dx} = \frac{df}{dx}gh + f\frac{dg}{dx}h + fg\frac{dh}{dx}[/tex]
[tex]\displaystyle \frac{dy}{dx} = \frac{3x}{(4+3x^2)^{1/2}} (x^2+1)^{-1/3} \pi^x - (4+3x^2)^{1/2} \frac{2x}{3(x^2+1)^{4/3}} \pi^x + (4+3x^2)^{1/2} (x^2+1)^{-1/3} \ln(\pi) \pi^x[/tex]
[tex]\displaystyle \frac{dy}{dx} = \frac{3x}{(4+3x^2)^{1/2}} \frac{1}{(x^2+1)^{1/3}} \pi^x - (4+3x^2)^{1/2} \frac{2x}{3(x^2+1)^{4/3}} \pi^x + (4+3x^2)^{1/2} \frac{1}{ (x^2+1)^{1/3}} \ln(\pi) \pi^x[/tex]
[tex]\displaystyle \frac{dy}{dx} = \boxed{\frac{\pi^x}{(4+3x^2)^{1/2} (x^2+1)^{1/3}} \left( 3x - \frac{2x(4+3x^2)}{3(x^2+1)} + (4+3x^2)\ln(\pi)\right)}[/tex]
You could simplify this further if you like.
In Mathematica, you can confirm this by running
D[(4+3x^2)^(1/2) (x^2+1)^(-1/3) Pi^x, x]
The immediate result likely won't match up with what we found earlier, so you could try getting a result that more closely resembles it by following up with Simplify or FullSimplify, as in
FullSimplify[%]
(% refers to the last output)
If it still doesn't match, you can try running
Reduce[<our result> == %, {}]
and if our answer is indeed correct, this will return True. (I don't have access to M at the moment, so I can't check for myself.)
(ii) Given
[tex]\displaystyle \frac{xy^3}{1+\sec(y)} = e^{xy}[/tex]
differentiating both sides with respect to x by the quotient and chain rules, taking y = y(x), gives
[tex]\displaystyle \frac{(1+\sec(y))\left(y^3+3xy^2 \frac{dy}{dx}\right) - xy^3\sec(y)\tan(y) \frac{dy}{dx}}{(1+\sec(y))^2} = e^{xy} \left(y + x\frac{dy}{dx}\right)[/tex]
[tex]\displaystyle \frac{y^3(1+\sec(y)) + 3xy^2(1+\sec(y)) \frac{dy}{dx} - xy^3\sec(y)\tan(y) \frac{dy}{dx}}{(1+\sec(y))^2} = ye^{xy} + xe^{xy}\frac{dy}{dx}[/tex]
[tex]\displaystyle \frac{y^3}{1+\sec(y)} + \frac{3xy^2}{1+\sec(y)} \frac{dy}{dx} - \frac{xy^3\sec(y)\tan(y)}{(1+\sec(y))^2} \frac{dy}{dx} = ye^{xy} + xe^{xy}\frac{dy}{dx}[/tex]
[tex]\displaystyle \left(\frac{3xy^2}{1+\sec(y)} - \frac{xy^3\sec(y)\tan(y)}{(1+\sec(y))^2} - xe^{xy}\right) \frac{dy}{dx}= ye^{xy} - \frac{y^3}{1+\sec(y)}[/tex]
[tex]\displaystyle \frac{dy}{dx}= \frac{ye^{xy} - \frac{y^3}{1+\sec(y)}}{\frac{3xy^2}{1+\sec(y)} - \frac{xy^3\sec(y)\tan(y)}{(1+\sec(y))^2} - xe^{xy}}[/tex]
which could be simplified further if you wish.
In M, off the top of my head I would suggest verifying this solution by
Solve[D[x*y[x]^3/(1 + Sec[y[x]]) == E^(x*y[x]), x], y'[x]]
but I'm not entirely sure that will work. If you're using version 12 or older (you can check by running $Version), you can use a ResourceFunction,
ResourceFunction["ImplicitD"][<our equation>, x]
but I'm not completely confident that I have the right syntax, so you might want to consult the documentation.
