Answer:
Step-by-step explanation:
I answered your question in #24317186. Apparently you asked it twice and no one helped you yesterday.
Mark and Allen were assigned the same book to read for class. Mark started reading on Saturday , and he is reading 40 pages per day. Allen didn't start until Sunday , but he is still reading 45 pages a day.
How many days will it take Allen to catch up to Mark, and how many pages will they each have read?
Let x represent the number of days Allen has been reading.
Given:
Mark started reading on Saturday , and he is reading 40 pages per day.
Allen didn't start until Sunday , but he is still reading 45 pages a day.
To find:
How many days will it take Allen to catch up to Mark, and how many pages will they each have read?
Solution:
Let [tex]x[/tex] represent the number of days Allen has been reading. Then the number of days Mark has been reading is [tex](x+1)[/tex].
Mark is reading 40 pages per day. So, he will read [tex]40(x+1)[/tex] pages.
Allen is reading 45 pages a day. So, he will read [tex]45x[/tex] pages.
Allen catch up to Mark when they read equal number of pages.
[tex]40(x+1)=45x[/tex]
[tex]40x+40=45x[/tex]
[tex]40=45x-40x[/tex]
[tex]40=5x[/tex]
Divide both sides by 5.
[tex]\dfrac{40}{5}=\dfrac{5x}{5}[/tex]
[tex]8=x[/tex]
In 8 days Allen will catch up to Mark.
[tex]45x=45(8)[/tex]
[tex]45x=360[/tex]
Therefore, they each have read 360 pages.
What is 4 5/8 x 9 8/9???
Answer:
3293/72
Step-by-step explanation:
change to improper fraction to times.
4(10x-4). PLEASE HELP
Which is the correct form of the partial fraction decomposition for the expression StartFraction 4 x cubed + 3 x squared Over (x + 1) squared (x squared + 7) squared EndFraction?
Given:
The expression is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
To find:
The correct form of the partial fraction decomposition for the given expression.
Solution:
We have,
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
By partial fraction decomposition, it can be written as:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex] ...(i)
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]
[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]
[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]
[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]
On comparing both sides, we get
[tex]A+C=4[/tex]
[tex]A+B+2C+D=3[/tex]
[tex]7A+C+2D=0[/tex]
[tex]7A+7B+D=0[/tex]
On solving these equations, we get
[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]
Substituting these values in (i), we get
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Therefore, the required partial fraction decomposition is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Answer:
A on Edg
Step-by-step explanation:
got it right
solve for x
pls this is for an assignment to get my credits i need this
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
Let the inverse of f(x) be h(x):
[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]
x/6=7
what is the value of x
Answer:
x = 6 x 7 = 42
Step-by-step explanation:
hope this helps
Answer:
[tex] \frac{x}{6} = 7 \\ x = 6 \times 7 \\ x = 42[/tex]
In 1993 eggs cost $0.87 a dozen. In 2003 it cost $1.56 a dozen. How much did the eggs appreciate (percent of increase)?
Show your work.
Answer:
190%
Step-by-step explanation:
$1.56 is close to nearly 2x the value of $0.87
You can start by multiplying $0.87 by 2 to get $1.74
Now put $1.56 / $1.74
This gets you 0.89655172
By rounding this, you can get to 0.90
Move the decimal places two spots over to get a percentage = 90%
Since the eggs didn't decrease in value, you can add the 100% from the beginning of the problem.
100+90=190%
(1 / 7 - 4√3)^3 + (1 / 7 + 4√3)^3
Given:
The expression is:
[tex]\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 [/tex]
To find:
The simplified form of the given expression.
Solution:
Formulae used:
[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]
[tex](a-b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
Adding this formulae, we get
[tex](a-b)^3+(a+b)^3=2a^3+6ab^2[/tex] ...(i)
We have,
[tex]\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 [/tex]
Using formula (i), the given expression can be written as:
[tex]=2\left(\dfrac{1}{7}\right)^3+6\left(\dfrac{1}{7}\right)\left(4\sqrt{3}\right)^2[/tex]
[tex]=2\times \dfrac{1}{343}+6\left(\dfrac{1}{7}\right)48[/tex]
[tex]=\dfrac{2}{343}+\dfrac{288}{7}[/tex]
[tex]=\dfrac{2+14112}{343}[/tex]
[tex]=\dfrac{14114}{343}[/tex]
Therefore, the simplified form of the given expression is [tex]\dfrac{14114}{343}[/tex].
On an electricity bill of $40.80, Mrs.
Miller pays only $38.76 because she pays
before a certain date. What percent
discount is Mrs. Miller allowed?
Answer:
100%_$40.80
? × _$38.76
Step-by-step explanation:
100%×$38.76÷$40.80=95%
Answer:
40.80
Step-by-step explanation:
guys, please help i can't move on
Answer:
15
Step-by-step explanation:
32-19 = 13 that have both
70-57= 13 that have both again from that sample
total number of people that have both : 13 + 13 = 26
11 kids don't have either one, so :
26-11 = 15
Use trigonometric identities to solve each equation within the given domain.
3 tan(x) = 2 sin(2x) from [0, 2π) PLEASE SHOW WORK!!!
Recall that the tangent function is defined by
tan(x) = sin(x)/cos(x)
Also recall the double angle identity for sine,
sin(2x) = 2 sin(x) cos(x)
Then the equation is the same as
3 sin(x)/cos(x) = 4 sin(x) cos(x)
Move everything to one side to prepare to factorize:
3 sin(x)/cos(x) - 4 sin(x) cos(x) = 0
sin(x)/cos(x) (3 - 4 cos²(x)) = 0
As long as cos(x) ≠ 0, we can omit the term in the denominator, so we're left with
sin(x) (3 - 4 cos²(x)) = 0
and so
sin(x) = 0 or 3 - 4 cos²(x) = 0
sin(x) = 0 or cos²(x) = 3/4
sin(x) = 0 or cos(x) = ±√3/2
On the interval [0, 2π),
• sin(x) = 0 for x = 0 and x = π
• cos(x) = √3/2 for x = π/6 and x = 11π/6
• cos(x) = -√3/2 for x = 5π/6 and x = 7π/6
(None of these x make cos(x) = 0, so we don't have to omit any extraneous solutions.)
What is 20% of 10% of 1000
Answer:
20% of 10% of 1000 = 20
Step-by-step explanation:
Now we have to,
→ find the 20% of 10% of 1000.
Let's find 10% of 1000,
→ (10/100) × 1000
→ 0.1 × 1000
→ 100
Then 20% of 10% of 1000 is,
→ (20/100) × 100
→ 0.2 × 100
→ 20
Hence, the answer is 20.
What is the 8th term of the binomial expansion (x + y) ^10?
Select the correct answer.
A. 120x^7y^3
B. 720x^7y^3
C. 720x^3y^7
D. 120 x^3y^7
Answer:
It is Option D. 120 x^3 y^7
Option D is correct i.e. the eighth term of the given expansion is [tex]120x^{3} y^{7}[/tex].
What is binomial theorem?The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.
Binomial expressionA binomial expression is an algebraic expression that contains two dissimilar terms .
Formula for finding the general term in binomial expansion[tex]T_{r+1} =nC_{r} x^{n-r} y^{r}[/tex]
According to the given question
We have,
The binomial expansion [tex](x+y)^{10}[/tex]
Therefore,
The eighth term of the given binomial expansion is given by
[tex]T_{7+1} = 10C_7x^{10-7} y^{7} \\T_{8} = \frac{10!}{7!3!} x^{3} y^{7}[/tex]
[tex]T_{8} = \frac{(10)(9)(8)(7!)}{7!(3)(2)(1)} x^{3} y^{7}[/tex]
[tex]T_{8} = 120x^{3} y^{7}[/tex]
Hence, option D is correct. i.e. the eighth term of the given expansion is [tex]120x^{3}y^{7}[/tex].
Learn more about the binomial expansion here:
https://brainly.com/question/12249986
#SPJ2
The travel distance from Atimonan, Quezon to Marikina City is about 177.0 Kilometers. In 5 hours and 53 minutes. How many kilometers did it drive in an hour.
Answer:
It drove 30.08 kilometers in an hour.
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
In this question:
177 kilometers in 5*60 + 53 = 353 minutes.
How many kilometers in 1 hour = 60 minutes?
177 km - 353 min
x km - 60 min
[tex]353x = 60*177[/tex]
[tex]x = \frac{60*177}{353}[/tex]
[tex]x = 30.08[/tex]
It drove 30.08 kilometers in an hour.
HELPPP ME OUTTTTTT!!!!!!!
Answer:
3/5
Step-by-step explanation:
cos A = adjacent side / hypotenuse in a right triangle
cos A = 24/40
Cos A = 6/10
cos A = 3/5
Question 8 of 49
Which definition best describes skew lines?
O A. Lines that intersect at a right angle
O B. Lines that intersect
O C. Lines that do not intersect and are not in the same plane
O D. Lines that do not intersect and are in the same plane
f(x) = x2 – 3x – 2 is shifted 4 units left. The result is g(x). What is g(x)?
Answer:
Answer A: g(x) = (x + 4)² - 3(x + 4) - 2
Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units left
f(x - n) - shift the graph n units right
f(x) = x² - 3x - 2.
shift 4 units left, f(x + 4) = (x + 4)² - 3(x + 4) - 2
Answer A: g(x) = (x + 4)² - 3(x + 4) - 2
3uq. when u = 2 and q=6
Answer:
[tex]3uq \\ 3 \times 2 \times 6 \\ = 36[/tex]
Answer:
[tex]36[/tex]
Step-by-step explanation:
[tex]3uq \\ = 3(2)(6) \\ = 36[/tex]
Hope it is helpful....How would you describe the difference between the graphs of f(x) = x^2 +4 and
g(y) - y^2 +4?
Answer:
Step-by-step explanation:
The function [tex]f(x)=x^2+4[/tex] is a positive upwards opening parabola with the vertex at (0, 4), whereas
the function [tex]g(y)=y^2+4[/tex] is a positive rightwards opening parabola (sideways parabola) with the vertex at (4, 0). This means that answer to this is that g(y) is reflected over the x axis whereas f(x) is reflected over the y axis.
An apple cost $6 and a peach costs $3.Mr Joe paid $60 in all for 12 fruits. How many of apples did he buy?
Answer:
8 apples
Step-by-step explanation:
costof 8 apples=48
cost of 4 peaches=12
A train leaves zurich at 2240 and arrives in vienna at 07 32 the next day workout out the time the train takes
Answer:
Total time taken by train = 8 hour 32 minutes
Step-by-step explanation:
Given:
Time train leave Zurich = 22:40 min
Time train arrives in Vienna = 07:32
Find:
Total time taken by train
Computation:
Total time taken by train = [23:60 - 22:40] + 7:32
Total time taken by train = 1:20 + 7:32
Total time taken by train = 8:52
Total time taken by train = 8 hour 32 minutes
An 18-foot flagpole casts a shadow 12 feet long forming a triangle as shown in the diagram. You are 5.75 feet tall and cast a shadow as shown. How long is the shadow you cast given the triangles shown are similar?
A. 3.83
B. 8.63
C. 11
Answer:
Option (A)
Step-by-step explanation:
From the picture attached,
ΔABC and ΔDEF are the similar triangles.
Therefore, by the property of similar triangles, their corresponding sides will be proportional.
[tex]\frac{AB}{DE}= \frac{BC}{EF}= \frac{AC}{DF}[/tex]
[tex]\frac{5.75}{18}=\frac{BC}{12}[/tex]
BC = [tex]\frac{12\times 5.75}{18}[/tex]
BC = 3.83 ft
Option (A) will be the correct option.
SOMEONE HELP ME PLEASE
Answer:
9/10 or 90 %
Step-by-step explanation:
There are 54+27+5+4 total people = 90
The people with diploma is 54+27 = 81
P (diploma) = number with diploma / total
= 81/90
=9/10
90%
please help with this problem!
Answer:
Second option
Step-by-step explanation:
Let's assume that x is 1 and y is 3
a) [tex]\frac{1}{2}[/tex] < [tex]\frac{3}{2}[/tex] = true
b) -1 < -3 = false
c) 1+2 < 3+2 = true
d) 2 x 1 < 2 x 3 = true
[tex]52 - 6 \times 1 + 75 \times 3 \div 2[/tex]
....................................................
ASAP!!!
THANKS ........
Answer:
158.5
Step-by-step explanation:
= 52 - 6 × 1 + 75 × 3 / 2
= 52 - 6 + 75 × 3 ÷ 2
= 52 - 6 + 112.5
= 46 + 112.5
= 158.5
Answer:
The solution is 158,5
Step-by-step explanation:
52-6×1+75×3÷2
= 52-6+75×3÷2
= 46+225÷2
= 46+112,5
= 46+112,5
= 158,5
Draw a plane, showing the three (non-linear) points that define it.
Draw a plane, showing the three (non-linear) points that define it.[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
See this attachment
Suppose f(x) = 6x2 + 2x - 7 and g(x) = 4x - 3. Find each of the following functions.
a.(f+g)(x)
b. (f-9)(x)
Hello,
Step-by-step explanation:
[tex]f(x)=6x^2+2x-7\\g(x)=4x-3\\(f+g)(x)=f(x)+g(x)=6x^2+2x-7+4x-3=6x^2+6x-10\\\\(f-g)(x)=f(x)-g(x)=6x^2+2x-7-(4x-3)=6x^2-2x-4\\[/tex]
(2x-3)(x-4)(3x-1)
How do u get the 35x2 and 47x?
Answer:
70 x 47x = 3290
.
. . . . . . . . . . ........
Answer: 6x^3-35x^2+47x-12
Step-by-step explanation:
(2x-3)(x-4)(3x-1)
=(2x^2-11x+12)(3x-1)
=6x^3-35x^2+47x-12
Please help me with this question! And please provide answer in inequalities form! Thanks so much!
Answer:
Step-by-step explanation:
For this, we kind of have to test points to solve it. First, we can test theh interval x<= -2. Plug in -2 and we get a negative value which works. Next, let's try -2<x<0. Plug in -1 and get a positive value which doesn't work.
Next try 0<=x<=7. Plug in any number like 4 and get a negative value which works.
Finally, try x>7. Plug in 8 for example and you would get a positive value. So the solution is
x <= -2 OR 0 <= x <= 7
