Answer:
x = [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x}{x+1}[/tex] - [tex]\frac{5}{x}[/tex] = [tex]\frac{4}{x^2+x}[/tex] ← factor denominator
[tex]\frac{4x}{x+1}[/tex] - [tex]\frac{5}{x}[/tex] = [tex]\frac{4}{x(x+1)}[/tex]
[ x ≠ 0, x ≠ - 1 as these would make the terms undefined ]
Multiply through by x(x + 1)
4x² - 5(x + 1) = 4
4x² - 5x - 4 = 4 ( subtract 4 from both sides )
4x² - 5x - 9 = 0 ← in standard form
(x + 1)(4x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
4x - 9 = 0 ⇒ 4x = 9 ⇒ x = [tex]\frac{9}{4}[/tex]
However, x ≠ - 1 for reason given above, then
solution is x = [tex]\frac{9}{4}[/tex]
NEED HELP ASAP!!!!!!!!!!!!!!!!!
Answer:
I think it is 6 sorry if it is wrong
Step-by-step explanation:
;-;
Answer:
Since 3^5 is equal to 243, that means if you were to evaluate 3^5, the answer would be 243. That means it would be very easy to evaluate as the answer is already stated to be equal to 243.
Drag and Drop the right answer in the answers below.
CAT ~ DOG
Answer:
Do ,Ct, OG hope it helps have a nice day
write the indicated trig ratio as a fraction
Sin K =
4x + y = 14. 5x +2y = 19 solve the simultaneous equation
Answer:
(3, 2 )
Step-by-step explanation:
Given the 2 equations
4x + y = 14 → (1)
5x + 2y = 19 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the y- term
- 8x - 2y = - 28 → (3)
Add (2) and (3) term by term to eliminate y
- 3x + 0 = - 9
- 3x = - 9 ( divide both sides by - 3 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
4(3) + y = 14
12 + y = 14 ( subtract 12 from both sides )
y = 2
solution is (3, 2 )
Step-by-step explanation:
[tex] \underline{ \underline{ \text{USING \: ELIMINATION \: METHOD}}}[/tex]
[tex] \underline{ \underline{ \text{ Solution}}} : [/tex]
[tex] \text{4x + y = 14 - - - - - (i)}[/tex][tex] \text{5x + 2y = 19 \: - - - - - (ii)}[/tex]Multiply equation ( i ) by 2 & Subtract from ( ii ). The equation ( i ) now becomes 8x +2y = 28 { 2 ( 4x + y ) = 2 × 14 }. Remember that while subtracting the sign of each term of equation ( i ) changes and now , it becomes -8x-2y = -28.
[tex] \text{5x + 2y = 19}[/tex]
[tex] \text{ - 8x - 2y = - 28}[/tex]
_____________________
[tex] \text{ - 3x = - 9}[/tex]
Solve for x :
⤑ [tex] \tt{x = \frac{ - 9}{ - 3}} [/tex]
⤑ [tex] \tt{x = 3}[/tex]
Now , substitute the value of x in equation ( ii ) :
⟼ [tex] \text{5 × \: 3 + 2y = 19}[/tex]
⟼ [tex] \text{15 + 2y = 19} [/tex]
⟼ [tex] \text{2y = 19 - 15}[/tex]
⟼ [tex] \text{2y = 4}[/tex]
⟼ [tex] \text{y = 2}[/tex]
[tex] \pink{ \boxed{ \boxed{ \tt{⤿ \: Our \: final \: answer : \boxed{ \boxed{ \tt{x = 3 \: and \: y = 4}}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day night ! ♡
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Help plz :)) I would appreciate it
Answer:
VW = 29
Step-by-step explanation:
Perimeter of the triangle = 82
Perimeter of the triangle = 4x + (x + 3) + (3x - 1)
4x + (x + 3) + (3x - 1) = 82
4x + x + 3 + 3x - 1 = 82
8x + 2 = 82
8x = 82 - 2
8x = 80
x = 10
VW = 3x - 1
VW = 3(10) - 1
VW = 30 - 1
VW = 29
Please help, I don't understand how to do this equation
Answer: B) -1/3i
Step-by-step explanation: 81(-1/3i)^4
Answer:
Step-by-step explanation:
81x^4=1
x^4=1/81
(x^4)^(1/4)=(1/81)^(1/4)
x=+\-1/3
so -1/3 is a solution
f(x) =
4/x²+1
Asymptotes
Answer:
vertical asymptotes at
x
=
±
1
horizontal asymptote at
y
=
0
Step-by-step explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.
solve:
x
2
−
1
=
0
⇒
x
2
=
1
⇒
x
=
±
1
⇒
x
=
−
1
and
x
=
1
are the asymptotes
Horizontal asymptotes occur as
lim
x
→
±
∞
,
f
(
x
)
→
c
(a constant)
divide terms on numerator/denominator by the highest power of x, that is
x
2
f
(
x
)
=
4
x
x
2
x
2
x
2
−
1
x
2
=
4
x
1
−
1
x
2
as
x
→
±
∞
,
f
(
x
)
→
0
1
−
0
⇒
y
=
0
is the asymptote
Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 1 , denominator-degree 2) Hence there are no oblique asymptotes.
graph{(4x)/(x^2-1) [-10, 10, -5, 5]}
Find the product of the monomial and the polynomial:
−3a·(7a^2−4)
Answer:
[tex]-21a^{3}+12a[/tex]
Step-by-step explanation:
We are given that
[tex]-3a\cdot (7a^2-4)[/tex]
We have to find the product .
To find the product we will multiply -3a with each term given in the bracket
[tex]-3a(7a^2)-3a(-4)[/tex]
[tex]-21a^{1+2}+12a[/tex]
By using the formula
[tex]a^{x}\cdot a^{y}=a^{x+y}[/tex]
[tex]-21a^{3}+12a[/tex]
Hence,
[tex]-3a\cdot (7a^2-4)=-21a^{3}+12a[/tex]
I need heeeelp please !
Write the an equation of a line that is perpendicular to y= 1/3x + 5 and intersects it at the y intercept
Answer:
y = -3x + 5
Step-by-step explanation:
For two lines to be perpendicular, the product of their slope must be -1.
Slope of the given line M = 1/3
Slope of the required line is m
If product is -1, then;
Mm = -1
1/3 m = -1
m = -3
SInce it intersects at the y intercept, y intercept c = 5
Get the required equation. Substitute m = -3 and c = 5 into the equation
y = mx+c
y = -3x + 5
Hence the required equation of the line is y = -3x + 5
Standard Questions
1
2
N
Question Progress
Rearrange t = 5s + 4 to make s the subject.
Answer:
[tex]s = \frac{1}{5}t - \frac{4}{5}[/tex]
Step-by-step explanation:
Subtract 4 and divide by 5 to obtain
[tex]t=5s + 4\\s = \frac{t-4}{5}\\s = \frac{1}{5}t - \frac{4}{5}[/tex]
Hey guys please help!!
Answer:
Yes
Step-by-step explanation:
g(x) = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{1}{4}[/tex] ....... (1)
(1) × 4
4y = - x + 1
x = - 4y + 1
y = - 4x + 1
f(x) = - 4x + 1
∴ f(x) and g(x) are inverses
Find the area of the rectangle.
a rectangle with a side length of three eighths and a side width of five sevenths. The lengths are measured in meters
2x + (3)(x) + (3)(4)
Answer:
if you were looking for the solution i think it is Solution
5 + 1 2
Step-by-step explanation:
Answer:
the answer is 5x + 12
Step-by-step explanation:
because its the tight answer.
write an equation that models the points (-1,4) and (3,2)
Answer:
Step-by-step explanation:
y=mx+b
m=(y2-y1)/((x2-x1)=(2-4)/(3- -1)=-2/4=-.5
y=-.5(3)+b, using point (3,2)
2=-1.5+b
b=3.5
y= -.5x+3.5
under the scale factor of the dilation (with center at the origin )if point U (6,2) becomes U' (12,4) ?
Answer:
im assuming that it it went up 6,2 and prolly has a pattern and that this is just a graph problem
Step-by-step explanation:
Answer:
umm i dont knowe sorry
Step-by-step explanation:
Taylor invested $650 in an account paying an interest rate of 2.3% compounded
daily. Assuming no deposits or withdrawals are made, how long would it take, to the
nearest tenth of a year, for the value of the account to reach $880?
Answer:
Step-by-step explanation:
Given that:
Principal = $650
Interest rate, r = 2.3% = 0.023 compounded daily
Time, t it takes for final amount, A to reach $880
Using the relation :
A = P(1 + r/n)^nt
n = number of times compounded per period
Hence, n = 365
880 = 650(1 + 0.023/365)^365t
880/650 = 1.0000630^365t
1.3538461 = 1.0000630^365t
Take the log
0.1315692 = 0.0000273596 * 365t
0.1315692 = 0.0099862t
t = 0.1315692 / 0.0099862
t = 13.175101
t = 13.18 years a
The trapezoids are similar. In the figure below ABCD ~ EFGH. What is the value of x?
Answer:
abcd
Step-by-step explanation:
Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim’s head to the furthest tip of the shadow is 13 feet.
A right triangle with side length 6 feet, s, and hypotenuse 13 feet.
[Not drawn to scale]
What is the length of Fahim’s shadow? Round to the nearest tenth of a foot.
7.0 feet
8.5 feet
11.5 feet
14.3 feet
Answer: 11.5 feet
Step-by-step explanation:
We should note that for a right angles triangle, the square of the hypothenuse equals to the square of the opposite side and its adjacent. This can be expressed as:
Let the length of Fahims shadow be x
hypotenuse² = opposite² + adjacent ²
13² = 6² + x²
169 = 36 + x²
x² = 169 - 36
x² = 133
x =✓133
x = 11.53
= 11.5 feet to nearest tenth
Answer:
C 11.5
Step-by-step explanation:
Have a great day!
Select all that apply.
Which representations show a direct variation?
y = - x
y = 2 x + 3
Input (x) 3 6 9 12 15
Output (y) 4 8 12 16 20
Answer:
Options 1 and 3 are direct variationStep-by-step explanation:
Direct variation is:
y = kxOptions:
1.
y = -x, k = -1, yes2.
y = 2x + 3, not a direct variation, no3.
Try the input/output to determine the direct variation:
4 = 3k k = 4/3Verify the other pairs:
x = 6, y = 6(4/3) = 8x = 9, y = 9(4/3) = 12x = 12, y = 12(4/3) = 16x = 15, y = 15(4/3) = 20This is also a direct variation
Help please and please make sure the answer is right please!!!!
Answer:
7
Step-by-step explanation:
Please help!
What is the intial value of the function represented by this graph?
A. 0
B. 1
C. 2
D. 5
The scale of a model train is 1 inch to 13.5teet One of the cars of the model train is 5 inches long-
What is the length, in feet, of the actual car?
Show work
Given :
The scale of a model train is 1 inch to 13.5 feet.
One of the cars of the model train is 5 inches long.
To Find :
The length, in feet, of the actual car.
Solution :
It is given that scale of the model is 1 inch to 13.5 feet. It means that 1 inch in the actual scale is equal to 13.5 feet in real.
So, length of car real is :
Length = 5 × 13.5 feet
Length = 67.5 feet
Therefore, the length of the actual car is 67.5 feet.
Need help with mymathlab problem
Answer:
not question no answer
Step-by-step explanation:
sana po magets nyo po
witch is longer distsance 20% of 320 miles of 1/2of 130 you must show your working out
Answer: [tex]\frac{1}{2}\ \text{of}\ 130> 20\%\ \text{of}\ 320[/tex]
Step-by-step explanation:
[tex]20\%\ \text{of}\ 320\ \text{is}\\\Rightarrow \frac{20}{100}\times 320=64\ \text{miles}[/tex]
[tex]\frac{1}{2}\ \text{of}\ 130\ \text{is} \\\Rightarrow \dfrac{130}{2}=65\ \text{miles}[/tex]
clearly, [tex]\frac{1}{2}\ \text{of}\ 130> 20\%\ \text{of}\ 320[/tex]
Ben and Carson went to the movies with friends. Ben purchased 3 popcorn and 2 boxes of candy for $41. Carson purchased 1 popcorn and 2 boxes of candy for $29. How much did the popcorn cost?
Answer:
$6
Step-by-step explanation:
B- 3P+2C=$41
C-1P+2C=$29
since they both bought at least 1 popcorn and 2 candy you can just subtract 29 from 41. you get 12 which equals the other 2 popcorns that ben bought
12/2=6
since you need to find the price of 1 popcorn you have to divide 12 by 2
How does paragraph 2 help to develop the main ideas of the text?
A
It argues that a university education is less important than national service,
B
It introduces the idea of giving back to society through national service,
It outlines the similarities between academic learning and national service
D
It presents some financial reasons for students to consider national service,
Lina has five more than seven times as many pictures as photo albums. If she has 75 pictures, how many photo albums does she have?
Answer:
photo albums = x
pictures =75( seven times of albums +5)
so
seven times of x is 7x and +5
7x +5 = 75
7x= 75-5
7x = 70
x=70÷7
x =10
x = 10 = photo albums
can someone help me out with this problem ?
I'll show a pic of my question
Answer:
Umm I think you forgot to send the pic with this question
Step-by-step explanation:
Hope I can help next time!!!!!!