Answers
Answer:
x = 4, 1/4
solving steps
[tex]\sf \rightarrow x + \dfrac{1}{x}=4\dfrac{1}{4}[/tex]
make the denominators same
[tex]\sf \rightarrow \dfrac{x(x)}{x} + \dfrac{1}{x}=4\dfrac{1}{4}[/tex]
simplify the following
[tex]\sf \rightarrow \dfrac{x^2}{x} + \dfrac{1}{x}=\dfrac{17}{4}[/tex]
join both fractions together
[tex]\sf \rightarrow \dfrac{x^2+1}{x}=\dfrac{17}{4}[/tex]
cross multiply
[tex]\sf \rightarrow 4(x^2+1)=17(x)[/tex]
simplify
[tex]\sf \rightarrow 4x^2-17(x)+4=0[/tex]
completing square
[tex]\sf \rightarrow 4x^2-16(x)-x+4=0[/tex]
factor
[tex]\sf \rightarrow 4x(x-4)-1(x-4)=0[/tex]
group the variables
[tex]\sf \rightarrow (4x-1)(x-4)=0[/tex]
simplify
[tex]\sf \rightarrow (x-4)=0, \ (4x-1) =0[/tex]
final answer
[tex]\sf \rightarrow x=4, \ x =\dfrac{1}{4}[/tex]
Answer:
[tex]\boxed{x = \dfrac{1}{4}}[/tex] and [tex]\boxed{x = 4}[/tex]
Step-by-step explanation:
Given equation:
[tex]x + \dfrac{1}{x} = 4\dfrac{1}{4}[/tex]
Step-1: Convert the mixed fraction on the R.H.S into improper fraction
[tex]x + \dfrac{1}{x} = 4\dfrac{1}{4}[/tex]
[tex]x + \dfrac{1}{x} = \dfrac{4 \times4 + 1}{4}[/tex]
[tex]x + \dfrac{1}{x} = \dfrac{16 + 1}{4}[/tex]
[tex]x + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
Step-2: Make common denominators on the L.H.S:
[tex]x + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
[tex]\dfrac{x^{2} }{x} + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
Step-3: Combine the denominators on the L.H.S
[tex]\dfrac{x^{2} }{x} + \dfrac{1}{x} = \dfrac{17}{4}[/tex]
[tex]\dfrac{x^{2} +1}{x} = \dfrac{17}{4}[/tex]
Step-4: Use cross multiplication
[tex]\dfrac{x^{2} +1}{x} = \dfrac{17}{4}[/tex]
[tex]x^{2} +1} = \dfrac{17x}{4}[/tex]
[tex]4(x^{2} +1}) = {17x}[/tex]
Step-5: Simplify the distributive property
[tex]4(x^{2} +1}) = {17x}[/tex]
[tex]4x^{2} +4} = {17x}[/tex]
[tex]-17x + 4x^{2} +4} = 0[/tex]
Step-6: Change "-17x" to "-16x - x" as it is equivalent
[tex]-17x + 4x^{2} +4} = 0[/tex]
[tex](-16x - x) + 4x^{2} +4} = 0[/tex]
Step-7: Factor the common terms
[tex](-16x - x) + 4x^{2} +4} = 0[/tex]
[tex]-16x - x + 4x^{2} +4} = 0[/tex]
[tex]4x(-4 + x) - 1(x - 4) = 0[/tex]
Step-8: Group the terms
[tex]4x(-4 + x) - 1(x - 4) = 0[/tex]
[tex](x - 4)(4x - 1) = 0[/tex]
Step-9i: Use cross multiplication for (x - 4)
[tex](x - 4)(4x - 1) = 0[/tex]
[tex]x - 4 = \dfrac{0}{4x - 1 } = 0[/tex]
Step-9ii: Use cross multiplication for (4x - 1)
[tex](x - 4)(4x - 1) = 0[/tex]
[tex]4x - 1 = \dfrac{0}{x - 4} = 0[/tex]
Thus [tex]x - 4 = 0[/tex] and [tex]4x - 1 = 0[/tex].
Step-10: Simplify both equations
[tex]4x - 1 = 0[/tex] [tex]x - 4 = 0[/tex]
[tex]4x = 0 + 1[/tex] [tex]x = 0 + 4[/tex]
[tex]4x = 1[/tex] [tex]\boxed{x = 4}[/tex]
[tex]\boxed{x = \dfrac{1}{4}}[/tex]
Related Questions
Erik is learning how to make hachapuris. He uses 5 eggs for each hachapuri.
Erik has 12 eggs, and he makes as many hachapuris as he can. How many
hachapuris does Erik make? How many eggs are left?
unters
Answers
Answer:
2
Step-by-step explanation:
he has 12 eggs and each hachapuri needs 5 so for one hachpuri we have 7 then for the second hachapuri we need 5 so we are left with 2 we cant make them anymore so there you go
Arron is getting new carpet in his bedroom. The dimensions of his room are 8 feet by 15 feet. How much carpet does he need to cover the whole floor?
Answers
Answer:
120 square feet ( 13.333 square yards)
Step-by-step explanation:
8 ft x 15 feet = 120 ft^2
a farmer has 47 eggs.He packs 6 eggs in each box. How many egg boxes does he need to packall the eggs?
Answers
We need to divide up 47 eggs into boxes of 6. Therefore, we are doing a division problem.
6 x 7 = 42
42 is as close as we can get to 47 without going over. So, at this point, we need 7 boxes.
BUT - There are 5 eggs left without a box. We cannot have part of a box either. Therefore, we need to add in another box.
7 + 1 = 8
He needs 8 boxes to pack all the eggs.
Hope this helps!
Answ
Step-by-step explanation:
17 boxes 47 divided by six so it is 17 boxes hope it helps:)
what value of x makes the equation 3^(x-5)=27^(x+4) true?
Answers
Answer:
The attached file contains the solution to the question
Which recursive sequence would produce the sequence 2, 11, 38,...?
Answers
Answer:
[tex]a_{1} =2[/tex] and [tex]a_{n} =4a_{n-1} + 3[/tex]
Step-by-step explanation:
hope this helps!! p.s. i really need brainliest :)
Betty has some bottles.
4
7
of the bottles are big and
4
5
of the remaining bottles are small. The rest of the bottles are tiny.
What fraction of the bottles are tiny?
Answers
Step 1: Determining and using scale factors The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a model of it using blocks. b) Suppose you are making a model where one block represents 5 feet. About how many blocks tall is your model of the Empire State Building? What is the scale factor? (2 points) What is the scale factor? About how many blocks tall is your model of the Empire State Building?
(no joke answer and no links please)
Answers
Answer:
See below ↓↓
Step-by-step explanation:
About how many blocks tall is your model of the Empire State Building?
Divide the actual height by the unit height of a block⇒ 1,450 / 5⇒ 290 blocksWhat is the scale factor?
Height of block model = 5 ftHeight of empire state building (actual) = 1,450 ftScale factor = Actual : modelScale factor = 5 : 1,450 = 1 : 290What Is the area in a triangle 9m 11m?
Answers
Answer:
49.5
Step-by-step explanation:
area of triangle = (b x h) / 2
9 x 11 = 99
99 / 2 = 49.5
Hope this helps!
- profparis
Explain how you know 1 5/8 is little greater than 1 1/2.
Answers
Answer:
1 5/8 is 1/8 greater than 1 1/2
Step-by-step explanation:
if we take off the one from both expressions, we're left with
5/8 and 1/2.
To better compare the fractions, we can make them have equal denominators. To do this, multiply both the numerator and denominator of 1/2 by 4: (1*4)/(2*4) = 4/8.
5/8 is larger than 4/8 by 1/8, therefore, 1 5/8 is larger than 1 1/2 by 1/8.
Step-by-step explanation:
1 5/8 is greater than 1 1/2 because if you draw 1 5/8 and on the bottom 1 1/2 you will see that 1 5/8 is greater.
0.3x =2.1 how would i solve this
Answers
[tex]0.3x = 2.1\\\\\implies 10\times 0.3x = 10 \times 2.1~~~~;[\text{Multiply both sides by 10}]\\\\\implies 3x = 21\\\\\implies x = \dfrac{21}3 = 7[/tex]
4. A pet store has 11 lizards, with these lengths in inches:
5 1/2, 5 3/4, 5 3/4, 5 7/8, 5 7/8, 6, 6 1/8, 6 1/8, 6 1/8, 6 1/4, 6 3/8
Draw a line plot for this data
Answers
Answer/Step-by-step explanation:
Before we draw a line plot for this data we first need to put then from least to greatest. As well as how many number are each.
Given the following data:
5 1/2
5 3/4
5 3/4
5 7/8
5 7/8
6
6 1/8
6 1/8
6 1/8
6 1/4
6 3/8
We can see that we have:
5 1/2 {1}
5 3/4 {2}
5 7/8 {2}
6 {1}
6 1/8{3}
6 1/4 {1}
6 3/8 {1}
Now put the following from least to greatest:
5 1/2 {1}
5 3/4 {2}
5 7/8 {2}
6 {1}
6 1/8{3}
6 1/4 {1}
6 3/8{1}
We can see that they already in order thus, let put it on a line plot from least to greatest.
~learn with lenvy~
Questione Simplify Cosa + 2Cos(a +240")
Answers
Step-by-step explanation:
[tex] \cos(a) + 2 \cos(a + 240) [/tex]
[tex] \cos(a) + 2 \cos(a) \cos(240) - \sin(a) \sin(240) [/tex]
[tex] \cos(a) + 2( - \frac{ \cos(a) }{2} + \frac{ \sqrt{3} }{2} \sin(a) )[/tex]
[tex] \cos(a) - \cos(a) + \sqrt{3} \sin(a) [/tex]
[tex] \sqrt{3} \sin(a) [/tex]
If you graph the new identity, and the og identiy, they will be conciding graphs, so they are the same identity.
Find the value of x.
52°
128°
38°
xº
x = [21°
Answers
Step-by-step explanation:
x = 360 - 128 + 52 + 38
x = 360 - 218
x = 142
HELP PLEASEEEEEEEEEWEEEEEEEE
Answers
Answer:
x = 27° , <EAF = 27°
Step-by-step explanation:
63° + x° = 90°
x = 27°
63° + <EAF = 90°
<EAF = 27°
How would you use the formula "V = BH" to find the volume of a tent? Explain.
Answers
Explanation:
The volume formula ...
V = BH
is a formula for the volume of a general prism whose cross sections parallel to the base all have area B. The distance between the parallel bases is represented by H.
__
To use this formula to find the volume of a tent, the area of the end of the tent would be substituted for B, and the length of the tent (distance between the ends) would be substituted for H.
An appropriate formula would need to be used for the end area.
solve the following pair of equations by elimination method: x+y=4, 2x+y=3
Answers
Answer:
x = 1
y = 5
Step-by-step explanation:
x + y = 4 __ (1)
2x + y = 3 __ (2)
equation (1) x 2, (2) x 1
2x + 2y = 8
2x + y = 3
0 + y = 5
y= 5 (ANS)
x + y = 4
x + 5 = 4
x = 5 - 4
x = 1 (ANS)
I HOPE MY ANSWER IS CORRECT IF NOT I APOLOGIZE.
Cole is buying a pair of sneakers. The expression shown represents the sales tax on the price of the sneakers, p.
0.045p
Write an expression in terms of p to represent the total amount Cole spends on the pair of sneakers, including tax.
Answers
By direct addition, we will see that the expression is:
T = 1.045*P.
What expression represents the total price of the sneakers?
We know that the price of the sneakers is P. We also know that the expression which represents the taxes of the sneakers is 0.045*P.
Now, we can assume that the total price of the sneakers will be the price plus the correspondent tax, then we can write:
T = P + 0.045*P = (1 + 0.045)*P = 1.045*P
This is the expression that represents the total amount Cole spends on the pair of sneakers.
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PLEASE HELP PLEASE HELP
Answers
Answer:
Option D - Line P
Step-by-step explanation:
Look at the coordinates in the (x, y) column of Max's table and see which line has the same points.
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. y = x squared + 2 x + 10 a. (1, 9) c. (1, 10) b. (-1, 10) d. (-1, 9)
Answers
Step-by-step explanation:
Answer: its d
Step-by-step explanation:
Right answer = brainliest! :>
The radius of a cylindrical construction pipe is 2.5 ft. If the pipe is 20 ft. long, what is its volume?
Use the value 3.14 for pi, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
Answer: The volume of the pipe is 412 cubic feet
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a cylinder = π x radius² x height (Length in this case)
Replacing with the values given:
V = 3.14 (2.5)² 21 = 3.4 (6.25) 21 = 412.12 = 412 cubic feet (rounded)
In conclusion, the volume of the pipe is 412 cubic feet
Feel free to ask for more if needed or if you did not understand something.
Answer:
V = 392.5 cubic feet
Step-by-step explanation:
[tex]v=\pi r^{2} h=\pi (2.5)^{2} (20)=\pi (6.25)(20)=125\pi[/tex]
[tex]\pi =3.14[/tex]
[tex]v=392.5cu.ft[/tex]
Hope this helps
What is your filed called when you open it in Photoshop?
A. PDF
B. MP3
C. JPEG
D. Doc
Answers
Answer:
B. MP3 idek if its right im just doing the 5 step thing
For circle B, BG = BE, BG is perpendicular to DC, and BE is perpendicular to FA. What conclusion can be made? a circle with center B and chords DC and FA, a segment from B to chord DC intersect chord DC at G, and a segment from B to chord FA intersects chord FA at E segment DC is parallel to segment FA segment CD is congruent to segment EB segment GB is parallel to segment EB segment DC is congruent to segment FA
Answers
Base on the equidistant chords theorem, chords FB and DA are congruent because they are equidistant from C.
What is the Equidistant Chords Theorem?The equidistant chords theorem states that two chords in the same circle are congruent to each other, if they are equidistant from the center of the circle.
Thus, based on the information given we can conclude that chords FB and DA are congruent because they are equidistant from C based on the equidistant chords theorem.
Learn more about the equidistant chords theorem on:
https://brainly.com/question/7511582
Answer:
Its D The one at the top is incorrect.
Step-by-step explanation:
I got A 100% which means i got it right...
Which is the solution set of this inequality?
-1/4r-3/5<5/8
A: r>-4 9/10
B: r<-4 9/10
C: r>4 9/10
D: r<4 9/10
Answers
Answer:
Step-by-step explanation:
The solution to the inequality will be (B) r<-4 9/10. Don't ask me why. I just know.
Write an equation of the line that passes through (3,1) and (0,10) .
Answers
Answer:
(1,1) and (0,1)
Step-by-step explanation:
i think thats it i dont know what it looks like i need a picture of it
Amy wants to her ice cream cone filled exactly to the top. The radius of the cone is 2 in. and the height is 6 in. How much ice cream will it take to fill the cone?
Answers
Answer:
Answer given below in the following pictures.
I hope my answer helps you.
f(x) = - 0.05(x ^ 2 - 26x - 120)
What do the zeros of this function represent? Remember the zeros are where f(x) =0.
Answers
We are given function for the path coming out of the cannon.
We also given x is the horizontal distance from the cannon.
We need to explain, what f(x) represents there.
f(x) represents y-axis.
And y-axis also represents height.
Height represents a vertical distance.
Therefore, we could say f(x) represents vertical distance (height) from the cannon for x horizontal distance from the cannon.
a swim team consists of seven boys and four girls a relay team of four swimmers is chosen at random from the team members what is the probability that two boys are selected for the relay team given that the first two selections were girls
Answers
Answer:
16/121
Step-by-step explanation:
First, we need to calculate the chance of a girl being selected for the first pick.
Since there are 4 girls and 7 boys, there are 11 total members on the team. Since 4 of them are girls, there is a [tex]4/11[/tex] chance that a girl is chosen first pick.
Next, to find the chance of the second selection to also be a girl, we have to multiply 4/11 by 4/11 to find that total.
[tex]\frac{4}{11} *\frac{4}{11} =\frac{16}{121}[/tex]
Therefore, the chance of the first two selections being girls is 16/121.
#LearnWithBrainly
27 + x = 42 what is the value of x
Answers
Answer: x = 15
Step-by-step explanation:
Given:
27 + x = 42
Subtract 27 from both sides of the equation:
x = 15
27 + x = 42
Subtract 27 from both sides:
X = 15
Mega Movers charges $19.50 per day for truck rentals, plus an additional mileage fee of $0.95 per mile. U-Move-It charges $42.00 per day for truck rentals, plus an additional mileage fee of $0.45 per mile for mileage over 20 miles. Which of the following systems of equations could be used to find the total mileage, m, that will make the cost, p, of renting a moving truck for one day equal at each rental company, assuming m≥20, is greater than or equal to, 20?
Answers
The equation used to find the total mileage, m, that will make the cost, p, of renting a moving truck for one day equal at each rental company is 45 miles
EquationTotal mileage = mCost = pMega movers:
Fixed cost per day = $19.50
Additional cost per mileage = $0.95
p = 19.50 + 0.95m
U-move:
Fixed cost per day = $42.00
Additional cost per mileage =$0.45
p = 42.00 + 0.45m
Equate the cost of both company19.50 + 0.95m = 42.00 + 0.45m
0.95m - 0.45m = 42.00 - 19.50
0.50m = 22.50
m = 22.50 / 0.50
m = 45 miles
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#SPJ1
For which values of x is the expression undefined
Answers
if you take 6x + 1 = 0 you can solve for x:
6x = -1
x = -1/6
