Solve:
x + 1/x = 4 1/4


Ans: 4,1/4​

Solve:x + 1/x = 4 1/4Ans: 4,1/4

Answers

Answer 1

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 2

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

BRAINLLY!!! PLEASE HELP I'll GIVE BRAINLY!!!!

Answers

Answer: 495

Step-by-step explanation:

Since the foil covers the object and does not fill it, this problem is a matter of surface area rather than volume. Surface area is finding the area of all the faces, and adding them up.

Since we know the two triangular ends are not covered, this actually makes the problem easier.

Going with our definition of surface area above, we do:

(16.5 * 13) + (16.5 * 12) + (16.5 * 5) = 495

Our answer is 495

Answer:

C: 495ft²

Step-by-step explanation:

You need to calculate and add the surface area of the three rectangular faces of this prism. The two triangular ends are not covered in the foil as stated in the question. You find this like any other rectangle by multiplying the length by the width. (a = lw)

Let's start with the bottom rectangle, it has dimensions of 5x 16.5ft

5 * 16.5 = 82.5

Now the rectangle on the right side.

13 * 16.5 = 214.5

Now the left or back side rectangle.

12 * 16.5 = 198

Now add these values together

82.5 + 214.5 + 198 = 495ft²

Find the missing sides

Answers

Answer:

i believe _=6 (the horizontal side, as it says on the picture,) | = 6 (the vertical side,) and \ = 8.48 (the diagonal)

Step-by-step explanation:

To find the diagonal, you have to use the Pythagorean Theorem, which is a^2 + b^2 = c^2

So, a and b both equal 6, square both of those, you got 36 for each.

Now, add them together and youll get 72

The square root of 72 is around 8.48

Although, im not entirely sure if thats correct or not, so i wouldnt really recommend putting this as your answer :|

V
Find the angle between v=i+2j+3k and w=4i-k.
:2
.

Answers

Answer:

86.28 degrees

Step-by-step explanation:

Angle between vectors is

[tex] \cos(x) = \frac{cross \: product}{magnitudes \: multiplied} [/tex]

The cross product is

[tex]4 + 0 - 3 = 1[/tex]

The magnitudes of first vector is

[tex] \sqrt{1 {}^{2} + 2 {}^{2} + 3 {}^{2} } = \sqrt{14} [/tex]

The second vector magnitude is

[tex] \sqrt{17} [/tex]

So the magnitudes multiplied is

[tex] \sqrt{14} \times \sqrt{17} = \sqrt{238} [/tex]

So our equation will be

[tex] \cos(x) = \frac{1}{ \sqrt{238} } [/tex]

[tex]x = \cos {}^{ - 1} ( \frac{1}{ \sqrt{238} } ) [/tex]

X is about 86.28 degrees

9)

What is the complete factorization of x2 + 4x-45?
OA (x + 15)(x-3)
OB. (x- 9)(x + 5)
OC. (x + 9)(x - 5)
OD. (x - 15)(x+3)​

Answers

Answer:

C

Step-by-step explanation:

x^2+4x-45

(x+9)(x-5)

since 4x is positive, the larger factor of 45 needs to be positive

that's why the 5 is negative

when solving problems like this, just find two factors of the last number that add up to the middle number

then throw them in parenthesis with an x

Hi,

x2 + 4x − 45 can be factorized to (x + 9)(x - 5).

the correct answer is C (x + 9)(x - 5).

I added a screenshot...

XD


50 POINTS! Please help me! I give Brainliest!
1. Given the following coordinates, complete the listed transformations in sequence, which means you do one after the other.
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwise
b) Dilation by a scaling factor of 2
c) Reflect across the x-axis
d) Translation 2 Up and 5 to the Left

4 PARTS TO THIS QUESTION! ANSWER ALL PLEASE!

Answers

#1

Clockwise 90° rotation rule (x,y)—»(y,-x)

X'=(4,-2)Y'=(-3,-5)Z'=(1,7)

#2

Dilation of scale factor 2

X''=(4×2,-2×2)=(8,-4)Y''=2(-3,-5)=(-6,-10)Z''=2(1,7)=(2,14)

#3

reflection across x axis rule (x,y)—»(x,-y)

X'''=(8,4)Y'''=(-6,10)Z"'=(2,-14)

#4

Rule for given translation (x-5,y+2)

X""=(8-5,4+2)=(3,6)Y""=(-6-5,10+2)=(-11,12)Z""=(2-5,-14+2)=(-3,-12)

Answer:

Given points:

X = (2, 4)Y = (5, -3)Z = (-7, 1)

Part (a)

Rotate 90° clockwise (about the origin): (x, y) → (y, -x)

X' = (4, -2)Y' = (-3, -5)Z' = (1, 7)

Part (b)

Dilation by a scale factor → multiply the points by the scale factor

scale factor = 2

X'' = (8, -4)Y'' = (-6, -10)Z'' = (2, 14)

Part (c)

Reflect across the x-axis:  (x, y) → (x, -y)

X''' = (8, 4)Y''' = (-6, 10)Z''' = (2, -14)

Part (d)

Translate 2 up and 5 to the left:  (x, y) → (x - 5, y + 2)

X'''' = (3, 6)Y'''' = (-11, 12)Z'''' = (-3, -12)

In a recent poll, 50 teenagers were asked do they exercise regularly. 35% of them said they do exercise regularly? What is the random Variable?

Answers

Step-by-step explanation:

In a recent poll, 50 teenagers were asked do they exercise regularly. 35% of them said they do exercise regularly? What is the random Variable?

Which statement is not true?
A. I7I = -7
B. I7I = 7
C. I5I= 5
D. I-5I = 5​

Answers

Answer:

a

Step-by-step explanation:

absolute value means the distance from 0 and it has to be a positive number so the answer has to be a

Given m n, find the value of x.
(7X-10)9
(6x-5)°

Answers

Answer:

x = 15

Step-by-step explanation:

Since m and n are parallel to the line t.

Then (7x - 10) + (6x - 5) = 180° supplementary angles for a linear pair.

(7x - 10) + (6x - 5) = 180°

13x -15 = 180°

13x = 195°

x = 15

Plug x into the angles to solve for angle.

(7x - 10)

(7*15 - 10) = 105 - 10 = 95°

(6x - 5) =

(6*15 - 5) = 90 - 5 = 85°

PLEASE HELP ILL GIVE THANKS, 5.0, AND BRAINLIEST TO WHOEVER ANSWERS CORRECTLY PLEASE HELP AND ILL GIVE A HIGH POINT COUNT
Sophie bikes at a speed of s miles per hour. Her friend Rana is slower, her biking
speed is only r miles per hour.
Tomorrow both girls are planning to spend 3 hours biking. How much longer will be
Sophie's route?

Answers

Answer:

FOR THIS PROBLEM I GOT..... (20/r)-(20/s)

Step-by-step explanation:

pls brainlest mee

Triangle JKL has vertices at the following coordinates: J(2, 2), K(-1, 3), and L(-2, -1). Determine whether or not triangle JKL is a right triangle. Show all calculations for full credit.

Answers

Triangle JKL is not a right triangle because its side lengths are not a Pythagorean triple.

What is a Right Triangle?

A right triangle is a triangle, whose set of sides are Pythagorean triple, that is, the square of the longest side equals the sum of the square of the other shorter sides.

Find the lengths of the sides of triangle JKL given:

J(2, 2)

K(-1, 3)

L(-2, -1)

Using the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], we have:

JK = √[(−1−2)² + (3−2)²]

JK = √10

KL = √[(−1−(−2))² + (3−(−1))²]

KL = √17

JL = √[(2−(−2))²+(2−(−1))²]

JL = √25

JL = 5

JL is the longest side. If triangle JKL is a right triangle, then, JL² = JK² + KL²

Plug in the values to confirm

5² = (√10)² + (√17)²

25 = 10 + 17

25 ≠ 27 (Not true)

Therefore, triangle JKL is not a right triangle because its side lengths are not a Pythagorean triple.

Learn more about right triangle on:

https://brainly.com/question/2437195

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

Blue stars are the hottest stars.

A six sided die is tossed. Determine the odds against rolling a four

Answers

Answer:

i think the answer would be 1/6 because 6 sides 1 number per side

Which expression is equivalent to 4/5x + 1 4/5
A 1/5(4x +1)
B 2/5(2x + 3)
C 4/5 (x + 2)
D 5/4 (x + 1)

Answers

There is none, but the closest is C.

It should be: 4/5( x + 2.25)

4/5 x x = 4/5x

4/5 x 2.25 = 9/5 (or 1 4/5)

(4 x? = 9) ==> 2.25

Step-by-step explanation:

A) 4/5 x + 1/5

B) 4/5x + 6/5 (or 1 1/5)

C) 4/5x + 8/5 (or 1 3/5)

D) 5/4 x + 5/4 (or 1 1/4)

Hope this helps!

A company sells confetti in boxes in the shape of a triangular
pyramid. Each box contains a volume of 240 cubic centimeters of confetti, If
the height of the box is 15 centimeters, which of the following
could be the area of the base of the box?
Volume Formula:
V number:
h of the 3-D shape number:

Answers

Answer:

who is William afton family?

Can y’all figure out the answer for me please

Answers

The answer is A. True.

Hope this helps

Answer:

True

Step-by-step explanation:

Two triangles are similar { ~ } only when they have same shape. And as these figures have same shape so they are similar. And their corresponding sides are equal too...

find the value of x super easy 7th grade math

Answers

Answer:

x = 50 degrees

Step-by-step explanation:

all the angles of a triangle add up to 180

a right angle is ninety degrees

90 + the 40 degrees on the top is 130 degrees

180 - 130 is 50

x = 50

Answer:

50°

[tex] \: [/tex]

Step-by-step explanation:

Before finding the value of x, we must know this first.

[tex] \\ \longrightarrow \qquad { \underline{ \boxed{ \pmb{ \frak{Sum \: of \: all \: \: angles_{(Triangle)} = 180 {}^{ \circ} }}}}} \: \: \bigstar \\ \\ [/tex]

This is a right angled triangle so,

[tex] \\ \longrightarrow \qquad { { { \pmb{ \sf{ \angle \: 1 +\angle \: 2 + \angle \: 3= {180}^{ \circ} }}}}} \\ \\ [/tex]

[tex]\longrightarrow \qquad { { { \pmb{ \sf{ x^{ \circ} + {90}^{ \circ} + {40}^{ \circ} = {180}^{ \circ} }}}}} \\ \\ [/tex]

Adding like terms we get :

[tex] \\ \longrightarrow \qquad { { { \pmb{ \sf{ x^{ \circ} + {130}^{ \circ} = {180}^{ \circ} }}}}} \\ \\ [/tex]

Subtracting 130° from both sides :

[tex] \\ \longrightarrow \qquad { { { \pmb{ \sf{ x^{ \circ} + {130}^{ \circ} - {130}^{ \circ} = {180}^{ \circ}- {130}^{ \circ}}}}}} \\ \\ [/tex]

[tex]\longrightarrow \qquad { \underline { \boxed{ \pmb{ \frak{ x^{ \circ} = {50}^{ \circ}}}}}} \: \: \bigstar\\ \\ [/tex]

Therefore,

The value of x° is 50°

((BEING TIMED))
A car dealership increased the price of a certain car by 11%. The original price was $33,800.
(a) Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal. (New price = x Original price)
(b) Use your answer in part (a) to determine the new price.

Answers

Answer:

A 37,518

Step-by-step explanation:

this is because you take 11% of 33,800 which is 3,718 and add that back too your orignial value which gives you 37,518. I think that also answers part B for you.

Multiply.


8×3/5


Enter your answer as a mixed number in simplest form by filling in the boxes.


$$

Answers

Answer:8x3/5=4.8

Step-by-step explanation:

Answer:

in simple form its 4.8

for a improper fraction its 43/5

I will comment for the mixed number but if this is correct can u mark me brainliest

On a map 0.5 inches is equal to 5 miles. Suppose Washington, D.C. is 1.25 inches from Baltimore Maryland. How far are the two cities apart ?

Answers

The two cities would be 12.5 miles apart.

please help
Find the volume of each prism. Round to the nearest tenth if nessary ​

Answers

5.2(2)*6=
5.2(2)*6=
I think it’s right

5 Write an equation for each of the following and solve it. (a) The sum of one-sixth ofx and -9 is -25.​

Answers

Answer:

x= -96

Step-by-step explanation:

1

[tex] \frac{x}{6} + ( - 9) = - 25 \\ \frac{x}{6 } = - 25 - ( - 9) \\ \\ \frac{x}{6} = - 25 + 9 \\ \frac{x}{6} = - 16 \\ x = - 16 \times 6 \\ x = - 96[/tex]

Answer:

[tex]\huge\boxed{\bf\: Equation \rightarrow \frac{1}{6}*x - 9 = - 25}[/tex]

[tex]\huge\boxed{\bf\: Solution \rightarrow - 96}[/tex]

Step-by-step explanation:

Take the variable as 'x'.

Let's breakdown the given statement.

⅙th of x =⅙*xThe sum of ⅙*x & - 9 = ⅙*x + (-9)Is equal to = ⅙*x + (-9) = - 25

Given equation,

⅙*x - 9 = - 25

By solving,

⅙*x - 9 = - 25

⅙*x = - 25 + 9

⅙*x = - 16

x = - 16 * 6

x = [tex]\boxed{\bf\: - 96}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

which term describes the point where the three medians of a triangle intersect?

Answers

Answer: It is the centroid of a triangle or A. Centroid  

Step-by-step explanation:The centroid of a triangle is the intersection of the three medians of the triangle (Where each median connecting a vertex with the midpoint of the opposite side)

The incenter of a triangle is the point where the angle bisectors of the all vertices of the triangle intersect.

The orthocenter of the triangle is the point where all three altitudes of the triangle intersect. where An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.

The circumcenter of the triangle is the point where the perpendicular bisector of the sides of the triangle intersect.

I’ve been stuck on this question can someone help?

Answers

practice harder and harder you will get what you want

What net is shown below?
triangular prism
rectangular prism
O square pyramid
triangular pyramid

Answers

Answer:

Rectangular Prism

as Opposite sides are equal

Answer:

rectangular prism because it has dimensions of 5 sides and if you fold it, it would turn into a rectangular prism

Show 9/12 as the sum of unit fractions

Answers

[tex]\cfrac{9}{12}\implies \cfrac{1+1+1+1+1+1+1+1+1}{12} \\\\\\ \cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}+\cfrac{1}{12}[/tex]

Answer:

1/4 +1/4 +1/4

or add 1/12 9 times

Step-by-step explanation:

9/12

try to find the greatest common factor of both the numerator and denominator.

(a number that you can divide both the top number and bottom number with)

in this case, the greatest common factor is 3. once you divide the numerator and denominator by 3, it leaves you with a fraction 3/4

you can add 1/4 3 times to get 9/12

1/4 +1/4+1/4

or you could just add 1/12 9 times

PLEASE I’LL MARK BRAINIEST

Simplifying expressions by combining like terms

2t - t - t + 5t + 6t + 10t

Answers

21(t)

Explanation:

[tex]\dashrightarrow \sf \ \ 2t-t-t+5t+6t+10t[/tex]

combine similar terms

[tex]\dashrightarrow \sf \ \ 5t+6t+10t[/tex]

addition

[tex]\dashrightarrow \sf \ \ 21t[/tex]

Answer:

21t

Step-by-step explanation:

2t-t-t+5t+6t+10t

=2t-t-t=0

Then,

         5t+6t+10t = 21t ans.

pls help me i will mark as brilliant​

Answers

Step-by-step explanation:

total number of student = 900number of girls = 300

1) to find the number of boys

number of boys = total no. of students - no. of girls

= 900 - 300

= 600

2) to find the ratio of boys and girls

ratio of boys and girls = no. of boys : no. of girls

= 600 : 300

= 200

3) ratio of boys and total no. of students

= 600 : 900

= 200: 300

= 2:3

4) ratio of girls and total no. of students

= 300 : 900

= 1:3

5)ratio of girls and boys

= 300 : 600

= 1:2

What is the value of x?

Answers

[tex]\sin 30^{\circ} = \dfrac{LJ}{8\sqrt 2}\\\\\implies LJ = 8\sqrt 2 \sin 30^{\circ} =8\sqrt 2 \cdot \dfrac 12 = 4\sqrt 2\\\\ \text{Now,}\\\sin 45^{\circ} = \dfrac{LM}{LJ} \\\\\implies LM = \sin 45^{\circ} LJ\\\\\implies x = \dfrac 1{\sqrt 2} \cdot 4\sqrt 2 = 4 ~~ units.[/tex]

Answer:

x = 4

Explanation:

[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]

Solve for LJ:

[tex]\hookrightarrow \sf sin(30) = \dfrac{LJ}{8\sqrt{2} }[/tex]

[tex]\hookrightarrow \sf sin(30)*8\sqrt{2} ={LJ}[/tex]

[tex]\hookrightarrow \sf {LJ} = 4\sqrt{2}[/tex]

Solve for LM:

[tex]\hookrightarrow \sf \sf sin(45)= \dfrac{LM}{4\sqrt{2} }[/tex]

[tex]\hookrightarrow \sf \sf sin(45)*4\sqrt{2} = {LM}[/tex]

[tex]\hookrightarrow \sf {LM} = 4[/tex]


You deposit $2000 in an account earning 8% interest compounded monthly. How much will you
have in the account in 15 years?
Round to the nearest penny.
$

Answers

Answer:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2

\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2

Now substitute the point (-7, 5) into the equation to find r²:

\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2

\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2

\sf \implies 149=r^2⟹149=r2

Final equation:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

HELPP ASAPP
FIRST PERSON GET BRAINIEST

Answers

Answer:

2,6 / Number 3

Step-by-step explanation:

Thats the right answer

Answer:

(2,6)

Step-by-step explanation:

moving 3units to the left gives (2,4) and 2units above gives (2,6) finally

Other Questions
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