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]
BRAINLLY!!! PLEASE HELP I'll GIVE BRAINLY!!!!
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
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
.
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)
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!
#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?
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
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)°
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?
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.
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
Answer:
Blue stars are the hottest stars.
A six sided die is tossed. Determine the odds against rolling a four
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)
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:
Answer:
who is William afton family?
Can y’all figure out the answer for me please
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
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.
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.
$$
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 ?
please help
Find the volume of each prism. Round to the nearest tenth if nessary
5 Write an equation for each of the following and solve it. (a) The sum of one-sixth ofx and -9 is -25.
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) = - 25Given 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?
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?
practice harder and harder you will get what you want
What net is shown below?
triangular prism
rectangular prism
O square pyramid
triangular pyramid
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 prismShow 9/12 as the sum of unit fractions
[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
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
Step-by-step explanation:
total number of student = 900number of girls = 3001) 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
= 1:2What is the value of x?
[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.
$
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
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