Step-by-step explanation:
We can rewrite the left-hand side as
[tex]2\log{x} + \log{3} = \log{3x^2}[/tex]
Here, we used the following properties of logarithms:
[tex]\log{x^a} = a\log{x}[/tex]
[tex]\log{ab} = \log{a} + \log{b}[/tex]
We can then write
[tex] \log{3x^2} = \log{75} \Rightarrow 3x^2 = 75[/tex]
or
[tex]x = 5[/tex]
GIVING BRAINLIEST PLS HELP
if image of a point (4,6) under enlargement with centre (0,0) and scale factor 'k' is (2,3) find value of k
Answer:
k = 2
Step-by-step explanation:
2 x 2 = 4
3 x 2 = 6
so (2,3) multiplied by 2 will be (4,6)
derivative : y=[(1+x^2)arctgx-x]/2
Answer:
s,-8*2-`±_'682-¥´owhsi
[tex]\lim_{n \to \0}(x/(tan(x))^(cot(x)^2 )[/tex]
It looks like the limit you want to compute is
[tex]\displaystyle L = \lim_{x\to0}\left(\frac x{\tan(x)}\right)^{\cot^2(x)}[/tex]
Rewrite the limand with an exponential and logarithm:
[tex]\left(\dfrac{x}{\tan(x)}\right)^{\cot^2(x)} = \exp\left(\cot^2(x) \ln\left(\dfrac{x}{\tan(x)}\right)\right) = \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)[/tex]
Now, since the exponential function is continuous at 0, we can write
[tex]\displaystyle L = \lim_{x\to0} \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right) = \exp\left(\lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)[/tex]
Let M denote the remaining limit.
We have [tex]\dfrac x{\tan(x)}\to1[/tex] as [tex]x\to0[/tex], so [tex]\ln\left(\dfrac x{\tan(x)}\right)\to0[/tex] and [tex]\tan^2(x)\to0[/tex]. Apply L'Hopital's rule:
[tex]\displaystyle M = \lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)} \\\\ M = \lim_{x\to0}\dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)}[/tex]
Simplify and rewrite this in terms of sin and cos :
[tex]\displaystyle M = \lim_{x\to0} \dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)} \\\\ M= \lim_{x\to0}\dfrac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)}[/tex]
As [tex]x\to0[/tex], we get another 0/0 indeterminate form. Apply L'Hopital's rule again:
[tex]\displaystyle M = \lim_{x\to0} \frac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)} \\\\ M = \lim_{x\to0} \frac{\cos^4(x) - 3\sin^2(x)\cos^2(x) - \cos^2(x) + 2x\cos(x)\sin(x)}{2\sin^2(x)+4x\sin(x)\cos(x)}[/tex]
Recall the double angle identity for sin:
sin(2x) = 2 sin(x) cos(x)
Also, in the numerator we have
cos⁴(x) - cos²(x) = cos²(x) (cos²(x) - 1) = - cos²(x) sin²(x) = -1/4 sin²(2x)
So we can simplify M as
[tex]\displaystyle M = \lim_{x\to0} \frac{x\sin(2x) - \sin^2(2x)}{2\sin^2(x)+2x\sin(2x)}[/tex]
This again yields 0/0. Apply L'Hopital's rule again:
[tex]\displaystyle M = \lim_{x\to0} \frac{\sin(2x)+2x\cos(2x)-4\sin(2x)\cos(2x)}{2\sin(2x)+4x\cos(2x)+4\sin(x)\cos(x)} \\\\ M = \lim_{x\to0} \frac{\sin(2x) + 2x\cos(2x) - 2\sin(4x)}{4\sin(2x)+4x\cos(2x)}[/tex]
Once again, this gives 0/0. Apply L'Hopital's rule one last time:
[tex]\displaystyle M = \lim_{x\to0}\frac{2\cos(2x)+2\cos(2x)-4x\sin(2x)-8\cos(4x)}{8\cos(2x)+4\cos(2x)-8x\sin(2x)} \\\\ M = \lim_{x\to0} \frac{4\cos(2x)-4x\sin(2x)-8\cos(4x)}{12\cos(2x)-8x\sin(2x)}[/tex]
Now as [tex]x\to0[/tex], the terms containing x and sin(nx) all go to 0, and we're left with
[tex]M = \dfrac{4-8}{12} = -\dfrac13[/tex]
Then the original limit is
[tex]L = \exp(M) = e^{-1/3} = \boxed{\dfrac1{\sqrt[3]{e}}}[/tex]
Solve for x
ax+bx=10
Answer:
[tex]ax + bx = 10 \\ \\ x(a + b) = 10 \\ \\ x = \frac{10}{a + b} [/tex]
I hope I helped you^_^
Given that f(x) = 2x³-7x²+7ax+ 16 is divisible by x-a, find
(i) the value of the constant a
(ii) the remainder when f(x) is divided by 2x+1.
Answer:
a = - 2, remainder = 21
Step-by-step explanation:
The Remainder theorem states that if f(x) is divided by (x - a) the remainder is f(a)
Since f(x) is divisible by (x - a) then remainder is zero , then
f(a) = 2a³ - 7a² + 7a² + 16 = 0 , that is
2a³ + 16 = 0 ( subtract 16 from both sides )
2a³ = - 16 ( divide both sides by 2 )
a³ = - 8 ( take the cube root of both sides )
a = [tex]\sqrt[3]{-8}[/tex] = - 2
Then
f(x) = 2x³ - 7x² - 14x + 16
Evaluate f(- [tex]\frac{1}{2}[/tex] ) for remainder on division by (2x + 1)
f(- [tex]\frac{1}{2}[/tex] ) = 2(- [tex]\frac{1}{2}[/tex] )³ - 7(- [tex]\frac{1}{2}[/tex] )² - 14(- [tex]\frac{1}{2}[/tex] ) + 16
= 2(- [tex]\frac{1}{8}[/tex] ) - 7([tex]\frac{1}{4}[/tex] ) + 7 + 16
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{7}{4}[/tex] + 23
= - [tex]\frac{8}{4}[/tex] + 23
= - 2 + 23
= 21
Do you guys know this because I was trying to submit but it don’t let me I put 7/6 but it say I need different Way
Answer:
is 5
Step-by-step explanation:
Hope it is helful...Answer:
5
Step-by-step explanation:
So first when dividing fractions you need to invert and multiply. Thus the fraction becomes:
1/4 * 20/1.
When simplified it becomes 20/4 which is 5.
HOPE THIS HELPED
express 3x-x^2 as m-(x-n)^2. Ill give brainliest to correct answer!
(Also please see the picture since you might mistake x having a square as a 2x)
This is simply done by Method of Completing the Square.
3x - x²
Add and subtract half the coefficient of x and square it.
( This is done so there'd be no alterations to the quadractic Expression)
So To start
We'd like x² to be positive...(So factor out a negative).
–(x² - 3x )
Now In this case
You see there's a Negative Outside the the bracket
Instead of adding and Subtracting squared values of half the coefficient of X... We'd Add Twice and do not subtract.
Reason: If you add outside the bracket and subtract the other inside the bracket... This will be wrong because there's a negative patiently waiting outside the bracket to Interact with the negative you subtracted to make it Positive.
See what I mean.
Let's say you added 2² and subtracted 2² in this problem
2² – ( x² - 3x - 2²)
If you decide to open the bracket
You'll have
2² – x² + 3x + 2²
NOW THIS IS WRONG BECAUSE WE ALTERED THIS EXPRESSION. WHERE'D 2² + 2² COME FROM?
THIS IS WHY YOU'LL ADD THE SQUARED COEFFICIENT OF X TWICE IN CASES LIKE THESE.
SO GOING BACK TO THE ORIGINAL QUESTION.
– (x² - 3x )
Adding the half the coefficient of x twice and squaring them...
Coefficient of x = 3
Half of 3 = 3/2
Squaring it gives (3/2)²
NOW PROCEEDING
(3/2)² – [ x² - 3x + (3/2)²]
If you open this bracket... (3/2)² will cancel out with —(3/2)²
Meaning that we haven't altered the expression in any way
Moving On...
Applying basic factorizing principle
9/4 – ( x - 3/2)².
Answer = 9/4 – ( x - 3/2)² Which is in the Form m – ( x - n )²
Therefore m = 9/4 and n = 3/2.
Hope This Helps
QUESTION 1 11 How does the term quartile relate to how data values are grouped when using a five- number summory?
Which statement describes the graph?
Answer:
the graph crosses the y-axis at -5 and x-axis at -6
find the value of a and b in (a,2)=(2,b)
Answer:
a=2 and b=2...............
divide write your answer in simplest form 2/3 divided by 1/4
Answer:
8/3 or 2.6667
Step-by-step explanation:
when you divide fractions you use a technique called KCF
K = keep
C = change
F = flip
You write the equation [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{4}[/tex]
you keep [tex]\frac{2}{3}[/tex]
you change the symbol, so from ÷ you change it to x
and flip the last fraction, so you would have [tex]\frac{4}{1}[/tex]
then you solve it
[tex]\frac{2}{3}[/tex] x [tex]\frac{4}{1}[/tex] = [tex]\frac{8}{3}[/tex]
The result of 2/3 divided by 1/4 in simplest form is 8/3 .
Division: It is one of the four basic mathematical operation, the other three being addition, subtraction, multiplication.
Given, division of [tex]\frac{2}{3}[/tex] by [tex]\frac{1}{4}[/tex].
Division of fractional terms:
[tex]=\dfrac{\frac{a}{b}}{\frac{c}{d}}\\= (a)\times(d)/(b)\times(c)[/tex]
Apply, division process of fractional terms.
[tex]=\dfrac{\frac{2}{4}}{\frac{1}{3}}\\ = (2)\times(4)/(1)\times(3)[/tex]
[tex]= \frac{8}{3}[/tex]
Know more about division,
https://brainly.com/question/29775887
#SPJ6
which graph represents the following system of inequalities?
a
b
c
d
Answer:
A
Step-by-step explanation:
Mark me brainliest.
Determine the sum by suitable re arrangement .
a) 6254 + 1297 + 446 + 103 Ans:
b) 1983 + 647 + 217 + 353 2.
Answer:
a.8100
b.3200
Step-by-step explanation:
hope you're okay
y=3x+2y is it a function how do you do it
9514 1404 393
Answer:
yes
Step-by-step explanation:
Solve for y. You can do this by subtracting 3x+y from both sides of the equation.
y -(3x+y) = 3x +2y -(3x +y)
-3x = y
Or ...
y = -3x
Each value of x maps to a single value of y, so this relation is a function.
_____
This equation is a first-degree polynomial in x. Any polynomial relation y=p(x) is a function, so this is a function.
Select the correct answer.
Based on these segment lengths, which group of segments cannot form a triangle?
OA 12,7,8
OB. 8, 7, 13
OC. 1,2,3
OD. 80,140, 70
Reset
Next
2021 EdimentumAll rights
Answer:
C
Step-by-step explanation:
If you add up the length of two sides, the sum must be greater than the third side of the triangle.
If you add 1 and 2, it equals 3
But that means it will be equal to the length of the third side, 3
It will be impossible to make a triangle with those lengths of sides no matter how the sides or angles are set.
It's sort of difficult to explain this without any visual
You can look up "triangle inequality" to find out more about this
The Earth scientist most likely to study volcanoes is a (n)
A. Meteorologist
B. Geologist
C. Oceanographer
D. Astronomer
The answer is B Geologist
Answer:
geologist
Step-by-step explanation:
they work with the earths surface and natural land that changes
What is the fraction or mixed number and write in its simplest form.
3.8416
3.8416=—- (type an integer,proper fraction, or mixed number.)
Answer:
38416/10000
plss mark me brainliestt
Step-by-step explanation:
3.8416=38416/10000
On solving equation 3*1/5b+5=50, the value of b will be?
Answer:
Step-by-step explanation:
14 1⁄16
State the transformations of the following function in order: = − 3|6 − 2| + 1
Answer:
6
Step-by-step explanation:
-3 | 6 - 2| + 1
-3 + 6 + 2 + 1
-3 + 9 = 6
19. When the members of a high school club are
arranged in rows of 2, 3, or 4, there is one
person always left over. But when the club
members are arranged in rows of 5, no one is
left over. What is the least number of people
who could be in the club?
À 15 people
C 45 people
B 25 people D 85 people
9514 1404 393
Answer:
B. 25 people
Step-by-step explanation:
The remainders tell you the number will be 1 more than some multiple of the least common multiple (LCM) of 2, 3, and 4. The LCM is 3·4 = 12, so we want some multiple (n) of that such that 12n+1 is a multiple of 5. We know this is the case for n=2.
The least number of people who could be in the club is 2·12+1 = 25.
Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its speed, as time increases?
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, is steady for a while, and then goes down over time.
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins in the middle of the vertical axis, goes down at first, is steady for a while, and then goes up over time.
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, goes down for a while, and then is steady over time.
9514 1404 393
Answer:
A
Step-by-step explanation:
If you read your own question, you find that it answers itself.
The problem statement tells you that speed ...
... increasing its speed, constant speed, then decreases
And it tells you the graphs show ...
(a) begins at 0, goes up, is steady for a while, and then goes down
(b) begins in the middle, goes down, is steady, and then goes up
(c) begins at 0, goes up, goes down, and then is steady
___
The first graph has the increasing, steady, decreasing pattern you're looking for.
The area of a circle is 78.5 cm^2. What is the diameter of the circle?
-5 cm
-10 cm
-12.5 cm
-39.25 cm
Answer:
10cm
Step-by-step explanation:
78,5=pi.r^2
Answer5:
Step-by-step explanation:
log base 4 (x+3)²- log base 4 y² = 0
Answer:
x = - |y| - 3
Step-by-step explanation:
Calculate 20% of 3 3/4 years in months.
Answer:
It is 9 months
Step-by-step explanation:
[tex] = 20\% \times 3 \frac{3}{4} \\ \\ = \frac{20}{100} \times \frac{15}{4} \\ \\ = \frac{300}{400} \\ \\ = \frac{3}{4} \: \: { \sf{years}}[/tex]
convert them to months by multiplying by 12:
[tex]{ \sf{ = \frac{3}{4} \times 12}} \\ \\ = { \sf{9 \: months}}[/tex]
La chispa de un relámpago artificial de 10.0 MV libera una energia de 0.125 MW .s ¿Cuántos coulombs de
carga fluyen?
Answer:
nzbzbzZnzbznzbzbzhzhsbsjs
Anyone’s knows how do this and the answer?
Answer:
12 -16. 19
4. 8. 22
3. -9. -4
Step-by-step explanation:
13-1 = 12
-10-6= -16
12 - -7 = 12+7=19
6-2 = 4
Keep subtracting
Solve using substitution.
6x + y = 7
8x + 9y = 17
(_,_)
Please help me I really need it
Name the two input device
Answer:
keyboard and mouse are two examples of input device
Answer:
keyboard and mouse
Step-by-step explanation:
If you like my answer than please mark me brainliest
Need answers in 2 minutes ASAP
Step-by-step explanation:
f(10)=10
f(-2)=-2
f(a)=a
f(a+b)=a+b
g(10)=5×10-12=3
g(-2)=5×(-2)-12=-10-12=-22
g(a)=5×a-12=5a-12
g(a+b)=5×(a+b)-12=5a+5b-12
h(10)=(10)^2 +4(10)-7=100+40-7=133
h(-2)=(-2)^2 +4(-2)-7=4-8-7=-11
h(a)=a^2 +4a -7
h(a+b)=(a+b)^2 +4a+4b-7=a^2+2ab+b^2+4b-7