Given:
The equation is:
[tex]3^x\times 9=3^{2n-1}[/tex]
To find:
The value of n in terms of x.
Solution:
We have,
[tex]3^x\times 9=3^{2n-1}[/tex]
It can be written as
[tex]3^x\times 3^2=3^{2n-1}[/tex]
[tex]3^{x+2}=3^{2n-1}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
On comparing the exponents, we get
[tex]x+2=2n-1[/tex]
Add 1 on both sides.
[tex]x+2+1=2n-1+1[/tex]
[tex]x+3=2n[/tex]
Divide both sides by 2.
[tex]\dfrac{x+3}{2}=n[/tex]
Therefore, the value of n is terms of x is [tex]n=\dfrac{x+3}{2}[/tex].
Please Help
please and thank you!
Answer:
Step-by-step explanation:
cube means 3D square.. right?
so for volume we want the height x width x length.. make sense?
since each edge is 9'
the volume is [tex]9^{3}[/tex] = 729 [tex]ft^{3}[/tex]
Answer: 729
Step-by-step explanation:
This is very simple all you do is cube 9
[tex]9^{3}\\729[/tex]
The square table has side lengths of 4 feet. What is the length of the diagonal?
fill in the missing steps of the following sequence:
104, 60, __, 27, 21.5
Answer:
38
Step-by-step explanation:
reducing by half of 44, half of 22, half of 11
HELP ME PLEASE 10 points!!!!!
tamika has $55 in her savings account. She plans on depostiting $5 per week into her account. Write and solve an inqequality to find out how many weeks she must save to have more than $100 in her account. Then interpet the solution
Answer:
x>9
Step-by-step explanation:
Tamika already has $55, which will stay the same independent of how much time passes. Since she deposits $5 per week, we can assign weeks a variable x. The amount of money in her account after x weeks is equal to 55+5x. If she must save over $100, we can create an inequality to solve for how many weeks must pass: 55+5x>100.
The question also asks to solve the inequality:
55+5x>1005x>100-55 (Subtract 55 from each side)5x>45x>9 (Divide each side by 5)This solution tells us that Tamika must save for more than nine weeks to have more than $100 in her account.
lmk if i made an error, hope this helps!!
A mother is 3 times as old as her daughter.In 12 years time she will be twice as old as her daughter will be then. How old is the mother now?
Answer:
The mother will be 36.
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
just multiply 12 and 3
A number Q has a remainder of 3 when divided by 5 and also has a remainder of 4 when divided by 8. What is the smallest value Q can have?
help asap
could someone please explain how to solve/answer this?
much appreciated
5m+2-m=12m. solve for m. simplify the answer to
the lowest term.
Answer:
m=1/4
Step-by-step explanation:
5m+2-m=12m
4m+2=12m
2=12m-4m
2=8m
2/8=m
1/4=m
m=1/4
Select all the sets of side lengths that will make a triangular shelf fit in a 90 1 point
degree corner of a room.
3 cm, 4 cm, 5 cm
2 cm, 3 cm, 4 cm
5 cm, 6 cm, 9 cm
6 cm, 8 cm, 10 cm
7 cm, 9 cm, 11 cm
This is Irequired question
PLEASE HELP AND LOOK AT MY OTHER RECENT QUESTIONS NOBODY EXCEPT A BOT IS ANSWERING 3
Answer:
1. 6cm , 8cm , 10cm
2. 3cm , 4cm , 5cm
Step-by-step explanation:
245 tickets in 5 days what is the unit rate
Answer:
245/5 = 49 tickets per day
Answer:
245 / 5 = 49 so
49 tickets per day
A town's population went from 40,000 to 50,000. What was the percent of change in the population?
Write the center and radius for the following circles
Given:
The equations of circle are
4. [tex]\left(x+\dfrac{2}{3}\right)^2+(y+1)^2=24[/tex]
5. [tex](x-1)^2+(y+2)^2=28[/tex]
6 .[tex](x+12)^2+y^2=\dfrac{3}{64}[/tex]
To find:
The center and radius for the given circles.
Solution:
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where, [tex](h,k)[/tex] is center and [tex]r[/tex] is the radius of the circle.
4.
The equation of the circle is
[tex]\left(x+\dfrac{2}{3}\right)^2+(y+1)^2=24[/tex]
The standard form of this circle is
[tex]\left(x-(-\dfrac{2}{3})\right)^2+(y-(-1))^2=(\sqrt{24})^2[/tex]
[tex]\left(x-(-\dfrac{2}{3})\right)^2+(y-(-1))^2=(2\sqrt{6})^2[/tex]
Therefore, the center of the circle is [tex]\left(-\dfrac{2}{3},-1\right)[/tex] and the radius of the circle is [tex]2\sqrt{6}[/tex].
5.
The equation of the circle is
[tex](x-1)^2+(y+2)^2=28[/tex]
The standard form of this circle is
[tex](x-1)^2+(y-(-2))^2=(\sqrt{28})^2[/tex]
[tex](x-1)^2+(y-(-2))^2=(2\sqrt{7})^2[/tex]
Therefore, the center of the circle is [tex]\left(1,-2\right)[/tex] and the radius of the circle is [tex]2\sqrt{7}[/tex].
6.
The equation of the circle is
[tex](x+12)^2+y^2=\dfrac{3}{64}[/tex]
The standard form of this circle is
[tex](x-(-12))^2+(y-0)^2=(\sqrt{\dfrac{3}{64}})^2[/tex]
[tex](x-(-12))^2+(y-0)^2=\dfrac{\sqrt{3}}{8}[/tex]
Therefore, the center of the circle is [tex]\left(-12,0\right)[/tex] and the radius of the circle is [tex]\dfrac{\sqrt{3}}{8}[/tex].
NOWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
Answer: 60 is the answer.
Step-by-step explanation: We can use the total sum, 180.
To get the missing angle, add the 2 angles, 60 and 60.
60 + 60 = 120.
Then subtract from 180.
180 - 120 = 60.
Hence, 60 is the answer.
Let me know if you have any questions.
~ Lily, from Brainly.
Note to asker: Write this down!
To find 1 missing angle:
A1 + A2 = TA - 180 = X (A1 = Angle1)
please help besties
Answer:
200.96
Step-by-step explanation:
64x3.14=200.96
Answer:
A= 200.96in2
Step-by-step explanation:
8×8=64
64×3.14=200.96
PLEASE HELP! 100 POINTS ! AND BRAINLIEST.
Find the area of the following figure. Explain or show how you got your answer.
Answer:
26.5 units
Step-by-step explanation:
i just counted the units on the inside.
but you could also split this shape into two rectangle like shapes and then find the area of both of those and then add them together.
hope this helps :)
Answer:
area =no of full square + half square =24+1/2×5=26.5 unit ²
Look at this equation. 3(x + 1) = 3x + Which number can be placed in the box that would create an equation that has an infinite number of solutions? OA) O OB) 1 C) 2 OD 3
[tex]52 - x = 52[/tex]
[tex]x = 52 - 52[/tex]
[tex]x = 0[/tex]
If side x has a length of 15 cm and side y has a length of 4 cm, then which value below could be the length of side z?
A.
20 cm
B.
21 cm
C.
17 cm
D.
10 cm
Given:
In a triangle, side x has a length of 15 cm and side y has a length of 4 cm.
To find:
The possible value of side z.
Solution:
In a triangle, the sum of two smaller sides must be greater than the largest side otherwise the triangle is not possible.
Case I: Let x be the largest side, then
[tex]y+z>x[/tex]
[tex]4+z>15[/tex]
[tex]z>15-4[/tex]
[tex]z>11[/tex] ...(i)
It is clear that [tex]y<x[/tex]. So, y cannot be a largest side.
Case II: Let z be the largest side, then
[tex]x+y>z[/tex]
[tex]15+4>z[/tex]
[tex]19>z[/tex] ...(ii)
From (i) and (ii), we get
[tex]11<z<19[/tex]
It means the value of z lies between 11 and 19.
From the given options, only 17 is the value which lies between 11 and 19. So, the possible length of side z is 17 cm.
Therefore, the correct option is C.
Maria's family drove 140 mi to her grandparents' house and averaged 56 mi/h on the way there. On the return trip, they averaged 50 mi/h.
What was the total time Maria's family spent driving to and from her grandparents' house?
2.5 h
2.6 h
5.2 h
5.3 h
Answer:
5.3!
Step-by-step explanation:
I took the test on k12 mathematics :)
Choose one answer
Pls fast anyone
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
Pythagorean theorem: [tex]a^{2}+b^{2}=c^{2}[/tex]
Answer:
B
Step-by-step explanation:
Pythagorean theorem states that a²+b²=c²
Through observation, I assumed that 8 was the hypotenuse
I sqaured both the known lengths of the leg and hypotenuse and plugged them into the equation: a²+36=64
I subtracted 36 from 64 leaving me with 28=a²
Then in order to isolate the variable I had to apply square root to both values, cancelling the "²" and leaving me with √28=a
someone please help me, whoever gets it right i will mark brainliest
3x^2 6x^2 + 4x -8
2x. 9x^3 + 6x^2 -12x
x^2. 18x^2 + 12x - 24
6x^2. 3x^2 + 2x - 4
Plz plz plz helpppppplllpl
Answer:
both 20 and 12 but, 12 can be more accurate. Depends on your teacher's point of view.
please mark as brainliest
please help!! I'll give you brainlyest (however you spell it) just please!! A bottle of orange juice contains 750 mg of vi C and has 6 servings. A bottle of cranberry juice contains 135 mg of vitamin C las 1.5 servings. Mrs. Kahn wants to compare the amount of vitamin C in the juices.
How does the amount of C in each type of juice compare? One serving of ____ (answers are orange or cranberry) juice has ____ mg more vitamin C per serving than one serving of _____ (answers are orange or cranberry) juice
Answer:
One serving of orange juice has 30 mg more vitamin C per serving than one serving of cranberry juice
Step-by-step explanation:
i cant find out the answer for
the life of me
Answer:
A. h = (S/2πr) - rStep-by-step explanation:
Solve the given for h:
S = 2πrh + 2πr²Isolate h:
2πrh = S - 2πr²Divide all terms by 2πr:
h = (S/2πr) - rCorrect choice is A
can someone help me please!!
Answer:
55°
Step-by-step explanation:
∠KJL=180° - 125 = 55°
KL=KJ
so, ∠KJL= ∠KLJ =55°
Which product of prime polynomials is equivalent to 3x4 – 81x?
3x(x – 3)(x2 – 3x – 9)
3x(x – 3)(x2 + 3x + 9)
3x(x – 3)(x – 3)(x + 3)
3x(x – 3)(x + 3)(x + 3)
Given:
The expression is
[tex]3x^4-81x[/tex]
To find:
The product of prime polynomials which is equivalent to the given expression.
Solution:
We have,
[tex]3x^4-81x[/tex]
Taking out the common factors, we get
[tex]=3x(x^3-27)[/tex]
It can be written as
[tex]=3x(x^3-3^3)[/tex]
[tex]=3x(x-3)(x^2+3x+3^2)[/tex] [tex][\because a^3-b^3=(a-b)(a^2+ab+b^2)][/tex]
[tex]=3x(x-3)(x^2+3x+3^2)[/tex]
[tex]=3x(x-3)(x^2+3x+9)[/tex]
Therefore, the correct option is B.
Answer:
It's B
Step-by-step explanation:
Which quadratic function has a vertex point of (3,5) and passes through the
point (-2,55)?
9514 1404 393
Answer:
f(x) = 2(x -3)² +5
Step-by-step explanation:
For vertex (h, k) and scale factor 'a', the vertex form is ...
f(x) = a(x -h)² +k
We can fill in the values of h and k from your vertex, and use the values of the extra point to find 'a'.
55 = a(-2 -3)² +5
50 = 25a . . . . . . . . subtract 5
a = 2 . . . . . . . . . . . divide by 25
So, the function is ...
f(x) = 2(x -3)² +5
__
In standard form, that will be ...
f(x) = 2x² -12x +23
Calculate the bond energies that correspond to arrows A, B and C in the diagram:
Answer:
Parted = farted and pooed, wafflebox = person who waffles (talking about random things), gogglebox = person who stares at people, battery brain = person who uses drugs. You might want to use these words so no one knows what you are talking about and you can talk about people badly without them knowing
Step-by-step explanation:
Item 6
Find the selling price.
Cost to store: $50
Markup: 10%
The selling price is?
50×100÷110=45.454545r6
Of 42 cities, 5 have a lake and 29 have a river running through them what fraction of these 42 cities have a lake or river running through them
Answer: 17/21
Step-by-step explanation:
Number of cities = 42
Fraction of cities that has lake = 5/42
Fraction of cities that have rivers = 29/42
The fraction of these 42 cities that have a lake or river running through them will then be:
= 5/42 + 29/42
= 34/42
= 17/21
Spoints
Aregular hexagon is dilated by a scale factor of 0.4 to create a new hexagon. The perimeter of the new hexagon is 0.4 times the perimeter of
the original hexagon
O True
False
Answer:
True.
Step-by-step explanation:
It is given that, a regular hexagon is dilated by a scale factor of 0.4 to make image.
It means, the perimeter of image is 0.4 times the perimeter of the original hexagon.
For example,
Let's take the rectangle with length of 12 and width of 4, it's perimeter is 12+12+4+4 =32
Let's find image using scale factor 0.4, we get
length =0.4(12)= 4.8
width =0.4(4)=1.6
So, perimeter of image = 4.8+4.8+1.6+1.6=12.8
If we compare the perimeters
0.4(32)=12.8.
So, it is true.