Step-by-step explanation:
Question:-To simplify the expression Expression:-[tex] \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]Solution :-[tex] = \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[In numerator we take 6^8 common][tex] = \frac{ {6}^{8} ( {6} + 1)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[On Simplification][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[In denominator as we know, a^x × a^y = a^(x+y)][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8 + ( -9)} )} [/tex]
[On Simplification][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{ - 1} )} [/tex]
[As we know, 1/a^-1 = a ][tex] = {6}^{8} \times 7 \times 6[/tex]
[On further multiplying of 6][tex] = {6}^{9} \times 7[/tex]
Result:-In exponential form:
[tex] = {6}^{9} \times {7}^{1} (ans)[/tex]
In numerical form:
70,543,872 (Ans)
[tex] \huge \: \bf \: Question:—[/tex]
[tex] \sf \longmapsto6^9+6^8)/(6^8 \times 6^{-9})[/tex]
[tex]\huge\bf Solution:—[/tex]
[tex]\sf \longmapsto \: \dfrac{ {6}^{9} + {6}^{8} }{ {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \dfrac{10077696 + {6}^{8} } { {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \dfrac{10077696+1679616}{ {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \: \dfrac{11757312}{{6}^{8} \times {6}^{ - 9}} [/tex]
[tex]\sf \longmapsto \dfrac{11757312}{1679616(6 {}^{ - 9} )} [/tex]
[tex] \boxed{\bf \: As \: a^{-n} = 1/a(n) \: ,}[/tex]
[tex]\sf \longmapsto \dfrac{11757312}{1679616 \bigg(\dfrac{1}{10077696} \bigg )} [/tex]
[tex]\sf \longmapsto \dfrac{11757312}{ \dfrac{1}{6} } [/tex]
[tex]\sf \longmapsto \: \: 70543872[/tex]
[tex] \boxed{\bf \: \: \: Convert\: 70543872 \: to\: scientific \: notation}[/tex]
[tex] \sf \longmapsto \: 7.0543872 × 10 {}^{7} [/tex]
[tex]\boxed{ \bf \: \: Convert\: 70543872 \: to\: exponent}[/tex]
[tex]\sf\longmapsto {6}^{9} \times 7 [/tex]
_________________________________
[tex] \boxed{\bf \: Answer\: in\: Number}:—[/tex]
[tex] \boxed{\bf \: 70543872}[/tex]
[tex]\boxed{ \bf \: Answer\: in\: Exponent:—}[/tex]
[tex] \boxed{\bf \: {6}^{9} \times 7}[/tex]
[tex]\boxed{\bf Answer\: in\: Scientific\: Notation:—}[/tex]
[tex]\boxed{ \bf \: 7.0543872 × 10 {}^{7} }[/tex]
5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square
that produce a minimum total area.
The dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
Represent the side length of the square with s, and the radius of the circle with r.
So, the perimeter (P) and the area (A) of the shape are:
[tex]P =4s + 2\pi r[/tex]
[tex]A =s^2 + \pi r^2[/tex]
The perimeter is 16. So, we have:
[tex]4s + 2\pi r = 16[/tex]
Divide through by 4
[tex]s + 0.5\pi r = 4[/tex]
Make s the subject
[tex]s = 4 - 0.5\pi r[/tex]
Substitute [tex]s = 4 - 0.5\pi r[/tex] in [tex]A =s^2 + \pi r^2[/tex]
[tex]A = (4 - 0.5\pi r )^2 + \pi r^2[/tex]
Expand
[tex]A = 16 - 4\pi r + 0.25(\pi r)^2 + \pi r^2[/tex]
This gives
[tex]A = 16 - 4\pi r + (0.25\pi^2 + \pi )r^2[/tex]
Differentiate with respect to r
[tex]A' = 0 - 4\pi + 2(0.25\pi^2 + \pi )r[/tex]
[tex]A' = - 4\pi + 2(0.25\pi^2 + \pi )r[/tex]
Set to 0
[tex]- 4\pi + 2(0.25\pi^2 + \pi )r =0[/tex]
Add 4pi to both sides
[tex]2(0.25\pi^2 + \pi )r =4\pi[/tex]
Divide both sides by 2
[tex](0.25\pi^2 + \pi )r =2\pi[/tex]
Make r the subject
[tex]r =\frac{2\pi}{(0.25\pi^2 + \pi )}\\[/tex]
Factor out pi
[tex]r =\frac{2\pi}{\pi(0.25\pi + 1 )}[/tex]
Cancel out the common factors
[tex]r =\frac{2}{0.25\pi + 1 }[/tex]
Express pi as 3.14
[tex]r =\frac{2}{0.25\times 3.14 + 1 }[/tex]
[tex]r =\frac{2}{1.785}[/tex]
Divide
[tex]r =1.12[/tex]
Recall that:
[tex]s = 4 - 0.5\pi r[/tex]
This gives
[tex]s =4 -0.5 \times \pi \times 1.12[/tex]
This gives
[tex]s =4 -0.5 \times 3.14 \times 1.12[/tex]
[tex]s =2.24[/tex]
Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
Read more about minimum areas at:
https://brainly.com/question/6427280
On a piece of paper, graph f(x) = 4x. Then determine which answer choice
matches the graph you drew.
Answer:
The Correct Answer is A
Step-by-step explanation:
You are able to put the equation into Desmos Online Graphing Calculator.
When inserting the equation:
[tex]f(x) = 4 {}^{x} [/tex]
You are able to determine that the graph looks like Graph A
I hope this helps and you have a great day!
Note: I am not a professional so take my opinion with caution!
Answer:c
Step-by-step explanation:
12 cars in 15 hours how many cars is in 10 hours
Answer:
8Step-by-step explanation:
12 cars in 15 hours how many cars is in 10 hours
12 : 15 = x : 10
x = 12 * 10 : 15
x = 8
-------------------
check
12 : 15 = 8 : 10
0.8 = 0.8
the answer is good
Order the following fractions from least to greatest: 11/5, 6/5, 1/5
Answer: 1/5, 6/5, 11/5.
Step-by-step explanation:
1/5 is the smallest, as it isnt even 1 whole! (5/5)
6/5 = 1 1/5.
11/5 = 2 1/5, so its the greatest
William has $22 to buy strings for his guitar. Each set of strings costs $5.
How many sets of strings can he buy? Do not include units in your answer.
Answer here
SUBMIT
Answer:
4
Step-by-step explanation:
4 sets of strings will cost:
4×5=20
He will have $2 left over. Not enough to buy another set.
Or 5x<=22 DIVIDE BOTH SIDES BY 5
x <= 4.4 since he cannot buy .4 sets (this is a fraction of a set) He can only buy 4 sets
Can you solve this? Please ( 15+ points)
Answer:
112+24x
Step-by-step explanation:
2(16+(10*4)+(x*12))
solve the inner bracket
2(16+40+12x)
solve this bracket
2(56+12x)
solve this now
112+24x
Answer:
[tex]24x+112[/tex]
Step-by-step explanation:
First of all we will start with the brackets inside the equation,
1. [tex]2[16+40+12x][/tex]
Now we can multiply 2 by all the values inside the parentheses
2. [tex]32+80+24x[/tex]
I just wanted to confirm that the big X is a variable?
Fact: Did you know that there are about 4 types of parenthese: ( ) - round brackets, [ ] - square brackets, { } - curly brackets, and < > - angle bracket.
Ahat costs $25. Tax is 8%. How much is the lax on the hot? O $20 $17 $0 20 $2 NEXT QUESTION ASK TORTILLP
Answer:
$2
Step-by-step explanation:
To use a percent you must change it to a decimal.
8% is .08
To find 8% of 25, we use multiplication.
.08 × 25
= 2
In case you cannot use a calculator or you want to be very quick about this, or just do a simple check... you can actually reverse the number (money, amount, etc) and the percent.
25% of 8 is not bad for doing mental math. 25% is a quarter, or 1/4 of 8 which again is 2.
Minh spent $3.50 on 25 stickers.
How much did each sticker cost?
Answer:
0.14
Step-by-step explanation:
brainliest please
Find the difference. 2/5(d-10)-2/3(d+6)
[tex]\dfrac 25(d-10) - \dfrac 23(d+6)\\\\\\=2 \left(\dfrac{d-10}5 - \dfrac{d+6}3 \right)\\\\\\=2\left[\dfrac{3(d-10) - 5(d+6)}{15}\right]\\\\\\=2 \left( \dfrac{3d-30-5d-30}{15} \right)\\\\\\=2\left(\dfrac{-2d-60}{15} \right)\\\\\\=2(-2) \left(\dfrac{d+30}{15} \right)\\\\\\=-4 \left(\dfrac{d+30}{15} \right)\\\\\\=-4\left(\dfrac d{15} +2 \right)\\\\\\=-\dfrac{4d}{15}-8[/tex]
HELP BRAINLY PPLS!!! Identify the transformation that was applied to this boomerang.
A.Translation
B.Rotation about the origin
C.Reflection over the x-axis
D.Reflection over the y-axis
Answer:
B should be the answer because it did rotate and the origin is in the middle 0,0 which it look like to me it is on.
help me please please
Answer:
17/18
Step-by-step explanation:
To add fractions, you need to have common denominators. (4/9)*(2/2)=8/18.
Now that they have common denominators, you can add 8 and 9 to get 17. So, the answer would be the second one, 17/18.
Answer:
r u just cheating ur way through a whole test lol
Step-by-step explanation:
its B or 17/18
Find the value of x need help
Answer:
x = 13
Step-by-step explanation:
180-52=10x-2
130=10x
13=x
What is the slope
A) 1/3
B) 3
C) 2
Answer:
3 (B)
Step-by-step explanation:
rise/run
rise=3
run=1
3/1=3
Worth 12 points do it soon pls
Step-by-step explanation:
9+(-5)=4
-8-4=-12
8-(-4)=12
-9+5=-4
Hope this helps, just go connect the equation to the answer that I put.
RULES
If you have a minus and a minus (- -) it is equal to +
If you have Plus and Minus (- +) it is equal to -
The first one when simplified is 9-5=4
The second one Simplified is -8-4=-12
The third one simplified is 8+4=12
The fourth one simplified is -9+5=-4
I hope this helped and that you got the concept. If you have questions, ask me
Ps. If you mark me branliest it would-be very appreciated
Some help please please
Answer:
[tex]8\sqrt{2}[/tex]
Step-by-step explanation:
To find the length of an isosceles triangle, you know that the angles of the triangle are 45-45-90, so let's use that triangle theorem.
Therefore, the length of the hypotenuse (BD) is [tex]x\sqrt{2}[/tex], and x is equal to 8 (length of BC).
[tex]x\sqrt{2}[/tex]
x=8
Therefore, [tex]8\sqrt{2}[/tex] would be the length of side BD.
Answer:
oh snap i have this question too sorry cant help :(
Step-by-step explanation:
but i can provide with advice bc is the side down and bd is across us this to your advantage
How are the two triangles congruent? If not congruent, select not
congruent.
1 point
SSS
SAS
ASA
AAS
ОО
Not congruent
Answer:
SAS
Step-by-step explanation:
there are vertical angles in the middle and the sides are already marked
what is the complete factorization of the polynomial below
[tex] {x}^{3} - {2x}^{2} + x - 2[/tex]
[tex]a. (x - 2)(x + i)(x - i)[/tex]
[tex]b.(x + 2)(x - i)(x - i)[/tex]
[tex]c.(x + 2)(x + i)(x - i)[/tex]
[tex]d.(x - 2)(x - i)(x - i)[/tex]
Answer:
[tex]a. \ (x-2)(x+i)(x-i)[/tex]
Step-by-step explanation:
First of all let's notice that [tex](x-i)(x-i)=(x-i)^2 = x^2+2xi-1 \in \mathbb{C}[/tex] while our original polynomial is real. So we can rule out the even options B and D. At this point, if the polynomial has a factor of [tex](x-\alpha)[/tex] it means tha [tex]\alpha[/tex] is a zero of the polynomial. Let's check both 2 (for option a) and -2 (for option c)
[tex]p(2)=2^3-2(2)^2+2-2= 8-8+2-2=0[/tex]
[tex]p(-2)= (-2)^3-2(-2)^2+(-2)-2=-8-8-2-2=-20[/tex]
At this point 2 is a zero, and our final factoring is a[tex](x-2)(x+i)(x-i)[/tex]
To make four cakes, Dena used 6 cups of sugar. Using the same recipe, how much sugar does she need to make one cake?
Answer:
Step-by-step explanation:
So 4 cakes = 6 sugars, right so try taking it slow and think to yourself, 3=? then take it even slower until you go to 1=0.67 repeated
1. Suppose 750 tickets were sold for a concert with a total revenue of $5300. If adult tickets were $8 and
student tickets were $4.50, how many of each type of ticket were sold?
a) Define your variables.
X=______
y =_______
b) Write the system of equations.
Equation 1:_______
Equation 2:______
c) Solve the system of equations and determine how many of each type of ticket were sold.
ha
Answer:
x=65
Step-by-step explanation:
y= 23213
If 8 boys are arranged in a row, what is the probability that 3 boys will sit together?
Answer:
100% if you have 8 boys in a row the change that three boys will sit next to each other is 100%
Hope This Helps!!!
Answer:
i think probably 3/28 ,that 3 boys will sit together
Subtract:
(3x^3– 10x^2+ 13x) – (5x^3+ 4x² – 9x)
A. 8x^3 + 14x^2 - 22x
B. 8x^3 - 6x^2 + 4x
C. 2x^3 - 6x^2 - 4x
D. -2x^3 - 14x^2 + 22x
Answer:
D
Step-by-step explanation:
(3x³ - 10x² + 13x) - (5x³ + 4x² - 9x)
3x³ - 10x² + 13x - 5x³ - 4x² + 9x Change all terms after the subtraction sign to
the opposite sign (definition of Subtraction)
(3x³ - 5x³) + (-10x² - 4x²) + (13x + 9x) Group like terms together
-2x³ - 14x² + 22x
Help help help help math math
Step-by-step explanation:
Relation
Hope it correct!!!
Will give brainliest!! Thank you
Answer:
All the mentioned can be constructed with the help of piling method. But, for construction of B and D we need a point as well.
Please give brainliest only need 3 more brainliest before next rank!
Step-by-step explanation:
a) Yes, a cube can be formed by stacking polygons. If we stack squares one upon another, then the resulting 3-D figure would be a cube.
b) Yes, a cone that does not include the point can be made by stacking disc. If we stack discs such that the discs are arranges in descending order then the resultant 3-D figure would be a cone that does not include a point.
c) Yes, a pyramid can be formed by stacking polygons.
If we stack squares such that they are arranged in descending order of their side length and stacked by a point on the top. Then the resultant figure would be a pyramid that includes a vertex.
f) There are many types of prism. Fro example a rectangular prism can be constructed by simply stacking rectangle polygon on one another.
e) Yes, a cone can be formed by stacking disc.
We need to stack disks arranged in descending order of their radius stacked with a point on the top. The resulting figure would be a cone that includes a point.
f) Yes, a cylinder can be formed by stacking. We need to stack discs of same radius to get a cylinder.
Answer:
B and D
Step-by-step explanation:
-
Which polynomial has a factor of (x - 5)?
A x² + 4x - 5
B x + 5x + 4
C x² – 2x - 15
D 2x + 11x + 5
-
Answer:
The correct answer is C
x² - 2x -15
5. How much would d dollars earn in one year at thē rate of p percent compounded annually?
Answer:
a
Step-by-step explanation:
a
What is the following simplified product? Assume x 0.
(sqrt6x^2+4sqrt8x^3)(sqrt9x-xsqrt5x^5)
Answer:
c
Step-by-step explanation:
Keep in mind, whatever is inside of the square root, stays inside of the square root, and whatever is outside, stays outside, they don't multiply together. With parenthesis, exponents multiply, if there's no parenthesis, the exponents don't multiply. In this case, the exponents add.
Multiply each one together:
sqrt(6x^2) x sqrt(9x) = sqrt(54x^3)
sqrt(6x^2) x -(x sqrt(5x^5)) = -x sqrt(30x^7)
4 sqrt(8x^3) x sqrt(9x) = 4 sqrt(72x^4)
4 sqrt(8x^3) x -(x sqrt(5x^5)) = -4x sqrt(40x^8)
Then simplify:
sqrt(54x^2) = 3x sqrt(6x)
x sqrt(30x^7) = -x^4 sqrt(30x)
4 sqrt(72x^4) = 24x^2 sqrt(2)
-4x sqrt(40x^8) = -8x^5 sqrt(10)
Write a multiplication equation that represents the question: how many 2/3 are in 9/8?
how many 2/3 are in 9/8?
or another way to put it will be
how many times does 2/3 go into 9/8?
well, is simply a division.
[tex]\cfrac{9}{8}\div \cfrac{2}{3}\implies \cfrac{9}{8}\cdot \cfrac{3}{2}[/tex]
9490 divided by 5.explain how you got the answer
Answer:
The number 9490 is called the numerator or dividend, and the number 5 is called the denominator or divisor.
The quotient of 9490 and 5, the ratio of 9490 and 5, as well as the fraction of 9490 and 5 all mean (almost) the same:
9490 divided by 5, often written as 9490/5.
Read on to find the result of 9490 divided by 5 in decimal notation, along with its properties.
What is the volume of a cube that has a height of 10 inches? 10 inches
A:600 cubic inches
B:100 cubic inches
C:40 cubic inches
D:1,000 cubis inches
Answer:
i think its B.
Thats only i know
HELP ASAP! TYSM IF U DO, WILL GIVE BRAINILEST!
its d becuase i used math-way
Step-by-step explanation:
b
=
4
Answer:
Option DStep-by-step explanation:
Given equation:
b - 12 = - 8Add 12 to both sides:
b - 12 + 12 = - 8 + 12b = 4Correct graph is D, where point 4 is marked