Answers
Answer:
C
Step-by-step explanation:
First, let's say 4³ is a and 5⁻² is b. We know that (a/b)ⁿ = aⁿ/bⁿ for any n, so
(a/b)⁵ = a⁵/b⁵
= (4³)⁵ /(5⁻²)⁵
Next, one power rule states that (4³)⁵ = 4 ⁽³ˣ⁵⁾ = 4¹⁵ and (5⁻²)⁵ = 5 ⁽⁻²ₓ⁵⁾=5⁻¹⁰, so
(4³)⁵ /(5⁻²)⁵ = 4¹⁵ / 5⁻¹⁰
Next, anything to a negative power (e.g. x⁻ⁿ) is equal to 1 over the absolute value of the power, so x⁻ⁿ = 1/xⁿ. Applying that here, we can say that
5⁻¹⁰ = 1/5¹⁰
4¹⁵ / 5⁻¹⁰ = 4¹⁵ / (1/5¹⁰) = (4¹⁵/1) / (1/5¹⁰) = 4¹⁵ * 5¹⁰
Related Questions
What would be the denominator after rationalizing 7/(5√3 - 5√2)?
Answers
Answer:
The denominator will be [tex]5\sqrt{3} +5\sqrt{2}[/tex]
Step-by-step explanation:
Rationalise the denominator of
2√3 + 3√2/4√3 +√2
Answers
Answer:
[tex]\frac{9+ 5\sqrt{6} }{23}[/tex]
Step-by-step explanation:
2√3 + 3√2 * 4√3 -√2
4√3 +√2 4√3 -√2
multiply by conjugate
2√3 + 3√2 * 4√3 -√2 = 18 +10√6 = 9 +5√6
4√3 +√2 4√3 -√2 46 23
Answer:
Step-by-step explanation:
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.
Conjugate of 4√3 + √2 is 4√3 - √2
(2√3 +3 √2)(4√3 - √2) = (2√3 * 4√3) - (2√3*√2) + (3√2*4√3) -(3√2*√2) {Use FOIL method}
= 8*3 - 2*√6+12√6 -3*2
= 24 -2√6 +12√6 - 6
= 24 - 6 + (-2+12)√6)
= 18 + 10√6
[tex]\frac{2\sqrt{3}+3\sqrt{2} }{(4\sqrt{3}+\sqrt{2} }\\\\=\frac{(2\sqrt{3}+3\sqrt{2})(4\sqrt{3}-\sqrt{2}) }{(4\sqrt{3}+\sqrt{2} )(4\sqrt{3}-\sqrt{2} )}\\\\=\frac{18+10\sqrt{6} }{(4\sqrt{3})^{2}-(\sqrt{2})^{2} }\\\\=\frac{18+10\sqrt{6} }{48-2}\\\\=\frac{18+10\sqrt{6} }{46}\\\\\\=\frac{2(9+5\sqrt{6} )}{46}\\\\=\frac{9+5\sqrt{6} }{23}[/tex]
Solve the system of equations.
6x – Зу = 3
-2x + y = 14
1.What number would you multiply the second equation
by in order to eliminate the x-terms when adding to the
first equation?
2.What number would you multiply the first equation by in
order to eliminate the y-terms when adding to the
second equation?
Answers
Answer:
1. Multiply by 3
2. Multiply by 1/3
Step-by-step explanation:
6x - 3y = 3
-2x + y = -14
1. In order to eliminate the x-terms, they would both have to equal the same number with opposite signs (positive and negative). Since we are only touching the second equation, how can we get from 2 to 6? We can multiply 2 by 3 to get to 6 (negative 6 in the end.) This would result as follows:
6x - 3y = 3
-6x + 3y = 42
2. In order to eliminate the y-terns through multiplying with the first equation, we have to figure out how to make 3y into 1y. We can do this by adding its reciprocal, 1/3. 1/3 × 3 = 1. This would result as follows:
2x - y = 1
HELPPPPPPPPPPP PLSSSSSSSSSSSSS
Answers
Answer:
6a+17
Step-by-step explanation:
This is an algebra 'expression' where you have to rearrange the question to the correct 'expression'
4a+2a= 6a
8+9= 17
Answer:
= 4a+2a+8+9
=6a+17
зх:
90
Х
2х:
What is the value of x?
Answers
Answer:
60
Step-by-step explanation:
To get the value of x;
3x:90
(90/3) = 30
x = 30
To get the value of 2x;
(2×X);
2 × 30
=60
find two consecutive odd number such that six times the smaller plus four times the greater comes to 138 hint let the number be x and x + 2
Answers
Step-by-step explanation:
here's the answer to your question
Round 832.078107648 to the nearest whole number
Answers
Answer:
8.32*10^2 or
832.08
Step-by-step explanation:
which set of ordered pairs represent a function
Answers
Answer:
A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.
Step-by-step explanation:
PLEASE I REALLY NEED HELP ON THIS I'LL GIVE BRAINLIEST!
Answers
Answer:
Yes Ella has enough to make 30 mince pies
Step-by-step explanation:
to make 36 mince pies you will need
400g of butter
500g of flour
300g of sugar
500g of mince meat
2 eggs
Ella has 1000g of butter
1000g of flour
500g of sugar
600g of meat
6 eggs
these ingredients are more than enough because
1000g-400g=600g-butter
1000g-500g=500g flour
500g-300g=200g sugar
600g-500g=100g mince meat
6-1= 5 eggs
if she were to follow the 36 pie recipe, which is two times the 18 pie recipe
but like I don't know, because it says a recipe for 18 mince pies, but in the box it says 12
Maxine is taking 5 gallons of drinking water on a camping trip. How many quarts of drinking water is Maxine taking on the camping trip?
Answers
Answer:
20 quarts
Step-by-step explanation:
There are 4 quarts in a gallon
5 gallons * 4 quarts / 1 gallon = 20 quarts
Answer:
20 US quarts
Step-by-step explanation:
there are 4 quarts in a gallon so you have to multiply 5 x 4 to get the total amount of quarts in a gallon.
Hope it helps c:
help help help pls pls
Answers
Answer:
abcd is a quadrilateral so ,
a is ( 0,-5 )
b is ( 2,-5 )
c is ( 1,-7 )
and d is ( 0,-7 )
The iPod costs $200.00. If Alex did his jobs every week, then how long would it take him to earn $200.00??
Plz help I’m confused
Answers
Answer:
It would take him 5.9 weeks (rounded). basically almost 6 weeks
Step-by-step explanation:
he makes 6 dollars a week by walking the dog out. he earns 2$ every time he walks the dog out, and he does it 3 times, so 2 x 3 = 6
he makes another 10 dollars a week by babysitting. he earns 2.50$ per hour of babysitting, and he does it for 4 hours per week, so 2.50 x 4 = 10
he makes another 18$ dollars a week by mowing the lawn. he does this once a week. he gets 15$ dollars if he mows, and another 3$ if he pulls weeds. if he does both, he would get 15+3 = 18$ per week by mowing
so add the numbers 6, 10, and 18, and you get 34.
he makes 34 dollars a week
divide the number he wants to make by what he earns in a week to figure out how many weeks it would take.
he wants to get 200$, so the equation is
200 / 34 = 5.88
Its 5.9 rounded or 5.88 weeks exact.
Answer:
6 weeks
Step-by-step explanation:
Job 1:
2 x 3 = 6
$6 per week
Job 2:
2.50 x 4 = 10
$10 per week
Job 3:
15 + 3 = 18
$18 per week
6 + 10 + 18 = 34
$34 per week
200/34 = 5.88
Simplify the expression.
40 -2.32
A. 4
B. 342
C.
22
D. 28
Answers
Answer:
37.68
Step-by-step explanation:
40 -2.32
= 37.68
Answer: is C. 22
Step-by-step explanation:
The perimeter of a rectangle is 25 2/5 ft. The length is
width. Find the length and width of the rectangle.
A. = 9.375 ft and w = 3.125 ft
B. = 9.525 ft and w = 3.175 ft
C. = 19.05 ft and w = 6.35 ft
D. = 7.85 ft and w = 4.85 ft
Answers
Answer:
Width = 4.85 feet
Length = 7.85 feet
Step-by-step explanation:
Given:
Perimeter of a rectangle = 25 2/5 ft = 25.4 feet
Length = 3 + Width
Computation:
Assume;
Width = a
So,
Length = 3 + a
Perimeter of a rectangle = 2(l + b)
25.4 = 2[(3 + a) + a]
25.4 = 2[3 + 2a]
25.4 = 6 + 4a
4a = 19.4
a = 4.85
Width = 4.85 feet
Length = 3 + 4.85
Length = 7.85 feet
6a²+11x-10= answer.
Answers
6a²+11x-10= (3a+5)(3a-2)
Answer:
Solution given:
6a²+11x-10
doing middle term factorisation
6a²+(15-4)x-10
6a²+15x-4x-10
3a(3a+5)-2(3a+5)
(3a+5)(3a-2)
Step-by-step explanation:
if
6a²+11x-10=0
(3a+5)(3a-2)=0
either
a=-5/3
it
a=⅔
Which rule is a recursive rule for the sequence 1, -6, 36, -216,...?
( I'll put the answers a screenshot )
PLZZ Help I've been stuck for so long
Answers
Answer:
The last answer
Step-by-step explanation:
We can check
For example,
a5=-6×a4
a5=-6×(-216)
a5=1296
I NEEDDDDD HELPPPPPPPPPP!!!!
Answers
Answer:
36 units squared
Step-by-step explanation:
10 times 10 - 4 times 4 = 100-16 = 84, take the square root of 84 = 9.12 which rounds to 9, now that we found the height, we use the area of a triangle formula, A=bh/2, so the base is 8 times height 9 = 72 divided by 2 = 36
Find f(-2) for f(x) = 3 *2^x
Answers
Answer:
3/4
Step-by-step explanation:
f(x) = 3 *2^x
Let x= -2
f(-2) = 3 *2^(-2)
= 3 * 1/2^2
= 3 /4
Answer:
It is 3/4
Step-by-step explanation:
pls help and pls provide workings
Answers
(x-h)²+(y-k)²=r²
(3-h)²+(3-0)²=5²
h²-6h+9+9=25
h²-6h-7=0 —> (h-7)(h+1)=0
h=7 , h=-1
h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>
x²-14x+49+y²=25 —> x²+y²-14x+24=0
h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>
x²+2x+1+y²=25 —> x²+y²+2x–24=0
I hope it helped you ^_^
Please help me asap! I don’t understand
Answers
Answer:
18
Step-by-step explanation:
4*3 = 12
1/2 * 3 * 4 = 6
Area = 18
Step-by-step explanation:
Area = length x width
but oops there isn’t a length so we must use Pythagorean theorem
Pythagorean theorem: a^2 + b^2 = c^2 in this case we’re looking for side a
a^2 + 4^2 = 5^2
a^2 + 16 = 25
a^2 = 25 - 16
a^2 = 9
Then square root 9 = 3
so the length is 3
Then we can start solving for area!
Area = length x width
Area = 3 x 4
Area = 12
Now for the triangle
Area = 1/2 bh
Area = 1/2 (4)(3)
Area = 1/2 12
Area = 6
6 + 12 = 18
Mark invests $8,008 in a retirement account with a fixed annual interest rate of 2% compounded 6 times per year. What will the account balance be after 16 years?
Please help i need the answer by tomorrow!
Answers
Given:
Principal value = $8,008
Rate of interest = 2% compounded 6 times per year.
Time = 16 years
To find:
The account balance after 16 years.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest, n is the number of times interest compounded in an year and t is the number of years.
Putting [tex]P=8,008, r=0.02,n=6,t=16[/tex] in the above formula, we get
[tex]A=8008\left(1+\dfrac{0.02}{6}\right)^{6(16)}[/tex]
[tex]A=8008\left(\dfrac{6.02}{6}\right)^{96}[/tex]
[tex]A=11022.1721148[/tex]
[tex]A\approx 11022.17[/tex]
Therefore, the account balance after 16 years is $11022.17.
Please help me find this angle
Answers
Answer:
x = 78
Step-by-step explanation:
We can find angle y
D + B + y = 180 since the sum of the angles of a triangle are 180
31+47+ y =180
78+y = 180
y = 180 - 78
y = 102
x+y = 180 since they form a straight line
x + 102 = 180
x = 180-102
x = 78
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
we have to find the value of the x°=<GHC
In the triangle BDH,
<D=31°<B=47°we know that,
Sum of three angle of a triangle is 180°
According to the question,
<D+<B+<BHD=180°31°+47°+<BHD=180°78°+<BHD=180°<BHD=180°-78°<BHD=102°But,
<GHC and <BHD forms a straight line
so,
<GHC+<BHD=180°102°+x=180°x=180°-102°x=78°Therefore,
The value of x is 78°
please help me with this fast please
Answers
Answer:
the last one
Step-by-step explanation:
SOMEONE PLEASE HELP ME ASAP !!!
Mrs. Pregnals's biology classes are going on a field trip. She has them break into groups of three or four students in order to do labs. She has a total of 120 students and 32 total groups are formed.
If t represents the number of three person groups and frepresents the number of four person groups, then write a system of equations that models this situation.
How many four person groups are there? Only an algebraic solution will receive full credit.
PLEASE HELP !!!!
Answers
x + y = 32 (1)
3x + 4y = 120 (2)
x = 8; y = 24
Step-by-step explanation:
Total students = 120
Number of groups = 32
If the number of three person groups = x
Number of four person groups = y
write a system of equations that models this situation
x + y = 32 (1)
3x + 4y = 120 (2)
From (1)
x = 32 - y
Substitute x = 32 - y into (2)
3(32 - y) + 4y = 120
96 - 3y + 4y = 120
- 3y + 4y = 120 - 96
y = 24
Substitute y = 24 into (1)
x + y = 32
x + 24 = 32
x = 32 - 24
x = 8
x = 8; y = 24
Find the values of p and q for which the following system of equations has infinitely many
solutions:
2x + 3y = 7
(p + q + 1)x + (p + 2q + 2)y = 4(p + q) + 1
Answers
Answer:
p = 3
q = 2
Step-by-step explanation:
they have infinitely many solutions, if they are basically the same equations. in other words, when they can be combined/reduced into a statement of tautology, a statement that is always true, no matter what.
like 15 = 15 or 8x = 8x
now we need to aim for creating the same (or multiples of the same) factors in the original equation 2 as in the original equation 1.
in other words we find the p and q, where we get the same ratios between the factors of squadron 1 and equation 2.
2/(p+q+1) = 3/(p+2q+2) = 7/(4p +4q +1)
p+q+1 = 2/3 × (p+2q+2) = 2/7 × (4p + 4q + 1)
3p + 3q + 3 = 2p + 4q + 4 = 6/7 × (4p+4q+1)
21p + 21q + 21 = 14p + 28q + 28 = 24p + 24q + 6
7p - 7q = 7
p - q = 1
p = 1 + q
14(1+q) + 28q + 28 = 24(1+q) + 24q + 6
14 + 14q + 28q + 28 = 24 + 24q + 24q + 6
42 + 42q = 30 + 48q
12 = 6q
q = 2
p = 1 + 2 = 3
Explain how you can find the constant of proportionality from a graph representing a proportional relationship when it shows a point with an x - value of 1 and if it doesn't show an x - value of 1 .
Answers
tienees que fijartelos extrreemos
if the price of an article is without tax is ₹ 800, and the price with tax is ₹ 860 the sales tax rate is_____________
Answers
9514 1404 393
Answer:
7.5%
Step-by-step explanation:
The tax as a proportion of the selling price is ...
₹(860 -800)/₹800 = 60/800 = 0.075 = 7.5%
Which are the solutions of x2 = -7x – 8?
Ž
17 7
4
+
17
4
-
글
그를
+
ZIA
+
V 17
4
4
7 - 17 7 + /17
-
-7 - V 17 -7 + v17 .
2
Answers
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Determine which quadratic equations have
2 real solutions. Select two that apply.
Answers
Answer:
A & D
First and last
Step-by-step explanation:
Can you answer this math homework? Please!
Answers
Dalia had an average airspeed of 42 miles per hour
The average wind speed was 12 miles per hour
Answers:
airspeed = 42 mphwind speed = 12 mph============================================================
Explanation:
Let's solve the first equation for y
[tex]18 = (x+y)\frac{1}{3}\\\\18*3 = x+y\\\\54 = x+y\\\\x+y = 54\\\\y = 54-x\\\\[/tex]
Then we'll plug this into the second equation and solve for x
[tex]18 = (x-y)*\frac{3}{5}\\\\18 = (x-(y))*\frac{3}{5}\\\\18 = (x-(54-x))*\frac{3}{5}\\\\18 = (x-54+x)*\frac{3}{5}\\\\18 = (2x-54)*\frac{3}{5}\\\\18*5 = 3(2x-54)\\\\90 = 6x-162\\\\6x-162 = 90\\\\6x = 90+162\\\\6x = 252\\\\x = 252/6\\\\x = 42\\\\[/tex]
This is the average airspeed of the plane, in miles per hour (mph). It's the speed without accounting for the wind. If there's no wind at all, then this would be the ground speed of the plane.
Use this value of x to find y
y = 54-x
y = 54-42
y = 12
The average speed of the wind is 12 mph.
