Explain why the following is correct x10/x3=x7
Answers
Answer:
see explanation
Step-by-step explanation:
Using rule of exponents
\(\frac{a^{m} }{a^{n} } \) = \(a^{(m-n)} \) , then
\(\frac{x^{10} }{x^{3} } \) = \(x^{(10-3)} \) = \(x^{7} \)
Related Questions
The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her hourly rate?
Answers
Answer:
$12 per hour
Step-by-step explanation:
51 -39 =12 minutes 31 -27=12minutes
also took the test
$12 per hour
just took the test hope this helps:)
PQ= RQ and PS= RS a=?
Answers
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
For more information on interior angles, refer to the link given below:
https://brainly.com/question/28795639
What is the simplified form of the expressions? a. −6a2b−1 b. 5/y−3
Answers
Given:
The expressions are
\(-6a^2b^{-1}\)
\(\dfrac{5}{y^{-3}}\)
To find:
The simplified form of each expression.
Solution:
We have,
\(-6a^2b^{-1}\)
\(=-6a^2(\dfrac{1}{b})\) \([\because x^{-n}=\dfrac{1}{x^n}]\)
\(=-\dfrac{6a^2}{b}\)
Therefore, the simplified form of \(-6a^2b^{-1}\) is \(-\dfrac{6a^2}{b}\).
We have,
\(\dfrac{5}{y^{-3}}\)
\(=\dfrac{5}{\dfrac{1}{y^3}}\) \([\because x^{-n}=\dfrac{1}{x^n}]\)
\(=5\times \dfrac{y^3}{1}\)
\(=5y^3\)
Therefore, the simplified form of \(\dfrac{5}{y^{-3}}\) is \(5y^3\).
I will give Brainlest!
The answers will either be yes or no
Answers
The classification of the equations as direct or indirect variations are;
1) Direct Variation
2) Direct Variation
3) Indirect Variation
4) Indirect Variation
How to find direct and indirect variation?Direct variation occurs when one quantity changes and the other quantity changes as well in direct proportion. Meanwhile, Inverse variation is exactly opposite of that.
Now, let us answer the questions;
1) y = 4x + 1
This shows that y is directly proportional to x because as x is increasing, y is increasing and vice versa. Thus, it is a direct variation.
2) y = 7.5x
This shows that y is directly proportional to x because as x is increasing, y is increasing and vice versa. Thus, it is a direct variation.
3) y = (1/15)x
This shows that y is inversely proportional to x because as x is increasing, y is decreasing and vice versa. Thus, it is an indirect variation.
4) y = 6/x
This shows that y is inversely proportional to x because as x is increasing, y is decreasing and vice versa. Thus, it is an indirect variation.
Read more about variation at; https://brainly.com/question/21139235
#SPJ1
Colin spends 1/3 of his wages on rent and 1/4 on food. If he makes £636 per week, how much money does he have left?
Answers
Answer:
£265
Step-by-step explanation:
Total fraction of money spent= \(\frac{1}{3} +\frac{1}{4}\)
= \(\frac{7}{12}\)
Actual money spent = \(\frac{7}{12}\) * £636
= £371
Money he has left = £(636 - 371)
= £265
Answer:
$265
Step-by-step explanation:
Determine the point ths of the way from point A: (-3,-2) to point B. (4, -3) shown on the coordinate plane below.
Answers
Answer:
Step-by-step explanation:
To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.
Let's first find the vector that points from point A to point B:
�
�
⃗
=
(
4
−
3
)
−
(
−
3
−
2
)
=
(
7
−
1
)
AB
=(
4
−3
)−(
−3
−2
)=(
7
−1
)
The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:
3
4
�
�
⃗
=
3
4
(
7
−
1
)
=
(
21
4
−
3
4
)
4
3
AB
=
4
3
(
7
−1
)=(
4
21
−
4
3
)
Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:
(
−
3
−
2
)
+
(
21
4
−
3
4
)
=
(
3
4
,
−
11
4
)
(
−3
−2
)+(
4
21
−
4
3
)=
(
4
3
,−
4
11
)
How long is 1 million minutes in days?
Please help its Quantitative Literacy.
Answers
Answer:
694.4444 Days
Step-by-step explanation:
1,000,000 Minutes = 16,666.6667 Hours (Minutes ÷ 60 = Hours)
16,666.6667 Hours = 694.4444458333 Days (Hours ÷ 24 = Days)
I hope this helps
Aaron borrows $150 from his friend Austin. He promises to pay back the money in 4 monthly installments. Each month he wants to pay half the
amount he paid the previous month. Assuming Austin does not charge any interest, how much should Aaron pay the first month to repay the money
as scheduled?
O A.
O в.
9.C.
O D.
$60
$70
$80
$90
• E.
$100
Answers
Answer:80
Step-by-step explanation:
80+40+20+10=150 cos he does half each month of the previous month
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
y=64
Step-by-step explanation:
3y /4 =48
( 3y 4 )*(4)=(48)*(4)
3y=192y
3y/3=192/3 =y=64
Which relationships have the same constant of proportionality between yyy and xxx as the following table?
x y
4 32
7 56
8 64
Choose 3 answers:
a) 3y=24x
b) graph
c) graph
d) x y
2 16
3 24
6 48
e)
x y
5 30
9 72
10 8
Answers
According to the following table, the same constant of proportionality between yyy and xxx in the relation y=8x is.
The proportionality constant k is defined as k=y/x when y and x are two numbers that are directly proportional to one another. If you are aware of the proportionality constant, you can use the equation y=kx, where k is the proportionality constant you are interested in, to determine the direct link between x and y. As an example, we may write y = kx, where k is the proportionality constant, x is the quantity of gas in gallons, and y is the cost in dollars. In other words, the cost is directly related to the number of gallons pumped.
By calculating
32=4*8
56=7*8
64=8*8
Therefore, y=8x.
Learn more about constant of proportionality here
https://brainly.com/question/28413384
#SPJ4
The linear system shown is equivalent
Answers
The linear system shown is "inconsistent" in nature.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given figure is represented linear system represents two parallel lines.
Now, the solution set of the two system of equations could be find by finding their points of intersection.
And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.
Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.
And when the system of linear equation has no solution , then the system is said to be inconsistent.
Hence, The linear system shown is "inconsistent" in nature.
Learn more about linear equations;
https://brainly.com/question/10413253
#SPJ9
The complete question is;
The linear system shown is _____.
independent
equivalent
inconsistent
(c) Show that for the Legendre polynomials Pn the following holds for all n EN: (n+1) Pn+1(x) - (2n+1)xP(x) +nPn-1(x) = (2n +1) Pn(x) Hint: Bonnet's recursion formula [6]
Answers
The Legendre polynomials Pn satisfy the following recursion formula:(n+1) Pn+1(x) - (2n+1)xP(x) +nPn-1(x) = (2n +1) Pn(x). This can be shown using Bonnet's recursion formula, which states that xPn(x) = (n+1)Pn+1(x) + nPn-1(x).
To prove the above formula, we can use Bonnet's recursion formula to rewrite the left-hand side as (n+1) Pn+1(x) - (2n+1)xP(x) +nPn-1(x) = (n+1) Pn+1(x) + nPn-1(x) - (2n+1)xP(x). We can then combine the first two terms on the right-hand side using the fact that the Legendre polynomials are orthogonal, which means that ∫ Pn(x)Pm(x)dx = 0 if n ≠ m. In this case, we have n = n+1 and m = n-1, so the integral of Pn+1(x)Pn-1(x) over the interval [-1, 1] is zero. This means that the first two terms on the right-hand side cancel out, leaving us with (n+1) Pn+1(x) - (2n+1)xP(x) +nPn-1(x) = - (2n+1)xP(x). We can then factor out a -1 from the right-hand side to get (n+1) Pn+1(x) - (2n+1)xP(x) +nPn-1(x) = - (2n+1)xP(x) = (2n +1) Pn(x). This completes the proof.
To know more about recursion formula here : brainly.com/question/1470853
#SPJ11
PLZ HELP ME ASAP NO LINKS OR ABSURD ANSWERS
Answers
Answer:
sorry,dont know......
Two department stores, A and B, sell the same item at different prices. Store A is putting the item on sale for 20% off its regular price. In that special, that store A sells the item for $50.00. If this amount is 75% of the regular price for that item at store B, what is the regular price at each store for that item? a. $62.50 in A and $200.00 in B b. $62.50 in A and $66.67 in B c. $66.67 in A and $62.50 in B and d. $250.00 in A and $200.00 in B and. $250.00 in A and $66.67 in B
Answers
The regular price at store A is $62.50, and the regular price at store B is $66.67. To determine the regular prices of an item at stores A and B, we use the given information that store A is selling the item at a discounted price of $50.00, which is 75% of the regular price at store B.
By setting up an equation and solving for the regular prices, we can determine the correct option among the given choices.
Let's assume the regular price of the item at store A is Pₐ and the regular price at store B is P_b. We are given that store A is selling the item for $50.00, which is 75% of the regular price at store B. This can be expressed as:
50 = 0.75 * P_b.
To find the regular price at store B, we divide both sides of the equation by 0.75:
P_b = 50 / 0.75 = $66.67.
Since store A is putting the item on sale for 20% off its regular price, the sale price is 80% of the regular price. Therefore, we can set up the equation:
50 = 0.8 * Pₐ.
Solving for Pₐ, we divide both sides by 0.8:
Pₐ = 50 / 0.8 = $62.50.
Hence, the correct option is b. The regular price at store A is $62.50, and the regular price at store B is $66.67.
To learn more about equation, click here:
brainly.com/question/29657988
#SPJ11
The amount of money in a bank account on Monday was $121.25. This represented a change of -$0.25 from the previous day. What was the account balance on Sunday?
Answers
Answer:13
Step-by-step explanation:
35% off a phone = £78 how much was the phone before the discount prices?
Answers
Answer:
£120
Step-by-step explanation:
Given that
The price after reduction = £78
So, 65% = £78.
We have to calculate 100 %
To do so, find 5% and multiply that by 20
65% = £78
5% = 78/13 = £6
So, 100% = 6 x 20 = £120
Hope this helps.
Good Luck
Please mark brainiest
what is the answer i need help
Answers
Answer:
\(588mm^3\)
Step-by-step explanation:
Each side of the blue pyramid is 3 times the size of the red pyramid.
Instead of just dividing by 3 for the volume we must divide by 9 instead because we're working in cubes.
Alex bought a television set for $900 and pay the sales tax of 8% how much did he pay for the television set
Answers
Answer:
$972
Step-by-step explanation:
900 * 0.08 = 72
900 + 72 = 972
Hope this helped, let me know if you need a better explanation!
HELP 30 pts
Prove this trigonometric identity. Any help is appreciated. Thanks!
Answers
Answer: See the attached image.
I've rearranged the tiles in the proper order
===================================================
Explanation
For step 2, we rewrite each expression in terms of sines and/or cosines. For instance, tan = sin/cos.
In step 3, we focus on the stuff in the numerator only. So we focus on sin/cos+cos/sin. In this step, we multiply top and bottom of the first fraction by sine. We multiply top and bottom of the second fraction by cos. These steps are done to get the LCD.
In step 4, we are able to add the fractions because both fractions have the same denominator.
In step 5, we use the pythagorean trig identity sin^2+cos^2 = 1.
In step 6, we use the idea that (A/B) divide by (C/D) = (A/B)*(D/C).
I need help on number 5 the answer is 28 but I don’t know how to work it
Answers
Answer:
The cost per person varies inversely with the number of people, so y = k/x for some fixed number k.
"It costs $90 each for five people", meaning that x = 5 and y = 90 pair up. Plug these values in and solve for k.
y = k/x
90 = k/5
90*5 = k
450 = k
k = 450
Therefore the equation updates to y = 450/x
Now we want to know how many passengers there are (x) when the cost per person is y = 56.25
Let's find out:
y = 450/x
56.25 = 450/x ... replace y with 56.25
56.25x = 450
x = 450/56.25
x = 8
If you have 8 people, then it costs $56.25 per person.
side note: the total cost is $450 which is the value of k we found earlier. Divide 450 over 8 and you should get 56.25 exactly. Optionally you can turn y = k/x into x*y = k form. So the equation y = 450/x is the same as x*y = 450.
Step-by-step explanation:
write of each of the following expressions in the form Ax^m*y^n where A is a real number and m and n are integers: 2x^2*3yx^2
Answers
The representation of the expression 2x²×3yx² in terms of A\(x^{m}\)\(y^{n}\)where A is a real number and m and n are integers is 6x⁴y¹.
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
In another word the mathematics of power or exponent of any number is called indices.
As per the given expression, 2x²3yx²
Rearrange the expression as
2x²3yx² = 2×3×x²x²×y
⇒ 6x²⁺²y
⇒ 6x⁴y¹
Hence"In terms of A\(x^{m}\)\(y^{n}\) where A is a real number and m and n are integers, statement 2x²×3yx² is represented as 6x4y.x⁴y¹".
To learn more about indices,
https://brainly.com/question/170984
#SPJ1
Evaluate the expression when a=-7 and y=4. -y+2a
Answers
Answer:
-18
Step-by-step explanation:
-4 + 2 * -7 = -18
-18 is the answer
\(\huge\fbox{Hi~there!}\)
We are given the expression: -y+2a
We are also given the values of y and a.
All we have to do is plug in the values and solve:
\(\rm{-y+2a\)
\(\rm{-4+2(-7)\)
\(\rm{-4-14\)
\(\rm{-18\) (Answer)
Hope you find it helpful.
Feel free to ask if you have any doubts.
\(\bf{-MistySparkles^**^*\) :)
graph each linear inequality (3.)x-y>5 m= , b=(5.) y ≥ -5/3 x + 1. m=. b= -2x+y<5 m=. b=(7.) 4x-2y -8. m=. b=2x-y<4 5. m=. b=
Answers
For a equation of the form:
\(\begin{gathered} y=mx+b \\ or \\ ymx+b \\ or \\ y\le mx+b \\ or \\ y\ge mx+b \end{gathered}\)m = slope
b = y-intercept
for:
\(\begin{gathered} x-y>5 \\ \text{solve for y:} \\ y-------(5)
\(\begin{gathered} y\ge-\frac{5}{3}x+1 \\ m=-\frac{5}{3} \\ b=1 \\ ----- \\ y<2x+5 \\ m=2 \\ b=5 \end{gathered}\)(7)
\(\begin{gathered} y<2x+4 \\ so\colon \\ m=2 \\ b=4 \\ ------- \\ y<2x+5 \\ so\colon \\ m=2 \\ b=5 \end{gathered}\)
A worker is getting a 4% raise. His current salary is $40,361. How much will his raise be?
Answers
We need to calculate the 4%
\(40361\cdot0.04=1614.44\)The raise will be $1614.44
(f o g)(x):
f(x)=x^2+9 and g(x)=x^2-9
Answers
The composite result function of ( f ° g )(x) in the given functions f( x ) = x² + 9 and g( x ) = x² - 9 is x⁴ - 18x² + 90.
What is the composite result function of ( f ° g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = x² + 9g( x ) = x² - 9( f ° g)(x) = ?First, we set up the composite result function f(g(x)).
f( x ) = x² + 9
f( g(x) ) = f( x² - 9 ) = ( x² - 9 )² + 9
f( g(x) ) = ( x² - 9 )² + 9
Expand the parenthesis
f( g(x) ) = ( x² - 9 )( x² - 9 ) + 9
f( g(x) ) = ( x²( x² - 9 ) -9( x² - 9 ) + 9
f( g(x) ) = x⁴ - 9x² - 9x² + 81 + 9
Collect and add like terms
f( g(x) ) = x⁴ - 18x² + 81 + 9
f( g(x) ) = x⁴ - 18x² + 90
Therefore, ( f ° g )(x) in the given functions is x⁴ - 18x² + 90.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
Officials at Dipstick College are interested in the relationship between participation in interscholastic sports and graduation rate. The following table summarizes the probabilities of several events when a male Dipstick student is randomly selected.
Event Probability Student participates in sports 0.20 Student participates in sports and graduates 0.18 Student graduates, given no participation in sports 0.82 a. Draw a tree diagram to summarize the given probabilities and those you determined above. b. Find the probability that the individual does not participate in sports, given that he graduates.
Answers
a. The tree diagram that summarizes the given probabilities is attached.
b. The probability that the individual does not participate in sports, given that he graduate sis 0.2 = 20%.
How do we calculate?We apply Bayes' theorem to calculate:
Probability (Does not participate in sports if graduates) = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)
The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating = 0.18
Probability (Does not participate in sports if graduates) = (0.02 * 0.82) / 0.18 = 0.036 / 0.18= 0.2
The Tree Diagram| Sports | No Sports |
|-------|--------|
Student participates | 0.18 | 0.62 |
|-------|--------|
Student does not participate | 0.02 | 0.78 |
Learn more about Bayes theorem at: https://brainly.com/question/29546122
#SPJ4
how do i solve this x^2 −12x+36=0
Answers
Step-by-step explanation:
x^2-6x-6x+36=0
x(x-6)-6(x-6)=0
(x-6)(x-6)=0
x=6
A rocket has positive velocity v(t) after being launched upward from an initial height of 0 feet at time =0 seconds_ The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds as shown in the table below 10 20 30 40 50 60 70 80 seconds v(t) (feet_per_second_ 22 29 35 40 44 47 49 Use a midpoint Riemann sum with 3 subintervals of equal length to approximate v(t)dt _ b) Using correct units, explain the meaning of v(t)dt in terms of the rocket's flight
Answers
Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\) is 2020 and \(\int^{70}_{10}v(t)dt\) means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.
From the given question,
An initial height of 0 feet at time t=0 seconds.
The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.
(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\).
\(\int^{70}_{10}v(t)dt\)
A midpoint Riemann sum with 3 sub intervals so, n=3
∆t= (70-10)/3
∆t = 60/3
∆t = 20
Intervals: (10, 30), (30,50), (50,70)
Midpoint: 20 40 60
Midpoint Riemann Sum
\(\int^{70}_{10}v(t)dt\) = ∆t[v(20+v(40)+v(60)]
From the table
\(\int^{70}_{10}v(t)dt\) = 20[22+35+44]
\(\int^{70}_{10}v(t)dt\) = 20*101
\(\int^{70}_{10}v(t)dt\) = 2020
(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight \(\int^{70}_{10}v(t)dt\).
It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.
To learn more about a midpoint Riemann sum link is here
brainly.com/question/28174119
#SPJ4
2. Determine el area y el valor de "y" de un triangulo isosceles si se conoce que uno de sus lados
es 5 veces mas grande que su base y su perimetro es de 495cm
Answers
Answer:
Mira con el gran boludin que me vengo a encontrar ahora, ya me pasaron 3 iguales a vos y a todos les rspondi y entendieron que al menos tienen que usar el 80% de su cerebro para resolver un problema que te lo resuelve un nene con sindrome de asperger en 7 segundos, así queres que te expliquemos algo nene desnutrido
Shelly bought a dress for $150 and sold it to Jenny there by suffering a loss of 10%. Find the selling price of the dress.
Answers
Answer: $135
Step-by-step explanation:
We know that:
Selling price = \((100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})\)
Using the given cost price and loss%, we can solve.
Selling Price = \((100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})\)
Selling Price = (100 - 10)(\(\frac{\text{150}}{100}\))
Selling Price = (90) * (1.5)
Selling Price = $135
This means the selling price of the dress is $135.