law of indices , show working
1. 10^8 × 10^4
2. (11^5)^4
3. 8^6 ÷ 8^3
4. (12^2) × 12^4
5. (13^4) ÷ 13^5
6. (5^2 × 5^3) ÷ 5^4
7. 18^4 ÷ 18^6
8. (19^2)^4 ÷ 19^8
Answer:
Below.
Step-by-step explanation:
1. 10^8 × 10^4 = 10(8+4) = 10^12.
2. (11^5)^4 = 11^(5*4) = 11^20.
3. 8^6 ÷ 8^3 = 8^(6-3) = 8^3.
4. (12^2) × 12^4 = 12^6.
5. (13^4) ÷ 13^5 = 13^(4-5) = 13^-1.
6. (5^2 × 5^3) ÷ 5^4 = 5^5 / 5^4 = 5.
7. 18^4 ÷ 18^6 = 18^-2.
8. (19^2)^4 ÷ 19^8 = 19^8 / 19^8 = 18^(8-8) = 18^0 = 1.
What number does this Roman numeral represent?
XXXII
Answer: 32
Step-by-step explanation:
The roman numeral XXXII is 32 and XXIII is 23.
The number for this Roman numeral XXXII is, 32
Given that,
We have to write the number for this Roman numeral XXXII.
Since, We know that,
X represent in number = 10
I represent in number = 1
Hence, The number for this Roman numeral XXXII is,
⇒ XXXII
⇒ (10 + 10 + 10 + 1 + 1)
⇒ 32
Therefore, the number for this Roman numeral XXXII is, 32
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What is 2.4 divided by 1.2?
Answer:
Your answer should be 2.
Avery bought a washing machine originally priced at $864.72 but on sale for 30% off. After 4% sales tax, what was the total cost?
Answer: 629.51
Step-by-step explanation: 30% of 864.72 is 259.416
864.72 - 259.416 = 605.304 4% of 605.3 = 24.212 605.3 + 24.21 = 629.51
Which situation can be represented by this inequality?
135 ≤ 10r + 15
Question 6 options:
A-Hugo has 10 songs in his music player. He will add 15 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at most 135 songs?
B-Hugo has 10 songs in his music player. He will add 15 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at least 135 songs?
C-Hugo has 15 songs in his music player. He will add 10 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at most 135 songs?
D-Hugo has 15 songs in his music player. He will add 10 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at least 135 songs?
The true option is: (d) Hugo has 15 songs in his music player. He will add 10 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at least 135 songs?
The inequality is given as:
[tex]\mathbf{135 \le 10r + 15}[/tex]
Rewrite as:
[tex]\mathbf{10r + 15\ge 135 }[/tex]
From the options, we can see that the inequality represents songs in a music player.
Linear inequalities can be represented as:
[tex]\mathbf{mx + b \ge y}[/tex]
Where:
m represents the rate i.e. 10
b represents the y-intercept or base i.e. 15
>= represents at least
So, the inequality can be interpreted as:
10 songs are added every monthThe base number of songs is 15He wants to have at least 135 songsHence, the true option is (d)
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What sentence represents this equation?
912=15−x
912 is the same as a number decreased by 15.
912 is the same as 15 decreased by a number.
15 decreased by 912 is the same as a number.
A number is the same as the difference of 15 and 912.
The sentence representing the equation is 912 is the same as 15 decreased by a number.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given an equation, 912 = 15 − x
Here, 912 is equal to a number which is being subtracted from 15.
Hence, The sentence representing the equation is 912 is the same as 15 decreased by a number.
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Someone please solve and explain part a(i)
Step-by-step explanation:
the way I understand the description :
C is below B. they are on a kind of straight hill, and there is a straight "road" going up from C to B.
then, at B there is an antenna or other firm of mast going straight up.
therefore, this is not a right-angled triangle with 90 degrees at B (as it would be, if this would be in a flat plane).
but because it goes downhill from B to C the angle is 105 degree.
(a)(i)
now, imagine, there would be a horizontal plane either at B or at C. AB would have a true 90 degree angle with this plane. so, what is the angle of CB with this plane ?
this angle is the "excess" of the 90 degrees, as CB angles down from the horizontal plane at B, or angles up with the same angle from the horizontal plane at C.
what is the "excess" of 105 degrees vs. the standard 90 degrees ? 105 - 90 = 15 degrees.
(a)(ii)
the extended Pythagoras for not right-angled triangles :
c² = a² + b² - 2ab×cos(B)
B being the angle opposite of the Hypotenuse c.
so, we have
c² = 15² + 10² -2×15×10×cos(105) = 225 + 100 - 300×cos(105) =
= 325 - 300×cos(105) = 402.6457135...
c = 20.06603383... ≈ 20 m
There are only red sweets and yellow sweets in a bag.
There are n red sweets in the bag.
There are 8 yellow sweets in the bag.
Sajid is going to take at random a sweet from the bag and eat it.
7
He says that the probability that the sweet will be red is
10
7
10
(a) Show why the probability cannot be
Using the probability concept, it is found that since the number of red sweets would be a decimal number, the probability cannot be [tex]\frac{7}{10}[/tex]
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem:
In total, there are 8 + n sweets in the bag.Of those, n are red.The probability of red is:
[tex]p = \frac{n}{n + 8}[/tex]
Supposing [tex]p = \frac{7}{10}[/tex], we solve for n:
[tex]\frac{n}{n + 8} = \frac{7}{10}[/tex]
[tex]10n = 7n + 56[/tex]
[tex]3n = 56[/tex]
[tex]n = \frac{56}{3}[/tex]
[tex]n = 18.67[/tex]
Since the number of red sweets would be a decimal number, the probability cannot be [tex]\frac{7}{10}[/tex]
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Find the number of sides of a regular polygon whose each interior angle is 150 degree ...pls give step by step explaination
Answer:
12
Step-by-step explanation:
the angle is defined by equation ((n-2)*180)/n,where n is number of sides of a regular polygon
so here 180n-360=150n
30n=360
n=12
Let A be a given matrix below. First, find the eigenvalues and their corresponding eigenspaces for the following matrices. Then, find an invertible matrix P and a diagonal matrix such that A = PDPâ’1.
(a) [ 3 2 2 3 ]
(b) [ 1 â 1 2 â 1 ]
(c) [1 2 3 0 2 3 0 0 3]
(d) [3 1 1 1 3 1 1 1 3]
It looks like given matrices are supposed to be
[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]
You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:
• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues
• det(A) = determinant of A = product of eigenvalues
(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since
[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]
[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]
and
λ₁ + λ₂ = 6 ⇒ λ₁ λ₂ = λ₁ (6 - λ₁) = 5
⇒ 6 λ₁ - λ₁² = 5
⇒ λ₁² - 6 λ₁ + 5 = 0
⇒ (λ₁ - 5) (λ₁ - 1) = 0
⇒ λ₁ = 5 or λ₁ = 1
To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.
• For λ = 1, we have
[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]
With v = (v₁, v₂)ᵀ, this equation tells us that
2 v₁ + 2 v₂ = 0
so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.
• For λ = 5, we would end up with
[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]
and this tells us
-2 v₁ + 2 v₂ = 0
and it follows that v = (1, 1)ᵀ.
Then the decomposition of A into PDP⁻¹ is obtained with
[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]
where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.
(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]
(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:
[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]
Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:
det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0
and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.
• For λ = 1,
[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]
tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]
tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.
• For λ = 3,
[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]
tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.
Then we have A = PDP⁻¹ for
[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]
(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,
• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃ ⇒ λ₂ + λ₃ = 7
• det(A) = 20 = 2 λ₂ λ₃ ⇒ λ₂ λ₃ = 10
and we find λ₂ = 2 and λ₃ = 5.
I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]
tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.
• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]
This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.
Then A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]
What percentage is a reduction from SEK 100 to SEK 90?
Answer:
10%
Step-by-step explanation:
The change is 90-100 = -10. As a percentage of the original amount, that is ...
-10/100 × 100% = -10%
The change from 100 to 90 is a reduction of 10%.
Which is the better deal? $39.55 for 7 pairs of jeans OR $22.48 for 4 pairs of jeans
Answer:
$22.48 for 4 pairs of jeans is a better deal.
Step-by-step explanation:
To find the price of one pair of jeans, you divide.
39.55 ÷ 7 = price of 1 pair of jeans
39.55 ÷ 7 = $5.65
22.48 ÷ 4 = price of 1 pair of jeans
22.48 ÷ 4 = $5.62
The price difference between the two prices is 3 cents. So, $22.48 for 4 pairs is a better deal that $39.55 for 7 pairs of jeans.
Hope this helps!
According to the glossary, what are large meteors that enter the Earth's atmosphere?
A) Active galaxy
B) Blueshift
С) Coma
D) Bolide
How is the graph of g(x) = [tex](x-10)^{2}[/tex] related to the graph of f(x)= [tex]x^{2}[/tex]
(x - 10)² is the graph x² by translation of 10 units moved to the right.
what is the simplified fractional equivalent of the terminating decimal 0.12?
Answer:
6/50
Step-by-step explanation:
0.12 as a fraction is 6/50.
Answer:
3/25
Step-by-step explanation:
12/100=6/50=3/25 .
Please help if you can! A photographer rented a booth at an art fair for $630. The photographer sold each photograph for $45 and made a total of $1,980 after paying for the booth. How many photographs did the photographer sell at the fair?
He needed to make a total of 1980 + 630 = $2610
$2610 / 45 = 58
Answer: 58
Which of the following properties could be used to rewrite the expression (2/3 . 1/5) . 5/2 as 2/3 . (5/2 . 1/5)
a. The commutative property used twice
b. The associative property followed by the commutative property
c. The commutative property followed by the associative property
d. The associative property used once
Answer:B
Step-by-step explanation:
What is QUzXTY . . .
Answer:
ANSWER MEEEEE
Step-by-step explanation:
What is free energy.
Answer:
free energy, in thermodynamics, energy-like property or state function of a system in thermodynamic equilibrium. Free energy has the dimensions of energy, and its value is determined by the state of the system and not by its history.
dont mind this i just need the achivement
Answer:
K cool
Step-by-step explanation:
Answer:
Step-by-step explanation:
p=5(q-2r)/r
solve for r
Answer:
r = 5q / (p + 10)
Step-by-step explanation:
p = 5(q - 2r)/r
multiply both sides by r
pr = 5(q - 2r)
distribute
pr = 5q - 10r
add 10r to both sides
pr + 10r = 5q
Factor out r
r(p + 10) = 5q
divide both sides by p + 10
r = 5q / (p + 10)
plsefgrffghttgrewe helppppppppppppppppppppppppppppp
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The slope of the given line is its constant of proportionality ~
so, let's find the slope ~
[tex] \sf\dfrac{y_2 - y_1}{x_2 - x_1} [/tex][tex] \sf \dfrac{4 - 0}{1 - 0} [/tex][tex] \sf 4[/tex]The required value is ~ 4
1) -x2
-Х2
I need help with this problem
A stadium has 35,000 seats. 4% of the seats have cushioned backs. How many seats are NOT cushioned in the stadium?
Answer:
1400
Step-by-step explanation:
b) Express 0.6363......as a rational number in its lowest term.
Answer:
[tex]\frac{7}{11}[/tex]
Step-by-step explanation:
We require 2 equations with the repeating digits (63) placed after the decimal point.
let x = 0.636363..... (1) multiply both sides by 100
100x = 63.6363... (2)
Subtract (1) from (2) thus eliminating the repeating digits
99x = 63 ( divide both sides by 99 )
x = [tex]\frac{63}{99}[/tex] = [tex]\frac{7}{11}[/tex] ← in simplest form
pls help with this question asap!
Answer:
ggggggggggggggggggggg
a square has a diagonal length of 10 meters. How long is the side of the square?
Answer:
5 × √2 or 7,071067811865475Step-by-step explanation:
the diagonal of a square splits the square into 2 right triangles. So we can use Pythagorean's theorem.
where c is the hypotenuse. So the diagonal is the hypotenuse here, and thus c = 10. Now, since we are dealing with a square, all the sides are the same length, so a = b. So we have:
a² + a² = c²
2a² = 100
a² = 50
a = √50
a = 5 × √2 or 7,071067811865475
--------------------------
Answer: 50
Step-by-step explanation :<
Can someone help me with this?
Answer:
the 20 dollars = the slope
the fee = the y-intercept
if a line has a slope of 20 and passes through the point (7,200), then what is the y-intercept?
y-intercept is 60
PLEASE HELP ME I NEED THIS DONE RIGHT NOW
I know it says the answers are on the back but the answers aren’t there!!
Solve.
x−(−2 3/8)=−1/4
What is the solution to the equation?
Enter your answer as a simplified mixed number in the box.
X= ??