Answer:
Step-by-step explanation:
x²+y²+2x+2y=0 ...(1)
x²+y²+2x+6y+9=0 ...(2)
subtract (1) from (2)
x²+y²+2x+6y+9-(x²+y²+2x+2y)=0
x²+y²+2x+6y+9-x²-y²-2x-2y=0
4y+9=0
4y=-9
[tex]y=-\frac{9}{4}[/tex]
put in (1)
[tex]x^{2} +(-\frac{9}{4} )^2+2x+2(-\frac{9}{4} )=0\\x^{2} +2x+\frac{81}{16} -\frac{9}{2} =0\\x^{2} +2x+\frac{81-72}{16} =0\\x^{2} +2x=-\frac{9}{16} \\adding 1 \\x^{2} +2x+1=-\frac{9}{16} +1\\(x+1)^2=\frac{-9+16}{16} \\x+1=\pm\sqrt{\frac{7}{16} } \\x=-1 \pm\frac{\sqrt{7} }{4} \\x=\frac{\sqrt{7} -4}{4} \\and\\x=\frac{-\sqrt{7} -4}{4}[/tex]
solution is ((√7-4)/4,-9/4)
and ((-√7-4)/4,-9/4)
What will be displayed when the following code is executed? number = 6 while number > 0: number -= 3 print(number, end = ' ').
With number = 6, the while condition is satisfied. Then number is decremented by 3, meaning we replace the value of number (6) with its current value minus 3 6 - 3 = 3.
Then with number = 6, we still have number > 0, so we decrement again and end up with number = 0.
With number = 0, number > 0 is no longer true, so we exit the loop.
Then the print statement simply prints the current value of number, which is 0.
Owen had 8,452 books donated to our school. If he shares with with 23 classes about how many books does each class get? Again assesment due tom :,)
Answer:
327.5
Step-by-step explanation:
8452/23 = 327.478
Round to about 327.5 books per class
Answer:
each class gets 367 books
explain each step please :)
Answer:
u need to use the quadratic formula
Step-by-step explanation:
I think this is about it
What is product in math.
Answer:
so when you Mutpliy #*# = #product
Step-by-step explanation:
EX: 3*4=12
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 .
PLS HELP WILL MARK BRAINLIEST, PLS HURRY
Answer:
B
Step-by-step explanation:
Find the missing angle measurement in each set of supplementary angles.
Supplementary angles sum up to 180°. Take the missing angle as 'x'.
148 + x = 180
x = 180 - 148
x = 32°
=》 Angle ABD = 32°
_________
Hope it helps!
RainbowSalt2222 ☔
Answer:
32 degrees
Step-by-step explanation:
Hi there!
Angle ABC measures 180 degrees since it's a straight line.
To find angle ABD, we simply subtract the given angle that measures 148 degrees from 180:
180-148 = 32
Therefore, angle ABD measures 32 degrees.
I hope this helps!
pls help with this question asap!
Answer:
ggggggggggggggggggggg
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]
A similar problem is given at https://brainly.com/question/15536019
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
Of the following sets which are equivalent to the set S = {an even number less than 10 } is
A = {Prime number less than 10 }
B = {Odd factor less than 15}
C= {Odd numbers less than 7}
D ={An even number between 10 and 15}
E ={An odd number between 10 and 16}
Answer:
A, 2
Step-by-step explanation:
We can immediately rule out B and C; they are odd numbers while S is an even number.
We can also rule out D and E. This is because D and E are greater than or equal to 10, while S is less than 10.
A number that can fulfill the requirements for both A and S is 2
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]
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 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!
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)
Read more about linear inequalities at:
https://brainly.com/question/11897796
(x+a)^2 -7 = x^2 +10x +b
Work out the value of a and b.
Answer:
(x+a)²-7=x²+10x+b
simplifying,we get
x²+2ax+a²-7=x²+10x+b
the coefficient of x on both sides should be equal
therefore
2a=10
a=10/2=5
also for b
a²-7=b
5²-7=25-7=b
b=18
a=5
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%.
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)
the average adult human has approximately 2.5 x10^13 red blood cells and 7 x 10^9 white blood cells ,about how many times greater is the number of red blood cells as the number of white blood cells
Step-by-step explanation:
The no. of red blood cells is 2.4993*10^13 more than the no. of white blood cells
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
(PICTURE PROVIDED)
HELPPPPPPPPP PLS
kokokokokkokokokokokookokokk.
Answer:
OMG️️
Step-by-step explanation:
What is this❓
what have you wrote✍️
Answer:
hye nice what have written tell then I will answer you.
С
12 yd.
5 yd.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
C=
yards
Answer:
C = 13
Step-by-step explanation:
A²+B²=C²
where c is the hypothenuse
5²+12²=c²
25+144=c²
169=c²
√169 = c
13 = c
20 points answer please
Answer:
just d
Step-by-step explanation:
Hope this helps!❆
Task 2: Components of Your Will
Describe the components of your will and how you will specify each one.
Type your response here:
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.
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= ??
What is the equation for the line in slope-intercept form?
Enter your answer in the box. I'll give you 100 points
Answer:
y = -4x + 5.
Explanation:
Count rise/run to find the slope, find the y-intercept.
Answer:
y = -4x + 3
Step-by-step explanation:
First, find the slope using two points [(-2, 13), (0, 5)] and the formula [ y2-y1/x2-x1 ].
5-13/0-(-2)
-8/2
-4
Second, find the y-intercept which we know is (0, 5) since we used it in the previous part.
Third, input everything we found.
y = -4x + 5
Best of Luck!
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.
For more references on equation, click;
https://brainly.com/question/10413253
#SPJ2
1) -x2
-Х2
I need help with this problem