Answer:
-1 ±4i
Step-by-step explanation:
The quadratic can be written in vertex form as ...
x² +2x +17 = 0
(x² +2x +1) +16 = 0 . . . . . . . . identify the part that can be a perfect square
(x +1)² = -16 . . . . . . . . . . . . subtract 16
x +1 = ±√(-16) = ±4i . . . . take the square root
x = -1 ±4i . . . . . . . . . . . subtract 1
The roots of the equation are x = -1-4i and x = -1+4i.
_____
Additional comment
It can be worthwhile to remember the form of a perfect square trinomial:
(x +a)² = x² +2ax +a²
If you know the coefficient of x, you can use half of it as the constant in each binomial factor.
In the above, we had 2a=2, so a=1 and a²=1. The constant 17 then is resolved into two parts: one part (1) is used to "complete the square" and the other part (16) is the y-coordinate of the vertex. It is used to find the "radical" portion of the roots.
The roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] are [tex]x = -1 +4i[/tex] and [tex]x = -1 - 4i[/tex].
To find the roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] in simplest a + bi form, we can use the quadratic formula.
The quadratic formula states that for an equation in the form[tex]ax^2 + bx + c = 0[/tex], the roots can be found using the formula:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
We have a = 1, b = 2, and c = 17.
Substituting these values into the quadratic formula, we get:
[tex]x = \frac{-2 \pm \sqrt{4 - 68}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{-64}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{64i^2}}{2}[/tex]
[tex]x = \frac{-2 \pm 8i}{2}[/tex]
[tex]x = -1 \pm 4i[/tex]
So, [tex]x = -1 +4i[/tex] and [tex]x=-1-4i[/tex] are roots.
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pleassssssssssssssssssssse HELP QUICKLY PLEASSSSSSE
Answer:
7/6 or A
Step-by-step explanation:
2/3(9-6)-5/6= 7/6
What is the simplest form of
(2p + 1)(2p - 5)?
Answer:
4p^2-8p-5
Step-by-step explanation:
Answer:
4p^2-8p-5
Step-by-step explanation:
Hope this helps :)
Whoever helps me with this I'll give brainliest and extra points! :)
What are the options
halfway between -23 and 23
Answer:
0
Step-by-step explanation:
-23+23= 0
0 + 23 = 23
To meet the character limit.
Answer:
0
Step-by-step explanation:
first, you need to calculate the entire distance:
23 + 23 = 46
Now divide it by half:
46 / 2 = 23
And now substract & add this
-23 + 23 = 0
23 - 23 = 0
help please
anybody?
Answer:
C.40%
Step-by-step explanation:
Answer:
Your answer would be 40%.
Step-by-step explanation:
If the pizza was cut into 10 pieces, each piece would equal 10%. Therefore, since she had ate 4 pieces, she had eaten 40% of the pizza.
How to find left and right inverse of a 3x2 matrix.
Let A be a 3×2 matrix, L its left inverse, and R its right inverse. L and R are then matrices such that LA = I₂ (the 2×2 identity matrix) and AR = I₃ (the 3×3 identity matrix). Clearly L must be 2×3 and R must be 3×2 in order for the matrix products to be defined.
To find L and R, we start by introducing a square matrix on the the left sides of either equation above. In particular, we uniformly multiply both sides by the transpose of A, then solve for the inverse.
For the left inverse, we have
[tex]LA=I[/tex]
[tex](LA)A^\top = IA^\top[/tex]
[tex]L\left(AA^\top\right) = A^\top[/tex]
[tex]\left(L\left(AA^\top\right)\right)\left(AA^\top\right)^{-1} = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]L\left(\left(AA^\top\right)\left(AA^\top\right)^{-1}\right) = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]LI = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]L = A^\top \left(AA^\top\right)^{-1}[/tex]
We do the same thing for the right inverse, but take care with how we multiply both sides of AR = I₃.
[tex]AR=I[/tex]
[tex]A^\top(AR)=A^\top I[/tex]
[tex]\left(A^\top A\right)R = A^\top[/tex]
[tex]\left(A^\top A\right)^{-1} \left(\left(A^\top A\right)R\right) = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]\left(\left(A^\top A\right)^{-1} \left(A^\top A\right)\right) R = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]IR = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]R = \left(A^\top A\right)^{-1} A^\top[/tex]
Find the slope of the line given the following points on the line:
(-6, 4) and 2, 7)
Answer:
3/8
Step-by-step explanation:
Answer:
[tex]\boxed{\sf Slope:3/8}[/tex]
Step-by-step explanation:
To determine the slope of a line given the coordinates of two points on the line, use the slope formula.
[tex]\boxed{\sf \sf{Slope\;(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]
x1 and y1 are the coordinates of the first point. The second point's coordinates are x2, y2.
Points: [tex]\sf (-6, 4) \:and \:(2, 7)[/tex]
[tex]\longmapsto\sf \left(x_1,\:y_1\right):\left(-6,\:4\right)[/tex]
[tex]\longmapsto\sf \left(x_2,\:y_2\right)=\left(2,\:7\right)[/tex]
_______________
[tex]\leadsto\sf m=\cfrac{7-4}{2-\left(-6\right)}[/tex]
[tex]\leadsto\sf m=\cfrac{3}{8}[/tex]
_________________________________________
Ophelia has 5 flower less than Daisy. Together they have 20 flowers. How many flowers have each of them?
What is the answer to this
what is the answer is 34 lekende eza
Answer:
Yes
Step-by-step explanation:
This is a function because every value in set A has only 1 value in set B.
kinyua spent
[tex] \frac{1}{4} [/tex]
of his net January salary on school fees
Answeby-step explanation:
zdssadads
what is the perimeter of a pool that is 30 meters long and 18 meters wide?
Answer:
Step-by-step explanation:
Perimeter=2(length+widht)
Given values:
length=30 m
width=18 m
Substitute values in formula:
Perimeter=2(20+18) m
Perimeter=2(38) m
Perimeter= 76 m
If you need to ask any questions, please let me know.
For reviewing purposes.
Answer:
88
Step-by-step explanation:
9 × 8 + [tex]2^{4}[/tex]
=> PEMDAS
so first exponent 2^{4} = 16
next multiplication
9*8 = 72
=> 72 + 16
=> 88
You have 2\3 of a pizza left from yesterday. You divide it into 4 equal pieces. What fraction of the pizza is each piece?
====================================================
Explanation:
Let's say for example this pizza had 6 slices to start with. Two-thirds of this is (2/3)*12 = 4 slices. So you have 4 slices left over from yesterday. Then let's say you hand one slice to each of your four friends. Each friend would have 1/6 of the original pizza.
HELP PLZ !!
The graph of f(x) = 7^x is stretched vertically by a factor of five. Which of the following is the equation of the new graph, g(x)
Answer:D
Step-by-step explanation:
Let B be the basis of P3 consisting of the Hermite polynomials in Exercise 21, and let p.t / D 7 ! 12t ! 8t 2 C 12t 3. Find the coordinate vector of p relative to B.
To calculate the relative vector of B we have to:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
The coordenates of:
[tex]p(t)= 12t^3-8t^2-12t+7[/tex], with respect to B satisfy:
[tex]C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3[/tex]
Equating coefficients of like powers of t produces the system of equation:
[tex]\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.[/tex]
After solving this system, we have to:
[tex]C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}[/tex]
And the result is:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
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The minute hand of a clock turns 6 degrees per minute. In ten minutes the minute hand turns what fraction of a full 360 turn?
Answer:
25%
Step-by-step explanation:
15 times 6 is 90
90 is 25 % of 360
help please with math i beg you
a) x=24b+8v
4 * 24 = 96
120 - 96 = 24
24 / 8 = 3
b) 3
6 * 8 = 48
120 - 48 = 72
72 / 24 = 3
c) 3
120 / 8 = 15
d) 15
120 / 24 = 5
e) 5
2 The salary of 157 employees in an office for a month is 710, 582, what is the annual salary of 1 employee, assuming all are paid equally
Answer: $4526
Step-by-step explanation:
Ratio of employees to cash
157:710528
Divide both sides by 157 to find how much 1 employees is paid
1: 4526
Answer:
710 582 - salary of all employees in a month
157 - number of employees
The monthly salary of each employee is 4526.
The 4526 is obtained by dividing the salary of all employees to their number which is 157.
The question is, "What is the salary of 1 employee assuming all are paid EQUALLY?"
To get it, just multiply 4526 into 12 (annually). So the answer is 54312
Lee is creating a garden with the dimensions shown.
Lines are drawn inside a large triangle at each point to create smaller triangles. Line A B is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to A B is 36 degrees. Line Z Y is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to Z Y is 65 degrees. Line X Y is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to X Y is 79 degrees.
He creates paths through the garden along Line segment A B, Line segment X Y, and Line segment Z Y. Which correctly compares the lengths of the paths?
The path along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B.
The path along Line segment A B is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment X Y.
The path along Line segment Z Y is longer than the path along Line segment X Y, and the path along Line segment X Y is longer than the path along Line segment A B.
The path along Line segment Z Y is longer than the path along Line segment A B, and the path along Line segment A B is longer than the path along Line segment X Y.
Mark this and return
What is the slope of this graph please no links or files
Answer:
2/3
Step-by-step explanation:
You go over 2 and down 3
You can wash a car 1.5 times as fast as your friend. Working together, the two of you can wash 1 car in 6 minutes. How long does it take each of you to wash the car when working alone? Leave your answer as a fraction!
If the two of you can wash 1 car in 6 minutes:
It will take you 10 minutes to wash the car alone
take your friend 15 minutes to wash the car alone
Let the duration you can work be represented by y
Let the duration your friend can work be represented by x
You can wash a car 1.5 times as fast as your friend
That is, y = 1.5x
Working together, the two of you can wash 1 car in 6 minutes
This can be represented by the equation
[tex]\frac{1}{x}+\frac{1}{y} = \frac{1}{6}[/tex]
Substitute x = 1.5y into the equation above
[tex]\frac{1}{1.5y}+\frac{1}{y} = \frac{1}{6}\\\\\frac{1+1.5}{1.5y} = \frac{1}{6}\\\\\frac{2.5}{1.5y} = \frac{1}{6}\\\\1.5y=2.5(6)\\\\1.5y=15\\\\y=\frac{15}{1.5} \\\\y=10[/tex]
It will take you 10 minutes to wash the car alone
Substitute y = 10 into x = 1.5y
x = 1.5(10)
x = 15 minutes
It will take your friend 15 minutes to wash the car alone
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Let g (x) = 5x^2 + 3x and r (x) = 2x^2 + 6x - 13. Find g (x) - r (x)
-3x^2 - 3x + 13
-3x^2 + 3x + 13
-3x^2 + 3x - 13
-3x^2 - 3x - 13
Answer:
none
Step-by-step explanation:
[tex] = 5 {x}^{2} + 3x - 2 {x}^{2} - 6x + 13 \\ = 3 {x}^{2} - 3x + 13[/tex]
What is the slope of the line whose equation is 12=4x−6y?
Please and thanks if you decide to answer.
Answer:
slope =4
Step-by-step explanation:
from, y=mx + c
where m is slope
Answer:
the slope formula is y=mx+b where b is the y intercept and m is the slope we rewrite the equation by subtracting 4x from either side and then dividing both sides by 6 so we have y=-0.6x+2 so m the slope is -0.6
help me brain pt Part 5
Doctors are interested in determining if the human body temperature is really 98.6 degrees. he selects 30 students and records their temperature using a digital thermometer. what type of test would they conduct to test this claim?
Answer:
I think its one mean, if it's not I'm very sorry
In order to corroborate his assertion that the average body temperature is lower than 98.6 degrees Fahrenheit, the croaker created a test statistic.
What's Test Statistic?A test statistic is a figure attained from a statistical analysis. It explains how far your observed data is from the null thesis, which states that there's no correlation between the variables or distinction between the sample groups.
Test statistics are statistics that are produced from samples to determine whether or not to accept the null thesis.
A sample is data that represents a portion of the population. In other words, it's a gauged - down interpretation of a larger group.
The croaker conducted a thesis test in order to corroborate the information that has been handed in the question. And he calculated the test statistic, or arbitrary data from the sample taken from the population data, for the thesis test.
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A coin will be tossed twice, and each toss will be recorded as heads (H) or tails (T).
Answer:
Sample Space {HH, HT, TH, TT}
Event that the second toss is heads {HH, TH}
The price of a cinnamon roll is $2.00. The bakery has a sale, and all prices are 10% off. What is the sale price of the cinnamon roll
Answer: $1.80
Step-by-step explanation:
10% is 1/10. To find 1/10 of $2 we must divide it by the bottom of the fraction and times the top. 200 divided by 10 is 20 cents, times that by 1 is still 20 so, 10% = 20 cents. To find the sale price, we must subtract the discount from the original price. $2 - 20 cents is $1.80.
what are the values of each variable
Answer:
Step-by-step explanation:
Katy kept a tally of the number of emails she received each day for a week.
Monday 10
Tuesday 0
Wednesday 10
Thursday 1
Friday 0
according to the table,what was the rate of changing between Wednesday and Thursday?
Answer:
9
Step-by-step explanation:
which one is correct
a.
b.
c.