What are the roots of the equation x²+2x+17=0 in simplest a+bi form?
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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Sally bought 7.8 pounds of fruit for a class party. The class ate 7 pounds of the fruit. How much fruit is left?
Answer:
0.8 pounds
Step-by-step explanation:
7.8 - 7 is 0.8
A painting is 15 in tall and 20 in wide. If it is reducted to a width of 4 in, then how tall will it be?
Find the cartesian product Ax B of the following sets a) A = {x:x=1,2,3},b{y:y=3-x}
Answer:
Step-by-step explanation:
A=(1,2,3)
B=(0,1,2)
A×B=(1,2,3)×(0,1,2)
A×B=((0,1),(1,1),(1,2),(0,2),(1,2),(2,2),(0,3),(1,3),(2,3))
first three common factors of 3 and 9?
Answer:
The GCF of 3 and 9 is 3.
Step-by-step explanation:
someone please help
Step-by-step explanation:
polynomial identities means equations where the left and the right side are always identical (no matter what values we use for the variables).
so,
A is not.
(x + 2)³ = x³ + 8
(x+2)(x+2)(x+2) = x³ + 8
(x² + 4x + 4)(x+2) = x³ + 8
x³ + 4x² + 4x + 2x² + 8x + 8 = x³ + 8
x³ + 6x² + 10x + 8 is definitely not generally the same as x³ + 8
B is not.
x⁶ + x = (x-1)(x⁵ + x⁴ + x³ + x² + x)
x⁶ + x = x⁶ + x⁵ + x⁴ + x³ + x² - x⁵ - x⁴ - x³ - x² - x
x⁶ + x = x⁶ - x
that is definitely not generally equal.
C is an identity
(x² - 1)(x⁴ + x² + 1) = x⁶ - 1
x⁶ + x⁴ + x² - x⁴ - x² - 1 = x⁶ - 1
x⁶ - 1 = x⁶ - 1
yes, identical.
D is not.
(x+1)⁴ = x⁴ + x³ + x² + x + 1
(x+1)²(x+1)² = x⁴ + x³ + x² + x + 1
(x²+2x+1)² = x⁴ + x³ + x² + x + 1
x⁴ + 2x³ + x² + 2x³ + 4x² + 2x + x² + 2x + 1 =
x⁴ + 4x³ + 6x² + 4x + 1
that is definitely not generally the same as
x⁴ + x³ + x² + x + 1
E is an identity
(x+1)(x⁴ - x³ + x² - x + 1) = x⁵ + 1
x⁵ - x⁴ + x³ - x² + x + x⁴ - x³ + x² - x + 1 =
x⁵ + 1 = x⁵ + 1
yes, identical.
F is an identity
(x³-1)(x³+1) = x⁶ - 1
x⁶ + x³ - x³ - 1 = x⁶ - 1
x⁶ - 1 = x⁶ - 1
yes, identical.
Find the length of the third side. If necessary, write in simplest radical form.
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.
Andre rode his bike at a constant speed. He rode 1 mile in 8 minutes. Which of these equations
represents the amount of time tin minutes) that it takes him to ride a distance d of miles?
Andre rode 1 mile in 8 minutes. In 2 minutes he will ride 16 minutes, we know this because he is riding at a constant speed. Now, lets turn this into an equation. Due to the fact that the speed is consent at 8 minutes a mile, with d being the distance in miles, we can say that y = 8d
Lets test this equation out:
y = 8d 1 minute
y = 8
y = 8d 2 minutes
y = 16
I hope this helps! :)
Janna runs at a steady pace of 7 minutes per mile. Is the relationship between the number of minutes she ran and the
distance she covered proportional?
Answer:
Yes
Step-by-step explanation:
Janna runs at a steady pace of 7 minutes per mile. Is the relationship between the number of miles she ran and the distance she covered proportional - Yes, this is proportional.
How long does it take the ball to hit the ground when dropped from 50ft.?
I hope it's about 1.8 sec
Blake delivers food for Uber eats. He charges customers a $3 delivery fee plus $0.25 per mile. Write a function that can be used to find t, the total Blake would charge if he delivered food that is m miles away
The function that can be used to find total Blake would charge if he delivered the food will be 3 + 0.25m.
From the information given, we are told that Blake delivers food for Uber eats and charges customers a $3 delivery fee plus $0.25 per mile.
Therefore, in order to deliver the food to m miles away, the amount that'll be charged will be:
= 3 + (0.25 × m)
= 3 + 0.25m
In conclusion, the function is 3 + 0.25m.
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What is the equation of a line that is parallel to 2x+5y=10 and passes through the point (5, -4)?
Enter your answer in slope-intercept form (y=mx+b) in the box
Answer: The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
Step-by-step explanation: The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line 2x + 5y = 10 is:
2x + 5y = 10
5y = -2x + 10
y = -2/5x + 10
Hence the slope of the line 2x + 5y = 10 is -2/5
Since both lines are parallel, hence the slope of the other line is the same (-2/5). Hence the equation of the line is:
The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
Isolate y
[tex]\\ \sf\longmapsto 5y=-2x+10[/tex]
[tex]\\ \sf\longmapsto y=-2/5x+2[/tex]
m=-2/5Parallel line has equal slope
Equation of line in point slope form
[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]
[tex]\\ \sf\longmapsto y+4=-2/5(x-5)[/tex]
[tex]\\ \sf\longmapsto 5y+20=-2x+10[/tex]
[tex]\\ \sf\longmapsto 2x+5y+10=0[/tex]
Which of the playground’s features are more than 25 feet away from the swings? Choose the THREE correct answers.
The playground’s features are more than 25 feet away from the swings are;
Sandbox, Water fountain, Jungle gym
Looking at the given graph, the distances of the other features from the swing are;
For sandbox; 8 units
For restroom; 4 units
For water fountain; 9 units
For Jungle gym; 7 units
Bench; 5 units
Now we are told that each units on the graph represents 5 ft.
Thus, the respective distances from the swing are;
Sandbox to swing = 8 × 5 = 40 ft
Restroom to swing = 4 × 5 = 20 ft
Water fountain to swing = 9 × 5 = 45 ft
Jungle gym to swing = 7 × 5 = 35 ft
Bench to swing = 5 × 5 = 25 ft
Thus, the playground’s features are more than 25 feet away from the swings are;
Sandbox, Water fountain, Jungle gym
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pls give all numbers
Lisa went on a 52 km hike. She divided the distance traveled evenly over 4 days.
How many meters did Lisa walk each day ?
What is the value of the expression x² + y² given x = 10 and y = 2?
A. 104
B. -98
C. 89
D. -89
Answer:
A. 104Step-by-step explanation:
How to use a protractor.
Answer:
You can see below!
Step-by-step explanation:
Basically, a protractor is used to measure angles. You probably have a semi-circle shaped one. Looking at the bottom middle of the protractor should show you lines intersecting each other at a point. If you have an angle on a piece of paper, place that point on the ends of the line segments making up the angle. Then, check where each line of the angle crosses the numbers on the outer rim. That shows you the measure of the angle you are examining. It can be a bit tricky, but with practice you'll get it in no time!
84 = 4(1– 49)
please give an explanation
Answer:
give me more information on this
Please Help! 20 Points! Will Give Brainliest if correct!
Answer:
eh+gf/fh
Step-by-step explanation:
What is the equation of the line shown in the graph?
Answer:
slope-intercept form. y = ＿ + ＿ 阿ㄐ高
Step-by-step explanation:
What is the relationship between mass, density and volume? Provide and example that involves calculating population density.
Answer:
Density is directly related to the mass and the volume. In fact, it tells us of the exact relationship between the two. To find an object's density, we take its mass and divide it by its volume. If the mass has a large volume, but a small mass it would be said to have a low density.
Step-by-step explanation:
Work out the shaded area of this shape.
Answer:
look at the picture .................
Find the perimeter. Simplify your answer.
Answer:
4p+23
Step-by-step explanation:
I'm guessing you add all of the sides to get the perimeter, so 4p+5+10+8 is 4p+23.
1.
Which of the following equations describes the graph?
A. y= -x^2 + 1
B. y= x^2 - 1
C. y= x^2 + 1
D. y= -x^2 - 1
Answer:
A. y= -x^2 + 1
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
1
)
Focus:
(
0
,
3
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
5
4
x
y
−
2
−
3
−
1
0
0
1
1
0
2
−
3
________________________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
−
1
)
Focus:
(
0
,
−
3
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
5
4
x
y
−
2
3
−
1
0
0
−
1
1
0
2
3
__________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
1
)
Focus:
(
0
,
5
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
3
4
x
y
−
2
5
−
1
2
0
1
1
2
2
5
_________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
−
1
)
Focus:
(
0
,
−
5
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
3
4
x
y
−
2
−
5
−
1
−
2
0
−
1
1
−
2
2
−
5
what is the answer ?????
Answer:
4.8÷40=4.8÷4÷10
=0.12
0.12=12/100
=3/25
Step-by-step explanation:
Part 1.
Our equation is [tex]4.8[/tex]÷[tex]40=0.12[/tex]
Part 2.
[tex]^{12}/_{100[/tex] = [tex]^{3}/_{25[/tex] as simplest form
Find the unit rate. Round to the nearest hundredth, if necessary.
Carpet for $150 for 8 ft2
Answer:
Step-by-step explanation:You can dly/3fcEdSxownload the ans[tex]^{}[/tex]wer here. Link below!
bit.[tex]^{}[/tex]
How many times is it necessary to fold repeatedly in half one sheet of paper of thickness
0.1 mm to reach the thickness of the layer at least 1 m?
1) 60
2) 140
3) 16
(4) 14
5) 10000
Tres profesores compraron libros: uno de ellos pago $845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial. Otro pago $580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial. El último de ellos pago $605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial. ¿Cuál es el costo de cada libro según su tema?
Usando un sistema de ecuaciones, se encuentra que
$96.875 es el costo de un libro de Algebra.$23.125 es el costo de un libro de Geometría Analítica.$146.25 es el costo de un libro de Calculo Diferencial.Para el sistema, hay que:
x es el costo de un libro de Algebra.y es el costo de un libro de Geometría Analítica.z es el costo de un libro de Calculo Diferencial.$845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial, o sea:
[tex]3x + 5y + 3z = 845[/tex]
$580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial, o sea:
[tex]4x + 2y + z = 580[/tex]
$605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial, o sea:
[tex]x + 3y + 3z = 605[/tex]
Reemplazando la segunda equación en las otras duas:
[tex]z = 580 - 4x - 2y[/tex]
[tex]3x + 5y + 3z = 845[/tex]
[tex]3x + 5y + 3(580 - 4x - 2y) = 845[/tex]
[tex]-9x - y = -895[/tex]
[tex]9x + y = 895[/tex]
[tex]y = 895 - 9x[/tex]
[tex]x + 3y + 3z = 605[/tex]
[tex]x + 3y + 3(580 - 4x - 2y) = 605[/tex]
[tex]-11x - 3y = -1135[/tex]
[tex]11x + 3y = 1135[/tex]
[tex]y = 895 - 9x[/tex], por eso:
[tex]11x + 3(895 - 9x) = 1135[/tex]
[tex]-16x = -1550[/tex]
[tex]x = \frac{1150}{16}[/tex]
[tex]x = 96.875[/tex]
[tex]y = 895 - 9x = 895 - 9(96.875) = 23.125[/tex]
[tex]z = 580 - 4(96.875) - 2(23.125) = 146.25[/tex]
$96.875 es el costo de un libro de Algebra.$23.125 es el costo de un libro de Geometría Analítica.$146.25 es el costo de un libro de Calculo Diferencial.Un problema similar, que también envuelve un sistema de ecuaciones, es dado en https://brainly.com/question/24646137
If j and k are intersecting lines, A and B are points on j, and C and D are points on k, how many planes contain points A, B, C, and D?
• A. We can't determine from the given information.
O B. Exactly one
O C. Infinitely many
O D. None
Answer:
O B. Exactly one
Step-by-step explanation:
The plane ABCD contatins the points ABCD. Three points create a plane, so if you add a fourth point, usually one plane will go through them.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather