Answer:
y = x² -2x +5
Step-by-step explanation:
When a polynomial has q as a zero, it has (x-q) as a factor. Your polynomial has factors (x -(1-2i)) and (x -(1+2i)). The polynomial will be the product of these factors.
__
y = (x -(1 -2i))(x -(1 +2i))
y = ((x -1) +2i)((x -1) -2i) = (x -1)² -(2i)² = x² -2x +1 -4(-1)
y = x² -2x +5
_____
Additional comments
i is the imaginary number √(-1), so i² = -1.
The two given roots differ only in the sign of their imaginary parts, so they are "conjugates" of each other. Complex roots of polynomials with real coefficients always come in conjugate pairs. (In some problems, you will be expected to supply the missing root of a conjugate pair.)
The expression for the product of the factors is simplified using the factoring for the difference of squares:
(a -b)(a +b) = a² -b² . . . . . . . here, we have a=(x-1); b=2i
9e +4= -5e + 14+ 13e
step by step pls
Answer:
e = 10
Step-by-step explanation:
9e +4= -5e + 14+ 13e
combine like terms on left side of the equation : -5e + 13e = 8e
9e + 4 = 8e + 14
subtract 8e from both sides : 9e - 8e = e and 8e - 8e cancels out
e + 4 = 14
subtract 4 from both sides : 4 - 4 cancels out and 14 - 4 = 10
we're left with e = 10
3 ½ pints = ___ cups
Answer:
8.40665 cups
Step-by-step explanation:
hope this is helpful!
how to graph transformations of quadratic functions
Answer:
Shift "h" units to the right, "k" units up, and reflect over the x or y axis when needed.
Step-by-step explanation:
1) I want to talk about reflections first.
Reflections across the x-axis --> [tex]y = ax^2[/tex], a is the coefficient. if a is negative, then the equation should be reflected across the x-axis. This is known as a vertical reflection. Reflections across the y-axis --> [tex]y=a(bx)^2[/tex], b is the coefficient. If b is negative, then reflect the equation over the y-axis. There are cases where the reflection across the y-axis does not change anything. But, let's say its [tex]y=(x-3)^2[/tex]... the reflection across the y-axis is different (that equation is: [tex]y=(-x-3)^2[/tex] )2) Rigid transformations
Horizontal transformations (to the left or right): [tex]y=a(bx-h)^2[/tex], factor out b from "bx-h" and whatever h equals is the units to the right. If h is a negative number, then you move to the left. Vertical transformations (up and down): [tex]y = a(bx-h)^2+k[/tex]... k is just the units up... if k is negative then we move it down.Example (check image for visual)
We transform [tex]y = x^2[/tex] to [tex]y = -(-x-3)^2+3[/tex] , you move right 3, then reflect across the x-axis, then reflect across y-axis, then move 3 up.
--------------------------------------------------------------------------------------------------------------
Note: In the image, the red line is the original function, the blue one is the transformed function. See if you can follow along with the verbal instructions I gave above.
7363626x726=???? Helpppppp
Answer:
The answer is 5345992476
Step-by-step explanation:
WHAT DOES AN ANIMAL BREEDER DO?????????
I LITERALLY NEED HELP ON THIS ONE!!
Some school commercial thingy.
Answer:
Breeders cross animals of the same species with desirable traits to create desirable offspring.
Step-by-step explanation:
A store owner bought 15001500 pencils at \$0.10$0.10 each. If he sells them for \$0.25$0.25 each, how many of them must he sell to make a profit of exactly \$100.00$100.00
Based on the information given, the number of pencils that should be sold will be 1000 pencils.
Let the number that should be sold be x.
A store owner bought 1500 pencils at $0.10 each. Therefore, the cost price will be:
= 1500 × $0.10 = $150
Profit = Selling price - Cost price
100 = 0.25x - 150
0.25x = 100 + 150
0.25x = 250
x = 250/0.25
x = 1000
Therefore, 1000 pencils should be sold.
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System practice problems
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
in a sale there is a 40% discount.what is the discount on a dress that costs $150.00
Answer:
$90 or $60
Step-by-step explanation:
A scale drawing of a rectangular park had a scale of 1 cm = 100 m. What is the actual perimeter of the park in meters?
10.1 and 8.8
Answer:
3780 m
Step-by-step explanation:
First, we find the perimeter of the scale drawing.
perimeter = 2(L + W)
perimeter = 2(10.1 cm + 8.8 cm)
perimeter = 2(18.9 cm)
perimeter = 37.8 cm
Now that we have the perimeter of the drawing, we use the scale to find the real perimeter.
1 cm (drawing) = 100 m (real)
37.8 cm × 100 m/cm = 3780 m
Answer: 3780 m
A cylinder has a height of 4 centimeters. Its volume is 12.56 cubic centimeters. What is the radius of the cylinder?
Step-by-step explanation:
hope it will help you...
Answer:
radius of cylinder = 1 cm
Step-by-step explanation:
Start with the formula for the volume of a cylinder: V = (pi)r²h, where r is the radius and h is the height. We want to solve this for the radius, r.
Dividing both sides of the Volume formula (above) by (pi)h, we get:
V
r² = -----------
(pi)h
If we now substitute 12.56 cc for V, 3.14 for pi and 4 cm for h, we get:
V 12.56 cc
r² = ---------- = ----------------- = 1 cm²
(pi)h 3.14(4 cm)
Taking the square root of both sides, we get r = 1 cm
16 =
ОА. 4
ОВ. 3
ОС. 8
O D. 6
Answer:
A. 4
Step-by-step explanation:
I hope this helps you!!!
Please help me Find the slope no links or bots please and thank you I really need help
Answer:
B) -7/4
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify.
y = -7/4x + 4
Step 2: Break
Slope m = -7/4
y-intercept b = 4
what is the area of the square units ? W (11,2), X (11,8), Y (14,8), Z (14,2)
Answer:
18 units²
Step-by-step explanation:
Find the side lengths then multiply the length and width to find the area.
solve this to pretty pretty pls
Answer:
3) 161
Step-by-step explanation:
Indeed this is pretty easy :D
What we need to find is the surface area of the rectangular prism excluding the area of the hole. First, let's find out the width of the box, we can do this by using the area, the length, and the height, and we can write:
[tex]V=lhw[/tex]
(Formula to find the volume of a rectangular prism)
[tex]140=(4)(7)w\\ 140=28w\\ 5=w[/tex]
Now that we have the width, can find the area of the top part of the prism:
[tex](5)(4)=20[/tex]
The area of the top part of the prism is 20, and the circle has 1/4 of the area of that:
[tex]A_{circle} = \frac{A_{top part} }{4}\\ A_{circle} = \frac{20}{4} \\ A_{circle} = 5[/tex]
So the area of the circle is 5. Now we just need to find the surface area of the rectangular prism and subtract that result with the area of the circle:
[tex]A_{circle}=5\\ SA_{rec.pri.}=2(lh+lw+wh)\\ SA_{rec.pri.}=2((4)(7)+(4)(5)+(5)(7))\\ SA_{rec.pri.}=2(28+20+35)\\ SA_{rec.pri.}=2(83)\\ SA_{rec.pri.}=166[/tex]
Subtract these two results...:
[tex]166-5=161[/tex]
And we are done!
Hello da 234234r32 ef3qew3e2wr3qefwasdwasd
triangle abc has an area of 6 and a perimeter of 12. if the triangle is dilated by a scale factor of 3 centered at the origin, what is the area and perimeter of its image, triangle a'b'c'?
Answer:
perimeter: 36 unitsarea: 54 square unitsStep-by-step explanation:
The perimeter is multiplied by the scale factor:
image perimeter = 3 × original perimeter = 3×12 = 36 units
The area is multiplied by the square of the scale factor:
image area = 3² × original area = 9×6 = 54 square units
Given the two similar triangles below, which proportion is true?
Answer:
B) 10/15 = 15/22.5
Step-by-step explanation:
For the two triangles, proportions that involve ratios of the corresponding sides are true.
‼️DUE TODAY‼️
(Question in the picture)
Answer:
I Don't know
Step-by-step explanation:
I don't know I don't know I don't know
Given that AABCDEF, solve for X.
B
A. 10
o
B. 6
C. 17
0 0
Answer:
D
Step-by-step explanation:
Given Δ ABC is similar to Δ DEF then the ratios of corresponding sides are in proportion, that is
[tex]\frac{EF}{BC}[/tex] = [tex]\frac{DE}{AB}[/tex] , substitute values
[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{30}[/tex] ( cross- multiply )
30x = 5 × 42 = 210 ( divide both sides by 30 )
x = 7
The ratio remains same
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{30}{42}[/tex]
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{15}{21}[/tex]
[tex]\\ \sf\dashrightarrow 15x=105[/tex]
[tex]\\ \sf\dashrightarrow x=7[/tex]
The diagram shows a map of three land masses, numbered region 1, region 2, and region 3, connected via bridges over water. Each bridge can be traversed in either direction. (diagram is attached)
Show that there are 10 walking routes that start and end in region 2, crossing over water exactly twice. Assume each bridge, when crossed, is fully traversed to the next land mass.
Answer:
Explanation
Step-by-step explanation:
If you look closely, every route connected to region 2 could go to either region 1 or 3, which each could go back to region 2 in 3 different formats. For example the top bridge of region 2, could go through region 1, then region 3 then to the middle bridge of region 2. This can happen for all three of the other route when going backs and works for all bridges in region 2.
Find the sum of all solutions to the equation $3x(x+4) = 135$.
Answer:
-4
Step-by-step explanation:
3x(x + 4) = 135
3x² + 12x = 135
3x² + 12x - 135 = 0
On dividing by 3
x² + 4x - 45 = 0
x² + (9x - 5x) - 45 = 0
x² + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x + 9)(x - 5) = 0
x = 5 & -9
Sum = -9 + 5
Sum = -4
The sum of the solutions of the given quadratic equation will be -4.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
As per the given equation,
⇒ 3x(x + 4) = 135
Multiply the 3x as,
3x² + 12x = 135
3x² + 12x - 135 = 0
Divide the above equation by 3 as
3x²/3 + 12x/3 - 135/3 = 0
x² + 4x - 45 = 0
x² + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x - 5)(x + 9) = 0
x = 5 and x = -9
Therefore the sum will be -9 + 5 = -4
Hence "The total of the quadratic equation's answers will be -4".
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I need help to find the radius
Answer:
Step-by-step explanation:
i think 0.6
Please help guys this is just domain and range
Answer:
domain: x>=0
range: y>=1
Step-by-step explanation:
domain: x>=0
range: y>=1
2(x-3) < 3(2x+2)
How do I solve for x
Answer:
x < -3
Step-by-step explanation:
2(x-3) < 3(2x+2)
Use the distributive property.
(2× x)-(2×3) < (3 × 2x) + (3×2)
2x-6 < 6x+6
add 6 to both sides
2x < 6x+12
subtract 6x from both sides.
-4x < 12
divide both sides by -4
x < -3
Find the length of OP.
Answer:
OP = 84
Step-by-step explanation:
The triangle is equilateral meaning all angles equal and all sides are equal.
5y - 6 = 4y + 12
y - 6 = 12
y = 12 + 6
y = 18
Now
OP = 4y + 12
OP = 4(18) +12
OP = 84
Please help me asap
ty :)
Answer:
y = -3x - 3
Step-by-step explanation:
Subtract 3x both sides
y = -3 - 3x
y = -3x + (-3)
2(t+1)=10
t= ? ............................................
Answer:
4
Step-by-step explanation:
2x5=10
5-1=4
2(4+1)=10
Can someone please help me!!?
Answer:
Step-by-step explanation:
Domain is all the x's on the graph. The graph does go from -3 to 4 (not including the -3 but including the 4). Pay attention to the use of () as well as [] on the answers. Those answers are not weird coordinates, they are intervals where the first number is the starting place and the second number is the end. Also on the graph one end point is an open circle which means it's not included on the graph and the other endpoint is a darkened circle which means it is included. The range is all the y's. It does go from -3 to 3. Increasing means the graph is going up from left to right and decreasing means the graph is going down left to right. The graph is positive when it is above the x-axis and negative when its below the x-axis. It seems like ALL of the statements about the graph are true.
Brady rode his bike 70 miles in 4 hours. He rode at an average speed of 17 mph for t hours and alah
respeed of 22 mph for the rest of the time. How long did Brady
ride at the slower speed? Use the variablet to
represent the time, in hours, Brady rode at 17 mph.
Answer:66 slower speed
Step-by-step explanation:
100
O () = 97 +18
or()- +2
x= +
OF (x) = 97 +2
F(x) = -27 + -
10
Answer:
9x+2
Step-by-step explanation:
the inverse of the function is the opposite. 1/9 becomes 9 and negative 2 becomes positive 2
Answer:
first option
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply through by 9 to clear the fraction )
9y + 18 = x
change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = 9x + 18