Step-by-step explanation:
1) Given quadratic expression is [tex]x^2-2x+2[/tex]
First equate the given expression to zero then we will find the roots.
Since the given equation is quadratic hence it has two roots.
To find the roots of the given quadratic equation :For the quadratic equation we have that [tex]ax^2+bx+c=0[/tex]
Therefore roots [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] here a and b are coefficients of [tex]x^2andx[/tex] respectively and c is a constant
[tex]x^2-2x+2=0[/tex] here a=1 ,b=-2 and c=2
Now Substitute the values in [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] we get
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\frac{2\pm \sqrt{4-8}}{2}[/tex]
[tex]=\frac{2\pm \sqrt{-4}}{2}[/tex]
[tex]=\frac{2\pm \sqrt{4i^2}}{2}[/tex]
[tex]=\frac{2\pm2i}{2}[/tex]
[tex]=2(\frac{1\pm i}{2})[/tex]
[tex]x=1\pm i[/tex]
Therefore [tex]x=1+i[/tex] and [tex]x=1-i[/tex] are the roots of the given quadratic equation.
2) Given that the number 16 has four roots.In other words, there are four complex numbers that can be entered in the square .
Let x be the given number 16
i.e., x=16
From the given we can write [tex]x^4=16[/tex]Since the number has complex number as its rootsTherefore we can write [tex]x^4=(2i)^4[/tex] as below[tex]=2^4i^4[/tex] ( by using the formula [tex](ab)^m=a^mb^m[/tex] )
[tex]=16(1)[/tex] ( by [tex]i^2=-1[/tex] and [tex]i^4=(i^2)^2=(-1)^2=1[/tex] )
[tex]x^4=16=(2i)^4[/tex]
Therefore [tex]x^4=(2i)^4[/tex]
Since powers are same we can equate the bases ( bases are equal )
Therefore x=2i,2i,2i,2i are the roots of the given number 16 and they are complex numbers too
Which graph represents the solution to the inequality 11 Less-than-or-equal-to y - 43?
A number line going from 50 to 60. A solid circle is at 54. Everything to the left of the circle is shaded.
A number line going from 50 to 60. A solid circle is at 54. Everything to the right of the circle is shaded.
A number line going from negative 35 to negative 25. A solid circle is at negative 32. Everything to the left of the circle is shaded.
A number line going from negative 35 to negative 25. A solid circle is at negative 32. Everything to the right of the circle is shaded.
11 <= y -43
Solve for y:
First rewrite so y is on the left side:
Y-43 >= 11
Add 43 to both sides:
Y >=54
Since 54 is included in the answer it would be a solid dot on 54 and the shaded area would cover all numbers greater than 54.
The answer Is:
A number line going from 50 to 60. A solid circle is at 54. Everything to the right of the circle is shaded.
Answer:
B. second choice
Step-by-step explanation:
I answered the question on Edge and got it right.
Divide 3x^3 - 2x^2 - 61x - 20 by x - 5.
3x^2 + 13x + 4
3x^2 - 13x + 4
3x^2 - 17x + 24 R 100
3x^2 + 17x - 24 R 100
Answer:
3x² + 13x + 4
Step-by-step explanation:
3x³ - 2x² - 61x - 20
3x³ - 15x² + 13x² - 65x + 4x - 20
[3x²(x - 5) + 13x(x - 5) + 4(x - 5)]/(x-5)
3x² + 13x + 4
how many 8 oz bags of trail mix can be filled from a 10 pound bag of trail mix?
Answer:
20 bags
Step-by-step explanation:
Find the product of 3 2/3 as a mixed number
Answer:
11/3
Step-by-step explanation:
HELP!!!! WILL MARK BRAINLEST IF CORRECT!
How is the distributive property used when finding the product of two polynomials? How are polynomials closed under multiplication?
Answer:
Multiplying polynomials is a bit more challenging than adding and subtracting polynomials. We must use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. We then combine like terms. We can also use a shortcut called the FOIL method when multiplying binomials. Certain special products follow patterns that we can memorize and use instead of multiplying the polynomials by hand each time. We will look at a variety of ways to multiply polynomials.
The legs of a right triangle measure 4 and 6 inches. The area of the triangle is
5 in.2
24 in.?
12 in.2
Answer:
12
Step-by-step explanation:
The area of a right triangle is base1 * base2 *.5
This means the area is 4*6*.5 = 12
Rocky walks his dog Fido 4 times around the
lock. If they walked a total of 1,144 feet,
how long is it to go around the block once?
Answer:
286
Step-by-step explanation:
1,144÷4=286
Given triangle JKL : triangle XYZ, find the scale factor.
Answer:
2/3
Step-by-step explanation:
i don't know how to explain it, but this is the answer :) good luck
5. Stan has a good driver discount on his automobile insurance policy. He pays 86% of the regular
premium rate of $279. The actual premium Stan pays is
O a. $86.00
O b. $193.00
O c. $239.94
O d. $279.00
OOOO
1. Solve the inequality for x
Show each step of the solution
16x > 2x - 3
Answer:
x > -3/14
Step-by-step explanation:
Step 1: Subtract 2x from both sides
16x - 2x > 2x - 3 - 2x
14x > -3
Step 2: Divide both sides by 14
14x / 14 > -3 / 14
x > -3/14
Answer: x > -3/14
namois fish is 40 millmeters her guniuea pig is 25 centimeters
Answer: the guniuea pig is bigger by 25 centimeters!
Step-by-step explanation:
Fish= 40 milimeters = 4 centimeters
Guniuea pig= 25 centimeters
Answer:
the guniuea pig is bigger by 25 centimeters!
just easy
Solve the following equation for d
M = d/F
What is 111%of 800 rounded to the nearest hundred
Answer:
[tex]900[/tex]
Step-by-step explanation:
Step 1: Make an expression
What is 111% of 800
[tex]800 * (1 + 0.11) = x[/tex]
[tex]800 * (1.11) = x[/tex]
Step 2: Multiply
[tex]800 * (1.11) = x[/tex]
[tex]888 = x[/tex]
Step 3: Round to the nearest hundred
888
Since the tens place is greater than 5, we round up.
[tex]900[/tex]
Answer: [tex]900[/tex]
undo the subtraction of x-2=6
Answer:
x = 8
Step-by-step explanation:
I am assuming that you want to solve for x.
Note the equal sign, what you do to one side, you do to the opposite side. Isolate the variable, x. Add 2 to both sides:
x - 2 (+2) = 6 (+2)
x = 6 + 2
x = 8
x = 8 is your answer.
~
The rectangle shown has a perimeter of 60 inches and a width of 12 inches. What is its length?
A.) 12 Inches
B.) 18 Inches
C.) 36 Inches
D.)48 Inches
Answer:
it is 18
Step-by-step explanation:
that the ansewer if you divid
Final answer:
The length of the rectangle with a perimeter of 60 inches and a width of 12 inches is 18 inches, calculated using the perimeter formula for rectangles and solving for the length.
Explanation:
The question asks us to find the length of a rectangle given its perimeter and width. To solve this, we use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. In this case, we have P = 60 inches and w = 12 inches.
So, substituting the given values into the formula, we get:
60 = 2l + 2(12)
First, calculate the double of the width:
2(12) = 24 inches
Now, subtract this value from the total perimeter to find the double of the length:
60 - 24 = 36 inches
Finally, divide by 2 to find the length of the rectangle:
36 / 2 = 18 inches
Therefore, option B, 18 inches, is the correct answer for the length of the rectangle.
Micahdisu please help
Answer:
1) A - 42°
2) 74°
3) B - 45°
4) B - 66°
Step-by-step explanation:
1) E = D+H
87 = 45 + H
H = 42°
2) 180 - 50 - D
D = 180 - 44 - 62 = 74°
3) F = 105
H = 180-105 = 75
I + H = C + E
I + 75 = 83 + 37
I = 45°
4) D = 180 - (E + F)
D = 180 - (30 + 57) = 93°
93 = A + 27
A = 66°
Answer: In figure 1, angle H = 42°. In figure 2, angle F = 56°. In figure 3, angle I = 45° and in figure 4, angle A = 66°
Step-by-step explanation: Please refer to the attached diagram for details.
From figure 1, if angle E measures 87, then angle F would be calculated as
Angle F = 180 - 87 {Sum of angles on a straight line equals 180}
Angle F = 93
Then looking at triangle FHD, we have angles D and F as 45 and 93. Angle H = 180 - (45 + 93) {Sum of angles in a triangle equals 180}
Angle H = 180 - 138
Angle H = 42
From figure 2, if triangle ACB has two angles given as 44 and 62, then the third angle C, would be calculated as
Angle C = 180 - (44 + 62) {Sum of angles in a triangle equals 180}
Angle C = 180 - 106
Angle C = 74
Note that angle D equals angle C {Opposite angles are equal}. So if angle D measures 74, then looking at triangle FED, we have two angles already, E and D which are 50 and 74. To calculate angle F, the equation would be
f = 180 - 50 - 74
f = 56
That is, angle F = 56.
From figure 3, we have angles C and E given as 83 and 37. To calculate angle G
Angle G = 180 - (83 + 37) {Sum of angles on a straight line equals 180}
Angle G = 180 - 120
Angle G = 60
Also, to calculate angle H,
Angle H = 180 - 105 {Sum of angles on a straight line equals 180}
Angle H = 75
Looking at triangle GHI, we have identified two angles which are 60 and 75. To calculate the third angle which is angle I,
Angle I = 180 - (60 + 75) {Sum of angles in a triangle equals 180}
Angle I = 180 - 135
Angle I = 45
From figure 4, if angles B and E measure 27 and 30 respectively then the whole of that angle measures 27 + 30 which equals 57.
So looking at the biggest of all three triangles, two angles have been identified which are angles F and {B + E}
To calculate angle A
Angle A = 180 - (57 + 57) {Sum of angles in a triangle equals 180}
Angle A = 180 - 114
Angle A = 66.
The perimeter of a triangle is 65 meters. The second side is 5 meters less than the first side The third side is 7
meters more than the first side. What is the length of each side?
Answer:
The length of each side is 31.5m, 26.5m, 7m
Step-by-step explanation:
Let the length of the first side of the triangle be x meters.
Then, the second side is x-5 meters.
The third side is given as 7 meters.
The perimeter is 65 meters
This gives us the equation:
[tex]65 = x + x - 5 + 7[/tex]
[tex]65 - 7 + 5 = x + x[/tex]
[tex]63 = 2x[/tex]
[tex]x = \frac{63}{2} = 31.5[/tex]
The length of each side is 31.5m, 26.5m, 7m
Difference between an integer and a real number
Answer:
Real number is any number. This includes integers, rational, and irrational numbers.
While integers are just positive or negative whole numbers that also includes 0.
Hope this helps!
Help, ill give brainliest
Answer:
its been awhile so i aint even going to try
Step-by-step explanation:
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I need help with this question ASAP Please pick all of the correct ones
Answer:
(a): 4(8x - 3)
Option B, 32x - 12 because 4(8x - 3) distributes as 4*8x + 4*-3 = 32x - 12
Option D, 4*8x - 4*3 because it simplifies into 32x - 12
(b): 7y + 2y + 8y
Option C, 17y because 7 + 2 + 8 = 17
Option A, 7y + 10y because it adds to 17y
Solving the elimination method what is 3x-y=9 2x-y=7
Answer:
x = 2 , y = -3
Step-by-step explanation by elimination:
Solve the following system:
{3 x - y = 9 | (equation 1)
2 x - y = 7 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{3 x - y = 9 | (equation 1)
0 x - y/3 = 1 | (equation 2)
Multiply equation 2 by 3:
{3 x - y = 9 | (equation 1)
0 x - y = 3 | (equation 2)
Multiply equation 2 by -1:
{3 x - y = 9 | (equation 1)
0 x+y = -3 | (equation 2)
Add equation 2 to equation 1:
{3 x+0 y = 6 | (equation 1)
0 x+y = -3 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 2 | (equation 1)
0 x+y = -3 | (equation 2)
Collect results:
Answer: {x = 2 , y = -3
Answer:
x=2 y=7.
Step-by-step explanation:
3x-y=9
-2x+y=7
x=2
2(2)+y=7
4+y=7
-4. -4
y=7
Do u simplify 7 wholes and 8/10
Answer: Simplify 8/10 which is 4/5.
Step-by-step explanation:
1/8 divided by 1/4 =
=
1 /8 / 1 /4
=( 1/ 8 )( 4 /1 )
= (1)(4)/ (8)(1)
= 4 /8
= 1 /2 or 0.5
Answer:
1/2
Step-by-step explanation:
To multiply fractions we do keep change flip, keeping the first fraction, changeing the division into multiplication and flipping the last fraction so we don't have to go into decimals so 1/8 divded by 1/4 becomes
1/8 * 4/1
Now we multiply the numerators together and the denominators together and then put it back in fraction form. Another option is to cross reduce, both will be shown.
Multiplying numerators and denominators
1 * 4 = 4
8 * 1 = 8
Put it into fraction form;
4/8 Now simplify
1/2
Cross Reducing
To cross reduce you can divde two numbers that are accross from each other in a fraction equation (Multiplication only) by the same number
1/8 * 4/1 The four and eight are across from each other so we can cross reduce by 4 because that is there gcf
then we have
1/2 * 1/1 now we multiply the numerators by numerators and the denominators by denominators in this case we don't have to go that far though because 1/1 is 1 and anything times one is itself, therefore the awnser is
1/2
Which is more work, pushing with 115 N over 15 m or lifting 20 kg 10 m?
Answer: THEY ARE THE SAME
Step-by-step explanation:
Therefore, lifting 20 kg 10 m requires more work than pushing with 115 N over 15 m.
Note: It's important to mention that the unit of work is the Joule (J), where 1 Joule is equal to 1 N·m. So, in both cases, the units of work are in Joules.
Share 160 sweets in the ratio 8:12
let's divide the whole by the sum of its ratios, namely let's 160 ÷ (8+12), and then distribute accordingly.
[tex]\bf \textit{160 at 8:12 ratio}\qquad \qquad \cfrac{8\cdot \frac{160}{8+12}}{12\cdot \frac{160}{8+12}}\implies \cfrac{8(8)}{12(8)}\implies \cfrac{64}{96}[/tex]
Solve the following system of equations. Enter the y-coordinate of the
solution. Round your answer to the nearest tenth.
5x+2y=7
- 2x + 6v=9
Y= 1.3 (Rounded to nearest tenth) x = 0.7 (rounded to the nearest tenth)
Step-by-step explanation:
You can solve this using substitution or elimination.
I used elimination.
-3(5x+2y =7) <---- On this step I used multiplicitive property of equality and multiplied everything by -3.
-15-6y=-21
-2x+6y=9
+_____________________
Add these and we get -17x=12
We divide by -17 and we get that x= 12/-17
Substitute this back into the original equation and we get that y=1.3 (rounded)
Answer:x=0.95
Y=1.12
Step-by-step explanation:
5x+2y=7...(1)
-2x+6y=9..(2)
Multiply (1) by -2
-10x-4y=7...(3)
Multiply (2) by 5
-10x+30y=45..(4)
Substrate (3) from (4)
34y=38
Y=38/34
Y=1.12
Substitute y=1.12 to(1)
5x+2(1.12)=7
5x+2.24=7
5x=7-2.24
5x=4.76
X=4.76/5
X=0.95
Distrubite and Combine like terms
4(2a-5b-7)-3(2a+3b+5)
Answer:
2a-29b-43 pls give me brainlist because my answer is the best
Step-by-step explanation:
8a-20b-28-6a-9b-15
2a-29b-43
Cheese sticks that were previously priced at "10 for $1" are now "2 for $1". Find each percent change.
Part 1 out of 2
Find the percent decrease in the number of cheese sticks you can buy for $1.
The percent decrease is
Answer:
80%
Step-by-step explanation:
Find the area of the sector with a central angle of 60° and a radius of 5 inches. Round to the nearest tenth.
Answer:
15.4 inches square
Step-by-step explanation:
Formula for finding the sector of a circle is:
[tex]A = \frac{\theta°}{360°} \times \pi {r}^{2} [/tex]
Given that,
[tex]{\theta} = {60}^{0} [/tex]
r= 5 inches
Take;
[tex]\pi = 3.14[/tex]
By substitution,
[tex]A = \frac{60°}{360°} \times 3.14 \times {5}^{2} [/tex]
A =15.4 inches square
How many cubed pieces of fudge that are 3 inches on an edge can be packed
into a Christmas tin that is 9 inches deep by 12 inches wide by 9 inches high with
the lid still being able to be closed?
1. 18
2. 24
3. 32
4. 36
5. 43
Answer:
36 cubed pieces of fudge
Step-by-step explanation:
9 x 12 = 108
108 ÷ 3 = 36