Answer:
[tex](x+3\mathbf{i})(x-3\mathbf{i})=x^2+9[/tex]
[tex](x-4\mathbf{i})(x+4\mathbf{i})=x^2+16[/tex]
[tex](x+8\mathbf{i})(x-8\mathbf{i})=x^2+64[/tex]
Step-by-step explanation:
Complex Numbers
The complex numbers are known by having an 'imaginary' part along with the real part. They can be expressed like a + bi, where
[tex]\mathbf{i}=\sqrt{-1}[/tex]
Or, equivalently:
[tex]\mathbf{i}^2=-1[/tex]
Let's find the result of the following products. On each one of them, there is a sum of a binomial multiplied by the subtraction of a binomial with the very same terms. It leads to a well-known polynomial identity:
[tex](a+b)(a-b)=a^2-b^2[/tex]
1. [tex](x+3\mathbf{i})(x-3\mathbf{i})[/tex]
Applying the above-mentioned identity:
[tex](x+3\mathbf{i})(x-3\mathbf{i})=(x^2-(3\mathbf{i})^2)[/tex]
[tex]=x^2-9\mathbf{i}^2[/tex]
Since [tex]\mathbf{i}^2=-1[/tex]
[tex](x+3\mathbf{i})(x-3\mathbf{i})=x^2-9(-1)[/tex]
[tex]=x^2+9[/tex]
2. [tex](x-4\mathbf{i})(x+4\mathbf{i})[/tex]
Proceed in the same way as before:
[tex](x-4\mathbf{i})(x+4\mathbf{i})=(x^2-16\mathbf{i}^2)[/tex]
[tex]=(x^2-16(-1))[/tex]
[tex]=x^2+16[/tex]
3. [tex](x+8\mathbf{i})(x-8\mathbf{i})[/tex]
[tex](x+8\mathbf{i})(x-8\mathbf{i})=(x^2-64\mathbf{i}^2)[/tex]
[tex]=(x^2-64(-1))[/tex]
[tex]=x^2+64[/tex]
The volume V of a solid right circular cylinder is given by V = πr2h where r is the radius of the cylinder and h is its height. A soda can has inner radius r = 1.5 inches, height h = 6 inches, wall thickness 0.04 inches, and top and bottom thickness 0.07 inches. Use linearization to compute the volume, in cubic inches, of metal in the walls and top and bottom of the can. Give your answer to 2 decimal places.
Answer:
8.20in³
Step-by-step explanation:
Given V = πr²h
r is the radius = 1.5in
h is the height = 6in
thickness of wall of the cylinder dr = 0.04in
top and bottom thickness dh 0.07in+0.07in = 0.14in
To compute the volume, we will find the value of dV
dV = dV/dr • dr + dV/dh • dh
dV/dr = 2πrh
dV/dh = πr²
dV = 2πrh dr + πr² dh
Substituting the values into the formula
dV = 2π(1.5)(6)•(0.04) + π(1.5)²(6) • 0.14
dV = 2π (0.36)+π(1.89)
dV = 0.72π+1.89π
dV = 2.61π
dV = 2.61(3.14)
dV = 8.1954in³
Hence volume, in cubic inches, of metal in the walls and top and bottom of the can is 8.20in³ (to two dp)
A, B and C are service stations
AB= 25 miles
BC= 25 miles
Aysha drives along the motorway from A to C
Aysha drives at an average speed of 50 mph from A to B.
She drives at an average speed of 60 mph from B to C.
Work out the difference in the time Aysha takes to drives from A to B and the time Aysha takes to drive from B to C.
Give your answers in minutes.
Answer:
shrek
Step-by-step explanation:
the answer to everything is shrek
X + 9 = X - 9
One Solution
Infinitely many
solutions
No Solutions
Please help
Answer:
no solution
Step-by-step explanation:
It's no solution because the first step to do is to subtract 9 from both sides which would give you x=x-18 but now your stuck here because if you subtract x from both sides then you wont have an x so this equation has no solution
Answer:
No solution
Step-by-step explanation:
Round 3.55 to the nearest whole number
Answer:
i think the answer is 4
A printing company needs to ship 7,000 team calendars to the city's basketball team.
The printing company can fit 700 calendars in each box. How many boxes will the printing company need to use?
Answer:
10
Step-by-step explanation:
please help me with this
HELP ME ASAP Given f(x) = 5x + 2 and g(x) = -x -3, find h(x) = f(x) + g(x).
Answer:
h(x) = 4x - 1
Step-by-step explanation:
h(x) = f(x) + g(x)
= 5x + 2 - x - 3 ← collect like terms
= 4x - 1
Answer:
4x-1
Step-by-step explanation:
h(x)=5x+2+ (-x-3)
h(x) = 5x+2-x-3
h(x)=5x-x+2-3
h(x)=4x-1
HELPS ME SOLVE THIS PROBLEM PLEASE please
Answer:
(0,4,8,12)
Step-by-step explanation:
Range is all the y values.
Answer:
A
Step-by-step explanation:
IF 48% of the students in a class are girls:
that percentage are boys?
Represent the percentage of boys as a fraction in it's lowest term
The percentage is 52% and the fraction is 13/25
5+ 2/3×= -x+20. This is equations with variables in both sides pls help fast I'll mark as brainliest
Answer:
x = 9
Step-by-step explanation:
5+ 2/3x= -x+20.
Add x to each side
5+ 2/3x +x= -x+x+20
5 + 2/3x+3/3x = 20
5 + 5/3x = 20
Subtract 5 from each side
5+5/3x -5 = 20-5
5/3x = 15
Multiply each side by 3/5
3/5 * 5/3x = 15*3/5
x = 9
Answer:
Step-by-step explanation: 5+2/3x= -x+20
-5. -5
2/3x= -x +15
+x +x
1 2/3x/1 2/3 = 15/1 2/3
X=9
can someone help me I will give 30 points
Answer:
40.
Step-by-step explanation:
Look on the graph under minutes and go to minute one and in one minute it can make forty. just go straight up to until you reach the line.
Can I have brainlliest? Hope it helps.
Answer:
30
Step-by-step explanation:
Which is a solution to the equation?
(x - 3)(x - 5) = 35
O x = -8
O x = -5
O x = 2
O x = 10
Answer:
x = 10
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
1. what is the distributive property of 8×59. 2.what is the distributive property of 9×84. 3. what is the distributive property of 6×78 4. what is the distributive property of 7×96
Classify the quotient as positive ,negative,zero undefined -15 divided by (-5)
Gregoria borrowed $2,450, to be paid back at 3.5% simple interest. She repays $3221.75. How many years was the loan period?
Answer:
90.7yrs.
Step-by-step explanation:
Given parameters:
Amount borrowed = $2450
Interest rate = 3.5%
Amount repaid = $3221.75
Unknown:
Number of years the load was paid = ?
Solution:
The formula of simple interest;
I = PRT
Where I is the interest
P is the principal
R is the rate
T is the time
To find the interest;
Interest = Amount paid back - loan = 3221.75 - 2450 = 771.75
Now;
P = IRT
2450 = 771.75 x [tex]\frac{3.5}{100}[/tex] x T
2450 = [tex]\frac{2701.25T}{100}[/tex]
T = [tex]\frac{245000}{2701.125}[/tex] = 90.7yrs
The number of years of the loan period was 90.7yrs.
what is the answer a b or c
Answer:
A
Step-by-step explanation:
I think
Answer:
66 tens
Step-by-step explanation:
66 hundreds is 6600, and if you divide it by 10, you get 660, or 66 tens.
You work on a concrete crew starting a construction project. Once the pouring begins, it must continue non-stop until it is completed. Your crew will work an 8-hour shift along with two other crews. The total project requires 175,000 yards of concrete. Your supervisor estimates that each crew will pour around 1200 yards per hour. How many consecutive days should you plan to work on this project?
A3
B.6
C. 18
D. 27
Answer: B. 6
Step-by-step explanation:
In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 6 days at random in January to go surfing. Let r be the number of days the surf is at least 6 feet.
Answer:
3 days.
Step-by-step explanation:
Based on the information provided we see that roughly 60% of the days in January have 6ft+ waves then we would need to use this value to calculate the number of days that are good for surfing. We calculate this by multiplying the number of days that you can surf by 60% using the equation below as r being the actual total amount of days....
r = 6 * 0.60%
r = 3.6
As we can see that there are roughly 3 days that see this amount of wave activity between the 6 chosen dates. We have to round down because we are talking about full days and 3.6 does not meet a fourth full day.
There are two twins. One twin wants to explore the planet near Proxima Centauri and leaves on a spaceship traveling at 90% of the speed of light, while the other twin stays home on Earth. How much does the twin on Earth age while the other twin travels to Proxima Centauri?
Answer:
4.7 years
Step-by-step explanation:
Distance of planet from Earth = 1.3 parsec
We know that 1 parsec = 3.26 light years
And a light year is the distance traveled by light in time period of 1 year.
So, Distance of planet from Earth = 1.3 [tex]\times[/tex] 3.26 = 4.24 light years
Given that, the person travels at a speed equal to 90% of the light speed.
To travel to the planet from Earth, Light takes 4.24 years.
To travel the distance [tex]D[/tex], at a speed [tex]s[/tex] light takes time of 4.24 years.
To travel the distance [tex]D[/tex], at a speed [tex]0.90s[/tex], the person takes time:
[tex]\dfrac{4.24}{0.90} = \bold{4.7\ years}[/tex]
So, the twin on Earth ages by 4.7 years.
Answer:
4.7 years
Step-by-step explanation:
It’s due tomorrow please someone help
Answer:
15a is 32oz 18c is 10
Step-by-step explanation:
I WILL MARK BRAINLEST I NEED THIS NOW THOUGH...
Use (2, 3) and (5,7) and put in Pt Slope Y-y1 = m ( x - x1)
Hint: 1 find slope y-y/x-X
2. Use first point for writing equation (2, 3)
Show Your Work
Answer:
Use (2, 3) and (5,7) and put in Pt Slope Y-y1 = m ( x - x1)
The slope is 7-3/5-2
So the answer is 4/3
Hint: 1 find slope y-y/x-X
2. Use first point for writing equation (2, 3)
Show Your Work
Step-by-step explanation:
You start at (6, 8). You move right 4 units and left 2 units. Where do you end?
Answer:
8,6
Step-by-step explanation:
What domain is a function below
Answer:
C
Step-by-step explanation:
Option C is the set of domain
Write as a simplified unit rate: same drove 250 miles with 10 gallons of gas
Answer:
25 miles per gallon
Step-by-step explanation:
hope that's what you were looking for
Sadie works 5 more hours than Kerry does, and Mark works 2 hours less than Kerry. Together they work 120 hours. How many hours does each person work?
Answer:
Sadie:44 Kerry:39 mark:37
Step-by-step explanation:
(5+w) + w + (w-2)=120
-5 from both sides
w+w+(w-2)=115
+2 from both sides
w+w+w=117
117/3 = w
Write an equation in slope-intercept form for the line that has a slope of 2/3 and passes through the point (2,9)
9514 1404 393
Answer:
y = 2/3x -23/3
Step-by-step explanation:
In a version of point-slope form this is ...
y = m(x -h) +k . . . . . line with slope m through point (h, k)
Expanding this, we have ...
y = mx +(k -mh) . . . . slope-intercept form
For the given point and slope, the equation is ...
y = 2/3x +9 -2/3(2)
y = 2/3x -23/3
Answer:
can you provide more information
Step-by-step explanation:
2.5(4+2/5)=-13 how do I solve this
Answer: You add 4+2/5 then multiply it times 2.5
Step-by-step explanation:
If you Evaluate it your answer will be: 11 = -13
PLEASE HELP!!
Mai has proven that triangle WYZ is congruent to triangle WYX using Side-Side-Side Triangle Congruence Therom. Why can can she now conclude that diangonal WY bisects angles ZWX and ZYX?
a. Corresponding parts of congruent triangles are congruent.
b. Alternate angles are congruent.
c. This is a quadrilateral.
d. The angles are not congruent.
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
Learn more here:
https://brainly.com/question/19520446
The zeros of the quadratic x^2+4x=-2x+16 are x=-8 and x=2. What does this tell you about the graph of this quadratic function?
a. The parabola crosses the x-axis at x=-8 and x=2.
b. The parabola touches the x-axis only at and x=2.
c. The parabola does not touch or cross the x-axis.
d. The parabola crosses the x-axis at x=-8 and x=2 but you can ignore the zero x=-8 because it is negative.
The graph of the quadratic function x²+4x=-2x+16 is a parabola that crosses the x-axis at x=-8 and x=2. Correct option is (a).
What are zeros and graph of an quadratic equation?Let ax² +bx +c = 0 is an quadratic equation its zeroes are the values of x for which the Left hand side becomes zero.
To find zeroes we can use quadratic formula that is
x = (-b ±√(b²-4ac))/2
Graph of the quadratic equation are points ( x , y(x) )
where y(x) = ax² +bx +c
when x= t is zero of quadratic equation ax² +bx +c = 0
then y(t) = 0
(t, 0) points are points on the x-axis.
Given an quadratic equation
x²+4x=-2x+16 has roots x =-8 and x =2
This can we written as x² +6x -16 =0
The graph of this quadratic equation is given by (x, y(x))
where y = x² +6x -16 which is a parabola
for x= -8 and x= 2 , y(-8) =y(2) = 0
Then (-8,0) and (2,0) are points on this parabola which are at x-axis
Therefore, the parabola y = x² +6x -16 crosses the x-axis at x=-8 and x=2.Thus (a) is the correct option.
Also learn more about the quadratic equations from the link below:
https://brainly.com/question/1863222
#SPJ2
What is the fraction to this equation 0.020
Pls help fast.
Answer: 1/50
Step-by-step explanation:
0.020 = 20/1000 = 1/50