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]
which expression would be easier to simplify if you use the associative property to change the grouping.
Answer:
the answer is D (27 + 4.5 ) + 1.5
Hope that helps
Answer:
Amswer is A
Step-by-step explanation:
if the time is 10pm what time will it be in exactly 12.82 minutes?
Answer:
.....................
Step-by-step explanation:
Answer:
10:13.22
Step-by-step explanation:
im stupid and dont want to help my little brother so. and you have to show your work
Answer:
242
Step-by-step explanation:
242
4/968 how many times does 4 go into 9? 2 times put the 2 above the 9
8 4 times 2 equals 8 so you put the 8 below the 9 and subtract
1 6 9 minus 8 equals 1 than you drop the 6
1 6 how many times does 4 go into 16? 4 times. put the 4 above the 6
0 8 than multiply 4 *4 =16 than 16-16=0 drop the 8
8 4 goes into 8, 2 times the 2 goes above the 8. 4*2=8
0 8-8=0
PLEASEEE HURRYYY -WILL MARK BRAINLIEST
please solve for both X and Y I will mark u BRAINLIEST if you do it fastttt
Answer:
Y=112 x=45
Step-by-step explanation:
y+68=180
so 180-68=112
y=112
y+(4x-2)+30=180
112+(4x-2)+30=180
140+4x=180
-140 to both sides
4x=180
divide by 4 to both sides
x=45
The value of a comic book in the dollars has been found to be 0.20y + 1.50, where y is tye number of years since it was released. for the question there is increasing per year for the comic and the initial value
The increase rate per year is 0.
What is calculus?Calculus is a branch οf mathematics that deals with the study οf rates οf change and hοw things change οver time. It has twο main branches, differential calculus which studies instantaneοus rates οf change, and integral calculus which deals with accumulatiοn and area.
here given equatiοn fοr the value οf the cοmic bοοk is:
V(y) = 0.20y + 1.50
where y is the number οf years since it was released.
Tο find the rate οf increase per year fοr the value οf the cοmic bοοk, we can take the derivative οf V(y) with respect tο y:
dV/dy = 0.20
This means that the value οf the cοmic bοοk increases by 0.20 dοllars per year.
Tο find the rate οf increase per year fοr the initial value οf the cοmic bοοk, we need tο lοοk at the y-intercept οf the equatiοn fοr V(y). The y-intercept is the value οf V when y is 0, which is:
V(0) = 0.20(0) + 1.50 = 1.50
Therefοre, the initial value οf the cοmic bοοk is $1.50.
Tο find the rate οf increase per year fοr the initial value, we can calculate the derivative οf the initial value with respect tο y, which is:
d/dy (1.50) = 0
This means that the initial value οf the cοmic bοοk dοes nοt change with respect tο time, sο its rate οf increase per year is 0.
To learn more about calculus, from the given link.
https://brainly.com/question/6581270
#SPJ1
8. Calculate the length of r or st
9514 1404 393
Answer:
30 miles
Step-by-step explanation:
The Law of Sines is used for this purpose. The angle at R is the difference ...
180° -(23° +34°) = 123°
Then the length r satisfies ...
ST/sin(R) = RT/sin(S)
ST/sin(123°) = (20 mi)/sin(34°)
ST = (20 mi)sin(123°)/sin(34°) ≈ 30.00 mi
The length of r or ST is 30 miles.
wendy already spent $10 on a necklace, and each additional charm is priced at $2 each. write a function that shows the relationship between the number of charms purchased, x and the total cost, f( x)
Answer:
f(x) = 2x + 10
Step-by-step explanation:
The amount of charms represents x, or the variable. The price of the charm is represented by 2, or the slope. The necklace is the constant, represented by 10.
Find the difference 3.4-(-1.5)
Answer:
4.9
Step-by-step explanation:
-×-=+
; 3.4 + 1.5=
4.9
-15x²+7x+23=0 i just need the answer of it even it's not correct charr cge na loves
Use the quadratic formula where -15 = a, 7 = b, 23 = c: [tex]\frac{-b +- \sqrt{b^2 - 4ac}}{2a}[/tex]
Plug in the values: [tex]\frac{-7 +- \sqrt{7^2 - 4(-15)(23)}}{2(-15)}[/tex]
And get: [tex]\frac{-7 +- \sqrt{49 +1380}}{-30}[/tex]
Which simplifies to: [tex]\frac{-7 +- \sqrt{1429}}{-30} = (-7 + 37.8021163)/-30 OR (-7 - 37.8021163)/-30 = 30.8021163/30 OR -44.8021163/30[/tex]
Those are approximately 1 and -1.5
- Heidi bought an 18 ounce bottle of Castor Oil. If each dose is ounce, how many doses are
in the bottle?
Answer:
18 doses
Step-by-step explanation:
Since it says each dose is a ounce.
Plz helpppp I think I know it but I need to check my answer
Answer:
D
Step-by-step explanation:
(2*6)^4=20736
2^4*6^4 is the same as the expression which is equal to 20736
what is 5 and one half minus three and one third?
Answer:
1 2/3
Step-by-step explanation:
5 1/2 = 11/2 x 3 = 33/6
3 1/3 = 10/3 x 2 = 20/6
30 - 20 = 10/6 = 1 4/6 = 1 2/3
Answer: 2 1/6
Step-by-step explanation:
5 1/2 - 3 1/3
=
5 3/6 - 3 2/6
=
5 - 3 = 2
3/6 - 2/6 = 1/6
= 2 1/6
I need some help please...
Answer:
option 3: 2x²+22xy
Step-by-step explanation:
perimeter of an rectangle = 2(l+b)
= 2{(3x²+5xy)+(6xy–2x²)
= 2(x² +11xy)
= 2x²+22xy
The amount of water in a pool varies directly with the amount of time it is filling up. The pool has 2,900 liters of water after 15 seconds. How many liters of water will the pool contain after 45 seconds?
Answer: 24kg
Step-by-step explanation:
DIG DEEPER At a restaurant, when a customer buys 4 pretzels, the fifth pretzel is free. Soft pretzels cost $3.90 each. You order 12
soft pretzels. What is your mean cost per pretzel?
The mean cost is $
per pretzel.
I RLLY NEED HELP BC THIS WAS DUE ALREADY!!! Answer ASAP thank you!
Answer:
10,560 yards
Step-by-step explanation:
5280 plus 5280 equals 10,560
Adrienne and Suki simplified the expression –8 – (–6). Whose answer is correct? Explain where the error was made. The image is below. * 1 point Suki's; Adrienne subtracted 6 instead of subtracting –6. Suki's; Adrienne subtracted 8 instead of subtracting –8. Adrienne's; Suki added 6 instead of subtracting –6. Adrienne's; Suki added 8 instead of subtracting 8.
Answer:
The answer is -2
Step-by-step explanation:
When you subtract a negative with a negative, you change the problem to an addition by adding the negative number to a positive. -8--6 would look like -8+6.
how do I solve for x?
Answer:
85
Step-by-step explanation:
The sum of the measures of the interior angles of a triangle is 180 deg.
x + 52 + 43 = 180
x + 95 = 180
x = 85
Answer: 85
The angles in a triangle add up to 180 degrees
180 - 52 - 43 = 85
x = 85 degrees
10 4 4) Maureen has spent 12 9/10hours tutoring students in math and 6 3/4 tutoring students in science, Which choice is the best estimate for how many hours Maureen has spent tutoring?
(A) 15 hours
(C) 20 hours
(B)25 hours
(D) 30 hours
Answer:
(C) 20 Hours
Step-by-step explanation:
Which equation below shows a correct first step for solving 3x = -12
A 3x+ 3 = -12 + 3
B 3x- 3 = -12 - 3
C 3(3x) = 3(-12)
D 3x/3=-12/3
YOU WILL GET BRAINLIES, LIKE AND COMMENT AND 10 POINTS IF YOU CAN PLEASE HELP ME BECAUSE NO ONE IS ANSWEING!
1- A kite has a width to length ratio of 4:5. If the length is 80 cm, what is the width? *
2- Which bottle of juice is the better buy? *
$1.00 for 150 mL
$1.75 for 500 mL
$4.00 for 1000 mL
$7.25 for 2000mL
3- Maya works in a clothing store and earns a commission of 3% on all her sales. If she sells $950 worth of clothing, what is her commission? *
$285
$138.50
$30
$28.50
3- A box of pancake mix suggests using 250 mL of milk and 325 mL of pancake mix. Rita has only 225 mL of pancake mix left in the box. How much milk should she use?
100 mL
125 mL
150 mL
175 mL
4- Of the 1120 spectators at a hockey game, about 80% are home team fans. How many of the spectators are fans of the visiting team?
918
896
224
202
1. A kite has a width to length ratio of 4:5, so let the width be 4x and the length be 5x. We know that the length is 80 cm. 80 = 5x
Divide by 5.
16 = x.
Now, the width is 4x.
16 times 4 is 64.
The width is 64.
2. Find the unit rate for each juice. The unit rate is ml / dollar.
The first juice has a unit rate of 150 / 1.
The second has a unit rate of 500 / 1.75.
The third has a rate of 1000 / 4.
The fourth has a rate of 2000 / 7.25
Put all values into a calculator. (First: 150, Second: 285.714285, Third: 250, Fourth: 275.862068966)
Whichever one can buy the most ml for a dollar is the best buy.
In here, that is the SECOND rate, which is 1.75 for 500 ml.
She earns 3% commission on all her sales, so if s represents her sales, she'd earn .03s. Inhere, she sells $950 in total. That is her total sales.
So you plug $950 into the equation as s.
.03 (950) = 28.5
She earned $28.50.
Poor Maya!
3. You set it up in ratios. She needs 250 mL of milk for every 325 mL of pancake mix. 250 milk / 325 mix.
But she only has 225 mix.
So you set up 250 milk / 325 mix = M milk / 225 mix
As in all proportions, you cross multiply.
250 x 225 = 325 x M
56250 = 325M
Divide by 325 on both sides.
173.076923077 = M
She needs about 175 mL. The fourth choice.
4. There are a total of 1120 spectators, made of only home team fans and visiting team fans.
There is a total of 100% of people, and 80% are supporters of the home team, so to find the supporters of the visiting team you subtract 100% by 80%.
100 - 80 = 20.
So 20% of the spectators are supporters of visiting team. Now 20% of the total, and 20% = .20.
.20 x 1120 = 224
224 people are fans of the visiting team.
5. A 500-mL bottle of insect repellent has 22 mg of DEET, a chemical used to keep mosquitos away. The same insect repellent sells in 710-mL bottles. Which of the following proportions can be used to find the amount of DEET in the larger bottle? *
If a 500 mL bottle has 22mg of DEET, then 500ml / 22mg
So set up the equation 500 / 22 = 710 / x
Now, cross multiply.
500x = 710 times 22.
500x = 15620
Divide by 500.
x = 31.24
Other possible proportions are:
22 / x = 500 / 710
x / 22 = 710 / 500
22 / 500 = x / 710
Hope this helps and hope I get Brainliest! Lol :)
I spent half an hour explaining and typing this :(
write an equation for a line perpendicular to y=5x+2 and passing through the point (-10,3)
Step-by-step explanation:
The perpendicular line *always* has a slope of the negative reciprocal. Your given line has a slope of -5, so the perpendicular slope is -1/(-5) = 1/5.
Use the point-slope form of a general line to find the equation.
(y - y_1) = m * (x - x_1)
y - 7 = (1/5) * (x - 15)
Solve the inequality and complete a line graph representing the solution. In a minimum of two sentences, describe the solution and the line graph.
8 ≥ 3x + 5
A girl scout troop hiked 5.8 kilometers southeast in 1.5 hours. What was
the troop's velocity?
O 3.9 km/h southeast
о
4.9 km/h southeast
5.8 km/h southeast
O 7.2 km/h southeast
Answer:
the answer is 3.9 km/h southeast
Working simultaneously, four fudge machines complete a big order in 32 hours. All the machines at the fudge factory work at the same pace. a If only half of the machines are working, in how many hours will the order be complete?
If only half the machines are working at the same rate as before, the order will be finished in 64 hours.
When the four big fridges were working simultaneously, they were able to finish the order in 32 hours.
With only half of these fridges, they will only be half as fast. This means that they will complete the order in double the time:
= 32 x 2
= 64 hours
In conclusion, the order will be completed in 64 hours.
Find out more at https://brainly.com/question/19465480.
Find (9.3 X 10^6) + (1.8 X 10^4).
Express your answer in scientific
notation.
Please answer i'm studying for a test tomorrow :D
Answer:
7.5 × 10²
Step-by-step explanation:
No. 2 BAC and 2 CAD remain congruent, and m 2 DAB is still the sum of mZBAC and m2 CAD.
AN
Question 4
Move point C so that ZBAC and CAD form a pair of supplementary angles, or angles whose sum is 180°. Record each of the angle measurements
for this case.
Answer:
I’m srry I don’t know about question 2 but here’s the answer to Question 4
When the two angles are supplementary, m<BAC = m<CAD = 90° and m<DAB = 180°
Step-by-step explanation:
Answer from Plato
Answer:
No. ∠BAC and ∠CAD remain congruent, and m∠DAB is still the sum of m∠BAC and m∠CAD.
Step-by-step explanation:
This is the answer for question 2
The ratio of boys to girls at a movie is 4:7. If there are 21. girls, how many boys are
at the movie?
Answer:
12
Step-by-step explanation:
7*3=21 so 4*3=12
Perimeter is a measure of the distance around a figure. If each side of a triangle measures 0.75 inches, what is the perimeter of the triangle?
Answer:
The perimeter of a triangle is the sum of all its three sides.
So,
0.75+0.75+0.75 = 2.25inches
factor the equation 25x^2+70x+49
Answer:
(5x+7)^2hope this helps