Answer:
21+12i i hope this will help you
Step-by-step explanation:
(3-4i)(1+5i)-(2-i)
=[3(1+5i)-4i(1+5i)]-(2-i)
=[3+15i-4i-20i²]-(2-i)
=(3+11i-20i²)-(2-i)
opening brackeys
=3+11i-20i²-2+i
=3+11i+1i-20i²-2
as we know that i²=-1
=3-20(-1)-2+12i
=3+20-2+12i
=21+12i
The expression (3 - 4i)(1 + 5i) - (2 - i) is simplified as 21 + 12i
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be A = (3 - 4i)(1 + 5i) - (2 - i)
Now , we know i² = -1
And , on simplifying the expression , we get
A = (3 - 4i)(1 + 5i) - (2 - i)
A = 3 + 15i - 4i - 20i² - 2 + i
A = -20i² + ( 3 - 2 ) + ( 15i - 4i + i )
A = -20 ( -1 ) + 1 + ( 11i + i )
A = 20 + 1 + 12i
A = 21 + 12i
Hence , the value of the expression (3 - 4i)(1 + 5i) - (2 - i) is ( 21 + 12i )
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Find the measure of each angle of a regular polygon with 8 sides.
Answer:
135 degree
Step-by-step explanation:
total sum of angle = (8-2) * 180 = 1080
each angle = 1080/8 = 135 degree
Given: Z1 is complementary to 22.
What is the missing statement in step 3 of the proof?
22 is complementary to 23.
0 m21 = m22
Prove: mz1 = m 23
OmZ1 + m22 = 90°
OmZ2 = m23
VV
m22 + m23 = 180°
Statements
1. 21 is comp. to 22
2. 22 is comp. to 23
3. ?
4. m21-90°-m22
5 m22+m23-90°
6. m23-90°-m22
7. m 1 m3
1
2.
3
4
5
6.
7
Reasons
given
given
def. of comp. ZS
subtr. equality prop.
def. of comp. ZS
subtr. equality prop
trans. prop.
Answer:
Option (2)
Step-by-step explanation:
Statements Reasons
1). ∠1 is comp. to ∠2 1. Given
2). ∠2 is comp. to ∠3 2. Given
3). ∠1 + ∠2 = 90° 3. def. of comp. angles
4). m∠1 = 90° - ∠1 4. Subtr. equality property
5). m∠2 + m∠3 = 90° 5. def. of comp. angles
6). m∠3 = 90° - m∠2 6. subtr. equality property
7). m∠1 = m∠3 7. Transitive property
Option (2) will be the answer.
Both angle ∠1 and ∠3 are complementary to ∠2, therefore, ∠1 + ∠2 = 90°
and by properties of equality, ∠1 = ∠3.
Response:
The missing statement in step 3 is; m∠1 + m∠2 = 90°Which property or definition is used to find the missing statement?The completed two column proof is presented as follows;
Statements [tex]{}[/tex] Reasons
1. ∠1 is comp. to ∠2 [tex]{}[/tex] 1. Given
2. ∠2 is comp. to ∠3 [tex]{}[/tex] 2. Given
3. m∠1 + m∠2 = 90° [tex]{}[/tex] 3. Definition of complementary angles4. m∠1 = 90° - m∠2 [tex]{}[/tex] 4. Subtraction equality property
5. m∠2 + m∠3 = 90° [tex]{}[/tex] 5. Definition of complementary angles
6. m∠3 = 90° - m∠2 [tex]{}[/tex] 6. Subtraction equality property
7. m∠1 = m∠2 [tex]{}[/tex] 7. Transitive property
The missing statement in step 3 is therefore; m∠1 + m∠2 = 90°Details of the solution:
Given that ∠1 is complementary to ∠2, we have;
∠1 + ∠2 = 90°
Similarly, by definition of complementary angles, we have;
∠2 + ∠3 = 90°
Which gives;
∠3 + ∠2 = 90°
Therefore;
∠1 + ∠2 = ∠3 + ∠2
Subtracting ∠2 from both sides (subtraction property of equality), gives;
∠1 + ∠2 - ∠2 = ∠3 + ∠2 - ∠2
∠1 + 0 = ∠3 + 0
Which gives;
∠1 = ∠3
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Find x 4sqrt3 2sqrt3 8 8sqrt3
Answer:
8
Step-by-step explanation:
sin 30° = 1/2
sin is opponent/hypotenuse
so
opp/hyp = 4/x = 1/2
x = 4 * 2 = 8
Answer:
[tex]\displaystyle x=8[/tex]
Step-by-step explanation:
[tex]\displaystyle x=\frac{sin(90) \times 4 }{sin(30)}[/tex]
[tex]\displaystyle x=8[/tex]
Which line segment is correct for this answer to the question?
Answer:
Option (A). OB
Step-by-step explanation:
Angle bisector of any angle is a line segment that divides the angle into two equal parts.
From the given picture,
m∠MOB ≅ m∠NOB
(25 + 35)° ≅ (28 + 32)°
60° ≅ 60°
Therefore, OB is the line segment that divides ∠MON into two equal angles. (∠MOB and ∠NOB)
Option (A). will be the answer.
Henry buys a candy bar worth $3.20 plus a chocolate bar worth $1.60. How much change does he have leftover from $8.50? EXPLAIN!
Answer:
$3.70
Step-by-step explanation:
So you have $8.50
You but a candy bar for $3.20
8.50-3.20=5.30
you have $5.30 left to spend
From your remaining $5.30 you buy a chocolate bar that is $1.60
5.30-1.60=3.70
Leaving you with $3.70
. It takes Serina 15 seconds to drive to school. Her route is 16,000 meters long. What is Serina’s average speed on her route?
[tex]answer \\ = 1066.67m / s \\ solution \\ distance \: travelled = 16000 \: m \\ time \: taken = 15 \: seconds \\ speed = \frac{distance}{time} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{16000}{15} \\ \: \: \: \: \: \: \: \: \: \: \: = 1066.67 \: m/s \\ hope \: it \: helps[/tex]
Answer:
[tex] = 1,066.67m {s}^{ - 1} \\ [/tex]
Step-by-step explanation:
[tex]speed = \frac{distantce}{time} \\ = \frac{16000}{15} \\ = 1,066.67m {s}^{ - 1} [/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
How do I find the arc of a circle?\
Answer:
Step-by-step explanation:
Step-by-steP
LA FÓRMULA ES:
arc = πrΘ/180
Please help ASAP! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
|a−b| − |c+d| , if a=−5; b=4; c=1; d=−3
Answer:
5
Step-by-step explanation:
|a−b| − |c+d| , if a=−5; b=4; c=1; d=−3
= a + b - c + d
= 5 + 4 - 1 + (-3)
= 5 + 4 - 1 - 3
= 5 + 4 - 4
= 5
Work out the size of angle x and give reasons for your answer. Image attached.
Answer:
The value of X is 75°
<EFB +105°=180° (Being straight line)
<EFB=180-105
<EFB= 75°
X = <EFB = 75°. (corresponding angle)
Please answer correctly !!!!! Will mark brainliest answer !!!!!!!!!!!
Answer:
[tex]y = \frac{5}{2} x^{2}[/tex]
Step-by-step explanation:
When you scale a parabola vertically, you multiply the [tex]x^{2}[/tex] by what you are scaling it vertically by.
For example, say you have [tex]y = 8x^{2}[/tex]. That means that [tex]y = x^{2}[/tex] was scaled vertically by a factor of 8.
I hope this helps!
a graph using y=mx+b
Answer:
A graph using y=mx+b would include a positive or negative line (slope) and a y-intercept. If there is a y-intercept between 1 & infinity then the line will not start on the origin. y=mx+b doesnt have to include a y-intercept though. It can include a y-intecept of 0. This would mean that the line would start on the origin. y=mx+b will ALWAYS be a straight line.
Step-by-step explanation:
Hope this helps :)
(-4,-1),(-3,-1),(-2,-3),(-1,0),(-3,2 )IS IT AN FUNCTION OR NOT
Answer:
No it isn't a function one of the x values, -3, repeats
Step-by-step explanation:
Jack's brother is 14 years older than him. In six years time, Jack's brother will be twice as old as him. How old is Jack now?
Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Statement Reason 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given 2. m∠H + m∠J + m∠K = 180° 2. ? 3. 30° + 50° + m∠K = 180° 3. substitution property 4. 80° + m∠K = 180° 4. addition 5. m∠K = 100° 5. subtraction property of equality 6. m∠J = m∠P; m∠K = m∠N 6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent 8. △HKJ ~ △LNP 8. AA similarity theorem Which reason is missing in step 2?
Answer:
[tex]2. m\angle H+m\angle J +m\angle K =180^{\circ}[/tex]
Reason: the sum of all interior angles of any triangle is equal to 180º.
Step-by-step explanation:
1) Organizing
Statement 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. Reason: given
2) Since the sum of all internal angles of any triangle is equal to 180º, just like the formula. N the number of sides of a triangle:
[tex]S_{i}=180^{\circ}(n-2)\rightarrow 180(3-2) \therefore S_{i}=180^{\circ}[/tex]
3) We can also say
[tex]m\angle K=180^{\circ}-(m\angle H+m\angle J)\\m\angle K=180^{\circ}-\left ( 30^{\circ}+50^{\circ} \right )\\m\angle K=100^{\circ}[/tex]
Similarly to the other triangle:
[tex]m\angle L=180^{\circ}-(m\angle N+m\angle P)\\m\angle L=180^{\circ}-\left ( 100^{\circ}+50^{\circ} \right )\\m\angle L=30^{\circ}[/tex]
4) Hence,
[tex]2. m\angle H+m\angle J +m\angle K =180[/tex]
Reason: The sum of interior angles is equal to 180º.
Answer:
B
Step-by-step explanation:
Find the percent increase in volume when 1 foot is added to each dimension of the prism. Round your answer to the nearest tenth of a percent.
Answer:
About 51.5%
Step-by-step explanation:
The volume of the prism currently is (9*4)/2*11=18*11=198 cubic feet. If you added a foot to each dimension, the volume would be 10*5/2*12=25*12=300. (300-198)/198=102/198 a percent increase of about 51.5%. Hope this helps!
Answer:
About 51.5%
Step-by-step explanation:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
10q - 30 is equivalent to?
Answer:
So in this question im guessing you simplify with parenthesis
Since its too easy, I cant really explain, but heres the answer:
(q+3)*10
A box contains 20 miniature golf putt-putt balls; 10 are
yellow, 6 are red, and 4 are pink. What is the probability of
picking a red golf ball, replacing it, and then picking a
yellow golf ball? Written as a percent?
Answer: The answer is provided below
Step-by-step explanation:
From the question, a box contains 20 miniature golf putt-putt balls out of which 10 are yellow, 6 are red, and the remaining 4 are pink.
The probability of picking a red golf ball will be:
= 6/20 × 100
= 600/20
= 30%
If the red ball is replaced, the probability of picking a yellow golf ball will be:
= 10/20 × 100%
= 50%
write 10 examples of rectangle that you observed in your daily life
Answer:
-a book
-a flash card
-the american flag
-post-it
-pencil case
-calculator
-phone
-dollar bill
-tv
-ruler
Step-by-step explanation:
________________________________
Hey!!
Ten examples of rectangles that I observed in my daily life are as follows:
BoxtelevisionMobile phoneswhiteboardClipboardCassetteBagChocolateBiscuitRuler________________________________
In the diagram, ABCD is a part of a right angled triangle ODC. If /AB/= 6 cm,
/CD/= 15cm, BC/= 8 cm, ZBCD = 90° and AB//DC, calculate, correct to 1 decimal
place, the:
2 points
1. height of triangle ODC;
Your answer
2 points
2. perimeter of triangle ODC.
Answer:
1) 13.3 cm
2) 48.3 cm
Step-by-step explanation:
1) Right angled triangle ODC and right angled triangle OAB are similar because AB//DC. The two triangles have the same proportion and are equiangular (having equal angles) but have different lengths.
Let OB = x, OC = OB + BC = x + 8
Therefore:
[tex]\frac{OC}{OB}=\frac{DC}{AB} \\\frac{x+8}{x}=\frac{15}{6}\\15x=6(x+8)\\15x=6x+48\\15x-6x=48\\9x=48\\x=5.3\ cm[/tex]
The height of triangle ODC = OC = x + 8 = 5.3 + 8 = 13.3 cm
2) Using Pythagoras theorem:
OD² = OC² + DC²
OD² = 13.3² + 15²
OD² = 401.89
OD = √401.89 = 20 cm
2) perimeter of triangle ODC = OD + OC + DC = 20 + 13.3 + 15 =48.3 cm
A recipe for a batch of blueberry muffins calls for 3/5
the cup of blueberries. If Riley wants to make 1/2
a batch of muffins for herself and her tennis partner, how many cups of blueberries will she need?
Riley will need cups of blueberries.
Answer:
3/10
Step-by-step explanation:
Half of 3/5 is 3/10
Brainliest plss
Answer:
3/10
Step-by-step explanation:
You multiply 3/5 by 1/2.
3/5 x 1/2= 3/10
Hope I could help :)
Which point is between points c and e
Answer:
the answer is D
Step-by-step explanation:
Please help me do this
Answer:
Step-by-step explanation:
This is part of the Isosceles Triangle Theorem. If one theta is equal to the other theta (and they are or else they wouldn't both be theta; one would be theta and the other might be beta), that means that the sides across from those congruent angles are also congruent. That means that
6x + 6 = 9x - 9 and
15 = 3x so
x = 5
20. A certain conditional statement is true. Which of
the following must also be true?
A. converse
B. inverse
C. contrapositive D. all of the above
Answer:
C
Step-by-step explanation:
Which of the following lists of ordered pairs is a function?
O A. (2, 4), (0, 2), (2, -4), (5,3)
O B. (1,6), (2,7),(4,9), (0,5)
O c. (0, 2), (2, 3), (0, -2), (4,1)
O D. (1, 2), (1, -2), (3, 2), (3, 4)
Answer:
B
Step-by-step explanation:
A function cannot have more than one point on the same x coordinate. So, B is the only option that works.
A sample of gold has a volume of 3 cm3 and a mass of 40.7 grams. What is the density of this sample?
Answer:
Density = 13.57 g/cm³
Step-by-step explanation:
▪Volume = 3 cm³
▪Mass = 40.7 grams.
▪Density (p) = Mass (m) ÷ Volume (v)
p = m ÷ v
p = 40.7 ÷ 3
p = 13.56666
p = 13.57 g/cm³
Please help me with this it's really important
A 40-question test has 108 possible points. There are m 4-point questions and n 2-point questions. How many of each type of questions are on the test?
Answer:
There are 14 4-point questions and 26 2-point questions.
Step-by-step explanation:
m = number of 4-point questions
n = number of 2-point questions
m+n =40
4m + 2n =108
You can solve system by elimination:
Multiply the 1st equation by -4 and keep the 2nd equation the same.
−4(m+n=40) → -4m -4n= -160
4m+2n=108 add them up
-2n = -52 divide both sides by -2
n = 26
plug it back in to solve for m
m + n = 40 →m + 26 =40 subtract 26 to both sides
m = 14
Answer:
m=14, n=26
Step-by-step explanation:
Please answer correctly !!!!!!! Will mark brainliest answer !!!!!!!!!!!!
=========================================================
How to get this answer:
Locate 6 on the x axis. Draw an arrow down until you reach the f(x) curve, then move to the left until you reach the y axis. We started at x = 6 and ended on y = -6. See the diagram below for this process in action.
So basically f(6) = -6. Visually the point (6,-6) is on the f(x) curve.
Through similar steps, we see that g(5) = -5
Therefore,
4*f(6) - 6*g(5) = 4*(-6) - 6*(-5) = -24 + 30 = 6
Henry decides to start an investment savings account. He initially deposits $500 dollars to the bank. Every year, Henry's bank account increases by 15%. Assume x represents the number of years and y is the amount of money in the bank. Which function models this situation below?
Answer:
[tex]y= 500(1+0.15)^x[/tex]
Step-by-step explanation:
This problem can be solved using concept of compound interest
In compound interest
if p is the principal amount
and r is the interest rate
then value of principal amount(A) after n years time is given by
A = p(1+r)^n
=>[tex]A = p(1+r)^n[/tex]
__________________________________
in the problem
in place of n we have x years
y is the amount which is the total amount after n years
p is the principal money deposited = $500
r = 15%
substituting these value in the formula for amount after n years we have
[tex]y= 500(1+15/100)^x\\y= 500(1+0.15)^x[/tex]
Thus, function modeling the situation is [tex]y= 500(1+0.15)^x[/tex]
