Answer:
43 + 7i
Step-by-step explanation:
Given: (1 + 5i)(3 - 8i)
To find: Multiplication and simplification
Solution:
i=[tex]\sqrt{-1}[/tex],
Now, we simply open the brackets as follows:
(1 + 5i)(3 - 8i)
1(3 - 8i) + 5i (3 - 8i)
3 - 8i + 15i - 40[tex]i^{2}[/tex]
3 + 7i - 40[tex]i^{2}[/tex] - (i)
[tex]i^{2}[/tex] = i * i
[tex]i^{2}[/tex] = [tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex]
[tex]i^{2}[/tex] = -1
Now, put [tex]i^{2}[/tex] = -1 into the equation (i)
we get
⇒ 3 + 7i -40(-1)
⇒ 3 + 7i + 40
⇒ 43 + 7i
∴ Final Answer : 43 + 7i
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
what we need to know here is that :
[tex]\qquad \sf \dashrightarrow \:i \cdot i = - 1[/tex]
Now, let's proceed accordingly ~
[tex]\qquad \sf \dashrightarrow \:(1 + 5i) \cdot(3 - 8i)[/tex]
[tex]\qquad \sf \dashrightarrow \:(1 \cdot3) - (1 \sdot8i) + (5i \cdot3) - (5i \cdot8i)[/tex]
[tex]\qquad \sf \dashrightarrow \:3 - 8i + 15i - ( - 1)(40)[/tex]
[tex]\qquad \sf \dashrightarrow \:3 + 7i - ( - 40)[/tex]
[tex]\qquad \sf \dashrightarrow \:3 + 40 + 7i[/tex]
[tex]\qquad \sf \dashrightarrow \:43 + 7i[/tex]
help! Solve each triangle (find all missing sides and angles) Round each answers to the nearest tenth
Answer:
D.
Step-by-step explanation:
sin 67 = b / 2.4
b = 2.4 sin 67
= 2.2
cos 67 = a / 2.4
a = 2.4 cos 67
= 0.9
M < A = 90-67 = 23 degrees.
A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400 please select the best answer from the choices provided a b c d
We will see that there are 156,000 different combinations, so the correct option is C.
How many possibilities are there?
First, we need to find the selections, here we have:
First letter.Second letter.Third letter.Number.Now we need to find the number of options for each of these selections.
First letter. (26 options)Second letter. (25 options, because we can't repeat letters)Third letter. (24 options)Number. (10 options).We assumed that the number can be any integer from 0 to 9.
The total number of possibilities is equal to the product between the numbers of options, we will have:
P = 26*25*24*10 = 156,000
So, the correct option is C.
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Find the x-intercept and the y-intercept.
3x-2y=6
Show work to get Brainliest
Answer:
There are several different ways to get the x-intercept and y-intercept of an equation. The way that I usually do it is setting one of the variables to zero and finding what the other variable is equal to. For example, if we set x to 0 that means that we are finding the y-intercept as the value of x is 0 which is the y-axis. This is also how it works when setting y to 0. First lets find the x intercept by setting y to 0.
[tex]3x - 2y = 6[/tex]
[tex]3x - 2(0) = 6[/tex]
[tex]\frac{3x}{3} = \frac{6}{3}[/tex]
[tex]x = 2[/tex]
We now know that the x-intercept is 2 and now we need to determine what the y-intercept is. Now we can just set the x to 0 and find the y-intercept.
[tex]3x - 2y = 6[/tex]
[tex]3(0) - 2y = 6[/tex]
[tex]\frac{-2y}{-2} = \frac{6}{-2}[/tex]
[tex]y =- 3[/tex]
Therefore, we know that our x-intercept is (2, 0) and our y-intercept is (0, -3) because the first spot in the coordinate pair is the x-value and the second one is the y-value.
Hope this helps
Cody's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 1 senior citizen ticket and 13 child tickets for a total of $111. The school took in $156 on the second day by selling 12 senior citizen tickets and 9 child tickets. What is the price each of one senior citizen ticket and one child ticket?
The price of one senior citizen ticket is $7 and the price of one child ticket is $8.
What are the linear equations that represent this question?s + 13c = 111 equation 1
12s + 9c = 156 equation 2
Where:
c = price of one child ticket s = price of one senior citizen ticket What is the price of one children's ticket?Multiply equation 1 by 12
12s + 156c = 1332 equation 3
Subtract equation 2 from equation 3
1176 = 157c
c = $8
What is the price of one senior citizen's ticket?
Substitute for c in equation 1:
s + 13(8) = 111
s = 111 - 104
s = $7
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I always have trouble with this
Answer:
[tex]\sqrt{64} < \sqrt{72} < \sqrt{81}[/tex]
Step-by-step explanation:
The closest perfect squares to 72 would be 81 and 64. Therefore, the square root of 72 must be between 8 and 9.
why is 64006 not a perfect square
Answer:
This might not be the best answer but here goes:
A perfect square has to be a number that is expressed by 2 of the same integer multiplied by each other.
To check if a number is a perfect square, you find the square root of it. 64006 does not have a whole square root, meaning it is not a perfect square number. Its square root is:
252.9940711... (very close but not quite whole)
1. A perfect square number always has its square root to be a whole number. But, the square root of 64006 is is 252.99407... (not whole), so it is not a perfect square.
2. A perfect square number can only be written as the product of 2 odd numbers or 2 even numbers. But, 64006 can be written as 32003 x 2 -> NOT a perfect square.
A researcher conducts a written survey to determine the opinion of subjects regarding their opinion of the favorability of a certain hospital. What does a large standard deviation on all the answers tell the researcher about the research sample
A large standard deviation means the view of the people is very dispersed and not near the mean or not similar.
What is the meaning of Standard Deviation ?Standard deviation is a very important terminology in Statistics which help to study dispersion of data from the mean
A lower value of standard deviation means the data is accumulated near the mean while a higher value means the data is dispersed in the entire range.
It is given in the question that
A researcher conducts a written survey to determine the opinion of subjects regarding their opinion of the favorability of a certain hospital.
The standard deviation value for the sample is large
A large standard deviation means the view of the people is very dispersed and not near the mean or not same.
There will be difference in the opinion as they deviate from the central value.
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3. Carmen received the following
scores on her last six homework
pages: 23, 24, 20, 19, 19, and 21.
What is Carmen's average
homework score?
A 19
8 20
C 21
D 22
Сот
"A
1
Ali is playing computer solitaire. He tallies the number of times he wins and loses.
A. Use Ali’s results to estimate the probability of him winning the next solitaire game.
B. How could Ali improve the accuracy of his estimate.
Answer:
use ali result to estimate the probability of him winning the next solitaire game
PLEASE HELP
Factor completely 2x3 + 6x2 + 2x + 6.
O 2[(x + 3)(x2 + 1)]
• (2x + 6)(x2 1)
O (x + 3)(2x2 + 2)
O 2(x3 + 3x2 + x + 3)
Answer:
A. 2(x+3)(x^2+1)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The given expression is
Taking out the common factor.
The complete factor form of given expression is . Therefore the correct option is A.
The width of a rectangle is 2/3 its length. The perimeter of the rectangle is 400 ft. What is the length, in feet, of the rectangle?
Answer:
here's your answer....
What is the area of adef with vertices d(-1,-5), e(4.-5),
and f(4,7)?
Answer:
Step-by-step explanation:
30 square unit is the area of the triangle DEF.
What are the properties of Triangle?The properties of the triangle are:
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.We can use the coordinates of the three vertices of the triangle to find the length of its base and height, and then use the formula for the area of a triangle.
The base of the triangle is the line segment from point E to point F, which has a length:
|EF| = √[(4-4)^2 + (7-(-5))^2] = √(0^2 + 12^2) = 12
The height of the triangle is the perpendicular distance from point D to the line containing the base, which is the horizontal line y = -5.
Therefore, the height of the triangle is the vertical distance from point D to the line y = -5, which is 5 units.
The area of the triangle is then:
Area = (1/2) x (base) x (height)
= (1/2) x 12 x 5
= 30 square units.
Therefore, the area of triangle DEF is 30 square units.
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Which figures can be circumscribed by a circle? Select all that apply.
Answer:
A, B, C, D
Step-by-step explanation:
They All add up to 360
Answer:
B and D
Step-by-step explanation:
figures which can be circumscribed by a circle are called cyclic quadrilaterals.
the opposite angles of a cyclic quadrilateral sum to 180°
A
∠ B + ∠ D = 82° + 56° = 138° ≠ 180° ← not cyclic
B
∠ B + ∠ D = 103° + 77° = 180° and ∠ A + ∠ C = 90° + 90° = 180° ← cyclic
C
∠ B + ∠ D = 112° + 90° = 202° ≠ 180° ← not cyclic
D
∠ B + ∠ D = 90° + 90° = 180° and ∠ A + ∠ C = 90° + 90° = 180°← cyclic
Then B and D can be circumscribed by a circle
Which of the following equations is not a linear equation?
x + y = 4
B. 2x – y = 1
C. x 3=2
D. y = 4
Answer:
C
Step-by-step explanation:
A linear equation consists of Ax+By=C
That is the only one without that kinda format
Answer:
The Answer Is C
Step-by-step explanation:
Help its due 11:59 and I am stuck please help i give brainiest
Answer:
188 cubic yards
Step-by-step explanation:
there are two ways to solve for this problem the first is to use the given numbers to find the missing one, then seperate the two cuboids and solve for their volumes independently, and finally add
the second way is too make one complete rectangular prism and simply find out the volume of the missing side and subtract that from the whole
explain how to correctly find the missing side
if correct, will mark brainlist :))
asap could really use someones help
Apply Pythagorean theorem
P²=H²-B²P²=13²-4²P²=169-16P²=153P=√153P=3√17Simplify
[tex]\sqrt{81-18\sqrt{7}+7 }[/tex]
Answer:
The given equation is expansion of (a-b)² = a²-2ab+b²
[tex]\sqrt{81-18\sqrt{7}+7} \\ \sqrt{ {9}^{2} -2 \times 9 \times \sqrt{7}+ { \sqrt{7} }^{2} } \\ \sqrt{ {(9 - \sqrt{7})}^{2} } \\ {(9 - \sqrt{7})}[/tex]
hope that help.
Answer:
[tex]9-\sqrt{7}[/tex]
Step-by-step explanation:
Given expression: [tex]\sqrt{81-18\sqrt{7}+7}[/tex]
To simplify the given expression, use the "A minus B Whole Square" identity.
A minus B Whole Square identity
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Comparing [tex]81-18\sqrt{7}+7[/tex] to the right side of the identity:
[tex]a^2=81 \implies a=\sqrt{81}=9[/tex][tex]b^2=7\implies b=\sqrt{7}[/tex][tex]-2ab=-18\sqrt{7}=-2 \cdot 9\sqrt{7}[/tex]Therefore:
[tex](9-\sqrt{7})^2=81-18\sqrt{7}+7[/tex]
Finally:
[tex]\sqrt{81-18\sqrt{7}+7}=\sqrt{(9-\sqrt{7})^2}=9-\sqrt{7}[/tex]
An equations that has zero POI with 2x -6y = 12
(must have different values)
Answer: Y= 1/3x - 2
Step-by-step explanation:
If a positive is subtracted from a negative, will the answer be true or false. ans:true
Answer:
It depends. If the negative number is greater than the positive, the answer is true. Otherwise, false.
What is the solution to the equation below?
√x-4=x-10
Answer:
[tex]x=13[/tex]
Step-by-step explanation:
Step 1: Isolate the square root on the left hand side
Radical already isolated
√x-4 = x-10
Step 2: Eliminate the radical on the left hand side
Raise both sides to the second power
(√x-4)2 = (x-10)2
After squaring
x-4 = x2-20x+100
Step 3: Solve the quadratic equation
Rearranged equation
x2 - 21x + 104 = 0
This equation has two rational roots:
{x1, x2}={13, 8}
Step 4: Check that the first solution is correct
Original equation
√x-4 = x-10
Plug in 13 for x
√(13)-4 = (13)-10
Simplify
√9 = 3
Solution checks !!
Solution is:
x = 13
Step 5: Check that the second solution is correct
Original equation
√x-4 = x-10
Plug in 8 for x
√(8)-4 = (8)-10
Simplify
√4 = -2
Solution does not check
2 ≠ -2
One solution was found :
x = 13
How would you write this expression as a sum or difference?
The provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
[tex]= \rm log_3(\sqrt[5]{x} . y)[/tex]
As we know:
log(mn) = logm + logn
logmⁿ = nlogm
[tex]= \rm log_3({x^{\dfrac{1}{5}}} . y)\\\\= \rm log_3({x^{\dfrac{1}{5}}} )+log_3 (y)\\\\= \rm \dfrac{1}{5}log_3({x^{}} )+log_3 (y)\\\\[/tex]
Thus, the provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.
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HELPPPP this is 7TH grade math and I don’t understand
Answer:
B.3x+8=66
Step-by-step explanation:
i think ito po Ang answer hehehe
Part A
x = some unknown number
x+8 = add on 8 to the number
3(x+8) = triple the previous result
Therefore, one equation to set up is 3(x+8) = 66
This is the same as 3x+24 = 66 because 3(x+8) = 3x+3*8 = 3x+24. Use the distributive property to multiply that outer 3 to each term inside.
Answers:C) 3x+24 = 66
D) 3(x+8) = 66
============================================================
Part B
Let's solve for x. I'll show the steps for each equation mentioned. When you write out the steps, you probably only need to pick one equation to solve.
3(x+8) = 66
x+8 = 66/3
x+8 = 22
x = 22-8
x = 14
Or
3x+24 = 66
3x = 66-24
3x = 42
x = 42/3
x = 14
Either way, we get the same x value. To confirm this answer, replace x with 14 in either equation and simplify fully. You should get 66 on both sides.
Answer: x = 14Select the correct answer from each drop-down menu. determine the number of real solutions for each of the given equations. equation number of solutions y = -3x2 x 12 y = 2x2 - 6x 5 y = x2 7x - 11 y = -x2 - 8x - 16
It should be noted that in the equation y = -3x² + x + 12, there are two real solutions.
How to calculate the real solutions?It should be noted that the number of real solutions of a quadratic equation is represented by y = ax² + bx - c.
In the equation, equation y = -3x² + x + 12, the coefficients are a = -3, b = 1 and c = 12. The discriminant will be:
= 1² - 4(-4)(12)
= 145
It is positive, therefore, it has two solutions.
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solve the equation
2x+9y=11
3x+8y=18
Using Elimination Method:
[tex]2x + 9y = 11 \\ 3x + 8y = 18 \\ 3(2x + 9y = 11) =( 6x + 27y = 33 )\\ - 2(3x + 8y = 18) = ( - 6x- 16y = - 36) \\ 11y = - 3 \\ y = \frac{ - 3}{11} \\ 2x + 9( \frac{ - 3}{11} ) = 11 \\ 2x - 9( \frac{3}{11} ) = 11 \\ 2x - \frac{27}{11} = 11 \\ 2x = 11 + \frac{27}{11} \\ 2x = \frac{121 + 27}{11} \\ 2x = \frac{148}{11} \\ 2x \div 2 = \frac{148}{11} \div 2 \\ x = \frac{74}{11} \\ x = \frac{ - 3}{11} \\ y = \frac{74}{11} [/tex]
question 4. evaluate the expression [tex]-6^3[/tex]
Answer:
The answer would be ~30~ because 2*2^3 = 2^4= 16 then 3*6=18 then 16+18-4=30
Hope this helps
Have a great day/night
Answer ~
whenever we see an expression in the form of [tex]x^{n}[/tex] we have to multiply x to itself " n " times !
here in the question ,
we're given with the expression ( - 6³ )
so ,
[tex] - 6 {}^{3} = - 6 \times - 6 \times - 6 \\ \dashrightarrow \: - 216[/tex]
hope helpful ~
7. Refer to the bar chart in question 6. Which age group recorded the highest number of children
Answer:
The age group that recorded the highest number of children is 7.
Step-by-step explanation:
We can clearly can see from the graph, that the 7 year old age group has 5 children, which is more than the rest of the age groups.
Hope this helps:) Goodluck!
HELP! need help ASAP, 50 points and brainiest will be given to whoever helps.
Answer:
10
Step-by-step explanation:
Joseph built a sandbox in his backyard that is 2 meters wide, 4 meters long, and 2 meters tall. What volume of sand does he need to completely fill the sandbox?
A) 20 cubic meters
B) 16 cubic meters
C) 8 cubic meters
D) 12 cubic meters
Answer: B) 16 cubic meters
Step-by-step explanation:
To find the volume of a rectangular prism like this sandbox, multiply the length, height, and width together. 2*2*4 = 16.
Answer:
the answer would be 16 cubic meter because l*w*t which is because l*w*t which is 4*2*2
Find the measure of the missing angles.
Answer:
d = 105° , e = 32° , f = 43°
Step-by-step explanation:
d and 105° are vertically opposite angles and are congruent , then
d = 105°
e and 32° are vertically opposite angles and are congruent , then
e = 32°
105° , e and f lie on a straight line and sum to 180° , that is
105° + e + f = 180°
105° + 32° + f = 180°
137° + f = 180° ( subtract 137° from both sides )
f = 43°
Answer:
d= 105° f= 43° e= 32°
Step-by-step explanation:
angle d = 105° ( vertically opposite angles are equal)
f°+d°+32°= 180 (angles on a straight line)
f+105+32= 180
f+137=180
f= 180-137= 43°
f= 43°
angle .d+f+e = 180° (angles on a straight line)
105+43+e = 180°
148+ e = 180°
e = 180-148
e = 32°
therefore,
d= 105° f= 43° e= 32°
PLEASE I NEED THIS RN!!!
Answer:
Increasing then decresing
Step-by-step explanation:
the graph is going up then down so therefore it is increasing then decresing.
Answer:
The left side of the parabola is increasing to the maximum, shown on the graph to be (3,6). Then, the right side is decreasing from the max point. The parabola opens down, which means it increases, then decreases.
Step-by-step explanation:
Always decreasing would mean it took a more linear shape, which this parabola is not doing. It is also not always increasing, because some x,y points are graphed on that curve which go from the center (0,0) to (3,6) back down to (6,0).