Answer:
(10 + 3i)(10 - 3i)=109
Step-by-step explanation:
[tex](10+3i)(10-3i)=(10^{2} -10*3i)+(3*10i-3*3i^2)\\ =100-30i+30i-9i^2\\=100-9*(-1)\\=100+9=109[/tex]
Answer:
B) 109
Step-by-step explanation:
I took the test and got a 100%
Which equation best represents the data given in the table ?
Answer:
B
Step-by-step explanation:
The equation that satisfies the above table is y = 8[tex](\frac{1}{2})^{x}[/tex]
Given,
Table between x and y .
Here,
To get the equation between x and y first justify the data given in the table.
So,
When,
x = -3 , y = 64
x = -2 , y = 32 .
In the equation y = 8[tex](\frac{1}{2})^{x}[/tex] substitute the values of x and check for y .
Put x = -3 ,
y = 8[tex](1/2)^{-3}[/tex]
y = 8 * 8
y = 64
Thus it satisfies the value given in the table .
So the correct equation will be Option B .
Know more about equations,
https://brainly.com/question/14686792
#SPJ2
Find the area. Will mark brainliest.
Step-by-step explanation:
Area of the parallelogram=bh
b=20cm
h=12cm
Area=12*20=240cm²
COME ON ITS 1 QUESTION FOR 50 POINTS!
If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!
Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
Drag the tiles to the correct boxes to complete the pairs.
Match each situation to the simulation that represents it.
Althea has to select 1 student
as the class representative
from 13 students.
Fiona is deciding which of three
forests to research for a
geography project: evergreen,
deciduous, or coniferous.
Jenny is picking a marble from
a jar with two green marbles, six
yellow marbles, and two red
marbles.
rolling a six-sided die
selecting a playing card from
the hearts suit
spinning a spinner divided into
five equal sections
Answer: rolling a six sided die☞︎Fiona forest research
Hearts suit☞︎Althea class representative
Spinner☞︎ Jenny marbles
Step-by-step explanation:
Answer:
Fiona= die
Althea=cards
Jenny=Spinner
Step-by-step explanation:
starting off Fiona has three which can evenly go into six.
Althea has 13 options which matches with the number of suits in the hearts
the Jenny would be spinner because 5 times 2 is 10
Solve 5(g-2)+g=6(g-4
Answer:
g = -13
Step-by-step explanation:
5(g-2)+g=6(g-4)
5g - 10 + g = 6g - 24
5g + g - 6g = -24 + 10
6g - 6g = -13
g = -13
Simplify: (1 + 3i) + (7 - 2i)
Answer:
8+i
Step-by-step explanation:
Answer:
8 + 1 i
if im wrong soooooorrrrrrryyyyyy
Step-by-step explanation:
The radius of the earth is 3959 miles. A meteor with a diameter of 750 miles strikes the earth in an unpopulated area. What percent of the earths surface is affected by the meteor strike? Is it a 36% be 0.9% C9% or D3.6%
Answer:
B. 0.9%
Step-by-step explanation:
If the diameter of the meteor is 750 miles, then its radius is 750/2 = 375 miles
The radius of the earth is 3959 miles
Assuming that both bodies are spherical, their surface are:
meteor's surface: π*r² = π*375² = 441786.467 miles²
Earth's surface: π*3959² = 49240321.1 miles²
If 49240321.1 miles² represents 100% then 441786.467 miles² represents:
49240321.1 miles² / 100% = 441786.467 miles² / x%
x = 441786.467/49240321.1*100
x = 0.9%
Answer:
B) 0.9%
Step-by-step explanation:
Twenty-four 4-inch wide square posts are evenly spaced with 5 feet between adjacent posts to enclose a square field, as shown. What is the outer perimeter, in feet, of the fence? Express your answer as a mixed number.
Answer:
129 1/3
Step-by-step explanation:
According to Alcumus, "There are 20 square posts which are not on a corner, so there are $20/4=5$ square posts on each side, not including the corner posts. Including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts. Altogether the length of a side is $7\left(\frac{1}{3}\right)+6(5)=32\frac{1}{3}$ feet. The perimeter of the square is four times the side length, so the perimeter is $4\cdot 32\frac{1}{3}=\boxed{129\frac{1}{3}}$ feet."
The outer perimeter is 129 1/3 feet.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Twenty-four 4-inch wide square posts are evenly spaced with 5 feet.
So, there are $20/4
=5$ square posts on each side, not including the corner posts.
and, including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts.
Then, the length of a side is
= 7 1/3 + 6(5)
= 32 1/3 feet
and, The perimeter of the square
= 4 x 32 1/3
= 129 1/3 feet
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
please help asap, 20 points
Solving for each equation:
A: True.
[tex]\frac{n}{2} +3 *4 = \frac{n}{2}+12\\\\\frac{n}{2} + 12 = \frac{n}{2} + 12[/tex]
B: False.
[tex]\frac{1}{3}z+\frac{2}{3}z * 9 = 9z\\\\\frac{1}{3} z+6z = 9z[/tex]
C: True, given that y = 1
[tex]-8y +4.3y + 3.7 = 0\\\\-3.7y = -3.7[/tex]
D: True, given that b = 6.66667
[tex]12-1.8b+1.8b=1.8b\\12 = 1.8b[/tex]
E: True.
[tex]\frac{m}{8} + 7(\frac{m}{8} ) =m\\\\\frac{m}{8} + (\frac{7m}{8} )= m\\\\\\\frac{8m}{8} = m\\[/tex]
Event A: stops on red
Event B: stops on yellow
Find P(A or B)
A.) 1/4
B.) 1/8
C.) 1/2
D.) 1/16
Answer:it is 1/2
Hopefully this helps
Answer:
Event A: stops on red
Event B: stops on yellow
Find P(A or B)
1/2
It’s on probability please help
Answer:
The number of meal combinations, She has to choose:
N = 3 x 4 x 3 =36
Hope this helps!
:)
Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 4x + 12
O A. (3.2 + 4)(x+4)
O B. (3x2+3)(x + 4)
O c. (3x2 + 4)(x+3)
O D. (3x + 3)(x+3)
Answer:
C. (3x^2+4)(x+3)
Step-by-step explanation:
3x^3+9x^2+4x+12
=(3x^3+9x^2)+(4x+12)
=3x^2(x+3)+4(x+3)
=(3x^2+4)(x+3)
Therefore, C. (3x^2+4)(x+3)
The correct factor of the polynomial is,
⇒ (x + 3) (3x² + 4)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3x³ + 9x² + 4x + 12
Now, We can factor the polynomial as;
⇒ 3x³ + 9x² + 4x + 12
⇒ 3x² (x + 3) + 4 (x + 3)
⇒ (x + 3) (3x² + 4)
Thus, The correct factor of the polynomial is,
⇒ (x + 3) (3x² + 4)
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ7
Help I will mark BRAINLIEST if correct please help
Answer:
[tex](-\frac{1}{4}, \frac{5}{8} )[/tex]
Step-by-step explanation:
If you label the points on the axes, it will show that point K is actually on [tex]\frac{5}{8}[/tex] not [tex]\frac{3}{4}[/tex]
please help me out! i have a few more of these questions, about 4
Step-by-step explanation:
You can make a table of values to find the points that belong to the line and then draw the line through those points. Here are some: (-6, -2), (0, -1), and (6, 5). You can use any value for x in your table. Hope this helps!
Answer:
Step-by-step explanation:
put a point in at negative 1 first; that is the y value.
Then, go up 1 then to the right six points. that should result in the next point being at (0,6).
Keep going and draw a line
How to solve a system of equation using a graph?
Answer:
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
Step-by-step explanation:
Suzanne bought a sweater at the sale price of $29.99. the original cost of the seater was $49.99. what percent represents the discount they suzanne received when buying the sweater?
a: 40% discount
b: 60% discount
c: 50% discount
d: none of the above
NEED HELP ASAP MASTERY GRADE
Answer:
= 40%
Step-by-step explanation:
Original price = 100%
Discount = Op - Np = $49.99 - $29.99 = $20
If $49.99 = 100%
What about $20 = ?
= (20 x 100) ÷ 49.99
= 2000 ÷ 49.99
= 40.008
= 40%
10 points need help asap
Answer:
D
Step-by-step explanation:
How does knowing the absolute value of an integer help in determining the distance of two ordered pairs?
5(x-10)=30-15x
Ox=1
Ox=4
Ox=5
Ox=8
Answer:
x = 4
Step-by-step explanation:
5x-50=30-15x
5x +15x =30+50
20x= 80
Divide both sides of the equation by 20
x = 4
I hope it helps
Below are two truths and one lie, choose the lie.
Answer:
The horizontal asymptote is x-axis
Step-by-step explanation:
The horizontal asymptote is the y axis not x axis
Mark placed a pool in his backyard, which is enclosed by a triangular fence. The radius of the pool is 20.5 feet.
Answer:
A. 3,864 ft²
B. 1,319.585 ft²
C. 2,544.415 ft²
Step-by-step explanation:
Area of triangle:
½ × 92 × 84
3864 ft²
Area of circle:
pi × r²
3.14 × 20.5²
1319.585 ft²
Difference:
3864 - 1319.585
2544.415 ft²
this box holds cereal. how many cubic inches of cereal can it hold the size of the box is 6 in,2 in,12 in
5. The length of a rectangle is 5 inches greater than the width.
Question
Answer
a. Write an expression for the width of the rectangle.
b. Write an expression for the length of the rectangle.
multiply
Answer:
see below
Step-by-step explanation:
Let w = width
L = length = w+5
The area is l*w
A = (w+5)*w
A = w^2 +5w
Both perpendicular lines and parallel lines must
A
never meet.
В
meet at right angles.
C
exist on the same plane.
D
be curved in the same place.
Answer:
A.) Never meet.
Step-by-step explanation:
It’s A they never meet
Solve this for me please
is there a picture to this??
Please help
find the area of a trapezoid base 1 measures 20 ft base 2 messages 10 ft height measures 3 ft
Answer:
Step-by-step explanation:
(20+10)*3/2 = 45
Answer:
45 ft squared
Step-by-step explanation:
Area of a trapazoid = a plus b divuded by 2 times h
20 plus 10 divided by 2 equals 15
then 15 times 3 equals 45
Will give brainliest answer
Answer
Step-by-step explanation:
To find the area of a shape multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
please mark me as brainliest.
Answer:
[tex]7 units^2[/tex]
Step-by-step explanation:
You can split this irregular shape into a square and a trapezoid.
The formula for a square is:
[tex]A=lw[/tex]
The formula for a right trapezoid:
[tex]A=\frac{1}{2} (h)(a+b)[/tex]
Area of square:
[tex]A=(2)(2)\\A=4[/tex]
Area of right trapezoid:
[tex]A=\frac{1}{2} (2)(1+2)\\A=3[/tex]
Add up the individual areas to find the overall:
4 + 3 = 7
Hey guys I need help with this exercise can someone plz help me for 20 points?? Also write the explamation to your answer plzz!
Math problem: 13 of the same cookbooks weigh 442 grams. What is the weight of 10 of these books?
Answer:
340
Step-by-step explanation:
442 / 13 = 34
34 × 10 = 340
Answer:
340
Step-by-step explanation:
442 / 13 = 34
34 × 10 = 340
What is the maximum of f(x) = sin(x)?
- 2π
-1
01
2π
Answer:
1
Step-by-step explanation:
The maximum value of sin(x) is 1.
When x = 90 degrees sinx = 1.
PLS HELP John’s patio needs to be re-painted.
He needs orange paint for one portion of his patio and gray paint for the other portion. Determine the total area of the patio that needs orange paint and the total area that needs gray paint. Show all calculations.
Answer:
368 square feet of orange paint.
292 square feet of grey paint.
Step-by-step explanation:
Here is a picture of my work that you can follow to show how i did it. hope this helps!
