Answer: B) -56i - 24
This is the same as -24 - 56i
=============================================
Explanation:
The 'i' refers to the imaginary number [tex]\sqrt{-1}[/tex]
In other words, [tex]i = \sqrt{-1}[/tex]
Squaring both sides gets us [tex]i^2 = -1[/tex]
So,
[tex]x = -8(7i - 3i^2)\\\\x = -8(7i - 3(-1))\\\\x = -8(7i + 3)\\\\x = -8(7i) -8(3)\\\\x = -56i -24 \ \ \text{ .... Answer: Choice B}\\\\x = -24 - 56i\\\\[/tex]
The result is in the form a+bi where a = -24 is the real part and b = -56 is the imaginary part.
Mikey Johnson shipped out 41 1/4 pounds of electrical supplies. The supplies are placed in individual packets that weigh 2 3/4 pounds each . How many packets did he ship out?
Answer:
15
Step-by-step explanation:
Number of packets shipped out = total weight of electrical supplies / weight of individual packets
[tex]41\frac{1}{4}[/tex] ÷[tex]2\frac{3}{4}[/tex]
to solve convert the mixed fractions to an improper fraction
to convert to improper fraction, take the following steps :
1. Multiply the whole number by the denominator
2. Add the numerator to the answer gotten in the previous step
3. divide the number gotten in the previous step by the denominator
[tex]\frac{165}{4}[/tex] ÷ [tex]\frac{11}{4}[/tex]
[tex]\frac{165}{4}[/tex] × [tex]\frac{4}{11}[/tex] = 15
What is the perimeter of a trapezoid?Units
Can anyone help me please I really need help.
Answer:
what do u need help with
Step-by-step explanation:
Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds? Henry's design would result in a larger flower bed because its area would be 2,500 square feet. Liani's design would result in a larger flower bed because its area would be 2,500 square feet. Henry's and Liani's designs would result in flower beds with the same area. Henry's and Liani's designs are not possible with the given amount of wood.
Answer:
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
Step-by-step explanation:
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
B. Liani's design would result in a larger flower bed because its area would be 2,500 square feet.
C. Henry's and Liani's designs would result in flower beds with the same area.
D. Henry's and Liani's designs are not possible with the given amount of wood.
Length of wood = 200 feet
Henry's square bed design = 200 feet / 4
= 50 feet
Note: A square has 4 equal sides, hence, the division by 4
Each side of the square bed = 50 feet
Area of the square bed = length ²
= (50 feet)²
= 2,500 square feet
Liani rectangular bed design
Length = 55 feet
Width = 45 feet
Note: adding of 2 length and 2 width = 200 feet
That is,
2(55) + 2(45)
= 110 + 90
= 200 feet of wood
Area of Liani rectangular bed design = length × width
= 55 feet × 45 feet
= 2,475 square feet
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
Answer:
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
Step-by-step explanation: magic
Math Problem Solving
statistics and probability
Answer:
Standard Deviation = 3.22
Variance = 10.36
Step-by-step explanation:
x P(x) x × P(x) x² x² × P(x)
19 0.20 3.8 361 72.2
10 0.20 2 100 20
11 0.30 3.3 121 36.3
12 0.20 2.4 144 28.8
13 0.10 1.3 169 16.9
____________________________________________
12.8 174.2 => Total
Mean Formula
[tex]\mu_x = \sum(x \times P(x))[/tex] [tex]= 12.8[/tex]
[tex]\mu_x^2 = 163.84[/tex]
Variance Formula
[tex]\sigma _x^2 = \sum[x^2 \times P(x)] - \mu_x^2[/tex]
[tex]= 174.2- 163.84\\\\=10.36[/tex]
Standard Deviation Formula
[tex]Standard\ deviation, \ \sigma_x = \sqrt{Variance}[/tex]
[tex]=\sqrt{10.36}\\\\=3.218[/tex]
Fill in the blank: 12(8x - 4) = __X - 48
Answer:
96x
Step-by-step explanation:
12(8x - 4)
=12*8x - 12*4
=96x - 48
Answer:
96
Step-by-step explanation:
You distribute the 12 to each term, the 8x term turns into 96x after distribution.
pleaseee help me with this questionnn
Answer:
itss8tsz85sz85s,85s,8td,8td,85dz85dzd85e,7554334567
Step-by-step explanation:
otdxd8td 8td 85sx8ts,ts8,8ts,8td,88ts8ts,8ts,8ts,8ts,8ts,8ts,8ts,8ts,8ts,,8ts8ts,8t,s8ts,8tz8txdxtitixtxtidittdxdctiti dttxdididez6z84gfiwz84wz85wzy0dcydcydc6dctr456887654
Work out
m
and
c
for the line:
y
=
3
x
+
1
Answer: m=3
Step-by-step explanation:
How many quarters does Annie have
A.35
B.49
C.3
D.7
Answer:
n = 7
Step-by-step explanation:
sarah = m
annie = n
sarah has 21 more than annie
m = 21+n
given sarah has 28 quareters
m = 21 + n
28 = 21 + n
28 - 21 = n
7 = n
annie has 7 quarters.
the graph of f(x) shown below resembles the graph of g(x)=x^2 but it has been changed somewhat which of the following could be the equation of f(x)
Answer:
C
Step-by-step explanation:
The Equation of red parabola is y = -(x-2)² - 1.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have a function,
g(x) = x²
It is a parabola with vertex at (0,0) and the sign is positive then the parabola opens up.
Then, General equation of parabola is
y= a(x - h)² + k
As, the The graph of F(x) opens down that is why it will have negative x²
and vertex at (2, -1)
So, the equation of parabola
y= -1(x - 2)² + (-1)
y = -(x-2)² - 1
Learn more about Equation of parabola here:
https://brainly.com/question/16954562
#SPJ7
solve for x. round to the nearest tenth of a degree, if necessary.
Answer: 46.3
Step-by-step explanation:
Tan = opposite/adjacent
Tan -1 =6.9/6.6
x=46.27
x=46.3
Please help me ASAP tysm
Answer:
?
Step-by-step explanation:
Solve the right triangle. Round decimal answers to the nearest tenth.
Answer:
Step-by-step explanation:
take angle A as reference angle
using cos rule
cos A = adjacent/hypotenuse
cos A =10/15
cos A =0.66
[tex]A=cos^{-1} (0.6666)[/tex]
A=48.194
A=48.2
angle A + angle B + angle C =180 degree (being sum of interior angles of a triangle)
48.2 + angle B + 90 =180
138.2 + angle B =180
angle B =180-138.7
angle B =41.8
for BC
using pythagoras theorem
a^2 + b^2 = c^2
AC^2 + BC^2 = AB^2
10^2 + BC^2 = 15^2
100 + BC^2 = 225
BC^2 = 225-100
BC^2 = 125
[tex]BC=\sqrt{125}[/tex]
BC=5[tex]\sqrt{5}[/tex]
BC=11.2
100 POINTS HELP! THIS IS A PROJECT. NOT IN A RUSH.
Describe how to find the terms mean, median, mode, and range of a group of numbers.
Pretend you are a teacher trying to describe these terms to a student. Make sure you write as if you are the teacher and explain each term as if the student is learning this for the first time. Be descriptive and give examples. Make sure you include the data set (the group of numbers) you will be working with. Be sure to use complete sentences. Be creative!
Answer
Hello class!
Step-by-step explanation:
1. The mean is the average of a data set.
2. The mode is the most common number in a data set.
3. The median is the middle of the set of numbers.
Of the three, the mean is the only one that requires a formula. I like to think of it in the other dictionary sense of the word (as in, it’s mean as opposed to nice!). That’s because, compared to the other two, it’s not as easy to work with.
Shape ABC has the following coordinate
A (3,9) B (27,-15) C (-12,-6)
The Image A'B'C' of a dilation has the coordinate
A' (1,3) B' (9,-5) C' (-4,-2)
What is the Scale Factor of the Dilation
Plssssss HELP ME WITH THIS
I need to find the area
Answer:
90 cm^2
Step-by-step explanation:
The area of a triangle is half of the base times height, so it is 1/2*15*12 = 7.5*12 = 90
A bag contains 8 red balls and 6 blue
balls.
Radhika takes three balls at random
from the bag, without replacement.
Calculate the probability that the three
balls are the same colour. *
Answer:
The probability that all 3 balls are red is 18.65%, while the probability that all 3 balls are blue is 7.87%.
Step-by-step explanation:
Since a bag contains 8 red balls and 6 blue balls, and Radhika takes three balls at random from the bag, without replacement, to calculate the probability that the three balls are the same color, the following mathematical operations must be performed:
8 + 6 = 14
14 = 100
8 = X
8 x 100/14 = X
800/14 = X
57.14 = X
100 - 57.14 = 42.86
0.5714 ^ 3 = X
0.1865 = X
0.4286 ^ 3 = X
0.0787 = X
Therefore, the probability that all 3 balls are red is 18.65%, while the probability that all 3 balls are blue is 7.87%.
Megan bought beads for $9.95. She received a 10% discount. She then paid, a sales tax of 6%. How much did she pay for the beads?
altogether i have 10 bags of sweets. the mean number of sweets in the bag is 40
Answer the question : I don't get what the question is suppose to be
Step-by-step explanation:
Find the volume of the shape with the given dimensions 8 in by 5 in by 3 in
Answer:
V = (8 in)(5 in)(3 in) = 120 in^3
Step-by-step explanation:
The likeliest name for this shape is "rectangular prism." Let's assume that the length, L, is 8 in; the width, W, is 5 in; and the height, H, is 3 in.
Then the volume of this rectangular prism is V = L * W * H, or
V = (8 in)(5 in)(3 in) = 120 in^3
Please help me! It is very important that I get this done but I am beyond confused!
Brandt invests an initial amount P of $180 into an account that pays interest at 2.5% compounded continuously. Carter invests $120 into an account that pays 4.8% compounded continuously. The balance of each investment, A, is calculated using the equation A=Peⁿ. The graph shows their investments over time.
When will their investments reach the same balance?
a. Their investments will never reach the
same balance.
b. Their investments will reach the same
value between years 15 and 16.
c. Their investments will reach the same
value between years 16 and 17.
d. Their investments will reach the same
value between years 17 and 18.
e. Their investments will reach the same
value between years 18 and 19.
Answer:
Step-by-step explanation:
i think it should be d 16 and 17
what is slop of the line that passes through the ponitss (5, -4) and (7, -4)
Answer:
The slope is 0
Step-by-step explanation:
Points on the graph:
(5, -4) and (7, -4)
Slope:
m=(y2 - y1)/(x2 - x1)
m=(-4 + 4)/(7 - 5)
m= 0/2
m=0
ANSWE PLEASEEEEEEEEEEEEEEE
Answer:
your answer is gonna be A!! <3
Step-by-step explanation:
1 Subtract 33 from both sides.
y-3=-2x
y−3=−2x
2 Divide both sides by -2−2.
-\frac{y-3}{2}=x
−
2
y−3
=x
3 Switch sides.
x=-\frac{y-3}{2}
x=−
2
y−3
Answer:
A
Step-by-step explanation:
In stage 2 of a rocket's takeoff, the speed of the rocket increases at a rate of 4.3% per minute. The speed of the rocket at the beginning of stage 2 was 5,000 kilometers per hour. Its speed at the end of Stage 2 will be 25,000 kilometers per hour.
If t is the time, in minutes, from the beginning of stage 2, which equation could be used to determine how long it will take for the speed of the rocket to reach 25,000 kilometers per hour, assuming it increases at the same rate for all of stage 2?
A.
5,000 = 25,000(0.043)t
B.
5,000 = 25,000(0.957)t
C.
25,000 = 5,000(1.043)t
D.
25,000 = 5,000(1.43)t
Solve 16x + 8 ≥ 12x + 20
Answer:
x ≥ 4
Step-by-step explanation:
16x + 8 ≥ 12x + 20
Subtract 12 from both sides
4x + 8 ≥ 20
Subtract 8 from both sides
4x ≥ 16
Divide both sides by 4
x ≥ 4
Write the equation of the line which has a slope of -5 and passes through (-4,4). Write the answer in slope-intercept
Answer:
y = - 5x - 16
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 5, then
y = - 5x + c ← is the partial equation
To find c substitute (- 4, 4) into the partial equation
4 = 20 + c ⇒ c = 4 - 20 = - 16
y = - 5x - 16 ← equation of line
Please help me with this
Answer: [tex]a_{n}=4n+-3[/tex]
Step-by-step explanation:
The way arithmetic sequences are usually written is:
[tex]a_{n} =a_{1} +(n-1)d[/tex]
[tex]a_{n}[/tex] is the the term you are looking for. It has an n because we aren't looking for a specific one.
[tex]a_{1}[/tex] is the first term of the sequence. In this case that is 1.
n is the term position. Meaning if you wanted to find the fifth term you'd sub 5 in for n.
d is the common difference. In this case it is 4.
Now we can sub these values in.
[tex]a_{n} =1 +(n-1)4[/tex]
We can simplify the right part of the equation.
[tex]a_{n} =1 +(n-1)4\\a_{n} =1 +(4)(n)-(4)(1)\\a_{n}=1+4n-4\\a_{n}=4n+1-4\\a_{n}=4n+-3[/tex]
you have a baker that is currently at 70°F what would happen if you added water to lower the temperature by 15°
Answer:
65
Step-by-step explanation:
easy
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
(-infinity, 9]
Step-by-step explanation:
The range of the function is 'all real numbers less than or equal to 9.' We are told that the vertex is at (-2, 9) and that the curve opens downward, which indicates that 9 is the maximum function value, and that the function can take on any value less than or equal to 9.
The domain is 'the set of all real numbers,' which is true for any polynomial.