Answer:
The answer is 30+7i.
Step-by-step explanation:
Imaginary Number Definition
[tex]\large\boxed{{i=\sqrt{-1}}}[/tex]
Simply evaluate like how you evaluate polynomials. Expand the expression in.
[tex]\large{(8-3i)(3+2i)=[(8*3)+(8*2i)]+[(-3i*3)+(-3i*2i)]}\\\large{(8-3i)(3+2i)=(24+16i)+(-9i-6i^2)[/tex]
Therefore, our new expression when cancelling out the brackets is:
[tex]\large\boxed{24+16i-9i-6i^2}[/tex]
Imaginary Number Definition II
[tex]\large\boxed{i^2=-1}[/tex]
Therefore, substitute or change i² to -1
[tex]\large{24+16i-9i-6(-1)}\\\large{24+7i+6}\\\large{30+7i}[/tex]
Complex Number Definition
[tex]\large\boxed{a+bi}[/tex]
Where a = Real Part and bi = Imaginary Part.
Therefore, it's the best to arrange in the form of a+bi.
Hence, the answer is 30+7i.
PLEASE HELP!!!!! FAST!!! I’ll mark brainliest
Answer:
the third one
Step-by-step explanation:
plan A is less expensive for more than 6 features
On a certain hot summer's day, 321 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $634.25. How many children and how many adults swam at the public pool that day?
Answer:
31 children and 290 adults
Step-by-step explanation:
Let a = number of adults and c = number of children.
a + c = 321
2a + 1.75c = 634.25
Multiply both sides of the the first equation by -2 and add it to the second equation.
-2a - 2c = -642
(+) 2a + 1.75c = 634.25
--------------------------------------
-0.25c = -7.75
Divide both sides by -0.25
c = 31
Use the first equation to find a.
a + c = 321
Substitute 31 for c.
a + 31 = 321
Subtract 31 from both sides.
a = 290
Answer: 31 children and 290 adults
What is the square root of –16?
A. –8i
B. –4i
C. 4i
D. 8i
Answer:
C. 4i
Step-by-step explanation:
Answer:
C. 4i
Step-by-step explanation:
[tex]\sqrt{-16} = \sqrt{16} \sqrt{-1}[/tex] (because [tex]\sqrt{ab} =\sqrt{a} \sqrt{b}[/tex])
Since [tex]\sqrt{16}[/tex]=4, and [tex]\sqrt{-1}[/tex]=i, [tex]\sqrt{-16}[/tex]=4i
The first bus stop on a bus route is 4 miles from school. How many yards is the first bus stop from school?
Answer:
7040 yards
Step-by-step explanation:
1 mile = 1760 yards
1 x 4 miles = 1760 x 4 yards
4 miles = 7040 yards
71 is 10% of what number?
52 is 97% of what Number?
Explain steps.
Answer:
71 is 10% of 710
52 is 97% of 5200/97
Step-by-step explanation:
Let’s start with 71 is 10% of what number.
basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.
so, 71=0.1x
divide on both sides,
710=x
now the second one.
repeat the same process.
52=0.97x
divide
5200/97 =x
What is the value of 5 units as a mixed number
5integer 0/1 is the mixed fraction of 5 units
The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 25%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
Answer:
The p-value for a two-tailed test of hypothesis is 0.0164.
Step-by-step explanation:
The test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
This means that we look at the z-table, and we have to find:
[tex]P(|Z| > 2.4)[/tex]
Which is the pvalue of Z = -2.4 multiplied by 2, or 2 multiplied by 1 subtracted by the pvalue of Z = 2.4.
Looking at the z-table, z = 2.4 has a pvalue of 0.9918
1 - 0.9918 = 0.0082
2*0.0082 = 0.0164
The p-value for a two-tailed test of hypothesis is 0.0164.
Anyone know the answer
Step-by-step explanation:
[tex]4x - 16 + 2x + 16 = 180 \\ 6x = 180 \\ x = 30[/tex]
Step-by-step explanation:
A straight line has 180° so we can set
4x-16+2x+16=180
6x=180
x=30
Hope that helps :)
Cassandra works for a company that is based off her sales. If she is paid 9.5% of her total monthly sales, calculate her pay for the month if she sells $15,670 of product.
Answer:
I don't understand what you mean. but 10.43 i guess
6x + 30 = -6 show your work
Answer:
its x=-6
Let's solve your equation step-by-step.
6x+30=−6
Step 1: Subtract 30 from both sides.
6x+30−30=−6−30
6x=−36
Step 2: Divide both sides by 6.
6x
6
=
−36
6
x=−6
Answer:
180
Step-by-step explanation:
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Step-by-step explanation:
You have to click the number of Xs for each kilometer travelled. For example, there are 2 "3 km" answers, so under the 3 column, you click 2 Xs.
Find the percent of change. Round to the nearest tenth of a percent if necessary.
1/4 to 1/2
9514 1404 393
Answer:
100%
Step-by-step explanation:
The percentage change can be computed from ...
pct change = ((new value)/(old value) -1) × 100%
= ((1/2)/(1/4) -1) × 100%
= (2 -1) × 100%
= 100%
The increase by 1/4 from 1/4 to 1/2 is an increase of 100%.
The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 32 inches square. What is the width ? The width is ___ inches
Answer:
I hope this helps dear
Step-by-step explanation:
P = 2(L + W) = 32 in
L = W + 4
2[(W + 4) + W] = 32 in ⇒
W = 6 in
L = W + 4 = (6 + 4) in = 10 in
A = LW = (10)(6) in2 = 60 in2
Find the value of each variable
Answer:
(x - 2)² + y² = 9
Step-by-step explanation:
Helppppp!!!!!!!!! Plz
Q:An athlete throws her javelin 9.5 yards. She throws it this distance 2 times. How far does she throw the javelin in total?
18.5 yd
19 yd
19.5 yd
20 yd
Answer: 19 yd
Step-by-step explanation:
hope this helped. :)
HELP ME Which One Doesn’t Belong?
7.9x
7.9 (-10)
7.9 + x
-79
Answer:
7.9 + x because all the others are equal to.each other
Solve the Following inequality by choosing the Possible range of Values that make the Statement True
x + 3 ≥ 13
Answer:
x has to be greater than or equal to 10 (x ≥ 10)
Step-by-step explanation:
x + 3 ≥ 13
x ≥ 13 - 3
x ≥ 10
A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly, and I choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and I again choose a card at random, observe its color, and replace it in the set. This is done a total of four times. Let X be the number of red cards observed in these four trials. The mean of X is:
Answer:
The mean of X is 2
Step-by-step explanation:
Given the data in the question;
set of 10 cards consist of 5 red card and 5 blacks
cards are chosen, replaced and shuffled four times;
number of independent trials n = 4
now, since its is replaced, the probability of getting a red card in each trial will be;
p = 5/10 = 0.5
let X rep the number of red cards observed in the four trials.
the random variable follows binomial distribution where
n = 4 and p = 0.5
so
E(X) = ∑xP( X = x )
E(X) = np
we substitute
E(X) = 4 × 0.5
E(X) = 2
Therefore, The mean of X is 2
Which expression is equivalent to ( + )?
Answer:
No entiendo que es lo que hay qué hacer
Mrs. Nesbitt had 97 books in her classroom library she received a grant to expand her classroom library After spending the money she had 213 books what is the percent increase?
Answer:
219 percent
Step-by-step explanation:
97 goes into 213 two times which is a 200 percent increase which leaves 18 books. 18.5 percent of 97 is about 18 so rounded up it is a 219 percent increase
Please help me
Adjust to compatible numbers that count by 50s, and then subtract to
estimate the difference.
301 - 52 =
Answer:
249
Step-by-step explanation:
301 - 52 = 249
Help please !! need it asap
What is the next term in the sequence below?
0.35, 1.05, 3.15, 9.45, …
A. 15.75
B. 27.75
C. 28.35
D. 85.05
Answer:
Its C
Step-by-step explanation:
someone please help me answer this!!
Answer:
8 units is the answer.
Step-by-step explanation:
Pythagorean theorem can be written as,
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(9-9)^2 + (-7-1)^2}\\\\d=\sqrt{(0\\)^2+(-8)^2} \\\\d=\sqrt{64} \\\\d=8[/tex]
∴ d = 8 units
Wat is a mixed number or whole number: 11/3
Answer:
Not exactly sure what your asking but 11/3 as a mixed number is 3 2/3
Answer:
3 2/3 is the simplified version of 11/3
Step-by-step explanation:
3. What is the axis of symmetry of the graph of function f(x) = x² - 6x – 1
Answer:
guihnijiop;kl;lkm
Step-by-step explanation:
Answer:
A parabola has an axis of symmetry at x = 3 if the x-value of the vertex is 3.
f(x) = x^2 + 3x + 1 = x^2 + 3x + 9/4 - 5/4 = (x + 3/2)^2 - 5/4 => vertex = (-3/2, -5/4)
f(x) = x^2 - 3x - 3 = x^2 - 3x + 9/4 - 21/4 = (x - 3/2)^2 - 21/4 => vertex = (3/2, -21/4)
f(x) = x^2 + 6x + 3 = x^2 + 6x + 9 - 6 = (x + 3)^2 - 6 => vertex = (-3, -6)
f(x) = x^2 - 6x - 1 = x^2 - 6x + 9 - 10 = (x - 3)^2 - 10 => vertex = (3, -10)
Therefore, f(x) = x^2 - 6x - 1 has an axis of symmetry at x = 3.
Step-by-step explanation:
plz mark me as brainlist
Help. I have no idea what to do
Answer: The answer is to ask your parents because something is definitely wrong with your teacher to give such a hard sun to solve like that.
Step-by-step explanation: sorry man that hard.
Imagine you deposit $4,500 into an account that pays 5,5 percent interest compounded
daily. How much interest will you earn in 30 days?
Answer:
500
Step-by-step explanation:
I don't know what to do I'm very confused
Answer:
x = 33.8°
Step-by-step explanation:
The resulting diagram we have is a right triangle. To find x, apply trigonometric function.
Reference angle = x
Opposite = 116
Adjacent = 173
Apply TOA:
Tan x = Opp/Adj
[tex] tan (x) = \frac{116}{173} [/tex]
[tex] x = tan^{-1}(\frac{116}{173}) [/tex]
[tex] x = tan^{-1}(\frac{116}{173}) [/tex]
x = 33.8° (nearest tenth)
