Part A
To shift the curve 3 units to the right, we'll replace x with x-3. What this does is move the xy axis 3 units to the left. If we held the curve in place as the axis moves, then it gives the illusion the curve is moving 3 units to the right.
[tex]f(x) = x^2 + 5\\\\f(x-3) = (x-3)^2 + 5\\\\g(x) = (x-3)^2 + 5\\\\[/tex]
Do not expand out the (x-3)^2 term, because you want to keep the function in vertex form. The old vertex of (0,5) moves three units to the right to arrive at (3,5)
Answer: [tex]g(x) = (x-3)^2 + 5[/tex]==============================================================
Part B
We use the same idea as before. This time we're moving the curve 10 units to the left, so we'll replace x with x+10
[tex]f(x) = x^2 + 5\\\\f(x+10) = (x+10)^2 + 5\\\\g(x) = (x+10)^2 + 5\\\\[/tex]
Multiply and simplify: (1 + 5i)(3 - 8i)
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]
89. 70 is what percent of 350?
Step-by-step explanation:
100% = 350
1% = 100%/100 = 350/100 = 3.5
how many % are 70 ? well, as many as often 1% fits into 70 :
70/3.5 = 20%
Luke gets paid $13/hour. He got an
additional bonus of $50 for staying late one
day. He got paid $641.50 this month.
Write an equation, define your variable and
solve. How many hours did he work?
Answer:
13x+50=641.50, where x is the about of hours Luke worked. (x=45,5[h])
Find the MAD:
98, 140, 220, 150
Answer:
I'm not too sure but I think It's 34
Step-by-step explanation:
Rusty in that particular area of math
Pls help will give brainilist
Answer:
Item #1
[tex]-\frac{27}{8}[/tex] fraction form
[tex]- 3.375[/tex] decimal form
[tex]-3\frac{3}{8}[/tex] mixed number
Item #2
$7.98 (rounded to nearest cent)
Help with these circle equation questions? will reward brainly
Answer:
Step-by-step explanation:
The coordinates of the vertices of quadrilateral HIJK are H (-2, -1), I (2, 1), J (5, 0), and K (-1, -3). Isabella states that quadrilateral HIJK is a parallelogram. Is Isabella correct? Support your answer and show all work.
Answer:
Step-by-step explanation:
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. which equation can be used to find the number of seconds it takes the object to hit the ground? 0 = –4.9t2 19.6t 24.5 0 = –4.9t2 24.5t 19.6 19.6 = –4.9t2 24.5t 24.5 = –4.9t2 19.6t
Check the picture below.
[tex]~~~~~~\textit{initial velocity in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&19.6\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&24.5\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-4.9t^2+19.6t+24.5\hspace{5em}\stackrel{\textit{when it hits the ground}}{0=-4.9t^2+19.6t+24.5}[/tex]
Answer:
A
Step-by-step explanation:
A runner ran a 400 m race in 1 min 35 sec. Calculate his average speed in m/sec.
Step-by-step explanation:
distance = 400m
time taken = 1 min 35 sec = 95 sec
average speed = 400m / 95 sec = 4=2105 m/ sec
Answer:
4.21 m / sec.
Step-by-step explanation:
1 min 35 sec.
= 60 + 35
= 95 sec.
So average speed = 400/95
= 4.21 m / sec.
I need help, please and thank you
Answer:
1 and 1/12
hope this helped
GUYS PLEASE HELP LIKE ASAP
What is the mean, median, mode, and range of the
following data set? Be sure to label which
measurement you are referring to.
7,9,6,9, 7, 4,7
Answer:
if im not wrong all answers are 7
Step-by-step explanation:
if you add all the numbers u get 49 and if u divide by 7 cuz u have seven numbers. you should get 7 thats you mean. then for median if u put them from least to greatest ur middle number would still be seven and then your mode would be seven since seven shows up the most.
What would be the volume of a sphere with a radius of 16 yd
Answer:
v=13117.69 m3
Step-by-step explanation:
Hope this helps.
Answer:
The answer is 803.84
Step-by-step explanation:
Carry on learning i hope this helps..
9000 dollars is placed in an account with an annual interest rate of 8% how much will be in the account after 17 years to the nearest cent
Last year, sam’s swimming pool cleaning had a gross profit of $105,355 and net income of $72,010. calculate sam’s operating expenses for last year. a. $3,335 b. $33,345 c. $17,734 d. $177,345 please select the best answer from the choices provided a b c d
Sam’s operating expenses for last year given the gross profit and the net income is $33,345.
What is the operating expense?Operating expense is the expense that a company incurs in the course of running its business. It is determined by subtracting net income from gross profit.
Operating expense = gross profit - net income
$105,355 - $72,010 = $33,345
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Answer:
B
Step-by-step explanation:
Use the diagrams to determine which statements are true. Select all statements that are true.
Answer:
I don't see your questions.
Egypt. Africa. America
Someone help, will give brainliest.
The correct answer is option C which is nine more than two-fifths of the number is nine.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.
The given expression is:-
( 2 / 5) x + 9 = 9
The expression can be written in the words nine more than two-fifths of the number is nine.
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Select all the correct figures.
Which figures show starting steps in the construction of an equilateral triangle?
The angle of elevation from a soccer ball on the ground to the top of the * 1 poi
goal is 34°. If the goal is 8 feet tall, what is the distance from the ball to
the goal?
Answer:
11.86
Step-by-step explanation:
A, B & C form a triangle where Z
BAC = 90°.
AB = 3.3 mm and CA = 7.7 mm.
Find the length of BC, giving your
answer rounded to 1 DP.
Answer:
BC≈8,38
Step-by-step explanation:
AB=a
BC=c
CA=b
a²+b²=c²
3.3²+7.7²=c²
√70,18=√c²
c≈8,38
please I really need help
Answer:
C=12
Step-by-step explanation:
The interior angle of a polygon is 360.
So just add them all up.
(3c-29)+(127)+(c+43)+(c+43)+(2c+36)+(c+44)=360
Combine like terms
8c+264=360
Simplify
8c=96 . Divide both sides by 8
C=12
39-50 find the limit.
41. [tex]\lim _{t \rightarrow 0} \frac{\tan 6 t}{\sin 2 t}[/tex]
Write tan in terms of sin and cos.
[tex]\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}[/tex]
Recall that
[tex]\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1[/tex]
Rewrite and expand the given limand as the product
[tex]\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)[/tex]
Then using the known limit above, it follows that
[tex]\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}[/tex]
Complete this statement:
THIS IS EASY BUT PLEASE HELP ME IM BIT SLOW
Answer:
A: Isosceles (two sides the same)
B: Equilateral (all sides the same)
C: Scalene (all sides different)
Step-by-step explanation:
9. Find the slope of the line between the
coordinates (-6, -13) and (3, -1).
H.
F.
G.
314 43
J.
3/4 4/3
Answer:
The slope is 4/3
Step-by-step explanation:
The solution is in the image
Which number added to -14 will equal 9?
Answer:
23
Add positive 14 and 9 to get 23
14 + 9 = 23
-14 + 23 = 9
RIGHT ANSWER GETS BRAINLIST WORTH 30+ POINTS
Two number cubes are rolled.
What is the probability that the first lands on 6 and the second lands on an even number?
Select your answer, as a fraction in simplified form.
Question 5 options:
1/6
2/6
1/12
1/3
Answer:
Hi. Here is your answer:
1/6
Step-by-step explanation:
this is because 1/6 is equal to 5/30 of your answer.
here is proof.
which school do you go to?
Hope this helps
Brainliest please
Have a great day
Please fully rate!
The probability that the first lands on [tex]6[/tex] and the second lands on an odd number is [tex]\frac{1}{12}[/tex]
Calculation of the probabilities:Since The probability of rolling a [tex]6[/tex] should be [tex]\frac{1}{6}[/tex] because there are [tex]6[/tex] total numbers.
Now The probability of rolling an odd number is [tex]\frac{1}{2}[/tex], since there are an equal number of odd and even numbers on a die.
Now the final probability should be
[tex]=\frac{1}{6}*\frac{1}{2}[/tex]
[tex]=\frac{1}{12}[/tex]
Therefore, The probability that the first lands on [tex]6[/tex] and the second lands on an odd number is [tex]\frac{1}{12}[/tex]
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109, 94, 87, 103, 89, 112, 98, 115, 99 Find the lower quartile
109, 94, 87, 103, 89, 112, 98, 115, 99 Find the median.
2 QUESTIONS TO ANSWER PLEASE ANSWER THIS ASAP WILL GIVE BRAINIEST
Answer:
Below in bold.
Step-by-step explanation:
109, 94, 87, 103, 89, 112, 98, 115, 99
First arrange them in ascending order.
87 89 94 98 99 103 109 112 115
The median is the middle value:
= 99.
The lower quartile
= (89+94) / 2
= 183/2
= 91.5.
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:1,024
Step-by-step explanation:
We will use the formula hint it gives:
[tex]\displaystyle {1^{st}\;term} * \text{common ratio}\,^{(\text{desired term -1})}[/tex]
[tex]-1 * -4^{6-1}[/tex]
[tex]-1 * -4^{5}[/tex]
[tex]-1*-1,024[/tex]
[tex]1,024[/tex]
The 6th term in the sequence is 1,024.
The water usage at a car wash is modeled by the equation w(x) = 3x3 4x2 − 18x 4, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 2x3 2x2 − 18x − 11 c(x) = 3x3 2x2 − 18x 11 c(x) = 3x3 2x2 − 18x − 11 c(x) = 2x3 2x2 − 18x 11
A function, c(x), that models the water used by the car wash on a shorter day is C(x) = 4x³ + 7x² − 14x - 6
Calculations and Parameters:Given:
The amount of water used in normal days:
W(x) = 5x³ +9x²-14x +9 -----(i)The amount of decrease in water used is modeled by the equation;
D(x)= x³+2x² +15--------(ii)To find the function C(x), we would have to subtract eq(ii) from eq(i)
5x³ +9x²-14x +9
- x³+2x² +15
= C(x) 4x³+7x²-14x-6
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Someone pls do this for me I give Brainly
Answer:
Kindly read through
Step-by-step explanation:
All have been solved step by step
