Parts of Complex Numbers
z=4.1i+85
Re(z)=_____
Im(z)=_____
John Street Barber Shop pays $25 per month for water for the first 8,000 gallons and $3.50 per thousand gallons above 8,000. Calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons.
Final answer:
The John Street Barber Shop pays a flat rate of $25 for the first 8,000 gallons of water, with an additional charge of $3.50 per thousand gallons above this threshold. Accordingly, the total costs for using 7,000 gallons is $25, for 10,000 gallons is $32, and for 13,000 gallons is $42.50.
Explanation:
The John Street Barber Shop pays $25 per month for the first 8,000 gallons of water and $3.50 per thousand gallons above 8,000 gallons. To calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons, we follow this methodology:
For 7,000 gallons, since it's below 8,000 gallons, the cost is just the flat rate of $25.For 10,000 gallons, the cost is $25 for the first 8,000 gallons, plus $3.50 for each of the 2,000 gallons above 8,000. This gives $25 + ($3.50 * 2) = $32.For 13,000 gallons, the cost is $25 for the first 8,000 gallons, plus $3.50 for each of the 5,000 gallons above 8,000. This gives $25 + ($3.50 * 5) = $42.50.Thus, the total costs for using 7,000 gallons, 10,000 gallons, and 13,000 gallons are $25, $32, and $42.50 respectively.
NEED HELP ASAP PLEASE HELP
Find m
Select one:
a. 120°
b. 100°
c. 90°
d. 80°
What is the value of x?
Enter your answer, as a decimal, in the box.
HELP!!! Which of the following is not a perfect square trinomial? A. 169 – 26y + y2 B. 81 + 18y + y2 C. 64 + 8y + y2 D. 25 + 10y + y2
What happens to the area when the perimeter of square efgh efgh is doubled? explain.answers?
Choose the option that correctly completes the statement.
A triangle has a total of ______ exterior angles.
six
nine
three
Answer:
The correct option would be 6 exterior angles in a Triangle.
Which function represents a reflection of f(x) = 2(0.35)x over the y-axis? h(x) = 2(0.35)x h(x) = –2(0.35)x h(x) = 2(0.35)–x h(x) = 2(–0.35)–x
Answer:
Step-by-step explanation:
c
What is 59.69 in expanded form
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Figure 1)
a) The area is A = 36( π - 2) ст²
b) The perimeter is P = 6 (π + 2√2) [tex]cm^2[/tex]
Figure 2)
a) The area is A = 576 cm²
b) The perimeter is P = 24(π+2) [tex]cm^2[/tex]
Figure 1)
a) To find the area of the figure 1 we have to do the substraction
The area of figure 1 is equivalent to the area of a triangle less the area of a quarter circle.
The area of quarter circle is equal to
A = 2
we have
r = 12 cm
Put the value r as given
A = (12)2
A = 36 [tex]cm^2[/tex]
Area of a triangle formula is
A = (b)(h)
Given information,
b=12 cm
h = 12 cm
substitute
A = (12) (12)
A = 72 cm²
therefore
The area of the figure is
A = (36π - 72) [tex]cm^2[/tex]
Simplify
A = 36(π -2) [tex]cm^2[/tex]
b)
The perimeter of the figure 1 is equal to the circumference of a quarter circle plus the side AC of triangle
The perimeter of a quarter of circle is formula
C = 2πr
simplify
C = r
we have
r=12 cm
substitute
C = (12)
C = 67 cm
Find the length side AC
Applying the Pythagorean Theorem
[tex]AC^2 = 12^2 + 12^2[/tex]
[tex]AC^2 = 144+ 144\\AC^2 = 288\\AC = \sqrt{288}[/tex]
AC = 12√2 cm
P = (6π +12√2) cm
Taking 6 as a common multiplier we get
P = 6(π+2√2)
The perimeter of the figure 1 is
P = 6(π+2√2) cm
Part 2)
a) As we can see,
The area of a semicircle plus the area of a square less the area of a semicircle equals the area of figure 2.
The figure's area and the square's area are equal.
A = [tex]24^2[/tex]
A = 576 cm²
b) Find the perimeter of the figure 2
we know that
The perimeter of the figure 2 is equal to the length side AB plus the length side DC plus the circumference of two semicircles
The perimeter of the figure 2 is equal to two times the length side AB plus the circumference of one circle
P = 2(AB) + π D
P = 2(24) + π(24)
P = 48 + π(24)
Take out 24
P = 24 (2 + π ) cm
Triangle FGH is similar to JKM.
If f = 14.4 cm, g = 16.56 cm, h = 25.92 cm, and k = 9.2 cm, what is the measure of m?
A. 5.104 cm
B. 14.4 cm
C. 10.58 cm
D. 8 cm
which statement about sqrt x-5 minus sqrt x=5 true?
-3 is a true solution
-3 is a extraneous solution
9 is a true solution
9 is a extraneous solution
Answer:
9 is an extraneous solution.
Step-by-step explanation:
Extraneous solution is a solution that when plugged into the equation do not hold true.
Here we are given an algebraic equation in terms of single variable x as:
[tex]\sqrt{x-5}-\sqrt{x}=5-----(1)[/tex]
Now, we will solve this equation to obtain the solution as:
on squaring both side of the equation we obtain:
[tex](\sqrt{x-5}-\sqrt{x})^2=5^2[/tex]
[tex]x-5+x-2\sqrt{x-5}\sqrt{x}=25\\\\2x-5-2\sqrt{x-5}\sqrt{x}=25\\\\2x-30=2\sqrt{x-5}\sqrt{x}\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=\sqrt{x-5}\sqrt{x}[/tex]
Again on squaring both side of the equation we obtain:
[tex]x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9[/tex]
Now when we plug x=9 back to the original equation i.e. equation (1) we get:
[tex]\sqrt{9-5}-\sqrt{9}=5\\\\\sqrt{4}-\sqrt{9}=5\\\\2-3=5\\\\-1=5[/tex]
Hence, the equation does not hold true.
Hence, 9 is a extraneous solution
If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.
Raul used the steps shown below to solve the equation. In which step did Raul make a mistake?
5x-3(2x+7)=2x+9
Step 1: 5x-6x-21=2x+9
Step 2: -11x-21=2x+9
Step 3: -12x=30
Step 4: x=-30/12
A. Step 1
B. Step 2
C. Step 3
D. Step 4
5x-3(2x+7)=2x+9
This is the equation and Raul had to solve it for x
So he started with simplifying the parenthesis first
To simplify the parenthesis -3 gets multiplied with 2x and 7 , to get rid of parenthesis
So it came out to be
5x-3(2x+7)=2x+9
STEP-1
5x-6x -21 = 2x+9 , So the STEP-1 is correct,
After this in Step -2 , he has combined the like terms on left side, the like terms are 5x and -6x , 5x-6x should combine to -x , because 5-6 = -1
So
STEP-2
-x -21 = 2x+9 , So STEP -2 is INCORRECT
So he made a mistake in STEP-2
After that subtract 2x from both sides
-3x -21 = 9
add 21 to both sides
-3x = 30
divide both sides by -3
x=-10
Hence Option B is correct , he made a mistake in STEP -2
The circumference (C) of a swimming pool is 47 feet. Which formula can you use to find the radius (r) if you know that C = 2πr ?
Answer:
r=C/2*pie
Step-by-step explanation:
I got it correct on TTM
what is the change of entropy for a heat engine using 500.0j at 20.0c
The formula to find change in entropy is given by :
[tex] Change in entropy = \frac{Q}{T} [/tex]
where Q is change in heat and T is temperature.
We are given Q = 500 joule and T = 20 degree C
Plugging these values in the formula,
[tex] Change in entropy = \frac{500}{20} [/tex]
We get change in entropy = 25 J/Celsius.
A 4040 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the shape of a rectangle whose length is twice the width. find the width of the rectangle that will minimize the total area. what is the width of the rectangle that will minimize the total area?
Which expression is equivalent to 8+18a−2+6a? A.24a+6 B.24a + 10 C.8(1+2a)−(2+6a) D.30a
Organize the following expressions from greatest to least by number of terms: x + 2xyz 9x2yz 18x2 + 5ab − 6y 4x3 + 3x2 − x − 4
Answer:
The answer is the option C
IV, III,I,II
Step-by-step explanation:
Find the midpoint of the line segment whose endpoints are (7,5) and (7,11)
Can someone please help me
I would appreciate it please.
I would mark brainliest if its right only.
(Explain)
(Not adding)
Choose the best answer.
For a given distribution the average is 15.5 and the standard deviation is 1.5.
If a sample is taken at random, which value is most likely?
20.2
10.1
16.3
12.9
Answer:
The answer is 16.3
Step-by-step explanation:
For a random distribution with an specific mean and standard deviation, the most probable values are the ones that lie between the ( means + or - standard deviation)
so in this case, the confidence range is:
Low = 15.5-1.5= 14
High = 15.5+1.5= 17
Values that lie between this range are more probable. So in this case 16.3, which is the only value in this range, has higher chance of occuring.
WILL GIVE ABRAINLEST AND 50PTS
Which solution to the equation 3/a+2 + 2/a = 4a-4/a^2-4 is extraneous?
a= -2
a= -2 and a= 4
neither a= -2 and a= 4
a= 4
Answer:
a=-2 is extraneous solution.
Step-by-step explanation:
Given the equation
[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]
we have to find the extraneous solution.
An extraneous solution is a solution to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.
[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]
[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}\\\\\frac{3a+2(a+2)}{a(a+2)}=\frac{4(a-1)}{a^2-4}\\\\\frac{5a+5}{a(a+2)}=\frac{4(a-1)}{a^2-4}[/tex]
On solving, we get
The solution is a=4 and a=-2
Here the solution a=-2 is the valid solution as it makes the denominator 0.
⇒ a=-2 is extraneous solution.
Option 1 is correct.
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How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? 10 25 35 45
What is the sum of the first eight terms of the series?
(−600)+(−300)+(−150)+(−75)+(−37.5)+...
Round the answer to two decimal places.
−1200.50
−1195.31
−1190.63
−1181.25
The given sequence is a geometric series.
Common ratio can be found as :
(-300/-600) = 0.5
(-150/-300) =0.5
So common ratio is 0.5
First term is -600
The attachment shows the required calculations.
Answer: Sum of eight terms is (-1195.31).
The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A' point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?
Answer:
The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).
Step-by-step explanation:
What is reconciling your bank statement?
Answer:
Compare your personal records to the bank's statement
factor the GCF: 15a+25b
The factored form of the expression 15a + 25b with respect to the Greatest Common Factor (GCF) is 5 (3a + 5b). The GCF of 15 and 25 is 5.
Explanation:To factor the Greatest Common Factor (GCF) from 15a + 25b, we first have to identify the GCF. The GCF of 15 and 25 is 5. Hence, we divide each term in the expression by this GCF.
We get: 5 (3a + 5b). So, the expression 15a + 25b factored by the GCF is 5 (3a + 5b).
Learn more about Factoring here:https://brainly.com/question/33624529
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Which expression is equivalent to 6(2m – 1) – 4(m + 8)?
A. 8m – 38
B.8m + 7
C.2m – 38
D.8m + 31
Final answer:
To find the equivalent expression to 6(2m - 1) - 4(m + 8), we first expand and simplify the given expression to 8m - 38, making option A the correct answer.
Explanation:
The question asks which expression is equivalent to 6(2m – 1) – 4(m + 8). To find the equivalent expression, we first expand both terms and then simplify the resulting expression.
First, distribute the 6 in the first expression: 12m - 6.Next, distribute the -4 in the second expression: -4m - 32.Combine like terms: (12m - 4m) + (-6 - 32) which simplifies to 8m - 38.Therefore, the expression that is equivalent to 6(2m – 1) – 4(m + 8) is 8m - 38, which corresponds to option A.