Answer:
x = 6
Step-by-step explanation:
Solve for x:
36 (x - 5) = 9 x - 18
Expand out terms of the left hand side:
36 x - 180 = 9 x - 18
Subtract 9 x from both sides:
(36 x - 9 x) - 180 = (9 x - 9 x) - 18
36 x - 9 x = 27 x:
27 x - 180 = (9 x - 9 x) - 18
9 x - 9 x = 0:
27 x - 180 = -18
Add 180 to both sides:
27 x + (180 - 180) = 180 - 18
180 - 180 = 0:
27 x = 180 - 18
180 - 18 = 162:
27 x = 162
Divide both sides of 27 x = 162 by 27:
(27 x)/27 = 162/27
27/27 = 1:
x = 162/27
The gcd of 162 and 27 is 27, so 162/27 = (27×6)/(27×1) = 27/27×6 = 6:
Answer: x = 6
cotA/tanA simplify each question
[tex]\bf \cfrac{cot(A)}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{\frac{tan(A)}{1}}\implies \cfrac{1}{tan(A)}\cdot \cfrac{1}{tan(A)} \\\\\\ \cfrac{1}{[tan(A)]^2}\implies \cfrac{1}{tan^2(A)}\implies \cfrac{1^2}{tan^2(A)}\implies \left( \cfrac{1}{tan(A)} \right)^2\implies cot^2(A)[/tex]
Final answer:
To simplify cotA/tanA, we recognize that cotA is the reciprocal of tanA. The expression simplifies to cosA^2/sinA^2, which can also be written as cotA^2.
Explanation:
To simplify the expression cotA/tanA, we can use the fundamental trigonometric identities that relate the cotangent and tangent functions. The cotangent function, cotA, is the reciprocal of the tangent function, tanA, which means cotA = 1/tanA. Therefore, when we simplify cotA/tanA, we are effectively dividing the reciprocal of the tangent function by the tangent function itself.
The simplification would thus be:
cotA/tanA = (1/tanA)/tanA = 1/(tanA^2)Since tanA = sinA/cosA, the expression can be rewritten as[tex]1/((sinA/cosA)^2)[/tex]Therefore, cotA/tanA simplifies to [tex]cosA^2/sinA^2, or cotA^2.[/tex]Solve this system of equations using the substitution method. If the system of equations
does not have one solution, indicate whether the system has no solution or infinitely
many solutions.
3x+y=5
4x + 2y = 20
Answer:
well i dont really get ehat yours saying but the qustions are
3x+y=5
3^1+1=5
and then
4z+2y=20
i think
4^6+2^6=20
Step-by-step explanation:
im really stuck :( can someone please help me ? it would mean a lot
Answer:
Step-by-step explanation:
Populations is who is surveyed or what the questions is targeting. More specifically who. That would be households with a car.
Use what I put as the definition for population to answer the other questions!
[Question Image Attached] If you are given the graph of g (x) = log 2 x, how could you graph f (x) = log 2 x + 5?
Answer:
Translate each point of g(x) 5 units up.
Step-by-step explanation:
The given the graph of the parent function
[tex]g(x) = log_{2}(x) [/tex]
We want to use this graph to draw the graph of
[tex]f(x) = log_{2}(x) + 5[/tex]
We can observe that:
[tex]f(x) = g(x) + 5[/tex]
This means the graph of the parent function, g(x) must be shifted up 5 units.
Therefore the correct answer is A.
The loan that Nate and Isaac got from their parents was at 2% interest for one year. How much will the boys pay in interest on their loan of \$2,500 ? Show your work .
Answer: they will have to pay 50 dollars
Step-by-step explanation: you have to multiply 2,500 by 0.02 as it is the same as a percent then you should get 50
10. Write an equation in slope-intercept form for a line that is perpendicular to the line
y= 2/5x +1
Step-by-step explanation:
Equation of given line is:
[tex]y = \frac{2}{5} x + 1 \\ equating\: it \: with \: y = m_1x + c, \:we\:find \\ slope \: of \: given \: line \: (m_1 )= \frac{2}{5} \\ y - intercept \: (c) = 1 \\ let \: the \: slope \: of \: required \: line \: be \: m_2. \\ \therefore \: m_1 \times m_2 = - 1..( \because \: lines \: are \: \perp) \\ \therefore \: \frac{2}{5} \times m_2 = - 1 \\ \therefore \:m_2 = - \frac{5}{2} \\ \\ equation \: of \: required \: line \: in \: slope \: \\intercept \: form \: is \: given \: as: \\ y = m_2x + c \\ \huge \orange{ \boxed{\therefore \: y =- \frac{5}{2}x + 1}} \\ [/tex]
A town has a population of 20000 and grows at 6% every year. What will be the population after 6 years to the nearest whole number
Answer:
27200 rounded will be 30000
Step-by-step explanation:
firstly you find 1% which is 200
then you multiply by 6 to get 6%
then you multiply by 6 again to get the total
-3 x [75/(9 - 4)^2]^2 simplify
Answer:
[tex]-27x[/tex]
Step-by-step explanation:
Given Equation:
[tex]-3 x [75/(9 - 4)^2]^2[/tex]
On simplifying the equation:
[tex]=-3 x [75/(9 - 4)^2]^2\\=-3 x [75/(5)^2]^2\\=-3 x [75/25]^2\\=-3 x [3]^2\\=-3x*9\\=-27x[/tex]
The value of 'x' can be find by equating the simplified value to some certain value according to the equation.
Beginning from a depth of 35 feet below the surface, a whale swims
upward and jumps to a height of nearly 17 feet above the surface.
a. Model with Math Use an inequality to model the possible change in the number of feet, r, of the whale's elevation.
b. Solve the inequality. Explain the meaning in terms of the situation.
a. The inequality that models the possible change in the number of feet, r, of the whale's elevation is: 35 - r ≤ 17.
This inequality represents the starting depth of 35 feet below the surface (35), minus the possible change in elevation (r), which should be less than or equal to the maximum height the whale jumps, which is nearly 17 feet above the surface (17).
b. By solving the inequality 35 - r ≤ 17, we can find the range of possible values for r.
First, subtract 35 from both sides of the inequality: -r ≤ 17 - 35. Simplifying further, we have -r ≤ -18. Then, multiply both sides by -1, remembering to reverse the inequality direction: r ≥ 18.
The solution to the inequality is r ≥ 18, meaning that the possible change in the number of feet of the whale's elevation must be equal to or greater than 18. This implies that the whale's jump cannot be less than 18 feet above the surface.
Therefore, the whale's elevation can change by any value equal to or greater than 18 feet, allowing it to jump to a height of nearly 17 feet above the surface.
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a) The inequality can be written as 35 - r ≤ 17. b) The solution to the inequality is r ≥ 18, which means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.
a.
Since the whale swims upward and jumps to a height of nearly 17 feet above the surface, we can represent the change in elevation as r.
The inequality can be written as:
35 - r ≤ 17
Here, 35 represents the starting depth below the surface, and 17 represents the height above the surface that the whale reaches.
By subtracting r from the starting depth, we account for the possible decrease in elevation as the whale swims upward.
b. To solve the inequality, we can isolate r on one side of the equation:
35 - r ≤ 17
Adding r to both sides of the inequality:
35 - r + r ≤ 17 + r
35 ≤ 17 + r
Subtracting 17 from both sides:
35 - 17 ≤ 17 + r - 17
Simplifying further:
18 ≤ r
Therefore, the solution to the inequality is r ≥ 18.
In terms of the situation, the inequality r ≥ 18 means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.
This indicates that as the whale swims upward and jumps to a height of nearly 17 feet above the surface, the whale's elevation can increase by at least 18 feet from its starting depth of 35 feet below the surface.
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The two circles shown above have radii of 2 in. and 6 in.
What is a circum A over b?
Answer:
1/3
Step-by-step explanation:
For the first circle 2 x 2in = 4 to find diameter
4 x 3.14 = 12.56
6in x 2 = 12
12 x 3.14 = 37.68
simplify
12.56/37.68
6.28/18.84
3.14/9.42
So the answer is 1/3 since 3.14 x 3 = 9.42
Also since the radius is 3 times longer
Answer:
1/3
Step-by-step explanation:
Find the coordinates of the reflected image.
A rectangle with vertices L(1, -1), M(1, -9). N(8.-9), and
(8.-1) is reflected over the y-axis.
1.)L'(-1.-1), M'(-1, -9), N'(-8.-9), and 0%(-8, -1)
2.)L (1.-1), M'(1.-9), N'(8.-9), and Oʻ(8.-1)
3.)L'(-1.–1). M?(-9,-1). N'(-9.–8). and O'(-1, -8)
4.)L'(-1. 1). M'(-1.9), N'(-8. 9), and O'(-8.1)
Answer:
The actual answer is A or 1 as you have it.
Step-by-step explanation:
All you have to do is just map out the coordinates yourself. You're looking for a reflection that goes across the Y axis, but NOT across the X axis.
Hope this helps you and anyone looking for an answer to their headache.
Final answer:
The reflected coordinates of the rectangle over the y-axis are L'(-1, -1), M'(-1, -9), N'(-8, -9), and O'(-8, -1), matching option 1.
Explanation:
The student is asking about finding the coordinates of a rectangle's vertices after it has been reflected over the y-axis. Reflecting a shape over the y-axis changes the sign of the x-coordinate of each vertex, while the y-coordinate remains the same. So, if we have a point (x, y), the reflected point over the y-axis would be (-x, y). Applying this to the rectangle's vertices we have:
For L(1, -1), the reflection L' would be (-1, -1).
For M(1, -9), the reflection M' would be (-1, -9).
For N(8, -9), the reflection N' would be (-8, -9).
For O(8, -1), the reflection O' would be (-8, -1).
Therefore, the correct reflected coordinates are L'(-1, -1), M'(-1, -9), N'(-8, -9), and O'(-8, -1), which corresponds to option 1.
sally works 40 hours a week and makes $10 an hour, but her kids are in child care each day, and the day care center charges her $20 per day. If you deduct her childcare expenses, how many dollars per hour does she actually make?
Answer:
She makes $60 per hour
Step-by-step explanation:
There are 5 days in a week and 40 divided by 5 is 8 and 8x10=80 and 80 subtracted by 20 gives you 60.
Final answer:
After deducting childcare expenses, Sally's actual hourly wage is $7.50 per hour.
Explanation:
The original question is about calculating Sally's actual hourly wage after accounting for childcare expenses. Sally works 40 hours a week and earns $10 per hour. However, she incurs a cost of $20 per day for childcare. Assuming she works 5 days a week, her weekly childcare expenses are $20 x 5 = $100. Therefore, her weekly take-home pay after childcare is (40 hours x $10/hour) - $100 = $400 - $100 = $300. Now, to find Sally's actual hourly wage after childcare expenses, divide her take-home pay by the number of hours worked: $300 / 40 hours = $7.50 per hour.
Solve the equation: x/2-18=(-28)
Answer:
x = -20
Step-by-step explanation:
First we can rearrange the equation:
[tex]\frac{x}{2}[/tex] -18 = -28
2 * [tex]\frac{x}{2}[/tex] - 18 = -28 * 2
The 2s canel out
x - 36 = - 56
x = -20
(12) Geographers use negative numbers to represent points below sea level and positive numbers for points above 1
level. A penguin dove 5 meters below sea level to catch fish for his family, who are sitting on an Iceberg 1 meter above
sea level. What is the difference in elevation between the family and the penguin?
Please!
Difference in elevation is 6 meters.
Answer: -4
Step-by-step explanation: -5 + 1= -4
The dimensions of a box are (x + 1), (4x - 2), and
(3x + 4). What is the volume of the box?
Answer:
Volume of box = 12x³ + 10x² - 14x - 8
Step-by-step explanation:
Volume of box = Length × Width × Height
Volume of box = (x + 1) (4x - 2) (3x + 4)
Volume of box = (4x² - 2x + 4x - 2) (3x + 4)
Volume of box = (4x² - 2x - 2) (3x + 4)
Volume of box = 12x³ + 10x² - 14x - 8
Answer:
12x^3+22x^2-2x-8
Step-by-step explanation:
i took the test ^^
What are the solutions to the equation x2 + 4x + 5 = 0?
Answer:
no answer
Step-by-step explanation:
x^2+4x+5=0
(x+2)^2+1=0
(x+2)^2=-1
this is impossible,
so this equation has no answer
Answer:
Step-by-step explanation:
What is the algebraic expression for b divided by 9
Answer:b/9
Step-by-step explanation: the expression b divided by 9 is b/9
Answer: b ÷ 9
Step-by-step explanation:
Well, since the question is to write an expression for b divided by 9, you just write b divided into 9 parts.
NOTE: Remeber, an expression is an equation but WITHOUT an answer.
Hope this helps! Please feel free to correct me if I'm wrong!
Which of the following is a complex number?
-7
2 + StartRoot 3 EndRoot
4 + 9i
Pi
Answer:
4 + 9i
Step-by-step explanation:
a complex number by definition must have a real and imaginary components
imaginary components are denoted by the letter i, where i = √(-1)
the only choice with a real and imaginary components is 4 + 9i
Answer:
4 +9i
Step-by-step explanation:
trust me bro
What is the solution to this system of equations?
2x - y = 8
x + y = 4
A. (2, -4)
B. (4, 0)
C. (6, 4)
D. (12, -8)
Answer:
Answer is B. (4,0)
Step-by-step explanation:
2x - y = 8
x + y = 4
solve the equation
2x - y = 8
y = 4 - x
substitute the value of y into the equation
2x - (4 - x) = 8
solve the equation
x = 4
substitute the value of x into an equation
y = 4 - 4
solve the equation
y = 0
answer is (4,0)
Pam has 24 pencils and 6 erasers. How many times as many pencils as erasers does Pam have?
Answer:
Pam had 4 times as many pencils as erasers
Step-by-step explanation:
24 pencils
6 erasers
24 pencils = x * 6 erasers
Divide by 6 on both sides to isolate x
x = 4
Pam had 4 times as many pencils as erasers
Hope this helps :)
Write an equation to solve for h. Check your answer.
__________________
| |
| | h Area = 96 ft
| | A = bh
----------------------------------
8 ft h = __________
A/b= h
h=12 ft
Step-by-step explanation:
The formula for area is given as ;
A=b*h
A/b= h .................equation for h
If Area=96 ft² and b =8 then h=96/8 =12 ft
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- Cindy spent $6 on her meal. She spent $4
on a sandwich and the rest on a smoothie.
How many smoothies could be bought
with $124?
Answer:
She can buy 62 smoothies
Step-by-step explanation:
What is 671 divided by 4 with remainders
add blank to each side of x^2-8x=9
Step-by-step explanation:
To complete the square, take half of the second coefficient, square it, then add the result to both sides.
(-8/2)² = (-4)² = 16
x² − 8x + 16 = 9 + 16
Solving:
(x − 4)² = 25
x − 4 = ±5
x = 4 ± 5
x = -1 or 9
Answer:
part 1: x^2 + -8 x=9
part 2: Add 16 to each side
part 3: (x-4)^2 =25
part 4: -1 and 9
the answer for this question someone answer fast pleaseeee
Answer:
???
Step-by-step explanation:
you don't have a question to answer
The _______ represents the number of standard deviations an observation is from the mean.
Answer:
The z-score represents the number of standard deviations an observation is from the mean.
Step-by-step explanation:
We want to complete the statement:
The _______ represents the number of standard deviations an observation is from the mean.
Whenever we calculate z- scores, we are finding how many standard deviations an observation is from the mean.
A z-score of 3, means an observation is 3 standard deviation above the mean.
Therefore the best complete is:
z-score.
The Z-score represents the number of standard deviations an observation is from the mean. It provides a comparative measure that standardizes data, making it easier to compare data from different sets.
Explanation:The Z-score represents the number of standard deviations an observation is from the mean. In statistics, it is a way to compare the position of any observation relative to the overall distribution.
Here's an example: if a Z-score of a data point is 2, it means that the data point is 2 standard deviations above the mean. Conversely, if a Z-score of a data point is -1, it means that the data point is 1 standard deviation below the mean.
Z-scores provide a standardized way to interpret data, which makes the comparison of different data sets more straightforward and undistorted by differences in units or scales.
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2) On a map two points are 7cm apart. The map has a scale of 1:10000. Work out the
actual distance. Give your answer in km.
Answer:
0.7 km
Step-by-step explanation:
Actual distance in cm = 7(10000)
= 70 000 cm
Actual distance in km = 0.7 km
Answer:
0.7
Step-by-step explanation:
There are 15 vocabulary words in Week I. There are 8 more vocabulary words in Week 2 than in Week I. How many words are there in both weeks?
Answer:
There are 38 vocab. words in both weeks
Step-by-step explanation:
There are a few steps to this problem:
First, we know that there are 15 vocab. words in week 1.
Then, in week 2 there are 8 more words than in week 1. So that means 15+8 which equals 23.
Finally, we know that there were 15 words in the first week, and 23 in the second week. So now how many words were there in both weeks? To answer that, you add the number of words in the first week, to the number of words to the second week.
23 + 15 = 38 words total in both weeks
What is the simplified answer for 8w = 5
Answer:
w = 5/8
Step-by-step explanation:
divide by 8 to both sides to get 8/8w = 5/8
8/8 = 1, w = 5/8.
Answer:
W= 5/8
Step-by-step explanation:
divide both sides by 8
at sal's carshop the salesman make 15 commission on every car they sell. If the dealership buys a car for $16,235 and the salesman sells the car for $22,245 how much is their commission ?
The salesman's commission for selling a car at Sal's car shop is $901.50.
To calculate the salesman's commission for selling a car at Sal's car shop, we must first determine the sale price's profit margin over the dealership's purchase price. The profit is found by subtracting the purchase price ($16,235) from the selling price ($22,245).
Profit = Selling Price - Purchase Price
Profit = $22,245 - $16,235
Profit = $6,010
Next, we calculate the commission by taking 15% of the profit:
Commission = Profit * Commission Rate
Commission = $6,010 * 0.15
Commission = $901.50
Therefore, the salesman's commission for selling the car is $901.50.