Answer: x = 7
Step-by-step explanation:
15(x+2) = R because they are equal angles.
set 135 = 15(x=2) because they are opposite each other so they equal each other
[tex]\frac{135}{15} =\frac{15(x+2)}{15} \\9 = x+2\\x=7[/tex]
1. Bank AAA is charging 4% in total fees to borrow money for a car loan. You want to buy a car that costs $25,000.
Calculate the total price for the car and the bank fees. Then, find the monthly payment if you get a $5 year loan to buy
the car from Bank AAA?
The total price for the car is $26000.
The monthly payment is $500.
How to calculate the price?From the information illustrated, Bank AAA is charging 4% in total fees to borrow money for a car loan and the person want to buy a car that costs $25,000.
The total amount that will be paid will be:
= Amount of car + Interest
= $25000 + ($25000 × 4%)
= $26000
The amount on a 5 year loan will be:
Interest = PRT
= ($25000 × 4% × 5)
= $5000
Total amount to be paid = $25000 + $5000
= $30000
Monthly payment = Total amount / Number of months
= $30000 / 60
= $500
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use synthetic division
The required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]
In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[3x^3+5x^2-18x+39\right]}{x+4}[/tex].
It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
As performing synthetic division of polynomials, the terms in the product remaining as fractions will be the remainder of the division while the polynomial is said to be the quotient of the division.
[tex]= \frac{\left[3x^3+5x^2-18x+39\right]}{x+4}\\=3x^2-7x+10-\frac{1}{x+4}[/tex]
Thus, the required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]
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Adam is wanting to start saving for retirement but they don’t know how much they can afford to save from their monthly budget. Help Adam find their monthly cash flow.
Adam works at Tim Horton’s making $15/hour, 32 hours a week. (Assume they take no vacations.)
Expenses are: Rent: $650/month, Groceries: $75/week, Utilities: $120/month, Car Insurance: $118/month, Gasoline: $30/week, and Miscellaneous: $400/month
Saving for Retirement (20 Pts)
Now, let’s pretend you are Adam. How much of your ending cash flow would you want to save for retirement? This will be the amount they will put in the IRA monthly.
Retirement Amount (20 Pts)
If Adam retires in 35 years and finds an IRA for 4.8%, how much money will be in their retirement account when they retire?
Amount Deposited (20 Pts)
How much will Adam deposit in total to their IRA?
Interest Accrued (20 Pts)
How much will Adam accrue in interest from their IRA?
1) Adam's monthly cash flows are:
Cash Inflows = $2,080Cash Outflows = $1,743.2) I would save $300 monthly from the ending cash flow balance for retirement savings.
3) If Adam retires in 35 years and finds an IRA for 4.8%, the future value of their retirement account will be $326,070.43 when they retire.
4) In 35 years, Adam will deposit $126,000 in total to their IRA.
5) The accrued interest from the IRA will be $200,070.43.
What is the future value?The future value represents the balance in Adam's retirement savings account after 35 years of depositing $300 monthly at 4.8% interest.
The future value is computed by compounding the periodic deposits (present values).
Adam's total monthly earnings = $2,080 ($15 x 32 x 52 x 1/12)
Monthly Expenses:
Rent $650
Groceries $325 ($75 x 52 x 1/12)
Utilities $120
Car Insurance $118
Gasoline $130 ($30 x 52 x 1/12)
Miscellaneous $400
Total monthly expenses = $1,743
Ending cash flows = $337 ($2,080 - $1,743)
Retirement period = 35 years
IRA interest rate = 4.8%
Monthly savings = $300
N (# of periods) = 420 months (35 years x 12)
I/Y (Interest per year) = 4.8%
PV (Present Value) = $0
PMT (Periodic Payment) = $300
Results:
Future Value (FV) = $326,070.43
Sum of all periodic deposits = $126,000 ($300 x 420)
Total Interest = $200,070.43
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A statistics class was given a pretest on probability (since many had previous experience in some other class). Then the class was given a six-page review handout to study for two days. At the next class they were given another test. Is there sufficient evidence that the scores improved?
Answer:
No, there is not sufficient evidence that the scores improved.
Step-by-step explanation:
Just because these people were given a six-page review handout doesn't mean that:
a. They actually did any of it
b. They learned anything
c. Since the kids have other experiences in class, the scores might not have necessarily improved that much, if at all
d. They had enough time to study
e. They cared enough in the first place
Generally, there is no rock-solid evidence at all pointing to the fact that their test scores improved. While you could make the assumption assuming every kid did what they were supposed to do, there isn't enough evidence to say that the scores improved.
TEXT ANSWER Gavin is stocking up on paper towel rolls. He already has some at his house, and begins buying more ev- ery week at a constant rate. The line y = 3x + 12 rep- resents this scenario. a. How many rolls of towels did he start with? I b. How many rolls of towels is be buying every week?
Gavin already had 12 rolls of towels, and he is buying 3 rolls per week.
What is slope?Slope tells us the change between two points given, and is shown by the change in the y coordinate divided by the corresponding change in the x coordinate.
Given that, Gavin is stocking up on paper towel rolls. He already has some at his house, and begins buying more every week at a constant rate. The line y = 3x + 12 represents this scenario.
Here the equation is y = 3x+12
When comparing with standard equation of the line, y = mx+c where m is slope, we get,
m = 3 and c = 12
Therefore, the change is 3, that means, he is buying 3 rolls per week,
and the constant is 12 that tells that he already have 12 rolls in stock.
Hence, a) he is buying 3 rolls every week, b) he has 12 rolls in stock.
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1000000000000000000000000000000x100000000000000000000000000000
Answer:
100000000000000000000000000000000000000000000000000
Step-by-step explanation:
Carter has 153 songs on a playlist. He's categorized them in the following manner: 20 country, 31 blues, 8 Latin American, 17 jazz, 26 rap, 14 folk, and 37 hip hop. If Carter begins listening to his playlist on shuffle, what is the probability that the first song played is a folk song? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
the probability that the first song played is a folk song is 9.1%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Carter has 153 songs on a playlist. He's categorized them in the following manner:
20 country, 31 blues, 8 Latin American, 17 jazz, 26 rap, 14 folk, and 37 hip hop.
The number of folk songs is 14
P(folk) = number of folk songs/ total
= 14/ 153
=0.091
Hence the probability that the first song played is a folk song is 9.1%.
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Please help me on this I’m really confused on this
Answer: c = 7
Step-by-step explanation:
180 = 86 + 31 + 9c
180 = 117 + 9c
63 = 9c
7 = c
Answer:
c = 7°
Step-by-step explanation:
You want the value of c given that angles in a triangle are marked 86°, 31°, and 9c.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°. Using given angle values, this means ...
86° +31° +9c = 180°
117° +9c = 180° . . . . collect terms
9c = 63° . . . . . . . subtract 117°
c = 7° . . . . . . . . divide by 9
The value of c is 7°.
compute the arc length of the curve:
x(t)=2t^(3/2)+2, y(t)=2t-3, 0<=t<=2
The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m
What is Integration ?In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
According to the given information
We can find the length of the arc by
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]
Find the derivative of x w.r.t to t
dx/dt = [tex]3t^{\frac{1}{2} }[/tex]
Find the derivative of y w.r.t to t
dy/dt = 2
Putting the values in above equation
We get
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]
L= [tex]\int\limits^2_0 {\sqrt{9t+4} } \, dt[/tex]
L = [tex]\frac{2}{27}(9t+4)^{\frac{3}{2} }[/tex]
limit approaches from 0 → 2
Hence
The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m
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Simplify:
10 x²y³ / 2xy
Answer:
Step-by-step explanation:
Find the inequality represented by the graph.
Answer:
[tex]\boxed{\bf{\underline{ y\le -\cfrac{3}{2}x-2}}}[/tex]
Step-by-step explanation:
From the given graph,
[tex]\bf y-intercept :\boxed{\tt -2}[/tex]
[tex]\bf Slope:\tt \cfrac{\Delta y}{\Delta x} =\cfrac{-3}{2} =\boxed{-\cfrac{3}{2} }[/tex]
Notice that graph is shaded below (not above), so y is less than the other side of the inequality. the graph elso has a solid line (not dashed), so we are dealing with an "or equal to" inequality.
Therefore, we should use the less than or equal to symbol.
[tex]\boxed{\bf{ y\le -\cfrac{3}{2}x-2}}[/tex]
_____________________
Hope this helps!
Have a great day!
multiply: 0.61 x 2.9.
Answer:
The anwser is 1.769
Step-by-step explanation:
I did this on a calculator
Challenge The members of the city cultural center have decided to put on a play once a night for a week. Their
auditorium holds 500 people. By selling tickets, the members would like to raise $2,050 every night to cover all expenses.
Let d represent the number of adult tickets sold at $6.50. Let s represent the number of student tickets sold at $3.50 each.
If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise
exactly $2,050? At one performance there were three times as many student tickets sold as adult tickets. If there were
480 tickets sold at that performance, how much below the goal of $2,050 did ticket sales fall?
There are 100 students and 400 adults.
The 480 tickets sold had a $10 fall in ticket sales.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
Let d be the number of adults and y be the number of students.
⇒ d + s = 500 ..(1)
The number of adult tickets sold at $6.50 and the number of student tickets sold at $3.50 each.
⇒ 6.5d + 3.5s = 2050 ..(2)
From equation (1) d = 500 - s
Plug the value of d in equation (2)
6.5(500 - s) + 3.5s = 2050
3250 - 6.5s + 3.5s = 2050
3250 - 3s = 2050
3s = 3250 - 2050
3s = 1200
s = 400
Plug s = 400 in d = 500 - s
⇒ d = 500 - 400 = 100
Hence, there are 100 students and 400 adults.
Now, at one performance there were three times as many student tickets sold as adult tickets.
⇒ s = 3d
3d - s = 0 ..(3)
d + s = 480 ..(4)
⇒ 4d = 480
d = 120 Adults
Plug d = 120 in equation (4)
120 + s = 480
s = 480 - 120
s = 360 Students
The money earned from these 480 people is
120 * 6.5 + 360 * 3.5 = 780 + 1260 = $2040.
$2040 - $2040 = $10
Hence, the 480 tickets sold had a $10 fall in ticket sales.
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Solve this system of equations using the Substitution method. All work and a brief phrase/sentence explaining what you're doing needs to be shown for each step for full credit. Write final answer as a coordinate point.
12x+4y=−8
y = 2x + 3
pls help
Answer: (-1,1)
Step-by-step explanation:
since y is equal to 2x+3 you can sub 2x+3 into the y value of 12x+4y=-8
12x+4(2x+3)=-8
Multiply the numbers inside the parentheses using the distributive property
12x+8x+12=-8
Combine like terms
20x+12=-8
Isolate x by moving all other numbers to the right side
Subtract 12 on both sides
20x+12-12=-8-12
20x=-20
divide both sides by 20 to isolate and get the value of x
x=-1
Now that we know the x value substitute the value of x in any of the above equations. I am using y=2x+3
y=2(-1)+3
Multiply the numbers inside the parentheses
y=-2+3
y=1
The x value is -1, and the y value is 1.
Use them as coordinate points
(x,y)
(-1,1)
The solution to the given system of equations is the point (-1, 1) which is determined by the substitution method.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The system of equations is given as:
12x + 4y = −8
y = 2x + 3
To solve this system of equations using the substitution method, you can substitute the second equation into the first equation to eliminate one of the variables.
Substituting y = 2x + 3 into the first equation gives:
12x + 4(2x + 3) = -8
12x + 8x + 12 = -8
20x + 12 = -8
20x = -20
x = -1
Substituting this value of x back into the second equation gives:
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, the solution to the system of equations is the point (-1, 1).
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Directions - Match the equations for parallel lines. (Note: you will not use all choices on the right side).
The equations for parallel lines:
y = -1/2 x - 2 ----- y = -1/2 x + 6
y = 1/2 x + 4 ----- y = 1/2 x - 4
y = 2x -4 ----- y =2/1x + 2
y = 5x + 2 ----- y = 5x - 1
y = 1/5 x + 10 ---- y = 1/5 x + 3
What is slope of line?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
If an equation in the form y = mx + c then m is the slope of the line.
Equation of line slope Slope parallel line
y = -1/2 x - 2 -1/2 -1/2
y = 1/2 x + 4 1/2 1/2
y = 2x -4 2 2
y = 5x + 2 5 5
y = 1/5 x + 10 1/5 1/5
Now identify the lines from the option whose slope are -1/2, 1/2, 2, 5, 1/5.
The slope of the line y = -1/2 x + 6 is -1/2.
The slope of the line y = 1/2 x - 4 is 1/2.
The slope of the line y = 2x -4 is 2.
The slope of the line y = 5x + 2 is 5.
The slope of the line y = 1/5 x + 10 is 1/5.
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Find the value of x in the image
Answer:
Step-by-step explanation:
73 = x + 85
x + 85 = 73
x = -12
(-12) is the value of x.
Solve the following inequality: 20t + 9, 200 ≤ 16,000
Answer in interval notation.
Answer:
[0, 799.95]
Step-by-step explanation:
First, we need to isolate the variable by subtracting 9 from both sides of the inequality:
20t + 9 - 9 ≤ 16,000 - 9
This gives us:
20t ≤ 16,000 - 9
Next, we can divide both sides of the inequality by 20 to isolate the variable:
20t / 20 ≤ (16,000 - 9) / 20
This simplifies to:
t ≤ 799.95
Finally, we need to express the solution in interval notation. Since the value of t cannot be negative, the solution is:
[0, 799.95]
Therefore, the solution to the inequality in interval notation is [0, 799.95].
y = 2x + 1
2x - y = 3
The slope of the equations is equal. Then the lines are parallel to each other.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
y = 2x + 1 ....1
2x - y = 3
y = 2x - 3 ....2
The slope of both equations is 2.
The slope of the equations is equal. Then the lines are parallel to each other.
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Which of the following is showing the correct ratio for Cosine of C ?
6 / 10
10 / 8
6 / 8
8 / 10
The value of Cosine of C is 8/10. So the option d is correct.
In the given question, we have to find which of the following is showing the correct ratio for Cosine of C.
The given options are:
(a) 6/10
(b) 10/8
(c) 6/8
(d) 8/10
As we know that cosine is the ration of adjacent side and hypotenuse.
From the given diagram we can see that;
Adjacent Side = 8
Hypotenuse = 10
Opposite Side = 6
Now the;
CosC = Adjacent Side/Opposite Side
CosC = 8/10
Hence, the value of CosC is 8/10. So the option d is correct.
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Tim's book collection is 12% nonfiction books. He has 36 nonfiction books in his collection.
Part A
What is the total number of books in Tim's collection? Explain your thinking.
Part B
If Tim adds 20 more nonfiction books to his collection, what will be the new percentage of nonfiction books? Explain your thinking.
a) The total number of books in Tim's collection is; 300 books
b) If Tim adds 20 more nonfiction books to his collection, the new percentage of nonfiction books is; 17.5%
How to solve Algebraic Word Problems?We are given;
Number of Non fiction books Tim has = 36
Percentage of non-fiction books = 12%
a) Let the total number of books in his collection be x. Thus;
(12/100) * x = 36
x = 3600/12
x = 300 books
b) He adds 20 more non fiction books to his collection. Thus;
New total non fiction books = 36 + 20 = 56
New total number of all books = 300 + 20 = 320
Thus;
New percentage of non fiction books = 56/320 * 100%
New percentage of non fiction books = 17.5%
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After a dilation with a scale factor of 2 about the origin,ΔABC maps onto ΔDEF Which of the following statements is true?
2. AB=DF
m ∠B=2. m ∠E
CA≅FD
BC/EF=CA/FD
Hello, I'm pretty sure this answer is D
Answer: D) BC/EF=CA/FD
Step-by-step explanation:
Select the inequality which represents the gragh shown below -6-y>=x2-7x
Answer:
The inequality which represents the graph shown is -6-y >= x^2 - 7x.
can someone who loves math do this and tell me the answers or do step by step please
Answer:
Step-by-step explanation:
3.) Slope: 15x
Y-int: 120
Y=15x+120
4.) For this one i'm not sure maybe..
5.) Slope: 5x
Y-int: 250
Y=5x+250
Which of the following is the correct if clause to determine whether y is in the range 10 through 50, inclusive? (Points : 1) A) ify>=10 and y <= 50: B) if10 > y and y < 50: C) if y >= 10 or y <= 50; D) if 10,y ory.50
We follow the inclusive rule, The answer to the question is (A) that is
if y>=10 and y <=50
What do you mean by intervals?In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.
What are the symbols and their meaning of the intervals?The intervals used are:
(a , b) , All the numbers between a & b without including them.
[a, b] , All the numbers between a & b including them.
y lies in [10,50].
And since it means that it includes 10 and 50 and all the numbers between them.
The final answer is (A) that is if y>1=10 and y <=50.
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A study showed that low-intensity shock therapy reduces pain levels in patients with lupus. During each session, electrodes were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity shock therapy also reduces pain in patients suffering from bulging disks in the thoracic region of the back. Two hundred female patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 100 male and 100 female patients instead of 200 female patients, would you change the study design? If so, how would you modify your design? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points) (10 points)
Answer:
part A: The appropriate design for the study includes;Treatment used; Chamomile oil treatment
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
Step-by-step explanation:
Activity 9: 1 Challenge You! 214 3/4/2/1 4/2/3/1 1 4 Hi there! I am the MATH WIZARD, I came here to challenge you. Simplify the following expressions. If you do these correctly, I will have you as my apprentice. Good luck!
1.) 6e⁰ + (11f)⁰ - 5/g⁰
2.) (3-⁴ + 5-³)-¹
3.) (3-⁴ + 5-³)-²
4.) 5(2a-¹b³)⁰
___________
10c-⁵ d⁶ e-⁸
5.) -5(m-⁴ n-⁵)-³
____________
7(p-⁶q⁸)-⁴
6.) ( 3x-⁴ y-⁵ z-²)-²
____________
The simplification of the expressions in the question using the rules of indices are as follows;
1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2
2. (3⁻⁴ + 5⁻³)⁻¹ = [tex]49\frac{31}{206}[/tex]
3. (3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]
4.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}[/tex] = [tex]\dfrac{c^5\cdot e^8}{2\cdot d^5}[/tex]
5.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}[/tex]
What is are indices in mathematics?An index or indices is the power by which a number or variable or expression raised.
1.) 6·e⁰ + (11·f)⁰ - 5/g⁰
6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1
6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2
Therefore;
6·e⁰ + (11·f)⁰ - 5/g⁰ = 2
2.) (3⁻⁴ + 5⁻³)⁻¹
(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))
1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))
1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209
10125/206 = 49 + 31/206
(3⁻⁴ + 5⁻³)⁻¹ = [tex]49 \frac{31}{206}[/tex]
3.) (3⁻⁴ + 5⁻³)⁻²
(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)
1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)
1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)
1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)
1/((206/10125)²) = (10125)²/(206)² = 102515625/42436
102515625/42436 = 2415 32685/42436
(3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]
4.) [tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}[/tex]
[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }[/tex]
[tex]\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]
[tex]\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]
[tex]\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]
[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]
5.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}[/tex]
[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }[/tex]
[tex]\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }[/tex]
[tex]\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }[/tex]
[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }[/tex]
[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]
[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]
6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²
(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = [tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)[/tex]
[tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2[/tex]
3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴
Therefore;
(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴
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Simplify -x-(-4x-6)=6
Answer:
To simplify the given equation, we can start by using the rules of algebra to rearrange the terms and combine like terms on both sides of the equation. This gives us:
-x - (-4x - 6) = 6
We can then distribute the negative sign on the left side of the equation to get:
-x + 4x + 6 = 6
We can then combine like terms on the left side of the equation to get:
3x + 6 = 6
We can then subtract 6 from both sides of the equation to get:
3x = 0
We can then divide both sides of the equation by 3 to get the final result:
x = 0
Therefore, the simplified form of the given equation is x = 0.
Step-by-step explanation:
θ is an acute angle. Find the value of θ in degrees.
sec(θ)=2
The value of θ is 60°.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin, cos , tan , cosec , sec and cot
Let the angle be θ , that is;
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Thus, tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data that the angle be represented as θ
Now , we are given that the angle θ is acute
Since Acute angles measure less than 90 degrees
So , the value of θ < 90°
when the value of sec θ = 2
cos θ = 1/sec θ
, cos θ = 1/2
The value of θ when cos θ is 1/2.
when the angle θ is 60°
Therefore ,
the value of θ is 60°
sec 60° = 2
Hence , The value of θ is 60°
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What is the product of 3 over 4x and 8x + 3?
Answer:
[tex]\frac{24x+9}{4x}[/tex] or 6 + [tex]\frac{9}{4x}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4x}[/tex] × 8x +3
= [tex]\frac{3}{4x}[/tex] × [tex]\frac{8x +3}{1}[/tex]
= [tex]\frac{3(8x+3)}{4x}[/tex]
= [tex]\frac{24x+9}{4x}[/tex]
or 6x + [tex]\frac{9}{4x}[/tex]
Last year the cost of Tom's train ticket was £42 This year the cost of Tom's train ticket increased to £50 Write down the increase in the cost of Tom's ticket as a fraction of last year's cost. (2 marks
Answer:
19.048%
Step-by-step explanation:
The formula for the increase in cost will be :
[(New cost - Original Cost)÷Original Cost] × 100
So let's substitute values in from the question :
[(50-42)÷42] × 100
[8÷42] × 100
0.19048 × 100
19.048%
Hope this helped and have a good day