Simplify the expression.
(m^-1 m^5/m^-2)^-3
a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18
Answers
Explanation:
(m^-2/m-1m5)^3
m^-6/m^-3m^15
1/m^6 / m^15/m^3
1/m^6 / m^12
1/m^6 (1/m^12)
1/m^18
let me know if you want clarification
Answer:
[tex]D)\frac{1}{m^{18} }[/tex]
Step-by-step explanation:
Multiply [tex]m^{-1}[/tex] by [tex]m^{5}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](\frac{m^{-1+5} }{m^{-2} } )^{-3} \\[/tex]
Add -1 and 5.
[tex](\frac{m^{4} }{m^{-2} } )^{-3}[/tex]
Move [tex]m^{-2}[/tex] to the numerator using the negative exponent rule [tex]\frac{1}{b^{-n} } =b^{n}[/tex].
[tex](m^{4} m^{2} )[/tex]
Multiply [tex]m^{4}[/tex] by [tex]m^{2}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](m^{4+2} )^{-3}[/tex]
Add 4 and 2.
[tex](m^{6} )^{-3}[/tex]
Multiply the exponents in [tex](m^6)^{-3}[/tex]
Apply the rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
[tex]m^{6*-3}[/tex]
Multiply 6 by -3.
[tex]m^{-18}[/tex]
Rewrite the expression using the negative exponent rule [tex]b^{-n} =\frac{1}{b^{n} }[/tex].
[tex]\frac{1}{m^{18} }[/tex]
Related Questions
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
What is the recursive rule?
Answers
The required recursive function will be expressed as an = 3000 + 500n
How to write recursive functionsGiven the following parameters
First year salary = $30,000
If it increases by $500 each year, let the number of years be "n", then the increment after "n" years is 500n
The required recursive function will be expressed as an = 3000 + 500n
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What is the measure of m?
6
24
m
m= 6y[?]
Give your answer in simplest form.
Answers
Similar triangles are those triangles whose corresponding sides are in the same ratio. The measure of m is 6√4.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
In the given triangles ΔABC and ΔBCD,
∠ACB = ∠DCB {Common Angles}
∠BDC = ∠ABC =90°
Therefore, the two triangles are so, for triangles.
(6+24)/BC = m/n = BC/24
BC² = 30×24
BC = √720
Now, using the Pythagorean theorem,
AC² = AB² + BC²
30² = m² + (√720)²
900 = m² + 720
180 = m²
m = 6√4
Hence, the measure of m is 6√4.
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Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Answers
Answer:
A. student A is correct; student B was confused by the division
B. 3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)
Step-by-step explanation:
Each student correctly made use of the trig identities ...
csc(θ) = 1/sin(θ)
1 -sin²(θ) = cos²(θ)
__
A.Student A's work is correct.
Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.
__
B.The transition from Step 2 can look like ...
[tex]\textsf{Step 3: }\ \dfrac{\left(\dfrac{1-\sin^2\theta}{\sin\theta}\right)}{\csc\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}\cdot\dfrac{1}{\csc\theta}=\dfrac{\cos^2\theta}{(\sin\theta)(\csc\theta)}\\\\\textsf{Step 4: }\ \cos^2\theta[/tex]
PLEASE ANSWER FOR EXTRA POINTS ⭐️⭐️⭐️!
Answers
Answer:
the answer is B.(3,6)
because y>2
so,the answer is 3&6.
Parallelogram RSTU is shown. The perimeter of parallelogram RSTU is 50
centimeters. What is the value of x? *
R.
(2x + 15) cm
S
(3x + 20) cm
U
T
-5
-2.
3
O 12
Answers
Answer: x = -2
Step-by-step explanation:
Given:
Perimeter = 50 cm
=> 2 (2x+15)+ 2(3x+20) =50
=> 4x+30+6x+40=50
=> 10x= -20
=> x= -20/10
=> x = -2
sophia is designig a logo with three lines,y, m, and n. Line m passes through point (-2, -1) and is perpendicular to the graoh of y=-2/3 x +6. line n is parallel to line m and passes through the point (4, -3). what is the equation in slope-intercept form of linen?
Answers
Answer:
y = 3/2x - 9
Step-by-step explanation:
Finding equation of line m
⊥ to the line y = -2/3x + 6new slope = -(-3/2) = 3/2Passes through the point (-2, -1)y + 1 = 3/2(x + 2)y + 1 = 3/2x + 3y = 3/2x + 2Equation of line n
Parallel ⇒ slope is same = 3/2Passes through the point (4, -3)y + 3 = 3/2(x - 4)y + 3 = 3/2x - 6y = 3/2x - 9Answer:
[tex]\textsf{Equation of line n}:\quad y=\dfrac32x-9[/tex]
Step-by-step explanation:
Equation of line m
If two lines are perpendicular to each other, the product of their slopes will be -1.
The slope of the line [tex]y=-\dfrac23x+6[/tex] is [tex]-\dfrac23[/tex]
Therefore, the slope of the line m is:
[tex]\implies m \times -\dfrac23=-1[/tex]
[tex]\implies m=\dfrac32[/tex]
If line m passes through point (-2, -1), then the equation of line m is:
[tex]\implies y-(-1)=\dfrac32(x-(-2))[/tex]
[tex]\implies y+1=\dfrac32(x+2)[/tex]
[tex]\implies y=\dfrac32x+2[/tex]
Equation of line n
If line n is parallel to line m, then they will have the same slope.
Therefore, slope of line n is [tex]\frac32[/tex]
If line n passes through point (4, -3), then the equation of line n is:
[tex]\implies y-(-3)=\dfrac32(x-4)[/tex]
[tex]\implies y+3=\dfrac32x-6[/tex]
[tex]\implies y=\dfrac32x-9[/tex]
PLEASE
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
y = -x - 4
Step-by-step explanation:
m = (-5-0)/(1+4) = -5/5 = -1
b = (0, -4)
y = mx + b
y = -x - 4
Answer:
y = -x - 4
Step-by-step explanation:
Slope-intercept form is:
y = mx + b
The b is the y-intercept. That is where the line crosses the y-axis. This line crosses the y-axis at -4.
You could calculate the slope, but with a graph, you can SEE the slope without doing any calculation. Find a point on the line, any point. To get to the next point, you go DOWN1 and OVER1, (down1, over1, down1, over1)
This is -1/1. The slope is -1. Fill that in for m.
Leave the x and y as-is in
y = mx + b
fill in -1 for m and -4 for b.
y = -x - 4
If your teacher/prof is expecting to see a calc for slope. Find two points on the line. Subtract y-y and put that on top. Subtract x-x and put that on the bottom. Simplify.
Given points:
(1,-5) and (-4,0)
-5 - 0 is -5, put on top.
1 - -4 is 5, put underneath. You get -5/5, which is -1. Slope is -1.
PLEASE HELP PLEASE HELP PLEASE
Answers
blue stars. let’s talk a bit about temperature. The color of a star is a function of its temperature. If a star looks red, that means its surface temperature is approximately 2,500 Kelvin. Just for comparison, our Sun, which actually looks white from space, measures about 6,000 Kelvin. The hotter the star, the further up the spectrum you go. The hottest stars are the blue stars. A star appears blue once its surface temperature gets above 10,000 Kelvin, or so, a star will appear blue to our eyes.
Please help me I will mark BRAINLY
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
5% of N 80000
= [tex]\frac{5}{100}[/tex] × 80000
= 0.05 × 80000
= N4000 ← VAT
(b)
total cost = 80000 + 4000 = N84000
Drag each expression to show whether it is equivalent to 54x + 18 or
(6 · 9x) + (6 · 1).
Answers
Answer:
The first one should belong in the 54x+18 due to multiplication
The second answer choice has distributive property which has to belong in the 54x+18 category
The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.
The last one should be in the 54x+18 category because of the distributive property
Step-by-step explanation:
The Objectives: 54x+18 and (6(9x) + 6
The first one should belong in the 54x+18 due to multiplication
The second answer choice has distributive property which has to belong in the 54x+18 category
The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.
The last one should be in the 54x+18 category because of the distributive property
Stuck on this math question can anyone help me please?!?
Answers
Answer:
1) f(-6) = 8
2) f(3) = -2
3) f(x) = -5 when x = 4
6 sushi rolls cost $8.99
Answers
1.4983
______
6|8.99
Hope this helps
Which answer is $734,596 rounded to the nearest thousand??
1) 734,500
2)734,600
3)735,000
4)734,000
Thank you so much
Answers
Answer:
2
Step-by-step explanation:
the 3 sides of triangle are n, 4n + 1 , 5n- 8. if the perimeter of the triangle is 93 cm, what is the length of each side?
Answers
Answer:
10, 41, 42
Step-by-step explanation:
(n)+(4n+1)+(5n-8)=93 because triangle perimeter
10n-7=93
10n=100
n=10
Answer: 10 cm, 41 cm, and 42 cm
Step-by-step explanation:
We can set up an equation knowing the perimeter to solve for the lengths of each side. Then, we will plug the value of n into the different expressions that represent each side.
Perimeter of a triangle:
P = side a + side b + side c
Plug in our known values:
93 cm = (n) + (4n + 1) + (5n - 8)
Simplify and combine like terms:
93 cm = n + 4n + 1 + 5n - 8
93 cm = n + 4n + 5n + 1 - 8
93 cm = 10n -7
Add 7 to both sides of the equation:
100 cm = 10n
Divide both sides of the equation by 10:
10 cm = n
n = 10 cm
-
Solve for the lengths of each side:
n = 10 cm
4n + 1 = 4(10) + 1 = 40 + 1 = 41 cm
5n - 8 = 5(10) - 8 = 50 - 8 = 42 cm
Find the measures of angles 1 through 6.
Answers
Answer:
<1 = 88° , <2 = 129°, <3 = 82°, <4 = 147°, <5 = 94°, <6 = 86°
Step-by-step explanation:
<1 + 92° = 180°
<1 = 88°
<2 + 51° = 180°
<2 = 129°
<3 + 98° = 180°
<3 = 82°
<4 + 33° = 180°
<4 = 147°
<1 + <2 + <3 + <4 + <5 = 540°
88° + 129° + 82° + 147 + <5 = 540°
<5 = 94°
<5 + <6 = 180°
94° + <6 =180°
<6 = 86°
What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers.
The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers such that –6 ≤ x ≤ –2.
Answers
Answer:
The domain is all real numbers greater than or equal to 4, and the range is all real numbers
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Answers
Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
A chef used one-half of a bag of potatoes for a meal. If the potatoes fed 2 people, what
fraction of the bag did each person get?
(Help plss as soon as you can)
Answers
Answer: 1/4
Step-by-step explanation: each person had half of the half of bag.
I need help!! I will give 5.0 star
Answers
So, here we need to differentiate tan³[tex](\theta)[/tex], wr.t.[tex]\theta[/tex], but let's recall some identities which will be very useful in this question :
[tex]{\boxed{\bf{\dfrac{d}{dx}\{\tan (x)\}=\sec^{2}(x)}}}[/tex][tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex][tex]{\boxed{\bf{\sec^{2}(\theta)=\tan^{2}(\theta)+1}}}[/tex]Coming back on the question, consider :
[tex]{:\implies \quad \sf \dfrac{d}{d\theta}\{\tan^{3}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{3-1}(\theta)\dfrac{d}{d\theta}\{\tan (\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\sec^{2}(\theta)}[/tex]
Using the identity ;
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\{1+\tan^{2}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)+3tan^{4}(\theta)}[/tex]
[tex]{:\implies \quad \sf 3\tan^{4}(\theta)+3\{\sec^{2}(\theta)-1\}}[/tex]
[tex]{:\implies \quad \boxed{\bf 3\tan^{4}(\theta)+3\sec^{2}(\theta)-3}}[/tex]
Hence, Proved
1/3 + 1/3=
5/10-2/10=
=
4/5-2/5=
11+1=
=
Answers
Answer:
Step-by-step explanation:
1/3 + 1/3= 2/3
5/10-2/10=3/10
4/5-2/5=2/5
11+1=12
A 2-pack of jump ropes costs $1.80. What is the unit price?
$
per jump rope
Answers
Answer:
90 cents
Step-by-step explanation:
you divide 1.80 by 2 and get .9 which is equal to 90 cents
Answer:
$0.90
Step-by-step explanation:
literally just divide by 2
Evaluate each expression if f = –4, g = 2, and h = 7.
h – f
Answers
Answer:
11
Step-by-step explanation:
h - f = 7 - (-4) = 7 + 4 = 11
"Last week you sold 30, 45, 50, 75, and 80 units each day of the week, in that order. On average, how many units did you sell per day?"
Answers
Answer:
56
Step-by-step explanation:
1) Add together all numbers. 30+45+50+75+80 = 280.
2) Divide result by amount of numbers. 280/5 = 56
3) You are welcome. :)
On an average, you sold 56 unit per, day.
What is average?A number that is calculated by adding quantities together and then dividing the total by the number of quantities.
Given that, Last week you sold 30, 45, 50, 75, and 80 units each day of the week.
To find the average, we will, first add together all numbers and then divide the result by the sum of numbers.
Therefore,
Adding together all numbers = 30+45+50+75+80 = 280.
Divide result by amount of numbers = 280/5 = 56
Hence, On an average, you sold 56 unit per, day.
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Jason bought 3 shirts that each cost the same.He has a coupon for $10 off and he spent $65 altogether.Which equation can be used to find the cost of each shirt
Answers
Answer:
3x-10=65
Step-by-step explanation:
So, since he used the coupon, you can do 65+10=75.
The cost before the coupon is 75.
The cost of each shirt is 75/3, but that doesn't solve the question.
You can do (assume each shirt's cost is x)
3x-10=65
I could give more in depth but I can't see the options, sorry!
Answer:
(65+10) / 3= x
x would equal what each shirt costs
Step-by-step explanation:
A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.
Please explain how to solve this problem, not just the answer.
Answers
The area of the square pyramid building is the amount of space on it
The maximum base length of the building is 67.42 cm
How to determine the maximum side length?The given parameters are:
Base = b
Slant height (l) = 5b
The lateral surface area is calculated using:
L = 2bl
So, we have:
L = 2 * b * 5b
Evaluate the product
L = 10b^2
The total surface area is calculated using:
T = L + b^2
So, we have:
T = 10b^2 + b^2
Evaluate the sum
T = 11b^2
The maximum surface area is 50,000 square feet
So, we have:
11b^2 = 50000
Divide both sides by 11
b^2 = 50000/11
Take the square root of both sides
b = 67.42
Hence, the maximum base length of the building is 67.42 cm
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Answer: 71 feet
Step-by-step explanation:
Let's assume that the side length of the base of the square pyramid is x. Then, the slant height of the pyramid would be 5x, as given in the problem.
The lateral surface area of a square pyramid can be calculated using the formula:
Lateral surface area = (perimeter of base) × (slant height) / 2
The perimeter of the square base is 4x. So, the lateral surface area of the square pyramid can be written as:
Lateral surface area = 4x × (5x) / 2 = 10x^2
We are told that the construction material used for the outside of the building is between 20,000 square feet and 50,000 square feet. So, we can set up the following inequality:
20,000 ≤ 10x^2 ≤ 50,000
Dividing both sides by 10, we get:
2000 ≤ x^2 ≤ 5000
Taking the square root of both sides, we get:
44.7 ≤ x ≤ 70.7
Since we are looking for the maximum possible value of x, we can round 70.7 up to the nearest foot, which is 71 feet.
Therefore, the maximum possible side length of the base of the building is 71 feet.
The average gas mileage (mpg) for vehicles produced by a particular automotive company is 26 mpg, with a standard deviation of 2 mpg. What percentage of the vehicles produced by the automotive company have a gas mileage greater than 24?
Note: Assume that a Normal model is appropriate for the distribution of the gas mileages for the vehicles.
Answers
Answer:
above 84°/. of the vehicles have a gas mileage greater then 24 mpg
Please assist me with these question. I am having a hard time
Answers
Step-by-step explanation:
[tex] \frac{1}{3x} + \frac{7}{ {x}^{2} } + \frac{x + 2}{x} [/tex]
[tex] \frac{x}{ {3x}^{2} } + \frac{21}{3 {x}^{2} } + \frac{3 {x}^{2} + 6x}{3 {x}^{2} } [/tex]
[tex] \frac{ {3x}^{2} + 7x + 21 }{ {3x}^{2} } [/tex]
Choice D
 Mrs. Lee earned a $3,000 bonus at work. She will use $1,737 of it to replace her water heater. If she wants to divide the rest of the bonus evenly between her 3 children, how much will each child receive?
Answers
Answer: 421
Step-by-step explanation:
Subtract 3,000 by 1,737 and the product of that divided by 3 which will give you 421
which best represents the relationship between x and y
y=2x
y=x+2
y=4x
y=x+4
Answers
Answer:
In y = 2x the value of y is twice the value of x, and in y = x + 2 the value of y is two more than the value of x.
Same for the y=4x and y=x+4, just plug the numbers into the sentence.
Step-by-step explanation:
Find the domain and range of the function graphed below.
Domain:
Range:
Answers
The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).
How to find the domain and range of a functionThe domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).
Note that point where the circles are shaded shows a closed interval
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