What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Superscript negative 12 Baseline q Superscript negative 3 Baseline EndFraction in simplified form? Assume p not-equals 0, q not-equals 0. Negative StartFraction 3 p Superscript 8 Baseline Over 4 q cubed EndFraction Negative StartFraction 3 Over 4 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction Negative StartFraction p Superscript 8 Baseline Over 5 q cubed EndFraction Negative StartFraction 1 Over 5 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction
Answers
can be simplified to
[tex]-\frac{3p^8}{4q^3}[/tex]
Hopes this helps
if not then I'm sorrr
The quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\) is \(-\frac{3p^8}{4q^3}\). This is found by dividing the numerical coefficients and subtracting the exponents for variables of the same base (negative exponents indicate reciprocals).
Explanation:To find the quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\), we perform division of the coefficients (15 divided by -20) and subtraction of the exponents for variables with the same base (p's and q's exponents) according to the rules of exponents. First, simplify the numerical coefficients:
\(\frac{15}{-20} = -\frac{3}{4}\)
Now, subtract the exponents for p (applying the formula x^p \cdot x^q = x^{(p+q)}):
\(p^{-4} - p^{-12} = p^{-4 + 12} = p^8\)
Next, apply the same process to the exponents of q:
\(q^{-6} - q^{-3} = q^{-6 + 3} = q^{-3}\)
Combine the results to get the simplified quotient:
\(-\frac{3}{4} × p^8 × q^{-3}\)
Remember that a negative exponent indicates a reciprocal, so we can write \(q^{-3}\) as \(\frac{1}{q^3}\). Therefore, the final answer is:
\(-\frac{3p^8}{4q^3}\)
Learn more about Simplifying Quotients with Exponents here:https://brainly.com/question/29771176
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Related Questions
The sum of two non-negative numbers is 4. Find the numbers if the sum of the square of one and the cube of the other is to be a maximum.
^ My brain is saying 2+2 here pals. I have no idea where to start. Okay so, I was out most of the last week because I was sick. And now there's a test on this optimization weird application idea in my pre-calc class. I could probably figure this out if I needed to in a bizarre backwards way, but knowing how to find it properly with a procedure and all will help very much. Thanks!
Answers
Answer:
I would say you're right, 2 + 2
Step-by-step explanation:
Final answer:
The mathematics optimization problem involves finding the maximum sum of the square of one non-negative number and the cube of the other, with their total being 4. Calculus is applied by taking the derivative of the function representing the sum, setting it to zero to find critical points, and checking the second derivative to ensure a maximum is found. The optimized numbers are x and 4-x, based on the critical point found.
Explanation:
To solve the optimization problem, we need to use calculus to find the maximum value of the sum of the square of one number and the cube of the other, given that the sum of the two numbers is 4. Let's call these numbers x and y, with x + y = 4. We want to maximize S = x^2 + y^3.
Since x + y = 4, we can express y as y = 4 - x. Substituting this into S, we have S = x^2 + (4-x)^3. This becomes a function of one variable.
To find the maximum value, we differentiate S with respect to x, set the derivative equal to zero, and solve for x. We can check the second derivative to ensure it is a maximum. The function S' will have a maximum when the first derivative is zero (S'(x) = 0) and the second derivative is negative (S''(x) < 0).
Therefore, the two non-negative numbers that maximize S are x and 4-x, with x being the value at which S' equals zero with S'' negative.
Determine whether the sequence 7, 21, 35, 49 is geometric. If so, find its common
ratio.
Answer:
a. no
b. yes, common ratio of 14
c. yes, common ratio of 2
Answers
Answer:
B
Step-by-step explanation:
Answer:
a. no
Step-by-step explanation:
The sequence is arithmetic. It has a common difference of 14.
7 + 14 = 21
21 + 14 = 35
35 + 14 = 49
A geometric series has a common ratio (multiplication). For example:
7 × 3 = 21
21 × 3 = 63
63 × 3 = 189
Write the slope intercept form of the equation of the line through the given points and slope 1,1 and slope of -3/5
Answers
Slope is already given in the question so we only need to solve for the y-intercept.
Slope intercept form: y = mx + b
m = slope
b = y-intercept
-3/5 = -0.6
1 = -0.6(1) + b
1 = -0.6 + b
1 + 0.6 = -0.6 + b + 0.6
1.6 = b
Now, write in slope-intercept form.
y = -3/5x - 1.6
______
Best of Luck,
Wolfyy :)
In a group 120 children there are teice as many boys as girls. How many girls are there?
Answers
Answer:
40 girls 80 boys
Step-by-step explanation:
80/2=40
40+80=120
Answer:
80 girls
Step-by-step explanation:
120/3 = 40.
40 x 2 = 80
line m contains the points -3,4 and 1,0. write the equation of a line that would be perpendicular to this one and pass through the point -2,6
How do you solve that
Answers
For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the statement we have two points through which the line passes:
[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 1,0)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-4} {1 - (- 3)} = \frac {-4} { 1 + 3} = \frac {-4} {4} = - 1[/tex]
By definition, if two lines are perpendicular then the product of their slopes is -1.
Thus, a perpendicular line will have a slope: [tex]m_ {2} = \frac {-1} {- 1} = 1[/tex]
Thus, the equation will be of the form:
[tex]y = x + b[/tex]
We substitute the given point and find "b":
[tex]6 = -2 + b\\6 + 2 = b\\b = 8[/tex]
Finally, the equation is:
[tex]y = x + 8[/tex]
Answer:
[tex]y = x + 8[/tex]
BC is parallel to DE.what is the length of CE?
Answers
Answer:
Option B [tex]2\frac{2}{3}\ units[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and ADE are similar by AA Similarity Theorem
so
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
substitute the given values
[tex]\frac{3}{3+2}=\frac{4}{AE}[/tex]
Solve for AE
[tex]\frac{3}{5}=\frac{4}{AE}[/tex]
[tex]AE=5(4)/3[/tex]
[tex]AE=\frac{20}{3}\ units[/tex]
Find the length of CE
[tex]AE=AC+CE\\CE=AE-AC[/tex]
substitute the values
[tex]CE=\frac{20}{3}-4[/tex]
[tex]CE=\frac{8}{3}\ units[/tex]
Convert to mixed number
[tex]\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units[/tex]
100 POINTS and BRAINLIEST to get both of these answer the third question on my profile :)
Answers
Answer:
1. f
2.b
3. d
4. a
5. e
6. g
7. c
Step-by-step explanation:
The parent function is [tex]y = 3 (5)^{x}[/tex].
So,
1. [tex]y = - 3 (5)^{x} + 4[/tex] ≡ f. reflected across x-axis and 4 units up
2. [tex]y = 3 (5)^{x - 4} - 4[/tex] ≡ b. 4 units down and 4 units right.
3. [tex]y = 3 (5)^{x + 4} + 4[/tex] ≡ d. 4 units up and 4 units left.
4. [tex]y = - 3 (5)^{x} - 4[/tex] ≡ a. reflected across x-axis and 4 units down.
5. [tex]y = 3 (5)^{x} - 4[/tex] ≡ e. 4 units down
6. [tex]y = 3 (5)^{x} + 4[/tex] ≡ g. 4 units up.
7. [tex]y = 3 (5)^{x - 4}[/tex] ≡ c. 4 units right. (Answer)
-3x – 4y=2
6x + 6y = -6
Answers
x=-2/3-4/3y
6(-2/3-4/3y)+6y=-6
-4-8y+6y=-6
-2y=-2
y=1
x=-2
Final answer:
To solve the system of equations -3x - 4y = 2 and 6x + 6y = -6, multiply the first equation by 2 to eliminate the coefficients of y, and then add the equations together. The solution is x = -2 and y = 1.
Explanation:
To solve the system of equations:
-3x - 4y = 2
6x + 6y = -6
First, multiply the first equation by 2 so that the coefficients of y will cancel when adding the equations together.
-6x - 8y = 4
Next, add the modified first equation to the second equation.
(-6x - 8y) + (6x + 6y) = 4 + (-6)
-8y + 6y = -2
-2y = -2
Divide both sides of the equation by -2 to solve for y.
y = 1
Substitute the value of y back into either equation to solve for x.
-3x - 4(1) = 2
-3x - 4 = 2
-3x = 6
x = -2
The solution to the system of equations is x = -2 and y = 1.
Are the fractions 3/9 ,3/10, 3/11, and 3/12 arranged in order from least to greatest or greatest to least? Explain.
Answers
Answer:
They are arranged greatest to least
1. Find the slope of a line passing through (56, 67) and (-12, -50)
Answers
Answer:
117/78
Step-by-step explanation:
(-50-67)/(-12-56)=-117/-78=117/78
what is the quotient when the sum of 0.2 and 0.05 is divided by the product of 0.2 and 0.05
Answers
Answer:
25
Step-by-step explanation:
0.25/0.01
=25
Find the difference between -14w - 3 and 5w.
-9 w - 3
-19 w + 3
-19 w - 3
-22 w
Answers
Answer:
C) -19w-3
Step-by-step explanation:
(-14w-3)-5w
-14w-3-5w
-19w-3
County fair charges 1.25 per ticket for rides. Tom bought 25 ride tickets and spent a total of $43.75 total for rides and admission. The price of admission is the same for everyone. Use y to represent total cost and x for the number of tickets.
Define variables
Write linear equation to determine the cost for rides tickets and admission
Answers
Answer:
The linear equation is 1.25x + 0.5x = y
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Price of ride ticket at country fair = US$ 1.25
Total spent by Tom for rides and admission= US$ 43.75
Number of ride tickets bought by Tom = 25
Price of admission is the same for everyone
Total cost = y
Number of tickets = x
2. Let's find out the cost of the admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Replacing with real values:
1.25 * 25 + Cost of admission * 25 = 43.75
31.25 + 25 * Cost of admission = 43.75
25 * Cost of admission = 43.75 - 31.25 (Subtracting 31.25 at both sides)
25 * Cost of admission = 12.50
Cost of admission = 12.50/25 (Dividing by 25 at both sides)
Cost of admission = 0.50
3. Let's write a linear equation to determine the cost for rides tickets and admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Total cost = y
Number of tickets = x
1.25x + 0.5x = y
At a local fitness center, members pay a $12 membership fee and $2 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Answers
Final answer:
The costs for members and nonmembers of a local fitness center will be the same after attending 6 aerobics classes. Members have an initial $12 membership fee plus $2 per class, while nonmembers pay $4 per class.
Explanation:
To find the number of aerobics classes for which the cost for members and nonmembers will be the same, we need to set up an equation that compares the two cost structures. For members, the cost is a $12 membership fee plus $2 per class, which we can express as Cm = 12 + 2n, where Cm is the cost for members and n is the number of classes. For nonmembers, the cost is $4 per class, so we can express that as Cnm = 4n, where Cnm is the cost for nonmembers.To find the number of classes where costs are the same, we set Cm equal to Cnm:
Subtract 2n from both sides: 12 = 2n
Divide both sides by 2: n = 6
Therefore, the costs for members and nonmembers will be the same when they attend 6 aerobics classes.
A scientist measured the width of a square flake of gold to be7.3 x 10 -4mm what is the area of the flake
Answers
The area of square flake of gold is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]
Solution:Given that width of square flake of gold is [tex]7.3 \times 10^{-4}[/tex] millimeter
To find : Area of square flake
Since gold flake is in shape of square, we can use area of square formula
The formula for area of square is given as:
[tex]area = s^2[/tex]
where "s" is the length of one side
[tex]\begin{array}{l}{\text { Area of a square flake }=\left(7.3 \times 10^{-4}\right) \times\left(7.3 \times 10^{-4}\right)} \\\\ {\text { Area of a square flake }=53.29 \times 10^{8}}\end{array}[/tex]
Hence , the calculated area of flake is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]
Your have 100$ in your savings account and plan to deposit 20$ each month. Write and graph a linear equation that represents the balance in your account
Answers
Answer:
Formula - y=mx+b
You have $100 and you're increasing it by $20 each month.
m=slope, b= initial value.
Thus, y=20x+100, is your linear equation.
Hope This Helps! :D
Answer:
.
Step-by-step explanation:
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 0.1, y = 0.9
A
y = [? ]x
Answers
Direct variation equation is y=kx . Your k is your variation or you could look at it as your slope. y=kx Plug in what you know, 4=k12 Divide both sides by 12 to cancel out your 12 that is being multiplied by k.
4(/12)=k12(/12) Simplify
1/3=k
y=1/3x This is your direct variation equation.
Answer:
Step-by-step explanation:
1) y=kx
plug in the #s
(0.9)=k(0.1)
divide both sides by 0.1
k=9
plug in k and that is your equation (y=9x)
Help!! Please!!
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
Answers
Step-by-step explanation:
x=10+4=14
14+14=28
the answer is 28 fts
Answer:
The answer is 6.67 feet, approximately.Step-by-step explanation:
The image attached shows the context that the problems refered.
Notice that two acute angles from those triangles are congruent, just because their complement are also congruent.
[tex]\angle AOB \cong \angle COD[/tex]
[tex]\angle AOB= \angle COD=90\° - a[/tex]
Remember that the tangent function is defined as
[tex]tan(\theta)=\frac{Opposite \ Leg}{Adjacent \ Leg}[/tex]
Replacing each equiavlence, we have
[tex]tan(90-a)=\frac{6}{4}=\frac{10}{x}[/tex]
Then, we solve for [tex]x[/tex]
[tex]\frac{6}{4} =\frac{10}{x}\\ x=\frac{40}{6}\\ x \approx 6.67 ft[/tex]
Thereofre, the answer is 6.67 feet, approximately.
if 12^-x=5, what does 12^2x equal
Answers
Answer:
0.04
Step-by-step explanation:
12^(-x) = 5 (taking log on both sides)
log [ 12^(-x)] = log 5
-x log 12 = log 5
-x = log 5 / log 12
x = - (log 5/log12)
x = -0.6477
12^(2x)
= 12^[2(-0.6477)]
= 12 ^ (-1.295)
= 0.04
How many square feet of outdoor carpet will
we need for this hole?
11 ft
13 ft
2 ft
3 ft
Answers
Answer:
39 square feet
Step-by-step explanation:
The outdoor carpet consists of two rectangles.
The area of the rectangle is
[tex]A=\text{Length}\times \text{Width}[/tex]
1st rectangle:
Length = 11 ft
Width = 3 ft
Area [tex]=11\cdot 3=33 \ ft^2[/tex]
2nd rectangle:
Length = 3 ft
Width = 2 ft
Area [tex]=3\cdot 2=6 \ ft^2[/tex]
Total area:
[tex]33+6=39\ ft^2[/tex]
The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .
What is the equation of the circle in standard form?
Answers
The equation of the circle in standard form is: (x + 2)² + (y - 1)² = 1
What is the equation of the circle?
The general form of the equation of a circle is:
(x - h)² + (y - k)² = r²
Where;
(h, K) is the coordinate of the center of the circle.
r is radius.
To find the equation of the circle in standard form, we need to determine the center and radius of the circle.
Since the center of the circle lies on the line y = 3x + 1 and is tangent to the x-axis at (-2,0), we can determine that the center of the circle is (-2,1) and the radius is 1.
Therefore, the equation of the circle in standard form is:
(x + 2)² + (y - 1)² = 1
Could someone help me please:(
Answers
Answer:
Domain: -∞ < x < +∞
Range : 2 ≤ f(x) < +∞
Step-by-step explanation:
See the graph attached to this question.
The two arrow shows the graph of a function y = f(x).
Now, the value of x varies from +∞ to -∞.
So, the domain of the function is -∞ < x < +∞
Again from the graph the range of the function i.e. values of y varies from 2 to +∞ and including 2.
Therefore, the range of the function is 2 ≤ f(x) < +∞ (Answer)
what is w in 10+15(w-2)=40
Answers
Answer:
w=4
Step-by-step explanation:
10+15(w-2)=40
distribute the 15
10+15w-30=40
combine like terms
-20 + 15w = 40
15w=60
w=4
Three more than the product of 12 and jose’s score
Answers
Answer:
the answer will be 48
Step-by-step explanation:
The answer 48 because 12 times 3 is 36 and then you add Jose's score and you get 48
Complete each geometric sequence.
A) 1/7, ___, 9/7, 27/7, ___
B) 24, 12, 6, ___, ___
Answers
Multiple the numerator by 3
B) 24, 12, 6, 3, 1.5
Divide by 2
Answer:
Step-by-step explanation:
A) 1/7, 3/7, 9/7, 27/7,81/7
Explanation: actually in it we simply multiply the nominator with 3.
B) 24,12,6,3,1.5
Explanation: In this we simply half the value or we can say that divided by 2.
expand (3x+7)(3x-7) =
Answers
Answer:
[tex]9 {x}^{2} - 49[/tex]
Step-by-step explanation:
Do FOIL, first outside inside last
3x × 3x = 9x^2
3x × -7 = -21x
7 × 3x = 21x
7 × -7 = -49
[tex]9 {x}^{2} - 21x + 21x - 49 \: midde \: cancels \: each \: other \: out[/tex]
So it would just be 9x^2 - 49
(3x + 7)(3x - 7) =
= 9x² + 21x - 21x - 49
= 9x² - 49
Paula bought a ski jacket on sale for $6 less than half it’s original price.She paid $86 for the jacket.What was the original price
Answers
Answer: Original price $184
Step-by-step explanation:
(X/2) - 6 = 86
X/2 = 86+6
X/2 = 92
X = 92*2
X = 184
A)11%
B)16%
C)19%
D)30%
Answers
Answer: C) 19%
Step-by-step explanation:250 +200 + 150 + 125 + 50 = 775 total complaints. 150 rude sales clerks out of 775 total complaints equals 150/775 = 0.1935 which is a 19 percent. So 19 percent of the complaints are about rude sales clerks.
1.
Marcy is comparing prices of
bottled water for 16.9-ounce
bottles. The table shows the
price for each brand. Complete
the table to sort the brands
from least to greatest price per
bottle. Round each unit price
to the nearest thousandth
dollar. 7.RP.2, 7.RP.2b
Answers
Answer:
Here is the complete question (in attachment).
The least price is for Water Spring brand and the greatest price is of Clear Mountain brand.
Step-by-step explanation:
To find the unit price we have to divide the full price with the whole of the quantity.
From least to greatest unit prices are arranged below.
Water Springs [tex]=\frac{19.99}{48}=0.416\$[/tex]Nature's River [tex]=\frac{20.35}{48}=0.423\$[/tex]Forest Air [tex]=\frac{10.49}{24}=0.437\$[/tex]Iceland Springs [tex]=\frac{5.49}{12}=0.457\$[/tex]Clear Mountain [tex]=\frac{11.99}{24}=0.499\$[/tex]In ascending order the number are.
[tex]0.416 < 0.423< 0.437< 0.457< 0.499[/tex]
So the least price is for Water Spring brand,and the greatest price is for Clear Mountain brand.
what is 1 5/8 divided by 5 1/7
Answers
Answer: 91/288
Step-by-step explanation: To divide mixed numbers, first write the mixed numbers as improper fractions.
We can do this by multiplying the denominator by the whole number and then adding the numerator. Then, we put our new numerator over our old denominator.
So here, we can write 1 and 5/8 as the improper fraction 13/8 and we can write 5 and 1/7 as the improper fraction 36/7.
So here, we have 13/8 ÷ 36/7.
Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.
So here, 13/8 ÷ 36/7 is the same as 13/8 × 7/36.
So now we are simply multiplying fractions and we do this by multiplying across the numerators and multiply across the denominators.
[tex]\frac{13}{8} x \frac{7}{36} = \frac{91}{288}[/tex]
So now we have 91/288 which is in lowest terms.
This means that 1 and 5/8 divided by 5 and 1/7 is 91/288.