3336_____________________________
Mollys jumprope is 61/3 feet long, Galis jumprope is 42/3 feet long. How musch longer is Mollys jump rope
61/3 - 42/3 = 19/3 feet
An expression is shown below. (4/3x)(2/3x) What is the product of the two factors?
Expand the following logs:
[tex]log_{7} \sqrt{a^{3}b^{9} }[/tex]
[tex]log_{6} (\frac{x^{5} }{y^{9} } )[/tex]
[tex]log_{8} (x^{3} y^{7} )[/tex]
QUESTION 1
The given logarithm is
[tex]\log_7\sqrt{a^3b^9}[/tex]
We rewrite to obtain;
[tex]\log_7(a^3b^9)^{\frac{1}{2}}[/tex]
Use the power rule of logarithm ; [tex]\log_a(m^n)=n\log_a(m)[/tex]
[tex]\frac{1}{2}\log_7(a^3b^9)[/tex]
Use the product rule; [tex]\log_a(mn)=\log_a(m)+\log_a(n)[/tex]
[tex]\frac{1}{2}[\log_7(a^3)+\log_7(b^9)][/tex]
Use the power rule of logarithms again;
[tex]\frac{1}{2}[3\log_7(a)+9\log_7(b)][/tex]
Or
[tex]\frac{3}{2}\log_7(a)+\frac{9}{2}\log_7(b)][/tex]
QUESTION 2
Given;
[tex]\log_6(\frac{x^5}{y^9})[/tex]
Apply the quotient rule of logarithm; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]
[tex]\log_6(\frac{x^5}{y^9})=\log_6(x^5)-\log_6(y^9)[/tex]
Apply the power rule to get;
[tex]\log_6(\frac{x^5}{y^9})=5\log_6(x)-9\log_6(y)[/tex]
QUESTION 3
Given;
[tex]\log_8(x^3y^7)[/tex]
Use the product rule to get;
[tex]=\log_8(x^3)+\log_8(y^7)[/tex]
Use the power rule now;
[tex]=3\log_8(x)+7\log_8(y)[/tex]
If the cost to the store is $20 and the selling price is $32 what is the markup?
Answer:
60%
Step-by-step explanation:
It went up 12 dollars, and you need to find how much 12 is of 20 as a percent. You do 12/20 times 5/5 and get 60/100, so 60% markup
Answer:
Step-by-step explanation:
The Answer Well -12$
20 - 32 = -12
You have 3\4 of a pie each guest takes home 1\6 of the pie how much pie does each guest take home
well, 1/6 of 3/4 is simply their product, thus
[tex]\bf \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3}{6}\cdot \cfrac{1}{4}\implies \cfrac{1}{2}\cdot \cfrac{1}{4}\implies \cfrac{1}{8}[/tex]
Please Help Me. How do you form an augmented matrix from the system of linear equations and solve.
This is Algebra 2. I need help solving questions 6.3 & 6.4. I've read the instructions and I am not understanding what their asking me.
Answer:
6.3 (x, y) = (3, 1)
6.4 (x, y) = (-4, 2)
Step-by-step explanation:
An augmented matrix in this context is an array of the coefficients in the equation. For example, the equation x -2y = 3 can be represented by the row of numbers 1 -2 3. When writing the matrix by hand, we usually just separate the elements in a row using blank space. Some calculators require a comma or other character between matrix elements. The entire array is enclosed in square brackets.
An augmented matrix may have a vertical line separating the square matrix of coefficients from the rightmost column of constants.
Many graphing calculators have functions available for entering and solving linear equations in this form.
__
6.3 The augmented matrix is ...
[tex]\left[\begin{array}{cc|c}2&3&9\\1&-4&-1\end{array}\right][/tex]
This array can be used to solve the system of equations using "row operations." The idea is that any row can be multiplied by any number, and any row can be added to any other row (multiplied by some number or not). So, the same techniques used to solve a system by elimination can be used here.
We can, for example, subtract twice the second row from the first. Then we have ...
[tex]\left[\begin{array}{cc|c}2-2(1)&3-2(-4)&9-2(-1)\\1&-4&-1\end{array}\right]\\\\\left[\begin{array}{cc|c}0&11&11\\1&-4&-1\end{array}\right] \quad\text{simplified}\\\\\left[\begin{array}{cc|c}0&1&1\\1&-4&-1\end{array}\right] \quad\text{first row divided by 11}\\\\\left[\begin{array}{cc|c}0&1&1\\1+4(0)&-4+4(1)&-1+4(1)\end{array}\right] \quad\text{4 times row 1 added to row 2}\\\\\left[\begin{array}{cc|c}0&1&1\\1&0&3\end{array}\right] \quad\text{simplified}[/tex]
When we turn this last matrix back into equations, we get ...
0x +y = 1
1x + 0y = 3
That is, the solution is (x, y) = (3, 1).
__
6.4 The augmented matrix is ...
[tex]\left[\begin{array}{cc|c}4&5&-6\\3&2&-8\end{array}\right][/tex]
Let's start the solution of this one by dividing the first row by 4.
[tex]\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\3&2&-8\end{array}\right] \\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\3-3(1)&2-3(\frac{5}{4})&-8-3(-\frac{3}{2})\end{array}\right] \quad\text{row 2 minus 3 times row 1}\\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\0&-\frac{7}{4}&-\frac{7}{2}\end{array}\right] \quad\text{simplify}\\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\0&1&2\end{array}\right] \quad\text{multiply row 2 by -4/7}[/tex]
We can eliminate the y-term in the first row by subtracting 5/4 times the second row. This will put the matrix in the form that shows us the solution directly.
[tex]\left[\begin{array}{ccc}1-\frac{5}{4}(0)&\frac{5}{4}-\frac{5}{4}(1)&-\frac{3}{2}-\frac{5}{4}(2)\\0&1&2\end{array}\right] \quad\text{row 1 minus 5/4 times row 2}\\\\\left[\begin{array}{ccc}1&0&-4\\0&1&2\end{array}\right][/tex]
This tells us ...
x = -4
y = 2
So the solution is (x, y) = (-4, 2).
An augmented matrix organizes the coefficients of a system of linear equations. After setting up the matrix with the coefficients from the equations, methods like Gaussian elimination or Gauss-Jordan elimination can be used to solve the matrix and consequently, solve the system.
Explanation:An augmented matrix is a compact way of keeping track of the coefficients in a system of linear equations. Here's how to form it and solve the system:
Identify the coefficients of the variables in the system of linear equations. Form a matrix based on these coefficients. For example, for the system of equations 2x + 3y = 7 and x - 4y = 11, the augmented matrix would be (2,3,7) on the first row and (1,-4,11) on the second row. Once the augmented matrix is formed, you can then use Gaussian elimination or Gauss-Jordan elimination methods to solve it.
Gaussian elimination involves using elementary row operations to manipulate the matrix to a form where the solution is easier to find, often called reduced row echelon form. For the Gauss-Jordan method, the main idea is to get zeros below (and above when possible) a leading 1, and make sure that leading 1 is the only nonzero entry in its column.
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Mr.Martin drove away from his house without his wallet.He did a 180.Where is he heading now?
Hey there!
He turned 180° degrees so he is going back to his house (to probably get his wallet)
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
A croissant shop has plain croissants, cherry croissants, chocolate croissants,almond croissants,apple croissants, and broccoli croissants. How many ways are there to choose a) a dozen croissants? b) three dozen croissants? c) two dozen croissants with at least two of each kind? d) two dozen croissants with no more than two broccoli croissants? e) two dozen croissants with at least five chocolate croissants and at least three almond croissants? f) two dozen croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants,and no more than three broccoli croissants?
Answer:
a) 110,880
b) 8.61x10^37
c) 7.18x10^19
Step-by-step explanation:
To find the amount of options, use the following combination equation.
n!/[r! * (n - r)]
In this equation, n represents the amount of possible options and r represents the amount being chosen at a time. We can now calculate out the answer for each possibility.
a) In this case, n would equal 12 and r would equal 6.
n!/[r! * (n - r)]
12!/[6! * (12 - 6)]
479001600/[720*6]
479001600/4320
110,880
b) In this case, n would equal 36 and r would equal 6
n!/[r! * (n - r)]
36!/[6! * (12 - 6)]
3.72x10^41/[720*6]
3.72x10^41/4320
8.61x10^37
c) For this one, n would equal 24 and r would equal 6. We would also then have to divide the answer at the end by 2.
n!/[r! * (n - r)]
12!/[6! * (12 - 6)]
6.20x10^23/[720*6]
6.20x10^23/4320
1.44x10^20 ÷ 2 = 7.18x10^19
This question deals with calculating combinations of croissants chosen under various conditions, which exemplifies the use of combinations with repetition in mathematics. Solutions depend heavily on the specifics of each part, many of which require customized approaches to account for constraints like minimum selections or caps on certain items.
Explanation:This question involves calculating different combinations of items from a set, which in this context are types of croissants being chosen in various quantities and conditions. Solving these problems requires understanding permutations and combinations, specifically combinations with repetition, as the order in which the croissants are selected does not matter but repeats are allowed.
We utilize the formula for combinations with repetition: C(n+r-1, r), where n is the number of types of items (in this case, croissants) and r is the number of items to choose.
For example, in part a) choosing a dozen croissants from 6 types would involve finding the combination with repetition of these 6 types over 12 selections.
However, specific formulas need to be applied to cater to the unique conditions stated in parts c) through f). Each of these parts imposes different constraints (e.g., minimum numbers of specific items, caps on how many of certain items can be chosen) that complicate the calculation and often require a piecewise approach or the inclusion/exclusion principle to accurately count the number of valid combinations.
Due to the complex and varied nature of each part of this question, and without specific formulas for parts c) through f), a general overview is provided instead of detailed solutions.
Each condition requires a tailored approach that involves breaking down the problem into smaller, manageable parts, and sometimes subtracting the cases that do not meet the given criteria from the total possible combinations.
A pair of shoes at Nordstrom’s costs $120. The shoes are on sale for 15% off. You have a coupon that allows you take an additional 10% off. How much will the shoes cost?
okay so you multiply .15 by 120 which is 18. then you multiply .10 by 120 which is 12. so you do 120 subtracted by 12 and 18 which the answer is 90
Final answer:
The shoes will cost $91.80 after both discounts have been applied.
Explanation:
To find the cost of the shoes, we need to apply two discounts.
First, we calculate the discount amount of 15% off $120 by multiplying $120 by 0.15, which gives us $18.
Then, we subtract this discount from the original price:
$120 - $18 = $102.
Next, we calculate the additional discount of 10% off $102 by multiplying $102 by 0.10, which gives us $10.20.
We subtract this discount from the discounted price:
$102 - $10.20 = $91.80.
So, the shoes will cost $91.80 after both discounts have been applied.
What is the distance between the points (3, 7) and (15, 16) on a coordinate plane?
The answer is 15 units
- Ap3x
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the larger circle (blue).
Answer:
380.13
Step-by-step explanation:
11^2 x pi = 380.13
Consider the enlargement of the rectangle. Use the proportion to find the missing dimension bod the original rectangle. (Sorry the pic is horrible)
Here's the right way:
[tex]\dfrac{x}{\frac 3 5} = \dfrac{20}{12}[/tex]
[tex]x = \dfrac{20}{12} \cdot \dfrac{3}{5} = 1[/tex]
Here's the way they want you to do it:
[tex]\dfrac{x}{\frac 3 5} = \dfrac{20}{12}[/tex]
[tex]12 x = 20 \times \dfrac{3}{5} = 12 \textrm{ FIRST BOX}[/tex]
[tex]x = 12/12 = 1 \textrm{ SECOND BOX}[/tex]
Answer: 12×=12
×=1, this the correct answer :3
The perimeter of a rectangle is 24 centimeters.Its length is 9 centimeters.Find the width
length of rectangle =9cm
width of rectangle = b
perimeter of rectangle =24cm
perimeter of rectangle =2(l+b)
24=2(9+b)
9+b=12
b=3cm
Using the perimeter formula for a rectangle, the width of the rectangle is calculated to be 3 centimeters.
To find the width of the rectangle when the perimeter is 24 centimeters and the length is 9 centimeters, we can use the formula for the perimeter of a rectangle: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. From the given information:
P = 24 cm
l = 9 cm
We can set up the equation as follows:
24 = 2(9) + 2w
24 = 18 + 2w
2w = 24 - 18
2w = 6
We then divide both sides by 2 to solve for w:
w = 6 / 2
w = 3 cm
Thus, the width of the rectangle is 3 centimeters.
Which of the following is the best estimate of the area of the irregular shape? HELP PLEASE!!
ANSWER: 15.5 units^2
if you had to read for 20 hours in total and you read 20 minutes a day how many days would it take you to finish?
Which expression is equivalent to
Answer:
Its the First choice.
Step-by-step explanation:
(3 m-2 n)^-3 / 6m n^-2
= (1/27) m^6 n^-3 / 6 m n^-2
= m^5 n ^-3 / 27*6 n^-2
= m^5 n^2 / 162 n^3
= m^4 / 162 n (answer).
The correct answer is option (A) m5 /162n
Step-by-step explanation:Let us solve step by step
See the attached figure for solution
A circle has a diameter of 26 units what is the area of the circle to the nearest hundredth of a square unit
Answer:
The area of the circle is [tex]530.93\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=26/2=13\ units[/tex] ----> the radius is half the diameter
assume
[tex]\pi=3.1416[/tex]
substitute
[tex]A=(3.1416)(13)^{2}=530.93\ units^{2}[/tex]
The independent variable of a data set is y while the dependent variable is z. Which of these is a response variable
Answer:
Dependant Variable
Step-by-step explanation:
Answer:
Step-by-step explanation:
The response variable is the dependent variable.
Aristole was born in 384 BC. Ron Howard was born in 1952 AD. How many years apart were they born?
1952 + 384 = 2336 years
The fishbowl has a diameter of 16 inches which measurement is closest to the volume of water in the fishbowl in cubic inches
Answer:
Volume of sphere = 4/3×22/7×radius×radius
4/3×22/7×8×8=268.19
Therefore the answer is approximately 268 cubic inches.
Hope this answer helps you.
A stack of 9 different cards are shuffled and spread out face down. If 4 cards are tired face up, how many different 4-card combinations are possible?
Answer:
126.
Step-by-step explanation:
This is the number of combinations of 4 cards from 9 cards:
= 9C4
= 9! / 4! 5!.
A quick way of calculating this is
9*8*7*6
----------- = 9*2*7 = 126 combinations.
4*3*2*1
There are 126 different 4-card combinations possible when selecting 4 cards from a shuffled stack of 9 different cards.
To find out how many different 4-card combinations are possible from a stack of 9 different cards when 4 cards are turned face up, we need to use combinatorial mathematics. The formula needed here is the combination formula, which for selecting r items from a set of n items is given by C(n, r) = n! / (r!(n-r)!), where '!' denotes factorial.
Substituting the given values, we get C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9×8×7×6) / (4×3×2×1) = 3024 / 24 = 126. So, there are 126 different combinations of 4 cards that can be turned face up from a shuffled stack of 9 different cards.
What is the distance between -1 and 7 on the number line? A) -8 B) -6 C) 6 D) 8
Answer:
D
Step-by-step explanation:
-1 0 1 2 3 4 5 6 7
9 units. distance is always positive.
ans. D
PLEASE HELP!
1. Given the following graph, would the point (1, 2) be a solution of the inequality? Explain
Answer:
No
Step-by-step explanation:
No because (1,2) falls on the line, and the line is a dotted line, which means that any point on the line is not a solution to the inequality.
Your basketball team scored 4 fewer than twice as many points, x, as the other team. a. Write an expression for the number of points your team scored. expression: b. The other team scored 24 points. How many points did your team score? Your team scored points.
Answer:
A) p = 2x - 4 for the expression. B) Your team scored 44 points.
Step-by-step explanation:
Let P represent the points your team made.
Since the question says "Your basketball team scored 4 fewer than twice as many points as the other team." this is how I came up with the expression.
p = 2x - 4 ( our points = 2 times more then the other teams points minus 4.
Using this expression and the given information that the other team made 24 points, I solved B.
44 = 2(24) - 4.
The expression for given statement can be found by system equation. We can create the system equation as per the statement.
(a) The expression for the number points your team scored is [tex]P=2x-4[/tex].
(b) Your team score 44 points.
Given:
Other team score [tex]x[/tex].
Let the [tex]P[/tex] is points scored by your team.
As per the statement, your basketball team scored 4 fewer than twice as many points, [tex]x[/tex] as the other team.
Convert the above statement in form of expression.
[tex]P=2x-4[/tex]
Thus, the expression for the number points your team scored is [tex]P=2x-4[/tex].
Substitute 24 for [tex]x[/tex] in above expression.
[tex]P=2\times 24-4\\P=44[/tex]
Thus, your team score 44 points.
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(Please show steps)
Graph the logarithmic function y=log(x-2)
Answer:
So the answer is (3, 0) on a graph.
Step-by-step explanation:
What I use is a graphing calculator. It helps tremendously. It is called desmos.com. Hope this helps.
Answer:
The given function is
[tex]y=log(x-2)[/tex]
To graph any function, we just have to five arbitrary values to x-variable, and see the y-values that gives to formed coordinate pairs to graph them then.
In this case, the table that shows these values is gonna be
X Y
2.5 -0.3
3 0
3.5 0.2
4 0.3
4.5 0.4
Notice that we started from [tex]x=2.5[/tex]. The reason is beacuse the given logarithmic function is not defined for values equal or lower than 2, when taht happens, the function becoms undetermined. This means the domain of the given function has to be restricted to [tex]D= (x>2)[/tex], otherwise the function won't be defined.
Next, we evalute the function for each case.
[tex]x=2.5[/tex]
[tex]y=log(x-2)=log(2.5-2)=log(0.5) \approx -0.3[/tex]
[tex]x=3\\y=log(x-2)=log(3-2)=log(1)=0[/tex]
[tex]x=3.5\\y=log(x-2)=log(3.5-2)=log(1.5) \approx 0.2[/tex]
[tex]x=4\\y=log(x-2)=log(4-2)=log(2) \approx 0.3[/tex]
[tex]x=4.5\\y=log(x-2)=log(4.5-2)=log(2.5) \approx 0.4[/tex]
When you have the table completed, you proceed to graph each coordinate.
In this case, the graph of the logarithmic function would be as the image attached. That's all the process to graph the function.
(In the graph, you can observe how fast the function drops when is near to x=2, that's the undetermination behaviour we talk about lines above).
The pair of numbers giving the location of a point are called its ___.
Answer:
coordinates
Step-by-step explanation:
The coordinates are the pairs of number giving a location of a point on the coordinate grid (example (4, 12) or (-3, 4) explain where the location point should be)
The pair of numbers giving the location of a point are called its coordinates.
What is Cartesian Plane?Two perpendicular number lines define a Cartesian plane, which is named after Rene Descartes, a mathematician who codified its use in mathematics: the horizontal x-axis and the vertical y-axis, respectively. Any point in the plane can be described by an ordered pair of numbers using these axes.
In every direction, the Cartesian plane has an infinite length.
Given
A pair of numbers that use the horizontal and vertical distances between the two reference axes to describe a point's position on a coordinate plane. typically represented by the x- and y-values in the form (x, y).
Coordinates are the numbers who gives the location of point.
Hence, the pairs are called coordinates.
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PLEASE HELP! Points A and B split the circle into two arcs. Measure of minor arc is 150°. Point M splits major arc with the ratio 2:5 (point M is closer to point B). Find m∠BAM.
Answer:
30 degrees
Step-by-step explanation:
Answer: Measure of ∠BAM is 30°.
Step-by-step explanation:
As given in the question, points A and B split the circle with center O into two arcs in the attached figure below. Major of the minor arc is 150°. And, the point M splits the major arc in the ratio 2 : 5.
We are to find the measure of ∠BAM.
Since the measure of minor arc AB is 150°, so the measure of major arc AB will be
360° - 150° = 210°.
Also, point M divides the major arc AB in the ratio 2 : 5, so we have
[tex]arc~BM:arc~MA=2:5.[/tex]
Therefore, the measure of ∠BOM is given by
[tex]m\angle BOM=\dfrac{2}{2+5}\times210^\circ=\dfrac{2}{7}\times 210^\circ=60^\circ.[/tex]
We know that
the measure of the angle subtended at the center by an arc is equal to twice the measure of the angle subtended at the circumference by the same arc.
That is, on arc BC, we get
[tex]m\angle BOM=2\times m\angleBAM\\\\\Rightarrow m\angle BAM=\dfrac{m\angle BOM}{2}\\\\\\\Rightarrow m\angle BAM=\dfrac{60^\circ}{2}\\\\\Rightarrow m\angle BAM=30^\circ.[/tex]
Thus, the measure of ∠BAM is 30°.
What is the area of this triangle? Enter your answer as a decimal. Round only your final answer to the nearest tenth.
___in^2
Answer:
56.1 in^2
Step-by-step explanation:
When given sides "a" and "b" and the angle α between them, the applicable formula for the area of the triangle is ...
A = (1/2)ab·sin(α)
Substituting the given values, we find the area to be ...
A = (1/2)(14.2 in)(8 in)sin(99°) ≈ 56.1 in^2
Answer:
56.1
Step-by-step explanation:
Diagram
Let's look at the diagram for a moment.
The 8 in line has been extended.
The dashed line is the height associated with the 8 inch line
The dashed line and the 8 inch line's extension meets at right angles.
Discussion
Normally you would take the 8 inch line and the height and divide their product by 2. You don't have the height. So you have to somehow get an expression for it.
The 81o angle is the supplement of the 99o angle. If you take the sine of both of them the sines are equal.
h = sin(81) * 14.2 because
sin(81) = opposite / hypotenuse.
opposite = hypotenuse * sin(81)
opposite = height = hypotenuse* sin(81)
height = 14.2 * sin(81)
Now we can find the area
Area
Area = height * base
base = 8
height = 14.2 * sin(81)
Area = 1/2 * 8 * 14.2 * sin(81)
Area = 56.1
Fred went to catch a minimun of 2 pounds of fish.He caught 5/16 pounds.He caught another fish that was 7/8 pounds.How many pounds of fish did he catch so far? What shoud be the minimun weight of the third fish so that he can catch at least 2 pounds of fish in total?
Answer:
1 3/16
Step-by-step explanation:
5/16 + (7/8= 14/16)
14/16 + 5/16= 19/16
16/16 = 1
3 LEFT OVER
1 3/16
Answer:
He caught 1 3/16 pounds of fish.
Minimum weight = 13/16 pounds.
Step-by-step explanation:
So far he caught 5/16 + 7/8
= 5/16 + 14/16 = 19/16
= 1 3/16 pounds.
Minimum wight of the third fish = 2 - 1 3/16
= 32/16 - 19/16
= 13/16 pounds.
(-3,5) is located in
It is located in the 2nd quadrant.
(x,y) - 1st quadrant
(-x,y) - 2nd quadrant
(-x,-y) - 3rd quadrant
(x,-y) - 4th quadrant
Answer:
Second quadrant
Step-by-step explanation:
That coordenates are located in the second quadrant of the cartesian plane
Best regards