The formula for finding the circumference of a circle is [tex]c=\pi *d[/tex] (where d is the diameter). So, simply plugging in 622 mm for d and 3.14 for pi, we find that c = 622 * 3.14 = 1953.08 mm.
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
Madison enjoys the game of golf. He knows that he will one-putt a green 15% of the time, two-putt 20% of the time, three-putt 35% of the time, and four-putt 30% of the time. Find the expected value for the number of putts Madison will need on any given green. Make sure to write down the entire equation that you used to solve this problem.
Answer:
The formula to calculate standard deviation from probability is \sqrt(n*p*(1-p)). n is the sample size, and 200 in this case (number of putts for practice). p is 80% or 0.8, the probability that he can make it. So the standard deviation is \sqrt(200*0.8*(1-0.8)=\sqrt(200*0.8*0.2)=\sqrt(16)=4.
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.
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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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]
HELP ASAP PLEASE!!!
In the equation
y=f(x)+k, the k value
A. Shifts the graph down k units
B. Shifts the graph up k unit
C. Shifts the graph to the left k units
D. Shifts the graph to the left k unit
im pretty sure it’s D
The k value in the equation y = f(x) + k causes a vertical shift of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down. Thus, the correct answer is B.
In the function transformation y = f(x) + k, the term k represents a vertical shift of the graph. Specifically:
If k is positive, the graph of the function f(x) shifts up by k units.If k is negative, the graph of the function f(x) shifts down by the absolute value of k units.Thus, the correct answer to the question is:
B. Shifts the graph up k units.
To summarize, the value k in the equation y = f(x) + k causes a vertical shift upwards if it's positive and downwards if it's negative.
what is a formula for the nth term of a given sequence
-12,-16,-20...
an = -12(-4)^n
a^n = -12 - 4 (n+1)
an = -8 - 4n
an = -12(-4)^n-1
Answer:
[tex]a_n=-12-4(n-1)[/tex]
Step-by-step explanation:
The given sequence is
-12,-16,-20...
The first term of this sequence is [tex]a_1=-12[/tex].
The common difference is
[tex]d=-16--12[/tex]
[tex]d=-16+12=-4[/tex]
The nth term of this arithmetic sequence is;
[tex]a_n=a_1+d(n-1)[/tex]
We substitute the values for the first term and the common difference to obtain;
[tex]a_n=-12-4(n-1)[/tex]
Answer:
[tex]a_{n} = -12-4(n-1)[/tex]
Step-by-step explanation:
We have given a arithmetic sequence.
-12,-16,-20,...
We have to find formula for a given sequence.
The general formula for nth term of sequence is :
[tex]a_{n} = a_{1}+d(n-1)[/tex]
In given sequence,
[tex]a_{1} = -12[/tex]
d is the common difference between consecutive terms.
d = -16-(-12) = -16+12
d = -4
Putting given values in formula, we have
[tex]a_{n} = -12-4(n-1)[/tex] which is the answer.
(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).
Determine whether the point (2, 0) is a solution to the system of equations. Explain your reasoning in complete sentences. graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2
Answer:
(2,0) is not a solution of the system. The point does not belong to any of the graphs.
Step-by-step explanation:
To easily solve this question, we can graph both equations in a graphing calculator, and verify the intersection point, which is equal to the solution of the system of equations.
Plotting the graphs
y = 3x + 2
g = |x-1| +1
We obtain the intersection point
(0,2)
Solution of the system of equations
An expression is shown below. (4/3x)(2/3x) What is the product of the two factors?
Which of the following is the best estimate of the area of the irregular shape? HELP PLEASE!!
ANSWER: 15.5 units^2
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]
A sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. Turning the radius-reduction screw on the top of the nozzle let's people reduce the radius by up to 25percent. To the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler if the radius reduction is used at full capacity?
Answer:
Area_lawn = 393.75 π ft^2
Step-by-step explanation:
Maximum radius : 30 feet
Minimum radius: 30 feet - 0.25*(30feet) = 22.5 feet
(25 percent reduction)
To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.
Since the sprinklers have a circular area:
Area = π*radius^2
Max area = π*(30 ft)^2 = 900π ft^2
Min area = π*(22.5 ft)^2 = 506.25π ft^2
Maximum area of lawn that can be watered by the sprinkler:
Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2
Area_lawn = 393.75 π ft^2
Answer:
1,590.4 sq ft
Step-by-step explanation:
Please help me out :)
Answer: x=12
Explanation:
In a parallelogram, adjacent angles equals 180 (consecutive angles). Therefore, (132-x)+(6x-12)=180
Simplify:
-x+6x+132-12=180
5x+120=180
5x=60
x=12
(-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
A square is 8 inches long each side a rectangle is 6 inches wide and 10 inches long wich shape has the greater perimeter? Explain
After calculating the perimeters, both the square and the rectangle have the same perimeter of 32 inches when the square has each side measuring 8 inches and the rectangle has dimensions of 6 inches by 10 inches.
Explanation:To determine which shape has the greater perimeter, calculate the perimeter of both the square and the rectangle. The formula for the perimeter of a square is 4 × side length, and the formula for the perimeter of a rectangle is 2 × (length + width).
For the square with each side measuring 8 inches, its perimeter is 4 × 8 = 32 inches.
For the rectangle with a width of 6 inches and a length of 10 inches, its perimeter is 2 × (10 + 6) = 2 × 16 = 32 inches.
Therefore, both the square and the rectangle have the same perimeter of 32 inches.
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 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.
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
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
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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A building in a downtown business area casts a shadow that measures 88 meters along the ground. The straight-line distance from the top of the building to the end of the shadow it creates a 32 angel with the ground. What is the approximate height of the building? Round your answer to the nearest meter
Answer:
=55m
Ahh. Correct me if I'm wrong.
Find the quotient. -71/-12
Answer:
5.92
Step-by-step explanation:
-71/-12=5.92
Answer:
[tex]\frac{71}{12}[/tex]
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Exact Form :
[tex]\frac{71}{12}[/tex]
Decimal Form :
5.916
Mixed Number Form :
5[tex]\frac{11}{12}[/tex]
Hope this helps,
Davinia.
5$ to get in and 0.80 to ride but he can only spend 25$ how many rides can he get on
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
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?
If Paul is 5 years old and mei is 2 years old, how old will mei be when Paul is 15
Harry got 42 out of 49 correct in his test. What fraction of marks did he get wrong
Answer:
42 correct; if all were answered, that means 7 were wrong. 7/49 reduces to 1/7; one seventh were wrong.
How many solutions does the system have? {y=−2x+2y=x2−3x Enter your answer in the box.
The system has two solutions: [tex]\( (2, -2) \) and \( (-1, 4) \),[/tex] found by solving their simultaneous equations.
let's solve the system step by step:
Given the system of equations:
[tex]1. \( y = -2x + 2 \)\\2. \( y = x^2 - 3x \)[/tex]
We want to find the values of [tex]\( x \) and \( y \)[/tex] that satisfy both equations simultaneously.
First, we set the equations equal to each other since they both equal [tex]\( y \):[/tex]
[tex]\[ -2x + 2 = x^2 - 3x \][/tex]
Now, let's rearrange this equation to get a quadratic equation:
[tex]\[ x^2 - 3x + 2x - 2 = 0 \]\[ x^2 - x - 2 = 0 \][/tex]
Now, we can use the quadratic formula to solve for [tex]\( x \):[/tex]
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
where [tex]\( a = 1 \), \( b = -1 \), and \( c = -2 \).[/tex]
[tex]\[ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}} \]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \]\[ x = \frac{{1 \pm 3}}{2} \][/tex]
So, we have two potential values for [tex]\( x \): \( x = 2 \) and \( x = -1 \).[/tex]
Now, let's find the corresponding [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex] value using either of the original equations:
For [tex]\( x = 2 \):[/tex]
[tex]\[ y = -2(2) + 2 = -4 + 2 = -2 \][/tex]
For [tex]\( x = -1 \):[/tex]
[tex]\[ y = -2(-1) + 2 = 2 + 2 = 4 \][/tex]
So, we have two solutions for the system:[tex]\( (2, -2) \) and \( (-1, 4) \).[/tex] Therefore, the system has 2 solutions.