What is the equation of the axis of symmetry for the parabola y equals start fraction one over three end fraction left parenthesis x plus one right parenthesis squared minus three?

To convert log4 14 to a logarithm of base 3, you can use the change of base formula. The required conversion would be log3 14 divided by log3 4.

To write log4 14 as a logarithm of base 3, we would use the change of base formula. The change of base formula is logba = logca / logcb, where logba is the logarithm we want to convert, c is the new base, a is the number, and b is the original base. So, in this case, we want to write log4 14 as a logarithm of base 3, so using the formula, it would be (log3 14) / (log3 4).

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Answer: The answer is 101!

Step-by-step explanation:

Call the first number in the sequence x

The next integer in the sequence is x + 1

The sum of the 5 consecutive integers is:

x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505

5x + 10= 505

5x = 495

x = 99

Since x is the first number, x + 2 is the third integer.

Thus, the third number in the sequence is 101

There will be, 590490 possible combinations.

The number of different groups which can be formed from the available things can be calculated using combinations.

Given that, A small combination lock on a suitcase has 6 wheels, each labelled with the 10 digits 0 to 9.

We have 10 for the first wheel, but second wheel only has 9 options because 2nd number can't be the same as first. The third and fourth wheels also has 9 options for the same reason.

10x9x9x9x9x9 = 590490 combinations

Hence, There will be, 590490 possible combinations.

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Answer with explanation:

Mean is sum of all the observation divided by total number of observation, where as median is middlemost observation of the data set, while mode is most occurring variate or data value in the data set.

1. Variate or Data set which is represented in Histogram is

 3,8,4,8,3

Arranging it in ascending order, we get

3,3,4,8,8

Data is skewed right.So, Mean >Median>Mode

Mean =5.2

Number of observation is 5. So,Median will be Middle term,that is third term equal to 4.

Mode =3 or ,8 which will be equal to 3,as data is skewed right.

→Mean gives better representation of data set,because, 5.2-3=2.2 and, 8-5.2=2.8

2. Variate or Data set which is represented through dots is

 2, 2, 3,5,5

Arranging it in ascending order, we get

2,2,3,5,5

Data is skewed right.So, Mean >Median>Mode

Mean=3.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =2 or 5 which will be equal to 2,as data is skewed right.

→Mean gives better representation of data set,because, 3.4-2=1.4 and, 5-3.4=1.6

3. Variate or Data set which is represented in Histogram is

 6,2,6,2,6

Arranging it in ascending order, we get

2,2,6,6,6

Data is skewed left.So, Mean <Median<Mode

Mean=4.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 6.

Mode =6

→Mode gives better representation of data set.

4.Variate or Data set which is represented through dots is

 1,3,4,3,1

Arranging it in ascending order, we get

1,1,3,3,4

Data is skewed left.So, Mean <Median<Mode

Mean=2.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =1 or 3,data is skewed left,so mode =3

Here, in this data set, both mode and median are better measure of center than Mean,as there are two modes in the data set, so choosing median as measure of center,because data is skewed left,

For ,Option 4: Median is the better measure of center.

The slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex].

A straight line is a combination of endless points joined on both sides of the point.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope 'm' of any straight line is given by:

The given equation in the problem is;

y = 4x + 5

The slope of the given equation is found from the standard equation of the straight line as;

y=mx+c

On comparing, we get, m = 4.

The perpendicular line slopes are reciprocals with the negative sign of each other.

Hence, the slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex]

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The area of the given sectors of circles is required.

The area of the sector is [tex]8.79\ \text{in}^2[/tex]

The area of the sector is [tex]151.98\ \text{cm}^2[/tex]

[tex]\theta[/tex] = Central angle = [tex]\dfrac{5\pi}{7}\ \text{rad}[/tex]

d = Diameter = 5.6 in

r = Radius = 2.8 in

Area of a sector is given by

[tex]A=\dfrac{\theta}{2}r^2\\\Rightarrow A=\dfrac{\dfrac{5\times 3.14}{7}}{2}\times 2.8^2\\\Rightarrow A=8.79\ \text{in}^2[/tex]

[tex]\theta=\dfrac{4\pi}{5}\ \text{rad}[/tex]

r = 11 cm

[tex]A=\dfrac{\dfrac{4\times 3.14}{5}}{2}\times 11^2\\\Rightarrow A=151.98\ \text{cm}^2[/tex]

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Determine the dimensions of the metal sheet by setting up and solving equations based on the given volume of the box and the relationship between its length and width.

This problem can be tackled by using a bit of algebra and understanding volume calculations. We can use the equation for the volume of a box which is V=length*width*height. The problem gave us the volume of 1014 cu in. When a 3 in. square is cut from each corner of the rectangular piece of metal, the sides fold up to form the box, the height of the box becomes 3 in. This means we're missing the length and width of the box to solve for volume.

Since the length equals to twice the width minus 6 in., we can express the length as 2W - 6. Substituting these into the volume equation we get: 1014 = (2W - 6)(W)(3) which when simplified gives W, the width of the metal piece. Then substitute W into the length formula 2W - 6 to solve for the length.

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The measurements given can form a triangle, and to solve it, we would use the Law of Sines. After confirming the possibility of a triangle, we solve for the unknown angle C using the known values and compute the remaining angle and side.

To determine if a triangle is formed by the given measurements and solve it using the Law of Sines, we need to check if the given angle and sides satisfy the triangle inequality. The measurements given are angle B = 137°, side c = 6, and side b = 11. A triangle is possible if the sum of the two smallest sides is greater than the length of the longest side. Here the angle is very large, suggesting that the opposite side (b) must be the longest; however, since side b is indeed longer than side c, this condition is satisfied, so a triangle can be formed.

To solve the triangle using the Law of Sines, we set up the following ratio:

    b/sin(B) = c/sin(C)

After substituting the known values into the equation, we get:

    11/sin(137°) = 6/sin(C)

Now, we solve for sin(C) to find the angle C, and subsequently use the sum of angles in a triangle (180°) to find the remaining angle A. Once angle A is known, we can use the Law of Sines again to find the remaining side a. If at any point we find that the calculation results in an invalid sine value (greater than 1 or less than -1), we must then state that no real solution exists.

It is important to note that if we find angle C to be obtuse (greater than 90°), the triangle will not have a unique solution because it would contradict our initial assumption that angle B, being the largest given angle, is opposite the longest side.

Final answer:

The equation of the line that passes through the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.

Explanation:

The question asks us to find the equation of a line that passes through a given point and is perpendicular to a given line. To solve this, we first need to determine the slope of the given line, then find the perpendicular slope, and finally, use the point-slope form of a line to write the equation for our new line.

Here are the steps:

Find the slope of the given line. For the equation 4x + 2y = 2, we rearrange it to slope-intercept form (y=mx+b), which gives us y = -2x + 1. The slope is -2.

Since we want a line that is perpendicular to the given line, we need the negative reciprocal of -2, which is 1/2.

Now we use the point-slope form of a line, y-y1 = m(x-x1), with point (5,6) and slope 1/2. This gives us y - 6 = 1/2(x - 5).

Solving for y to get the slope-intercept form, we multiply both sides by 2 to get rid of the fraction: 2y - 12 = x - 5, and then solve for y: y = 1/2x + 7/2.

The equation of the line that contains the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.

Answer:

The graph is that one which corresponds to the equation y = x-1. The graph is shown in the image below.

Step-by-step explanation:

Translate a linear curve means to move the whole curve up or down, where the final line will be in parallel to the original curve.

For translate the graph up to 2 unit, it must to be summed 2 unit in the right member of the original equation:

[tex] y = (x-3) + 2 [/tex]

[tex] y = x-3 + 2 [/tex]

[tex] y = x-1 [/tex]

we have

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}[/tex]

Multiply the numerator and denominator by the conjugate of the denominator

so

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}*\frac{4-\sqrt{12}}{4-\sqrt{12}}=\frac{(2-\sqrt{8})(4-\sqrt{12)}}{4^{2}-(\sqrt{12})^{2}}\\ \\= \frac{2*4-2*\sqrt{12}-4*\sqrt{8}+\sqrt{12}*\sqrt{8}}{16-12}\\ \\=\frac{8-4\sqrt{3}-8\sqrt{2}+4\sqrt{6}}{4} \\ \\=2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

therefore

the answer is

[tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

Answer:

[tex]\text {Area of figure is }44 units^2[/tex]

Step-by-step explanation:

Given the figure and we have to find the area of given figure.

Area of figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(GHF)

From the figure, dimensions according to square boxes can be written as

AE=HF=8 units, EF=3 units, BI=3 units, GH=2 units, AC=CE=4 units.

[tex]ar(ABC)=ar(CDE)=\frac{1}{2}\timesAC\times BI=\frac{1}{2}\times4\times3=6 units^2[/tex]

[tex]ar(AEFH)=HF\times EF=8\times 3=24 units^2[/tex]

[tex]ar(GHF)=\frac{1}{2}\timesHF\timesGH=\frac{1}{2}\times8\times 2=8units^2[/tex]

∴ [tex]\text {Area of figure is }44 units^2[/tex]