6. What is the length of side AB?

The intersection of sets A and B

The intersection of two sets is the set of elements that are common to both sets. To find the intersection of sets A and B, we simply look for the elements that are in both sets. In this case, the intersection of A and B is {h, o, e}.

The union of two sets is the set of elements that are in either one of the sets or both. To find the union of sets A and B, we simply combine the elements from both sets, making sure to not include any duplicates. In this case, the union of A and B is {h, o, m, e, u, s}.

So, the intersection of sets A and B is {h, o, e} and the union of sets A and B is {h, o, m, e, u, s}.

Here is the solution in HTML:

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The end behaviour of g(x) = log₁,₃(-x + 4) is as x approaches 4, g(x) approaches ∝ and as x approaches 4, g(-∝) approaches -∝

From the question, we have the following parameters that can be used in our computation:

g(x) = log₁,₃(-x + 4)

The maximum input value of the above function is 4

This is so because

-x + 4 = 0

x = 4

Set the value of x in the function to 4

So, we have

g(4) = log₁,₃(4 + 4)

g(4) => ∝

Set the value of x in the function to -∝

So, we have

g(-∝) = log₁,₃(-∝ + 4)

g(-∝) => -∝

Hence, the end behaviour is as x approaches 4, g(x) approaches ∝

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Answer:

m<6 = 78°

Step-by-step explanation:

I hope your drawing of this problem looks somewhat like this:

                                                                ^  t

                                                              /

                                                            /

                                                   1     /    2

<----------------------------------------------------------------------------->   ℓ

                                               3     /    4

                                                    /

                                         5       /    6

<------------------------------------------------------------------------------>  m

                                      7       /   8

                                            /

                                          /

                                        V

Sorry about the terrible drawing, but I hope I got the angle numbers correctly written.

Angles 3 and 6 are are called alternate interior angles.

They are "interior angles" because they are on the inside of lines l and m. They are "alternate angles" because they are on different sides of the transversal, t.

There is a Geometry theorem about this situation.

Theorem:

If parallel lines are cut by a transversal, then alternate interior angles are congruent.

In this case, since the pair of angles 3 and 6 is a pair of alternate interior angles, then by the theorem above, they are congruent.

m<6 = m<3

Since m<3 = 78°, then m<6 = 78°.

Answer:

1st page:

To determine if Jason and Arianna made a mistake in their solution, we can examine the slopes and y-intercepts of the two equations.

The first equation, 5x - 3y = -1, can be written in slope-intercept form as y = (5/3)x + 1/3, where the slope is 5/3 and the y-intercept is 1/3.

The second equation, 3x + 2y = 7, can be written in slope-intercept form as y = (-3/2)x + 7/2, where the slope is -3/2 and the y-intercept is 7/2.

To solve the system of equations, we need to find the point of intersection of the two lines. We can see from the slopes that the lines are not parallel, so they must intersect at some point. However, the slopes are not perpendicular either, so they do not intersect at a right angle.

By graphing the two equations on the same coordinate plane, we can see that the point of intersection is (2, 2), not (4.04, 7.31) as Jason and Arianna calculated. Therefore, they must have made a mistake in their solution.

In summary, we can tell that Jason and Arianna made a mistake in their solution by examining the slopes and y-intercepts of the two equations and graphing them to find the actual point of intersection.

2nd page:

To determine if Jason and Arianna made a mistake in their solution, we can graph the two linear equations on the same coordinate plane and look for the point of intersection.

We can begin by rearranging the equations into slope-intercept form:

5x - 3y = -1 → y = (5/3)x + 1/3

3x + 2y = 7 → y = (-3/2)x + 7/2

Now we can graph the two lines. We can plot two points for each line and connect them with a straight line to obtain the graphs.

For the first equation, when x = 0, we get y = 1/3. When x = 3, we get y = 6/3 = 2. Plotting these two points and connecting them, we get:

Graph of the first equation

For the second equation, when x = 0, we get y = 7/2. When x = 2, we get y = 1/2. Plotting these two points and connecting them, we get:

Graph of the second equation

We can see from the graphs that the lines intersect at the point (2, 2), not at (4.04, 7.31) as Jason and Arianna found. Therefore, they must have made a mistake in their solution.

In summary, we can tell from the graphs of the equations that Jason and Arianna must have made a mistake because the lines do not intersect at the point they found.

3rd page:

We can determine if there is a unique solution to the system of linear equations by examining the slopes of the two equations.

The slope of the first equation, 5x - 3y = -1, can be found by rearranging the equation into slope-intercept form y = (5/3)x + 1/3. We can see that the slope of the line is positive and not equal to the slope of the second equation, which is -3/2.

Similarly, the slope of the second equation, 3x + 2y = 7, can be found by rearranging the equation into slope-intercept form y = (-3/2)x + 7/2. Again, we can see that the slope of the line is negative and not equal to the slope of the first equation, which is 5/3.

Since the slopes of the two lines are not equal, they will intersect at a unique point. In other words, there is only one solution to the system of equations.

Therefore, we can conclude that there is a unique solution to the system of linear equations given by 5x - 3y = -1 and 3x + 2y = 7, based on the slopes of the graphs of the equations in the system.

Step-by-step explanation:

the total money will be spent is 47.4 ∈.

What is trapezoid?

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or polygon with four sides. It has a set of parallel opposite sides as well as a set of non-parallel sides. The bases and legs of the trapezoid are referred to as parallel and non-parallel sides, respectively. A trapezoid is a four-sided closed 2D figure with a perimeter and an area. The bases of the trapezoid are two of the shape's sides that are parallel to one another. The legs or lateral sides of a trapezoid are its non-parallel sides. The altitude is the shortest distance between any two parallel sides.

Here the parallel sides are given 12m and 20m.

The perpendicular line will be the fence

so the other line is given 17m.

The area of the trapezoid is (a+b/2)*h

h =√17²-8² =15

So the area will be 12+20/2 * 15

A= 16*15 = 240m²

For 100 m² cost 19.75

For 240 it will be 19.75/100 * 240= 47.4

Hence the total money will be spent is 47.4 ∈.

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Answer:

$7.35

Step-by-step explanation:

no step by step lol heres ur answer

Answer:

420km/12km = 35

1×35l = 35lites

rate it 5 stars pls TANXX

Answer:

35 litres

Step-by-step explanation:

We can use a ratio to solve.

1 litre               x litres

-------------  = ----------------

12 km             420 km

Using cross products

1 * 420 = 12x

Divide each side by 12.

420/12 = x

35 =x

35 litres

Answer:

Let the base of the triangle and parallelogram be denoted by 'b' and their respective altitudes be denoted by 'h1' and 'h2'.

Given that the area of the triangle is equal to the area of the parallelogram, we have:

Area of triangle = (1/2)bh1 Area of parallelogram = b*h2

Since the areas are equal, we have:

(1/2)bh1 = b*h2

Simplifying the above equation, we get:

h1 = 2*h2

Substituting the given value of h2 as 100 m, we get:

h1 = 2*100 = 200 m

Therefore, the altitude of the triangle is 200 meters

No, the function g will be the same as the graph of f, translated to the right by 2.

What is transformation?

A point, line, or geometric figure can be changed in four different ways that are all collectively referred to as transformations. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

f(x + a)horizontally shift the graph of f(x) left by a units.

The graph of f(x) is horizontally shifted by a units right side by f(x - a).

The graph of f(x) is vertically shifted upward by a unit by f(x)+a.

f(x)- a one-unit vertical shift downward of the f(x) graph.

The given function is

g(x) = f(x-2)

According to rule,

The function g will be the same as the graph of f, translated to the right by 2.

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Answer:

We can use the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Plugging in the given values, we get:

6,430.72 = π(16)^2h

Simplifying:

6,430.72 = 256πh

Dividing both sides by 256π:

h = 6,430.72 / (256π)

h ≈ 8.05

Therefore, the height of the cylinder is approximately 8.05 yards.

Answer:

Therefore, the lower fence is 1.5 and the upper fence is 5.5.

Step-by-step explanation:

To determine the upper and lower fences for a boxplot, we first need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1). Then, we can use the following formulas:

Lower Fence = Q1 - 1.5 * IQR

Upper Fence = Q3 + 1.5 * IQR

In the given boxplot, the box extends from 2 to 5, with the median (Q2) at 3.5. The first quartile (Q1) is 3 and the third quartile (Q3) is 4. Therefore, the IQR is:

IQR = Q3 - Q1 = 4 - 3 = 1

Using the formulas above, we can calculate the lower and upper fences:

Lower Fence = Q1 - 1.5 * IQR = 3 - 1.5 * 1 = 1.5

Upper Fence = Q3 + 1.5 * IQR = 4 + 1.5 * 1 = 5.5

Therefore, the lower fence is 1.5 and the upper fence is 5.5.

25.628 pounds of her weight is made up of fat.

We can use the formula Weight of Fat = Body Fat % x Body Weight. To find out how much of her weight is made up of fat, we need to multiply her body fat percentage by her weight. We can do this by using the following formula:

Body fat weight = Body fat percentage x Weight

In this case, the body fat percentage is 14.9% and the weight is 172 pounds. Plugging these values into the formula, we get:

Body fat weight = 14.9% x 172 pounds
Body fat weight = 0.149 x 172 pounds
Body fat weight = 25.628 pounds

In this case, 14.9% of 172 pounds is 25.628 pounds.

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The parent function f(x) = 2^(x) is transformed into the function g(x) = 2^((x+3)) by shifting the graph 3 units to the left.

This means that the maximum value on the interval [-2,2] for the parent function will now occur at the point (-2+3) = 1 for the transformed function.

Therefore, the maximum value for the transformed function on the interval [-2,2] will be 2^(1) = 2.

In summary, the transformation shifts the graph of the parent function 3 units to the left, causing the maximum value on the interval [-2,2] to occur at x = 1 and have a value of 2.

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Tο depict the relatiοnship between twο numerical variables using Data visualizatiοn that is knοwn as a scatterplοt.

Using this scatterplοt, we graphed a line using linear regressiοn. This line can use as οur reference pοint and ignοre the rest οf the pοints οn the graph.

We will examine this graph and try tο find apprοximately what value οf y is given when we prοvide an x value.

Since the number οf hits is the x value, tο find hοw high the graph gοes at that x value we can lοοk at the graph tοο.

Right between 100 and 150 is 125, sο we can nοw start there and mοve up.

When we mοve up, we get a line that's between 10 and 20. We can alsο view it's in the tοp half οf that bοx. That means the value οf y fοr this will be mοre than 15.

Since it's nοt lying directly οn 20, we have the οnly οptiοn left is 18.

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The formulas for the exponential functions that pass through the two points given are:
f(x) = 6 * 7^x
g(x) = 1280 * 0.125^x

To find the formula for an exponential function that passes through two points, we can use the general form of an exponential function, which is f(x) = a * b^x, where a and b are constants. We can plug in the x and y values from the two points and solve for a and b.

For part a:
f(x) = a * b^x
6 = a * b^0 (from point (0,6))
294 = a * b^2 (from point (2,294))

From the first equation, we can see that a = 6. We can substitute this value into the second equation:
294 = 6 * b^2
49 = b^2
b = 7

So the formula for the exponential function that passes through the two points is f(x) = 6 * 7^x.

For part b:
g(x) = a * b^x
1280 = a * b^0 (from point (0,1280))
20 = a * b^2 (from point (2,20))

From the first equation, we can see that a = 1280. We can substitute this value into the second equation:
20 = 1280 * b^2
0.015625 = b^2
b = 0.125

So the formula for the exponential function that passes through the two points is g(x) = 1280 * 0.125^x.

In conclusion, the formulas for the exponential functions that pass through the two points given are:
f(x) = 6 * 7^x
g(x) = 1280 * 0.125^x

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The required measure of q in the given triangle is 3.

Trigonometric ratios are mathematical functions used to relate the angles of a right-angled triangle to the lengths of its sides. There are three basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan), which can be defined as follows:

Sine (sin) = opposite/hypotenuse

Cosine (cos) = adjacent/hypotenuse

Tangent (tan) = opposite/adjacent

Here,
Applying the Sine rule,
sin45 = q/3√2
q = 3

Thus, the required measure of q in the given triangle.

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a)CD and AA

b)CD + AA = 190,000

c)0.06CD + 0.11AA = 18,900

d)AA = 187,333.17.

(a) Let CD be the amount invested in Certificates of Deposit and AA be the amount invested in AA bonds.

(b) The total amount invested is given by the equation CD + AA = 190,000.

(c) The total amount earned from the investment is given by the equation 0.06CD + 0.11AA = 18,900.

(d) To solve this system of equations using elimination, we multiply the first equation by 0.11 and the second equation by 0.06 and add the resulting equations together, yielding the equation 12.06CD + 10.11AA = 214,084. We then subtract the original equation from this new equation to get 9.06CD = 24,084. Solving for CD, we get CD = 2,666.83. We can then substitute this value into either of the original equations to get AA = 187,333.17.

(e) Sally should invest $2,666.83 in Certificates of Deposit and $187,333.17 in AA bonds to earn exactly $18,900 per year.

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Answer:

97271.1577

multiply 3374.60 by 2882.45%

Answer: 3,600

dont quote me on it doing it the way i learned how to lol

Step-by-step explanation:     Volume = length x width x height.

Answer:

917.33

Step-by-step explanation:

Top conic volume formula: ⅓ r²h=⅓(16/2)²*(18-12.5)

                                                      =⅓8²*5.5

                                                      =⅓352

                                                      =117.33

Volume formula of a cylinder: V=r²h

                                                =8²*12.5

                                                =800

117.33+800=917.33

[tex]-\dfrac{3}{4}x-\dfrac{1}{3}+\dfrac{7}{8}x-\dfrac{1}{2} = -\dfrac{3}{4}x+\dfrac{7}{8}x -\dfrac{1}{3}-\dfrac{1}{2} = \\[/tex]

[tex]= -\dfrac{3(2)}{4(2)}x+\dfrac{7}{8}x -\dfrac{1(2)}{3(2)}-\dfrac{1(3)}{2(3)} = -\dfrac{6}{8}x+\dfrac{7}{8}x -\dfrac{2}{6}-\dfrac{3}{6} \\[/tex]

[tex]= \dfrac{-6+7}{8}x -\dfrac{2+3}{6} = \dfrac{1}{8}x -\dfrac{5}{6} \\[/tex]

Answer: 4

Step-by-step explanation:

We can start by simplifying each term step by step:

First, the cube root of 1 is 1, so -3 times the cube root of 1 is simply -3.

Second, the square root of 49 is 7, so 49 divided by the square root of 49 is also 7.

Putting it all together, we have:

-3 × ∛1 + 49 ÷ √49 = -3 + 7 = 4

Therefore, the value of the expression is 4.

The tabs can be completed in the following way:

1. Fraction for 25% = 25/100 = 5/20 = 1/4

2. 90 percent: Decimal 0.90: Fraction: 90/100 =9/10

3. 60 percent: Decimal 0.60: Fraction: 60/100 = 6/10 = 3/5

4. 35 percent: Decimal 0.35: Fraction: 35/100 = 7/20

5. 33 percent: Decimal 0.33: Fraction: 33/100

6. 65 percent: Decimal 0.65: Fraction: 65/100 = 13/20

A percentage is a value that is obtained as a fraction of the number 100. In the above question, we are given a list of values in percentages and told to convert them to decimal and fraction forms.

To do this, we need to divide the number 90 by 100 for the second expression and express this as a decimal. The resultant figure is 0.9. When converted to a fraction, the value now has a denominator and numerator.

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The coordinates of the centroid (,)(△) of triangle ABC are (-1, 8/3).

To find the coordinates of the centroid, we can use the formula:

(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.

Plugging in the coordinates of A (0, 4), B (0, 2), and C (-3, 2), we get:

(x, y) = ((0 + 0 - 3)/3, (4 + 2 + 2)/3) = (-1, 8/3)

In a two-dimensional plane, the centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side. The centroid divides each median into two segments, with the ratio of the length of the segment closer to the vertex to the length of the segment closer to the opposite side being 2:1.

In a three-dimensional space, the centroid of a solid can be found by dividing the solid into smaller parts, finding the centroid of each part, and then averaging them. The centroid of a solid is the point where the lines connecting the centroids of each part intersect.

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Complete Question: -

Give the coordinates of the centroid of triangle ABC, which is denoted by (,)(△) and is the point where the medians of the triangle intersect for a (0 , 4) , b (0 ,2) , and C  (-3 ,2 ).

The equation of line in the point-slope form is y - 2 = -1(x + 2)

The equation of a straight line is a relationship between x and y coordinates, The point-slope form of the equation of a straight line is,

y-y₁ = m(x-x₁), where m is the slope of the line.

Given that,

A graph having straight line,

and it can be seen in the graph it is passing through (-2, 2) & (-1, 1)

Slope m = (y₂-y₁)/(x₂-x₁)

              = (2 - 1)/ (-2 -(-1))

              =  1/-1

              =   -1

So now taking point (-2, 2) and slope is -1

The point slope form of the equation is:

y - 2 =  -1 (x - (-2))

y - 2 = -1(x + 2)

Hence, the equation is y - 2 = -1(x + 2)

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In other words, the quotient is 2x+4 and the remainder is 10x+7.

To solve this problem, we will use polynomial long division. The steps are as follows:

1. Divide the first term of the dividend (4x^(3)) by the first term of the divisor (2x^(2)) to get the first term of the quotient (2x).
2. Multiply the first term of the quotient (2x) by the divisor (2x^(2)+4x) to get (4x^(3)+8x^(2)).
3. Subtract the result from step 2 (4x^(3)+8x^(2)) from the dividend (4x^(3)+16x^(2)+18x+7) to get the remainder (8x^(2)+18x+7).
4. Repeat steps 1-3 with the new dividend (8x^(2)+18x+7) and the same divisor (2x^(2)+4x) until the degree of the remainder is less than the degree of the divisor.

The final quotient and remainder are as follows:

Quotient: 2x+4
Remainder: 10x+7

So, the final answer is:

(4x^(3)+16x^(2)+18x+7)-:(2x^(2)+4x) = 2x+4+(10x+7)-:(2x^(2)+4x)

In other words, the quotient is 2x+4 and the remainder is 10x+7.

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Answer: About 942.48 pounds

Step-by-step explanation:

The volume of a cylinder is πr²h

Plug in values:

(diameter is 2, so the radius is 1)

Volume = π(1)²6

Volume = 6π

Volume ≈ 18.8496 (to 4 decimal places)

Multiply that by 50:

18.8496 x 50 = 942.48

The smallest cylinder will weigh about 942.48 pounds.

Note the answer may change depending on how many decimal places you were told to go out. The standard is 4 places.

Hope this helps!

[tex]\cfrac{1}{3}(9x+12)=15\implies \cfrac{9x+12}{3}=15\implies 9x+12=45 \\\\\\ 9x=33\implies x=\cfrac{33}{9}\implies x=\cfrac{3}{3}\cdot \cfrac{11}{3}\implies x=\cfrac{11}{3}\implies x=3\frac{2}{3}[/tex]

The solution to the exponential equation is given as follows:

x = 4.

The equation for this problem is defined as follows:

4^(2x+4) = 16^(3x-6).

Looking at the left-side of the equality, we can apply the power of power property, as 16 = 4², hence:

16^(3x-6) = 4^[2(3x - 6)] = 4^(6x - 12)

(the power of power property means that we keep the base then multiply the powers relative to the same base).

Hence the equation can be written as follows, considering the simplification to the right side of the equality.

4^(2x+4) = 4^(6x - 12)

Applying the one to one property, the solution is obtained as follows:

6x - 12 = 2x + 4

4x = 16

x = 16/4

x = 4.

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The exact value of the distance between L1 and L2 is 131 / √221. Enter this value in the box.

The distance between two parallel lines can be found by taking the distance between a point on one line and the other line. We can use point C and line L1 to find the distance between the two lines.

First, we need to find the direction vector of line L1. The direction vector can be found by subtracting the coordinates of point A from point B:

u = B - A = (-6,-4,3) - (8,1,3) = (-14,-5,0)

Next, we need to find the vector between point C and point A:

v = C - A = (9,-8,3) - (8,1,3) = (1,-9,0)

Now, we can find the distance between point C and line L1 by taking the cross product of u and v and dividing by the magnitude of u:

w = u x v = (-5*0 - 0*(-9), 0*0 - (-14*0), -14*(-9) - (-5*1)) = (0,0,131)

||w|| = √(0^2 + 0^2 + 131^2) = 131

||u|| = √((-14)^2 + (-5)^2 + 0^2) = √221

distance = ||w|| / ||u|| = 131 / √221

Therefore, the distance between L1 and L2 is 131 / √221.

The exact value of the distance between L1 and L2 is 131 / √221. Enter this value in the box.

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