Classify the polygon. Be as specific as possible.

Quadrilateral JKLM with JK = 10, KL = 7, ML = 10, and JM = 7

In the following question, among the various parts to solve- a- "x = [[3/2x3-3/2x3x3]]", b- the dimension of the solution set of Ax = 3x is 1.

(a) To find all solutions of the equation system Ax = 3x, we need to solve the following system of linear equations:

(3 4 3) (x1) (3x1)

(2 5 3) (x2) = (3x2)

(0 2 6) (x3) (3x3)

This can be written as (A - 3I)x = 0, where I is the identity matrix. To find the solutions, we need to find the null space of A - 3I.

(A - 3I) = [[0 4 3 2 2 3 0 2 3]]

To find the null space of this matrix, we row-reduce it to obtain:

[[1 0 -3/2 0 1 3/2 0 0 0]]

The last row tells us that x3 is a free variable, while the first two rows give us:

x1 = (3/2)x3

x2 = (-3/2)x3

Therefore, the general solution to Ax = 3x is:

x = [[3/2x3-3/2x3x3]]

where x3 is any real number.

(b) We can speak about the dimension of the solution set of Ax = 3x because it is a linear homogeneous equation. In this case, the solution set is a subspace of the vector space R^3, and the dimension of this subspace is the number of linearly independent solutions. Since we have one free variable in the solution, the set of solutions is a line in R^3, and its dimension is 1. Therefore, the dimension of the solution set of Ax = 3x is 1.

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'x' is an unknown variable, so a value that is not known

a) alternate- angle a is 60 degrees

b) corresponding- 75 degrees

c) corresponding- 108 degrees

Using the lengths of the time spent we can plot the histogram by the values in the table.

A histogram is a visual depiction of a frequency distribution with continuous classes that has been categorised.

To create a histogram, follow the steps shown below.

Mark the class intervals on the X-axis and the frequencies on the Y-axis to get started.

Both axes must have the exact same scales. Intervals between classes must be exclusive. Create rectangles with appropriate frequencies as the heights and bases acting as class intervals.

As the class limits are shown on the horizontal axis and the frequencies are shown on the vertical axis, a rectangle is constructed on each class interval.

If the intervals are identical, the height of each rectangle is proportional to the associated class frequency.

From the given information, we have the following:

Length of time (t)     Frequency

0 ≤ t < 10                    5

10 ≤ t < 25                  24

25 ≤ t < 30                 12

30 ≤ t < 50                 8

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The complete question is:

The constant proportionality between the x-coordinates and y-coordinates of these four points is 12.

What is Proportionality?

Proportionality refers to the relationship between two quantities that change in a consistent and predictable way. In a proportional relationship, when one quantity changes, the other quantity changes in a constant ratio or proportion to the first.

Assuming that you want to find the constant proportionality between the x-coordinates and y-coordinates of these four points:

First, we can calculate the ratios of the y-coordinates to the x-coordinates for each point:

For (3,36): y/x = 36/3 = 12

For (5,60): y/x = 60/5 = 12

For (6,72): y/x = 72/6 = 12

For (7,84): y/x = 84/7 = 12

We can see that the ratios are all equal to 12. Therefore, the constant proportionality between the x-coordinates and y-coordinates of these four points is 12.

Note that if you had asked for the constant proportionality between the differences in the y-coordinates and the differences in the x-coordinates of these points, the answer would be different. That constant proportionality is known as the slope of the line passing through these points.

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The equation y^(2)-x+10=0 has no symmetry.

Symmetry is when one part of an equation is the mirror image of another part. In this case, there is no symmetry because the equation cannot be mirrored on any axis.

To check for symmetry with respect to the y-axis, we can replace x with -x and see if the equation is still true. In this case, y^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the y-axis.

Similarly, to check for symmetry with respect to the x-axis, we can replace y with -y and see if the equation is still true. In this case, (-y)^(2)-x+10=0 is not the same as the original equation, so there is no symmetry with respect to the x-axis.

Finally, to check for symmetry with respect to the origin, we can replace x with -x and y with -y and see if the equation is still true. In this case, (-y)^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the origin.

Therefore, the equation y^(2)-x+10=0 has no symmetry.

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Answer:

sorry I don't know the answer :(

Step-by-step explanation:

Make sure all words are spelled correctly.

Try different keywords.

Try more general keywords.

Try fewer keywords.

Answer:

6.72^2

Step-by-step explanation:

6.72^2 is an expression correctly written in scientific notation

The areas of the three polygons are 102.87m², 726cm², and 288 ft², respectively.

To find the area of a regular polygon, we can use the formula A = (1/2)ap, where A is the area, a is the apothem, and p is the perimeter.

1. For a regular pentagon with radius 9m, we can first find the apothem using the formula a = r*cos(180/n), where r is the radius and n is the number of sides.

In this case, n = 5, so

a = 9*cos(180/5) ≈ 7.07m.

Next, we can find the perimeter using the formula

p = 2nr*sin(180/n),

where n = 5 and r = 9, so

p = 2(5)(9)sin(180/5) ≈ 29.08m.

Finally, we can plug these values into the formula for the area to get

A = (1/2)(7.07)(29.08) ≈ 102.87m².

2. For a regular hexagon with apothem 11cm, we can find the perimeter using the formula

p = 2na,

where n is the number of sides and a is the apothem.

In this case, n = 6 and a = 11, so

p = 2(6)(11) = 132cm.

Then, we can plug these values into the formula for the area to get

A = (1/2)(11)(132) = 726cm².

3. For an octagonal floor of a gazebo with apothem 6 ft, we can find the perimeter using the formula

p = 2na,

where n is the number of sides and a is the apothem.

In this case, n = 8 and a = 6, so p = 2(8)(6) = 96 ft.

Then, we can plug these values into the formula for the area to get

A = (1/2)(6)(96) = 288 ft².

Therefore, the areas of the three polygons are 102.87m², 726cm², and 288 ft².

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The simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].

The given expression is [[-2,-2,4],[-6,-2,5],[-5,-1,5]] + [[5,2,2],[2,-4,-2],[4,5,-5]]. To simplify it, add the corresponding elements of each matrix:

[[-2,-2,4] + [5,2,2] = [3,0,6],
[-6,-2,5] + [2,-4,-2] = [-4,-6,3],
[-5,-1,5] + [4,5,-5] = [-1,4,0]]

Therefore, the simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].

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The area of the middle rectangle is 720 square units.

Let's label the areas of the left and right rectangles as A and C, respectively. Let's also label the area of the middle rectangle as B. We know the distance between the first and second rectangles is 18, and the distance between the second and third rectangles is 14.

Using the formula for the area of a rectangle, we can write:

90 = lw

60 = sw

where l and w are the length and width of the left rectangle, and s and w are the length and width of the right rectangle. We want to find the width of the middle rectangle, so we can label it as x:

B = lx

We know the length of the middle rectangle is 32, so we can write:

B = 32x

Now we have three equations and three unknowns. We can use the distances between the rectangles to set up two more equations:

l + s = 18

s + 32 = 14

Simplifying, we get:

l + s = 18

s = -18 + 32 = 14

We can now solve for l and s in terms of x:

l = 18 - s = 18 - 14 = 4

s = 14

Substituting these values into the equations for the areas of the left and right rectangles, we get:

90 = 4w

60 = 14w

Solving for w in each equation, we get:

w = 22.5

Now that we have found the width of the middle rectangle, which is x = 22.5, we can use the formula for the area of a rectangle to find its area:

B = lx = 32(22.5) = 720

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The response to the given question would be that As a result, when equation comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

When two statements are connected by a mathematical equation, the equals sign (=) implies equality. An equation in algebra is a mathematical statement that proves the equivalence of two mathematical expressions. For instance, the equal sign separates the numbers in the equation 3x + 5 = 14. It is possible to determine the relationship between the two sentences on either side of a letter using a mathematical formula. The logo for the particular piece of software is frequently the same. as 2x - 4 = 2, for instance.  

From Quesnel Lake to Lake Baikal, the distance is 506 metres.

Lake Baikal is 5369 ft (or 1637.74 m) deep (one foot is equal to 0.3048 m).

Ratio of depths is 506 / 1637.74 0.31 (Depth of Quesnel Lake/Deep of Lake Baikal).

Around 31% of Lake Baikal's depth is in Quesnel Lake.

Great Slave Lake to Quesnel Lake: Quesnel Lake is 506 metres deep.

Great Slave Lake's depth is 2015 feet, or 614.18 metres (1 foot = 0.3048 m).

Ratio of depths is 506 / 614.18 0.82 (Depth of Quesnel Lake / Depth of Great Slave Lake).

Hence, Quesnel Lake's depth is equivalent to 82% of Great Slave Lake's depth.

As a result, when comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

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The cheapest straightedge and compass construction of two perpendicular straight lines will cost you 11¢. This is because each use of the straightedge costs 3¢, and each use of the compass costs 5¢. Therefore, it takes three uses of the straightedge (3 x 3¢ = 9¢) and two uses of the compass (2 x 5¢ = 10¢) to create the two perpendicular straight lines, for a total of 11¢. So it will cost you  11¢

To create the perpendicular lines, first move the straightedge to create a line segment with one endpoint at the origin. Next, place the compass at one endpoint of the line segment and draw an arc with the desired radius, cutting the line segment at another point. Then, repeat this process with the straightedge and compass, but with the compass at the new endpoint and draw a perpendicular arc, intersecting the original arc. This will create the two perpendicular lines.

Each time you move the straightedge or compass, you incur a new charge. As outlined above, it will take three moves of the straightedge and two moves of the compass, for a total of five moves and a cost of 11¢.

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Answer:

Option A.

Step-by-step explanation:

We are asked to add these 2 expressions.

First, we should know how to combine like terms.

Combining like terms is adding 2 or more numbers, or variables that are alike.

[tex]-\frac{4}{5} t+\frac{5}{3} s \ + -3 - \frac{7}{5} s+2t=?[/tex]

Let's first begin by combining s and t. We can combine like terms for these two variables.

[tex]-\frac{4}{5} t + 2t = \frac{6}{5} t \ \checkmark[/tex]

[tex]\frac{5}{3} s \ + \frac{7}{5} s \\Which \ can \ also \ be \ represented \ as...\\\frac{25}{15} s \ - \frac{21}{15} s = \frac{4}{15} s \ \checkmark[/tex]

-3 doesn't have any like terms, meaning it'll stay as -3.

[tex]\frac{6}{5} t + \frac{4}{15} s - 3[/tex]

Therefore, our answers matches with Option A.

Answer:

x = 32

Step-by-step explanation:

(41)² - (40)² = 1681 - 1600

= 81

[tex] \sqrt{81} = 9[/tex]

|EC| = 9

x = 41 - 9

x = 32

The 2 triangles share 2 sides of common lengths and a common angle between these sides, therefore they are congruent.

The coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

From the given graph, triangle ABC have A(1, 3), B(7, 1) and (1, 1).

Triangle ABC is enlarged with a scale factor of -2 and the origin of the Centre to give triangle A'B'C'.

Now, A(1, 3) → -2(1, 3)→A'(-2, -6)

B(7, 1) → -2(7, 1) → B'(-14, -2)

C(1, 1) → -2(1, 1) → C'(-2, -2)

Therefore, the coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

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The possible arrangement is 3960.

Permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.

Given that, Bart wants to plant 8 trees in a row along his fence.

Possible arrangement of 4 birches = 5 x 4 x 3 x 2 x 1 = 120

If 3 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

Similarly,

If 2 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

If 4 birches are not next to each other, therefore, possible arrangement are possible = A₄⁴ x A₅⁴ = 2880

Therefore, total arrangements = 120+480+480+2880 = 3960

Hence, the possible arrangement is 3960.

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The given equation is true. The solution has been obtained by using arithmetic operations.

It is believed that the four fundamental operations, often referred to as "arithmetic operations", can explain all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are divide, multiply, add, and subtract.

We are given an equation as (1.8 x 3) x (2.1 x 7) = (3 x 7) x (1.8 x 2.1)

In order to see whether it is true or false, we will solve both the sides.

So, first solving L.H.S., we get

⇒(1.8 x 3) x (2.1 x 7)

⇒5.4 x 14.7

⇒79.38

Now, solving R.H.S., we get

⇒(3 x 7) x (1.8 x 2.1)

⇒21 x 3.78

⇒79.38

Since, L.H.S. = R.H.S., so the given equation is true.

Hence, the given equation is true.

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Answer: [tex]\frac{3}{5} *4[/tex]

Step-by-step explanation:

      The expression represented is  [tex]\frac{3}{5} *4[/tex]. See attached. It shows [tex]\frac{3}{5}[/tex] four times, representing   [tex]\frac{3}{5} *4[/tex].

The output of Badger's function machine when the input is 3.

To find the output of Badger's function machine, we need to first find the output of Bucky's function machine when the input is 3.

1. Input 3 into Bucky's function machine.
2. Follow the instructions on the function machine to find the output.
3. Input the output from Bucky's function machine into Badger's function machine.
4. Follow the instructions on Badger's function machine to find the final output.

Without knowing the specific instructions on the function machines, it is impossible to give a specific answer.

However, by following these steps, you can find the output of Badger's function machine when the input is 3.

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Answer:

D. The other solution to function g is 9 + √2i

Step-by-step explanation:

The roots of a quadratic equation of the form ax² + bx + c = 0

are

[tex]x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\[/tex]

If one of the roots is 9 - √2i then
[tex]-\dfrac{b}{2a} = 9[/tex]

and

[tex]\dfrac{\sqrt{b^2-4ac}}{2a} = 2i[/tex]

So if one root is 9 - √2i then the other root must be 9 -+ 2i

This is answer choice D

a. angle 2 and angle 1, angle 2 and angle 3 are linear pairs. b. angle 9 and angle 8, angle 9 and angle 5 are linear pairs. c. angle 4 and angle 2 form vertical angles.

A linear pair of angles in geometry is a pair of neighbouring angles created by the intersection of two lines. When two angles share a vertex and an arm but do not overlap, they are said to be adjacent angles. Due to their formation on a straight line, the linear pair of angles are always complementary. Thus, the total of two angles in a pair of lines is always 180 degrees.

a. angle 2 and angle 1, angle 2 and angle 3 are linear pairs.

b. angle 9 and angle 8, angle 9 and angle 5 are linear pairs.

c. angle 4 and angle 2 form vertical angles.

d. angle 8 and angle 5 form vertical angles.

e. The rays that form angle 7 and angle 9 do not for, opposite rays.

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Answer:

<RHF = 68°

Step-by-step explanation:

<RHG and <FHY are vertical opposite angle which mean they equal to each other.

<RHG = <FHY

(6m+88) = (7m+84)

88 - 84 = 7m - 6m

4 = m

Plug m=4 into the <RHG to solve for the measurement.

<RHG = 6m+88

<RHG = 6*4+88

<RHG = 24+88

<RHG = 112°

<RHG and <RHF are supplementary angle which mean they both linear adding up to 180°

<RHF + <RHG = 180°

<RHF + 112° = 180°

<RHF = 68°

The fraction of the whole cake they eat is 1/10

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

From the question, we have the following information:

Left over = 1/2

Fraction of left over cake eaten = 1/5

Using the above as a guide, we have the following:

Fraction eaten = 1/2 * 1/5

Evaluate

Fraction eaten = 1/10

Therefore, the fraction is 1/10

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Answer:

A) 59°

Step-by-step explanation:

m<ADC is a right angle, therefore it is 90°

so that means you can now subtract the angle that you already know [31°] from it to get the angle that is left over, m<ADB

90°-31°= 59° (subtracting m<ADC [90°] from m<BDC [31°] leaves your remaining angle m<ADB [59°]

The sets A and B define a function, while the set C does not.

To determine whether a set defines a function, we need to check if there is one and only one output for each input. In other words, there should not be two different outputs for the same input.

\( A=\{(a, d),(c, d),(e, f),(b, f)\} \)

In this set, there are no repeated inputs, so it does define a function.

\( B=\{(1,3),(2,4),(5,6),(3,4)\} \)

In this set, there are also no repeated inputs, so it does define a function.

\( C=\{(1, a),(2, b),(3, c),(2, a),(4, d),(5, c)\} \)

In this set, there are two different outputs for the input 2 (b and a), so it does not define a function.

Therefore, the sets A and B define a function, while the set C does not.

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Answer:

Twenty Seven (27) cubic yards

Answer:

volume =27 cubic yards

Step-by-step explanation:

Volume = Base Area x Height

Volume= 3·3·3

Volume= 27

The population after 4 years will be 12,155.06. It will take approximately 22.52 years for the population to triple.

The population of a town grows proportionally to its current population. This means that the larger the population, the more it will grow. To determine the population after 4 years, we can use the formula:

P = P0 * (1 + r)^t

Where P is the final population, P0 is the initial population, r is the growth rate, and t is the time in years. Plugging in the values given in the question, we get:

P = 10,000 * (1 + 0.05)^4

P = 10,000 * 1.21550625

P = 12,155.06

Therefore, the population after 4 years will be 12,155.06.

To determine how long it will take the population to triple, we can use the same formula, but set P to 3 * P0 and solve for t:

3 * 10,000 = 10,000 * (1 + 0.05)^t

3 = (1 + 0.05)^t

ln(3) = t * ln(1.05)

t = ln(3) / ln(1.05)

t = 22.52

Therefore, it will take approximately 22.52 years for the population to triple.

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If the discount net price is $7,800 and Net Price Factor, trade discount are to be calculated, then trade discount is equal to $1,170 and Net Price Factor is equal to 0.9216.

The formula used for Trade Discount is given as product of List Price and Trade Discount Rate. The value of list price is given as $7,800.00 and that of Trade Discount Rate is 0.15. Putting the given values in the formula, we get the following result:

Trade Discount = $7,800.00 x 0.15 = $1,170.00

Cash Discount 2 = 4% of (Net Price - Cash Discount 1)

∵ Net Price Factor = (100% - 4%) x (100% - 4%) / 100%

⇒ Net Price Factor = 0.9216

Single Equivalent Discount = (1 - Net Price Factor) x 100%

∴ Single Equivalent Discount = (1 - .9216) x 100%

Single Equivalent Discount = 7.84%.

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Refer to complete question below:

Complete the following table by finding the net price factor, single equivalent discount, trade discount (in dollars), and net price in dollars). Round the net price factor and single equivalent discount to five decimal places, and the trade discount and net price to the nearest cent, when necessary. List Price Trade Discount Rate Net Price Factor Single Equivalent Discount Trade Discount Net Price $7,800.00 15/4/4

Answer:

Step-by-step explanation:

1) ballet club

2) ballet club

Answer: The answer is A

Step-by-step explanation: