In trapezoid ABCD, line AC is a diagonal and angle ABC is congruent to angle ACD. Find AC if the lengths of the bases line BC and line AD are 12m and 27m, respectively

The measure of the three missing angles in the parallelogram are,

⇒ ∠x = 122

⇒ ∠ y = 122°

⇒ ∠z = 58°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The parallelogram shown in figure.

We know that;

By Opposite Angles Theorem,

In parallelogram, The two opposite angles of a parallelogram are equal to each other.

Hence, We get;

⇒ ∠y = 58°

⇒ ∠x = ∠z

And, The sum of all angles in a parallelogram is 360°.

Hence, We get;

⇒ ∠x + ∠y + ∠z + 58° = 360

⇒ ∠x + ∠x +58+58 = 360

⇒ 2∠x + 116 = 360

⇒ 2∠x = 360 - 116

⇒ 2 ∠x = 244

⇒ ∠x = 122

And, ∠ z = 122°

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a) 17210368 different ways can the program select which students will answer the five questions

b) 11,793,600 different ways.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Given:

Each of the 28 students in her class is equally likely to be chosen every time she runs the program.

a) The number of ways can the program select which students will answer the five questions

= [tex]28^5\\[/tex]

= 17210368

b) using Permutation

[tex]P^{28}_2[/tex] = 28! / (28-5)!

      = 28! / 23!

      = 28 x 27 x 26 x 25 x 24 x 23! / 23!

      = 11,793,600

So, there are 11,793,600 different ways.

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The median and its meaning as it relates to the runners include the following: A. The median is 18.5, and it represents the typical age of the runners.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the observations (data set) from the least to greatest as follows:

14,14,15,17,17,18,19,20,28,31,34,35

The median for 12 observations is the average of the 6th and 7th number:

Median = (18 + 19)/2

Median = 37/2

Median = 18.5.

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The median and its meaning as it relates to the runners include the following: A. The median is 18.5, and it represents the typical age of the runners.

What is a median?

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

How to calculate the median age?

First of all, we would sort the observations (data set) from the least to greatest as follows:

14,14,15,17,17,18,19,20,28,31,34,35

The median for 12 observations is the average of the 6th and 7th number:

Median = (18 + 19)/2

Median = 37/2

Median = 18.5.

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Answer: The result can be shown in multiple forms.

Inequality Form:

x>−5

Interval Notation:

(−5,∞)

Step-by-step explanation:

Answer:because if we plug this in it will be -7 > -5, this is false because this is saying that -7 has a greater value that -5.

Step-by-step explanation:

hope the helps<3

5 in :2ft

170 in :68ft

The value of cos t from the unit circle is cos t = 0.94868

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 3√10/10,√10/10 )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

x = 3√10 / 10

x = 3/√10

And , y = √10/10

y = 1/√10

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = ( 3/√10 ) and sin θ = ( 1/√10 )

On simplifying the equation , we get

cos t = ( 3/√10 )

cost t = 0.94868

Hence , the value of cos t = 0.94868

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The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15

What is equation of a straight line ?

Equation of straight line as follows , y = mx + b

where m is the slope of line.

Given equation ,

x - 5y = 75

and the points are (0,-3)

First lets find the slope of a line

we get,

x - 5y = 75

5y = x - 75

y = 1/5 x  - 15

m = 1/5

Here the point (0,-3) and slope m = 1/5
Therefore,

The equation of the line

y + 3  = 1/5  (x-0)

5y + 15 = x

5y - x + 15

Therefore, The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15

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The table D represents the relationship between the number of minutes and the number of gallons of water in the pool.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A pump fills a pool at a constant rate.

At the end of 12 minutes,

it has filled 3 gallons of water.

From the given choices:

The table D represents the relationship between 12 minutes and 3 gallons of water in the pool.

Therefore, the table D is the correct table.

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The area of this rectangle is 4 * √11 square units

The perimeter of a regular hexagon can be divided equally into the lengths of its six sides.

So, the length of each side of the hexagon is 12 / 6 = 2 units.

Since the hexagon is inscribed in a rectangle, the length of the rectangle is equal to the length of two sides of the hexagon, or 2 * 2 = 4 units.

Let's call the height of the rectangle "h."

Then, the length of one side of the equilateral triangle is 2 units and the height is h, so using the Pythagorean theorem:

h^2 + (2/2)^2 = (2 * √3)^2

h^2 + 1 = 12

h^2 = 11

h = √11

So, the area of the rectangle is equal to its length multiplied by its width:

4 * √11 square units

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Answer:

2^3 x 5^3

Step-by-step explanation:

Both the side of triangle DEF have equal distance  DF = DE. so it is isosceles triangle.

The distance between any two of the supplied points must be the same for two pairs of the given points in order to determine whether the given points are the vertices of an isosceles triangle. We can infer that DF = DE from the DF, FE, and DE data mentioned above.

we have 3 coordinates of triangle .

D(x1,y1) = D(1 , 2)

F(X2,Y2) = F(-2 , -2)

E(X3,Y3) =  E(-3 , -1)

if given triangle is  isosceles triangle than distance DF = DE.

Distance between two points :-

Distance  (DF) =[tex]\sqrt{((x_1 - x_2)^{2} + (y_1 - y_2)^{2})} = \sqrt{((1 + 2)^{2} + (2 +2)^{2})} = 5[/tex].

Distance   (DE)= [tex]\sqrt{((x1 - x3)^{2} + (y1 - y3)^{2})}= \sqrt{((1 + 3)^{2} + (2 + 1)^{2})} = 5[/tex]

hence, both the side have equal distance  DF = DE. so it is isosceles triangle.

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Answer:

The technique used to graph the equation y = 9x + 4 using the slope and y-intercept is to mark a point at 4 on the y-axis, go up 9 and right one and mark this point. This is because the slope of the equation is 9 and the y-intercept is 4, so the graph can be plotted by starting at the y-intercept and moving up 9 units and right 1 unit. Unfortunately I need to wrap this conversation up and can only talk a little more. Is there anything you'd like to discuss before we close?

Step-by-step explanation:

The values:

[tex]\bar p[/tex]  = 0.547.

And  [tex]\bar q[/tex] = 0.453.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Given:

The values,

X₁ = 23,

X₂ = 29,

n₁ = 43,

And n₂ = 52.

Now, using the formula for mean,

[tex]\bar p[/tex] = (X₁ + X₂) / (n₁ + n₂)

=(23 + 29) / (52 + 43)

= 0.547.

And [tex]\bar q[/tex] = 1 -  [tex]\bar p[/tex] = 1 - 0.547 = 0.453.

Therefore, all the required values are given above.

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Answer:

The answer is 768.0 square inches.

Step-by-step explanation:

The surface area of a square pyramid can be calculated by adding the area of its four triangular faces to the area of its base, which is a square.

First, we'll find the area of the base:

24 inches x 24 inches = 576 square inches

Next, we'll find the area of each triangular face:

1/2 * 24 inches * 20 inches = 240 square inches

So, the total surface area of the pyramid is:

576 square inches + 4 * 240 square inches = 1,536 square inches

Finally, we'll find the surface area that is yellow:

1,536 square inches / 2 = 768 square inches

Rounding to the nearest tenth, we have:

768 square inches = 768.0 square inches

So, the surface area of the toy that is yellow is 768.0 square inches.

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Have a nice day.

Answer:

[tex] y = - \frac{5}{4}x - \frac{5}{2} [/tex]

Step-by-step explanation:

Don't know if it's right but yeah that's what I got.

The least number of square yards of paper required to make the poster is 11 square yards.

The area of a rectangle can be found by multiplying the length of its sides. To find the length and width of the rectangle, we can subtract the x and y values of the opposite vertices.

The length of the rectangle is 34 - 2 = 32 inches, and the width is -44 - 4 = -48 inches. We will have to make the width positive to find the area, so the area is 32 * 48 = 1536 square inches.

Since 1 square yard is equal to 144 square inches, we need to divide 1536 by 144 to find the number of square yards: 1536 / 144 = 10.67 square yards.

Therefore, the least number of square yards of paper required to make the poster is 11 square yards.

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Henry has to choose bank Z.

Two or more expressions with an Equal sign is called as Equation.

Given there are three banks Bank X, Bank Y and  Bank Z

For bank X, No monthly fees if balance stays above $500, otherwise $7 per month.

No monthly fees if check card is used less than 6 times per month

$5 monthly fee, No minimum balance, $25 minimum balance, No minimum balance

Has Henry has  about $300 in his account at any given time during the month. He limits his ATM visits to one per week and is interested in banking online options he has to choose bank Z.

Hence, Henry has to choose bank Z.

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Answer: Bank Z

Step-by-step explanation:Bank Z is his best option

Answer:

The third option

Step-by-step explanation:

Step-by-step explanation:

you made so many typos.

let's see :

the point-slope form of a line is

y - y1 = a(x - x1)

"a" being the slope, (x1, y1) being a point on the line.

in our case

y - -16 = 1/2 × (x - 16)

y + 16 = x/2 - 16/2 = x/2 - 8

y = x/2 - 24

or

y = (1/2)x - 24

The ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on is 0.75.

The Fibonacci series is the sequence of numbers (also called Fibonacci numbers), where every number is the sum of the preceding two numbers, such that the first two terms are '0' and '1'. In some older versions of the series, the term '0' might be omitted. A Fibonacci series can thus be given as, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .

1) To represent any (n+1)th term in this series, we can give the expression as, Fₙ=Fₙ₋₁+Fₙ₋₂.

2) A sequence in which every number in the Fibonacci sequence is the sum of two numbers preceding it in the sequence.

Yes, the Fibonacci sequence written using a formula that connects successive terms of the sequence.

3) The Fibonacci sequence in nature:

A perfect example of this is the nautilus shell, whose chambers adhere to the Fibonacci sequence's logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space.

4) The ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on.

Now, the ratio is 3/2 ÷ 2/1

= 3/2 × 1/2

= 3/4

= 0.75

Therefore, the ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on is 0.75.

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The graph of f(x) has a vertical asymptote at x = -2 and x = 6, as the denominator of the fraction approaches zero and the numerator approaches a finite value as x approaches those values from either direction.

Answer:

The graph of the function F(x) has vertical asymptotes at x = 2 and x = 6. This is because the denominator of the function (x2 + 2x - 24) is equal to 0 when x = 2 and x = 6.

Step-by-step explanation:

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Answer:

is that the question?

Step-by-step explanation:

Rosa's change in elevation, relative to the diving board, in meters during the dive, which is a measure of her displacement, is -5.8 meters.

Displacement is the change in the position of an object, with regards to a frame of reference. Displacement is a vector quantity, that has both magnitude and direction, indicated by the sign (positive or negative), and the magnitude, which is the measured value.

The height of the diving board above the surface of the water = 3 meters

The depth to which Rosa descends relative to the water surface = -2.3 meters

Therefore, Rosa's initial elevation when on the diving board = 3 meters

Rosa elevation when at the depth to which she dives = -2.8 meters

Her change in elevation can be obtained by finding her displacement from the diving board, when she descends to the depth of -2.8 meters.

Rosa's change in elevation, Δh = Final elevation - Initial elevation

Therefore, Δh = -2.8 m - 3 m = -5.8 m

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Given:-

[tex] \: [/tex]

now , put the value of x = 7 in da eqⁿ

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: \: [/tex]

hope it helps!:)

the total economic investment by BBQ is $(10 +2=)12 million and purely financial investment accounts for $6 million.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given,a national restaurant chain called BBQ builds 10 new restaurants at a cost of $1 million per restaurant.

Economic investment is the amount of money used to increase the productivity or output of the economy. Since BBQ builds 10 new restaurants at the cost of $1 million per restaurant, the total capital investment in all restaurants by BBQ is $1 million × 10 = $10 million.

Also, the BBQ makes an additional investment of $200,000 in each restaurant to increase the productivity of restaurants. Therefore, total economic investment in all the restaurants is

$200,000 × 10 = $2,000,000.

Hence, the total economic investment by BBQ is $(10 +2=)12 million.

Financial investment by BBQ

The financial investment includes investments in bonds, shares, real estate, or any financial assets. The cost per share is $30, and the total number of shares issued is 200,000.

Thus, the total funds raised from shares are

$30 × 200,000 = $6,000,000.

Therefore, purely financial investment accounts for $6 million.

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The minimum number of switches that Ruby needs to make would be = 39,916,800

Permutation is defined as the arrangement of different values of a data set into a definite order.

The total number of the shapes of the blocks are = 11

Therefore, the minimum number of switches that Ruby needs to make would be the permutation of the total number = 11*10*9*8*7*6*5*4*3*2*1 = 39,916,800.

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As a fraction: 26/32 = 13/16

As a decimal: 26/32 = 0.8125

As a percent: 26/32 * 100 = 81.25%

The value of x in the quadrilateral is 112 degrees and the angle relationship is vertical angles.

A quadrilateral is a plane figure that has four sides , and also has four corners or vertices. The sum of angles in a quadrilateral is 360 degrees. Examples of quadrilateral are parallelograms, rectangle, square, rhombus etc.

The quadrilateral above has two diagonals that intersect each other. The diagonal AC and BD intersect each other at a points.

The relationship formed are vertically opposite angles. Vertically opposite angles are congruent.

Hence, the sum of angles in a point is 360 degrees.

Let's find x as follows;

2x + 68 + 68 = 360

2x = 360 - 136

2x = 224

x = 224 / 2

x = 112 degrees.

Therefore,

x = 112 degrees

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