ABCD is a quadrilateral.
Work out the length of BC.
Give your answer correct to
1 decimal place.
Optional working
Ansv
+
cm
B,
7.5 cm
A
5 cm
38°
D
13 cm

The required equation of the line will be y = 2x + 6 which passes through the points (-2,10), (10 -14).

The slope of a line is defined as the gradient of the line.

Given that line passes through the points (-2,10), (10 -14)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -2, y₁ = 10

x₂ = 10, y₂ = -14

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 10 = (-14 - 10)/(10-(-2))[x -(-2)]

⇒ y - 10 = (-24)/(12 )[x +2]

⇒ y - 10 = -2(x +2)

⇒ y = -2x - 4 + 10

⇒ y = -2x + 6

Therefore, the equation of the line would be y = 2x + 6 which passes through the points (-2,10), (10 -14).

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The value of the summation will be equal to 3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that X=3/5, Y=1/3, and z=2⁴/₅.

The value of the Z+ ( X x Y ) will be calculated as,

E = Z + ( X x Y )

E = 2⁴/₅ + ( 3 / 5 ) x ( 1 / 3 )

E = 14 / 5 + 1 / 5

E = 15 / 5

E = 3

Therefore, the value of the summation will be equal to 3.

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The solution set for the given equations is x = 4.

What is a set?

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.

Here,

we put the value of x in the given equation and justify our answer

when we x=4, we get

5x−5=15

5(4) - 5 = 15

20 - 5 = 15

15 = 15

Hence, the solution set for the given equations is x = 4.

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Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.

In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).

Step-by-step explanation:

==========================================

Explanation:

If it is possible to draw a single vertical line through more than one point on the blue graph, then that graph is not a function. We consider it failing the vertical line test. Such a thing happens in the middle of the top row (graph 2). A vertical line intersects the sideways parabola at more than one point.

Recall a function is when any given input leads to exactly one output. We can't have the input x = 4 lead to both y = 1 and y = -3 at the same time for instance.

Graph 4 is another instance where we don't have a function for similar reasoning. This graph fails the vertical line test. So does graph 6.

The other graphs (1, 3, and 5) all pass the vertical line test since it's not possible to draw a single vertical line to intersect through more than one  blue point.

The theatre sold 178 adult tickets and 261 children tickets for the play.

It is given that the total number of seats is 439 seats.

There are two types of tickets available- children and adults.

The price for adult tickets is $48 and that for children is $28.

Let the number of adult tickets sold be x

Let the number of children's tickets sold be y.

The show was a sold-out

Hence,

x + y = 439                                 [1]

48x + 28y = 15852                    [2]

From equation [1] we get

x = 439 - y

putting this result in equation [2] gives us

48(439 - y) + 28y = 15852

or, 21072 - 48y + 28y = 15852

or, -20y = - 5220

or, y = -5220/ -20

or, y = 261

Therefore,

x + 261 = 439

or, x = 439 - 261

or, x = 178

Hence, 178 adult tickets were sold and 261 children's tickets were sold.

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3/3 * 3/4 is fraction of green color .

What is fraction in math?

green colored boxes = 3

blue colored boxes = 3

fraction of green = 3/3 * 3/4

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The P value of the question in the given condition is less than 0.05 hence it reject the null hypothesis.

According to the null hypothesis, an independent variable and a dependent variable have no association with one another. The results might be the result of an experimental or sampling error if the hypothesis indicates a link between the two factors. There is a relationship in the measured phenomena, but, if the null hypothesis is incorrect.

First we find the value of small z

z = (x - μ) / (α / [tex]\sqrt{100}[/tex])

z = (7275 - 7100) / (1500/[tex]\sqrt{100}[/tex])

z = (175) / 150

z = 1.1667

As we have verified the test statistic value and it matched.

Then,

P value approach

Hence P value must be equal to 0.0013

As p value is less than 0.05 , Reject the null hypothesis.

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Based on the amount that she paid in the first month, the amount Ronda will pay for the next month is $396.

When a loan is amortized, it means that one can pay it off by paying the same amount every period until they would have paid off both the loan and the associated interest.

The amortized amount contains:

A portion going towards the principal(debt )

A portion going towards the interest accumulated.

In conclusion, as the amount is the same every time, Ronda will have to pay the same amount of $396 the next month.

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Perimeter of the parallelogram is 20 units.

According to question,

3 + x = 2a - 4

     x = 2a - 4 - 3

    x = 2a - 7

Diagonals in a parallelogram bisects each other.

Therefore, 2a - 7 = 3

                       2a = 3 + 7

                       2a = 10

                          a = 10/2

                          a = 5

a - 1 = 4b - 6

5 - 1 = 4b - 6

    4 = 4b - 6

  4b = 4 + 6

   4b = 10

     b = 10/4

     b = 5/2

Opposite sides of a parallelogram are equal.

Therefore, c - 2 = 2b

                  c - 2 = 2(5/2)

                  c - 2 = 5

                       c = 5 + 2

                       c = 7

Sides of parallelogram,

Side 1 = 12 - c

          = 12 - 7

          = 5

Side 2 = c - 2

           = 7 - 2

           = 5

Perimeter of parallelogram = 2(length of side 1 + length of side 2)

                                             = 2(5 + 5)

                                             = 2 * 10

                                             = 20

Hence, perimeter is 20 units.

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The solutions for the equations in each of the questions given are as follows;

It follows from the task content that the solution for all of the given word problems are to be determined.

25. If a number, n, divided by 8 equals 2.5, what is n?

The algebraic representation is; n/8 = 2.5.

Hence, the value of n is; n = 8 × 2.5 = 20.

26. The sum of a number, n, and 6.05 is 12.4. What is n?

The algebraic representation is; n + 6.05 = 12.4.

Hence, the value of n is; n = 12.4 - 6.05 = 6.35.

27. Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?

The algebraic representation is; 36/4 = n.

Hence, Stacy's age, n is; n = 9.

28. One-third of a painting job takes 24 hours. How long will it take to finish the entire job?

The algebraic representation is; n/3 = 24.

Hence, the value of n is; n = 3 × 24 = 72 hours.

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The value of the 48 cm will be equal to 480 mm.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that the number is 48 cm. Here 48 cm is the length of any object the value of 48 cm in the unit mm will be calculated as below,

1 cm = 10 mn

48 cm = 48 x 10 mm

48 cm = 480 mm

Therefore, the value of the 48 cm will be equal to 480 mm.

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Answer:

  -1/11, +1/11

Step-by-step explanation:

You want the two square roots of 1/121.

A square root can be either positive or negative.

  [tex]\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}[/tex]

__

Additional comment

The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).

The area of the model on the right is given by 96 sq cm

The correct answer option is option D.

A model represents a real object on a drawing paper.

Given that the model is triangular in shape, the model on the right is 2 times the model on the left.

Therefore, area of model on the left = area of model on the left × 2².

Area of model on the left = 24 × 4

Area of model on the left = 96 square cm.

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Answer:

x

Step-by-step explanation:

The numerical coefficient is x.

Answer:

4√3 (about 6.9) cm.

Step-by-step explanation:

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Here, the length of the longer leg is 4√3, or about 6.9, cm.

The dimensions of the kennel and the size of the cylinder indicates;

4.1.1. The two 3D objects which the figure consists of are a triangular prism that lays on top of a rectangular prism at the bottom.

4.1.2. The area of the wood needed to build the dog kennel is approximately 2.85 m²

4.1.3. The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers

4.2. The new height of the water in the container will be approximately 18 cm.

The surface area of a solid is found by adding together the area of the surfaces that enclose the solid.

4.1.1. The two 3D objects in the figure are;

4.1.2. The amount of wood needed is found by finding the surface area, A, of the dog kennel as follows;

A = 2×80×60+2×50×60+50×80+2×0.5×80×40+2×√(40²+40²)×50

A = 22800 + 80·√2×50 = 22800 + 4000·√2

The amount of wood needed = (22800 + 4000·√2) cm²

1 m² = 10,000 cm²

(22800 + 4000·√2) cm² = ((22800 + 4000·√2))/10,000 m²

((22800 + 4000·√2)) cm² = (2.28 + 0.4·√2) m² ≈ 2.85 m²

4.1.3. 500 milliliters of paint is enough to for 1.5 m² area

The number of containers of paint containers required, n, is therefore;

[tex]n = \dfrac{(2.28 + 0.4\cdot \sqrt{2}) \, m^2 }{1.5 \, m^2/container} = (1.52+0.\overline 6\cdot\sqrt{2} ) \, containers \approx 2 \, containers[/tex]

4.2 Diameter of the base of the water container = 20 cm

Radius of the base = (20 ÷ 2) cm = 10 cm

Height of water in the container = 15 cm

Volume of water added = 1,000 cm³

The new height will be 15 + (1,000/(π×10²)) = (15 + 10/π) cm ≈ 18 cm

The height of the water in the container will rise to approximately 18 centimeters

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The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, Tran planned a rectangular pool and made a scale drawing using cm as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm,

The scale factor of drawing to original pool was 1/5 before changing the length but when length changed to 32 m scale factor now is 1/4

Hence, The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

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If the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]

The zeros of the polynomial = 7i and 9/5

Here the degree of polynomial is 3, therefore there will be three zeros in polynomial, here only 2 zeros are given. We have to find the third zero of the polynomial.

Here one of the polynomial is complex number, therefore another zero will be the conjugate of the complex zero

Therefore the equation will be

(x+7i)(x-7i)(5x-9) = 0

We have to solve the equation

([tex]x^2[/tex] -7ix+7ix+49)(5x-9) = 0

([tex]x^2[/tex] + 49)(5x - 9) = 0

[tex]5x^3-9x^2+245x-441 =0[/tex]

Therefore

f(x) = [tex]5x^3-9x^2+245x-441[/tex]

Hence, if the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]

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Sheri should invest $2000 in mutual fund and $13,200 in bond.

Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -

1%×x + 4%×(15,200 - x) = 548

x/100 + 60,800/100 - 4x/100 = 548

60,800 - 3x = 54800

3x = 60800 - 54800

3x = 6000

x = 6000 ÷ 3

x = 2000

Amount to be invested in mutual fund = $2000

Amount to be invested in bond = 15,200 - 2000

Amount to be invested in bond = $13,200

Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.

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Answer:

150

Step-by-step explanation:

The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.

⇒The volume is given and the height is give. In the equation [tex]V=\pi r^{2} h[/tex]plug in the known value V which is equal to [tex](160\pi )m^{3}[/tex] and h which is equal to 8m and solve for r which is the radius

⇒[tex]160\pi =\pi r^{2} *(8)\\\frac{160\pi}{\pi } =\frac{\pi r^{2} *(8)}{\pi } \\160=8r^{2} \\8r^{2} -160=0\\8(r^{2} -20)=0\\\frac{8(r^{2} -20)}{8} =\frac{0}{8} \\r^{2} -20=0\\(r+\sqrt{20} )(r-\sqrt{20} )=0\\r+\sqrt{20} =0\\or\\r-\sqrt{20} =0\\\\r=2\sqrt{5} \\or\\r= -2\sqrt{5}[/tex]

⇒Note radius is a distance therefore it cannot be negative meaning radius r is equal to [tex]\sqrt{20} =2\sqrt{5}[/tex]m

expressed in decimal is 4.5m

The probability distribution of all possible values of the sample mean is called the sampling distribution of the mean.

What is meant by the sampling distribution of the mean?

Why is sampling essential and what does it mean?

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The other sides of the new triangle are  13, 26 and 26 inches as calculated by the properties of similarity.

We know that when two triangles are similar then the ratio of the sides are also equal.

Let the original triangle be ΔABC and the new triangle be ΔXYZ

So from the property of similarity.

AB/XY = BC /YZ = CA/ ZX

Now it is given AB = 3 inches

XY = 13 inches

Hence AB/XY = 13/3

Hence YZ = 13 / 3 × 6 =26 inches

Again ZX = 26 inches

Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another.

Triangles can have different diameters despite having comparable exteriors. Triangles that are congruent and similar to each other usually don't match up.

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According to the discriminant, the quadratic equation y = 2 · x² - x + 1 has two roots that are complex and conjugate.

Quadratic equations are algebraic expressions of the form a · x² + b · x + c, where a, b, c are real coefficients. In this case, we can infer the nature of its roots by means of a discriminant:

D = b² - 4 · a · c

Whose possible results are listed below:

If we know that a = 2, b = - 1 and c = 1, then the nature of the roots of the polynomial:

D = (- 1)² - 4 · 2 · 1

D = 1 - 8

D = - 7

Then, the quadratic equation has two conjugate complex roots.

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