The circle below is centred at O.
a) Work out the size of angle x.
b) Which of the circle theorems below allows
you to calculate this angle?
O
X
Not drawn accurately
31°
The perpendicular line from the centre of a circle to a chord
bisects the chord
Two tangents that meet at a point are the same length
The angle at the circumference in a semicircle is a right angle
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between the tangent and the radius at a point
on a circle is 90°

Answer:

Step-by-step explanation:

the answer is -26 but it is not in the choices

-32+(-4+7)*(2)=

-32+3*2=

-32+6=

-26

The domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}

The given relation is {(-3,2), (-1,3), (0,0), (-2,-1)}. Here, the relation is given as a set of ordered pairs. Domain in mathematics is defined as the all the inputs that are possible to be part of functions. Range refers to the values assumed by function and these are the output values.

The domain of the function is the set of x- coordinates.

∴ The domain is {0, -1, -2, -3}

The Range of the function is the set of y- coordinates.

∴The Range is {0, -1, 2, 3}

Hence, the domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}.

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The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 5/6 and (x1 , y1) = (22 , 12)

(y - 12) = 5/6(x - 22)

In slope-intercept form, the equation of the line is:

(y - 12) = 5/6(x - 22)

y - 12 = 5/6 x - 110/6

y = 5/6 x - 19/3

In standard form, the equation of the line is:

y = 5/6 x - 19/3

5/6 x - y = 19/3

Multiplying both sides by 6,

5x - 6y = 38

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The correct equation is:

|x - 32| = 0.78

In this case, x represents both the maximum and minimum accepted volumes.

We know that the mean volume is 32 fluid ounces, and the acceptable error is 0.78 fluid ounces.

Then the maximum acceptable volume is 32 + 0.78 fluid ounces, and the minimum acceptable volume is 32 - 0.78 fluid ounces.

This means that the absolute value of the difference between x, the volume, and 32, must be equal to 0.78

This is written as:

|x - 32| = 0.78

In this case, x represents both the maximum and minimum accepted volumes.

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The equation in point-slope form of the line having the slope m=1/4 and contains the point (3,-1) is [tex]y+1=\frac{1}{4}(x-3)[/tex]

Given,

The slope m= [tex]\frac{1}{4}[/tex]

The point = (3,-1)

We know the point-slope form,

[tex]y-y_{1}=m(x-x_{1})[/tex]

Substitute the values in the equation

[tex]y-(-1)=\frac{1}{4} (x-3)\\y+1=\frac{1}{4}(x-3)[/tex]

Hence, the equation in point-slope form of the line having the slope m=1/4 and contains the point (3,-1) is [tex]y+1=\frac{1}{4}(x-3)[/tex]

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Referring  to the circle ED  is the chord that is not a diameter.

The circle is one of the shapes with consists of all points with identical distances from its center. A particular circle is named by its center.Here diameter of the circle is the distance across the circle through the center, whereas a chord is a line segment that joins two points on a curve on the circle since the diameter is satisfieding the points of a chord but a chord is not a diameter, as diameter are the line that just passes through the center of the circle, whereas the chord doesn't cross from the center of the circle, thus it can be quoted that, every diameter is a chord, but not every chord is a diameter.

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Answer:  x=55 over 6

Step-by-step explanation:

Ф2 = E2 L² is  the electric flux through the cube face in the plane z = 0.

What exactly are electric flux and unit?

given ,

          edge length = L

 Area of each surface = L²

Ф = E . A

    = E . A Cos θ

Φ1 = E1  A Cosθ

Φ1 = E1 L²

Similarly we get

Ф2 = E2 L²

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If ∠A ≅ ∠X and ∠C ≅ ∠Z , then ΔABC ∼ ΔXYZ by the AA Similarity Postulate.

Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.

example:

If ΔABC ∼ ΔXYZ, then ∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z, and

AB/XY = BC/YZ = AC/XZ

AA (or AAA) or Angle-Angle Similarity Postulate states that if any two angles of a triangle are congruent to any two angles of another triangle, then the two triangles are similar to each other.

So, given that ∠A ≅ ∠X and ∠C ≅ ∠Z, then ΔABC ∼ ΔXYZ by the AA Similarity Postulate.

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Answer:True

Step-by- by step

Irrational numbers are square roots of numbers , when two irrational numbers are multiply together, it is called rationalization and this gives a rational value, So the answer is true.

The value of b (real number) can be anything greater than zero so we cannot be determined with the given information so option (C) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

Given the absolute equation,

|x| = b for b >0

b is a set of all positive real numbers and we know that real number goes 0 to infinite means,

b could be 1,2,3... anything.

It means the corresponding solution will also be 1,2,3... anything.

Therefore we cannot determine the solution.

Hence "We cannot predict the number of solutions of the given mode function  |x| = b, such that b>0 without more information".

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Answer:

The point of intersection is the number of gigabytes and the total cost when the two plans cost the same.

Step-by-step explanation:

Company A doesn't charge a fee "per gigabyte", there's just a flat fee and it is $100. Company B only charges a flat fee of $20, BUT there IS a "per gigabyte" charge. These two plans actually cost exactly the same when the customer uses 16 gigabytes.

Answer: x = 3/4

Step-by-step explanation:

The first step to solve this equation would be to simplify both sides of the equation by multiplying

1/4*12 - 1/4*8x = 2/3*6x

3 - 2x = 2x

3= 2x+2x

3=4x

x=3/4

Answer:

Step-by-step explanation:

AS THERE ARE 2 fractions 1/4 and 2/3, one way would be to first get rid of these by multiplying through by the LCM  12, giving:

12*1/4(12 – 8x) = 12*2/3(6x)

3(12 - 8x) = 8(6x)

36 - 24x = 48x

36 = 72x

x = 1/2.

Answer:

42 feet

Step-by-step explanation:

1 1/2 * 28 = 42

Answer:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

The coordinates are (100, 173.2) after 5 seconds.

What are examples of coordination?

Let x represent the angle of rotation in 5 seconds.

[tex]\frac{Irotation }{time} = \frac{current position}{time}[/tex]

360° / 30 = x°/ 5

30x = 1800

x = 60°

To find the coordinates, use sine and cosine ratios.

Sin60 = opposite/ hypotenuse

sin60 = y / 200

 y = 200sin60

y ≈ 173.2

cos60 = adjancent/ hypotenuse

cos60 = x / 200

x = 200cos60

x = 100

The coordinates are (100, 173.2).

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Answer:

2.08 × [tex]10^{7}[/tex]

Step-by-step explanation:

Multiply 4 × 5.4 to get 20.8. Then multiply [tex]10^{-2}[/tex] × [tex]10^{8}[/tex] = [tex]10^{6}[/tex]

However, that is not an answer. So, you can divide 20.8 by 10 and multiply [tex]10^{6}[/tex] × 10.

Then you get 2.08 × [tex]10^{7}[/tex]

What error did your classmate make? This series is divergent so does not have a sum.

How is the divergence of the series proved?

Given:

[tex]a(\text{ the first term })=1\\\\r(\text{ the common difference })=1.1[/tex]

Since, [tex]\vert r \vert > 1[/tex] the infinite series diverges.

What is an infinite geometric series?

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Answer: Yes

Step-by-step explanation:

If these lengths were to form a right triangle, then 51 and 68 would be the legs and 85 would be the hypotenuse.

[tex]51^2 +68^2 =7225\\\\85^2 =7225\\\\\therefore 51^2 +68^2 =85^2[/tex]

So, the side lengths form a right triangle.

The coordinates of the vertices of new triangle are [tex]A^{I}[/tex](-1,3),[tex]B^{I}[/tex](-1,0),[tex]C^{I}[/tex](0,0).

Given that the coordinates of the triangle be (-5,5), (-5,-1) and (3,-1)

We are required to find the coordinates of the new triangle.

Scale Factor is basically used to scale shapes in different dimensions.

Coordinates are the points that lie on the plane surface.

As we can see in the picture, the coordination of the vertices of the triangle be A(-5,5), B(-5,-1) and C (-3,-1).

=1/2 [tex]\left[\begin{array}{ccc}-5+3&-5+3&-3+3\\5+1&-1+1&-1+1\\\end{array}\right][/tex]

=1/2 [tex]\left[\begin{array}{ccc}-2&-2&0\\6&0&0\\\end{array}\right][/tex]

=[tex]\left[\begin{array}{ccc}-1&-1&0\\3&0&0\\\end{array}\right][/tex]

Hence the coordinates of the vertices of new triangle are [tex]A^{I}[/tex](-1,3),[tex]B^{I}[/tex](-1,0),[tex]C^{I}[/tex](0,0).

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Answer:

[tex]x = -1, -3[/tex]

To solve by factoring, we will split up the equation using our factoring rules.

In this particular instance, we will factor out common variables.

We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.

[tex]x^2 + 4x + 3 = 0[/tex]

[tex](x+3)(x+1)=0[/tex]

Set each factor equal to zero and solve.

Root 1

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

Root 2

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

The final answer is [tex]\boxed{x = -1, -3}[/tex].

As requested in the question, we must now check with the quadratic formula.

To solve this quadratic equation, we will utilize the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].

We will define our variables:

Now, we will plug these into the equation and solve the equation.

[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]

[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]

[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]

[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]

Root 1

[tex]\displaystyle x=\frac{-4+2}{2}[/tex]

[tex]\displaystyle x=\frac{-2}{2}[/tex]

[tex]\boxed{x=-1}[/tex]

Root 2

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

[tex]\displaystyle x=\frac{-6}{2}[/tex]

[tex]\boxed{x=-3}[/tex]

The final answer is [tex]\boxed{x = -1, -3}[/tex].

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Given the equation, we can start by rewriting:

x^2 + 4x + 3 = 0

Now, let’s write in factored form:

(x + 1) (x + 3) = 0

since x is the only variable and there are 2 numbers, we can make 2 equations:

x + 1 = 0

x + 3 = 0

This forms:

(X + 1) (x + 3) = 0

Now, we can solve:

? + 1 = 0

? + 3 = 0

-1 + 1 = 0 and -3 + 3 = 0

x = -1 AND -3

The mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is   and   .

For Discrete Uniform Distribution the probability mass function (pmf) is denoted by P(x)=1/n , where x=1,2,3,...,n.

in the given question

The mean of the Discrete Uniform Distribution is given by [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex]

By substituting the value of P(x)=1/n

[tex]E(x)=\[\sum_{x=1}^{n}\frac{1}{n} *x\][/tex]

[tex]=\frac{1}{n}\[\sum_{x=1}^{n}x\][/tex]

[tex]=\frac{1}{n} (1+2+3+4+...n)[/tex]

[tex]=\frac{1}{n} *\frac{n(n+1)}{2}[/tex]    ( as we know that sum of n terms is [tex]\frac{n(n+1)}{2}[/tex]  )

=[tex]\frac{n+1}{2}[/tex]

hence , [tex]\mu=\frac{n+1}{2}[/tex] ....(i)

The Variance of the Discrete Uniform Distribution is denoted by Var(x) and is given by [tex]Var(x)=E[(x-\mu)^{2}][/tex]

As we know that [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex]   similarly for E[(x-μ)²] we get

[tex]E[(x-\mu)^{2}]=E[x^{2} ]-\mu^{2}[/tex]

[tex]=E[x^{2}]-(\frac{n+1}{2} ) ^{2}[/tex]        ( we have found [tex]\mu=\frac{n+1}{2}[/tex] )  ....(ii)

For E[x²]

[tex]E(x^{2} )=\[\sum_{x=1}^{n}\frac{1}{n} *x^{2} \][/tex]

[tex]=\frac{1}{n}\[\sum_{x=1}^{n} x^{2} \][/tex]

[tex]=\frac{1}{n} (1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} )[/tex]

We know that [tex]1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} =\frac{n(n+1)(2n+1)}{6}[/tex]

Substituting the value in above equation we get we get

[tex]E[x^{2} ]=\frac{1}{n} *\frac{n(n+1)(2n+1)}{6}[/tex]

[tex]E[x^{2} ]=\frac{(n+1)(2n+1)}{6}[/tex]

Substituting the value of E[x²] back in equation (ii)

We get

[tex]Var[x]=\frac{(n+1)(2n+1)}{6} -( \frac{n+1}{2})^{2}[/tex]

[tex]=\frac{(n+1)(2n+1)}{6} -\frac{(n+1)^{2} }{4}[/tex]

[tex]=(n+1)(\frac{(2n+1)}{6} -\frac{(n+1) }{4})[/tex]

taking LCM as 12 and solving further we get

[tex]=(n+1)(\frac{4n+2-3n-3}{12} )[/tex]

[tex]=\frac{(n+1)(n-1)}{12}[/tex]

[tex]=\frac{n^{2}-1 }{12}[/tex]     (using identity of (a+b)(a-b)   )

Therefore , the mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is [tex]\frac{n+1}{2}[/tex]  and [tex]\frac{n^{2}-1 }{12}[/tex]  .

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Using linear functions, the costs are given as follows:

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

A linear function is modeled by:

y = mx + b

In which:

For Company A, we have two points on the column: (2, 33), (3, 49). Hence for one additional hour, the cost increased by $16, hence the slope is of 16 and:

A(x) = 16x + b.

When x = 2, A(x) = 33, hence we use it to find b as follows:

33 = 16(2) + b

b = 1.

Hence:

A(x) = 16x + 1.

Companies B and C have intercepts of 0, while the slopes are hourly costs, hence:

For 4 hours, the costs are given as follows:

The difference is:

72 - 57 = 15.

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

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FA recursive formula allows us to find each term in the geometric sequence using the previous term. Each new term is the product of the common ratio for that sequence and the previous term of that unknown or to-be-found term. If the common ratio is 9, each term is nine times the previous term.

The general term for the geometric sequence is,

an= a1 * r ^ (n-1)

Where "an" refers to the nth term of the sequence, a1 is the first term known as the sequence, and r is the common ratio, n is its position or the number.

Now the given values are,

a₁ = -1 and r = -1

Sequence: -1, 1, -1, 1, -1, 1, -1, 1, -1 ...

We can easily identify the first three terms from the above sequence.

3rd value: -1

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Answer:

no 1 answer is asia

no 2 answer is europe

Applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°

In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°

All interior angles of a triangle have a total sum of 180 degrees when added together, according to the triangle sum theorem.

Given:

Measure of angle C = 90 degrees

In △CAD, we have the following angle measures:

m∠A = 65° (given)

m∠ADC = 90° [right angle]

m∠ACD = 180 - 90 - 65 [triangle sum theorem]

m∠ACD = 25°

In △CBD, we have the following angle measures:

m∠CDB = 90° [right angle]

m∠BCD = 90 - m<ACD [complementary angle]

m∠BCD = 90 - 25

m∠BCD = 65°

m∠CBD = 180 - m∠BCD - m∠CDB [triangle sum theorem]

m∠CBD = 180 - 65 - 90

m∠CBD = 25°

In summary, applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°

In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°

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