The circumference
of the circle shown above
is 108. The length of the minor arc AB is a pi. What is the value of a

The numeric values for the functions are given as follows:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For the first problem, we have that:

For the second problem, we have that:

For the third problem, we have that:

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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 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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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:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

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

Answer:

42 feet

Step-by-step explanation:

1 1/2 * 28 = 42

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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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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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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Using the Fundamental Counting Theorem, it is found that the website would have 30,891,577,600 passwords.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the first six spaces of the password are letters, and each can assume 26 values, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 26[/tex]

The last two spaces are composed by digits, and each can assume 10 values, hence the parameters are:

[tex]n_7 = n_8 = 10[/tex]

Hence the number of possible passwords is given by:

N = 26^6 x 10² = 30,891,577,600.

The website would have 30,891,577,600 passwords.

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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.

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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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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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]

Answer:

no 1 answer is asia

no 2 answer is europe

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:

[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

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.

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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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 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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Answer:  x=55 over 6

Step-by-step explanation:

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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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: 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:

The sun of 10 is 2 times much 4.

Answer:

x=3

Step-by-step explanation:

➡️ Let x be the number;

4(x+2)=20

x+2=5

x=3

The number is 3.