A circle with a radius of 6 m has an arc of 4pi m. What is the measure of the central angle?
A) 120°
B) 90°
150°
D) 60°

Answer:

Step-by-step explanation:

    diameter = 12 cm

                  r =  12 ÷ 2 = 6 cm

                 h = 6 cm

      [tex]\sf \boxed{\text{\bf Volume of cone = $\dfrac{1}{3} \pi r^2h$ }}[/tex]

                                    [tex]\sf = \dfrac{1}{3}*3.14*6*6*6\\\\ = 226.08 \ cm^3[/tex]

To find the surface area, we need to find the slant 'l'

       [tex]\sf l = \sqrt{h^2+r^2}\\\\ =\sqrt{6^2+6^2}\\\\ = \sqrt{36+36}\\\\ =\sqrt{72}\\\\= 8.49 \ cm[/tex]

       [tex]\sf \boxed{\text{\bf Total surface area of cone = $\pi r(r+l)$}}[/tex]

                                                         = 3.14 * 6 * (6 + 8.49)

                                                        = 3.14 * 6 * 14.49

                                                        = 273 cm²

Using the Fundamental Counting Theorem, it is found that a simulation with 8 equally likely outcomes would be generated from:

D) A coin and a spinner.

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]

In this problem:

The total number of equally likely outcomes is given by:

N = 2 x 4 = 8.

Hence option D is correct.

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Answer:

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

The triangle is congruent with the ASA property.The two triangles are having same sides AB = XY, BC = YZ and CA = ZX and the same angles ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z.

If two triangles are congruent, this means they are the same shape and the same size.

By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

The triangle is congruent by the ASA theorem. Here in the question, we can see in the figure that two angles ∠A = ∠X and ∠B = ∠Y so the third angle must be equal so ∠C = ∠Z.

Since side XY = AB and the three angles are equal so the other two sides will also be equal for the two triangles.

Therefore triangle is congruent with the ASA property.The two triangles are having same sides AB = XY, BC = YZ and CA = ZX and the same angles ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z.

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Answer:

64 cm²

Step-by-step explanation:

Formula(s):

Clearly, we can see that there are 4 triangles and a square included in the prism. Therefore,

We know the following:

Since the base of the triangle is equivalent to the side of square (As shown in picture), the side of the square must be 4 cm.

Therefore, the surface area of the prism is 64 cm².

Answer: The number of miles increases as time increases.

The number of hours causes a change in the number of miles ridden.

The variable h is the independent variable.

The variable m is the dependent variable.

Step-by-step explanation:

Answer:

Part A: total pizza cost = 2.50s + 2.25t + 18

Part B: 30 dollars

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks"!

Answer:

Part A: 18 + 2.25t + 2.50s

Part B: $30

Step-by-step explanation:

Let t= each additional topping

Let s=each side

First we add the cost of one pizza ($18)

Then we add each additional topping (t) multiplied by its cost (2.25 dollars)

Finally we add each side (s) multplied (2.50 dollars)

Part B:

Plug in 2 for t and 3 for s into the expression from earlier and simplify:

Expression: 18 + 2.25(2) + 2.50(3)

=18+ 4.50 + 7.50

=30

And there you have it- the total cost is $30.

Hope this helps and good luck in your studies :)

Answer:

a

Step-by-step explanation:

x² - 3 = 2x ( subtract 2x from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are - 3 and + 1 , since

- 3 × + 1 = - 3 and - 3 + 1 = - 2 , then

x² - 2x - 3 = (x - 3)(x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

Answer: The median is 6

Step-by-step explanation:

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}~\hfill \textit{we also know that} \begin{cases} x= 35\\ y = 7 \end{cases} \\\\\\ 7=k(35)\implies \cfrac{7}{35}=k\implies \cfrac{1}{5}=k~\hfill \boxed{y=\cfrac{1}{5}x}[/tex]

Answer:

[tex]y = x^2 - 8x + 38[/tex]

Step-by-step explanation:

Hello!

The standard form of a quadratic is [tex]ax^2 + bx + c[/tex].

To convert the vertex form to standard form, we have to expand the parenthesis and add the constant.

Convert:

The standard form is [tex]y = x^2 - 8x + 38[/tex]

Answer:

x=2

x=-2

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x^2-3-(1)=0

1.1      Factoring:  x2-4

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check :  x2  is the square of  x1

Factorization is :       (x + 2)  •  (x - 2)

Equation at the end of step

1

:

 (x + 2) • (x - 2)  = 0

STEP

2

:

Theory - Roots of a product

2.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2      Solve  :    x+2 = 0

Subtract  2  from both sides of the equation :

                     x = -2

Solving a Single Variable Equation:

2.3      Solve  :    x-2 = 0

Add  2  to both sides of the equation :

                     x = 2

Answer:

(1) 6

Step-by-step explanation:

Let's start by solving the inequality.

7x +2 > 58

Minus 2 on both sides:

7x > 58 -2

7x > 56

Divide both sides by 7:

x > 56 ÷7

x > 8

This means that the value of x has to be greater than 8. 6 is smaller than 8, and is therefore not in the solution set. Thus, option 1 is the correct answer.

              [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

            Given 7x+2>58, which number is not in the solution set?

      [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer \& how to solve:-}}}\rule{50}{1}[/tex]

        First, subtract 2 on both sides:-

       [tex]\sf{7x > 56}[/tex]

       Now divide by 7 on both sides:-

        [tex]\sf{x > 8}[/tex]

        Henceforth, We conclude that

          [tex]\large\textsf{Numbers greater than 8 make this inequality true}[/tex].

Edit:- Option A (6) is the correct answer, since it's not greater than 8, so it doesn't satisfy the inequality.

[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

Answer:

cos(θ) = 3/4

Step-by-step explanation:

Since cos=adj/hyp, the Hypotenous is 24, and the adjacent is 18. We write cos(θ)=18/24, which can be simplified to cos(θ)=3/4.

Answer:

b. more money

Step-by-step explanation:

Randy's original position lets him make:

50*500 = $25,000

The new position will let him make:

$27,500

Therefore,

original position < new position = $25,000 < $27,500

Answer:

2160

Step-by-step explanation:

You just have to mutiply, 72 x 30 is 2160. So the answer is there are still 2160 marbles in the bag that are grey!

Please mark branliest!!!

Answer:

30 ≥ x ≥ 0

Step-by-step explanation:

I don't think this is the full question but if it is the answer above should be right.

Have a nice day! :)

The probability that a student chosen at random will play an instrument other than drums is 31/36.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Total number of elements of sample space is 36.

Based on these results, express the probability that a student chosen at random will play an instrument other than drums as;

31/36

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Answer:

5.69

Step-by-step explanation:

22.76/4 = 5.69

Answer:

4ln 2+ln 5

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

To find the y value, one must replace x value, meaning that it's a multi step problem and it's not direct because y=exact value is not given

Answer:

Step-by-step explanation:

x=(1-sqrt(13))/2=-1.303

x=(1+sqrt(13))/2=2.303

steps

 (2x2 -  2x) -  6  = 0

step 2 pull out like terms

2x2 - 2x - 6  =   2 • (x2 - x - 3)

step 2 continued

3.2     Factoring  x2 - x - 3

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2

     -1    +    3    =    2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

step 3

 2 • (x2 - x - 3)  = 0

Step 4

4.2      Find the Vertex of   y = x2-x-3

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.5000  

Plugging into the parabola formula   0.5000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 0.50 * 0.50 - 1.0 * 0.50 - 3.0

or   y = -3.250

step 4

4.4     Solving    x2-x-3 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -1

                     C   =   -3

Accordingly,  B2  -  4AC   =

                    1 - (-12) =

                    13

Applying the quadratic formula :

              1 ± √ 13

  x  =    —————

                   2

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          x  =  ( 1 ±  3.606 ) / 2

Two real solutions:

x =(1+√13)/2= 2.303

or:

x =(1-√13)/2=-1.303

concluision

x =(1-√13)/2=-1.303

x =(1+√13)/2= 2.303

Answer:

5x + 3x = 28x
8x = 28x
x must be 0

Answer:

The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.

An equation is an expression that shows the relationship  between two or more numbers and variables.

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.

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Answer:

A. -180

Step-by-step explanation:

Edge2022

Answer: 4/15

Step-by-step explanation:
1. Change 1/3 to 4/3 by multiplying the numerator by 3 and adding one.

2. Multiple 4/3 by 1/5 to get 4/15.

Answer:

A

Step-by-step explanation:

step 3 is correct

x = 1

in step 4 the student has substituted x = 1 into y instead of x, that is

3x + 2(1) = 7 ← Incorrect substitution

Should be

3(1) + 2y = 7

3 + 2y = 7 ( subtract 3 from both sides )

2y = 4 ( divide both sides by 2 )

y = 2

Answer:

A. Step 4

Step-by-step explanation:

Identifying the error

In step 4 the value of x is supposed to be substituted into the second equation however the value of x is instead substituted for y which is the first error made

Solving it correctly and explaining each step.

We have the two equations 3x + 2y = 7 and 5x - 4y = -3

It appears that the elimination method is being used as the first step consist of multiplying the first equation by 2 so that we have the two variables -4y and 4y which can cancel out in the next step so we are going to use the elimination method as well to solve it correctly.

What is the elimination method?

The elimination method is a method used to solve a system of equations. When you have two variables that have the same coefficient ( number before variable; x or y ) but different signs ( it works if they have the same too ) you can add the two equations eliminating one of the variables. Using this method will leave you with a singular variable in which you can solve

Solving it using the elimination method

Again we have the two equations 3x + 2y = 7 and 5x - 4y = -3

(step 1) Notice how the first equation has 2y which can be multiplied by 2 resulting in us getting 4y which is opposite of -4y. This sets us up exactly for using the elimination method.

Thus the first step would be too multiply the first equation by 2

3x + 2y = 7

x2

------------------

6x + 4y = 14

Now we have the two equations 6x + 4y = 14 and 5x - 4y = -3

(step 2)Our next step would be to add the two equations so that the variable y is eliminated

6x + 4y = 14

+ 5x - 4y = -3

--------------------

11x 0 = 11

We're left with 11x = 11

(step 3)Our next step would be to solve for x

11x = 11

==> divide both sides by 11

x = 1

(step 4) Now that we have defined one of are variables we plug it in into one of the equations and solve for the other, this is step 4.

5x - 4y = -3

==> plug in x = 1

5(1) - 4y = -3

(step 5)==> simplify

5 - 4y = -3

(step 6) ==> subtract 5 from both sides

-4y = -8

(step 7) ==> divide both sides by -4

y = 2

The real solution would be (1,2)

The logical conclusion to the conditional statements in the question is; hamburger => hands.

Logic deals with the process of arriving at a conclusion based of certain premises. If the premises are true, then the conclusion must be true and vice versa.

Thus, in this case, the logical conclusion to the conditional statements in the question is; hamburger => hands.

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