Find the length of the arc of a sector of a circle whose angle at the centre is 120° and area of the sector is 462 cm².​

I) we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

II) The 30th term of this arithmetic sequence is 29.

To solve this problem, we can use the fact that in an arithmetic sequence, the difference between consecutive terms is constant.

(i) Let's call the common difference d. Then we can set up the equation:

x + d = 2x + 1

d = x - 1

Since we know that x; 2x + 1; 11 are three consecutive terms of an arithmetic sequence, we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

(ii) To find the 30th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the number of the term we want to find.

Substituting the known values into this formula:

a30 = x + (30 - 1)d

a30 = 0 + (29)(1)

a30 = 29

So the 30th term of this arithmetic sequence is 29.

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The expressions that are equivalent to 9/7x−3/4 are:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

All of the following expressions are equivalent to 9/7x−3/4:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

When you multiply or divide both the numerator and denominator of a fraction by the same non-zero number, the fraction remains equivalent.

Hence, the expressions that equivalent to 9/7x−3/4 are:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

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Answer: 25q and 3d

Step-by-step explanation:

23 dimes and 17 quarters equal $6.55.

To find the number of dimes and quarters which equals $6.55, we can use the following method:

Let D = number of dimes

Let Q = number of quarters

40 coins  ==>  D + Q = 40  ==>  D = 40 - Q

$6.55 total  ==>  10*D + 25*Q = 655

After the value for D is substituted in the second equation,

10*(40 - Q) + 25*Q = 655

400 - 10*Q + 25*Q = 655

15*Q = 255

Q = 17

i.e., D = 40 - 17 = 23

Check:  23 dimes = $2.30

           17 quarters = $4.25

           Total = $6.55 

Therefore, 23 dimes and 17 quarters equal $6.55.

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The tens digit of k when sum of its digits is 5 and tens digit of k + 6 is 3.

Let tens digit of k be x and units digit be y. Then

k = 10x + y

The sum of the tens digit of k and the units digit of k is 5, that is

x + y = 5

So possible combinations of (x, y) is (1, 4), (2, 3), (3, 2), (4, 1) and (5, 0).

The tens digit of k+6 is 3.

So x<=3.

14 + 6 = 20

23 + 6 = 29

32 + 6 = 38

So k is 32.

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Think of a bracelet made of five different coloured beads. Be sure to account for flipping and rotating. Check to see whether your solution is right by applying the same logic to a bracelet with four beads of four different colours.

Properties. The form with the biggest area for a given perimeter is a circle (see Isoperimetric inequality). The circle has excellent spherical shape around the centre for all angles and every line thru the centre generates a path of reflection symmetry.

My response is: There are (n-1)!/2 potential bracelets for n different colours, as in our example. Therefore, there are 4!/2=12 various bracelets that might be made for n=5.

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Answer:

[tex]26u + 14v[/tex]

Step-by-step explanation:

[tex]2(8u - 2v) + 2(5u + 9v) \\ 16u - 4v + 10u + 18v \: \: \\ 26u + 14v \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer: 18

unclear but appears its 18.

Step-by-step explanation:

Because x is 7; 4x+8/2 = 36.

but its not clear what is being halved: 8 or (4x+8)? so answer could be 32 as well.

The probability of getting 1st even and second odd is 9/36 = 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the sum of the probabilities of all the events in a sample space.

Number of outcomes with 1st even and second odd is 9

Total number of outcomes = 36

So, the probability of getting 1st even and second odd is 9/36 = 1/4

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By using the piecewise function that shows the amount of money that will be charged for people in the amusement park , then the value of C(25) is $1425  .

The Piecewise function is given as ⇒ [tex]\{ \begin{array}{lr} 65p \; , & 0\leq P\leq 10\\ 55+100 \; , & 10 < P\leq 20\\ 45p+300 , & 20 < p\leq 30\\ 35p+600& 30 < p \end[/tex]   ;

we need to find the value of C(25) , that  means we have to find the amount of money that will be charged for 25 people in the amusement park ,

From the given piecewise function , we can see that [tex]p =25[/tex] lies  in the range [tex]20 < p\leq 30[/tex] ,

So , we substitute [tex]p =25[/tex] in [tex]C(p)= 45p+300[/tex] ;

we get ;

C(25) = [tex]45 \times 25 + 300[/tex]

= [tex]1125+300[/tex]

= 1425 .

Therefore , the amount that will be charged for 25 persons will be $1425 .

The given question is incomplete , the complete question is

Use the piecewise function showing the amount of money that will be charged, C(p) , for a group to go to an amusement park based on the number of people, p , n the group .

[tex]C(p)= \{ \begin{array}{lr} 65p \; , & 0\leq P\leq 10\\ 55+100 \; , & 10 < P\leq 20\\ 45p+300 , & 20 < p\leq 30\\ 35p+600& 30 < p \end[/tex]

Find C(25) ?

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Answer: C - The statement is false.

Step-by-step explanation: Rhombuses also have perpendicular diagonals.

Answer:

.

Step-by-step explanation:

Answer:

$60 / 6 barbecue sticks = $x / 1 barbecue stick

Where x is the value of 1 barbecue stick.

To find the value of x, we can cross-multiply and divide by 6:

$60 = 6 barbecue sticks * $x/1

$60 = $6x

$x = $10

So, $10 will equal 1 barbecue stick, if $60 = 6 barbecue sticks.

We know that you earned $300, so we can substitute that into the proportion:

$60 / 6 barbecue sticks = $300 / n barbecue sticks

We can cross-multiply and divide by 60:

6 barbecue sticks * $300 = $60 * n barbecue sticks

n barbecue sticks = $300 * 6 / $60

n barbecue sticks = 30

Therefore, you sold 30 barbecue sticks.

[tex]\sqrt[3]{6x}[/tex] has no real end behavior as x can be both positive and negative.

[tex]\sqrt[3]{x-5}-6[/tex] will approach negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

[tex][-3 \sqrt[3]{x+3}+7][/tex]will approach positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.

Generally, The behavior of a function's graph at the "ends" of the x-axis is referred to as the function's "end behavior," and it is described by the symbol f. To put it another way, the trend of the graph may be described by the end behavior of a function if we look to the right end of the x-axis (as x approaches +) and to the left end of the x-axis (as x approaches ).

Take a look at the leading term of the polynomial function to get an idea of how it will behave in the end.

Because the power of the leading term is more than that of the other terms, whether x is made extremely big or very tiny, the leading term's behavior will predominate the graph because it will increase substantially quicker than the growth of the other terms.

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William should use 0.625 pounds of peanuts, and 0.375 pounds of cashews in the mixture.

Given that,

The selling price of peanuts= $2.40

The selling price of cashews= $3.20

Let x be the amount of that pound composed of peanuts. (1-x) of that pound is composed of cashews.

The total price of such a pound mix is 2.4x + 3.2(1-x) = 2.7

2.4x + 3.2(1-x) = 2.7

2.4x + 3.2 - 3.2x = 2.7

-0.8x + 3.2 = 2.7

-0.8x = -0.5

x = 5/8 = 0.625 pounds of peanuts, and 1-5/8=3/8= 0.375 pounds of cashews.

Thus, William should use 0.625 pounds of peanuts, and 0.375 pounds of cashews in the mixture.

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The system of inequalities that models this situation is given as follows:

One possible solution is given as follows:

(9,4).

Meaning that he works 9 hours lifeguarding and 4 hours clearing tables.

The variables for the system of inequalities in this problem are given as follows:

The number of hours cannot be negative, hence the first two restrictions are given as follows:

He can work a maximum of 14 total hours, hence:

x + y ≤ 14.

He must earn no less than $180, hence, considering the rates for each job, we have that:

18x + 10y ≥ 180.

Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables, hence:

The shaded region represents all possible solutions for the system of inequalities.

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Answer:

|x+3|=2

Step-by-step explanation:

We need to make the equation so that -5 and -1 both work, so this equation is one of many that we can construct.

Answer: i cant see

Step-by-step explanation:

The measure of the angle ∠CFE is 330°.

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc.

Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The angle ∠CFE is calculated as:-

∠CFE = 360 - ∠CEF

∠CFE = 360 - 30

∠CFE = 330

Hence, the angle ∠CFE is 330°.

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Consequently, the yield to maturity of a P7000 bond purchased at 90 with 15 years left to maturity is approximately 6.769%.

The rate of return an investor will receive if they hold the bond until maturity is known as the yield to maturity (YTM) of the bond. We need to know a bond's face value, coupon rate, market price, and time until maturity in order to determine its YTM.

Here,

Given :

Face value (FV) equals P7,000

Discount rate is 6%.

Market price as of today (CP) is $90.

15 years is the time to maturity (T).

To determine the YTM, we can use the bond pricing formula:

CP is equal to (FV * C) / (1 + r)T plus (FV / (1 + r)T)

Where:

(FV * Coupon Rate) / 2r = YTMT = time to maturity in years, where C is the annual coupon payment.

The result of solving the equation is 6.769% for the YTM.

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Answer:

4 I think

Step-by-step explanation:

A vertex is a point where two or more edges meet (i.e the sharp points of the figure).

A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner.

Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]\angle ACB \cong \angle HFB[/tex] by the corresponding angles theorem.

On solving the provided question, we can say that Area of square = SxS=846 and perimeter of square = 4xS= 846/4=S= 211.5=Side.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

Area of square = SxS=846

Perimeter of square = 4xS= 846/4=S= 211.5=Side.

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The correct question is -

A parking lot is shaped like a trapezoid as shown. If the area of the parking lot is 846 square meters, what is the perimeter? (Hint: The formula for the area of a trapezoid is (A=h2(b1+b2)

The inverse function of y = 2(x - 5)² is  [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Let, y = 2(x - 5)².

y/2 = (x - 5)².

Solving for 'x'.

[tex]x - 5 = \pm\sqrt\frac{y}{2}[/tex].

[tex]x = \pm\sqrt\frac{y}{2} + 5.[/tex]

Now, We have to interchange the positions of x and y.

[tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

So, The inverse of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

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If the graph only touches the x-axis at the x-intercept, then it is said to "touch" the x-axis. This indicates that the graph does not pass through the x-axis at the x-intercept, but rather just touches it.

The x-intercept of a graph is the point at which the graph crosses the x-axis. It is also known as the abscissa. The x-coordinate of the x-intercept is the value where the graph intersects the x-axis.

The x-intercept of a graph is the point at which the graph crosses (or, in some cases, touches) the x-axis. A graph can have one or more x-intercepts. If the graph only crosses the x-axis once, then it has only one x-intercept. If the graph crosses the x-axis twice or more, then it has multiple x-intercepts. In either case, the x-intercepts can be described as either "crosses" or "touches" the x-axis.

If the graph crosses the x-axis at the x-intercept, then it is said to "cross" the x-axis. This indicates that the graph passes through the x-axis at the x-intercept.

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A function can be obtained from the table provided with the values of x and y in the form of a y=mx+b equation.

The above equation can be solved by plotting the graph or from table itself and after calculating its y-intercept, the value of y in the form of y= mx+ b can be obtained. Suppose the table has values of x and y as follows:

x: 0   1   2  3

y: 2  4   6  8

However, it can be seen that when x=0, y= 2, so the y-intercept i.e. the value of y obtained at x=0 is 2. And the slope can be calculated as:

m=[tex]\frac{change in y}{ change in x}[/tex]

m= [tex]\frac{4-2}{1-0}[/tex]

m=2

So the function can be written as y=2x+2

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The measurement that you can use in your future career depends on the exact career and there are many more options.

Depending on the exact career but measurements are plentiful in the healthcare business. First, you'll most likely deal with weight and height... since that's part of most healthcare consultations. Then, if you deal with medication, you'll use grams, milligrams, milliliters, and liters all the time. depending if the medication is in solid or liquid form.

Even as a nutritionist, you'll deal with grams and such for portion sizes. There are countless ways you'll use mathematics and measurements in the healthcare sector.  

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The answer and prove are AD = RC, <A≅<R, <AMD≅<RMC

the table shows the statement and the reasons for the proves of congruency of the angles and triangles

The table appears as follows

sn                  Statement                               Reason

1                     AD = RE                                 Given

2                   <A ≅<R                                    Given

3                     <AMD ≅<RMC                      Vertically opposite angles

4                     ΔMAD≅ΔMRC                      Congruent by ASA or SSA

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We would need more information to answer this question. For example, Sally’s speed.

Step-by-step explanation:

Answer: 8.7

Step-by-step explanation:

The remaining interior angle is [tex]95^{\circ}[/tex].

[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]

Answer: x= 337/70 or 4 57/70

Step-by-step explanation: