Find (a) arc length and (b) Area of a sector.

Answer:

Step-by-step explanation:

Since the x-axis is the line of symmetry, the missing vertex is the reflection of the given vertex over the line of symmetry.

Connect these points with the vertex on the x-axis to complete the triangle.

See the attachment

Answer:

[tex]x=13[/tex]

Step-by-step explanation:

Step 1: Isolate the square root on the left hand side

 Radical already isolated

  √x-4 = x-10

Step 2: Eliminate the radical on the left hand side

Raise both sides to the second power

    (√x-4)2 = (x-10)2

    After squaring

    x-4 = x2-20x+100

Step 3: Solve the quadratic equation

    Rearranged equation

    x2  - 21x  + 104 = 0

    This equation has two rational roots:

      {x1, x2}={13, 8}

Step 4: Check that the first solution is correct

    Original equation

    √x-4 = x-10

    Plug in 13 for  x

     √(13)-4 = (13)-10

     Simplify

     √9 = 3

     Solution checks !!

    Solution is:

     x = 13

Step 5: Check that the second solution is correct

    Original equation

    √x-4 = x-10

    Plug in 8 for  x

     √(8)-4 = (8)-10

     Simplify

     √4 = -2

     Solution does not check

     2 ≠ -2

One solution was found :

     x = 13

Step-by-step explanation:

A. AT1,2).B1.0).C'(4.0).D*(4,2)

your answer

Answer:

y = -2x + 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

The slope of the line, m, is -2 because the line shows a negative trend and moves right 1 unit every time a point moves down 2 units.

The y-intercept, b, is 5 because the line crosses that number once on the y-axis.

Answer:

159.25cm²

Step-by-step explanation:

A=lw

A=12×10cm

The rectangle’s area is 120cm² 

First, substitute the given information into the equation for the area of a circle.

A=πr²

A=(3.14)(5²)

A=3.14×25

A=78.5

Next, because the figure is only half of a circle, divide this in two.

78.5/2= 39.25cm²

Asc=39.25cm²

Add the two areas together.

A=Ar+Asc

120cm²+39.25cm²

The area of the combined figure is 159.25cm²

Answer:

2

Step-by-step explanation:

2x -4= 0

2x-4+4=0

2x=0+4

2x=4

2x/2=4/2

x=2

Answer: 31.0

Step-by-step explanation:

The visitor data is best modeled by a quadratic function, and the state park management should plan for more than 400 visitors next year.

To do this, we simply plot the points on a graph.

See attachment for the graph that represents the table.

From the attached graph, we can see that the points on the graph follows an approximately quadratic path

Hence, the visitor data is best modeled by a quadratic function

Also, the state park management should plan for more than 400 visitors next year.

This is so because the range of a quadratic function is the set of all real numbers.

This means that the table can accept a value of 400 (or greater) as one of its data points

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Answer:

( x-7)^2+(y-6)^2 = 25

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x-7)^2+(y-6)^2 = 5^2

( x-7)^2+(y-6)^2 = 25

Answer:

(x-7)^2+(y-6)^2=25

Explanation:

If I were you, I would mark 7 as x and 6 as y. Whatever is in your parenthesis for center of the circle, do the opposite in your equation. Since you have positive 7 & positive 6, turn those into negative numbers for your equation. And for the radius, just times it two times. So 5•5=25

Answer:

3/25

Step-by-step explanation:

1/5 x 3/5 = 3/25

The interest rate which is required in order for Leah to end up with $40,000 in his account which is compounded daily, is 4.11%.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

Leah is going to invest P=$30,000 and leave it in an account for t=7 years.

Put the values in the above formula to find rate of interest.

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\40000=30000\times\left(1+\dfrac{r}{12\times30\times100}\right)^{12\times30\times(7)}\\r=4.11 \5[/tex]

Thus, the interest rate which is required in order for Leah to end up with $40,000 in his account which is compounded daily, is 4.11%.

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Answer:

[tex]3^{n}+3^{n-1}[/tex]

Step-by-step explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be [tex]x^n + yn[/tex]

Because the sequence multiplies by 3 each time, The base number in that equation would be [tex]3^n +yn[/tex].

So [tex]3^n[/tex] of the equation would be:
[tex]3, 9, 27[/tex].

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: [tex]3^{n-1}[/tex].

Combine these 2 equations together and you get:

[tex]3^{n}+3^{n-1}[/tex].

Answer:

Amanda's percent of error: = .03 or 3% Dwyane's percent of error: = .02 = 2%

Looks like Amanda had the larger error.

Answer:

  9.  AB = (40/3)√3

  10.  BC = (20/3)√3

Step-by-step explanation:

The ratios of side lengths in the "special" 30-60-90° triangle are ...

  1 : √3 : 2

__

If D is the point where the altitude meets AB, then we have for the left triangle ...

  CD : AD : CA = 1 : √3 : 2 = 10 : 10√3 : 20

and, for the right triangle ...

  BD : CD : BC = 1 : √3 : 2 = (10/√3) : 10 : (20/√3)

and for the large triangle ...

  BC : CA : AB = 1 : √3 : 2 = (20/√3) : 20 : (40/√3)

__

The hypotenuse of ΔABC is AB, shown above to be ...

  AB = 40/√3 = (40/3)√3

__

The shorter leg of ΔABC is BC, shown above to be ...

  BC = 20/√3 = (20/3)√3

Answer:

4

Step-by-step explanation:

The figure can be split into 2 triangles, the larger one is the whole figure with base 18 and height 9. while the other small triangle has base 8 and height h. Since they are both right angled triangles with a shared angle, they are similar.

With similar triangles, we get the ratio of base : height = 8 : 8+10 = h : 9

Hence, 8 : 18 can be simplified to 4 : 9, which is also equal to h : 9. From here, we get h = 4.

Answer:

4

Step-by-step explanation:

The figure can be split into 2 triangles, the larger one is the whole figure with base 18 and height 9. while the other small triangle has base 8 and height h. Since they are both right angled triangles with a shared angle, they are similar.

Using geometric sequence concepts, it is found that:

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

As a function of the mth term, the nth term is given by:

[tex]a_n = a_mq^{n - m}[/tex]

Hence, considering the 8th and the 11th term, the common ratio is found as follows:

[tex]a_{11} = a_8q^3[/tex]

[tex]32q^3 = 256[/tex]

[tex]q^3 = 8[/tex]

q = 2.

Then, considering the 11th term and the common ratio, the 13th term is given as follows:

[tex]a_{13} = a_{11}q^2 = 256 \times 2^2 = 1024[/tex]

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Answer:

0.16666666666667.

Step-by-step explanation:

Answer:

i got 17.4km/H pretty sure im right

Answer:

The integers are 2.

Step-by-step explanation:

Answer: 3 and 6

Step-by-step explanation:

3+6=9

3x6=18

Answer:

B.3x+8=66

Step-by-step explanation:

i think ito po Ang answer hehehe

Part A

x = some unknown number

x+8 = add on 8 to the number

3(x+8) = triple the previous result

Therefore, one equation to set up is 3(x+8) = 66

This is the same as 3x+24 = 66 because 3(x+8) = 3x+3*8 = 3x+24. Use the distributive property to multiply that outer 3 to each term inside.

C)  3x+24 = 66

D)   3(x+8) = 66

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

Part B

Let's solve for x. I'll show the steps for each equation mentioned. When you write out the steps, you probably only need to pick one equation to solve.

3(x+8) = 66

x+8 = 66/3

x+8 = 22

x = 22-8

x = 14

Or

3x+24 = 66

3x = 66-24

3x = 42

x = 42/3

x = 14

Either way, we get the same x value. To confirm this answer, replace x with 14 in either equation and simplify fully. You should get 66 on both sides.

Answer:

7/10

Step-by-step explanation:

There are 20 students in the class.

The scores are :

100, 95, 88, 62, 74, 90, 100, 58, 72, 60, 85, 90, 70, 72, 54, 100, 60, 80, 75, 51

* scores ≥ 70 have been highlighted in bold

Out the 20, 14 students have passed.

Hence, the fraction of students passed :

Answer:

31.5 units.

Step-by-step explanation:

The area is the height times the base divided by 2.

9x7 = 63

63/2 = 31.5

If an event is likely to occur, the probability that the event will occur is between 3/4 and 1.

Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

If the probability lies between 0 and 1/5, it is likely that the event would not occur. If the probability lies between 1/5 and 1, it is likely that the event would occur.

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Answer:

75% and 100%

Step-by-step explanation:

The probability spectrum is (the spaces are supposed to be equal):

|----------------------|--------------------|--------------------|---------------------|

0%                    25%               50%              75%                   100%

impossible   unlikely          equal            likely                  certain

Answer:

∠ EDF = 23°

Step-by-step explanation:

angles on the circumference of a circle ( inscribed angles) subtended by the same arc are congruent.

∠ FGE and ∠ EDF are inscribed angles subtended by arc EF

then ∠ EDF = ∠ FGE = 23°

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The size of ∠EDF is 23°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

As it is known that the angles made from the same chord in a circle are of equal measurement.

Since EF is the chord of the circle and the measure of ∠EGF is 23°, the measure of ∠EDF will be 23° as well.

Hence,  the size of ∠EDF is 23°.

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Answer:

$ 30, 021.39

Step-by-step explanation:

3759( 1 + .11875/12 )^(211)  = 30, 021.39

Answer:

3

Step-by-step explanation:

Coefficient in the number behind the variable.

In 3x + 7,

x is the variable.

3 is the coefficient.