What is the area of the sector
shown in the diagram below?


OA. 11.1 cm²
OB. 2.5 cm²
OC. 39.3 cm²
OD. 50 cm²

We now have three equations, so we can solve them.

Let's define the length of the 3 boards in terms of x:

F=x

S=2x-3

T=2

F+S+T =26

x+2x-3+2 =26

3x =26+1=27

x =27/3 = 9 feet for First section

2x-3 =18-3 = 16 feet = Second

2 = Third

9+16+2 = 27

27 is the length of the shortest piece.

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The value of x is

1. x= -37/48

2. x=0

3. x = 33/4

4.  x= -20/7

A mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

1.  6(8 x + 6) + = - 1

   48x + 36 = -1

 x= -37/48

2.  9x/7 + 6 = 6

9x/7= 6-6

9x/7 =0

x= 0*7/9

x= 0

3. 2x/11 (11 - 7) = 6

    x * 4= 6*11/2

    4x= 33

    x = 33/4

4. 11x/4 (4 - 2) = 9x + 10

 11x/4 * 2 = 9x +10

11/2*x = 9x +10

-7/2x = 10

x= -20/7

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[tex]\bf{\dfrac{1}{2}(27+6)10 }[/tex]

Add 27 and 6 to get 33.

[tex]\bf{\dfrac{1}{2}(33)(10) }[/tex]

Multiply 1/2 by 3 to get 33/2.

[tex]\bf{\dfrac{33}{2}(10) }[/tex]

Express 33/2 (10) as a single fraction.

[tex]\bf{\dfrac{(33)(10)}{2} }[/tex]

Multiply 33 and 10 to get 330.

[tex]\bf{\dfrac{330}{2} }[/tex]

Divide 330 by 2 to get 165.

[tex]\bf{165 \ \ \to \ \ \ Answer}[/tex]

Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$[/tex]

And

[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]

Since, both slopes are reciprocal of each other.

Therefore, the lines are perpendicular.

Using proportions, it is found that Paula Radcliffe's World Record time was of 2h 15 min 25s.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In seconds, Dale Grieg's time is of:

3 x 3600 + 27 x 60 + 45 = 12,465s.

The Womens' World Record Marathon time has improved by 34.82%, that is, it was reduced by 34.82%, which means that the time is 65.18% of what it was, hence Paula Radcliffe's time is seconds is given by:

P = 0.6518 x 12465 = 8,125s.

In hours, minutes and seconds, we have that:

8,125s = 2h 15 min 25s.

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For the given experiments there are following outcomes.
A) Independent
b) Dependent
C) Dependent
D) Dependent
E) Independent

Probability can be defined as the ration of favorable outcomes to the total number of events.

For A)
A coin is tossed and a dice is flip. Both the event are independent of each other.

For B)
Choosing of clips have same total number of events that why both the events are dependent to each other.

For C)
It also have same number of total samples cause both cherries and nuts contained chocolate belongs to the same box. That's why its also dependent.

For D)
It is also dependent because the total number of sample is same for both the marbles.

For E)
It is independent, because for every box that picked reduces the size of sample and probability of picking new box wont depends on previous box.

Thus, this is how events are dependent and independent

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The simplification of each form of expression is;

(6r + 7) + (13 + 7r)

= 6r + 7 + 13 + 7r

= 13r + 20

(13 - 3/2r) - (1 - r)

= 13 - 3/2r - 1 + r

= 12 - 3/2r + r

= 12 -3r+2r/ 2

= 12 - 1/2r

(-8 - r) + (2r - 4)

= -8 - r + 2r - 4

= -12 + r

(7r - 3/2) - (2/3 + 6r)

= 7r - 3/2 - 2/3 - 6r

= r -9-4/6

= r - 13/6

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Answer:

Actually this question is easy. Mutual angles are equal to each other. Then 152-90=62

Answer:

18+62=80x

12+18=30x

x=80÷30=2

x>2

Answer:

my ans will be wrong also and right also 50%5$chances it is an opposite angle so it is in out manner so iys sum is 180 so we have to subbtract

Step-by-step explanation:

65०to 180०(180०-65०=115०) i think ans is 115०the missing angle measurement is 115०in my opinion

The probability that the 2-digit number is prime is 3/8

The sets are given as:

First digit = {1, 2}.

Second digit = {1, 2, 3, 4}

When the 2-digit is formed, we have:

Numbers = {11, 12, 13, 14, 21, 22, 23, 24}

In the above set, there are 3 prime numbers out of the 8 numbers.

Hence, the probability that the 2-digit number is prime is 3/8

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Answer:

(x+5)² + (y+5)² = 18

Step-by-step explanation:

Since the outline of the circle intersects with the point (-8,2), you can substitute to find the equation of the circle in the form (x-h)² + (y-k)² = r². First the center of the circle is given in the form (h,k). So (-5, -5) → (x – (-5))² + (y – (-5))² = r² → (x + 5)² + (y + 5)² = r².

Then to find r², substitute the given point with x and y.

((-8) + 5)² + ((-2) + 5)² = r²

(-3)² + (3)² = r²

18 = r²

r² = 18.

There's no "whole" number that gets exactly to 2230 (but the question that you are asking is the square root of 2230 I believe) but the answer would essentially be about 47.22.

The required range of the x in the inequality [tex]\left|x+3\right|-2\le0[/tex] is [-1, -5]
and the graph is attached below

Inequality, can be define as when the equations contain [≤ , ≥   <, >] is called inequalities.

Simplifying

[tex]\left|x+3\right|-2\le0[/tex]
[tex]|x+3|\leq 2\\-2\geq x+3\leq2 \\-5\geq x \leq-1[/tex]

Thus, the required range of x in inequality  [tex]\left|x+3\right|-2\le0[/tex] is [-5, -1].

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Answer: The answer to the question is Answer Choice "B"

where it says x=-1

Step-by-step explanation:

Proof that It's actually correct as you can see it on the screenshot :)

Answer:

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

Let the cost price is x.

We have:

Solve it for x:

The cost is 22500, find selling price with 20% profit:

Answer:

The LCM is 20

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the LCM of 4, 10

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The lcm stands for the least common multiple.

Using our times tables, let's find the lcm of 4 and 10.

[tex]\bf{Which\;is\;20}[/tex]. 40 is indeed a common multiple of 4 and 10, but it's not the least common multiple. The lcm is 20.

We can also list some multiples of 4 and 10 and find the lcm.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...

10: 10, 20, 30, 40, 50, 60...

As you can see, we end up with the same answer: the lcm of 4 and 10 is indeed 20.

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=Lcm=20}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.

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

The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.

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Answer:

All 3 are right triangles.

Step-by-step explanation:

In a right triangle c^2 = a^2 + b^2   where c is the longest side.  ( by Pythagoras).

a) 3^2 = 9, 6^2 = 36 and √27 ^ 2 = 27

36 = 9 + 27

So this is a right triangle.

b)

17^2 = 289, 15^2 = 225 and 8^2 = 64

289 = 225 + 64

Also right triangle.

c) √50 ^ 2 = 50, 5^2 = 25 and 5^2 = 25

So also right triangle.

The true statements about the pool are

The given parameters are:

To measure the drain, we simply calculate the perimeter of the edge of the pool.

This means that (a) is correct

When the volume is calculated, the unit is cubic yard or yd³.

This means that (b) is wrong

The area of the cover is:

Area = Length * Width

This gives

Area = 25 yards * 10 yards

Evaluate

Area = 250 square yards

This means that (c) is correct

The length of the drain is calculated as:

Perimeter = 2 *(Length + Width)

This gives

Perimeter = 2 * (25 + 10)

Evaluate

Perimeter = 70

This means that (d) is wrong

Lastly (e) is correct, because the width of pool is 10 yards

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We have been able to prove that the area of the triangle formed by the joining midpoints of triangle ABC is 1/4 the area of triangle ABC.

Area of triangle joining the points A, B & C is;

A₁ = ¹/₂[tex]\left[\begin{array}{ccc}1&1&1\\3&-2&5\\4&0&0\end{array}\right][/tex]

A₁ = ¹/₂(-1 * -20) + (1 * 8)

A₁ = 14

Thus;

Midpoint of AB is (¹/₂, 2)

Midpoint of BC is (³/₂, 0)

Midpoint of AC is (4, 2)

A₂ = [tex]\frac{1}{2} \left[\begin{array}{ccc}1&1&1\\\frac{1}{2} &\frac{3}{2} &4\\2&0&2\end{array}\right][/tex]

A₂ = ¹/₂(3 - 1(-7) + (1 * -3))

A₂ = ⁷/₂

Since A₁ = 14, we can equally say that;

A₂ = ¹/₄A₁

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Answer:

Below.

Step-by-step explanation:

It's the Alternate Angle Theorem.

The opposite sides of the quadrilateral are parallel.

Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

According to the function,

Let the function be represented by f(x).

Step 1- Multiplying the number x by 4 results in 4x.

Step 2 - Subtracting 2 from results give 4x - 2.

So the function becomes:

f(x) = 4x - 2

We will find the inverse function by Replacing f(x) by y, and isolate x on one side of the equation and find the inverse:

[tex]y=4x-2\\\\ < br/ > y+2=4x\\ < br/ > x =\frac{1}{4} (y+2)\\ < br/ > f^-^1(y) = \frac{1}{4} (y+2)\\ < br/ > f^-^1(x) = \frac{1}{4} (x+2)[/tex]

Here,

The inverse function represents the reverse process.

Here, Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

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Answer: B. X = [tex]4\sqrt{6}[/tex]

Step-by-step explanation:

sec(45) = hyp/12

12sec(45) = hyp

hyp = 16.9

cot(60) = x/16.9

16.9cot(60) = x

x = 9.7

B. X = [tex]4\sqrt{6}[/tex]

It will take approx. 22 minutes and 30 seconds for the speeches.

It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here, Time duration of each learner = 1 minutes 30 seconds

                                                            = 3/2 minutes.

        Total number of learners = 15

Time taken by all the speech category = 15 X 3/2

                                                                 = 45/2

                                                                = 22 minutes 30 seconds

Thus, It will take approx. 22 minutes and 30 seconds for the speeches.

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Answer:

D : (0 ≤t ≤6)

R : (-2 ≤d ≤0)

Step-by-step explanation:

your domain is your x and your range is your y.

this means that you start by looking at your x axis. in this problem, x goes from 0 to 6, so 0 ≤t ≤6

this is the same for y.

y goes from -2 to 0 (remember that you read the y axis down and up, so you need to have the negative number written first)  

so -2 ≤d ≤0

Answer:

(domain: 0 ≤ t ≤ 6)

(range: -2 ≤ d ≤ 0)

Step-by-step explanation:

domain of a function: all possible x-values

range of a function: all possible y-values

here, we know that we can't have negative time (note: time is along the x-axis and is x-variable; it is describing the domain)

(and yes, while time still goes on forever, this graph does not have an arrow on the end of it, meaning that is where we are considering time to stop--and because its an ≤ sign, it wouldn't be infinity)

so, time goes from 0 to 6

(domain: 0 ≤ t ≤ 6)

here, we also know that our submarine won't go above the water level (it's not going to keep floating up into space forever), so the maximum value of our range (depth) is going to be 0

we also won't be going any lower than where the toy starts--which we can see to be -2

so, the depth goes from -2 to 0

(range: -2 ≤ d ≤ 0)

hope this helps!! have a lovely day :)

Answer: C

Step-by-step explanation:

[tex]\sin x=\frac{13}{18}\\\\x=\sin^{-1} \left(\frac{13}{18} \right) \approx \boxed{46.24^{\circ}}[/tex]

Let

[tex]S_N = \displaystyle \sum_{n=1}^N -7 \left(\frac38\right)^n = -7\left(\dfrac38 + \dfrac{3^2}{8^2} + \dfrac{3^3}{8^3} + \cdots + \dfrac{3^N}{8^N}\right)[/tex]

Then

[tex]\dfrac38 S_N = -7\left(\dfrac{3^2}{8^2} + \dfrac{3^3}{8^3} + \dfrac{3^4}{8^4} + \cdots + \dfrac{3^{N+1}}{8^{N+1}}\right)[/tex]

[tex]S_N - \dfrac38 S_N = -7 \left(\dfrac38 - \dfrac{3^{N+1}}{8^{N+1}}\right)[/tex]

[tex]\dfrac58 S_N = -\dfrac{21}8 \left(1 - \left(\dfrac38\right)^N\right)[/tex]

[tex]S_N = -\dfrac{21}5 \left(1 - \left(\dfrac38\right)^N\right)[/tex]

As [tex]N\to\infty[/tex], the exponential term will converge to zero, so the infinite sum converges to

[tex]\displaystyle \sum_{n=1}^\infty -7 \left(\frac38\right)^n = \lim_{n\to\infty} S_N = \boxed{-\dfrac{21}5}[/tex]