67. Extensions
Find the equation of the line that passes through the following points: (a, 0) and (c, d)

Answer:  69m^2

Step-by-step explanation:

we can find the area of shaded region by  subtracting the area of removed region.

so,

area of rectangle= length*width

for area of removed region

=4m*2m=8m^2

for area of  larger region

=11m*7m=77m^2

Now final destinaltion

area of shaded region=area of lareger region-area of smaller region

                                     =77m^2-8m^2

                                    =69m^2

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 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:

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

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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Answer:

3.57 taps

Step-by-step explanation:

14/5 = 10/x hours (divide both sides by 10)

50/14 = x (3.57 taps)

Brainliest, please :)

Answer:

7 taps

Step-by-step explanation:

rate =    1 tank / 5 taps = 14 hr

1 tank = 70 tap-hr

70 tap -hr  / x tap  = 10 hr

x = 7 taps

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.

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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The strategy that Lucy uses to recall her phone number is what is known as Chunking.

This refers to the place where information is stored for future use and can either be a short or long-term memory.

Hence, we can see that based on the breaking down of her phone numbers of Lucy into a particular format that separates them using country/state code, she is making use of chunking.

This method of chunking is effective because it would help Lucy to recall her number quite easily.

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Answer: [tex]55^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line add to [tex]180^{\circ}[/tex].

Answer:

√41, or about 6.4 units

Step-by-step explanation:

[tex] \sqrt{ {5}^{2} + {4}^{2} } = \sqrt{25 + 16} = \sqrt{41} [/tex]

√41 is about 6.4 units

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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Angles around a point equal 360°, so n = 360 - 291 = 69°

Thus, as angles in a triangle add to 180°, m = 180 - 31 - 69 = 80°

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]

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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Answer:

Below.

Step-by-step explanation:

It's the Alternate Angle Theorem.

The opposite sides of the quadrilateral are parallel.

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:

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 :)

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 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:

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.

Answer:

Irrational number

Step-by-step explanation:

  Prime factorize the number and then simplify.

[tex]\sf \sqrt{5}*\sqrt{5}*\sqrt{8}=\sqrt{5*5*8}[/tex]

                     [tex]\sf = \sqrt{5*5*2*2*2}\\\ = 5* 2* \sqrt{2}\\\\= 10\sqrt{2}[/tex]is an irrational number.

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.

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]

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]

Answer:

m>35

Step-by-step explanation:

We have to find the least m for 65 + 0.8m > 93.

subtract 93 from each side of the inequality: 0.8m > 28

divide both sides of the inequality by 4: 0.2m > 7

multiply both sides of the inequality by 5 to find m: m>35.