Which number line correctly shows 0.8+ 0.3?
O
O
CO
0 01 02 03 04 05 06 07 08 09 11 12 13
0 0.1 0.2 0.3 04 05 06 07 08 09 11 12 13
0 01 02 03 04 05 06 07 08 09 1 11 12 131
0 01 02 03 04 05 06 0
08 09
31

The equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

In order to find the measure of LM, we will take the ratio of the sides of the similar triangles.

Using the equation as shown

DF/EF = LK/LM

DF/LK = EF/LM

Substitute the measure of the sides

9/13.5 = 14/LM

Hence the equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

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[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]

[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]

[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]

[tex]10y {}^{2} + 90y + 200 = 0[/tex]

[tex]y {}^{2} + 9y + 20 = 0[/tex]

[tex](y + 4)(y + 5) = 0[/tex]

[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]

[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]

[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]

Answer:

[tex]\left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]

Step-by-step explanation:

[tex]2*cos^2\theta-1=0\ \ \ \ (0^0\leq \theta\leq 360^0)\ \ \ \ \ \theta=?\\2*cos^2\theta-(sin^2\theta+cos^2\theta)=0\\2*cos^2\theta-sin^2\theta-cos^2\theta=0\\cos^2\theta-sin^2\theta=0\\cos2\theta=0\\0^0\leq \theta\leq 360^0\ \ \ \ \Rightarrow\\\left \{ {{2\theta=\frac{\pi }{2}\ |:2 } \atop {2\theta=\frac{3\pi }{2}\ |:2 }} \right. \ \ \ \ \left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]

Good luck and have a nice day!

The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).

In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:

By applying the basic trigonometry functions, we have:

sin(A) = Opp/Hyp = a/c.

sin(C) = Opp/Hyp = c/b.

cos(A) = Adj/Hyp = c/b.

cos(C) = Adj/Hyp = a/c.

From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).

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Answer:

Step-by-step explanation:

The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).

How to apply basic trigonometry?

In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:

Angle (θ) = 45°.

Opposite (Opp) side = a.

Hypotenuse (Hyp) = c.

Adjacent (Adj) side = b.

By applying the basic trigonometry functions, we have:

sin(A) = Opp/Hyp = a/c.

sin(C) = Opp/Hyp = c/b.

cos(A) = Adj/Hyp = c/b.

cos(C) = Adj/Hyp = a/c.

From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).

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The range for the length of the third side is it must be greater than 10 feet and less than 30 feet.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.

The length of the third side had to be greater than the difference between the two given sides and less than the sum of the two given sides.

(20 – 10) < S <(20+ 10) ; 10< S < 30

Therefore, the range for the length of the third side is it must be greater than 10 feet and less than 30 feet.

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Equation: x² + 10x + 21

Step 1: Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21

Step 2: Get the new equation bracketed → (x² + 7x) (+3x + 21)

Step 3: Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).

Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)

(x+3) (x+7)

Answer:

A. (x + 3)(x + 7)

Step-by-step explanation:

Got it correct… You’re welcome

The statement that proves that that quadrilateral JKLM is a kite is: (Option B) which indicates that:
LM = MJ = 3; a

JK = KL = √17

We know the following:

J = (4,5)

K = (5,1)

L = (1,2)

M = (1, 5)

We must commence by computing the length of the sides of the quadrilateral using:

D = [tex]\sqrt{((x1-x2)^{2} + (y1 -y2)^{2} }[/tex]

JK = [tex]\sqrt{(4-5)^{2} + (5-1)^{2} }[/tex]

= [tex]\sqrt{17}[/tex]

KL = [tex]\sqrt{(5-1)^{2} + (1-2)^{2} }[/tex]

= [tex]\sqrt{17}[/tex]

LM = [tex]\sqrt{(1-1)^{2} + (5-5)^{2} }[/tex]

= [tex]\sqrt{9}[/tex]

= 3

MJ = [tex]\sqrt{(1-4)^{2} + (5-5)^{2} }[/tex]

= [tex]\sqrt{9}[/tex]

= 3

From the above, it is clear that

LM = MJ = 3; and

JK = KL = [tex]\sqrt{17}[/tex]

QED

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Answer: B

Step-by-step explanation:

A triangle is a three-edged polygon with three vertices. Only the law of Sine can be applied to solve the triangle.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The sum of all three angles can be written as,

118° + 22° + x = 180°

x = 40°

For the sine rule to be applicable, two angles and a side or an angle and two sides are needed. Therefore, the law of Sine can be applied to solve the triangle.

For the cosine rule to be applicable, two sides and an angle between them is needed to be known, hence, the law of cosine can not be applied.

Hence, Only the law of Sine can be applied to solve the triangle.

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Answer:

The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.

Step-by-step explanation:

A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.

It is required to determine whether the given relation is a function.

To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.

Step 1 of 1

The given relation is {(a, b),(c, d),(e, d)}.

The set of the first components of each ordered pair is called the domain.

From the relation, the domain is {a, c, e}.

The set of the second components of each ordered the range.

From the relation, the range is {b, d, d}.

The given relation is a function. But it is not a one-to-one function.

The closest surface area of the container is: 1,696 ft².

Curved surface area of a cone = πrl

Surface of a cylinder = 2πr(h + r)

Surface area of the container = Curved surface area of a cone + Surface of a cylinder - area of circular base

= πrl + 2πr(h + r) - πr²

r = 24/2 = 12 ft

l = 13 ft

h = 10 ft

Plug in the values

Surface area of the container = π(12)(13) + 2π×12(10 + 12) - π(12²) = 1,696.5 ft².

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Answer:

E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.

E must be 6.

E = 6

Step-by-step explanation:

16 * 6 = 96

When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.

Given With each km from the lightning 3 seconds passes.

a) The table of values for distances from 0 to 5 km.

     Distances                     Time

            0                              0

            1                               3

            2                              6

            3                               9

            4                               12

            5                                15

b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x

c) When distance =1  , the time be 3 seconds

when distance =4.5  , the time=3*4.5

=13.5 seconds.

d) When time is 3 seconds = 1km

when time =1.5 seconds , the distance be 1/2=0.5 km.

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The domain and the range of the function are all set of real numbers

The function is given as:

f(x) = 4x + 3

The above function is a linear function

Linear functions have a domain and a range of all set of real numbers

Hence, the domain and the range of the function are all set of real numbers

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Answer:

22

Step-by-step explanation:

BD bisects <ABC, this means the half-line divided the angle into two equal parts.

If m<ABC is equal to 44 then m<ABD is

44/2 = 22

Step-by-step explanation:

the area is

(x² + 17x + 72) m²

it is the result of the usual

length × width

calculation.

length = x + g

width = x + h

length × width = x² + gx + hx + ab = x² + (g+h)x + gh =

= x² + 17x + 72

g + h = 17

gh = 72

just by looking at it that gives us 9 and 8 as g and h.

FYI - formally to calculate them we can say

g = 17 - h

(17 - h)h = 72

17h - h² = 72

h² - 17h + 72 = 0

the solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = h

a = 1

b = -17

c = 72

h = (17 ± sqrt(17² - 4×1×72))/(2×1) =

= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2

h1 = (17 + 1)/2 = 18/2 = 9

h2 = (17 - 1)/2 = 16/2 = 8

as we can see

g = 17 - h

if we say h = 9, then g = 8.

if we say h = 8, then g = 9.

so, these are our solutions.

we simply pick that length is longer than width, so, g = 9, h = 8.

the area including the walkway is then

(length + 3)(width + 3) =

= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²

and the dimensions incl. the walkway are

length = x + 9 + 3 = x + 12

width = x + 8 + 3 = x + 11

Answer:

C

Step-by-step explanation:

first you need to memorize

SOH CAH TOA

IT means

Sine =opposite/hipotenuse

Cosine = adjecent/hipotenuse

tangent = opposite/adjecent

in this case, we need to find sine

so it's SOH

opposite of theta Θ is 15

and it's hipotenuse , we don't know yet. so need to find it by using Pythagorean theorem

let it be x

x =√ 15²+ 8²

=√ 225+ 64

=√289

= 17

so the answer is 15/17

Answer:

The inverse is  -1/7(x+4)

Step-by-step explanation:

We have the function

y = -7x-4

To find the inverse, exchange x and y

x = -7y -4

Solve for y

Add 4 to each side

x+4 = -7y -4+4

x+4 = -7y

Divide each side by -7

-1/7(x+4) = -7y/-7

-1/7(x+4) = y

The inverse is  -1/7(x+4)

The linear function which represents the line given by the point slope equation y+1=-3(x-5) is f(x) =-3x+14 which is option D.

Given the equation y+1=-3(x-5) and we have to find the equation of line that represents this equation.

An equation is a relationship between two or more variables which are expressed in equal to form. Equation of two variables looks like ax+ by=c. It is solved in order to get the values of variables. Linear function is like equation whose graph shows a straight line.

We have to just find out the value of y in terms of x to find the linear function which can be done as under:

y+1=-3x(x-5)

y+1=-3x+15

y=-3x-1+15

y=-3x+14

Hence y=-3x+14 is the linear equation which represents the point slope equation y+1=-3(x-5).

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Answer:

So the shorter version of what the guy above me is saying is that it is:

[tex]f(x) = -3x + 14[/tex]  or

D

Step-by-step explanation:

I got it right on the test.

Hello!

The mean is the average of the terms.

⇒ Mean = Sum of terms / Number of terms

⇒ 130 = 104 + 137 + 154 + 131 + x / 5

⇒ x + 526 = 650

⇒ x = 124

∴ The missing number is 124.

The sample space is a combination of these two dice as we have shown in the attachment

This is the defined to be the set of all of the possible outcomes that can exist or be possible in a random experiment.

The question has two dice. These dice are made up of numbers from 1 to 6  each.

Die A = {1,2,3,4,5,6}

Die b = {1,2,3,4,5,6}

The sample space would be pairs of two of these two dices. The total number in the sample space would be 36.

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Answer:

The length of one side is 12ft

Step-by-step explanation:

The triangle is equilateral so all the sides are the same length.

So you are simply going to divide 36ft by the 3 sides.

36ft/3 = 12ft

Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The total number of legs in the room would be 10.

From the given information, it can be inferred that none of the legs of the animals is on the floor of the room.

It is given that 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.

The legs of the bed and the chair do.

So we can say that the chair and the bed each have four legs.

so that would be two more legs.

In total we have:

4 + 4 + 2 = 10.

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The mean score of class B is 82. 92

Class A = 30 pupils

Class B = 26 pupils

Mean score for class A = 70

Mean score of class B = unknown

Total mean score = 76

We have, [tex]\frac{(76 *( 30 + 26) - 70 *30) }{26}[/tex]

Then simply,

Calculate the sum or difference between the classes = [tex]\frac{76 * 56 - 70 * 30}{26}[/tex]

Calculate the product or quotient of the classes = [tex]\frac{4256 - 70 * 30}{26}[/tex]

= [tex]\frac{4256 - 2100}{26}[/tex]

= [tex]\frac{2156}{26}[/tex]

= [tex]\frac{1078}{13}[/tex]

= [tex]82. 92[/tex]

Thus, the mean score of class B is 82. 92

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Answer:

Step-by-step explanation:

Well since the questions are related to geometric series I'm assuming the reasoning for 0.99999.... = 1, is going to be a geometric series in this instance. All though there are other ways to prove this.

1.

 a. So if you think about it, 0.999 can be represented as: [tex]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}....[/tex] and so on. This is a geometric series. The geometric sequence explicit equation can be determined by realizing each term is the previous term multiplied by 1/10, since the numerator is staying the same, but the denominator is being multiplied by 1/10. So the explicit equation for the sequence is: [tex]a_n=\frac{9}{10}*(\frac{1}{10})^{n-1}[/tex]. The sum of an infinite series can be defined as: [tex]S_\infty=\frac{a_1}{1-r}[/tex] when |r| <1 , which in this case it is. So plugging the values into the equation you get: [tex]S_\infty=\frac{\frac{9}{10}}{1-0.10}=\frac{\frac{9}{10}}{\frac{9}{10}} = 1[/tex]. So the sum of this infinite series that represents [tex]0.\overline{9}[/tex] is equal to 1.

 b. Another repeating decimal can easily be determined using the repeating decimal 0.9. If you multiply both sides by 10, you'll get: [tex]9.\overline9 = 10[/tex].

2.

 a. So this is an arithmetic sequence and it appears to be increasing by 5, with the first term being 3. So an explicit formula can be written using these two values: [tex]a_n=3+5(n-1)[/tex] which can also be simplified by distributing the 5, to get: [tex]a_n=3+5n-5=5n-2[/tex]. A recursive rule can also be easily defined using these two values, it's simply: [tex]a_n=a_{n-1}+5\\a_1=3[/tex]

 b. The 1000th term can be evaluated using the explicit formula by plugging in 1000 in as n: [tex]a_{1000} =5(1000)-2=5000-2=4998[/tex]

 c. The explicit formula, since it's much easier to evaluate values, by simply plugging in 1000 as n

 d. The issue with a recursive rule, is you need to know all previous values, to determine [tex]a_n[/tex], because it's doing some operation on the previous value, except to know that previous value, you need the previous previous value, and so on. This is an issue with much larger numbers, which is why the explicit formula is generally more better.

The roots are (x + 1), (x - 4), (2 + 5i), and (2 - 5i).

g(x) = (x2 - 3x - 4)(x2 - 4x + 29)

Let us first consider x^2 - 3x - 4

By splitting the middle term

= x^2 + 1x - 4x - 4

= x(x + 1) - 4(x + 1)

= (x + 1)(x - 4)

Now let us consider x^2 - 4x + 29

First group the terms with variable on LHS and move the constant on the other side

x^2 - 4x = -29

Add 4 on both sides

x^2 - 4x + 4 = -29 + 4

x^2 - 4x + 4 = -25

It can be written as perfect squares

(x - 2)^2 = -25

We know that

i =√1

Take square root on both sides

x - 2 = ± 5i

x = 2 ± 5i

So we get,

x = 2 + 5i and x = 2 - 5i

g(x) = (x + 1)(x - 4)(2 + 5i)(2 - 5i)

A square root of a number is a price that, whilst extended by means of itself, offers variety. instance: four × four = 16, so a square root of 16 is four. The word that (−four) × (−four) = 16 too, so −four is likewise a square root of sixteen. The symbol is √ usually way the wonderful rectangular root. example: √36 = 6 (because 6 x 6 = 36).

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Answer:

Find the derivative using the chain and power rules.

-6csc^(2 )(x^(3)-2x^(2))(3x^(2)-4x)

Step-by-step explanation:

The number line that shows that x ≥ -4 is; Option B

We want to find the number line that represents x ≥ -4

Now, for greater than sign, the number line would point to the right while  for less than sign the number line would point to the left.

Now, for greater than or equal to sign the dot would be shaded and as such looking at the correct number line would be that in Option B.

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Answer:

y-intercept: (0,2)

x-intercepts: (-4,0), (2,0)

Step-by-step explanation:

y-intercepts are found where the graph intersects the y-axis

same with x-intercepts, are found where the graph intersects the x-axis

The y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Where the line segment crosses the y-axis is the y-intercept,

And where the line segment crosses the x-axis is the x-intercept,

From the graph,

y-intercept is at (0,2)

x-intercepts is at (-4,0), (2,0)

Thus, the y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.

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Answer:

Step-by-step explanation:

Let the first number be x.

Then, given:

Since their sum is 131, we get the following equation:

or

This is matching the answer choice C.

The larger angle is 55 deg at the larger angle.

We have to know which angles are called Complementary Angles...

if we add two angles and the total will be equal to 90 deg

let's say one angle is x and  another angle is  y

as they are complementary angles from the definition we can write the equation x + y =  90

one angle is 20 deg more  than another one  so from the above condition  we write x = 20 + y

Substitute the value of x  in the first eaquation we get, 20 + y + y =  90

Then,  20 + 2y =  90

subtracting 20 from both sides,

 2y  =  90-20 = 70  

 dividing both sides by 2,

2y/ 2 = 70 / 2

 y  =  35

 So we got one angle is 35 deg

another angle is  35 + 20 = 55 deg.

Our answer is 55 deg the larger angle.

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