Find the first four terms of the sequence given by the following. an= 4(2)^n-1 n=1, 2, 3...

Answer:

Answer is in the 2nd attachment

Step-by-step explanation:

the first attachment is the work done.

The simplification that represents ∛7=[tex]7^{1/3}[/tex] is [tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]

The simplification that accurately explains the statement ∛7 = [tex]7^{1/3}[/tex] is as follows;

Therefore, the simplification is as follows

[tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]

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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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Answer:

If compounding = rs 11547.36

If not compounding = rs 11484

The length of AL in the triangle is 12cm.

From the information given, angle C = 90° and BAC is given as 2ABC.

In this case, the length of angle BC is given as 24cm. Therefore, the length of AL will be:

= 24/2

= 12..

Therefore, AL = 12cm

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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

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:

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)

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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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 area of the composite shape is 136 square cm

The area of the composite function is expressed as;

Area = area of triangle + area of rectangle

Area of the composite shape = (1/2* 4 * 5) + (7*18)

Area of the composite shape = 10 + 126

Area of the composite shape = 136 square cm

Hence the area of the composite shape is 136 square cm

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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:

[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!

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.

If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.

In accordance with the statement, Susan's calculator performs the following operation by pressing the "cubing" key:

x → x³

If we need to display a number that is greater than 10⁹, then we need to press the "cubing" key as many as needed. By algebra we have the following property for a power:

[tex](x^{m})^{n} = x^{m\cdot n}[/tex]     (1)

Since we have a "cubing" key and we are supposed to make consecutive operation, we derive the following operation:

x → [tex]x^{3^{i}}[/tex], where i is the number of consecutive "cubing" operations.

If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.

The statement presents typing mistakes, correct form is shown below:

Susan's calculator has a key that replaces the number displayed with its cube. If a³, is displayed, how many time must Susan press the "cubing" key to display a number that is greater than 10⁹.

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For the function f(x) = -3|x - 2| - 1, we have that:

The x-intercept of a function is the value of x when y = f(x) = 0, hence:

0 = -3|x - 2| - 1

-3|x - 2| = 1

|x - 2| = -1/3

The absolute value cannot be negative, hence the function has no x-intercepts.

The x-intercept of a function is the value of y = f(x) when x = 0, hence:

f(0) = -3|0 - 2| - 1 = -6 - 1 = -7.

The y-intercept is of y = -7.

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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:

Answer:

ab=48

Step-by-step explanation:

96/2=48

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

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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The interval on the number line is (-∞, 2) U [3, ∞)

From the number line, we have the following inequalities

x < 2 and x ≥ 3

In inequalities, < and > are represented by brackets i.e. ( and )

While ≤ and ≥ are represented by square brackets i.e. [ and ]

So, we have:

x < 2 and x ≥ 3 = 2) and [3

The intervals must be closed and opened with infinity symbols.

So, we have:

x < 2 and x ≥ 3 = (-∞, 2) and [3, ∞)

Replace and with U

x < 2 and x ≥ 3 = (-∞, 2) U [3, ∞)

Hence, the interval on the number line is (-∞, 2) U [3, ∞)

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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 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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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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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:

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

[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:

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

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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