2. aₙ-1=aₙ-1 ÷ 2 where a₁=50 for n≥2

Answer:

Number 2

Step-by-step explanation:

Step-by-step explanation:

Solve the inequality for x.

10x > 9(2x - 5) - 11

10x > 18x - 45 - 11

10x > 18x - 56

subtract 18x from both sides:

10x - 18x > 18x - 56 - 18x

-8x > - 56

divide both sides by -8 and remember to flip the sign:

-8x/-8 < - 56/-8

x < 7

This means that x can be any number below 7.

In set builder notation: (-∞ , 7).

Answer:

------------------------------

Given is a quadratic equation:

A quadratic equation has no real solutions if its discriminant is negative.

The discriminant of ax² + bx + c is:

Apply to given equation:

Find the value of n when D < 0:

y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3, 19)

What is a gradient?

A straight line's steepness can be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative. A line's gradient can either be uphill (positive value) or downward (negative value).

Here, we have

Equation of line

y = mx  + c

m = Slope of line = Gradient  = 6

= y = 6x + c

a line passes through (3, 19)

so, we find the value of c

= 19 = 6(3)  + c

= c = 1

Now, we put the value of c in the equation and we get

= y = 6x  + 1

Hence,y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3  19)

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Answer:

simplify 8/6, and you get 4/3.

This is a coincidence, because this is a Pythagorean triple,

which means: opp = 4, adj = 3, hyp = 5

now, we can solve the rest easily

sin(0) = 4/5

cos(0) = 3/5

sec = 5/3 (opposite of cos)

Answer:

f(x)

Step-by-step explanation:

the function g(x) has y-interception in point (0;0), the function f(x) has y-interception in point (0; 1/3). For more details see the attachment.

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

What is a transformation of a shape?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

If the geometry is rotated, then there is no change in angles.

The translation does not change the shape and size of the geometry. But changes the location.

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

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Disclaimer

The question given by you is incomplete, so a similar question have been solved here and the image is attached.

Determine a series of transformations that would map Figure M onto Figure N.

Answer:

A.  56

Step-by-step explanation:

Let the three consecutive integers be:

Given:

Create an equation with the given information and solve for x:

[tex]\implies x+(x+1)+(x+2)=2x+30[/tex]

[tex]\implies 3x+3=2x+30[/tex]

[tex]\implies 3x+3-2x=2x+30-2x[/tex]

[tex]\implies x+3=30[/tex]

[tex]\implies x+3-3=30-3[/tex]

[tex]\implies x=27[/tex]

Therefore, the three consecutive integers are:

So the sum of the first and last integer is:

[tex]\implies 27+29=56[/tex]

Answer:

a) 56 --- (27, 28, 29)

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) + (x + 2) = 2x + 30

Now the value of x will be,

→ x + (x + 1) + (x + 2) = 2x + 30

→ x + x + 1 + x + 2 = 2x + 30

→ 3x - 2x = 30 - 3

→ [ x = 27 ]

The last integer will be,

→ x + 2

→ 27 + 2 = 29

Sum of first and last integer is,

→ x + (x + 2)

→ 27 + (27 + 2)

→ 27 + 29 = 56

Hence, required answer is 56.

x + 2 = 10

x + 2 - 2 = 10 - 2

x = 8

x - 2 = 10

x - 2 + 2 = 10 + 2

x = 12

2x = 10

2x/2 = 10/2

x = 5

x/2 = 10

x/2 × 2 = 10 × 2

x = 20

The student who can write more words per minute is Marcus because he writes at a speed of 1.3 words per second, that is, in one minute he writes 79.8 words while Rhys writes at a speed of 1.1 words per second and in one minute he writes 66.66 words.

To identify the speed at which students write we must divide the number of words the student writes in time (seconds) as shown below.

Marcus

Rhys

Using the information above, we need to multiply the number of words each student types per second by the number of seconds that equals one minute.

Rhys

Marcus

According to the information above, Marcus has a faster typing speed than Rhys because he types 79.8 words in one minute, while Rhys types 66.6 words in the same time.

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Answer:

y= -x+1

Step-by-step explanation:

The slope of a line that is perpendicular to a graph is equal to the negative reciprocal of the graph's slope.

slope = 1  negative reciprocal = - (1/1) = -1

Now, you have to find the y-intercept by using the given points (3,-2) and the slope that was found (-x)

y= -x+b

-2=-3+b

1=b

y= -x+1

Answer: 105 words

Step-by-step explanation:

15x7=105

The given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).

The given trigonometric expression is 1-tan(a).

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

We know that, tanθ=sinθ/cosθ

Now, 1-tan(a) =1-sin(a)/cos(a)

= (cos(a)-sin(a))/cos(a)

Therefore, the given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).

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Answer:

A) [tex]\frac{484}{7}[/tex]cm

B)[tex]44[/tex]in

C)[tex]\frac{880}{7}[/tex]mi

D)[tex]\frac{660}{7}[/tex]yd

Step-by-step explanation:

The formula for the circumference of a circle is:

[tex]C=2\pi r[/tex]

Within the problem it is stated to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex] so our equation will be:

[tex]C=2\frac{22}{7}r[/tex] which simplifies to  [tex]C=\frac{44r}{7}[/tex]

The variable [tex]r[/tex] in the equation for the circumference represents 'radius' which is half the diameter, for circle's A and C we are given a diameter. We can divide these numbers in half to get a radius. From there we plug in each radius to get circumference of each circle!

A)

[tex]\text{Diameter}=22\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{22}{2}=11\\\text{Circumference}=\frac{44(11)}{7}=\frac{484}{7}[/tex]

B)

[tex]\text{Radius {\it (r)}}=7\\\text{Circumference}=\frac{44(7)}{7}=\frac{308}{7}=44[/tex]

C)

[tex]\text{Diameter}=40\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{40}{2}=20\\\text{Circumference}=\frac{44(20)}{7}=\frac{880}{7}[/tex]

D)

[tex]\text{Radius {\it (r)}}=15\\\text{Circumference}=\frac{44(15)}{7}=\frac{660}{7}[/tex]

Remember to include units of measurement in your answers.

The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8) thus option (A),(B) and (D) are correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

3x - y = 1

Substitute, x = -2

3(-2) - y = 1

y = -7 thus  (-2,-7) satisfied.

Similarly (-1,-4) and (3,8) are also satisfied.

Hence "The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8)".

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The Vertical opposite angles are ∠1 = 141° ; ∠2 = 39° ; ∠3 = 141° ; ∠4 =39°

The given angle cover the whole circle which will have 360°

∠1 + ∠2 +∠3 + ∠4 = 360°

∠1 + 39° +∠3 + ∠4 = 360°

Vertically Opposite angle:

Hence, ∠1  = ∠3 and ∠2 = ∠4. So  ∠4 = 39°

∠1 + 39° +∠3 + 39° = 360°

Let x be the ∠1 and ∠3;

x + 39° +x + 39° = 360°

2x = 360° - 78°

2x = 282°

x = 141°

Now, we know all the angles with respect to Vertical opposite Angles  .

∠1 = 141°

∠2 = 39°

∠3 = 141°

∠4 =39°

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Answer:

Step-by-step explanation:

You need a take a picture so I know what question your talking about

The given term of the arithmetic sequence is -18. The correct option is (A).

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

The given arithmetic sequence is as below,

27, 22, 17, 12, 7, 2,...

Since the nth term of an arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

Where d is the common difference.

The common difference for the given sequence is,

d = 22 - 27

  = -5

Substitute d = -5 and n = 10 in the general form of nth term to obtain,

a₁₀ = a₁ + (n - 1)d

     = 27 + -5(10 - 1)

     = 27 - 45

     = -18

Hence, the value of the 10th term of the given sequence is -18.

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The exponential function f(x)=(1/8)^-x can be evaluated to give us:

An exponential function  serves as Mathematical function in the form f (x) = ax hving “x” as  variable,the conceptis the concept of  exponential function.

The given function is f(x)=(1/8)^-x

Then f(2)=(1/8)^-2 = 1/(1/8)^2 =1/(1/64) =64

f(-3)=(1/8)^-(-3) = 1/512

f(-3)=(1/8)^-(1/2) =[tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]

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The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. The ratio of the angles in the triangle is 1:2:3.

When two rays are joined at one point, they produce the geometric shape known as an angle. The vertex is the shared point between the two rays, which are known as the arms or sides of the angle. When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolised by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.

Given,

A first angle of let x

2x = 2nd angle

3x = 3rd angle

Angle sum = 180

x + 2x + 3x = 180

6x = 180

Dividing,

x = 30°

2x = 2(30)

2nd angle = 60

3x = 3(30)

3rd angle = 90

30°, 60°, and 90° are the three angles.

Ratio 1:2:3

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Answer:

-33

Step-by-step explanation:

just fill in the values

3-6^2

3-36

-33

Hopes this helps please mark brainliest

Answer:

-33

Step-by-step explanation:

a = 3; b = -6

a - b² = 3 - (-6)² = 3 - 36 = -33

El polígono regular tiene las características de un pentágono, cuya medida de ángulo central es 72° y la suma de todos los ángulos centrales es igual a 360°.

En este problema debemos determinar que polígono regular tiene un ángulo central con medida de 72°, la suma de todos los ángulos centrales de un polígono es igual a 360°. El número de lados del polígono se puede determinar mediante la siguiente operación:

n = 360° / θ

Donde θ es la medida del ángulo central, en grados.

Si sabemos que θ = 72°, entonces el número de lados del polígono:

n = 360° / 72°

n = 5

El polígono regular es un pentágono.

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Answer:

7650 rupees

Step-by-step explanation:

Use I = Pnr

Here P = Principal = 20000 rupees

n = time = 4.5 years

r = rate of interest = 8.5% = 8.5/100

The cosine and sine functions are presented as follows;

(a) cosine function is; f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) f(x) = -5·sin((4/3)·x - 530/3) + 2.5

A sine function is a periodic function used bases on the sine of an angle.

(a) The cosine function is f(x) = a·cos(b·x - c) + k

Where;

a = The amplitude

The amplitude = (Max - Min)/2

Therefore;

a = (7.5 - (-2.5))/2 = 5

f = b/(2·π)

c = The phase shift

k = The vertical shift

The minimum is at x = 200° = (200/360)·(2·π) = 10·π/9

The period = 270° = 3·π/2

Frequency, f = 2/(3·π)

b = 2·π·f = 2·π×2/(3·π) = 4/3

When the function is at the minimum point, θ = π

Therefore;

(4/3)×(10·π)/9 - c = π

c = 13·π/27

k = The minimum value + a

Therefore, k = -2.5 + 5 = 2.5

The cosine function is therefore;

f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) The negative sine function is found as follows;

f(x) = a·sin(b·x - c) + k

b = 4/3

k = 2.5

Minimum point sin((4/3)200 - c) = 180

((4/3)200 - c) = 180

c = 260/3

Using a negative sign function, we get;

((4/3)200 - c) = 90

c = 530/3

The equation is therefore;

f(x) = -5·sin((4/3)·x -530/3) + 2.5

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Answer:

55 Hot dogs were sold

Step-by-step explanation:

Let d = hot dogs

Let h = hamburgers

d + h = 175

d + 1.50h = 235

Re-write

d + h = 175 for d and then substitute this into the second equation

d = 175 - h

d + 1.5 h = 235

175 - h + 1.50h = 235  Combine like terms

175 + .5h = 235  Subtract 175 from both sides

.5 h = 60  Divide both sides by .5

h = 120

120 Hamburgers were sold.  

Plug in 120 for h to solve for hot does

d + h = 175

d + 120 = 175  Subtract 120 from both sides

d = 55

Check

d + 1.5h = 235

55 + 1.5(120) = 235

55 + 180 = 235

235=235

The length of the rectangular garage will be 13 while the width will be 10.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

The perimeter of the rectangle = 2( length + width).

It is known that,

Area of rectangle = length × width.

130 = L× W

L = 130/W

The perimeter of the rectangle = 2( length + width).

46= 2( L+ W)

L + W = 23

130/W + W = 23

130 + W² = 23W

W² - 23W + 130 = 0

W² -13W - 10W + 130 = 0

W(W - 13) -10(W - 13) = 0

(W - 13)(W - 10) = 0

W = 13,10

For W = 13

L = 23 - 13 = 10

For W = 10

L = 23 - 10 = 13

Let's say the bigger dimension is the length and the smaller is the width.

Length = 13 and Width = 10

Hence "The length of the rectangular garage will be 13 while the width will be 10".

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not defined because 848 has no unit

Using the definition of isosceles and equilateral triangles:

12. x = 77°; y = 58°; z = 122°

13. x = 60°; y = 120°; z = 60°

All three sides and angles of an equilateral triangle are equal in measure. On the other hand, two sides and two base angles of an isosceles triangle are equal to each other.

12. x = 1/2(180 - 26) [based on the definition of isosceles triangle]

x = 1/2(154)

x = 77°

y = 1/2(180 - (90 - 26)) [based on the definition of isosceles triangle]

y = 1/2(180 - 64)

y = 1/2(116)

y = 58°

z = 180 - 58 [base angles of isosceles triangle are equal]

z = 122°

13. Each interior angle of an equilateral triangle is equal to 60 degrees.

Therefore, x = the measure of one interior angle

x = 60°

y = 180 - 60 [linear pair]

y = 120°

The base angles of the triangle that has two equal sides would be 60° [180 - 120]

Therefore:

z = 180 - 2(60)

z = 60°

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The measure of angle VUT is ∠VUT = 70°.

What are angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

In the given figure, ∠RVU and ∠UVT are in linear pair, so by using the property of angles in a linear pair, we can write

                ∠RVU + ∠UVT = 180°

                  120° + ∠UVT = 180°

                         ∠UVT = 60°

Now as we know the sum of all angles of a triangle is equal to 180°,

               ∠UVT + ∠VTU + ∠VUT = 180°.

                   60° + 50° + ∠VUT =180°

                       110° + ∠VUT = 180°

                        ∠VUT = 180° - 110°

                        ∠VUT = 70°

Hence, the measure of angle VUT is ∠VUT = 70°.

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The cos, tan, sec, csc and cot of the angle θ in quadrant IV are 3/5, -4/3, 5/3, -5/4 and -3/4 respectively

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Given that: sin(θ) = -4/5 and θ is in quadrant 4.

Using this information, we can sketch the location of the angle θ in the quadrant (See the attached image). Therefore:

(a) cos(θ) = 3/5     (adj/hyp)

(b) tan(θ) = -4/3     (opp/adj)

(c) sec(θ) = 1/cos(θ) = 5/3

(d) csc(θ) = 1/sin(θ) = -5/4

(e) cot(θ) = 1/tan(θ) = -3/4

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