Given that a geometric progression has a = -2 and r = -0.5, Determine values for the: (i) fifth term of the GP. [3 marks] (ii) sum of the first 20 terms [4 marks]

Answer:

Your answer would be 2.1.

Step-by-step explanation:

The square root of 3 is:

1.73205080757

Then since 1/3 is equal to 0.33, I added 0.33 to the square root of 3 to get:

2.06205080757

Then, I rounded it:

2.1

Answer: [tex]6/(x-7) +( -5)/(x-5)[/tex]

Step-by-step explanation:

Let

   [tex](x+5)/(x-7)(x-5) = A/(x-7) +B/(x-5)[/tex]

⇒[tex](x+5)/(x-7)(x-5)=( A(x-5) +B(x-7))/(x-7)(x-5)[/tex]

Comparing both the sides

[tex](x+5)= A(x-5)+B(x-7)\\x+5=Ax-5A+Bx-7B\\x+5= (A+B)x + (-5A-7B)\\[/tex]

Comparing both sides of the equation we get,

[tex]A+B= 1[/tex]   ....eq(1)

[tex]-5A-5B=5[/tex]   ..... eq(2)

solving eq(1) and eq(2),

we get B=-5 and A=6.

Hence the solution is [tex]6/(x-7) +( -5)/(x-5)[/tex]

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The dividend is 35286 and the divisor is 7. The value of the division is $540.8571

When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.

On the other hand, the number that is being divided by which is in this case 7 is the dividend.

The division will be:

= $35286 ÷ 7

= $540.8571

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The height of the stack of paper is 3145.73 in.

Since the Notebook paper is about 0.003 in. thick, and you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times.

Since each piece of paper is halved, that means that the number of paper sheets doubles every time.

So, after halving n times, we would have 2 sheets of paper. Since the thickness of the Notebookpaper is 0.003 in, then the height after cuttin half n times is h = 2ⁿ × 0.003 in.

Since the paper is folded 20 times, n = 20.

So, the height h = 2ⁿ × 0.003 in.

h =  2²⁰ × 0.003 in.

h = 1048576  × 0.003 in.

h = 3145.728 in

h ≅ 3145.73 in

So, the height of the stack of paper is 3145.73 in.

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The equation of the line representing the given situation is y = (3/4)x , the graph of the equation is shown below .

In the question ,

it is given that ,

a refreshment stand makes 3 large serving of frozen yogurt from 4 pints .

also given that number of pints is represented by x - axis .

the number of servings is represented by y - axis  .

the equation of the line is represented by y = mx + c .

we get c = 0, because at 0 pint there is no servings

hence , the  equation becomes y [tex]=[/tex] mx .

According to the question ,

3 = m*4

m = 3/4 .

Substituting the value of m in the equation , we get

y = (3/4)x

the graph of the equation is shown below .

Therefore , The equation of the line representing the given situation is y = (3/4)x .

The given question is incomplete , the complete question is

A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write its equation. Let the x-axis represent the number of pints and the y-axis represent the number of servings. Use only fractional form, if necessary.

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The number of square inches of the wrapping paper left over is 380 square inches

From the question, we have the following parameters that can be used in our computation:

Box:

Dimension = 8 inches by 9 inches by 10 inches

Rectangular-shaped wrapping paper

Dimension = 2 feet by 3 feet.

The surface area of the box is

Box = 2(lw + lh + wh)

So, we have

Box = 2 * (8 * 9 + 8 * 10 + 9 * 10)

Evaluate

Box = 484 square inches

The surface area of the wrapping paper is

Wrapper = lw

So, we have

Wrapper = 2 * 3

Evaluate

Wrapper = 6 square feet

Convert to square inches

Wrapper = 864 square inches

The amount of square inches left is

Amount left = Wrapper - Box

Amount left = 864 square inches - 484 square inches

This  gives

Amount left = 380 square inches

Hence, the amount left is 380 square inches

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The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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Equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.

Given points:

(-4, 7), (-3, 9), and (4,-5).

Let parabola equation be y = a[tex]x^{2} +bx+c[/tex].

substitute (-4,7)

7 = a(16)+b(-4)+c

16a-4b+c-7 = 0.

substitute (-3,9)

9 = a(9)+b(-3)+c

9a-3b+c-9 = 0

substitute (4,-5)

-5 = 16a+4b+c

16a+4b+c+5=0.

solving three equations we get,

a = -1/2 , b = -3/2 and c = 9

substitute a,b and c values we get,

y = (-1/2)[tex]x^{2}[/tex] + (-3/2)x + 9

y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.

Therefore the equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.

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Answer:

The answer is C: 20 ÷ f

Step-by-step explanation:

The value of the sets are A ∩ ∅  = ∅ and A' ∪ U  = {f, g, h, p, q, r}.

Given: U = {f, g, h, p, q, r} and A = {g, p, r}

We are to find: (a)A ∩ ∅  and (b) A' ∪ U

(a) A ∩ ∅  

The symbol ∩ means intersection. This tells us what sets have in common. Also, the symbol ∅ means an empty set or null. That is a set that does not have any element

The intersection of a set with the empty set is the null set. Thus:

A ∩ ∅  = ∅

(b) A' ∪ U

The set U is called the universal set

A' means elements not in set A but in set U

The symbol ∪ means union, A' ∪ U will give a list of elements in A' and U combined without repetition. Thus:

A' ∪ U = {f, h, q} ∪  {f, g, h, p, q, r}  = {f, g, h, p, q, r}

Therefore, A ∩ ∅  = ∅ and A' ∪ U  = {f, g, h, p, q, r}. They should be entered into the boxes accordingly

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Answer:

the answer according to my solution is 06

The solution is x > -2 and x > 3

x is greater than -2 and x is greater than 3.

This can be represented by the number line Option D.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

(x + 2) (x - 3)² > 0

This can be written as,

x + 2 > 0 and (x - 3)² > 0

x + 2 > 0

x > -2 _____(1)

(x - 3)² > 0

Squaring both sides.

x - 3 > 0

x > 3 _____(2)

From (1) and (2) we get,

x > -2 and x > 3

Thus,

The solution is x > -2 and x > 3

x is greater than -2 and x is greater than 3.

This can be represented by the number line Option D.

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912

Step-by-step explanation:

[tex](2x-7)^9[/tex]

In this problem we use the following formula:

                              [tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]

a=2x         b=-7        n=9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

..........................................................

The 6th term of (2x-7)^9 is k=5

Hence,

[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]

- 33889212x⁴ is the coefficient of the 6th term in  binomial theorem .

What is binomial theorem?

( 2x - 7 )⁹

compare with formula

a = 2x    b = - 7  n = 9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

...................................................

The 6th term of (2x-7)^9 is k=5

hence

⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵  = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵

                            = 9!/4! * 5! 2⁴x⁴( -7)⁵

                              = 126(16) ( - 16807 )(x)⁴

                              =  - 33889212x⁴

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A few points (co-ordinates) for the given equations are :

(1,-1/2),(-1,1/4),(0,1),,(2,-1/4)

These points are called Coordinates, where the horizontal line denotes the x-axis and the verticle line is the y-axis.

Each point is identified by both x and y coordinates. A point's x-coordinate is a value that indicates how far the point is from the horizontal or x-axis origin.

y denotes the distance of the point on the vertical line from the origin

x denotes the distance of the point on the horizontal line from the origin

In the given equation y=-1/3x-1

We can substitute x with any integer (i.e any number among the positive or negative numbers)

Putting, x=1 in the given equation we get

y=-1/(3x1)-1

⇒ y=-1/3-1

⇒y=-1/2

Thus the coordinate when x=1 is (1,-1/2)

Similarly by putting x=0, 1, 2, -1 ;we get the following co-ordinates respectively

(0,1), (1,-1/2), (2,-1/4),(-1,1/4)

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For the given two sets A and B, the set B is equal to A.

Set:

A set is the collection of well-defined objects or elements. It is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

Given.

Here we have the two sets

A =  {piano, guitar, violin) and

B = (guitar, piano, violin)

Now, we need to find the relation between  B and A.

While we looking into the given sets,

Set A has 3 elements in it and

Set B has 3 elements in it.

So, the size of both sets are equal.

And now we have to looking at the elements in it.

While we checking the elements, instead of the order both have the same elements.

Therefore, the set B is equal to set A.

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The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.

Given:

The total no cupcakes = 52,

The no of sprinkled cupcakes = 39,

Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100

Percentage of sprinkled cupcakes = 39 / 52 × 100

Percentage of sprinkled cupcakes = 75%

Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

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50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies​.

How to solve equations in word problems?

Let x be the number of bags she bought:

50 + 20x ≥ 250

3x ≥ 200

x ≥ 200/3

x ≥ 66.67

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Answer:

row-echelon form

Step-by-step explanation:

Matrixes are commonly used to do Gaussian elimination. By reducing the need to manually specify the parameters at each step, this strategy decreases the work required to obtain the solutions. A system of equations equations is solved using the Gauss elimination method. Let's review the definitions of these equation systems. A set of linear equations with numerous unknown components is defined as a system of linear equations. Unknown factors can be found in various equations, as we all know.

The inequality will be represented by p ≥ 33 for at least 15 points.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Mark must score at least 11 points to have an average of 10 points per game.

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...

 (8+14+10+20+5++p)/6 ≥ 15

 57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify

 p ≥ 33

Mark must score at least 33 points in the next game to average at least 15 points per game.

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Answer:

Scalene

Step-by-step explanation:

a scalene triangle has three sides different angles none of its sides are equal in length

Answer:

A scalene triangle or quadrilateral has no equal sides.

After 35 years, Anthony's account is going to be worth $34193.12

The formula for the compound interest is given as

[tex]A = P(1 + r)^t[/tex]

Where we have the principal = 3000

the rate of interest = 7.2%

The period of time = 35 years

We have to input these values in the formula above so that we would have

A = 3000 ( 1 + 0.072)³⁵

A = 3000 x 11.398

= $34193.12

Hence we would have that after the period of 35 years, the account would be worth $34193.12

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The speed of the aircraft is 682 mph

Given that: A speed of 60 mph is equal to 88 ft/sec

If an aircraft travels at a speed of 1000 ft/sec, the speed to the nearest mile per hour can be calculated by using the unit  ratio of

of mph to ft/s, that is:

60/88 = m/1000

m = 6x1000/ 88 = 60000/88 = 682 mph

Therefore, the speed of the aircraft to the nearest mile per hour is 682 mph

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Answer:

Step-by-step explanation:

The measure of h from the triangle is h = 55

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

And , the measure of ∠ABC = 40°

Now , Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

So , the measure of ∠ACB = ∠BAC = y° = 70°

And , 2h + y° = 180° ( angles on a straight line )

On simplifying , we get

2h + 70° = 180°

Subtracting 70 on both sides , we get

2h = 110

Divide by 2 on both sides , we get

h = 55

Hence , the measure of h = 55

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The complete question is attached below :

(2h)

40°

(2h)

What is the value of h of the triangle?

O h=20

O h=35

O h=55

O h=70

We will need 7 quart package if we want 62 strawberries

What is division?

Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.

We are given that there are 9 strawberries in a quart package

Also we want 62 strawberries

Then how many quart will be required

Now we perform division to find the number of quart

62/9 = we get a value of 8.88

Which is very close to nine

Hence we will need 9 quart packages if we want 62 strawberries

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Answer: x = -135.59

Step-by-step explanation:

20 = 0.694(x + 150)(2)

Step 1: Simplify both sides of the equation.

20 = 0.694 (x + 150)(2)

20 = 1.388x + 208.2 (use the distributive property)

20 = 1.388x + 208.2

Step 2: Flip the equation.

1.388x + 208.2 = 20

Step 3: Subtract 208.2 from both sides of the equation.

1.388x + 208.2 − 208.2 = 20 − 208.2

1.388x = −188.2

Step 4: Divide both sides by 1.388.

1.388x/1.388 = −188.2/1.388

x = −135.590778

Optional: Simplify

x = -135.59

Answer:

4(67 + 22)

Step-by-step explanation:

1. Find the greatest common factor(in this case it is 4)

2. Divide both 268 and 88 by 4 and you get 67 and 22

3. Put it in the requested format and you are left with 4(67 +22)

If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

What do you mean by traversal line?

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

What do you mean by angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

From the figure,

x + 1 = 180°

y + 2 = 180°

Adding above equations,

x + y + 1 + 2 = 360°

Given ,

x + y = 1 +2

x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Angles made on same side of transversal is supplementary . So the lines are parallel.

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