Find the sum of the first 6 terms of the following sequence. Round to the
nearest hundredth if necessary,
12,
4,
4
3
Sum of a finite geometric series:
Sn
-
1-r

Answer:

z = 4 , y = 6 , 4 and 13

Step-by-step explanation:

1

8z - 15 = 17 ( add 15 to both sides )

8z = 32 ( divide both sides by 8 )

z = 4

2

22 = 4y - 2 ( add 2 to both sides )

24 = 4y ( divide both sides by 4 )

6 = y

3

3(- 7) + 25 = - 21 + 25 = 4

4

16 - 6 ÷ 2 ← perform division before subtraction

= 16 - 3

= 13

For the middle par, using the answers associated to the colours

13 + (6 ÷ 4) - 4

= 13 + 1.5 - 4

= 14.5 - 5

= 10.5

Answer: 9 and 2/3

Step-by-step explanation:

Step-by-step explanation:

This is a composit figure of a 20 x 30 m rectangle and a circle of radius 10m

area of rectangle + area of circle = total area

     l x w                +     pi r^2           = total

       20 x 30         + pi (10^2)   = 914.2 m^2

The graph of the given inequalities is Attached below.

From the given inequalities:

As the first inequality is not strictly true, the graph of it is a straight solid line that passes through the points (0, 2) and (2/3, 0), with the shaded area being further from the origin ( as it fails the zero point test )

As the second inequality is not stringent, the graph of the inequality is a straight solid line that passes through the points (0,-4) and (8,0), with the shaded area pointing in the direction of the origin (since the inequality passes the zero point test)

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Complete question:

Which graph represents the system of inequalities?

y + 3x ≥ 2

y + 4 ≥ 1/2x

Answer:  x=3   <W=27

Step-by-step explanation:

<Y is half of the arc XW

<Y=78/2 =39

The sum of all the angles in a triangle is 180

so add all angles ang make =180

114+39+7x+6=180          Simplify

159+7x=180                   Subtract 159 from both sides

7x=21                              Divide 7 to both sides

x=3

plug back in x to find <W

<W=7(3)+6

=21+6

27

Tatiana is the athlete who trains a weekly amount of kilometers equal to the median of the 11 competitors.

To find the median, we need to first arrange the values in order from lowest to highest:

4, 5, 5, 5, 5.5, 6, 7, 8, 8, 9, 10

Since there are 11 values, the median is the middle value. In this case, the middle value is 5.5. Therefore, the athlete who trains a weekly amount of kilometers equal to the median of the 11 competitors is Tatiana, who trains 5.5 kilometers per week.

None of the other athletes in the table trains exactly 5.5 kilometers per week, so Tatiana is the only correct answer.

It's worth noting that the median is a measure of central tendency that is less sensitive to outliers than the mean. In this case, the values range from 4 to 10, which is a relatively wide range, but the median still provides a useful measure of the typical training distance among the 11 athletes.

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a. The definite integral ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx = πr²/2

A definite integral is an integral evaluated on an interval.

Given the figure, to evaluate the definite integral ∫₀²f(x)dx and ∫₂⁴f(x)dx, we proceed as follows.

a.  The definite integral ∫₀²f(x)dx

Observe the graph, the integral ∫₀²f(x)dx is the area occupied by the square on the interval (0, 2).

So,  ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx

Observe the graph, the integral ∫₂⁴f(x)dx is the area occupied by the circle on the interval (2, 4).

So,  ∫₂⁴f(x)dx = πr²/2

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The value of x is given as follows:

x = 2.5 cm.

Similar triangles are triangles that share these two features listed as follows:

The logic for similar triangles can be expanded for any similar polygons, as is the case for this problem.

The proportional relationship for the side lengths is given as follows:

x/5 = 4/8

Applying cross multiplication, the value of x is obtained as follows:

8x = 20

x = 2.5 cm.

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The correct option regarding the simplification of the expression is given as follows:

B. [tex]12\sqrt{2} + 4\sqrt{3}[/tex]

The expression in the context of this problem is defined as follows:

[tex]4\sqrt{18} - 2\sqrt{27} + 5\sqrt{12}[/tex]

To simplify the expressions, first we must obtain the simplest radical form of each expression, as follows:

Hence the simplified expression is obtained as follows:

[tex]4(3\sqrt{2}) - 2(3\sqrt{3}) + 5(2\sqrt{3}) = 12\sqrt{2} - 6\sqrt{3} + 10\sqrt{3} = 12\sqrt{2} + 4\sqrt{3}[/tex]

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The surface area of the figure in this problem is given as follows:

S = 48m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The figure in this problem is composed as follows:

Hence the surface area of the figure is given as follows:

S = 2 x (2 x 2 + 2 x 4 + 2 x 4) + 4 x 1/2 x 2 x 2

S = 48m².

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The value of x rounded to 1 decimal place is 15.9 cm.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

First of all, we would determine length of sides or side lengths of the opposite side of the ight-angled triangle as follows;

12.5² + y² = 19.5²

156.25 + y² = 380.25

y² = 224 cm.

y = √224 cm

Now, we can determine value of x;

x² = (√224)² + (5.5)²

x² = 224 + 30.25

x = 15.9 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

By simplification we get: [tex]2^4p^8q^1^2[/tex]

Simplify  the expression:

=> [tex](2p^2 q^3)^4[/tex]

We use the property for simplification i.e.,:

[tex](a^m)^n=a^m^n[/tex]

So, We solve by using above property:

[tex]p^2[/tex] raised to the 4 th power = [tex](p^2^.^4) =p^8[/tex]

[tex]q^3[/tex] raised to the 4 th power = [tex](q^3^.^4)=q^1^2[/tex]

Complete simplification, we get:

[tex](2p^2 q^3)^4=[/tex] [tex]2^4p^8q^1^2[/tex]

Hence, By simplification we get: [tex]2^4p^8q^1^2[/tex]

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Answer:

x=28

x=-28

Step-by-step explanation:

Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

Using the net, the correct surface area of the prism is 216 square units

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

The triangular prism

Using the net, the surface area is

Surface area = Sum of areas of individual shapes

So, we have

Surface area = 2 * 1/2 * 3 * 4 + 17 * 5 + 17 * 4 + 17 * 3

Evaluate

Surface area = 216

Hence, the surface area of the prism is 216 square units

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An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

We know that,

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

a_n = a_1 + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.

When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.

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complete question:

what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other​

The total interest paid is $58.52.

We are given that;

P = 800

r = 0.015

n = 18

Now,

We can plug in the values given in question:

EMI = 800 x 0.015 x (1+0.015) ^ 18 / { (1+0.015) ^ 18-1}

EMI = 47.64

This means that your monthly payments are $47.64.

To find the total interest paid, we can multiply the EMI by the number of months and subtract the loan amount12:

Total interest paid = EMI x n - P

Total interest paid = 47.64 x 18 - 800

Total interest paid = 58.52

Therefore, by the given interest the answer will be $58.52.

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The inverse function of f(x) = (x - 3)²- 4 is f-1(x) = 3 + √(x + 4)

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

f(x) = (x - 3)²- 4

Rewrite as

y = (x - 3)²- 4

Swap x and y

So, we have

x = (y - 3)²- 4

This gives

(y - 3)² = x +  4

Take teh square roots of both sides

y - 3 = √(x + 4)

So, we have

y = 3 + √(x + 4)

So, the inverse function is f-1(x) = 3 + √(x + 4)

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The value of x in the triangle is 7 units.

The triangle has three sides. Let's find the value of x in the triangle as follows:

x + 12  - 15 = 4

Therefore,

x  - 3 = 4

add 3 to both sides of the equation

x  - 3 = 4

x  - 3 + 3 = 4 + 3

x = 7 units

Therefore, the value of x in the triangle is 7 units.

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Answer:10

Step-by-step explanation:

Answer:

Set your calculator to degree mode.

[tex] x = {cos}^{ - 1} \frac{5}{7} = 44.4[/tex]

Angle x measures 44.4 degrees.

It is fair to assume that the spinner will land on an odd number 160 times.

The likelihood of landing on any one of the eight congruent portions of the spinner is 1/8. This information allows us to reasonably forecast the frequency with which the spinner will fall on an odd number.

The likelihood of landing on an odd number is 4/8 or 1/2 since the spinner has four odd numbers (1, 3, 5, and 7) and four even numbers (2, 4, 6, and 8). Thus, we may anticipate that the spinner will land on an odd number on average 50% of the time.

If the spinner is spun 320 times, we would expect it to land on an odd number about half of those times, or approximately:

(1/2) x 320 = 160

Therefore, the probability that the spinner will fall on an odd number 160 times is fair.

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A reasonable prediction for the number of times the spinner will land on an odd number is 160.

We have,

Since the spinner has eight congruent sections, each odd number (1, 3, 5, and 7) appears once on the spinner, and there are a total of four odd numbers.

Since the spinner is spun 320 times, we can expect each section of the spinner to be landed on equally, on average.

Therefore, the expected number of times the spinner will land on any one section is 320/8 = 40.

Since each odd number appears once on the spinner, we can expect the spinner to land on an odd number 4 times in every 8 spins, or once in every 2 spins.

Therefore, the expected number of times the spinner will land on an odd number in 320 spins is approximately 320/2 = 160.

Thus,

A reasonable prediction for the number of times the spinner will land on an odd number is 160.

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Answer:

20

Step-by-step explanation:

2L + 2W = P :))

The fraction can be represented as follows:

[tex]\frac{6^8}{6^8} = 6^0[/tex]

Remember the rule for exponents:

[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]

So we just need to subtract the exponents

Here we have the following quotient:

[tex]\frac{6^8}{6^8}[/tex]

Using the rule above, we can rewrite that fraction as follows:

[tex]\frac{6^8}{6^8} = 6^{8 - 8} = 6^0[/tex]

So the exponent at the end is zero, this means that the correct option is B.

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The area of the decagon with side length 10 is 769.42 square units

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

side length, l = 10

The area of the decagon is calculated as

Area = 5/2l² * √[5 + 2√5]

Where

l = 10

Substitute the known values in the above equation, so, we have the following representation

Area = 5/2 * 10² * √[5 + 2√5]

Evaluate

Area = 769.42

Hence, the area is 769.42

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Answer:

  (a) ∠7 = 47°. Angles 5 and 7 are vertical angles, hence congruent.

  (b) 47 +(2x -5) = 180

  (c) 69

Step-by-step explanation:

Given angles identified as ∠5, ∠6, ∠7 where two lines cross, and the measure of ∠5 as 47°, you want the measure of ∠7, and an equation and solution when ∠6 is (2x-5).

Angles that share a vertex and are formed from opposite rays are "vertical angles." They are congruent.

Angles 5 and 7 are vertical angles, so the measure of angle 7 is the same as the measure of angle 5.

  ∠7 = 47°

Angles that form a linear pair are supplementary. This means the sum of angles 5 and 6 is 180°.

  ∠5 +∠6 = 180°

  47° +(2x -5)° = 180°

  2x = 138 . . . . . . . . . . . . divide by °, subtract 42

  x = 69

Answer: Answer

Step-by-step-explanation: 4:2 plays a sport 13:9 does not

The real answer is 29.8x14.2= 410.38m, so it differs by 4.38m squared

The measures the angle 3 is given by 45°.

Hence the correct option is (B).

The quadrilateral which has four equal sides and the adjacent sides of which are in perpendicular that is called Square.

The given figure is a Square.

We know that the angle between two adjacent sides = 90°.

We also know that the diagonal of square divides angles into two equal parts of angles.

So here angle 3 is a one equal part of angle between two adjacent sides of  square.

So angle 3 is given by = (1/2)*90° = 45°.

Hence the correct option will be (B).

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The standard form of the equation of the hyperbola is

[(y + 6)²/4] - [(x - 3)²/16] = 1.08

We have,

To find the standard form of the equation of a hyperbola, we need to know the locations of the vertices and the foci.

In this case, we are given the coordinates of the vertices, but we need to find the foci. However, we are also given that the hyperbola passes through the point (7, −12), which will allow us to find the foci.

First, let's find the center of the hyperbola.

Since the vertices have the same x-coordinate of 3, the center must be the point (3, −6), which is the midpoint of the two vertices.

Next, we can find the distance between the center and one of the vertices. Using the distance formula, we get:

d = √[(3 - 3)² + (-8 - (-6))²] = 2

Since the vertices are vertically aligned, we know that the distance from the center to each vertex is the same.

Therefore, the distance from the center to each vertex is also 2.

We can now use the Pythagorean theorem to find the distance from the center to each focus, which we will call c.

We know that c² = a² + b², where a is half the distance between the vertices (in this case, a = 2), and b is half the distance between the foci.

We want to solve for b.

Since the hyperbola passes through the point (7, −12), we know that the distance from this point to each focus is constant and equal to the distance from this point to the center of the hyperbola.

Using the distance formula, we can set up the following equation:

√[(7 - 3)² + (-12 - (-6))²] = sqrt[(7 - 3)^²+ (-12 - (-8))²] + b

Simplifying this equation, we get:

2 √(37) = 2 √(20) + b

b = √(37) - √(20)

Now that we have the values of a and b, we can write the standard form of the equation of the hyperbola:

[(y + 6)²/4] - [(x - 3)²/16] = 1 + [(√(37) - √(20))²/16]

Simplifying, we get:

[(y + 6)²/4] - [(x - 3)²/16] = 1.08

Therefore,

The standard form of the equation of the hyperbola is

[(y + 6)²/4] - [(x - 3)²/16] = 1.08

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