8
(b) Then determine whether the above relation is a function.
A) Function
B Not a function

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

1

3

gives the next term. In other words,

a

n

=

a

1

r

n

−

1

.

Geometric Sequence:

r

=

1

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of

a

1

=

486

and

r

=

1

3

.

a

n

=

486

(

1

3

)

n

−

1

Apply the product rule to

1

3

.

a

n

=

486

1

n

−

1

3

n

−

1

One to any power is one.

a

n

=

486

1

3

n

−

1

Combine

486

and

1

3

n

−

1

.

a

n

=

486

3

n

−

1

Substitute in the value of

n

to find the

n

th term.

a

5

=

486

3

(

5

)

−

1

Simplify the denominator.

Tap for more steps...

a

5

=

486

81

Divide

486

by

81

.

a

5

=

6

y-intercept= 0

asymptote =[tex]lim_{n}[/tex]→-0 (8/x) = -∞

[tex]lim_{n}[/tex]→+0 (8/x) = +∞

range = R : { x ∈ R / {0} }

What is Range ?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

I think the formula is:

f(x) = 8/x

(You wrote 8x; since a linear function has no asymptotes and you wrote 8x, I'm assuming the true function was 8/x.)

The amount that makes f(x) equal to 0 is the y-intercept.

Keep in mind that there is no value of x such that 8/x = 0 (because the quotient cannot be zero if the numerator is never zero).

Therefore, there is no y-intercept.

The asymmetry:

These are the four:

If the negative side of x tends to zero, then 8/x tends to negative infinity.

If x from the positive side approaches to zero, then 8/x tends to positive infinity.

These two asymptotes are expressed as follows:

[tex]lim_{n}[/tex]→-0 (8/x) = -∞

[tex]lim_{n}[/tex]→+0 (8/x) = +∞

Additionally, there are two cases where x tends to plus infinity (and 8/x goes to zero) and when x tends to minus infinity, where the function tends to zero once more. These two cases are denoted by the formulas:

[tex]lim_{n}[/tex]→-∞ (8/x) = -∞

[tex]lim_{n}[/tex]→∞ (8/x) = +∞

Lastly, the scope:

Only on limitations, y never reaches the following value:

y = 0

If so, the set of all real numbers excluding zero is the range, or

R : { x ∈ R / {0} }

Hence, y-intercept= 0

asymptote =[tex]lim_{n}[/tex]→-0 (8/x) = -∞

[tex]lim_{n}[/tex]→+0 (8/x) = +∞

range = R : { x ∈ R / {0} }

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6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given three vertices are D(1, 1), E(3, −1), and F(4, 4)

we need to find the area of triangle

Area of triangle=1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

x₁=1, x₂=3, x₃=4, y₁=1, y₂=-1, y₃=4

put in the formula

Area of triangle=1/2|1(-1-4)+3(4-1)+4(1-(-1))|

=1/2|-5+9+8)|

=1/2 |12|

=6 square units.

Hence 6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)

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Total surface area = 620

Moreover, The total area covered by an isosceles triangle is called its area. For an isosceles triangle, the area is easily calculated if the height and base are known. Multiplying the height by the base and dividing it by 2 gives us the area of ​​an isosceles triangle.

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The equation of the parabola in intercept form exists

y = -2/7(x + 14)(x + 2).

The intercept form exists y = a(x - r)(x - s), where r and s exists the x-intercepts on the graph. The intercept form will tell us if there exists two x-intercepts, one x-intercept, or no x-intercepts.

Let x-intercepts of -14 and -2; passes through (-16, -8)

The equation of the parabola in intercept form y = a(x - r)(x - s)

substitute the values in the above equation, and we get

-8 = a(-16 + 14)(-16 + 2)

simplifying the above equation, we get

-8 = a(-2)(-14)

-8 = 28a  

a = -2/7

y =-2/7(x + 14)(x + 2)

Therefore, the equation of the parabola in intercept form exists

y = -2/7(x + 14)(x + 2).

The complete question is:

Write an equation of the parabola in intercept form X-intercepts of -14 and -2; passes through (-16, -8)

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Step-by-step explanation:

79 degrees plus X would make 180 degrees, because these two angles make up a straight angle.

So, 79 + X = 180

    -79          -79

         X=101 degrees.

Y is 79 degrees because it is an alternate interior angle to the other 79 degree angle.

Z is 101 degrees because X and Z are corresponding angles, which means they are equal.

If Z is 101 degrees, Y must be 79 degrees because Y and X make up a straight angle.

Answer:

X is 101 degrees. Y is 79 degrees. Z is 101 degrees.

Hope this helped! :)

A) The ingredient she needed = Fruit juice  = 21 litres

                                                      Lemonade = 14 litres

B) The extra punch she can make = 20litres

C) The ratio of fruit juice and lemonade for second batch = 7:6

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

A)

Let 3x be fruit juice and 2x be the lemonade

3x + 2x = 35litres

5x = 35

x = 35/5

x = 7

Then, required ingredient she needed

Fruit juice = 3x7 = 21 litres

Lemonade = 2x7 = 14 litres

B)

According to question

The amount of fruit juice she had = 12litre

Let x be 12litre

as we know that the ratio of fruit juice to the lemonade is 3 : 2

Thus,

Fruit juice = 3(x) = 12 litres

                    x = 12/3

                    x = 4

Fruit juice = 3 x 4 = 12litres

putting the value in lemonade

Lemonade = 2(4) = 8 litres

So, The extra punch she can make :

12 + 8 = 20litres

C)

The ratio for new second batch she added 4litres in lemonade

Then it become :

Fruit juice = 21 litres

Lemonade = 14 litres + 4litres = 18

The ratio will be

21:18

7:6

Thus, the ratio of fruit juice to lemonade in second batch will be 7:6

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Answer:

B) 50

Step-by-step explanation:

its in tens place

hope this helps you!!!

Answer:

8500/10=850

value of digit 5=50

The probability that out of 5 pencils taken, 2 are blue and 3 are black is 0.4381.

Probability simply means the likelihood that something will occur or happen.

In this case, the the box contains 8 blue and 4 black pencils. The probability of drawing 2 blue balls will be:

= 8/12 × 7/11

= 0.4242

The probability of drawing 3 blacks will be:

= 4/12 × 3/12 × 2/12

= 1/3 × 1/4 × 1/6

= 0.0139

The probability will be the addition of the values. This will be:

= 0.4242 + 0.0139

= 0.4381

The probability is 0.4381.

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Answer:

Each friend paid $5 for parking.

Step-by-step explanation:

[tex]23.5[/tex] - [tex](6.75[/tex][tex](2)[/tex][tex])[/tex] = [tex]10[/tex]

[tex]10[/tex] ÷ [tex]2 = 5[/tex]

I'm not sure about the rest of the question.

Answer:

b x 8 = 40 and 40 / 8 =b

Step-by-step explanation:

well, 8 charms makes one bracelet, so add up 8 until you run out of charms:

We only have 40 charms, so we can make 5 bracelets!

Now, plug this number (5) back into the equations:

b x 8 = 40

(5) x 8 = 40

40 = 40

this checks out!

40 - 8 = b

40 - 8 = (5)

32 = 5

32 does not equal 5, so this equation doesn't work.

40 / 8 = b

40 / 8 = (5)

5 = 5

This equation works :)

b + 8 = 40

(5) + 8 = 40

13 = 40

13 does not equal 40, so this is also a bad equation..

since b x 8 = 40 and 40 / 8 = b both produced the right results, we know those two are our answers!

Answer:

63.7 inches to nearest tenth.

Step-by-step explanation:

The legs of the right triangles formed are 21 inches and 1/2*18 = 9 inches.

So, the hypotenuse (which is one of the congruent sides of the isosceles triangle)

= √(21^2 + 9^2

= √522 inches

Therefore, the triangles perimeter

= 2 * √522 + 18

= 63.695 inches.

The simplified form of the expression as a fraction is -43/390.

Fractions are expression written as a ratio of two integers. For instance, a/b are known as fractions.

Given the expression below:

[2-|-2/3-2(-1/5)|]÷(-13)

In order to solve the expression, we will use the PEMDAS rule to have:

[2-|-2/3-2(-1/5)|]÷(-13)

[2-|-2/3+1/10)|]÷(-13)

Find the LCM

[2-|-20+3/30|]÷(-13)

[2-|-17/30|]÷(-13)

[2-(17/30)]÷(-13)

[60-17/30]÷(-13)

43/30÷(-13)

Change the division sign to multiplication

43/30÷(-13)

43/30 * -1/13

-43/390

This gives the simplified form of the expression.

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Given: The angle

To Determine: The supplement of the given angle

Solution

Please note that two angle are supplement if they are add up to 180⁰

So if the supplement is x. Therefore

Hence, the supplement of 123⁰ is 57⁰, OPTION C

The equation of a function that results in a graph that shows exponential decay is f(x) = 3(0.7)ˣ

An exponential function is represented as

f(x) = abˣ

Where

A function that represents an exponential decay would have a rate less than 1

This is represented as b <1

From the list of options, we have

f(x) = 3(0.7)ˣ

By comparing f(x) = 3(0.7)ˣ and f(x) = abˣ, we have

b = 0.7

0.7 is less than 1

Hence, the exponential decay function is f(x) = 3(0.7)ˣ

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Answer:

   See below, where we have used the definitions of vertical angles and complementary angles, and used the substitution property of equality.

Step-by-step explanation:

You want a proof that angles complementary to congruent angles are congruent. That is, ∠1 ≅ ∠4.

1. ∠1 and ∠3 are complementary . . . . given

2. ∠2 and ∠4 are complementary . . . . given

3. ∠2 ≅ ∠3 . . . . vertical angles are congruent

4. ∠1 +∠3 = 90° . . . . definition of complementary

5. ∠2 +∠4 = 90° . . . . definition of complementary

6. ∠1 +∠3 = ∠2 +∠4 . . . . substitution property of equality

7. ∠1 +∠2 = ∠2 +∠4 . . . . substitution property of equality

8. ∠1 = ∠4 . . . . subtraction property of equality

9. ∠1 ≅ ∠4 . . . . definition of angle congruence

__

Additional comment

The idea of congruence applies to the shape of the geometry. The idea of equality applies to the measures of the angles. Angles are congruent when they have the same measure.

Using the Central Limit Theorem, the formulas are given as follows:

The Central Limit Theorem states that a random variable X with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] can have the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

A distribution of proportions, with a  proportion p in a sample of size n, also respects the Central Limit Theorem, as the the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation given as follows:

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Given :

R is the midpoint of QS

QR = 6x - 9

RS = 2x - 1

We need to find QS

So, as R is the midpoint

Solve the equation to find x :

Substitute with x to find QR and QS

The arithmetic mean is 59.

What is arithmetic mean?

It is the sum of collection of numbers divided by the count of the numbers.

Conider AB is the nuber satisfying the condition. Hence,

[tex]10A+B=A+B+A\times B\\9A=A\times B\\[/tex]

Since AB is a two digit number hence, [tex]A\neq 0\\[/tex]. Hence, divide both sides by [tex]A[/tex].

[tex]9=B[/tex]

Hence, B is 9 and A can take any value from 1 to 9.

Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.

Now, calculate arithmetic mean as follows:

[tex]AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59[/tex]

Hence, arithmetic mean of numbers is 59.

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Using Pythagoras's theorem, the set of measurement that can be used to form a right triangle is √2, √7 and 9.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right angle triangle can be found using Pythagoras's theorem.

Therefore, Pythagoras's theorem is described as follows;

c² = a² + b²

where

Therefore, the sides of the triangle that can be used to form a right triangle will have to obey the Pythagoras's theorem,

(√2)² + (√7)² = 9

2 + 7 = 9

Therefore, the last option can form a right triangle.

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Answer:

False

Step-by-step explanation:

Check using Pythagorean theorem (proof for right triangles)

[tex]10^2+24^2=25^2[/tex]

[tex]100+576=625[/tex]

[tex]676\neq 625[/tex]

False

Answer:

for the first one: d ≥ 1

for the second one: d > 5

The balcony can hold 25 people of 160-pound weight.

According to the question,

We have the following information:

The maximum weight balcony can hold = 1816 kg

Weight of 1 person = 160 pound

Now, we will convert this weight into kilogram so that both the measurements have same units.

1 pound = 0.454 kg

160 pound = 160*0.454 kg

160 pound = 72.64 kg

Now, let's take the number of people balcony can hold to be x.

So, we have:

72.64x = 1816

x = 1816/72.64

x = 25

Hence, the number of people the given balcony can hold is 25.

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Multistage cluster sampling with stratification, systematic sampling, simple random sampling and disproportionate stratified sampling are examples of probability sampling.Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection.

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Answer:

(1,3)

Step-by-step explanation:

You are at (-3,5).  Ordered pairs are written (x,y)  The x tells you how far right or left you are from the origin (0,0) and the y tells you how high above or below You are from the origin (0,0).

(-3+ 4,5 -2)  We are 3 unit to the right of (0,0) to begin with and the directions tell us to go 4 more units right.  We will now be 1 units to the right of zero.  We started at 5 units above zero, the directions tells us to move two units down.  That would be at 3.

So, our new order pair will be (1.3)

The possible coordinates of the other points are (3 + √7, -1) and (3 - √7, -1)

From the question, we have

Where (x, -1) represents the other points

The distance between the points is the number of units between them

It is calculated using the following distance formula

d = √[(x₁ - x₂)²+ (y₁ - y₂)²]

Where x and y represent the coordinates of the given points

Substitute the known values in d = √[(x₁ - x₂)²+ (y₁ - y₂)²]

So, we have

d = √[(3 - x)²+ (2 + 1)²]

Evaluate the expression

d = √[(3 - x)²+ 9]

Recall that d = 4

So, we have

√[(3 - x)²+ 9] = 4

Square both sides

(3 - x)²+ 9 = 16

This gives

(3 - x)² = 7

So, we have

3 - x = ±√7

Solve for x

x = 3 ± √7

Hence, the coordinates are (3 + √7, -1) and (3 - √7, -1)

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It is to be noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.

IGHJ is a paralellogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.

CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.

VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.

A parallelogram, rhombus, rectangle, or square is a quadrilateral with opposing sides that are congruent and parallel.

There are six crucial parallelogram qualities to understand:

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Since there are 128 fluid ounces in one gallon, we need to divide 14 by 128 to change ounces into gallons.

Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour.

Combining these:  14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr)  =  6.5625 gal per hour.

Written as a mixed fraction:  6 9/16 gal per hour.