Determine the domain and the range of the graph.

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The value of x are:

(A) = 10

(B) = 39

(C) = 56

(D) = 8

(E) = 99

(F) = 12

The arc length of a circle is the distance between two points on the curve of the circle.

We have,

The angle formed by two chords inside a circle:

=  1/2 x the sum of the intercepted arc.

Straight line angle = 180°

Now,

(A)

180 - 129 = 51

51 = 1/2 x (4x - 4 + 5x + 16)

51 = 1/2 x (9x + 12)

51 x 2 = 9x + 12

102 = 9x + 12

90 = 9x

x = 10

(B)

47 = 1/2 x (x + 20 + x - 4)

47 x 2 = 2x + 16

94 = 2x + 16

78 = 2x

x = 39

(C)

Arc length = 2 x angle subtended at the circle by the arc length.

2(x-3) = 106°

2x - 6 = 106

2x = 112

x = 56

(D)

40 = 1/2 x (6x + 4x)

40 = 1/2 x 10x

80 = 10x

x = 8

(E)

180 - x = 1/2 x (95 + 67)

180 - x = 1/2 x 162

180 - x = 81

180 - 81 = x

99 = x

x = 99

(F)

2(6x - 1) = 360 - (152+ 66)

12x - 2 = 142

12x = 142 + 2

12x = 144

x = 12

Thus,

The value of x are:

(A) = 10

(B) = 39

(C) = 56

(D) = 8

(E) = 99

(F) = 12

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ANSWER

EXPLANATION

We want to solve the given system of linear equations:

From the first equation, make x the subject of the formula:

Substitute the equation above into the second and third equations:

and:

Now, we have a system of two equations with two variables:

From the second equation, make z the subject of the formula:

Substitute the equation above into the first equation and solve for y:

Substitute the value of y into the equation for z:

Finally, substitute the values of y and z into the equation for x:

Hence, the solution to the system of linear equations is:

The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

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

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

The required equation is :

\(\qquad \sf  \dashrightarrow \:a \cos(bx) + k\)

Now, let's find the required values :

period (p) = 6

[distance between any successive Crest or trough]

a = - 4 (flipped)

b = 2π/p = 2π/6 = π/3

k = -2

Distance of starting position from origin = k

Now, plug in the values ~

\(\qquad \sf  \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2\)

Not passing through origin (it's cosine)

Period:-

Now

Frequency:-

\(\\ \rm\dashrightarrow \nu=\dfrac{1}{T}\)

\(\\ \rm\dashrightarrow \nu=\dfrac{1}{6}\)

\(\\ \rm\dashrightarrow \nu=0.167Hz\)

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The following relation P = {(x, y), (1 ,3), (2,9), (3,17), (4,27) ,(5,39) ,(6,53)} is a quadratic relation by virtue of its second differences.

The kind of function which is defined by the pair of coordinates as given in the task content can be determined by assessing the first, second or third differences in y-values at a constant increment of x.

Hence, for the pair of coordinates given, we have;

P = {(x, y), (1 ,3), (2,9), (3,17), (4,27) ,(5,39) ,(6,53)}

First differences are; +6, +8, +10, +12, +14.

Hence, since the differences are not constant, we must check for the second differences;

Second differences; +2, + 2, +2, +2.

On this note, since the second differences are constant, it follows that the relation in discuss represents a quadratic function.

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Step-by-step explanation:

how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .

Answer:

35 (C)

Step-by-step explanation:

Answer:

B) 30

Step-by-step explanation:

This is a pretty tricky question. If you draw the line of best fit and go to 9 salespeople, it would be closer to 30 compared to any of the other choices.

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

The instantaneous rate of change is -6 words per day,

the number of words Alex remembers after 5 days, option (D).

What is the instantaneous rate of change ?

An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.

Have given,

Alex learned 80 new vocabulary words

and after t days he learned,

W(t) = \(80 (1-0.1t)^{3}\)

differentiate respect of t

W'(t) = \(80 \frac{d}{dt} (1-0.1t)^{3}\)

W'(t) = \(80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)\)

W'(t) = \(240(1-0.1*5)^{2} (0.1)\)

W'(t) = 6

That's mean , the instantaneous rate of change is -6 words per day.

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899,452 is greater than 756,451

899,452 > 756,451

Given,

899,451

756,451

We need to compare these numbers.

Consider 967543

3 - ones

4 - tens

5 - hundreds

7 - thousands

6 - ten thousands

9 - hundred thousands

Find the highest place value in 899,452.

-  8 hundred thousands

We can read this as eight hundred ninety-nine thousand four hundred fifty-two.

Find the highest place value in 756,451.

- 7 hundred thousands

Seven hundred fifty-six thousand four hundred fifty one

Thus,

899,452 is greater than 756,451

899,452 > 756,451

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Answer:

-18y =1

It is simple addition

The mean length (rounded to 2 DP) of these 15 people's index finger is 12.15 cm.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that:

The mean length of 4 children's index fingers is 8.7cm.

The mean length of 11 adults' index fingers is 13.4cm.

The mean of 15 people = [8.7x4 + 13.4x11]/15

The mean of 15 people = [34.8 + 147.4]/15

= 182.2/15

= 12.1466 cm

= 12.15 cm

Thus, the mean length (rounded to 2 DP) of these 15 people's index fingers is 12.15 cm.

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Answer: c

Step-by-step explanation:

Answer:

+1/-1

Step-by-step explanation:

assuming the original phrase is  x^2

x^2 + 10 = 9

x^2 = 1

x = +/- 1

The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer: 59 cars per month

Step-by-step explanation:

Answer:

Trapezoid

Step-by-step explanation:

It's a quadrilateral and it only has one pair of parallel sides.

By formula,

Midpoint between two points PQ =

So, (-1,-4) (option 3)

Answer:

3/4 pepper

Step-by-step explanation:

if you add 1/4 3 time you get the answer

Answer:

Since 9 is 3 times the denominator of the first ratio, multiply the numerator of the first ratio by 3 to get the numerator of the second ratio. The amount of pepper is 3/4 teaspoon.

Answer:

\((4f)^3 = 64*f^3\)

\((-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4\)

Step-by-step explanation:

Solving (a):

\((4f)^3\)

Apply law of indices:

\(x^3 = x * x * x\)

So, we have:

\((4f)^3 = 4f * 4f * 4f\)

Rewrite as:

\((4f)^3 = 4 * 4 * 4*f*f*f\)

\((4f)^3 = 64*f^3\)

Solving (b):

\((-\frac{3}{2}t^2)^2\)

Apply law of indices:

\(x * x = x^2\)

So, we have:

\((-\frac{3}{2}t^2)^2 = (-\frac{3}{2}t^2) * (-\frac{3}{2}t^2)\)

Remove brackets

\((-\frac{3}{2}t^2)^2 = -\frac{3}{2}t^2 * -\frac{3}{2}t^2\)

Rewrite as:

\((-\frac{3}{2}t^2)^2 = -\frac{3}{2}*-\frac{3}{2}*t^2 * *t^2\)

\((-\frac{3}{2}t^2)^2 = \frac{3}{2}*\frac{3}{2}*t^4\)

\((-\frac{3}{2}t^2)^2 = \frac{9}{4}*t^4\)

\((-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4\)

The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.

Given are the closing prices of two stocks in three days.

If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,

Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25

If the stock is sold in day 2,

Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25

Profit = $1435.25 - $1448.25 = -$13

If the stock is sold in day 3,

Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7

Profit = $1450.7 - $1448.25 = $2.45

The profit is more for day 3 than day 2.

Hence it is best to sell on day 3 by $2.45.

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Answer:

Shop B

Step-by-step explanation:

\(Shop\ A\ sells\ eggs\ at\ $1.50\ per\ half\ dozen,\ so\ it\ sells\ egg\ at\ $1.50\times2\ per\ dozen,\ which\ means\ $3.00\ per\ dozen.\)

\(\left\{$3.00\ is\ more\ than\ $2.40\right\}\)}               \(Shop\ B\ sells\ eggs\ cheaper\ than\ Shop\ A.\ So\ we\ should\ buy\ the\ eggs\ from\ shop\ B\)

I hope this helps you

:)

Answer:

i think is 3.3 but i dont know

Step-by-step explanation:

Answer:

y=7

Step-by-step explanation:

The probability of randomly selecting two women from 884 subjects is 1.

The probability of randomly selecting two women from 884 subjects can be calculated using the following formula: P(A and B) = P(A) x P(B). In this case, A is the event of randomly selecting a woman from 884 subjects and B is the event of randomly selecting a second woman from the remaining 883 subjects.

Therefore, P(A) = 884/884 = 1 and P(B) = 883/883 = 1. Thus, P(A and B) = 1 x 1 = 1. Then, the probability of randomly selecting two women from 884 subjects is 1. To round to four decimal places, the probability is 0.0000.

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Answer: any values between a and 3a

Step-by-step explanation:

To determine the possible side lengths for the third side of the triangle, we need to use the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's call the length of the third side x. Then, based on the Triangle Inequality Theorem, the following two inequalities must be true:

a + 2a > x (the sum of the first and second sides is greater than the third side)

a + x > 2a (the sum of the first and third sides is greater than the second side)

2a + x > a (the sum of the second and third sides is greater than the first side)

Solving the first inequality for x gives us:

x < 3a

Solving the second inequality for x gives us:

x > a

Solving the third inequality for x gives us:

x > -a

Combining these three results, we find that the possible values for the third side length x are:

a < x < 3a

So, the possible lengths for the third side in terms of a are any values between a and 3a, inclusive.

Hi

Below the formulas to convert Celsius into Fahrenheit.

9/5 C +32 = degree in fahrenheit.

Where C is the degree in celsius. So have a try and find the answer.