Which is the function g(x) for a restricted domain?
O g(x) = 3x-4; 2-4
O g(x) = 3x + 4; x > 0
O g(x) = 3/x+4; x 24
O g(x) = 35-4;> 0

Step-by-step explanation:

The value of the digit 1 in the number 213,456 is 10,000.

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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The system of equation that does not belong to the other two is the third system of equations; y = -4·x - 3, y + 4·x = -5, This is so because, the third system has no solutions.

A linear system of equations consists of two or more linear equations that consists of common variables.

The possible equations are;

y = x + 6, y = -x + 2

3·x + y = -1, y = 4·x + 6

y = -4·x - 3, y + 4·x = 5

Evaluation of the system of equations, we get;

First system of equations;

y = x + 6, y = -x + 2

x + 6 = -x + 2

x + x = 2 - 6 = -4

2·x = -4

x = -4/2 = -2

x = -2

y = x + 6

y = -2 + 6 = 4

y = 4

The solution is; x = -2, y = 4

Second system of equation;

3·x + y = -1, y = 4·x + 6

3·x + 4·x + 6 = -1

7·x + 6 = -1

7·x  = -1 - 6 = -7

x = -7/7 = -1

x = -1

y = 4·x + 6

y = 4 × (-1) + 6 = 2

y = 2

The solution to the second system of equation is; x = -1, y = 2

Third system of equation;

y = -4·x - 3, y + 4·x = 5

y + 4·x = 5

-4·x - 3 + 4·x = 5

-4·x + 4·x - 3 = 5

0 - 3 = 5

-3 = 5

The third system of equation has no solution

The system of equations that does not belong with the other two is the third system of equation; y = -4·x - 3, y + 4·x = 5, that has no solution.

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Answer:

4

Step-by-step explanation:

50 is 12\(\frac{1}{2}\)% of 400.

Given is the expression as -

50 is 12\(\frac{1}{2}\)% of {x}.

We can write the expression as -

50 = (25/2)/100 {x}

50 = (25/2) x (1/100) {x}

50 = {x}/8

{x} = 400

Therefore, 50 is 12\(\frac{1}{2}\)% of 400.

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Answer:

x = 29.15

Step-by-step explanation:

a^2 + b^2 = c^2

15^2 + 25^2 = 890

square root of 850 is 29.154759....

:)

Answer:

The correct answer is 30.

Step-by-step explanation:

To find this out I found the fraction of 6 and 8 to 10. This is 3/5 and 4/5 to find x on the other triangle all I had to do was multiply 25 times 1 1/5. Sorry for the bad explanation it was kind of confusing to word but I hope this helps!

Let x be the number of pounds of Kenyan coffee and y be the number of pounds of Sumatran coffee. We know that x + y = 26 and 9x + 11y = 260.

Solving the system of equations, we get

x = 14 and y = 12

Therefore, the Coffee Counter should use 14 pounds of Kenyan coffee and 12 pounds of Sumatran coffee to make a 26 pound blend that sells for $10.00 per pound.

To confirm, the average price of the blend is: (9*14 + 11*12) / 26 = 10.00

So the answer is 14,12

Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Answer:(2I3O-9247)

Step-by-step explanation:

Answer:

Ms. Duncan should leave a $8.40. tip.

9514 1404 393

Answer:

  a, b, c --- all not representative

Step-by-step explanation:

The question posed by the engineer is "are residents of the city in favor of ...".

The only representative sample is one from a pool that includes all residents of the city—not just those who (a) use the road, (b) live along the road, or (c)  own homes.

__

Additional comment

The engineer may want to refine the question. As posed, it would include children, homeless, and/or institutionalized residents of the city as well as drivers and tax-payers. In inclusive cultural traditions, "residents of the city" may also include animals, plants, water, air, and other holders of spiritual energy.

The surface area of the pyramid is approximately 74.24 square inches.

What is a pyramid?

A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.

To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.

The area of each triangular face can be found using the formula:

Area = (1/2) * base * height

where the base is one of the sides of the square base and the height is the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

slant height² = height² + (1/2 * base)²

where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.

height = 7 in.

base = 4 in.

slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53

slant height = √53 ≈ 7.28 in.

Now we can find the area of each triangular face:

Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2

There are four triangular faces, so the total area of the triangular faces is:

4 * 14.56 = 58.24 in²

The area of the square base is:

Area = side² = 4² = 16 in²

Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:

Surface Area = 58.24 + 16 = 74.24 in²

Therefore, the surface area of the pyramid is approximately 74.24 square inches.

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Answer:

i thinck its just 1 and 2

Step-by-step explanation:

Answer:

\(\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}\)

Step-by-step explanation:

Given

\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {[ \ ]} \\ \end{array}\)

Required

Fill in the box

From the question, the range is:

\(Range = 60\)

Range is calculated as:

\(Range = Highest - Least\)

From the box, we have:

\(Least = 1\)

So:

\(60 = Highest - 1\)

\(Highest = 60 +1\)

\(Highest = 61\)

The box, becomes:

\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)

From the question:

\(IQR = 20\) --- interquartile range

This is calculated as:

\(IQR = Q_3 - Q_1\)

\(Q_3\) is the median of the upper half while \(Q_1\) is the median of the lower half.

So, we need to split the given boxes into two equal halves (7 each)

Lower half:

\(\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } \\ \end{array}\)

Upper half

\(\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)

The quartile is calculated by calculating the median for each of the above halves is calculated as:

\(Median = \frac{N + 1}{2}th\)

Where N = 7

So, we have:

\(Median = \frac{7 + 1}{2}th = \frac{8}{2}th = 4th\)

So,

\(Q_3\) = 4th item of the upper halves

\(Q_1\)= 4th item of the lower halves

From the upper halves

\(\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)

We have:

\(Q_3 = 32\)

\(Q_1\) can not be determined from the lower halves because the 4th item is missing.

So, we make use of:

\(IQR = Q_3 - Q_1\)

Where \(Q_3 = 32\) and \(IQR = 20\)

So:

\(20 = 32 - Q_1\)

\(Q_1 = 32 - 20\)

\(Q_1 = 12\)

So, the lower half becomes:

Lower half:

\(\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {12 } & {15} & {18}& {[ \ ] } \\ \end{array}\)

From this, the updated values of the box is:

\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)

From the question, the median is:

\(Median = 22\) and \(N = 14\)

To calculate the median, we make use of:

\(Median = \frac{N + 1}{2}th\)

\(Median = \frac{14 + 1}{2}th\)

\(Median = \frac{15}{2}th\)

\(Median = 7.5th\)

This means that, the median is the average of the 7th and 8th items.

The 7th and 8th items are blanks.

However, from the question; the mode is:

\(Mode = 18\)

Since the values of the box are in increasing order and the average of 18 and 18 do not equal 22 (i.e. the median), then the 7th item is:

\(7th = 18\)

The 8th item is calculated as thus:

\(Median = \frac{1}{2}(7th + 8th)\)

\(22= \frac{1}{2}(18 + 8th)\)

Multiply through by 2

\(44 = 18 + 8th\)

\(8th = 44 - 18\)

\(8th = 26\)

The updated values of the box is:

\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)

From the question.

\(Mean = 26\)

Mean is calculated as:

\(Mean = \frac{\sum x}{n}\)

So, we have:

\(26= \frac{1 + 2nd + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 12th + 58 + 61}{14}\)

Collect like terms

\(26= \frac{ 2nd + 12th+1 + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 58 + 61}{14}\)

\(26= \frac{ 2nd + 12th+304}{14}\)

Multiply through by 14

\(14 * 26= 2nd + 12th+304\)

\(364= 2nd + 12th+304\)

This gives:

\(2nd + 12th = 364 - 304\)

\(2nd + 12th = 60\)

From the updated box,

\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)

We know that:

The 2nd value can only be either 2 or 3

The 12th value can take any of the range 33 to 57

Of these values, the only possible values of 2nd and 12th that give a sum of 60 are:

\(2nd = 3\)

\(12th = 57\)

i.e.

\(2nd + 12th = 60\)

\(3 + 57 = 60\)

So, the complete box is:

\(\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}\)

Answer:

172.27 in

Step-by-step explanation:

Apply the Sine Rule

Sine Rule is given as:

\( \frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)} \)

c = x = ?

C = 180 - (52 + 48) = 80° (sum of triangle)

b = 130 in.

B = 48°

Plug in the values

\( \frac{130}{sin(48)} = \frac{x}{sin(80)} \)

Multiply both sides by sin(80)

\( \frac{130*sin(80)}{sin(48)} = x \)

172.274641 = x

x = 172.27 in. (to 2 decimal places)

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

The correct answer is (b) 54 in.², which Matches just performed.

The area of a triangle, we use the formula:

Area = (1/2) * base * height

Given that the base (b) is 9 inches and the height (h) is 12 inches, we can substitute these values into the formula:

Area = (1/2) * 9 * 12

Simplifying the equation:

Area = (1/2) * 108

Area = 54

Therefore, the area of the triangle with a base of 9 inches and a height of 12 inches is 54 square inches.

Among the options given:

(a) 90 in.²

(b) 54 in.²

(c) 10.5 in.²

(d) 162 in.²

The correct answer is (b) 54 in.², which matches the calculation we just performed.

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Answer:Point X= 1600m, Point Z= 2050m

Step-by-step explanation:

Answer:

(5+8) (5-8)

Step-by-step explanation:

They are both perfect squares.

Answer:

(5+8x)(5-8x)

Step-by-step explanation:

This is a 'difference of two squares" Difference means subtraction and 25 is a perfect square and 64x^2 is a perfect square.

If you know how to factor quadratic trinomials like

ax^2 + bx + c, you can do the same thing here, using:

64x^2 +0x + 25

BUT, there's a shortcut. It is a pattern that you memorize. Since 25 is 5^2, put 5 first in the parenthesis. And since 64x^2 is 8x squared, put 8x second in the parenthesis like this:

(5 8x)

Make two of them:

(5 8x)(5 8x)

Make one a plus and one a minus.

(5 + 8x)(5 - 8x)

Done!

Well, if the directions say "factor" then you are done. If the directions say "solve" then put each piece equal to zero and solve for x.

Hope this helps!

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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9514 1404 393

Answer:

  17

Step-by-step explanation:

The number of handshakes among n people is n(n -1)/2. Then ...

  n(n -1)/2 = 136

  n(n -1) = 272 = 17×16*

  n = 17

There were 17 people at the party.

_____

* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.

Answer:

-5/6

Step-by-step explanation:

By the application of Analytical geometry the rate of change of y with respect to x is -5/6.

what is Analytical geometry?

Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.

The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.

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Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

Answer:

2c^3

Step-by-step explanation:

The greatest common divisor of 6 and 10 are 2

The factors that are common to 6c^3, 10c^4 would be 2ccc

Simplify that and you have 2c^3

ANSWER

Biodiversity index = 0.096

EXPLANATION

Given 7 different organisms with their individual numbers.

Biodiversity Index is:

i.e:

Hence, the Biodiversity Index of Fraya's local park is 0.096. This is a low biodiversity since it's closer to 0.

Answer:

The zeros are (-5,0) and (4,0)

Step-by-step explanation:

Answer:

-5 and 4

Step-by-step explanation:

Answer:

\(a-2b\)

Step-by-step explanation:

1) Remove parentheses.

\(a-b+c-c-b\)

2) Collect like terms.

\(a+(-b-b)+(c-c)\)

3) Simplify.

\(a-2b\)

Therefor, the answer is a - 2b.