X + 4y = -8 x-4y=-8 elimination

The function g(x) = 2f(6x) + 8 is a function transformation of the function f(x)

The function g(x) is given as:

g(x) = 2f(6x) + 8

The table is not given.

So, I will provide a general explanation

Using the following values of x:

x = 0, 1, 2, 3......

We have:

g(0) = 2f(6 *0) + 8

g(0) = 2f(0) + 8

g(1) = 2f(6 *1) + 8

g(1) = 2f(6) + 8

g(2) = 2f(6 *2) + 8

g(2) = 2f(12) + 8

g(3) = 2f(6 *3) + 8

g(3) = 2f(18) + 8

Next, we assume the following values

f(0) = 4, f(6) = 5; f(12) = 6 and f(18) = 7

The values become:

g(0) = 2f(0) + 8 = 2 * 4 + 8 = 16

g(1) = 2f(6) + 8 = 2 * 5 + 8 = 18

g(2) = 2f(12) + 8 = 2 * 6 + 8 = 20

g(3) = 2f(18) + 8 = 2 * 7 + 8 = 22

So, the table of values would be:

x     g(x)

0     16

1     18

2   20

3   22

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Answer:

it is not a function because there are 2 y- values for 1 x value.

Step-by-step explanation:

it doesn't pass the vertical line test (put hand up and down if it hits 2 points that share x value but different y value its not a real function.

Answer:

5th or 6th grade

Step-by-step explanation:

The reason why we learn geography in 5th grade is to prepare us for 6th grade geography. The reason why we learn geography in 6th grade is because Geography helps us understand basic physical systems that affect everyday life. In other words, geography is a nice skill to have when you're learning about the water cycle or rock formations, or the moving of the tectonic plates (and other natural disasters). It's also a very important skill to have when you want to start traveling.

Answer:

0.96 or .96

Step-by-step explanation:

40 divided by 100 = 0.4 to change the percent to a decimal

and multiply 2.40 to 0.4, 0.4 times 2.40 is 0.96 or .96

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

33km

Step-by-step explanation:

Let the distance traveled by bus be x, then distance traveled by train would be 2x

Therefore,

5 + x + 2x = 104

5 + 3x = 104

3x = 104 - 5

3x = 99

x = 33

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

The domain restrictions for (f/g)(x) are (c) x = 0, 6

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

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

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

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

A and D.

Step-by-step explanation:

A sequence is a set of the objects or numbers in a specific order. It is a function whose domain is a set of natural numbers or non-negative integers i.e. {1, 2, 3,..}

(A)

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."

The general form an arithmetic sequence is:

\(a_{n}=a_{1}+(n-1)d\)

The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.

So, the statement provided is True.

(D)

"A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers."

The general form an geometric sequence is:

\(a_{n}=a_{1}\cdot r^{n-1}\)

The function is exponential. The sequence consists of either numbers that are exponentially increasing or decreasing by the factor r, the common ratio.

So, the statement provided is True.

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

b

Step-by-step explanation:

b

Answer:

Step-by-step explanation:

These are mostly calculator problems. The only trick is the last one. Your calculator will have either a y^x button or ^ button. They both do the same thing.

So for the last one, you must do it as

64 y/x (1÷6)= and you will get 2. Perhaps all of them should be done that way.

If your calculator uses ^ then you would do it

64^(1÷6)= which is the same thing.

Answers

a 4

b 10

c 5

d 2

Answer:

each person would getb3 dollars back

Step-by-step explanation:

since each friend pays $10 and there are 4 friends the total is 40 but now you have to do $40.00 minus $25.00 because of tax and gratuity so when you do that you get $15.00 now you have to do 15 ÷ 4 and that equals $3.75 and since you cant divide 75 coins to 4 people we dont add that but now you have your answer each friend gets $3.00

Based on the information in the triangle, the measure of ZDEB is 54°.

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. Triangles are commonly represented by drawing three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.

The sum of the measures of the angles of a triangle is 180 degrees. Therefore,

mZAEC + m/AED + mZDEB = 180

(2x+4) + (5x+1) + mZDEB = 180

7x+5 = 180

7x = 175

x = 25

mZDEB = 2x+4 = 2(25)+4 = 54 degrees

Hence, the answer is 54

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Answer:

x = 17

Step-by-step explanation:

4x-10 and 58 are alternate interior angles since the lines are parallel

Alternate interior angles are equal.

4x-10 = 58

Add 10 to each side

4x-10 +10 = 58+10

4x = 68

Divide each side by 4

4x/4 = 68/4

x = 17

Answer:

17

i did the math at home.

1.25 Step-by-step explanation:

Answer:

1.75

Step-by-step explanation:

3.5/2 = 1.75

hope this helps

Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.

To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.

Let's denote the length of the actual tank as "x".

According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.

So, we can set up the following proportion:

1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)

Cross-multiplying and solving for x, we get:

x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm

The actual tank is 1620 cm long.

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Answer:

5 pens

Step-by-step explanation:

$10 - 6$ = $4

$4/$0.80

she can afford 5 pens

According to the information, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely.

In probability, an event is considered likely if its probability is high, and it is considered unlikely if its probability is low. An event is considered neither likely nor unlikely if its probability is close to 0.5 or 50%. In this case we have to consider the probability of each option to establish a conclusion. Here is the analysis:

According to the above, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely because its probability is exactly 0.5 or 50%.

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Answer:

Step-by-step explanation:

1)

Congruency shortcuts:  

HL, SSS, SAS, ASA, and AAS

where S=side

A=angle

H=hypotenule

L=leg

HL is only for a right triangle

If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent

Similarity shortcuts:

AA, SAS, SSS

We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)

2)

BG ≅ GD              >Given from image

IG ≅ GO               >Given from image

<BGI ≅ <DGO        >Vertical Angles

ΔBGI  ≅ ΔDGO        >SAS            

You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent

What are the expressions?

The polynomial for the total sales of electricity (in billion kilowatt-hours) to all of the sectors during this period is P(x) = 10.9m² + 20.36m + 3285

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

Since the polynomial 2.17m² + 21.82m + 1190 represents the sale of electricity (in billion kilowatt-hours) in the largest sector during 2000-2005. The polynomial 8.73m² - 1.46m + 2095 represents the sale of electricity (in billion kilowatt-hours) in all other sectors during 2000-2005. In both polynomials, m represents the number of years after 2000.

To find a polynomial for the total sales of electricity (in billion kilowatt-hours) to all of the sectors during this period, we sum up to polynomials to give a new polynomial.

So, the new polynomial P(x) = 2.17m² + 21.82m + 1190 + 8.73m² - 1.46m + 2095

=  2.17m² + 8.73m² + 21.82m - 1.46m + 1190 + 2095

= 10.9m² + 20.36m + 3285

So, the total sales Polynomial is P(x) = 10.9m² + 20.36m + 3285

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Answer:49

Step-by-step explanation:

A = \(\frac{3+11}{2}\) · 7

= \(\frac{14}{2} \\\) · 7

= 7·7

=49

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

Answer:

attach a picture

Step-by-step explanation:

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6