write a question in y=a x b^x whose graph passes through the Coordinate points (2,12) and (3,24)

Answer:

-24x + 30y

Step-by-step explanation:

Step 1:

−4(x − 15y) + 5(−4x − 6y)

Step 2:

−4x + 60y + (−20x − 30y)

Step 3:

Combine like terms within each set of parentheses:

−4x + 60y − 20x − 30y

Step 4:

Combine like terms:

(-4x - 20x) + (60y - 30y)

Step 5:

Simplify:

-24x + 30y

Final result:

-24x + 30y

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Option 4,option 6, and option 2 are the respective contrapositive to the statements given.

A contrapositive statement is obtained by interchanging both the hypothesis and conclusion of a given statement after contradicting them.

For "if p then q" the contrapositive is "if not-q, then not-p "

From the information given, we have;

Statement 1: If two figures are congruent, then their corresponding sides are equal.

Contrapositive: If the corresponding sides of two figures aren't equal, then the two figures aren't congruent. (Option 4)

Statement 2: If two numbers are even, then their product is even.

Contrapositive: If the product of two numbers isn't even, then the two numbers aren't even. (Option 6)

Statement 3: If a figure is a pentagon, then the sum of its interior angles is 540°.

Contrapositive: If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon. (Option 2)    

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The sum of the first 12 whole numbers of the sequence is 156.

Given that, the sum of the first n whole numbers is given by the expression (n²+ n).

Here, n=12

Substitute n=12 in the expression n²+ n, we get

12²+ 12

= 144+12

= 156

Therefore, the sum of the first 12 whole numbers of the sequence is 156.

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To complete squares we need to add 8 units to the function.

Here we want to find how many units we need to complete squares in the quadratic:

f(x) = x² - 6x + 1

Remember the perfect square trinomial:

(a + b)² = a² + 2ab +b²

Now we can rewrite the function as:

f(x) = x² - 6x + 1 = f(x) = x² - 2*3x + 1

Then the missing term is a 3² = 9, so what we need to add to complete squares is 8 units (1 + 8 = 9)

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The scale factor represents the Ratio of the side lengths between the two similar figures. side length in triangle D' is four times larger than the corresponding side length in triangle D.

The scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

Triangle D has side lengths of 6, 8, and 10 units, while triangle D' has side lengths of 24, 32, and 40 units.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

For the first side, D' has a length of 24 units, while D has a length of 6 units.

24/6 = 4

For the second side, D' has a length of 32 units, while D has a length of 8 units.

32/8 = 4

For the third side, D' has a length of 40 units, while D has a length of 10 units.

40/10 = 4

Since all the ratios are equal to 4, we can conclude that the scale factor used to dilate triangle D to create triangle D' is 4.

The scale factor represents the ratio of the corresponding side lengths between the two similar figures. In this case, every side length in triangle D' is four times larger than the corresponding side length in triangle D.

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Answer: it is 4

Step-by-step explanation:

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There are 1287 ways in which the group of twelve people can take a ride on the roller coaster.

To determine the number of ways the group of twelve people can take a ride on the roller coaster, we need to consider the different combinations of people that can fit in each train.

Let's analyze the possibilities:

If the train that can fit 8 passengers is chosen:

There are 12 people to choose from, and we need to select 8 of them to ride in this train.

The number of ways to choose 8 people out of 12 can be calculated using the combination formula, denoted as C(12, 8) or 12C8, which is equal to 12! / (8! × (12-8)!).

Simplifying this expression, we find that C(12, 8) = 12! / (8! × 4!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495.

If the train that can fit 7 passengers is chosen:

There are 12 people to choose from, and we need to select 7 of them to ride in this train.

The number of ways to choose 7 people out of 12 can be calculated using the combination formula as well, denoted as C(12, 7) or 12C7, which is equal to 12! / (7! × (12-7)!).

Simplifying this expression, we find that C(12, 7) = 12! / (7! × 5!) = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1) = 792.

Therefore, the total number of ways the group can take a ride on the roller coaster is the sum of the possibilities from both scenarios:

495 (for the train fitting 8 passengers) + 792 (for the train fitting 7 passengers) = 1287.

Hence, there are 1287 ways in which the group of twelve people can take a ride on the roller coaster.

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The closest time the temperature of the liquid reaches 90 degrees is (1) 25 minutes

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

[tex]f(m) = 112e^{-0.058m} + 64[/tex]

When it reaches 90 degrees, we have

f(m) = 90

So, the equation becomes

[tex]112e^{-0.058m} + 64 = 90[/tex]

Subtract 64 from both sides

[tex]112e^{-0.058m} = 26[/tex]

Divide both sides by 112

[tex]e^{-0.058m} = 0.232[/tex]

Take the natural logarithm of both sides

m = ln(0.232)/(-0.058)

Evaluate

m = 25 (approx)

Hence, the closest time the temperature reaches 90 degrees is (1) 25 minutes

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