-2(bx - 5) = 16

What’s does b and x equal?

Answer:

C.

Step-by-step explanation:

The absolute maximum and minimum values of the function f(x) = ln(x^2 + 5x + 12) on the interval [-3, 1] are f(1) = ln(18) (maximum) and f(-2) = ln(4) (minimum).

To find the absolute maximum and absolute minimum values of the function f(x) = ln(x2 + 5x + 12) on the interval [-3, 1], we first need to find the critical points of the function within this range. The critical points are those at which the derivative equals zero or does not exist.

The absolute maximum value within the interval is ln(18) and the absolute minimum value is ln(4).

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The absolute maximum value of f(X)  on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749 ), which occurs at ( x = -5/2).

To find the absolute maximum and minimum values of[tex]\( f(x) = \ln(x^2 + 5x + 12) \)[/tex] on the interval [tex]\([-3, 1]\)[/tex], we first need to find the critical points and check the values of the function at those points and at the endpoints of the interval.

1. Find the critical points: Critical points occur where the derivative of the function is zero or undefined.

First, let's find the derivative of (f(x):

[tex]\[ f'(x) = \frac{1}{x^2 + 5x + 12} \cdot (2x + 5) \][/tex]

Setting ( f'(x)) equal to zero:

2x + 5 = 0

x = -5/2

Since this value x = -5/2 lies within the interval [-3, 1], it's a critical point.

2. Check the endpoints and critical point:

[tex]- \( f(-3) = \ln((-3)^2 + 5(-3) + 12) = \ln(9 - 15 + 12) = \ln(6) \)[/tex]

[tex]- \( f(1) = \ln(1^2 + 5(1) + 12) = \ln(1 + 5 + 12) = \ln(18) \)[/tex]

[tex]- \( f\left(-\frac{5}{2}\right) = \ln\left(\left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 12\right) = \ln\left(\frac{25}{4} - \frac{25}{2} + 12\right) = \ln\left(\frac{25 - 50 + 48}{4}\right) = \ln\left(\frac{23}{4}\right) \)[/tex]

3. Compare the values:

  - ln(6) = 1.792

  - ln(18) = 2.890

  - [tex]ln\left(\frac{23}{4}\right)[/tex] = 1.749

So, the absolute maximum value of f(X)  on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749), which occurs at ( x = -5/2).

The ratio of tulips to daffodils in Robert's garden is 3:2. This is obtained by dividing the number of tulips by the number of daffodils (36/24), and simplifying the result.

This problem pertains to ratios. Given that Robert planted 24 daffodil bulbs and 36 tulip bulbs, the ratio of tulips to daffodils is obtained by dividing the number of tulips by the number of daffodils. Thus, the ratio is 36/24. This simplifies to 1.5 when expressed as a decimal. However, we need the ratio in its simplest form, so let's convert 1.5 into a whole number. By multiplying both numbers by 2, we get the ratio 3:2. Therefore, the ratio of tulips to daffodils in Robert's garden is 3:2

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The students recycle 17 5/12 pounds of glass and paper all together.

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now it is given that,

Pounds of glass recycled = 7 2/3

⇒ Pounds of glass recycled = 23/3

Pounds of paper recycled = 9 3/4

⇒ Pounds of paper recycled = 39/4

Thus, total pounds of glass and paper recycled = Pounds of glass recycled + Pounds of paper recycled

⇒ total pounds of glass and paper recycled = 23/3 + 39/4

⇒ total pounds of glass and paper recycled = 209/12

⇒ total pounds of glass and paper recycled = 17 5/12 pounds

Thus, the students recycle 17 5/12 pounds of glass and paper all together.

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to resolve this type of exercise  you must in first place to verify The determinant of the function to know if it cuts to the x axis, with the following formula  b^2-4ac, if this value is less than zero then the function , do not cut the x axis, now  -(2)^2-4(1)(3) =  -8, as this value is negative, it means that is less than zero nd the function do not cut the x axis

2) the graph cut the y axis eN Y = 3  for x= o,  F(0) = 0+2*0+3 = 3

3) This is the graph

why you just give the question give the question && the answer !!!

Answer:

why you just give the question give the question && the answer !!!

Answer: [tex]x^2 + y^2 = 64[/tex]

Step-by-step explanation:

Since, the equation of a circle that having the center (h,k) and radius r is,

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Here the circle is centered at the origin,

That is, h = 0 , k = 0

Also, the radius of the circle is 8,

That is, r = 8 unit,

Thus, the equation of the given circle,

[tex](x-0)^2 + (y-0)^2 = 8^2[/tex]

[tex]x^2 + y^2 = 64[/tex]

Answer:

A tool.

Now I just need to put filler so I'm just gonna copy and paste. Now I just need to put filler so I'm just gonna copy and paste.

Tony's gross pay for 46 hours of work, including 6 hours of overtime, is $563.50. The Social Security tax on this amount is $34.94, and the Medicare tax is $8.17.

Calculating Tony's Gross Pay

Tony's regular pay for 40 hours at an hourly rate of $11.50 is calculated by multiplying the hourly rate by the number of regular hours he worked. Therefore, his regular pay is 40 hours × $11.50/hour = $460. To calculate the overtime pay, we must first determine the overtime rate. The overtime rate is 1.5 times the normal hourly rate, thus the overtime hourly rate is 1.5 × $11.50/hour = $17.25/hour. Tony worked 6 hours overtime, so his overtime pay is 6 hours × $17.25/hour = $103.50. Tony's gross pay is the sum of his regular pay and overtime pay, which is $460 + $103.50 = $563.50.

Calculating Deductions for Social Security and Medicare

The Social Security tax and Medicare tax are calculated as percentages of the gross pay. The Social Security tax at 6.2% of $563.50 is $563.50 × 0.062 = $34.937, which rounds to $34.94. The Medicare tax at 1.45% of $563.50 is $563.50 × 0.0145 = $8.17075, which rounds to $8.17.

Control variable r is not manipulated, but measured and represents the data being recorded.

What is mean by Variables?

A variable is a value that can change, depending on information.

Given that;

In an experiment, the control variable is r and the response variable is s.

Now,

Control variable is a variable that's always constant in an experiment.

It is not a variable of interest in the study, but its controlled because it could influences the outcomes.

Thus, Control variable r is not manipulated, but measured and represents the data being recorded.

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A multiplication problem shows the process of calculating the product when one number is multiplied by another. This can be represented using an array model, an area model, or a multiplication sentence. Specific representation will depend on the model provided.

In mathematics, a multiplication problem represents the process of finding the product or result when one number is multiplied by another.

However, without a specific model being given in the question, providing a precise answer becomes challenging. In general terms, a multiplication model could be in the form of an array, an area model, or a multiplication sentence. To understand this better, let's illustrate with an example.

In all the cases, the multiplication problem is demonstrating how to find the product of two numbers or quantities.

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Final answer:

By establishing a relationship between the total number of aquatic plants and animals and knowing that animals are 80% of the plants, we can determine that there are 72 aquatic animals in the eco-garden.

Explanation:

To calculate the number of aquatic animals in the eco-garden, we need to first establish the relationship between the number of animals and plants. According to the information, the number of aquatic animals is 80% of the number of aquatic plants. If we denote the number of aquatic plants as 'P' and aquatic animals as 'A', then A = 0.80 × P.

Given that there are a total of 162 aquatic plants and animals, we can represent this as A + P = 162. Since A is 80% of P, we can substitute the first relationship into the second equation, which gives us 0.80 × P + P = 162. Simplifying this, we get 1.80 × P = 162.

To find the value of P, we divide both sides by 1.80 to get P = 162 / 1.80, which yields P = 90. This indicates there are 90 aquatic plants. To determine the number of aquatic animals, we use the relationship A = 0.80 × P, so A = 0.80 × 90, resulting in A = 72.

Therefore, there are 72 aquatic animals in the eco-garden.

Final answer:

To find out how far south the jogger went, we use the Pythagorean theorem. Given the distances of 1.5 km west and 1.7 km from the start, the jogger went 0.8 km south.

Explanation:

To determine how far south the jogger went, we can use the Pythagorean theorem, as the jogger's path forms a right-angled triangle where one leg of the triangle is the distance west, the other leg is the distance south, and the hypotenuse is the distance from the starting point.

The question states the jogger goes 1.5 km west and ends up 1.7 km from the starting point. We denote the distance travelled south as y. According to the Pythagorean theorem:

west^2 + south^2 = distance from start^2

y = √0.64

y = 0.8 km

So the jogger went 0.8 km south.