MATHEMATICS HIGH SCHOOL

The graphs of ​ f(x)=−32x+2 ​ and ​ g(x)=3x−10 ​ intersect at (2, −1) What is the solution of −32x+2=3x−10 ?

Answers

Answer 1
Answer:

Answer:

The solution of the equation is 2.

Step-by-step explanation:

The given functions are

f(x)=-(3)/(2)x+2

g(x)=3^x-10

It is given that the graph of f(x) and g(x) intersects each other at (2,-1).

The given equation is

-(3)/(2)x+2=3^x-10

The solution of this equation is the value of x where both the functions are eqaul.

Since both functions are equal at x=2, therefore the solution of the equation is 2.
Answer 2
Answer: The solution of -32x+2=3x-10 is (2,-1)

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Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle Rob will be three times Tonya’s age.
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Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s garden produced 8 bulbs. In the second year, it produced 16 bulbs, and in the third year it produced 32 bulbs. If this pattern continues, how many bulbs should Geoff expect in the sixth year?A. 64
B. 512
C. 128
D. 256

Answers

1st = 8, 2nd = 16, 3rd = 32, doubling each time so 4th = 64, 5th = 128,

6th = 256

-1 1/5 + -3/5 in simplest form

Answers

Answer:

-1 4/5

Step-by-step explanation:

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction 3  5, the numerator is 3, and the denominator is 5. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be 5  8 as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

What is the solution of log3x − 5 16 = 2?

the base is 3x - 5, and the argument is 16

Answers

Answer:

x=3

Step-by-step explanation:

The given equation is \log_(3x-5)16=2

The relation between logarithmic function and exponential function is given by

\text{If }y=b^x\text{ then }x=\log_b(y)

On comparing, we get

b = 3x-5

y = 16

x = 2

Hence, using the relation, we have

16=(3x-5)^2

Take square root both sides

\pm√(16)=3x-5

On simplifying

3x-5=\pm4\n\n3x=\pm4+5\n\nx=(1)/(3)(5\pm4)\n\nx=(1)/(3)*1,(1)/(3)*9\n\nx=(1)/(3),3

For x = 1/3

3x-5\n\n=3\cdot (1)/(3)-5\n\n=-4

Base cannot be negative.

Hence, the value of x is 3
Hello,

log (16)=2 in base 3x-5
==>16=2^(3x-5)
==>2^4=2^(3x-5)
==>4=3x-5
==>3x=9
==>x=3

Convert base 2 number 10001 in decimal?

Answers

To convert a base 2 (binary) number to decimal, we can use the following method:

Starting from the right, multiply the value of each binary digit (0 or 1) by 2 raised to the power of its position, where the position of the rightmost digit is 0, the one to its left is 1, and so on. Then, add up these values to get the decimal equivalent.

For the binary number 10001:

1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0

= 16 + 0 + 0 + 0 + 1

= 17

Therefore, the decimal equivalent of the binary number 10001 is 17.

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.a)What are the values of the mean and standard deviation after converting all pulse rates of women to z-scores using z=(x−μ)/σ?


b)The original pulse rates are measured with units of "beats per minute." What are the units of the corresponding z-scores?

Answers

Answer:

a) Mean=0 and Standard deviation=1

b) The z-scores have no units of measurement

Step-by-step explanation:

When we convert all the pulse rates of women to z-scores using the formula;

z=(x-\mu)/(\sigma) the mean is 0 and the standard deviation is 1.

The reason is that, the resulting distribution of z-scores forms a normal distribution which has a mean of 0 and a standard deviation of 1.

b) The z-scores are standardize scores and has no units of measurement. They give us how many standard deviations below or above the mean of the corresponding values.

Final answer:

Converting pulse rates into z-scores standardizes them into a standard normal distribution, yielding a mean of zero and a standard deviation of one. Z-scores are dimensionless and do not carry original physical units of measurement.

Explanation:

The question is asking about the properties of a z-score in the context of pulse rates of women. Here is the answer:

a) When converting to z-scores, regardless of the population parameters, the mean (μ) will always be 0 and standard deviation (σ) always 1. This conversion process is called standardization, which results in a standard normal distribution.

b) In the context of z-scores, the units are dimensionless. Because a z-score result is derived from a mathematical manipulation and not a direct measurement, it does not carry physical units like "beats per minute" in pulse rates. This characteristic enables us to make meaningful comparisons between different types of data.

Learn more about z-scores here:

brainly.com/question/15016913

#SPJ3

which polynomial can be simplified to a difference of squares? 10a2 3a – 3a – 16 16a2 – 4a 4a – 1 25a2 6a – 6a 36 24a2 – 9a 9a 4

Answers

For the polynomial: 10a^2 + 3a - 3a - 16 = 10a^2 - 16 but 10a^2 is not a perfect square hence does not simplify to a difference of two squares. For the polynomial: 16a^2 - 4a + 4a - 1 = 16a^2 - 1 = (4a - 1)(4a + 1). This polynomial simplifies to a difference of two squares. For 25a^2 + 6a - 6a + 36 = 25a^2 + 36. This ia a sum of two squares and not a difference of two squares. For 24a^2 - 9a + 9a + 4 = 24a^2 + 4. This ia a sum of two squares and not a difference of two squares.

The polynomial 16a² - 4a + 4a - 1 can be simplified to a difference of squares

What is a polynomial?

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

The difference of two squares is given by:

a² - b² = (a + b)(a - b)

Hence:

16a² - 4a + 4a - 1 = 4a(4a - 1) + 1(4a - 1)

= (4a + 1)(4a - 1)

The polynomial 16a² - 4a + 4a - 1 can be simplified to a difference of squares

Find out more on polynomial at: brainly.com/question/2833285
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