In an isometric transformation, the preimage and image must not __________. A. change size B. rotate C. preserve angle measures D. reflect across the 2004-01-04-01-00_files/i0150000.jpg-axis

To divide the given polynomial by x + 2, use polynomial long division, which involves dividing the leading term, multiplying the divisor, subtracting, and repeating the process until all dividend terms are addressed.

To divide the polynomial -2x^3 - 5x^2 + 4x + 2 by x + 2, we can use the process of polynomial long division. This method is similar to long division with numbers, where we divide, multiply, subtract, bring down the next term, and repeat the process until we have gone through all terms of the dividend.

The process would look like this:

The final result would be the quotient of the division, which may or may not have a remainder.

Answer:

Option 3 - [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.

Step-by-step explanation:

To find : Which statement is true?

Solution :

As the function defined in all statement is logarithmic function.

So, The definition of logarithmic function is defined as

[tex]y=\log_bx\Rightarrow b^y=x[/tex] where, b>0 and b ≠ 1.

Now, The following statement

1) [tex]y=\log_{10}x[/tex] is not a logarithmic function because the base is greater than 0.

The statement is False as by definition, the base of a log must be greater than zero but cannot equal one.

2) [tex]y=\log_{\sqrt3}x[/tex] is not a logarithmic function because the base is a square root.

The statement is False as by definition, the base [tex]\sqrt3[/tex]  is a positive number not equal to one.

3) [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.

The statement is True as by definition log cannot have a base of one.

4)  [tex]y=\log_{\frac{3}{4}}x[/tex] is not a logarithmic function because the base is a fraction.

The statement is False, as 3/4 is a legitimate base, just like any other positive number other than one.

Therefore, Option 3 is true.

Answer:

C

Step-by-step explanation:

Answer:

The area if this figure is 35cm2

Step-by-step explanation:

Answer:

She gave out a total of 250 fliers and 99 of them were given out Wednesday. The fraction for that would be 99/250.

Step-by-step explanation:

Consider the provided information.

She gave out 85 fliers on Monday 66 fliers on Tuesday, and 99 fliers on Wednesday.

Now, calculate the total number of fliers she give:

She give 250 fliers in total.

We need to find the fraction of the fliers she give out on Wednesday.

On Wednesday she give 99 fliers and total she give 250 fliers.

99/250

Hence, she give out 99/250 fraction of fliers on Wednesday.

Answer: The required function formula is,

S(t) = 2 - 0.25 t

Step-by-step explanation:

Here, the initial thickness of the ice sheet = 2 meters,

After 3 weeks, the thickness of ice sheet = 1.25 meters

Total changes in the thickness in 3 weeks = 2 - 1.25 = 0.75 meters,

⇒ Total changes in the thickness in 1 weeks = 0.75/3 = 0.25 meters,

Since, the ice is melting with the constant rate.

⇒ The rate of ice decreasing = 0.25 meters per week.

⇒ Total changes in t weeks = 0.25 t meters

The new thickness of ice after t weeks = Initial thickness - Total changes in t weeks.

⇒ S(t) = 2 - 0.25 t

Which is the required function's formula.

The function's formula for the ice sheet's thickness as a function of time is S(t) = -0.25t + 2.

To write the function's formula, we can use the slope-intercept form of a linear equation, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope represents the rate at which the ice thickness decreases over time. From the given information, we know that the thickness decreases by 0.75 meters over 3 weeks. Therefore, the slope is -0.75/3 = -0.25 meters per week.

Since the ice thickness is 2 meters in the beginning, the initial point on the graph is (0, 2). Using the slope-intercept form, we can write the formula for the ice sheet's thickness as a function of time as:

S(t) = -0.25t + 2

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Answer:

a x n

Step-by-step explanation:

There are a pounds in n identical boxes. That means you would have to multiply to get the answer.

Answer : Surface area of pyramid = 4406832 square cm.

Explanation :

Since we have given that

Side of square base = 1212 cm

Slant height of pyramid = 1818 cm

As we know that ,

[tex]\text{Surface area of pyramid }=\frac{1}{2}\times perimeter\times \text{ slant height}[/tex]

[tex]\text{ Since, perimeter of square }=4\times side\\=4\times 1212\\=4848 cm[/tex]

Now,

[tex]\text{ Surface area of pyramid }= \frac{1}{2}\times 4848\times 1818\\\\\text{ Surface area of pyramid }=4406832\text{ square cm}[/tex]

Hence, surface area of pyramid = 4406832 square cm.

There are 9 ways to choose eight coins from a piggy bank.

Total number of ways =

(Combinations of 8 pennies) + (Combinations of 7 pennies and 1 nickel) + ... + (Combinations of 0 pennies and 8 nickels)

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9 ways

x = sqrt(17^2 + 15^2)

x = 8

 missing side = 8

Answer:

it is 16

Step-by-step explanation:

Answer:

The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

If np >= 15 and n(1-p) >= 15

Can be approximated to the normal distribution, with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

So

The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The area of a circle is calculated with the formula A = πr², where pi is the mathematical constant approximately equal to 3.14159 and r represents the circle's radius. Considering significant figures is crucial for maintaining precision, as demonstrated in rounding the calculated area of a circle with radius 1.2 m to 4.5 m², based on the initial data's precision.

The area of a circle is calculated using the formula A = πr², where π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. When calculating the area with a given radius, it's important to consider the significance of figures in your final answer. For instance, if a circle's radius is given as 1.2 meters (with two significant figures), and you calculate the area to be 4.5238934 square meters using a detailed value of pi, you need to round your final answer to maintain the precision of your initial data, resulting in an area of 4.5 m².

It's also valuable to note how ancient civilizations, like the Greeks, approximated mathematics related to circles and how such estimations have evolved into our modern understanding, where the concept of significant figures plays a critical role in ensuring accuracy across varying fields of study and applications.

The sequence 1/4, 1/2, 3/4 increases by 1/4 for each subsequent term, defining it as an arithmetic sequence with a common difference of 1/4.

To find a rule for the sequence 1/4, 1/2, 3/4, we can examine the pattern and observe that the sequence consists of fractions that increase by 1/4 each step. Starting with 1/4, when we add 1/4, we get 1/2, and adding another 1/4 to 1/2 gives us 3/4. So the rule of the sequence can be written as 'start at 1/4 and add 1/4 each step'. This pattern is an arithmetic sequence with a common difference of 1/4.

Final answer:

The inequality to represent the number of days, d, Kyle can rent equipment with $121 is 25 + 13d ≤ 121. After solving, the result is d ≤ 7, meaning Kyle can rent the equipment for at most 7 days.

Explanation:

To represent the number of days, d, that Kyle can rent equipment given he has $121, we set up an inequality taking into account the flat rate and the daily insurance cost. The equipment rental company charges a flat rate of $25 plus $13 per day for insurance. Therefore, the cost for d days would be $25 + $13d. Since Kyle has $121, we can write the inequality as:

25 + 13d ≤ 121.

This inequality shows that the total cost of renting the equipment for d days, which includes the flat rate and the per-day insurance cost, must be less than or equal to the amount Kyle has.

To solve for d, subtract 25 from both sides:

13d ≤ 121 - 25

13d ≤ 96

Now, divide both sides by 13 to find the maximum number of days Kyle can rent the equipment:

d ≤ 96 / 13

d ≤ 7

Thus, Kyle can rent the equipment for at most 7 days.

Kyle can rent equipment for at most 7 days with $121, considering a flat rate of $25 and a $13 per day insurance charge, as represented by the inequality 25 + 13d ≤ 121.

To find the inequality that represents the number of days, d, for which Kyle can rent equipment given that he has $121, we need to consider both the flat rate and the per day insurance charge.

The flat rate for renting equipment is $25, and the daily insurance charge is $13 per day. So, the cost for d days would be the flat rate plus the daily charge times the number of days, which can be represented by the following equation:

Cost = Flat rate + (Insurance charge per day × Number of days)

Cost = 25 + 13d

Since Kyle only has $121, he can spend up to that amount. Therefore, the inequality would be:

25 + 13d ≤ 121

To solve for d:

13d ≤ 121 - 25

13d ≤ 96

d ≤ 96/13

≤ 7.38

Since Kyle can't rent equipment for a fraction of a day, we take the whole number part of the division result. This means that Kyle can rent the equipment for at most 7 days.