The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

The required three consecutive even integers are 56, 58, and 60.

Given that,
The sum of three consecutive even integers is 174 what are integers is to be determined?

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
Let the three even integers be 2x, 2x+ 2 and 2x + 4
Now, accoding to the question,

2x + 2x + 2 + 2x + 4 = 174
6x + 6 = 174
x = 28

Now,
2x =28 * 2 = 56

2x + 2 = 56 + 2 = 58
2x + 4 = 56 + 4 = 60

Thus, the required three consecutive even integers are 56, 58, and 60.

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Answer:

C. 9

Step-by-step explanation:

Ron is five years older than twice his cousin's age. Lets assume that Pat's age is 'x' years.

So Ron's age is [tex]2\times x+5=2x+5[/tex]

The question says:

[tex]x+2x+5<35[/tex]

[tex]3x+5<35[/tex]

[tex]3x<35-5[/tex]

[tex]3x<30[/tex]

[tex]x<10[/tex]

Pat's age [tex](x)[/tex] should be less than 10. Therefore, the greatest age (in integer) that Pat can be is 9 years.

Final answer:

The composition h = f о g is only guaranteed to be an odd function if both g and f are odd functions. If f is an even function or neither odd nor even, h will not necessarily be an odd function. The property of the composition depends on the nature of both functions involved.

Explanation:

Whether the composition of functions h = f о g is always an odd function when g is an odd function depends on the nature of f. If g(x) is an odd function, it follows that g(-x) = -g(x). However, for h to also be odd, f must satisfy the condition h(-x) = -h(x). This can only be the case if f is also an odd function.

If f were an even function, then f(g(-x)) = f(-g(x)) would equal f(g(x)) due to the even property of f. In this scenario, h would not be an odd function since h(-x) = f(g(-x)) = f(g(x)) = h(x), which violates the definition of an odd function.

When an odd function and an even function are multiplied, the result is an odd function, as exemplified by g(x) = x³ - 3x and h(x) = x². But when composing functions, the outer function's properties dominate the result. Therefore, the composition h = f о g can only be assured to be odd if f itself is odd.

The domain will consist of all non-negative real numbers (x ≥ 0).

And, the range will consist of all real numbers (-∞, +∞).

Given that;

The function is,

c (x) = 10x - 50

Now for the domain and range of the function c(x) = 10x - 50,

Since the domain refers to all the possible input values (x) for the function.

In this case, since c(x) represents the profit from selling candles, x would represent the number of candles sold.

The number of candles sold cannot be negative, as it wouldn't make sense to sell a negative number of candles.

So, the domain will consist of all non-negative real numbers (x ≥ 0).

And, The range refers to all the possible output values (c(x)) of the function.

In this case, c(x) represents the profit. The profit can be any real number because it can be positive, negative, or zero.

Therefore, the range will consist of all real numbers (-∞, +∞).

Thus, Domain: All non-negative real numbers (x ≥ 0).

Range: All real numbers (-∞, +∞).

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The required number, whose sum with its square is 210, is -15 and 14.

Given that,
The sum of a number and its square is 210. To determine the​ number(s).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number be x,
according to the question,
x + x² = 210
x² + x -210 = 0
x² + 15x - 14x  - 210 = 0
x(x + 15) -14 (x + 15) = 0
(x + 15)(x - 14) = 0
x = -15 and 14

Thus, the required number, whose sum with its square is 210, is -15 and 14.

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Approximately 99.73% of Jen's phone bills are between $49 to $103. This is calculated by transforming the prices into z-scores regarding the normal distribution and then checking these z-scores in a standard normal distribution table.

The problem is a question about the normal distribution. Using the properties of a normal distribution, we can solve it as follows:

In conclusion, about 99.73% of Jen's phone bills are between $49 and $103.

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99.74% of Jen's monthly phone bills are between $49 and $103.

To answer this question, we need to understand the properties of the normal distribution. For a normally distributed variable with a mean (μ) of $76 and a standard deviation (σ) of $9, we can use the Z-score formula:

[tex]Z = \frac{(X - \mu)}{\sigma}[/tex]

We now convert $49 and $103 to Z-scores:

For $49:

[tex]Z = \frac{(49 - 76)}{9} = -3[/tex]

2. For $103:

[tex]Z = \frac{(103 - 76)}{9} = 3[/tex]

Next, we use the Z-table to find the probabilities corresponding to these Z-scores:

For Z = -3, the probability is 0.0013 (or 0.13%)

For Z = 3, the probability is 0.9987 (or 99.87%)

To find the percentage of phone bills between $49 and $103, we subtract these values:

[tex]P(49 < X < 103) = 0.9987 - 0.0013 = 0.9974[/tex]

Finally, converting this to a percentage, we get:

[tex]0.9974 \times 100\% = 99.74\%[/tex]

Therefore, 99.74% of Jen's monthly phone bills are between $49 and $103.

divide 32 miles by 2 1/3 hours

32/2.33333 = 13.7143

 to nearest tenth = 13.7 miles per hour

Answer: [tex]13.7\text{ miles per hour}[/tex].

Step-by-step explanation:

Given : A snowmobile traveled 32 miles in [tex]2\dfrac{1}{3}[/tex] hours i.e.[tex]\dfrac{7}{3}[/tex] hours.

The distance is the product of the rate and the time.

i.e. The formula we use to find the average speed is given by :-

[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}\\\\\Rightarrow\ \text{Average Speed}=\dfrac{32}{\dfrac{7}{3}}=\dfrac{32\times3}{7}=13.7142857143\approx13.7\text{ miles per hour}[/tex]

Hence, the average speed of the snowmobile was [tex]13.7\text{ miles per hour}[/tex].

Answer:

the answer is the option C

[tex]KJ=3\sqrt{5}\ units[/tex]

Step-by-step explanation:

we know that

The triangle KMJ is a righ triangle

so

Applying the Pythagoras Theorem

[tex]KJ^{2}=KM^{2}+MJ^{2}[/tex]

in this problem we have

[tex]KM=6\ units[/tex]

[tex]MJ=3\ units[/tex]

substitute

[tex]KJ^{2}=6^{2}+3^{2}[/tex]

[tex]KJ^{2}=45[/tex]

[tex]KJ=\sqrt{45}=3\sqrt{5}\ units[/tex]

Answer: 32 quarts

Step-by-step explanation:

We know that there area 4 quarts in one gallon.

i.e.[tex]1\text{ gallon}=4\text{ quarts}[/tex]

Now, to convert 8 gallons into quart we need to apply unitary method.

Using unitary method , to convert 8 gallons into quart , multiply 8 to 4 , we get

[tex]8\text{ gallon}=8\times4\text{ quarts}\\\\\Rightarrow\ 8\text{ gallon}=32\text{ quarts}[/tex]

Hence there are 32 quarts in 8 gallons.

There are 32 quarts in 8 gallons of quantity.

The given quantity is 8 gallons.

We know that, 1 gallon = 4 quarts

Here, 8 gallons = 8×4

= 32 quarts

Therefore, there are 32 quarts in 8 gallons of quantity.

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To find 60% off of $33.00, you multiply 33 by 60, then divide the product by 100. The result is $19.80, which is the discount amount. So after the discount, the cost is $13.20.

To find out what 60% off of $33.00 is, you need to multiply 33.00 by 60 and then divide that product by 100, as percentages are always out of 100. Here's the process:

So, 60% off of $33.00 equals $19.80. Hence, after a 60% discount, you would pay $13.20 (33 - 19.80), as this is the remaining cost after the discount has been applied.

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