1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions?
f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value.

2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions?
f is continuous on [ 4 , 5 ], takes on no rational values.

3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions?
f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.

Answer:

-5, 4

Step-by-step explanation:

the solutions to the equation [tex]3(x - 4)(x + 5) = 0[/tex]

To solve for x we set each factor =0 and solve for x

[tex]3(x-4)=0[/tex]

divide each term by 3

[tex](x-4)=0[/tex]

Add 4 on both sides

[tex]x=4[/tex]

[tex]x+5=0[/tex]

Subtract 5 on both sides

[tex]x=-5[/tex]

So x values are -5 and 4

Answer:

A line that rises from left to right has a positive slope

Step-by-step explanation:

Verify each statement

case A) A horizontal line has no slope

The statement is False

Because a horizontal line has a slope equal to zero

case B) A vertical line has a slope of zero

The statement is False

Because a vertical line has a undefined slope

case C) A line that rises from left to right has a positive slope

The statement is True

case D) A line that falls right to left has a negative slope

The statement is False

Because a is a positive slope

Answer:

5000

Step-by-step explanation:

400 ÷ 4% = 5000

Part 1)

In this problem we know that

[tex]4y\°+112\°=180\°[/tex] ------> by supplementary angles

solve for y

[tex]4y\°=180\°-112\°[/tex]

[tex]y=68\°/4[/tex]

[tex]y=17\°[/tex]

Part 2)

In this problem we know that

[tex]7x+7=112\°[/tex] ------> by vertical angles

solve for x

[tex]7x=112\°-7\°[/tex]

[tex]x=105\°/7[/tex]

[tex]x=15\°[/tex]

therefore

the answer is the option A

[tex]x=15\°, y=17\°[/tex]

Answer:

absolute value is 6

Answer: The fraction of pounds of fruits over total pounds of fruits and vegetables is given by

[tex]\frac{25125}{66724}[/tex]

Step-by-step explanation:

Since we have given that

Total amount of vegetables = 208 pounds

Total amount of fruits is given by

[tex]125\frac{5}{8}\text{ pounds}[/tex]

Total amount of fruits and vegetables is given by

[tex]208+125\frac{5}{8}\\\\=208+\frac{1005}{8}\\\\=\frac{1664+1005}{8}\\\\=\frac{2669}{8}\\\\=333.625\text{ pounds }[/tex]

So, we need to find the fraction of pounds of fruits over the total pounds of fruit and vegetables :

[tex]\frac{\text{Pounds of fruits }}{\text{ total pounds of fruits and vegetables}}\\\\=\frac{\frac{1005}{8}}{333.62}\\\\=\frac{1005}{8\times 333.62}\\\\=\frac{1005}{2668.96}=\frac{25125}{66724}[/tex]

The fraction of the total pounds of fruit and vegetables that fruits represent is approximately 0.377, or 37.7%.

To find out what fraction the pounds of fruits represent out of the total pounds of fruits and vegetables, we first need to calculate the total pounds of fruits and vegetables consumed. This is found by adding the pounds of vegetables (208) to the pounds of fruits (125 5/8). So, 208 + 125 5/8 = 333 5/8 pounds.

Now, to determine the fraction, we take the pounds of fruits and divide by the total. Hence, the fraction is given by 125 5/8 ÷ 333 5/8. To divide fractions, we multiply by the reciprocal of the divisor, which gives us (125 5/8) * (8/333) = 0.377 (rounded to three decimal places).

Therefore, fruits represent approximately 0.377, or 37.7% of the total pounds of fruits and vegetables consumed.

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Final answer:

By using the counting principle and multiplying the choices for ice cream flavors (3) by the choices for toppings (4), we find there are 12 possible sundae combinations.

Explanation:

To determine the number of possible sundae combinations with the given choices, we can use the counting principle. We multiply the number of options for each category. In this case, there are three choices for ice cream flavors (chocolate, vanilla, and strawberry) and four choices for toppings (chocolate syrup, sprinkles, caramel, and whipped cream).

Since a sundae consists of one ice cream flavor and one topping, we simply multiply the number of options for ice cream by the number of options for toppings.

3 ice cream flavors × 4 toppings = 12 possible combinations.

Therefore, there are 12 unique sundae combinations a customer can choose from.

Answer:

x=8 or just x+2=10

Step-by-step explanation:

if you wanted to know this without absolute value, its still x+2=10. if you wanna know what 'x' is, its 8.

Answer:

[tex]F(64)=2[/tex]

Step-by-step explanation:

Given the funtion:

[tex]F(x)=log_8(64)[/tex]

We need to find the value of the function at x=64:

[tex]F(64)=log_8(64)= z[/tex]

Where z is the value we are trying to find. In order to find z, let's use the definition of the base of a log:

[tex]log_xy=z\Rightarrow x^z=y[/tex]

So:

[tex]8^z=64[/tex]

Express [tex]8^z[/tex] as:

[tex]2^{3z}[/tex]

And express 64 as:

[tex]2^6[/tex]

Which leads to:

[tex]2^{3z}=2^6[/tex]

Equate exponents of 2 on both sides:

[tex]3z=6[/tex]

Solving for z:

[tex]z=\frac{6}{3} =2[/tex]

Therefore:

[tex]F(64)=log_8(64)= z=2[/tex]

The complement of set A with respect to the universal set U (A') is {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}, which contains all elements in U that are not in set A.

The student is asked to use the roster method to write the set A', which represents the complement of set A with respect to the universal set U. The set A' consists of all elements in the universal set U that are not in set A.

First, we list all the elements of the universal set U, which are {21, 22, 23, ..., 40}. Set A contains {21, 22, 23, 24, 25}. To find A', we remove the elements of A from U, resulting in A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}.

Final answer:

The set A' includes all numbers from 26 to 40 in the universal set U, which are not included in set A.

Explanation:

To find the set A' or the complement of set A in the universal set U, we need to list all the elements in U that are not in A. Given that the universal set U consists of the numbers 21 through 40, and the set A includes the numbers 21, 22, 23, 24, and 25, we can determine A' by subtracting these from U.

The roster method simply lists out all of the elements. Doing so for A' yields the following:

A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}

These are all the numbers in U that are not in A.

Answer:

Option C

Step-by-step explanation:

A function is a relation that does not contain two pairs with same first component.

Option A

{(-1,2),(3,-2),(0,1),(5,2)}  is a function, since there are no two pairs with the same first component.

option B

{(-1,2),(3,2),(-2,2),(0,2)} is a function, since there are no two pairs with the same first component.

option C

{(-1,2),(3,-2),(0,1),(3,5)} is not a function, since there are two pairs with the same first component i.e, 3

OptionD

{(-1,2),(2,3),(3,-2),(-2,0)} is a function, since there are no two pairs with the same first component.

So, {(-1,2),(3,-2),(0,1),(3,5)} is the required  answer.

To find the length of a side of a square with an area of 80 square inches, we take the square root of the area. This results in each side of the square being approximately 8.944 inches long.

The question is asking to find the length of a side of a square that has an area of 80 square inches. In geometry, the area of a square is calculated by squaring the length of one side. Therefore, to find the length of a side when you know the area, you need to take the square root of the area.

So, in this case, we take the square root of 80. Using a calculator, this results in approximately 8.944 inches. Therefore, each side of the square is about 8.944 inches long.

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