What is the measure of angle AXB

Answer: Explanation is given below.

Step-by-step explanation: Given that Patti is using mental mathematics to evaluate the expression (70+12.8+30)+6.1 and recognises that it will be easier to simplify if she can combined 70 and 30 in the beginning. We are to explain the way in which the properties of operation allow Patti to take that approach.

We will be using the following associative property of real numbers:

[tex](a+b+c)+d=(a+c)+(b+d).[/tex]

Therefore, the simplification is as follows:

[tex](70+12.8+30)+6.1\\\\=(70+30)+(12.8+6.1)\\\\=100+18.9\\\\=118.9.[/tex]

Hence explained.

Answer:

She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1

( D )

7% = 0.07

14.50 *1.07 =  15.52 new price

We need to find how much longer is the baby alligator compared to a baby.

The baby alligator is [tex]\dfrac{45}{8}[/tex] times longer than the baby.

The baby alligator is 3/4 ft long.

The baby is 2/15 ft long.

According to the question

[tex]\dfrac{3}{4}=\dfrac{2}{15}x[/tex]

The value of x will give us how many times is the baby alligator longer by

[tex]x=\dfrac{\dfrac{3}{4}}{\dfrac{2}{15}}\\\Rightarrow x=\dfrac{3\times 15}{4\times 2}\\\Rightarrow x=\dfrac{45}{8}[/tex]

So, the baby alligator is [tex]\dfrac{45}{8}[/tex] times longer than the baby.

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Answer:

This is an algebraic expression which means that 12 multiplied by the value of a variable "f", plus 24 would give an integer.

Step-by-step explanation:

This expression can be solved when the value of f is known. Thus its solution is dependent on the known value of "f".

So, assuming the value of f is 2, then the answer would have been 48.

The gcf for the numbers 28, 56 and 84 is 28

Since

28: 1, 2, 4, 7, 14, 28

56: 1, 2, 4, 7, 8, 14, 28, 56

84: 1,2,3,4,6,7,12,14,21,28,42,84

Since the biggest number they all have is 14 so the gcf is 14.

The gcf for the numbers 30, 45, and 75 is 15

30: 1,2,3,5,6,10,15,30

45: 1,3,5,9,15,45

75: 1,3,5,15,25,75

Since the biggest number they all have is 15 so the gcf is 15.

Hope this helped

The question is about using the Pythagorean Theorem to calculate the length of the hypotenuse of a right triangle. It also asks how to calculate the area of a square when the hypotenuse of the right triangle is one of its sides. The hypotenuse's length would be useful to determine the square's area, as the square's area is calculated as the square of the length of one side.

The subject of this question is Mathematics, and it is appropriate for a High School level student. The question is discussing a scenario where a square has the hypotenuse of a right triangle as one of its sides, and the student is asked to estimate the value of the length of the hypotenuse and calculate the area of the square.

To solve this problem, we will use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (let's call it 'c') is equal to the sum of the squares of the lengths of the other two sides (let's call them 'a' and 'b'). In other words, c² = a² + b². The length of the hypotenuse is the square root of this sum, √(a² + b²).

Since we aren't given specific lengths for the sides of the triangle, I cannot provide exact values. However, let's say that the length of the hypotenuse is 'd', then the area of the square, which is calculated as the length of one side squared (d²) would be equal to the given value.

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Matt needs to sell approximately 28 books to make $30 for the week.

To find the number of books Matt needs to sell to make $30 for the week, we need to use the given information that Matt gets $6 for selling 9 books and $9 for selling 11 books.

Let's first find the amount of money Matt makes for each book:

For 9 books, Matt makes $6, so he makes $\frac{6}{9} = \frac{2}{3}$ dollars per book.

For 11 books, Matt makes $9, so he makes $\frac{9}{11}$ dollars per book.

Now, we can set up an equation to find the number of books Matt needs to sell to make $30:

2/3 x + 9/11 x=30

where (x) is the number of books Matt needs to sell.

Simplifying the equation, we get:

x = 28

Therefore, Matt needs to sell approximately 28 books to make $30 for the week. Since he cannot sell a fraction of a book, he would need to sell either 28 or 29 books to make $30.

The required number to represent the situation is 67/24.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

Given that,

The cloth required for jacket is 1(⁵/₈) = 13/8 yards.

Then the remaining cloth for the three other items = 10 - 13/8 = 67/8 yards.

Now, the cloth for each of the items is calculated by taking the ratio as,

(67/8)/3

= 67/24

Hence, the yards of cloth available for each of the item is given as 67/24 yards.

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Therefore, since the slope of f(x) is defined and g(x) has an undefined slope, the correct option is: d) The function f(x) has a larger slope.

To determine the slopes of the functions f(x) and g(x), we need to calculate the rate of change or the slope of each function.

The slope of a function represents how much the output (y-value) changes for a given change in the input (x-value).

For function f(x), the rate of change can be calculated as follows:

[tex]\[ \text{Slope of } f(x) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{200 \text{ pages}}{40 \text{ minutes}} = 5 \text{ pages/minute} \][/tex]

Now, let's calculate the slope for function g(x) using the given data points:

[tex]\[ \text{Slope of } g(x) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{28 - (-8)}{4 - 4} = \frac{36}{0} \][/tex]

As the denominator is zero, the slope for g(x) is undefined.

Order the numbers from least to greatest.

95, 85, 75, 90, 70, 95, 85, 80, 75, 95, 70, 80, 65 becomes

65, 70, 70, 75, 75, 80, 80, 85, 85, 90, 95, 95, 95

The Median is the number in the middle:

80 is your answer

hope this helps

Answer:  Fourth option is correct.

Step-by-step explanation:

Since we have given that

[tex]x+4y=25.50------------------(1)\\\\3x+2y=24.00-----------------------(2)[/tex]

Here, x is the number of strawberry smoothies.

and y is the number of protein shakes.

So, using elimination method, we get that,

Multiplying 2 by eq(2), we get that

6x+4y=48---------------(3)

From eq(1) and (3), we have

[tex]x+4y=25.50\\\\6x+4y=48\\\\-----------------------------------\\\\-5x=-22.5\\\\x=\dfrac{22.5}{5}\\\\x=4.5[/tex]

Put the value of x in eq(1), we get that

[tex]4.50+4y=25.50\\\\4y=25.50-4.50\\\\4y=21\\\\y=\dfrac{21}{4}\\\\y=5.25[/tex]

Hence, the price of protein shake is $5.25.

Thus, Fourth option is correct.

Answer:

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