what is the slope of the line?

A. 0

B. 6

C. 9

D. undefined

Sum of 3√2 and 4√2 is an irrational number.

" Irrational numbers are those numbers which cannot be written in fraction or rational form."

According to the question,

Suppose 3√2 + 4√2 be a rational number.

which can be expressed in form of (p / q) form such that 'q' does not divides 'p'

   3√2 + 4√2 = (p / q)

⇒ 7√2 = ( p / q)

Squaring both the sides we get,

  49 × 2 = ( p² / q² )

⇒ 2 ×(49q²) =  p²  

⇒ p is an even number

⇒p = 2k , k≠0

Therefore,

2 × ( 49q²) = (2k)²

⇒2×(49q²) = 4k²

⇒q² = (2k² / 49)

Both p and q are even which implies 'q' divides 'p'.

It is contradictory to our supposition,

Therefore, 3√2 + 4√2  is an irrational number.

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Given is the shape of a rectangular prism. All the parallel edges are diagonally opposite to each other, it means that parallel edges directly face opposite to each other and they do not have any common vertex. So we have two sets of parallel edges that are {AB, CD, EF, and GH} and {AD, BC, EH, and FG}.

It says to select all edges from the given options that are parallel to AD.

Given options are :- 1. DH, 2. BC, 3. EF, 4. FG.

We have AD ║ BC ║ EH ║ FG.

Hence, only BC and FG are the final answers.

When an expression or a number is raised to the negative exponent, you have to reciprocate the expression or the number.

In this problem, the expression is raised to the power of -2

Therefore, the expression would become like this after reciprocating:

1/ (3x^2) ^2

Simplifying the expression:

1/ 9x^4

The answer is 4x to the 10th power

To find the numbers, we can set up a system of equations and solve it using substitution.

To find the numbers, we can set up a system of equations based on the given information. Let's call the bigger number 'x' and the smaller number 'y'. We know that x is bigger than y by 406, so we can write the equation x = y + 406. We also know that when x is divided by y, the quotient is 3 and the remainder is 66. This can be expressed as the equation x = 3y + 66.

We can solve this system of equations by substitution. First, we substitute the expression for x from the first equation into the second equation:

3y + 66 = y + 406

Next, we can subtract y from both sides of the equation:

2y + 66 = 406

Then, we subtract 66 from both sides:

2y = 340

Finally, we divide both sides by 2 to solve for y:

y = 170

Now we can substitute the value of y back into the first equation to find x:

x = 170 + 406 = 576

Therefore, the numbers are 576 and 170.

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Answer:

18.9 years.

Step-by-step explanation:

We have been given that Felicia put $85 into a CD that pays 3.8% interest.

We know that rule of 72 gives us the time it will take an amount to be double, when we divide 72 by the interest rate.

Upon dividing 72 by 3.8 we will get,

[tex]\text{Time it will take to double Felicia's money}=\frac{72}{3.8}[/tex]

[tex]\text{Time it will take to double Felicia's money}=18.9473684\approx 18.9[/tex]

Therefore, it will take approximately 18.9 years for Felicia's money to double.

Answer:

Ricardo is wrong.

Step-by-step explanation:

Ricardo's recipe for 4 loaves of bread requires 2/3 cup of olive oil.

Now we are given that he wants to make 1 loaf.

So, 4 loaves requires cup of oil = [tex]\frac{2}{3}[/tex]

So, 1 loaf requires cup of oil =  [tex]\frac{\frac{2}{3}}{4}[/tex]

                                               =  [tex]\frac{2}{12}[/tex]

                                               =  [tex]\frac{1}{6}[/tex]

Thus he requires 1/6 cup of oil to make 1 loaf .

While he decided he needs 1/4 cups .

So, Ricardo is wrong

Answer:

6 boys

Step-by-step explanation:

if all the boys(x) were at the meeting but only half the (y), you would have two equations : x+y=26 and x+y/2 = 16. Solving the system gives you 6 boys 20 girls.

Answer:

Length = 9 cm, width = 6 cm

Step-by-step explanation:

If the length of the rectangle is labeled as length equal to 36 cm, and the width is labeled as width equal to 24 cm.

Length = 36cm

Width = 24cm

One fourth the current size of the rectangle will be;

New length= 1/4×36 = 9cm

New width = 1/4 × 24 = 6cm

The new dimension of the poster is therefore 9cm×6cm

Length = 9cm

Width = 6cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total pound of candy with Noah = [tex] \frac{1}{2} [/tex]

Total pound of candy eaten by his friends = [tex] \frac{3}{8} [/tex] of [tex] \frac{1}{2} [/tex]

= [tex] \frac{3}{8} \times \frac{1}{2} [/tex]

= [tex] \frac{3}{16} [/tex]

Pound of candy left with Noah = [tex] \frac{1}{2} - \frac{3}{16} [/tex]

= [tex] \frac{8-3}{16} [/tex]

= [tex] \frac{5}{16} [/tex] pound

Therefore, [tex] \frac{5}{16} [/tex] pound of candy is left with Noah.

Answer: the same as the other person is righti

Step-by-step explanation:

Final answer:

The average rate of change of the function f(x) from x = -3 to x = 1 is -0.625, calculated using the values of f(-3) and f(1) in the average rate of change formula.

Explanation:

The average rate of change of a function f(x) from x = a to x = b is computed by finding the difference in function values at these points and dividing by the difference in x values, following the formula (f(b) - f(a)) / (b - a). To apply this to the quadratic function [tex]f(x) = -1/2(x + 2)^2 + 5[/tex] from x = -3 to x = 1, we evaluate f at both -3 and 1 and use these results in our formula.

First, find f(-3):
[tex]f(-3) = -1/2(-3 + 2)^2 + 5 = 4[/tex]

Then, find f(1):
[tex]f(1) = -1/2(1 + 2)^2 + 5 = 1.5[/tex]

Now, we calculate the average rate of change:
(f(1) - f(-3)) / (1 - (-3)) = (1.5 - 4) / (1 - (-3)) = -2.5 / 4 = -0.625

Therefore, the average rate of change of the function f(x) from x = -3 to x = 1 is -0.625.