The measure of the largest scale of a triangle is 40o more than the measure of the smallest angle, and the measure of the remaining angle is 20o more than the measure of the smallest angle. Find the measure of each angle.

The value of the expression [tex]\sqrt[4]{a}^3[/tex] when evaluated is [tex]a^\frac34[/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]\sqrt[4]{a}^3[/tex]

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

[tex]\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}[/tex]

Apply the exponent rule of indices

[tex]\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14[/tex]

Apply the power rule of indices

[tex]\sqrt[4]{a}^3 = a^\frac34[/tex]

Hence, the expression [tex]\sqrt[4]{a}^3[/tex] when evaluated is [tex]a^\frac34[/tex]

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The converse of the parallelogram angle theorem is proved.

The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.

Here we are given that  LM ≅ ON and  LO ≅ MN

Here we have also know that ∠LNO and ∠NLM are alternative and interior angles

Then according to the reflexive property, it can be written as

=> LN ≅ LN

Then as per the SSS similarity the given triangle is written as,

ΔLNO ≅ ΔNLM

Here we have also it can be written as ∠OLN ≅ ∠MNL and  ∠LNO ≅ ∠NLM

Then it can be written as LM || ON and  LO || MN

Then the LMNO is a parallelogram

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The slope of line WX is 2.Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which means we flip the fraction and change its sign:

slope of WX = -1 / (-1/2) = 2.

a) To find the slope of the line RK, we can use the formula:

slope = (change in y) / (change in x)

Given the points R(6, 9) and K(-6, 15), we can calculate the change in y and change in x:

change in y = 15 - 9 = 6

change in x = -6 - 6 = -12

Plugging these values into the slope formula:

slope = (6) / (-12) = -1/2

Therefore, the slope of line RK is -1/2.

b) Since line VB is parallel to line RK, it will have the same slope as RK. Therefore, the slope of line VB is also -1/2.

c) To find the slope of line WX, which is perpendicular to RK, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which is 2.

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The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

The correct ordered pairs represented in the table are (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).

The given table represents a function f(c) where c represents the quantity of furniture and f(c) represents the per unit cost in hundreds of dollars. We need to determine the correct ordered pairs based on the given information.

From the table, we can see that the values of c increase by 1 each time, starting from 1 and going up to 5. Similarly, the values of f(c) represent the square of the corresponding value of c. For example, f(1) = 1, f(2) = 4, f(3) = 9, and so on.

Based on this pattern, we can determine the correct ordered pairs:

(1, 1) corresponds to c = 1 and f(c) = 1

(2, 4) corresponds to c = 2 and f(c) = 4

(3, 9) corresponds to c = 3 and f(c) = 9

(4, 16) corresponds to c = 4 and f(c) = 16

(5, 25) corresponds to c = 5 and f(c) = 25

Therefore, the correct ordered pairs represented in the table are (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).

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