taking a pretest and am very confused, please help !

The circle that passes through the vertices of triangle ΔABC (A, B, C) is the

circumscribing circle of triangle ΔABC.

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

Reasons:

The given parameters are;

Side length of isosceles triangle ΔABC; \(\overline{AB}\) = \(\overline{AC}\) = 3·√6

Radius of circle tangent to \(\overline{AB}\) at B and \(\overline{AC}\) at C = 5·√2

Required:

Area of the circle that passes through vertices A, B, and C

Solution:

Angle ∠BAO is given as follows;

\(\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}\)

Therefore;

\(\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\)

\(\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }\)

∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')

\(\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}\)

Therefore;

\(\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\)

From sine rule, we have;

\(\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}\)

Which gives;

\(\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}\)

Using a graphing calculator, we get;

\(\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}\)

The radius of the circumscribing circle \(\overline{BO'}\) = √(26)

Therefore, area of the circumscribing circle, \(A_{O'}\) = π·(√(26))² = 26·π

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

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The possible question options obtained from a similar question online are;

(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π

Answer:

D.18

Step-by-step explanation:

6-x=-12

-x=-12-6

-x=-18   divide both sides by -1

x=18

Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

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Explanation:

Let's consider the expression (x-y)^2. It expands out to x^2-2xy+y^2. The terms are:

Each of those terms either has a single variable with an exponent of 2, or has the exponents add to 2. Think of 2xy as 2x^1y^1.

In short, this means that the degree of each monomial term is 2.

----------

Now consider (x-y)^3. It expands out into x^3-3x^2y+3xy^2+y^3.

We have terms that either have a single variable and the exponent is 3, or the exponents add to 3. The degree of each term is 3.

----------

This pattern continues.

In general, for (x-y)^n, where n is any positive whole number, the degree of each term in the expansion is n. If you picked any term, added the exponents, then the exponents will add to n.

Answer:

35

Step-by-step explanation:

47-12=35

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer:

Replace one equation with itself where the same quantity is added to both sides

Yes

Yes, the systems are equivalent. In other words, they have the same solution.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The Systems of equation given for A and B:

A: x−4y=1

5x+6y=−5

B: x=1+4y

5x+6y=−5

So, we get System B from System A by the following step;

A; Replace one equation with itself where the same quantity is added to both sides.

Hence, Yes the systems are equivalent. In other words, they have the same solution.

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ANSWER

EXPLANATION

Slope is defined as the numerical value that determines the steepness of a line

Mathematically, slope is expressed below as

Based on the model, a player with 30 assists will have approximately 46.2 points.

a. The slope of a line in a scatter plot represents the relationship between the two variables being plotted. In this case, the slope of the model y = 1.5x + 1.2 is 1.5, which means that for every 1 unit increase in the number of assists, there is a corresponding 1.5 unit increase in the number of points.

b. To find the number of points for a player with 30 assists, we can substitute x = 30 into the model equation to get:

y = 1.5x + 1.2

= 1.5(30) + 1.2

= 45 + 1.2

= 46.2

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Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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Answer:

true

Step-by-step explanation:

im really not sure. it just sounds true

Answer:

false

Step-by-step explanation:

the x-axis is the indipendent variable

The volume of the pyramid is 576 cubic inches.

To find the volume of a square base pyramid, you can use the formula:

Volume = (1/3) x base area x height

In this case, the side of the square base is given as 12 inches, and the height is given as 12.5 inches.

First, calculate the base area of the pyramid:

Base area = side²

= 12²

= 144 square inches

Now, substitute the values into the volume formula:

Volume = (1/3) x 144 x 12.5

Volume = 576 cubic inches

Therefore, the volume of the pyramid is 576 cubic inches.

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A. the identified base and corresponding height in figure A are 3 in. and 6 in. respectively.

The area is 9 sq. in.

B. the identified base and corresponding height in figure B are 6 cm and 4 cm in. respectively.

The area is 12 sq. cm

Recall:

The formula for area is given as: A = 1/2(base)(height)

The base of a triangle will be perpendicular to its height.

A. In the figure given in A, here, the dimensions are:

height = 6 inches

base = 3 inches

Area = 1/2(base)(height)

Area = 1/2(3)(6)

Area = 9 sq. in.

B. In the figure given in B, here, the dimensions are:

height = 4 cm

base = 6 cm

Area = 1/2(base)(height)

Area = 1/2(6)(4)

Area = 12 sq. cm

In summary,

A. the identified base and corresponding height in figure A are 3 in. and 6 in. respectively.

The area is 9 sq. in.

B. the identified base and corresponding height in figure B are 6 cm and 4 cm in. respectively.

The area is 12 sq. cm

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-8/27

Step-by-step explanation:

Just multiply this fraction by itself 3 times and you will get the answer then simplify.

Answer: The first four terms are 33/4, 63/8, 15/2, and 57/8.

Step-by-step explanation: To make it easier, turn 8 1/4 into an improper fraction: 33/4. 33/4=66/8. Because the denominator is the same, it’s easier to subtract.

66/8 - 3/8 = 63/8

63/8 - 3/8 = 60/8

60/8 - 3/8 = 57/8

The first 4 terms in the sequence are 66/8, 63/8, 60/8, and 57/8. But we’re not done b/c we need to simplify. That means the first four terms are 33/4, 63/8, 15/2, and 57/8.

The length of unknown side x is 58.

The correct answer is option D.

To find the unknown side length, x, in a right triangle with the base measuring 42 and the perpendicular measuring 40, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let x be the hypotenuse. Applying the Pythagorean theorem, we have:

\(x^2 = 42^2 + 40^2\)

Simplifying:

\(x^2\) = 1764 + 1600

\(x^2\)= 3364

Taking the square root of both sides to solve for x:

x = \(\sqrt{3364}\)

Simplifying the square root:

x = (\(\sqrt{4 * 841)}\)

Since 841 is a perfect square (\(29^2\)), we can further simplify:

x = 2 * 29

x = 58

Therefore, the unknown side length, x, is equal to 58.

From the options provided the correct option is D.

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The values of the missing terms are 1) 24 and 2) 1.6.

Given are two similar figures, we need to find the value of x,

According to the definition of similar figures, the ratios of the corresponding sides are equal,

So,

1) GE / EF = RS / TR

5/6 = 20/x

5x = 120

x = 24

2) JH / LK = WX / ZY

3.84 / 2.04 = 3.2 / x

3.84x = 2.04 × 3.2

3.84x = 6.528

x = 1.7

Hence, the values of the missing terms are 1) 24 and 2) 1.6.

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a. total estimated uncollectible accounts is $21,190

b. to entry the adjustment, we have to debit bad debt expense and credit allowance for doubtful accounts in the amount of $14,690

a. to compute the estimated uncollectible accounts, we have to multiply the specific % to the accounts receivable plus the beginning balance;

•Accounts not due

$36,000 x 4% = $1,440

•Accounts 1 - 60 days past due

$21,000 x 25% = $5,250

•Accounts more than 60 days past due

$16,000 x 50% = $8,000

So the total uncollectible accounts would be; $6,500 + $1,440 + $5,250 + $8,000 = $21,190

b. to record the year-end adjustment of the uncollectible accounts, we have to debit bad debt expense and credit allowance for doubtful accounts in the amount of $14,690. This figure is the uncollectible amount we computed earlier based on the aging.

Therefore, the total estimated uncollectible accounts is $21,190 and to entry the adjustment, we have to debit bad debt expense and credit allowance for doubtful accounts in the amount of $14,690

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Disclaimer

The question given by you is incomplete, so the above answer has been done as per a similar question

Spade Agency separates its accounts receivable into three age groups for purposes of estimating the percentage of uncollectible accounts. In addition, the balance of Allowance for Uncollectible Accounts before adjustment is $6,500 (credit).Accounts not yet due = $36,000; estimated uncollectible = 4%.Accounts 1–60 days past due = $21,000; estimated uncollectible = 25%.Accounts more than 60 days past due = $16,000; estimated uncollectible = 50%.Required:a. Compute the total estimated un-collectible accounts.b. Record the year-end adjustment for estmated un-collectable accounts.

Answer:

b  -  c   -  a

Step-by-step explanation:

Volume of each cube x number of cubes = total volume

a )  (3 * 2 * 6)  *  (1/4 )^3  = .5625

b)   (2 * 3 )     *   (1/2)^3  =  .75

c)   ( 8 * 4 * 11) *  (1/8)^3  = .6875    

The representation of the volume of the prism in greatest to least volume is third > first > second.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

As per the given cuboid prism.

The volume of the cuboid = length × height × width.

First cube = 1/4 x 3 x 6 x 2 = 9 units³

Second cube = 1/2 x 2 x 3 x 1 = 3 units³

Third cube = 1/8 x 8 x 11 x 4 = 44 units³

So, 44 > 9 > 3.

Hence "The representation of the volume of the prism in greatest to least volume is third > first > second".

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when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.

We have,

Absolute value:

The absolute value of a number represents its distance from zero on the number line. It is always a non-negative value.

For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.

|x - 5|:

In this expression, we have the absolute value of the quantity (x - 5).

It means that we are looking at the distance between x and 5 on the number line.

x < 5:

The condition x < 5 states that x is less than 5.

It means that x is located to the left of 5 on the number line.

Simplification:

When x is less than 5, it implies that x is located to the left of 5.

In this case,

The quantity (x - 5) becomes negative because we are subtracting a larger value (5) from a smaller value (x).

Now,

The expression |x - 5| can be simplified to -(x - 5), which means taking the negation of (x - 5).

- If x = 3, which is less than 5, we can substitute it into the expression:

|x - 5| = |3 - 5| = |-2| = 2

- If x = 7, which is greater than 5:

|x - 5| = |7 - 5| = |2| = 2

In both cases,

The value of |x - 5| is 2.

However, when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.

Thus,

when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.

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Given:

1. \(\Delta HJI\cong \Delta IQP\)

3. \(\Delta JLK\cong \Delta FGH\)

To find:

The missing values to complete the congruence statements:

1. \(\overline{IH}\cong \_\_\_\_\)

3. \(\angle KJL\cong \_\_\_\_\_\)

Solution:

1.

We have,

\(\Delta HJI\cong \Delta IQP\)

Here, vertices H, J, I are corresponding to I, Q, P. So,

\(\overline{IH}\cong \overline{PI}\)

Therefore, the complete statement is \(\overline{IH}\cong \overline{PI}\).

3.

We have,

\(\Delta JLK\cong \Delta FGH\)

Here, vertices J, L, K are corresponding to F, G, H. So,

\(\angle KJL\cong \angle HFG\)

Therefore, the complete statement is \(\angle KJL\cong \angle HFG\).

Answer:

40% \((\frac{40}{100})\)

Step-by-step explanation:

According to the given description of the 10 by 10 grid, 40 out of 100 squares are shaded.

Convert into a Fraction:

\(\frac{Shaded}{Squares} =\frac{40}{100}\)

Convert the fraction into a decimal:

\(\frac{40}{100} =0.4\)

Convert the decimal into a percent:

\(0.4*100=40\\\)

40%

So, the grid should represent 40%.

Answer:

40% got it right on the unit test.

Step-by-step explanation:

The true statement is if k = - 1 there are solutions, but if k = - 3 there are no solutions

Given: |x+3|-2=k

Below are rules for solving absolute value equations:

1. If p is positive and |y| = p, then

x = p   OR    y = -p

(two equations are set up)

2. If p is negative and |y| = p, then

No solution

3. If p is zero  and |y| = p, then

One solution

Using the rules:

|x+3|-2=k

when k = -1

|x+3|-2= -1    

|x+3| = 1

Rule 1 is applicable here. Thus, there are solutions  

when k = -3

|x+3|-2 = -3

|x+3| = -1

Rule 3 is applicable here. Thus, no solution

Therefore, if k = - 1 there are solutions, but if k = - 3 there are no solutions.     The 2nd option is the true statement

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The correct radical form of b^1/5 is 5^√b.

Square root and nth roots are represented by the symbol "radical," which. a square root is a component of a radical expression, which is an expression.

A number's or an algebraic expression's simplest radical form is referred to as this. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

Explanation:

Convert to radical form using the formula

a^x/n=n^√a^x

5^√b.

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Answer:

4/3

Step-by-step explanation:

Z-4/9-1/3=5/9

Z-7/9=5/9

Z=5/9+7/9

Z=4/3 not sure

Answer:

each bag of chips are 0.37 cents

Step-by-step explanation:

1 case =29.60

29.60 divided by 8 (number of boxes in case)=3.70

3.70 divided by 10(number of chip bags in box)=0.37

Therefore each bag of chips = 0.37cents

Answer:

2

Step-by-step explanation:

These two are similar triangles. 3 corresponds to 9, and x corresponds to 6. Since 3 is being multiplied by 3 to get 9, x*3 should equal 6. Therefore, x is 2.

Answer:

x≤−1 or x≥1

Step-by-step explanation: