Square Root Property

The correct term in each box, if necessary, use / for the fraction bar are a = 1/7-4i, b = 1/13.

In mathematics, a fraction bar is a visual representation of fractions that facilitates fraction comparison and fraction operation. Part-to-whole representational models like fraction bars or fraction strips are used. One unit out of a whole is represented by each segment of a fraction bar.

We need to be aware of an aspect of imaginary numbers in order to determine the values of variables a and b. The following rule applies to the hypothetical unit:

Therefore, the correct terms are 1/7-4i, b = 1/13.

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By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).

We can use the formula for compound interest to solve this problem. The formula is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

A = the total amount in the account

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know the values for A, r, n, and t, so we can solve for P:

[tex]A = P(1 + r/n)^{(nt)[/tex]

[tex]22,099.87 = P(1 + 0.022/2)^{(2*13)[/tex]

[tex]22,099.87 = P(1.011)^{26[/tex]

22,099.87 = 1.329P

P = 22,099.87 / 1.329

P = 16,637.55

Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

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Answer:

(a) 56%

(b) 28%

Step-by-step explanation:

Hope this helps! :)

1) The length of the segments BC =√53   FG =√53  JK =√53

2) The statements that are true are;

BC ≅ FG

BC ≅ JK

FG ≅ JK

To find the lengths of the segments, we use the formula d = √((x2 - x1)² + (y2 - y1)²)

For BC, it would be √((1 - (-6))² + (2 - 4)²) = √53.

It would ordinarily be 7.3. However, since approximations are not needed, it has been left in the form of squareroot

For  FG: √((-5 - (-7))² + (-1 - 6)²) = √53.

The answers provided are based on the questions seen in the image

Here are the endpoints of the segment BC, FG and JK.

B (-6, 4)  C (1, 2)        F (-7, 6),  G (-5, -1)        J (1, -8), K (3, -1)

Find the length of each segment. give an exact answer (not a decimal approximate)

BC =     FG =      JK =

Check all the statement that are true below;

BC ≅ FG

BC ≅ JK

FG ≅ JK

None of these are true.

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Answer:

43

Step-by-step explanation:

at the upper horizontal plane the angles add up to 180 degrees so you add the right angle with the 47 degrees and then you subtract the answer from180 degrees.the value you obtain is oppositely equal to the value of x hence,43

The best type of graph for the data set below is a bar graph. So the correct option is A.

The pictorial representation of data which is generally grouped, in the form of vertical or horizontal rectangle-shaped bars is called a bar graph. In this type of graph, the length of bars is a representation of the measure of data. They are also called bar charts. In statistics, bar graphs are one of the ways of data handling.

Statistics is the collection, presentation, analysis, organization, and interpretation of data observations. There are various methods for the representation of this statistical data. These can be tables, bar graphs, pie charts, histograms, frequency polygons, etc.

There are three main characteristics of bar graphs. These are:

It helps in comparing the different sets of data among different groups.

The relationship using two axes is shown where the categories are on one axis and the values are on the other axis.

Major changes in data over time are shown.

Therefore the correct option is A.

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The complete question is:

Answer:

5)

$332.19

6)

$16,857.36

7)

$248.91

Step-by-step explanation:

monthly premium = Base Rate * [tex]\frac{Monthly Payroll}{100}[/tex]

5)

given:

Base rate = $2.24
Monthly payroll = $14,830.00

unknown = monthly premium

 [tex]2.24 * \frac{14,830.00}{100}[/tex] = $332.192≈$332.19

6)

given:

Base rate = $19.89
Monthly payroll = $84,752.96

unknown = monthly premium

[tex]19.89 * \frac{84,752.96}{100}[/tex] = $16,857.364≈$16,857.36

7)

given:

Base rate = $2.90
Monthly payroll = $8,582.94

unknown = monthly premium

[tex]2.90 * \frac{8,582.94}{100}[/tex]=$248.90526≈$248.91

The rationalized form of the expression 6/√x is 6√x/x.

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

6/√x

To rationalize the denominator of 6/√x, we can multiply both the numerator and denominator by √x.

This gives:

6/√x * √x/√x = 6√x/x

So the rationalized form of 6/√x is 6√x/x.

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Answer:

The question is asking about the line of reflection that would transform polygon ABCDE to its image A' B' C' D' E'.

To determine the line of reflection, we need to identify the axis or line that reflects each point of polygon ABCDE to its corresponding point on polygon A' B' C' D' E'.

Looking at the coordinates of the vertices, we can see that the x-coordinates of the corresponding points are the same, but the y-coordinates are opposite in sign. This suggests that the line of reflection is parallel to the x-axis.

Furthermore, we can see that the reflected image is below the original polygon, so the line of reflection must be the x-axis itself, reflecting the polygon downward.

Therefore, the correct answer is "Reflection across the x-axis."

You can form a right triangle by cutting a square in half diagonally.

A square is a quadrilateral with four equal sides and four right angles. When a square is cut in half diagonally, it forms two congruent right triangles. The two halves of the square, which are the two legs of the right triangle, are equal in length.

The diagonal of the square, which is the hypotenuse of the right triangle, can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

Therefore, in a right triangle formed by cutting a square in half diagonally, the length of the hypotenuse can be found by taking the square root of the sum of the squares of the lengths of the two legs.

In summary, cutting a square in half diagonally allows us to form two congruent right triangles with equal leg lengths, making it a suitable shape to form a right triangle.

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Answer:

To determine if the given equations are symmetric with respect to the origin, we need to check if replacing x with -x and y with -y results in the same equation.

For the equations given:

y=7x-4 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=-7x+4, which is not the same equation.

y= -x+7 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=x-7, which is not the same equation.

y = -7x^2 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y = -7(-x)^2, which simplifies to -y = -7x^2. Thus, the equation remains the same.

y = 6x^2 - 9 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y = 6(-x)^2 - 9, which simplifies to -y = 6x^2 - 9. Thus, the equation is not the same.

x=1/4 y^2 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -x = 1/4 (-y)^2, which simplifies to -x = 1/4 y^2. Thus, the equation is not the same.

x = -y^2 + 9 is symmetric with respect to the origin since replacing x with -x and y with -y gives -x = -(-y)^2 + 9, which simplifies to -x = -y^2 + 9. Thus, the equation remains the same.

y=-1/6 x^3 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y=-1/6(-x)^3, which simplifies to -y=-1/6 x^3. Thus, the equation remains the same.

y=x^3-1 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=(-x)^3-1, which simplifies to -y=-x^3-1. Thus, the equation is not the same.

y=sqrt(x) is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x), which is not the same equation.

y=sqrt(x)-6 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x)-6, which is not the same equation.

Therefore, the only equation that is symmetric with respect to the origin is y = -7x^2.

Answer:

i can only see b not c

Step-by-step explanation:

Answer:3-7=5

Step-by-step explanation: 3-7=5

We can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml

To determine the optimal dosage amount A for each Delay Type, we need to first define the surge function for each delay type as:

Extended: f(t) = [tex]At^2e^-^0^.^3^t[/tex]

Medium: f(t) = [tex]At^3e^-^0^.^5^t[/tex]

Rapid: f(t) = [tex]At^3e^-^0^.^7^t[/tex]

To find the optimal dosage amount A, we need to maximize the treatment effect while ensuring that the dose does not exceed 100ng/ml at any time and falls to be at or below 20ng/ml by 24 hours.

The treatment effect can be calculated by integrating the surge function over time from 0 to 24 hours and then adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20ng/ml

For the Delay Type and dosage level selected, we can calculate the treatment effect over the first 24 hours by integrating the surge function from 0 to 24 hours.

Then, we can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml..

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The net value of the $10,000 bonus in a normal savings account after taxes and interest in five years will be $9,181.

Assuming an 8 percent nominal interest rate and a 30 percent tax bracket, the after-tax return on the normal savings account is 5.6 percent. Thus, after five years, the $10,000 bonus will grow to $14,693.

However, since Sarah is in the 30 percent tax bracket in every year, she will owe taxes on the interest income earned each year. This reduces the after-tax return to 3.92 percent. Therefore, in five years, the $10,000 bonus in the normal savings account will be worth $9,181 after taxes.

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Answer:

[tex]4k < -\frac{3}{2}[/tex]

Step-by-step explanation:

"A number k multiplied by 4 is less than -3/2"

First, let's look at the first part:

"A number k..."
We know the number we are operating is called k.

Let's look at the second part.

"...multiplied by 4..."

Now, we are multiply k by 4. After doing so, we get:

[tex]4k[/tex]

Finally, let's look at the last part.

"...is less than -3/2"

The quantity "a number k multiplied by 4" (or 4k) is less than -3/2.

We can rewrite this as:

[tex]4k < -\frac{3}{2}[/tex]

The value of (a) in given triangle is approximately 7.44 cm.

A triangle is a three-sided polygon consisting of three sides and three vertices. The most important property of a triangle is that the sum of its interior angles  is  180 degrees.

Let ΔABC is a triangle

Given ∠ B = 75°

∠ C = 31.8°

AB = 12cm

AC = 22cm

find BC = ?

We can use the law of cosines to solve for BC:

BC² = AB² + AC² – 2(AB)(AC)cos(B)

We know that angle B = 75 degrees, so we can substitute:

BC² = 12² + 22² - 2(12)(22)cos(75)

Evaluating cos(75) with a calculator, we get:

BC² ≈ 144 + 484 - 572.59

BC² ≈ 55.41

Taking the square root of both sides gives us:

BC ≈ 7.44

Therefore, BC is approximately 7.44 cm.

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Answer: 40

Step-by-step explanation:

math

The common difference of the sequence is - 100.

The explicit formula of the sequence is  131 - 100n.

The 52 term of the sequence is -5069.

Let's find the explicit formula of the arithmetic sequence as follows:

31, -69, -169, -269

We will find the common difference and the 52 terms.

Therefore,

a + (n + 1)d = nth term

where

Therefore,

d = common difference = -69  - 31 = - 100

Therefore,

nth term = 31 + (n - 1)-100

nth term = 31 - 100n + 100

nth term = 131 - 100n

Let's find the 52 term

Hence,

52 term = 131 - 100(52)

52 term = 131 - 5200

52 term = -5069

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The right circular cylindrical tank which is 5 m long and 13 m in diameter holds about 663,325 liters of liquid approximately.

The formula to find the volume of a right cylindrical tank is

V = πr²h, where 'r' is the radius and 'h' is the height.

Given that, the height is 5 m and the diameter is 13 m.

Radius = Diameter/2.

Radius = 13/2 = 6.5 m.

We know that, π = 3.14.

Now, we can substitute the values in the formula.

V = 3.14×(6.5)²×5.

V = 3.14×6.5×6.5×5

V = 663.325 cubic meters.

Now, we have to convert cubic meters into liters.

We need to multiply by 1000 as a thousand liters are in one cubic meter.

663.325×1000 = 663,325.

Therefore, the tank holds about 663,325 liters of liquid approximately.

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The amounts needed to make 6 servings are given as follows:

The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.

From the first line of the table, we get the amounts of sauce and oregano per serving are follows:

Hence the amounts for six servings are given as follows:

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Answer:

D. 1,0 & -3,0

Step-by-step explanation:

because the two lines pass through points 1,0 and -3,0 at the x-axis

Answer:

your answer is D. 1,0 & -3,0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: Pete is twice as old as Chris.p = 2c  Seven years ago the sum of their ages were 31.(p-7) + (c-7) = 31p + c - 14 = 31p + c = 31 + 14p + c = 45Find their ages now replace p with 2c2c + c = 453c = 45c = 45/3c = 15 is Chris's agethenp = 2(15)p = 30 is Pete's age::Check solutions in the statement"Seven years ago the sum of their ages were 31"30-7 + 15-7 = 31

The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.

When an account is found to be uncollectible, the direct write-off method records the expense for uncollected accounts receivable. This approach involves simply writing off the uncollectible account as a bad debt expense and deducting the outstanding quantity from the accounts receivable total.

Despite being quite easy to understand and basic, this method does not adhere to generally accepted accounting principles (GAAP) because it does not match expenses to the time period during which income was generated.

In contrast, the allowance approach establishes an allowance for doubtful accounts contra-asset account and estimates the amount of uncollectible accounts before recognizing the expense for uncollected accounts receivable.

This allowance account is used to lower the balance of accounts receivable to the anticipated amount of collection. Instead of when the account is found to be uncollectible, the expense is recognized at the time the estimate is made. Because it matches the expense to the time period in which the revenue was received, this method is thought to be more accurate than the direct write-off method.

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Note to recite the numbers, you have repeat alound the tiven numbers. Often, the purpose of recitation is to memorize and become aquatinted with.

Recitation is often a smaller subset of a larger lecture course, commonly conducted by teaching assistants, meant to offer time for conceptual knowledge application and extension of training that happens in lecture through problem-solving or discussion.

Consider this a learning process in which knowledge is recalled from memory.

You have been handed numbers to recite in this case. Reciting numbers can help you increase your numeric intelligence.

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The volume of the complete prism is  1625 cubic in

The volume of the figure is solved by dividing the figure into two sections and solving for each volume then adding the individual volume together.

The divisions are section 1 and section 2

section 1 has dimensions: 20 x 15 x 5

volume = 20 x 15 x 5 = 1500 cubic in

section 2 has dimensions: 5 x 5 x 5

volume = 5 x 5 x 5 = 125 cubic in

Volume of the complete figure

section 1  + section 2

= 1500 cubic in + 125 cubic in

= 1625 cubic in

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Answer:

[tex]f(x)=4(3)^x[/tex]

Step-by-step explanation:

The general equation for an exponential function is:

[tex]\boxed{f(x) = ab^x}[/tex]

where:

To find the values of a and b that satisfy the given conditions, we can use the two points (1, 12) and (3, 108) to form a system of equations:

[tex]\begin{cases}12 = ab^1\\108 = ab^3\end{cases}[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\dfrac{ab^3}{ab} = \dfrac{108}{12}[/tex]

[tex]b^2=9[/tex]

[tex]\sqrt{b^2}=\sqrt{9}[/tex]

[tex]b=3[/tex]

Substitute the found value of b into the first equation and solve for a:

[tex]12&=3a[/tex]

[tex]\dfrac{12}{3}=\dfrac{3a}{3}[/tex]

[tex]4=a[/tex]

[tex]a=4[/tex]

Therefore, the equation of the exponential function that passes through the points (1, 12) and (3, 108) is:

[tex]\boxed{f(x) = 4(3)^x}[/tex]

Answer:

Step-by-step explanation:

To find the equation of an exponential function passing through the given points (1,12) and (3,108),

we can use the standard exponential form y=a(b^x). We know that when x=1, y=12,

so we can substitute these values into the equation to find a.

So  12 = a(b^1). Similarly, when x=3, y=108, so 108 = a(b^3). We can divide the second equation by the first to eliminate a and get (108/12) = b^2, or 9 = b^2. Thus, b=3 (taking only the positive root). We can now substitute this value of b into either equation to find a. Using the first equation, we get 12 = a(3^1), so a=4. Therefore, the exponential function passing through the given points is y=4(3^x).

Answer:

[tex]\pi {r}^{2}h = 51\pi[/tex]

[tex] \frac{1}{3} \pi {r}^{2} h = \frac{1}{3} \times 51\pi= 17\pi[/tex]

The volume of the cone is 17π cubic centimeters.

The correct statement is C. asking questions, identifying problems, and gaining new information is the most accurate option.

The definition of "observation" given by Merriam-Webster is "an act of recognizing and noting a fact or occurrence often involving measurement with instruments," or "a record or description so obtained."

C. asking questions, identifying problems, and gaining new information is the most accurate option.

Making observations often involves the process of asking questions, identifying problems, and gaining new information. Observations are made to gather data and information about a phenomenon or event, which can then be used to answer questions or develop hypotheses for further research.

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Answer:

206 inches

Step-by-step explanation:

1 feet = 12 inches

17 feet = 17 x 12 = 204 inches

17 feet 2 inches = 204 + 2 = 206 inches

So, 17 feet 2 inches = 206 inches