Without solving, determine the character of the solutions of the equation in the complex number system.
3x^2 + 7×=3.
(Simplify your answer.)

Answer:

Marianna will have $19,700 in her annuity after 6 years.

Step-by-step explanation:

To find the amount of money in the annuity after 6 years, we need to calculate the compound interest earned over that time period.

First, let's find the interest rate per quarter: 8% annual interest divided by 4 quarters per year = 2% interest per quarter.

Next, we'll calculate the number of quarters that the money is invested: 6 years x 4 quarters per year = 24 quarters.

Now we can use the formula for compound interest to find the total amount of money in the annuity after 6 years:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = initial investment ($10,000 in this case)

r = interest rate per quarter (2% or 0.02)

n = number of times the interest is compounded in a year (4)

t = number of years invested (6)

Plugging in the values:

A = $10,000 * (1 + 0.02)^(24)

A = $10,000 * 1.96634438

A = $19,663.44

Rounding to the nearest hundred dollars: $19,700

So, Marianna will have $19,700 in her annuity after 6 years.

Answer:

$ 546.00

Step-by-step explanation:

Simple Interest = P x r x  t

where t = number of years

r = interest rate per year as a decimal

P = amount invested(deposit)

We are given that r = 7.8% per year = 7,8/100 = 0.078

However, since this is the yearly interest, the monthly interest = 0.078/12

The time period is 42 months

Initial deposit = $2,000

Therefore interest
I = 2000x (0.078/12) x 42 =  $ 546.00

[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]

Answer:

89392i + 788

Step-by-step explanation:

The divide by 5 and the multiply by 5 cancel out, and we cannot simplify 89392i + 788 any further, since we don't know what i is. Therefore the answer is 89392i + 788.

Hope that helps!

The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.

We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of

y² = x, x = 3y.

=> x = 3y --(1)

=> y² = 3y

=> y² - 3y = 0

=> y( y - 3 ) = 0

=> y = 0 or y - 3 = 0

=> y = 0 , y = 3

from (1), x = 3y => x = 0, x = 9

Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is

[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]

where R = 3y , r = y²

[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]

[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]

[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]

[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]

[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]

Hence, the required volume is 162π/5 cubic units.

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Answer: no exact answer

Step-by-step explanation:

The result of fraction multiplication are:

2/3 x 2/5 = 4/15

4/2 x 6/3 = 4

2/4 x 3/6 = 1/4

2/3 x 6/3 = 4/3

Given that, simplify the following:

2/3 x 2/5

4/2 x 6/3

2/4 x 3/6

2/3 x 6/3

For the expression 2/3 x 2/5:

To multiply fractions, we multiply the numerators together and the denominators together.

So, (2 x 2)/(3 x 5) = 4/15.

For the expression 4/2 x 6/3:

Again, we multiply the numerators together and the denominators together.

Thus, (4 x 6)/(2 x 3) = 24/6 = 4.

For the expression 2/4 x 3/6:

Following the same process, we multiply the numerators and denominators.

Therefore, (2 x 3)/(4 x 6) = 6/24 = 1/4.

Lastly, for the expression 2/3 x 6/3:

Similarly, we multiply the numerators and denominators together.

Hence, (2 x 6)/(3 x 3) = 12/9 = 4/3.

Therefore, the result of fraction multiplication are:

2/3 x 2/5 = 4/15

4/2 x 6/3 = 4

2/4 x 3/6 = 1/4

2/3 x 6/3 = 4/3

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The graph of the function is added as an attachment

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

h(x) = (1/3)ˣ - 4

The above function is an exponential function shifted down from the origin by 4 units

An exponential function of this form is represented as

h(x) = a(b)ˣ + c

Where

Initial value = a

Rate = b

Shift = c

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

a = 1

b = 1/3

c = -4

Next, we plot the graph

See attachment for the graph of the function

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Answer:

R207

Step-by-step explanation:

R180 times 15% =27

27+180=207, therefore, R270 ir correct

Answer:

Option C. (x + 5)

Step-by-step explanation:

This quadratic equation can either be solved using the quadratic formula or be factorised using The Double Bubble Method.

Double Bubble Method:

After listing the different pairs of factors 10, the pair (that would add together to give 7) are 2 and 5. These two factors will be used to rewrite +7x:

[tex]x^{2} + 2x + 5x + 10[/tex]

Factorization by grouping (i.e factorising each separate group sharing a common factor) will then be applied:

[tex]= x(x + 2) + 5(x + 2)[/tex]

The common factor, which is the (x + 2) expression, will be extracted:
[tex]= (x + 2)(x + 5)[/tex]

∴ [tex]x^{2} + 7x + 10[/tex] can be factorised to [tex](x + 2)(x + 5)[/tex]

It is observed that a factor of the given quadratic equation is x + 5

∴Option C

After answering the provided question, we can say that the function's midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2. midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5

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Answer:

2 . of(0)=2/1/2 this is answer number 2

The solution is, option 2 neither linear nor exponential.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The given function is

x    : -5       -3      -1       1      3

f(x) :8192   512   32      2    18

when we plot this function in the excel we get to know that it a regression as shown in the figure attached  

because value of  lies between (0,1)

which shows regression

therefore it is neither linear nor exponential.

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The slope for:

1 = 1/2  (Option E)

2 = 2 (Option C)

3 = -1/2 (Option H)

4 = -2 (Option A)

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

The formula for slope (m) is given as:

m = Rise/Run = y2-y1/x2-x1

(x1,y1) = Coordinates of the first point in the line

(x2,y2) = Coordinates of the second point in the line.

1) The points are:

x1= -2

y1 = 2

x2 =2

y2  = 4

m = (4 - 2) / (2 - (-2))

m = 2 / 4

m = 1/2

Thus, Δy/Δx = 1/2

2) The points are:

x1= -1

y1 = -12

x2 =5

yx  = 0

m = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

m = (0 - (-12)) / (5 - (-1))

m = 12 / 6

m = 2

Thus, Δy/Δx = 2


3) Where the points are:
x1= 2

y1 = -6

x2 = - 4

y2  = -3

Substituting the given values, we get:

m = (-3 - (-6)) / (-4 - 2)

m = 3 / (-6)

m = -1/2

Thus, Δy/Δx = -1/2


4)  Where the points are:
x1= 0

y1 = 3

x2 = 1.5

y2  = 0

Substituting the given values, we get:

m = (0 - 3) / (1.5 - 0)

m = -3 / 1.5

m = -2


Thus, Δy/Δx = -2

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In 30 minutes the two friends 2 miles apart.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.

We know that, Time= Distance/Speed

Now, T₁= 2/3

T₂= 2/6 =1/3

T=T₁-T₂

T=2/3+1/3

T=1/3

T=0.33 hours

= 30 minutes

Therefore, in 30 minutes the two friends 2 miles apart.

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The solution to the system of equations is x = -1 and y = 1.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The system of equation is given as:

2x - 3y = -5 .........(1)

3x + y = -2 ........(2)

Equation 2 can be written as:

y = -2 - 3x

Substituting the value of y in equation 1 we have:

2x - 3(-2 - 3x) = -5

2x + 6 + 9x = -5

11x + 6 = -5

11x = -5 -6

11x = -11

x = -1

Substituting the value of x in equation 2 we have:

3x + y = -2

3(-1) + y = -2

-3 + y = -2

y = -2 + 3

y = 1

Hence, the solution to the system of equations is x = -1 and y = 1.

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Answer:

563

Step-by-step explanation:

The Shanika Company's inventory levels changed during 20Y6. The materials inventory increased, the work in process decreased, and the finished goods slightly increased.

Based on the information provided, it appears that the Shanika Company has gone through some changes in its inventory levels during the 20Y6 period.

The company's materials inventory has increased from $274,730 on January 1 to $346,160 on December 31, indicating that the company has acquired more raw materials over the course of the year.

On the other hand, the work-in-process inventory has decreased from $494,510 to $470,780, suggesting that the company has been able to efficiently process its raw materials into partially completed goods over the year.

Finally, the finished goods inventory has increased slightly from $475,280 to $481,160, indicating that the company has been able to produce more finished products over the course of the year and has had sufficient demand for its products to keep the finished goods inventory at a relatively stable level.

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Answer:

D

Step-by-step explanation:

using the rules of logarithms

• log a - log b = log ([tex]\frac{a}{b}[/tex] )

• log [tex]x^{n}[/tex] = nlog x

then

[tex]log_{4}[/tex] [tex]\frac{7}{x^3}[/tex]

= [tex]log_{4}[/tex] 7 - [tex]log_{4}[/tex] x³

= [tex]log_{4}[/tex] 7 - 3[tex]log_{4}[/tex] x

Answer:

(B) "1 to 5."

Step-by-step explanation:

The ratio of single to married instructors is 1 to 5. Since 4 instructors are single out of 24 total instructors, the ratio of single instructors to married instructors is 4 to (24 - 4) = 4 to 20. Simplifying the ratio to its simplest form, we get 4:20 = 1:5, which is the answer choice (B) "1 to 5."

Answer: See the attached image below for the proof table.

Explanation:

We start with what we're given. Simply repeat the given information word for word. This is statement 1 of the proof.

Statement 2 mentions AB is parallel to CD. This is valid due to the definition of a parallelogram. The name means "two sets of opposite parallel sides. Statement 3 is a similar situation.

Statement 4 relies on statement 2. The red angles in the diagram are congruent alternate interior angles. They are only congruent because of AB parallel to CD.

Statement 5 relies on statement 3 for similar reasoning as the previous paragraph. Focus on the blue angles.

Statement 6 is hopefully self explanatory so there's not much for me to mention here.

Statement 7 has us connect statements 4, 5, and 6 to prove triangle ADB is congruent to triangle CBD. We use the ASA (angle side angle) theorem here.

Statements 8 and 9 finish up the proof. CPCTC stands for "Corresponding parts of congruent triangles are congruent". If two triangles are congruent, then their corresponding pieces must be congruent as well. It would be like saying two houses are identical if and only if their front doors are identical.

Answer:

4,233,000

Step-by-step explanation:

4,232,000                 4,4232,852                  4,233,000

4,4232,852 is between 4,232,000 and 4,233,000.  It is closer to 4,233,000.

The rule is to look a the digit in the hundreds' place.  That number is 8.  If the digit in the hundreds' place is 5 or larger, you round up.

The composite function is given below with examples.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Consider two functions f(x) and g(x).

Now,

f o g = f(g(x)) is called a composite function.

f(x) = 2x + 1

g(x) = x + 2

So,

(f o g)(x)

= f(g(x))

= f(x + 1)

= 2 (x + 1) + 1

= 2x + 2 + 1

= 2x + 3

Thus,

The composite function is given above with examples.

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The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

where:

μ1 = mean bumper repair cost for small pickups ($1090)

μ2 = mean bumper repair cost for small utility vehicles ($485)

s1 = standard deviation of bumper repair cost for small pickups ($403)

s2 = standard deviation of bumper repair cost for small utility vehicles ($382)

n1 = sample size for small pickups (5)

n2 = sample size for small utility vehicles (8)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator. Since the degrees of freedom (df) for a Welch's t-test are unequal, the critical value can be approximated using the degrees of freedom formula:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / (((s1^2 / n1)^2) / (n1 - 1) + ((s2^2 / n2)^2) / (n2 - 1))

Plugging in the values, we get:

df = ((403^2 / 5) + (382^2 / 8))^2 / (((403^2 / 5)^2) / (5 - 1) + ((382^2 / 8)^2) / (8 - 1)) = 9.57

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.

In the given figure, there are two pairs of vertical angles~

That are :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]

Also, vertical opposite angles are equal in measure.

The equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Hence, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = (y2 - y1) / (x2 - x1)

The coordinates of the points are:

(-8, 3) and (-6, 0)

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates we have:

m = (0 - 3)/ (-6 + 8)

m = -3/2

Using the point slope form:

y - y1 = m (x - x1)

Substituting the values of slope and coordinates we have:

y - 3 = -3/2(x + 8)

2(y - 3) = -3(x + 8)

2y - 6 = -3x -24

2y = -3x -18

Hence, the equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.

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Percentage of change in the stock's price since the beginning of the year is: 12.32%

The price at which a stock's share is currently trading on the market is referred to as the stock price. Every publicly listed company issues its shares at a price, which is an estimation of their value that, ideally, corresponds to the worth of the firm itself.

The market forces of supply and demand govern a company's share price once it becomes public and its shares begin trading on a stock exchange. Price increases will occur if there is a large demand for its shares. A stock's price might be reduced by sellers if the company's prospects for future growth appear uncertain.

Given that,

Closing price today = $21.20

Closing price on the previous trading day= $28.83

Difference between closing price today and closing price on the previous trading day= $21.20 - $28.83

= $7.63

Percentage of change in the stock price since the beginning of the year

= Year-to-date % change

= 12.32%

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The time Jim takes alone to mow the lawn is 10 hours.

Jim and Craig, working together  can mow the lawn in 8 hours. Working alone, Craig take 4 times as long as Jim.

Therefore, the time it takes Jim to mow the lawn alone can be calculated as follows:

let

x = time use by Jim to mow the lawn

Therefore,

time Craig use to mow the lawn = 4x

Hence,

1 / 8 = 1 / 4x + 1 / x

1 / 8 =  1 + 4/ 4x

1 / 8 = 5 / 4x

cross multiply

4x = 40

x = 40 / 4

x = 10

Therefore,

time Jim takes alone to mow the lawn = 10 hours.

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Felix's English score would be around 72 points if he spends 7 hours a week studying English.

the answer is option b, 72 points.

What is a graph of an equation?

A graph of an equation is a visual representation of the relationship between the variables in that equation. In mathematics, an equation typically involves one or more variables, and the graph of that equation shows how the value of one variable changes as the value of another variable change.

Look at the horizontal axis of the graph to find the point that corresponds to 7 hours of studying per week. In this case, it is approximately halfway between 6 and 8, so we can estimate it to be around 7.

From that point, draw a vertical line up to the graph to find the corresponding English score.

Follow the line until it intersects with the blue line representing Felix's English scores.

From that intersection point, draw a horizontal line over to the y-axis to read the corresponding score.

Based on this analysis, we can estimate that Felix's English score would be around 72 points if he spends 7 hours a week studying English.

Therefore, Felix's English score would be around 72 points if he spends 7 hours a week studying English.

the answer is option b, 72 points.

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The probability of getting exactly one head after flipping a coin three times is equal to ( 3 / 8 ) .

Possible outcomes of flipping a coin three times are :

= { HHH, THH, HTH, HHT, TTH, THT, HTT, TTT }

Possible outcomes of getting exactly one head are:

= { TTH, THT, HTT }

Total number of outcomes are equal to 8

Favourable number of outcomes are 3

Probability of getting exactly one head is equal to

= ( Number of favourable outcomes ) / ( total number of outcomes)

= 3 / 8

Therefore, the probability of getting exactly one head by flipping a coin three times is equal to ( 3 / 8 ).

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Answer: A) $725

Step-by-step explanation:

The value of the asset that the business bought with $300 cash and $425 on credit is $725. The total amount that the business spent on the equipment is equal to the sum of the cash and the credit, which is $300 + $425 = $725.