Someone help me out pls!

    In other terms, imaginary numbers are those that have no known value and are represented by the square root of negative numbers. Most of the time, it is expressed as real values multiplied by an arbitrary unit called "i."

    Answer and justification Therefore, a quadratic equation with rational coefficients cannot have both a real and an imaginary root.

How can you find complex roots using Descartes' Rule of Signs?

    We may determine the total number of positive + negative real roots using the rule of signs. We may get the potential number of complex roots by deducting this total from the polynomial's degree.

    An imaginary integer is referred to as an imaginary zero if it produces a zero output when plugged into a polynomial (or a complex zero).

   Complex numbers are those that are expressed as a+b, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1).

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If She was entitled to a personal exemption of $2900 and had deductions totaling $5090. her gross income is $36,100, adjusted gross income is  $33,400 , and taxable income is $25,410.

Gross Income:

Gross Income= Wages + Interest received

Gross Income= 34,600 + $1500

Gross Income= $36,100

Adjusted Gross Income:

Adjusted Gross Income  = Income - Tax Def Contribution

Adjusted Gross Income = $36,100- $2,700

Adjusted Gross Income = $33,400

Taxable Income :

Taxable Income = AGI - Deductions - Personal exemption

Taxable Income= $33,400- $5,090 - $2,900

Taxable Income= $25,410

Therefore her  gross income is $36,100.

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Answer: 105

Step-by-step explanation:

Angles in a triangle add up to 180 degrees always, you already have two angles. Subtract those two angles from 180 then you have 75. A straight line always equals 180, and since we just found one angle on that line which is 75, just subtract 75 from 180 to get the answer.

Answer:

25%

Step-by-step explanation:

(40-32 / 32) × 100% = 25%

    A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

    Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).

      We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

        This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

       If you can locate the x-intercept of a linear function, finding the zero should be simple. The x-coordinate of the x-intercept is zero.

Summary

         Consider the numbers as being on the x-axis to help you remember this. The positive values are located to the right of the origin, and the negative values are located to the left of the origin.

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Answer:

k = 4

Explanation:

1) The triangles in example 1 are similar triangles but differs in size

We are to calculate the scale factor k

Using the formula

Scale factor k = size of the larger triangle/size of the smaller trinagle

Since they are similar triangles;

k = DF/AB

Given

DF = 48

AB = 12

Substitute the given values into the expression for k above to have;

k = 48/12

k = 4

Hence the scale factor from triangle ABC to DEF is 4

65.03x + 74757 is Marginal profit function .

What is profit?

P(x) = 143 - 0.03x

C(x) = 75000 + 65x

C(x) - P(x) = 75000 + 65x - ( 143 - 0.03x)

                = 75000 + 65x - 143 + 0.03x

                 = 65.03x + 74757

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3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.​

________________________________

# of Chocolates​ Price Ratio (Price per chocloate)

Store A 36 pack box 54 54/ 36 = 3/2 = 1.5

Sotre B 6-pack boxes 12 12/ 6 = 2

_____________________________

Store A 1.5

______________________________

Answer

Store A offers a better deal

Answer:

2346 dl sheep

Step-by-step explanation:

all well STrxrcgvw'#'zuucrb if ivAr4w3ws4

The angle m∠FCD is 56°

Here the line CF is an angle bisector of ∠GCD.

By this we have,

∠GCF = ∠FCD

It is given that

∠GCF = ∠GCB - 12°

Let ∠GCB be x.

∠GCF = x - 12° = ∠FCD

BCD is a straight line which form 180°.

∠BCG + ∠GCF + ∠FCD = 180°

x + x - 12° + x - 12° = 180°

3x = 204°

x = 68°

∠FCD = x - 12°

          = 68° - 12°

          = 56°

Therefore m ∠FCD = 56°.

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The equivalent of one square meter in square feet is  10.89 [tex]ft^{2}[/tex]  and of one cubic meter in cubic feet is  35.937 [tex]ft^{2}[/tex].

One meter is about 3.3 ft. So, we can write

1 meter = 3.3 ft

Part : A

We know, 1 meter = 3.3 ft

On squaring both sides of this equation, we will get

[tex](1 meter )^{2}[/tex]= [tex](3.3 ft )^{2}[/tex]

1 [tex]meter^{2}[/tex] = 10.89 [tex]ft^{2}[/tex]                                   equation 1

The equivalent of one square meter in square feet is  10.89 [tex]ft^{2}[/tex] .

Part : B

We know, 1 meter = 3.3 ft

On taking cube on both sides of this equation, we will get

[tex](1 meter )^{3}[/tex]= [tex](3.3 ft )^{3}[/tex]

1 [tex]meter^{3}[/tex] = 35.937 [tex]ft^{3}[/tex]                                   equation 1

The equivalent of one cubic meter in cubic feet is  35.937 [tex]ft^{2}[/tex]

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Answer: 1 3/4

1/4= 15 minutes

1/2 = 30 minutes

add 1/2 to 1/4 and you get 3/4 because 1/2 is equal to 2/4 if you add the 1/4 to it

heres the actual math:

1/2 = 2/4

2/4 + 1/4 = 3/4

slap that one in front of it so its 1 3/4 and therea your answer

The length of the three sides of the triangle are 11 feet, 12 feet and 15 feet.

A triangle is a polygon with three sides.

The perimeter of a triangle is 38 feet.

The perimeter of the triangle is the sum of the whole three sides.

One side of the triangle is one foot longer than the second side.

let

the second side = x

longer side = x + 1

The third side is four feet longer than the second side.

Hence,

Third side = 4 + x

Therefore,

38 = x + x + 1 + x + 4

38 = 3x + 5

3x = 38 - 5

3x = 33

x = 33 / 3

x = 11

Therefore, the sides of the triangle are 11 ft, 12 feet and 15 ft.

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The types of transformations that occur as a result of the motion on the ball are;

A) Rotation

B) Translation

Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.

Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.

Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.

Rotation is a method of transformation that involves  turning a given figure at an angle about a reference point.

Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.

A) When James spins a basketball on his finger, it is clear that this transformation is rotation because it involves turning the ball at an  angle about a given point.

B) When James passes the basketball, the transformation would be translation because it involves moving the ball from one point to another without changing the dimension of the ball.

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slope=1.43

y-intercept=1

x-intercept=-1.43

Explanation

Step 1

get the slope intercept form of the equation

where

m is the slope and b is the y-intercept

to do this, isolate y

so,

Step 2

to find the x-intercept replace the y value with zero in the equation

so, the x intercept is

I hope this helps you

Answer:

y = 3(e)^(-0.69x)

Explanation:

Taking into account the following property

We can replace (0.5)^x by

So, now we can rewrite the function as

Therefore, the answer is

y = 3(e)^(-0.69x)

Answer:

y=3e^(ln0.5)x

Step-by-step explanation:

A motion sensor, sometimes known as a motion detector, is a piece of technology that use a sensor to find nearby individuals or objects. Any security system needs motion sensors as a crucial part. A sensor will alert your security system and, with newer systems, your cell phone when it senses motion.

How does a motion sensor function?

Active ultrasonic motion detectors emit ultrasonic sound waves, which bounce off surrounding objects and return to the source of emission. The sensor initiates and completes the required action, whether it be turning on a light or sounding an alert, when a moving object interferes with the waves.

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Answer:

Step-by-step explanation:

To understand the situations we must do a Venn diagram:

The total of people asked is 3400. Then,

a) For People who enjoyed vanilla but not chocolate or mint, seeing the diagram of Venn, we can deduce the equations:

b) For people who did not enjoy chocolate, vanilla or mint:

Given that

The population of a certain city is 1.50 million initially and it gets increased by 6.5% exponentially. And we have to find the number of years in which the population becomes 2.31 million.

Explanation -

The formula for the exponential growth is given as

Here we have f(x) = 2.31 million, a = 1.50 million , r = 6.5% and x = ?

So let the time be t.

Then, on substituting the values we have

You have the following data set:

x 1 0 -3

y 5 4 1

Where y is a function of x. In order to translate the previous function 2 unitd downward, you take into account that you subtract 2 units to the given values for y. Then, you have:

y (5-2) (4-2) (1-2)

which becomes:

y 3 2 -1

Finally, the given table becomes:

x 1 0 -3

y 2 2 -1

The range of the number of hours spent watching tv for the 5th grade is 6.

The range of the number of hours spent watching tv for the 7th grade is 7.

Th ratio of variation is 6/7.

A dot plot is a graph used to represent a dataset using dots. A dot plot is made up of a number line and dots.  The dots in the dot plot represent the frequency of the data.

Range is a measure used to measure the variation of a dataset. Range is the difference between the largest number in a data and the smallest number in the dataset.

Range = largest number - smallest number

Range of the 5th grade students = 8 - 1 = 6

Range of the 7th grade students = 7 - 0 = 7

Ratio of variation of 5th grade to 7th grade = range of 5th grade / range of 7th grade

6 / 7

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The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.

The compound interest formula is expressed as;

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

Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.

Given the data in the question;

First, convert rate from percent to decimal.

Rate r = 6%

Rate r = 6/100

Rate r = 0.06 per year

To determine the principal, plug the given values into the formula above and solve or P

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

P = $50,000 / (1 + 0.06/12)^( 12 × 30 )

P = $50,000 / (1 + 0.05)³⁶⁰

P = $50,000 / (1.05)³⁶⁰

P = $8,302.10

Therefore, the principal investment is $8,302.10.

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ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following expression:

We solve and reduce like terms, just like this:

Answer:

have you heard of the genger bread man

Step-by-step explanation:

Answer:

[tex]y=\frac{-1}{3}x+5[/tex]

Answers being -1/3 and 5

Step-by-step explanation:

In slope-intercept form, you seem to be missing your slope and intercept.  Luckily, the graph has everything you need.

Recall slope is rise over run or y over x.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

The slope of this line can be determined by counting the x and y movements of the line between two intersections where it evenly collides.  For instance, between (0,5) and (3,4), the line moves right three and down one.  

This would give you a slope of -1/3.

Another way to find the slope is to choose any two points and use the slope formula above.  Using those same two points:

[tex]m=\frac{4-5}{3-0}[/tex]

[tex]m=\frac{-1}{3}[/tex]

Now you have the first part of your answer.  The slope is -1/3.

The second part is the y coordinate of the y-intercept.  In this case, the graph includes the intercept, which we can clearly determine is (0,5).  Therefore, your second answer would be 5.

The full answer being [tex]y=\frac{-1}{3}x+5[/tex].

Answer

The amount that Diana's sister would buy the remaining 720 square inches piece of cloth = $5

Step-by-step Explanation

We are told that Diana bought a piece of cloth that was 48 inches wide and 1 yard long for $12.

Then, she had different parts of the cloth taken to do different stuff until the remaining piece of the cloth was to be bought by her sister at the same rate that she bought the original full piece of cloth.

Before we proceed, we need to establish and find the initial rate of the cloth, that is, how much is 1 unit of area.

Area of a rectangular figure (the cloth) = Length × Breadth

Length of the cloth = 1 yard = 36 inches

Breadth of the cloth = 48 inches

Area of the cloth = 36 × 48 = 1728 square inches.

1728 square inches of the cloth = $12

1 square inch of the cloth = (12/1728) = (1/144) dollars

So, now, we can now find how much of the cloth is removed.

- She cut off one-fourth of the cloth to make a tablecloth.

One-fourth of the 1728 square inches piec of cloth = (1/4) × 1728 = 432 square inches

- She used a piece that was 12 inches wide and 12 inches long to make a scarf.

Area of the piece she used to make a scarf = 12 × 12 = 144 square inches

- She used a piece that was 1.5 feet by 2 feet to make a cover for a pillow.

To find the area of this piece, we need to convert the dimensions into inches.

1 feet = 12 inches

So,

1.5 feet = 18 inches

2 feet = 24 inches

Area of this piece of cloth = 18 × 24 = 432 square inches

So, her sister now wants to buy the remaining piece of cloth from Diana.

Originally, the piece of cloth was 1728 square inches.

The total area removed from the original piece of cloth sum up to

432 + 144 + 432 = 1008 square inches.

The remaining piece of cloth will now have an area calculated by subtracting the area of pieces removed from the original area of the piece of cloth.

The area of the remaining piece of cloth = 1728 - 1008 = 720 square inches

Recall that the Diana's sister wants to but the remaining piece of cloth at the rate that Diana bought the original piece of cloth.

We have calculated this rate at which Diana bough the original piece of clothing to be (1/144) dollars for 1 square inch. So, we can then use this rate to calculate the amount Diana's sister will pay for the remaining piece of cloth

Area of the remaining piece of cloth = 720 square inch

1 square inch costs (1/144) dollars.

Let the cost of 720 square inches be x.

1 square inch = (1/144) dollars

720 square inches = x dollars

We can from a mathematical relationship simply by cross multiplying

1 × x = 720 × (1/144)

x = 5 dollars.

Hence, the amount that Diana's sister would buy the remaining 720 square inches piece of cloth = $5

Hope this Helps!!!

For the guess and check method, we would still need to first find the cost of 1 square inch of material which we obtained to be (1/144) dollars per square inch of cloth.

We would also still need to calculate the total area removed from the cloth, which we calculated to be 1008 square inches.

But now, we will now use the cost of 1 square inch, to calculate the cost of the pieces that have been removed from the cloth.

1008 × (1/144) = 7 dollars.

We can now guess how many dollars will top up the 7 dollars so that it gives the original 12 dollars that the cloth was bought.

After a series of guess, we will end up to get that it is (7 + 5) that is equal to 12 dollars.

So, guess and check would give us 5 dollars too as the answer.

Solution

Step 1

Write the equation

Step 2

Apply the addition equality theorem

Step 3

Use the division equality theorem:

Final answer

x = 5

Proportionately, the total number of registered doctors, based on the ratio of female doctors, is 150,637.

Proportion refers to the quantity relationship of a variable contained in another.

Using proportion, two values are equated to each other.

For instance, we equate the percentage of registered female doctors to the number of registered female doctors.

Proportions, like ratios, are stated as fractions, decimals, or percentages because they depict the portion of a variable in another.

The ratio of registered female doctors = 31.4%

The number of registered female doctors = 47,300

31.4% = 47,300

100% = 47,300/31.4% x 100

The total number of registered doctors = 150,637  (47,300/31.4%)

Thus, the total number of registered doctors is 150,637, given that 47,300 female registered doctors proportionately represent 31.4% of the population.

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We must solve the following quadratic equation by completing squares:

1) First, we rewrite the equation in the following way:

2) We sum to both sides of the equation (5/2)², get:

3) Expressing the first term as a square, we have:

4) Passing the +6 at the left as -6 at the right:

5) By taking the square root on both sides, we get two solutions:

1) Re-writing the equation:

2) Summing (5/2)² on both sides:

3) Expressing the first term as a square:

4) Simplifying:

5) Taking the square root: