Construct the simplest polynomial with integer coefficients with the given roots:
3i, -2,2,0

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{18}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{18}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{ 12 }{ 2 } \implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 6}(x-\stackrel{x_1}{3}) \\\\\\ y-6=6x-18\implies {\Large \begin{array}{llll} y=6x-12 \end{array}}[/tex]

Answer:

1 year ---->12 months

8 years ---> 12×8 =96 months

so there will be 96 months in a 8 years .

Answer:

can you connect me private?

Answer:

Step-by-step explanation:

This distance can be calculated by using the distance formula. The distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) can be defined as d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .Jun 2, 2017

Answer:

9

Step-by-step explanation:

3(x-5)=12

Use distributive property on with the 3 and parenthesis (3 times x and 3 times -5)

3x-15=12

Add fifteen to both sides (15 on the left side cancels out)

3x=27

Divide both sides by 3 (3 on the left side cancels out)

x=9

The congruence theorem that can be used to prove △ bda ≅ △ bdc is D. SSS.

Side-Side-Side, or SSS, is a type of triangle congruence rule that states that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the measurements of the corresponding sides and angles are identical, two or more triangles are said to be congruent.

Given that ΔBDA is similar to ΔBDC and:

AD ≡ DC

AB ≡ BC

BD ≡ BD (shared side)

Then the best postulate to use is the side-side-side (SSS) postulate. The correct option is D.

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Answer:

the height of the goalpost is approximately 10.48 meters.

Step-by-step explanation:

To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.

Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.

The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.

In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:

1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)

Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.

Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:

sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.

In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:

sin(52.22) / 13.25 = sin(37.78) / h

Solving for h, we find that the height of the goalpost is approximately 10.48 meters.

Therefore, the height of the goalpost is approximately 10.48 meters.

The given quadratic equations are:

Is in fact a quadratic equation.

The options are:

(i) x^2 - x + 3 = 0

(ii) 2x^2 +5/2x - √3 = 0

(iii) √2x^2 + 7x + 5√2

(iv) 1/3x^2 + 1/5x - 2 = 0

(v) x^2 - 3x - √x + 4 = 0

(vi) x - 6/x = 3

A general quadratic equation is a polynomial of degree 2:

a*x² + b*x + c = y

Where the variable is x, and we can see that the maximum exponent on a power of x is 2.

In this case, we have the first equation:

x^2 - x + 3 = 0

You can see that we have a polynomial of degree 2 (the maximum exponent is 2 and we only have positive integers as exponents) then this is in did a quadratic equation.

The other quadratics are:

Where you also can see polynomials of degree 2.

(the third option also seems to be quadratic, but it is not an equation)

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The complete question is:

Which of the following are quadratic equation in x?

The options are:

(i) x^2 - x + 3 = 0

(ii) 2x^2 +5/2x - √3 = 0

(iii) √2x^2 + 7x + 5√2

(iv) 1/3x^2 + 1/5x - 2 = 0

(v) x^2 - 3x - √x + 4 = 0

(vi) x - 6/x = 3

Answer:

$9430 / $10,230 * 100% = 92.4%

Step-by-step explanation:

To find the car's rate of depreciation, we need to first calculate the total amount of depreciation that occurred over the 5 years of use. This can be done by subtracting the sale price of the car from its original price:

$10,230 - $800 = $<<10230-800=9430>>9430

Next, we need to divide the total amount of depreciation by the original price of the car and multiply by 100% to express the result as a percentage:

Therefore, the car's rate of depreciation was 92.4%, to the nearest tenth percent. This means that the value of the car declined by 92.4% over the 5 years of use.

The equation part of the given word problem is x+y=52 and y=x+16.

a) Let x = number of green eyed dolls

And let y = number of blue-eyed dolls

Now we are told the following:

x+y=52 → eq1

and

y=x+16 → eq2

b) substitute y = x+16 from eq2 into eq1:

x+x+16 = 52 subtract 16 from each side

x+x+16-16 = 52-16 collect like terms

2x = 36 divide each side by 2

x = 18 → number of green-eyed dolls

substitute x = 18 into equation2

y = 18+16 =34 → number of blue-eyed dolls

18+34=52

52=52

and

18+16=34

34=34

THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:

Let x = Number of green-eyed dolls

Then 52-x = Number of blue-eyed dolls

Now we are told that:

x+16 = 52-x add x to and subtract 16 from each side

x+x+16-16 = 52-16-x+x collect like terms

2x=36 → same as before

x = 18.

Hence, the equation part of the given word problem is x+y=52 and

y=x+16.

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Answer:

You multiple the 1/4 into the inside which 1/4 x 4 is  

Step-by-step explanation:

sorry

The surface area of the prism is 166 mm² in the given figure.

The total surface area of the given prism can be expressed in terms of length (l), width (w), and height of cuboid (h) as:

Surface area of prism = 2 (lw + wh + lh) ....(i)

As per the given figure, we have

length (l) = 5 mm

width (w) = 4 mm

height (h) = 7 mm

Substitute the values in the formula, and solve

Surface area of prism = 2 (5 x 4 + 4 x 7 + 7 x 5)

Surface area of prism = 2 (20 + 28 + 35)

Surface area of prism = 2 (83)

Surface area of prism = 166 mm²

Thus, the surface area of the prism is 166 mm² in the given figure.

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The equation to find how much money they will save after 3 weeks is y = 68x, and they will save $518, so yes they have enough money to buy the gift.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

Total money Jason and his 3 brothers have = $314,

Each of them will save $17 a week until they have at least $515,

At the end of three weeks, the money saved by Jason and his brothers,

Money saved = 17 × number of person × number of weeks

Assume the number of weeks is x and the money saved is y then,

y = 17x × 4

y = 68x

Money saved, y = 68 × 3

Money saved = $204

Total money after the end of three weeks = $314 + $204

Total money after the end of three weeks = $518

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The smallest unit of matter is an atom. The fundamental building block of an element is an atom, which is made up of protons, neutrons, and electrons. This statement is true.

An atom is made up of a nucleus and one or more electrons that are bound to the nucleus. The nucleus is made up of one or more protons, a significant number of neutrons, and other particles. Only the most common form of hydrogen lacks neutrons.

An atom, which is the smallest part of a material, retains all of its properties. A molecule is made up of protons, neutrons, and electrons, which are the building components of matter. Protons and neutrons, which are the only particles in an atom that contribute to its atomic mass, are found in the nucleus of each atom. These early 20th-century discoveries of particles that  a nuclide itself and chemical components are explained by contemporary atomic theory.

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Laurel must increase her net income to $10,000 in order to keep her housing costs at 25%.

To determine how much Laurel must increase her net income in order to keep her housing costs at 25%, we need to know the following information:

The amount of Laurel's new mortgage, which is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

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Laurel must increase her net income to $10,000 to keep her housing costs at 25%.

The amount of Laurel's new mortgage is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

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it takes 2.25 seconds

oh, and it's 18 seconds for the next question assuming we had the same test.

The values of the missing angles in the parallelograms are as follows;

A parallelogram can be defined as a quadrilateral that has a pair of opposite parallel sides that have the same lengths.

Let x represent the missing angle in the figures in the question;

1) The adjacent angles of a parallelogram are supplementary

The angle x which is the adjacent angle to the angle 72° is a supplementary angle to the angle 72° in a parallelogram KLMN, therefore, we get;

x + 72 = 180, definition of supplementary angles

x = 180 - 72 = 108, by subtraction property

2) The missing angle x is the adjacent angle to the 95° angle in the parallelogram ABCD

Therefore; x + 95 = 180

x = 180 - 95 = 85

3) The missing angle is the opposite angle to the 139° angle

Opposite angles of a parallelogram are congruent

Quadrilateral TUVW is a parallelogram, therefore; x = ∠W = ∠T = 139°

4) The missing angle is an adjacent angle to the 105° in the parallelogram KLMN

Therefore, x + 105° = 180°

x = 180° - 105° = 75°

5) The missing angle, x, is the alternate interior angle to the 19° angle in the diagonal of the parallelogram BCDE

Alternate interior angles between parallel sides CD and BE are congruent.

Therefore, the missing angle is congruent to the 19° angle

6) Adding the missing angle and the 50° together, we get;

x + 50° = m∠E

∠E is the adjacent angle to the 95° angle, therefore;

∠E + 95° = 180°

∠E = 180° - 95° = 85°

∠E = 85°

Therefore; ? + 50° = 85°

x = 85° - 55° = 30°

7) The missing angle and the 29° angle are alternate interior angles

Alternate interior angles formed between parallel lines and their common transversal are congruent, therefore;

8) The sum of the missing angle and the 28° angle is the angle ∠F

∠F and the 110° angle are adjacent angles in the parallelogram DEFG, therefore;

∠F + 110° = 180°

∠F = 180° - 110° = 70°

∠F = 70°

x + 28° = 70°

x = 70° - 28° = 42°

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Answer:

8/15

Step-by-step explanation:

There is no GCF (greatest common factor) in this. These numbers are relatively prime.

Answer:

Below

Step-by-step explanation:

(5x+6) / 2   =  3 - ( 4x+12)    expand R side

(5x+6) / 2 = -4x - 9                      answer B     now multiply both sides by 2

5x + 6 = -8x - 18                          answer E

and finally

(5x+6) / 2 = 3 - (4x+12)          expand L side

5/2 x + 3  = 3 - (4x+12)         answer C

The indicated critical value for significance level of 0.03 should be approximately 1.88.

In standard normal distribution, the critical value is the mark or point that seperates region of acceptance and rejection. In one-tailed test having significance level of 0.03, it will indicate the probability of getting a value that will be more than or equal to 0.03.

The calculation of critical value can be done in many ways. Either look through the standard table or use calculator for the same. The latter is done by using inverse function on standard normal cumulative distribution function. It should be around 1.88.

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Answer:

Step-by-step explanation:

3(15.50 + x) = 60

46.5 + 3x = 60

3x = 60-46.5

x = 13.5/3

x = 4.5 or $4.50

Step-by-step explanation:

This is the answer for 1., but the steps are the same for the rest of the questions, so I am sure you will be able to get the rest!

Slope is the value in front of the X and basically tells us how far up or down the line moves in 1 square across the line. It goes up if it is positive, and down if it is negative.

Y-intercepts can be found by plugging in 0 for x.

For question 1:

y=[tex]\frac{3}{5}[/tex](0)+3=3 so the y-intercept is 3 up from 0.

Then, we can use our slope which is a fraction, the top can be thought of as rise and the bottom is run. This means each point will be 3 up and 5 to the right.

Answer:

2/ Points at (0,-5), ( 1,-4), (2,-3)

Step-by-step explanation:

The slope is rise/run

The slope is x, which mean = 1

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The total length of a boundary defines the perimeter of an equilateral triangle.

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Answer:

The equation for scenario is 2(l + b) = 3a

The rectangle’s perimeter is 2(l + b)

The equilateral triangle’s perimeter is 3a

What is perimeter ?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

According to question

The perimeters of a rectangle and an equilateral triangle are equal.

So

let,

The length and breadth of the rectangle are l & b

And

Side of an equilateral triangle is a

Now

The rectangle’s perimeter = 2(length + breadth)

⇒ 2(l + b)

And

The equilateral triangle’s perimeter = Sum of All sides

⇒ a + a + a

⇒ 3a

Therefore

    perimeters of a rectangle = perimeters an equilateral triangle

              2(l + b) = 3a

hence, 2(l + b) = 3a is the equation which show that perimeter of rectangle and equilateral triangle is equal.

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The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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The expression for the exact number of inches in 1 centimeter is 1/2.54.    Using a calculator to evaluate the expression gives 0.39370074. There may be a slight difference when converting due approximation of figures

Given the conversion facts:

1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch

a. The expression for the exact number of inches in 1 centimeter will be:

1 centimeter  = 1/2.54           (Since 1 inch = 2.54 centimeters)

b. Using a calculator to evaluate the expression in (a) will give:

1 centimeter  = 1/2.54  = 0.39370074

The measurement conversion may be slightly different when converting between metric units and U.S. custumary units because of the approximation of figures when converting from one unit to the other

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26 points are scored in the fifth game.

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

First four games, a netball team scores an average of 31 points per game.

x/4=31

Let x represents four games

x=124

After the fifth game, the average for the first five games is 30

y/5=30

Let y represents five games

y=150

We need to find the number of points scored in fifth game.

x-y

124-150

26

Hence, 26 points are scored in the fifth game.

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The measure of angle JIL is 59°.

We are given that;

Ray IL bisects angle HIJ, we know that the measure of angle HIL is equal to the measure of angle JIL.

Using the given expressions for these angles, we can write:

m∠HIL = m∠JIL

(6x − 7)° = (5x + 4)°

To solve for x, we can subtract 5x from both sides and add 7 to both sides:

x − 7 = 4

x = 11

Now that we have the value of x, we can plug it into the expression for m∠JIL and simplify:

m∠JIL = (5x + 4)°

m∠JIL = (5 × 11 + 4)°

m∠JIL = (55 + 4)°

m∠JIL = 59°

Therefore, by the angle the answer will be 59°.

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Since, there are 08 students in the class, among 02 of  them should be selected as the best students in the class. In 28 different ways this can be done.

Use the formula of combinations given as ⁿ[tex]C_{r}[/tex] to find the numbers of possible ways to select r things out of a total of n things. Let n be the total number of students in the class and r as the number of students required to be selected as best students in the class. Now, use the formula

ⁿ[tex]C_{r}[/tex] = [tex]\frac{r!}{(n- r)!}[/tex] to simplify the expression .

Given that a class has 8 students in which 2 students will be selected for a best students in the class. .

Therefore, n = 08 and r = 02, substituting these values in the formula we get,

Number of possible ways of selection = ⁿ [tex]C_{r}[/tex] = ⁸C₂

Now,

Number of possible ways of selection = [tex]\frac{8!}{2! ( 8 - 2)!}[/tex]

Or, Number of possible ways of selection = [tex]\frac{8!}{2! 6!}[/tex]

Solving further,

Number of possible ways of selection = 8 × 7× 6!/ 2× 1 ×6!

Number of possible ways of selection = 4 × 7 = 28

Hence, the total number of ways to select the required number of students is 28.

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As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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Answer: plug -15 in for x and if we get get -9 out because 2/3 of -15 is -10 and -10+1 =-9
we can do the same for the rest of these and we see that they'll come out to the y value