the diagonals of a rectangle ABCD meet at O if AO=(2x+3)cm and DO=(5x)cm find the length of its diagonals also find the perimeter of the rectangle if AB=8cm.
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The polynomial function of least degree with only real coefficients will be;  y = x³ - 8 · x² + 22 · x - 20.

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.

The statement indicates that the polynomial has  real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.

By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;

y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)

y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 3) · (x² - 6 · x + 9 - i²)

y = (x - 3) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer:

\(p(x)=x^3-5x^2+16x-30\)

Step-by-step explanation:

Given information:

For any complex number  \(z = a+bi\) , the complex conjugate of the number is defined as  \(z^*=a-bi\).  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.

Therefore, the polynomial in factored form is:

\(p(x)=a(x-3)(x-(1-3i))(x-(1+3i))\)

As the leading coefficient is 1, then a = 1:

\(p(x)=(x-3)(x-(1-3i))(x-(1+3i))\)

Expand the polynomial:

\(\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))\)

\(\implies p(x)=(x-3)(x-1+3i)(x-1-3i)\)

\(\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)\)

\(\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)\)

\(\implies p(x)=(x-3)(x^2-2x+1-9(-1))\)

\(\implies p(x)=(x-3)(x^2-2x+10)\)

\(\implies p(x)=x^3-2x^2+10x-3x^2+6x-30\)

\(\implies p(x)=x^3-2x^2-3x^2+10x+6x-30\)

\(\implies p(x)=x^3-5x^2+16x-30\)

Answer:

P (subject had a positive test result or a negative test result) = 1

Step-by-step explanation:

Given

The table above

Required

P (subject had a positive test result or a negative test result)

This is calculated as follows;

P (subject had a positive test result or a negative test result) =

P (subject had a positive test result) + P (subject had a negative test result)

Calculating P (subject had a positive test result)

This can be calculated by number of subjects with positive results divided by 1000

Only data from the column of subjects with positive results will be considered.

Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs

Number of subjects = 76 + 95

Number of Subjects = 171

P (Subject had a positive test Result) = 171/1000

Calculating P (subject had a negative test result)

This can be calculated by number of subjects with negative results divided by 1000

Only data from the column of subjects with negative results will be considered.

Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs

Number of subjects = 6 + 823

Number of Subjects = 829

P (Subject had a negative test Result) = 829/1000

Hence, P (subject had a positive test result or a negative test result) =

P (subject had a positive test result) + P (subject had a negative test result) = 171/1000 + 829/1000

P (subject had a positive test result or a negative test result) = (171 + 829)/1000

P (subject had a positive test result or a negative test result) = 1000/1000

P (subject had a positive test result or a negative test result) = 1

Answer:

3 ⅙

Step-by-step explanation:

38 and 12’s common factor would be 2. Now the fraction is 19/6.

How many 6’s can fit into 19? 3. With a remainder of 1 we have:

3 ⅙

Answer:

area = (0.5*6*8)+(0.5*3.14*4*4) = 49.12 ft2

Answer: 49.12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

you need to get rid of brackets and as you can see they equal to each other

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

3)  \(f^{-1}(x)=\frac{4x+3}{5}\)

The value of diameter and radius of circle is 7 cm and 3.5cm.

According to the statement

we have given that the a figure of circle and we have to find the radius and the diameter of the circle.

So, We know that the

The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.

Here from the figure it is clear that the

Diameter of circle = 7cm

and the radius of circle we have to find

So,

Radius of circle = Diameter /2

Substitute the values in it then

Radius of circle = 7cm /2

Radius of circle = 3.5 cm.

So, The value of diameter and radius of circle is 7 cm and 3.5cm.

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Answer:

The first number is 272 and the second number is 273

Step-by-step explanation:

Let x = the first number

Let x+1 = the second number

Consecutive just means two numbers in order like 6 and 7  or 152 and 153.

x + (x+1) = 545  I put the parentheses in so that you can see the first number and the second number.  It is not needed, so I will remove

x + x + 1 = 545  Combine the x's)

2x + 1 = 545  Subtract 1 from both sides of the equation

2x = 544  Divide both sides by 2

x = 272 Is the first number, so the second number is 273

Check:

272 + 273 = 545

An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73

The formula for finding the equation of a circle is expressed as:

(x-a)^2 + (y - b)^2 = r^2

Determine the value of r^2 using the distance between two points

r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9

r^2 = 73

Given the centre (a, b) as (-3, 2), the equatio of the circle will be;

(x-(-3))^2 + (y - 2)^2 = 73

(x+3))^2 + (y - 2)^2 = 73

Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73

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Answer:

Nia answerd 45% of the questions correctly.

9514 1404 393

Answer:

  P(x) = x³ -5x² +12x -8

Step-by-step explanation:

If the coefficients are real, then the complex roots must be conjugates. The third root is 2+2i. For root r, (x -r) is a factor, so the factorization is ...

  P(x) = (x -1)(x -2 +2i)(x -2 -2i) = (x -1)((x -2)² +4) = (x -1)(x^2 -4x +8)

Expanding further, we find ...

  P(x) = x³ -5x² +12x -8

Answer:

the answer is c becaus it id the longes tone

Step-by-step explanation:

Answer:

I believe the answer is B.

sorry if i'm wrong .-.

Step-by-step explanation:

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{MN}\\ o=\stackrel{opposite}{18} \end{cases} \\\\\\ MN=\sqrt{ 30^2 - 18^2} \implies MN=\sqrt{ 576 }\implies MN=24 \\\\[-0.35em] ~\dotfill\\\\ \cos(M )=\cfrac{\stackrel{adjacent}{24}}{\underset{hypotenuse}{30}} \implies \cos(M)=\cfrac{4}{5}\)

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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Answer:

31°

Step-by-step explanation:

The total triangle is 180°

Subtract 180-(33+116)

Answer:

I think the one on the left is 285.26

Rounding to the nearest whole number. The correct option is D) 216 m²; 244 m².

Since the prism has a rectangular base, we know that its lateral faces are all rectangles with heights equal to the height of the prism. Let's first find the lateral area of the prism using the formula:

Lateral Area = Perimeter of Base * Height

The perimeter of the base is the sum of the lengths of all four sides of the rectangle. Since there are two bases, we will add their perimeters together. The length and width of each base are 12 m and 7 m, respectively, so:

Perimeter of Base = 2 * (Length + Width) = 2 * (12 + 7) = 38 m

The height of the prism is given as 10 m, so:

Lateral Area = 38 * 10 = 380 m²

Next, we need to find the surface area of the prism. This consists of the lateral area we just found, plus the areas of the two bases. Each base has an area of 12 * 7 = 84 m², so:

Surface Area = 2 * Base Area + Lateral Area = 2 * 84 + 380 = 548 m²

Rounding to the nearest whole number, we get:

Lateral Area ≈ 380 m²

Surface Area ≈ 548 m²

Therefore, the answer is option D) 216 m²; 244 m².

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Answer:

Step-by-step explanation:

Area of a triangle is a*b divided by 2

Lets assume a = 8 and b= 9

8 *

9=72

72/2=36

Answer:

Step-by-step explanation:

Test scores:

Average:

Required score is 95

Through the use of a protractor, angles are measured in degrees (°). In order to calculate or draw angles in terms of degrees, a protractor is a measuring tool that is utilized.

Does a linear pair have a 180 degree angle?

How to find the measure of the angle?

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Answer:

2.069, 2.69, 2.6912, 2.7

Step-by-step explanation:

Step-by-step explanation:

from which text book please

Answer:

7250%

Step-by-step explanation:

To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.

72 1/2 is equivalent to 72.5 as a decimal.

To convert it to a percentage:

72.5 * 100 = 7250

Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.

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