The quadratic function g(x)=ax^2+bx+c has the complex roots (-5+9i) and (-5-9i).
What is the value of a?
What is the value of b?
What is the value of c?

The given information of the base length and the height of the

rectangle are sufficient to find the area of the triangle.

Correct response:

Given that the parameters are;

The base of the triangle = [tex]\sqrt{245}[/tex] cm

The height of the triangle = [tex]\mathbf{\sqrt{20}}[/tex] cm

Required:

To find the area of the triangle

Solution:

Therefore, the area, A, of the given triangle is given as follows;

[tex]A = \dfrac{1}{2} \times \sqrt{245} \ cm \times \sqrt{20} \ cm= \dfrac{1}{2} \times \sqrt{4,900} \ cm^2= \dfrac{1}{2} \times 70 \ cm^2 = 35 \ cm^2[/tex]

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The radius of the table top, rounded to 1 dp is 5.6 cm

From the question,

We are to determine the radius of the table top

First, we will determine the volume of the cylindrical wooden table

From the given information

Density = 0.42 g/cm³

Mass = 0.25 kg = 250 g

Using the formula

[tex]Volume = \frac{Mass}{Density}[/tex]

∴ [tex]Volume = \frac{250}{0.42}[/tex]

Volume = 595.238 cm³

Now, for the radius of the table top

Using the formula for volume of a cylinder

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

Where V is the volume

r is the radius

and h is the height or depth

From the given information

h = 6cm

Putting the parameters into the formula

[tex]595.238 = \pi r^{2} \times 6[/tex]

∴ [tex]r^{2} = \frac{595.238}{6\pi }[/tex]

[tex]r^{2} =31.57835667[/tex]

[tex]r =\sqrt{31.57835667}[/tex]

r = 5.6 cm

Hence, the radius of the table top, rounded to 1 dp is 5.6 cm

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[tex]\huge\textbf{Hey there!}[/tex]

[tex]\huge\textsf{-1 - [-z]}\\\\\huge\textsf{= -1 - [- -2]}\\\\\huge\textsf{= -1 - - 2}\\\\\huge\textsf{= -1 + (-2)}\\\\\huge\textsf{= -1 - 2}\\\\\huge\textsf{= -3}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

-3

Step-by-step explanation:

Evaluate - 1 - ( - z ) where z = -2

you can find this out because when there are two minuses by each other it equals a positive but then z = -2 so that adds another minus so it narrows it down to -1+-2 which equals 3

Answer:

67.5% or 68%

Step-by-step explanation:

Say each group has 100 students. 25% of 100, is 25 students.

25 students of group 1 prefers acrylic. That leaves 75 students that prefer watercolor.

60% of group 2, or 60 students, prefer water color. That leave 40 students that prefer acrylic.

25+40=65

60+75=135

That is true, since there are 200 students in total.

Now set up a ratio, with watercolor over acrylic.

135:65

135 is 67.5% of 200.

I really don't know if that is a choice, so maybe 68%?

-hope it helps

Answer:

76, 76 104

Step-by-step explanation:

Angle 3 is vertical so it is congruent to Angle 2.

Angle 6 is corresponding, so it is congruent to Angle 2.

Angle 8 is linear to Angle 6, so they add to 180

Answer:

see explanation

Step-by-step explanation:

(a)

∠ 2 and ∠ 3 are vertically opposite angles and are congruent , then

∠ 3 = 76°

(b)

∠ 3 and ∠ 6 are corresponding angles and are congruent , then

∠ 6 = 76°

(c)

∠ 2 and ∠ 8 are same- side exterior angles and sum to 180° , that is

∠ 8 + 76° = 180° ( subtract 76° from both sides )

∠ 8 = 104°

Answer:

x = 5/8

Step-by-step explanation:

[tex]\frac{8x}{8} = \frac{5}{8}[/tex]

x=[tex]\frac{5}{8}[/tex]

Answer:

a) not one to one function; horizontal line intersects the graph of the function more than once.

b) yes it's a one to one function; the graph passes the horizontal line test

c) not one to one function; the graph doesn't pass the horizontal line test

d) yes it's a one to one function; the horizontal line doesn't intersect the function more than once

Answer:

155

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

it's the point T.

Hope it helps

Answer:

Compare the constants of the two variables.

Changed at the same rate, or by the same factor, then they are directly proportional. For example, since the x-coordinates changed by a factor of 2 while the y-coordinates also changed by a factor of 2, the two variables are directly proportional.

Step-by-step explanation:

Answer:

reflection over the y axis

Step-by-step explanation:

3(x+3-4+5-x-4-x-6)=10

-3x/-3= -28/3

x= -28/3

Answer:

33

Step-by-step explanation:

Let the number be x,

=> (x - 16) -2 = - 34

=> -2x + 32 = -34

=> -2x = - 34 - 32 (by transposing)

=> -2x = -66

=> x = -66/-2 = 33

Peter's number is 33.

Hope you understood.

Answer:

C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5.

Step-by-step explanation:

Answer:

h = a * sin α

Step-by-step explanation:

The easiest answer is utilizing Law of Sines: a / Sin A = b / Sin B = c /Sin C

a and ∠α : known

∠AEB = 90°

a / Sin 90° = h / Sin α   .. Sin 90° = 1

h = a * sin α

In writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X

Recall:

Thus, Tina's comparison is given in the diagram attached below.

The comparison labelled X is incorrect because -(-9) = 9. Opposite of 9 is -9.

Therefore, in writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X

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Equivalent expressions are expressions that have the same value, and can be used interchangeably.

The result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]

The expression is given as:

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex]

Rewrite the expression as:

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})[/tex]

Evaluate the roots

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})[/tex]

Open the brackets

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})[/tex]

The above expression cannot be further simplified.

Hence, the result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]

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The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].

We have to determine, the sum of the given expression.

According to the question,

Expression; [tex]2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})[/tex]

To determine the sum of the given expression following all the steps given below.

Rewrite the expression term in the form of their cubes,

[tex]\rm = 2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})\\\\ = 2(\sqrt[3]{2^4x^3y} +4(\sqrt[3]{3^3 \times 2 \times x^6y^5})\\\\= 2\times 2(\sqrt[3]{x^3y} +4\times 3(\sqrt[3]{ 2 \times x^6y^5})\\\\= 4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\\\=4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex]

Hence, The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].

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Answer:

5 pints is needed

Step-by-step explanation:

2 pints of white paint for pink

1 pint of red for pink

10 pints of white paint = 5 pints of red

Answer:

look at the pivots (the leading 1's of the rows)

Step-by-step explanation:

Then, look at the pivots (the leading 1's of the rows). If we have a pivot in every column, then the nullspace of the matrix (and hence the kernel of T) is zero-dimensional. So, T is one-to-one if and only if the REF has pivot in every column.

Answer:

4

Step-by-step explanation:

Answer:

3.95 ≈ 4

Step-by-step explanation:

A whole number refers to a whole integer, meaning there can be no decimals or fractions. Follow the rule 4 and below to round down, and 5 and above to round up.

Answer:

5 + 5 = 10

10 + 10 = 20

20 + 20 = 40

40 + 40 = 80

80 is the answer.

Answer: 10,400

Step-by-step explanation:

I=  ?        P=   10,000       R=   4%        T= 3 yrs

Answer:

the asnwer is (2,3)

Step-by-step explanation:

Answer:

  yes; the distributive property applies to dot products

Step-by-step explanation:

The product of (a-b) with itself is ...

  (a -b)·(a -b) = a² -2ab +b²

because the commutative and distributive properties apply to multiplication.

  (a -b)·(a -b) = a(a -b) -b(a -b) = a² -ab -ba +b² = a² -ab -ab +b² = a² -2ab +b²

__

The same expansion works for the dot product operation, because the commutative and distributive properties hold for that operation, as well.

  (u −v)•(u −v) = u•(u -v) -v•(u -v) = u•u -u•v -v•u +v•v

  = u•u -u•v -u•v +v•v = u•u -(u+u)•v +v•v = u•u -2u•v +v•v

_____

Additional comment

The proof of any of the properties of the dot product relies on expressing the vectors in component form. The distributive property is no exception.

Answer:

1. if x + 5 = 12, then x = 7

:Subtraction property of equality

2. If x + y = 20, and y = 5, then x + 5 = 20.

:Substitution property of equality

3. If 2x3 = 11, then 11 = 2x - 3.

:Symmetric property of equality

x^2 = 25

x = -5, 5

Check your work!

(-5)^2 = 25

(5)^2 = 25

Hope this helps! :)

Answer:

39

Step-by-step explanation:

There is a possibility that this triangle is isosceles. Angles in triangles add up to 180. 102-180=78. Since we are assuming this triangle is isosceles, we can just divide 78 by 2 and get 39 which might be the other two angles. They might both be 39 degrees.

Since triangle angles must add up to 180 degrees, the other angles must add up to 78 degrees. One possible pair could be if you divided 78 in half, which is 39. There could also be tons of more I can provide a list of below:

39,39

40,38

35,43

Answer:

10

Step-by-step explanation:

Answer:

image 1 : 3.78

image 2 : 10.20

Step-by-step explanation:

I haven't done geometry in a bit but I'll try to help!