Multiply each pair of factors. type the product in the space provided. (6 3i)(6 − 3i) = (4 − 5i)(4 5i) = (−3 8i)(−3 − 8i) =

Any value in the interval (-∞,-2√5] ∪[2√5,∞) will cause the quadratic equation x2+bx+5 = 0 to have two real number solutions.

Given quadratic equation is:

[tex]x^{2} +bx+5=0[/tex]

Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a≠0.

To have two real number solutions the discriminant of a quadratic equation should be greater than or equal to zero.

[tex]D\geq 0[/tex]

[tex]b^{2} -4(1)(5)\geq 0[/tex]

[tex]b^{2}-20 \geq 0[/tex]

[tex]b^{2} -(2\sqrt{5}) ^{2}\geq 0[/tex]

[tex](b+2\sqrt{5} )(b-2\sqrt{5} )\geq 0[/tex]

b∈[tex](-\infty,-2\sqrt{5}][/tex]∪[tex][2\sqrt{5},\infty)[/tex]

Hence, any value in the interval (-∞,-2√5] ∪[2√5,∞) will cause the quadratic equation x2+bx+5 = 0 to have two real number solutions.

To get more about quadratic equations visit:

https://brainly.com/question/1214333

The probability that client D will be able to live to be 59 years old is 0.4.

Youe information is incomplete. Therefore, an overview of probability will be given.

Let's assume that there is an entire population of 50 people and the number of those that lives to 59 years is 20.

Therefore, the probability that can be deduced of those that live to 59 years will be:

= 20/50 × 100

= 2/5 × 100.

= 40%

= 0.4

In conclusion, the probability is 0.4.

Learn more about probability on:

https://brainly.com/question/24756209

Answer:

high chance tat it is 405/88. mixed farction = 4 53/88

Step-by-step explanation:

Answer:

B) Rs. 200 is C.P. when shopkeeper gains 20% even though he offers 20% discount on a watch having M.P. Rs 300

Answer:

Hamilton

Hamilton

Hamilton

Circuit

Circuit

Answer:

∅

Step-by-step explanation:

y = -x - 2

3x + 3y = 6

3x + 3(-x - 2) = 6

3x - 3x - 6 = 6

0x - 6 = 6

0 = 12

SOLUTION DNE (∅)

I hope this helps!

Check the picture below.

The graph of this equation runs through the point (2/3, 9/5), and it illustrates an inverse proportion, where y is inversely proportional to x.

An inverse proportion in mathematics is a relationship between two variables where a rise in one variable causes a fall in the other and vice versa. The two variables are thus inversely proportional to one another.

Let x be the independent variable and y be the dependent variable in an inverse proportion. Then the general form of an inverse proportion is:

y = k/x

where k is a constant of proportionality.

To find the specific formula for an inverse proportion that goes through the point (2/3, 9/5), we can substitute these values into the equation and solve for k:

y = k/x

9/5 = k/(2/3)

Multiplying both sides by (2/3), we get:

k = (9/5) * (2/3) = 6/5

Therefore, the specific formula for the inverse proportion is:

y = (6/5) / x

y = 6/(5x)

This equation represents an inverse proportion, where y is inversely proportional to x, and the graph of this equation passes through the point (2/3, 9/5).

To know more about inverse proportion follow

https://brainly.com/question/21294876

#SPJ2

Answer:

y = -1/2x+1

Step-by-step explanation:

First step is to find the slope

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

    = ( 4-2)/(-6 - -2)

       (4-2)/(-6+2)

       2/-4

     -1/2

Then we can use the slope intercept form of a line

y = mx+b  where m is the slope and b is the y intercept

y = -1/2x+b

Substitute a point into the equation to find b

2 = -1/2(-2) +b

2 = 1+b

Subtract 1 from each side

1 =b

y = -1/2x+1

y = mx + b

Where m = slope and b is the y intercept

Let's find the slope = change in y/change in x

m = (4-2)/(-6+2) = 2/-4 = -1/2

Now we have:

y = (-1/2)x + b

Now substitute point (-6,4)

4 = (-1/2)(-6) + b

4 = 3 + b

b = 1

So y = (-1/2)x + 1 is the equation

ANSWER:

[tex]y=(-\frac{1}{2})x[/tex]+1

so letter c

Answer:

I guess both of the answers are correct.Hope the picture will help you.....

Answer: the answer on khan academy is 144 pie units^3

Answer:

18 Games

Step-by-step explanation:

For this problem we will have to use the same percentage Therom again, except this time we are solving for a diffrent variable.

Total Games * Percentage won in fraction form = Games won

Fill the values.

30 * 3/5 = X

Simplify

18=X

Step-by-step explanation:

[tex] = 1 \frac{1}{2} - 1 \frac{1}{4} \\ [/tex]

[tex] = \frac{1 \times 2 + 1}{2} - \frac{1 \times 4 + 1}{4} \\ [/tex]

[tex] = \frac{3}{2} - \frac{5}{4} \\ [/tex]

[tex] = \frac{3}{2} \times \frac{2}{2} - \frac{5}{4} \times \frac{1}{1} \\ [/tex]

[tex] = \frac{6 - 5}{4} \\ [/tex]

[tex] = \frac{1}{4} \\ [/tex]

The value of the definite integral is 68.

We have,

Break down the integral into two parts:

[tex]\int\limits^6_2 (5f(x) + 2)dx = \int\limits^6_2(5f(x)dx + \int\limits^6_2(2)dx[/tex]

Given that the average value of f(x) on this interval is 3, replace 5f(x) with 5 * 3 = 15:

[tex]\int\limits^6_2 (5f(x)dx = \int\limits^6_2(15)dx[/tex]

= 15(6 - 2)

= 15(4)

= 60

And,

[tex]\int\limits^6_2 2 dx = 2 [6 - 2] = 8[/tex]

Adding both parts of the integral:

= 60 + 8

= 68

Therefore,

The value of the definite integral is 68.

Learn more about integrations here:

https://brainly.com/question/27360126

#SPJ12

Answer:

Sector area= 3.143 units²

Arc length = 2.095 units

Answer:

arc length = 3 * 40° * (PI / 180)

arc length = 2.0943951024

sector area = (radius * angle (radians))

sector area = (3 * 0.6981317008)

sector area = 3.1415926536

Source: https://www.1728.org/radians.htm

Step-by-step explanation:

Answer:

∠ E ≈ 71°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos E = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EG}{EF}[/tex] = [tex]\frac{21}{63}[/tex] , then

∠ E = [tex]cos^{-1}[/tex] ( [tex]\frac{21}{63}[/tex] ) ≈ 71° ( to the nearest degree )

Answer:

1/3rd a cup

Step-by-step explanation:

make me brainly

Answer:

B

Step-by-step explanation:

Is the correct answer

Answer:

16.3 ft

Explanation:

circumference of circle = 2πr       ( r is the radius )

Here radius = 2.6 ft

Circumference:

Digram :

[tex] \setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 2.6ft\ cm}\end{picture}[/tex]

[tex] \\ \\ [/tex]

Given :

[tex] \\ \\ [/tex]

To find :

[tex] \\ \\ [/tex]

Solution :-

We know :

[tex] \boxed{ \rm Circumference_{(\sf circle)} = 2\pi \: radius}[/tex]

[tex] \\ [/tex]

So:-

[tex] \dashrightarrow\sf Circumference_{(\sf circle)} = 2\pi \: radius \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf Circumference_{(\sf circle)} = 2 \times \dfrac{22}{7} \times 2.6\\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf Circumference_{(\sf circle)} = 2 \times \dfrac{22}{7} \times \dfrac{26}{10} \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf Circumference_{(\sf circle)} =\dfrac{44}{7} \times \dfrac{26}{10} \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf Circumference_{(\sf circle)} =\dfrac{1144}{7 \times 10} \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf Circumference_{(\sf circle)} =\dfrac{1144}{70} \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\bf Circumference_{(\bf circle)} =16.34~ft\{approx\} \\ [/tex]

Answer:

I think the answer is No

Step-by-step explanation:

It is not a function because there cannot be two points on the same x value. Hope I remembered this correctly.

For ellipses:

-First, let's use completing the square method to determine values of a(semi-major axis), b(semi-minor axis), and the coordinates of the center of the ellipse.

-The center of the ellipse is at C(5, 3), semi-major axis, a = 4, and semi-minor axis, b = 2.

-Since the major axis of the ellipse is horizontal, the distance between the center of the ellipse and the co-vertices of the ellipse is ±b.

-The coordinates of the co-vertices of the ellipse are:

For the parabola:

-We have the following data:

The parabola is opening to the left and axis symmetry along the major axis of the ellipse (axis of symmetry: y = 3):

The focus of the parabola is the center of the ellipses.

-The parabola is passing through the co-vertices of the ellipse:

-The parabola is passing through poînts (5, 5) and (5, 1)

-From the first data, we know that the value of k is equal to 3 because the axis of symmetry of the parabola is y = 3.

-From the second data, we know that the x-coordinate of the vertex is at h = 5 + a. (Note: the distance of the focus of the parabola and the vertex of the parabola is equal to ±a, since the parabola is opening the the left we use -a)

[tex]\mathsf{F=(5,3)}[/tex]

-Substitute the coordinates of the vertex of the parabola

-From the third data, we know that if the poînts lies on the parabola, the coordinates of the poînts must satisfy the equation of the parabola.

Using the point (5, 5), x = 5, y = 5:

-Another way to solve for the value of a is using the formula for the length of the latus rectum (LR = 4a). Since the length of the latus rectum is equal to the minor axis of the ellipse, we can easily solve for the value of a.

-Substitute the value of a in the equation:

(ノ‥)ノ

The total amount accrued, principal plus interest, with compound interest on a principal of $3,500.00 at a rate of 2.25%  is $4,779.19.

Given Data

A = P + I where

P (principal) = $3,500.00

I (interest) = $1,279.19

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.25/100

r = 0.0225 rate per year,

Then solve the equation for A

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

A = 3,500.00(1 + 0.0225/1)^(1)(14)

A = 3,500.00(1 + 0.0225)^(14)

A = $4,779.19

Learn more about compound interest here:

https://brainly.com/question/24924853

Answer:

x = 85°

y = 45°

Step-by-step explanation:

For x, a line measures 180°, so subtract 95° from 180° to get 85°.

For y, all the angles in a triangle measure to 180°, and since we know x, add it to 50° and subtract it from 180°. 85° + 50° = 135°, and 180° - 135° = 45°

Answer:

x = 85

y = 45

Step-by-step explanation:

for x, angles on a straight line add up to 180 so 95 + x = 180 then evaluate for x

for y, angle in a triangle add up to 180 so 50+85 (as evaluated for x) +y= 180 and evaluate for y

Answer:

=d+6c

Step-by-step explanation:

I hope this is the right answer

Answer:

3(5x^2+7x+2)

Step-by-step explanation:

(5x+2)(3x+3)

I use the foil method, but if you need to use a different method you can look online at how it is done, but this should give you the correct answer.

First

Outside

Inside

Last

First you multiply 5x and 3x together (the first values in each bracket), which gives you 15x squared (15x^2)

Then you multiply the 5x and 3 (the values on the "outside" of the equation --> first and last) which gives you 15x

Then you multiply the "inside" values (the ones in the middle of all the terms), which is 2 and 3x, and gives you 6x

Last you multiply the 2 values that are last in each bracket, 2 and 3, which gives you 6

So then you put then in order of the exponent

15x^2+15x+6x+6

Then you collect like terms (which means terms that have the same number of the variable) and you're left with the answer

15x^2+21x+6

Then most likely you need to further simplify and you can common factor a number out (take the highest number that evenly mutiplies into each term and divide it out of each), so that you have,

3(5x^2+7x+2)

The method which is used for every third person on a list of soccer players selected for a survey is known as systematic sampling.

The sampling method is the method of selecting the subset from the set to make a statical inference.

Because of its simplicity, systematic sampling, also known as the nth name selection approach, is frequently employed instead of random sampling. Following the collection of the sample, every nth person of the population is registered in the sample.

Thus, the systematic sampling method is used.

More about the sample method link is given below.

https://brainly.com/question/15125943

#SPJ1

Answer:

(

x

,

y

)

=

(

26

5

,

−

6

5

)

Step-by-step explanation:

Answer:

120 degrees

Step-by-step explanation:

the angle at the center is called the central angle and you can tell because J is the center of the circle

The minor arc that is between point H and point K (the shorter way) is the same measure as the central angle