use the discriminant to determine the number of solutions to the quadratic equation −6z2−10z−3=0. What are the real solutions and complex solutions?

Answer:

11

Step-by-step explanation:

y-1=10

Any figure that crosses equal sign, the operational sign changes.

y=10+1

y= 11

Answer:

157.8

Step-by-step explanation:

Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)

Given:

The sum of the first three terms = 12

The sum of the first six terms = (−84).

To find:

The third term of a geometric progression.

Solution:

The sum of first n term of a geometric progression is:

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Where, a is the first term and r is the common ratio.

The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).

[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex]               ...(i)

[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex]               ...(ii)

Divide (ii) by (i), we get

[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]

[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]

[tex]r^3+1=-7[/tex]

[tex]r^3=-7-1[/tex]

[tex]r^3=-8[/tex]

Taking cube root on both sides, we get

[tex]r=-2[/tex]

Putting [tex]r=-2[/tex] in (i), we get

[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]

[tex]\dfrac{a(-8-1)}{-3}=12[/tex]

[tex]\dfrac{-9a}{-3}=12[/tex]

[tex]3a=12[/tex]

Divide both sides by 3.

[tex]a=4[/tex]

The nth term of a geometric progression is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get

[tex]a_3=4(-2)^{3-1}[/tex]

[tex]a_3=4(-2)^{2}[/tex]

[tex]a_3=4(4)[/tex]

[tex]a_3=16[/tex]

Therefore, the third term of the geometric progression is 16.

Answer:

9.5hrs

Step-by-step explanation:

since they are working together you have to take the average time since is the same order

Answer:

5%

Step-by-step explanation:

Hospital A (with 50 births a day), because the more births you see, the closer the proportions will be to 0.5.

Hospital B (with 10 births a day), because with fewer births there will be less variability.

The two hospitals are equally likely to record such an event, because the probability of a boy does not depend on the number of births

Two hospitals have an equal chance of recording such an event.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given

Hospital A (with 50 births per day), as the proportions will be closer to 0.5 the more births you see.

Hospital B (with 10 births per day), thus there will be less unpredictability with fewer births.

Due to the fact that the likelihood of a boy does not rely on the number of births, the two hospitals have an equal chance of recording such an event.

To learn more about probability refer to:

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Answer:

C

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

Since you didn't mention which question.

Step-by-step explanation:

13.

[tex]1.\overline{52}\\[/tex] = 1.525252...

Let x = 1.525252...

    10x = 15.2525252....

    100x = 152.525252...

100x - x = 151.00

99x = 151

[tex]x = \frac{151}{99}\\\\or\\\\x = 1 \frac{52}{99}[/tex]

14.

4x + 10 = 8x - 26                        [ corresponding angles are congruent ]

4x - 8x = - 26 - 10

- 4x = - 36

[tex]x = \frac{-36}{-4} \\\\x = 9[/tex]

15.

Given breadth of a rectangle is ( 2/3) its length.

Let the length be x

Therefore, breadth = ( 2 /3) of x

                             [tex]= \frac{2}{3} \times x\\\\=\frac{2}{3}x[/tex]

Given perimeter = 40m

Perimeter of a rectangle = 2( length + breadth)

                                [tex]40 = 2 (x + \frac{2}{3}x )\\\\\frac{40}{2} = \frac{2}{2}(x + \frac{2}{3}x)\\\\20 = x + \frac{2}{3}x\\\\20 = \frac{3x + 2x}{3}\\\\20 \times 3 = 5x \\\\x = \frac{60}{5}\\\\x = 12\\\\Therefore, Length = x = 12 \ m \ and \ breadth = \frac{2}{3}x = \frac{2}{3} \times 12 = 8 \ m[/tex]

16.

Sum of the angles of a triangle = 180°

Given ratio = 2 : 3 : 4

Sum of the ratio = 9

Therefore,

            [tex]first \ angle = \frac{2}{9} \times 180 = 2 \times 20 = 40 ^\circ\\\\Second \ angle = \frac{3}{9} \times 180 = 3 \times 20 = 60^\circ\\\\Third angle = \frac{4}{9} \times 180 = 4 \times 20 = 80^\circ[/tex]

17.

Sum of interior angles of a polygon with n sides = ( n - 2) x 180°

Given polygon is pentagon, that is n = 5

Therefore, sum of the interior angles = ( 5 - 2) x 180 = 3 x 180 = 540°

That is ,

          x + 125 + 125 + 88 + 60 = 540°

          x + 398 = 540°

          x = 540 - 398

          x = 142°

Answer:

Please can you say which question?

Thank you

Answer:

dddddddddv

Step-by-step explanation:

Answer:

0.371

Step-by-step explanation:

The ratio comparing students enrolled in a French course to students enrolled in a Spanish course rounded to the thousandths place is 0.371.

A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.

Now it is given that,

Students enrolled in a French course = 92

Students enrolled in a Spanish course = 248

So, Ratio comparing students enrolled in a French course to students enrolled in a Spanish = Students enrolled in a French course / Students enrolled in a Spanish course

⇒ Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 92/248

⇒ Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 0.370967

To rounded to the thousandths place, the digit at the thousandth place is 0 and right to it is 9 which is greater than 5 so round up the place value at thousandths place.

⇒ Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 0.371

Thus, the ratio comparing students enrolled in a French course to students enrolled in a Spanish course rounded to the thousandths place is 0.371.

To learn more about ratio:

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Answer:

16?

Step-by-step explanation:

I'm not sure. I hope so.

Answer:

-18

Step-by-step explanation:

Answer: -18 is the difference

Step-by-step explanation:

Evaluate = -18

Answer:

see graph

Step-by-step explanation:

Answer:

Let's solve for k.

x2−y2=k

Step 1: Flip the equation.

k=x2−y2

Answer:

k=x2−y2

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

You can say lots of things about the y-values of these functions. A couple of observations are listed above. In addition, we can say the y-values of g(x) will be greater than those of f(x) for x-values not equal or between the x-values where the y-values are the same.

Answer:

• g(x) has the smallest possible y-value.

• The minimum y value of g(x) is -3.

Step-by-step explanation:

Ap3x

Answer:

B. h = 7.4 inches

Step-by-step explanation:

height of the laptop screen = h

d = 12.1 in.

w = 9.6 in.

We are given the formula,

d = √(w² + h²)

Plug in the values and solve for h

12.1 = √(9.6² + h²)

Square both sides

12.1² = 9.6² + h²

146.41 = 92.16 + h²

146.41 - 92.16 = h²

54.25 = h²

√54.25 = h

7.4 = h (nearest tenth)

h = 7.4 inches

Answer:

= x^2 + 3 + √3x^2 - 1

Step-by-step explanation:

Remove parentheses: (a) = a

= x^2 + 3 + √x . 3x - 1

x . 3x = 3x^2

= x^2 + 3 + √3x^2 - 1

Hi there I hope you are having a great day :) I am pretty sure that you do 280 degrees around angle so i would say you would add 63 + 73 + 83 = 219 then you would take away it 280 - 219 =  61 so y must equal to 61 this is because we can see a z shape and a z shape adds up to 280.

Hopefully that helps you.

Answer:

1.5%

Step-by-step explanation:

house value x property tax rate = property taxes

70,000 x property tax rate = 1050

property tax rate = 1050/70000

property tax rate = .015 0r 1.5%

Answer:

annual -  $9,231.74  

quarterly - $9,363.06  

monthly -  $9,394.09  

continuously -$9,409.87  

Step-by-step explanation:

Answer:

128 for 4.99

64 for 2.99 times 2 is more than 4.99.

12 oz. for 0.99 is also more than 4.99.

Answer:

[tex]x = 2[/tex]

[tex]y = -2[/tex]

Step-by-step explanation:

Given

[tex]2x + y = 2[/tex]

[tex]2x + 2y = 0[/tex]

Required

Solfe for x and y

Subtract both equations

[tex]2x- 2x + y - 2y = 2 -0[/tex]

[tex]-y = 2[/tex]

Divide by -1

[tex]y = -2[/tex]

Substitute [tex]y = -2[/tex] in [tex]2x + 2y = 0[/tex]

[tex]2x+2 *-2 = 0[/tex]

[tex]2x-4 = 0[/tex]

[tex]x - 2 = 0[/tex]

Collect like terms

[tex]x = 2[/tex]

Answer:

$2419469.58

Step-by-step explanation:

You are given the original player salary and told that there is a pay decrease of 2.7%.

So New Salary= Original Salary-Pay Decrease.

If original is 100% and pay decrease is 2.7% then the new salary is 97.3% of original.

New Salary= 0.973*2486609=$2419469.58

Given:

The numbers are [tex]\dfrac{3}{5},2,0,1,-0.45, 1.44[/tex].

To find:

All the values that cannot be probabilities.

Solution:

We know that,

[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

The minimum value of favorable outcomes is 0 and the maximum value is equal to the total outcomes. So, the value of probability lies between 0 and 1, inclusive. It other words, the probability lies in the interval [0,1].

[tex]0\leq \text{Probability}\leq 1[/tex]

From the given values only [tex]\dfrac{3}{5}, 0, 1[/tex] lie in the interval [0,1]. So, these values can be probabilities.

The values [tex]2,-0.45, 1.44[/tex] does not lie in the interval [0,1]. So, these values cannot be probabilities.

Therefore, the correct values are [tex]2,-0.45, 1.44[/tex].

Answer:

5/9

Step-by-step explanation:

What we have in this question are four white balls and 5 red balls.

This is the sample space

[(4w,0R) (4w,1R)(4w,2R)(4w,3R)(4w,4R)(0w,5R)(1w,5R)(2w,5R)

So we have 9 possible sets of events

The event number with the last ball being white = 5

Probability of the last ball drawn being white = 5/9

= 0.56

Answer:

2 kilometers

Step-by-step explanation:

every 1 kilometer is a 1/2 hour. double that and you get 2

Answer:

X<6 or X>24

Step-by-step explanation:

9514 1404 393

Answer:

  (b)  √55

Step-by-step explanation:

The right triangles in this geometry are all similar, so the ratio of long side to short side is the same:

  y/5 = 11/y

  y² = 55 . . . . . . multiply by 5y

  y = √55 . . . . . take the square root

__

And x=4√5 by looking at ratios of short side to hypotenuse.

Answer:

1

Step-by-step explanation: