For each expression, combine like terms.

The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

The equation is given as:

x^2 + (1 - k).x+k-3 = 0

For an equation to have real root, then the following must be true:

[tex]b^2 \ge 4ac[/tex]

In x^2 + (1 - k).x+k-3 = 0, we have:

a = 1

b = 1 - k

c = k - 3

So, we have:

[tex](1 - k)^2 \ge 4 * 1 * (k - 3)[/tex]

Evaluate

[tex]1 - 2k + k^2 \ge 4k - 12[/tex]

Collect like terms

[tex]k^2 - 2k - 4k + 1 + 12 \ge 0[/tex]

[tex]k^2 - 6k + 13 \ge 0[/tex]

Using a graphing calculator, the value of k is all real numbers

Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

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Answer:

25x + 35(2x) = 380

25x + 70x = 380

95x = 380 so

x = 4

then i think that mean it might be 8 then im not completly sure

Answer:

B) 114.511m^3

Step-by-step explanation:

Formula of a cylinder is πr^2 x h

r = radius (half of diameter)

h = height

Since it is 3/4 full you only do 3/4 of the height so- 0.75 x 9.60 which equals 7.2

Half of the diameter is 2.25. 2.25^2 = 5.0625.

The volume of the cylinder = 5.0625π x 7.2

By solving this, you will get approximately 114.511 m^3 as your answer.

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

             water. Colin uses a pump to empty the pond. The level goes

             down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

               to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = [tex]\frac{1}{2}[/tex]× (sum of sides)× height

                             =  [tex]\frac{1}{2}[/tex]× (0.6 + 1.4)× 2

                             =  [tex]\frac{1}{2}[/tex]× (2)× 2

                             =  2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

                          = 2 m² × 1 m

                          = 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = [tex]\frac{1}{100} m[/tex] = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

                                           = 2 m² × 0.8 m

                                           = 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

                                       = 2 m³ - 1.6 m³

                                       = 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in [tex]\frac{30}{0.4}[/tex] = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

Answer:

y=1.8

Step-by-step explanation:

first change the fraction into a decimal.

4/5 =0.8

plus the 0.8 to both sides

y=1.8

Answer:

[tex]y - \frac{4}{5} + \frac{4}{5} = 1 + \frac{4}{5} \\ y = \frac{5 + 4}{5 } \\ y = \frac{9}{5} [/tex]

Answer:

Step-by-step explanation:

(4,3) and (6,9)

difference of x-coordinates = 6-4 = 2

difference of y-coordinates = 9-3 = 6

distance between points = √(2²+6²) = √40 = 2√10

Answer: there were 12 chocolates in each box. (Originally, before any got eaten)

Step-by-step explanation: let x represent the total amount of chocolates in each box.

8x - 3(8) = 72

8x - 24 = 72 add 24 to both sides

8x = 96 divide both sides by 8

X = 12

Answer:

That means you had 48 chocolates in each box

Step-by-step explanation:

Since you eat 3 chocolates from all 8 boxes, you do this:

8 x 3 which = 24

Now since you have 72 chocolates left you do this:

72 - 24 which = 48

So, therefore, there were originally 48 chocolates in each box

(Don't eat so much chocolate lol you could get sick)

Answer:

The next one is 64. Can you mark branliest if it's right?

Answer:

F(x) = x^1 * 2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Hope this will help

Answer:

I think so it is option A)

I hope this might help u

Answer:

$5760

Step-by-step explanation:

Given data

Principal= $8,000

Tax= 28%

Let us compute 28% tax deduction

=28/100*8000

=0.28*8,000

=$2240

Hence the net expenses is

=8000 -2240

=$5760

Answer:

she walked the fastest around the 2 hour mark and she walked 4 miles per hour

Step-by-step explanation:

This slope is the steepest if we count it, and it comes out to 4 miles per hour.

Thanks for Brianliest :D

Answer: -1/8 OR -0.125, -2^-3

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

Trust me

Answer:

0

Step-by-step explanation:

I did it on edge

Answer: Samples A and B have the same mean, but Sample A has a larger median then Sample B.

Step-by-step explanation:

The median is the middle number in the sequence.

To find the median, place the numbers in order. Then take away, or cross out, one number from each side. Keep going until you are down to one or two numbers. If there is only one number left, that’s your median. If two, add the numbers together and divide by 2.

The mean is the average. To get the mean you add up all the values and subtract that sum by how many numbers there are in the sequence.

Option D is correct for the given conditions, Samples A and B have the same mean, but Sample A has a larger median than Sample B.

The descriptive summary of a data set is known as the central tendency in statistics. It reflects the center of the data distribution through the use of a single number from the dataset. Additionally, it only provides a summary of the dataset rather than information on specific data within the dataset. In general, several statistical metrics can be used to determine a dataset's central tendency.

Given  the data sets of two sets of quiz scores,

Sample A = 5, 5, 5, 5, 5

sample B = 2, 2, 2, 2, 17

mean is the average of total samples,

mean of sample A = (5 + 5+ 5 + 5 + 5 )/5

mean of sample A = 5

Mean of sample B = (2 + 2 + 2+ 2 + 17)/5

mean of sample B = 5

since the mean of both sample are same,

median is the central digit of sets

median of A is 5 and the median of B is 2,

so the median of sample A is larger than sample B.

Hence option D is correct.

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Answer:

1: 25c+10

2: 29a+18b

3: -2b+24n+11-12m

4: 23m+10

5: 8x+3y+16

Answer:

2 hours

Suzy would earn $40

Bill will earn $40

they will both earn $80

Step-by-step explanation:

The total amount suzy earns is a function of the total hours worked. Let t represent time

total income of suzy = $20t eqn 1

Bill's income = starting bonus + variable pay

= $20 + $10t

We are looking for when they would earn the same amount :

20t = $20 + $10t  eqn 2

collect like terms and solve for t

10t = $20

t = 2 hours

Substitute for t in either eqn 1 or 2

20(2) = $40

Suzy would earn $40

Bill will earn $40

they will both earn $80

Answer: The number is 0

Step-by-step explanation:

8 = 7x + 8

Then we solve it:

8 = 7x + 8

8 - 8 = 7x

0 = 7x

0 ÷ 7 = x

x = 0

hope this helps have a nice day

Answer:  B. 2/3; 1

Use the slope-intercept form  y  =  m  x  +  b  to find the slope  m  and y-intercept  b .

Slope:  

(2) /(3)

y-intercept:  

( 0 ,  1 )

Step-by-step explanation:

Find the slope and y-intercept of the equation. y = (2)/(3)x + 1

Find the Slope and y-intercept

Answer:

100 km/hour, or 16.67 km/minute

Step-by-step explanation:

Answer:

The GCF of 4x^2 + 6x

is. (2x )

hope it helps

2x

Answer:

o dpB

Step-by-step explanation:

Answer: y = -4

Step-by-step explanation: to find the y intercept substitute x=0

0-3y=12

Then solve for y

0-3y=12---> y= 12/-3

y=-4

Answer:

random sampling

Step-by-step explanation:

Answer:

A.

Step-by-step explanation: Cluster sampling

Answer:

54

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Hope this helps:)

Answer: -46

Step-by-step explanation: Place -7 into the equation. 4(-7-5)+2= 4*-7=-28,-4*5=20. Negative 28 minus 20 is -48. Negative 48 + 2 is -46.