Determine the values of k for which the function f(x) = 4x^2-3x + 2kx + 1 has two zeros. Check these values in the original equation. ​

Answer:

[tex]x = -5 \pm \sqrt{26}[/tex]

Step-by-step explanation:

[tex]x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}[/tex]

Answer:

Step-by-step explanation:

The equation factors into

(x^2 + 14x + 49) =16                      Factor

(x + 7)^2 = 16                                 Take the square root of both sides

√(x + 7)^2 = √16

x + 7 = +/- 4

x + 7 = + 4                                      Subtract 7 from both sides

x  = 4 - 7

x = - 3

x + 7 = - 4                                      Subtract 7 from both sides.

x = - 4 - 7

x = - 11

x1 = -11

x2 = - 3

Answer:

Step-by-step explanation:

Use the volume formula of a right rectangular prism!

V=whl

Just plug the values in and throw them in your calculator.

w stands for width

h stands for height

l stands for length

Hope that helps. Since it is part of a quiz, I can't give you the answer, but I believe in you!

Answer:

hope it helps

also do write the givens

The average daily balance of the transactions given for the billing period will be $1798.

From the complete question, the average daily balance is completed below:

Billing date = 2645.92 × 5 = $13229.6

Repayment on June 6 = $1345.92 × 2 = $2691.84

June 8 = $1381.85

June 9: = $1518.53 × 8 = $12148.24

Gas = $1560.90

Groceries = $1687.37 × 10 = $16873.70

Clothing = $1902.49 × 4 = $7609.96

Total = $53935.19

Therefore, the average daily balance will be:

= $53935 / 30

= $1798

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Answer:

  90°

Step-by-step explanation:

The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.

__

The slope to point 'a' is y/x = 2/1 = 2.

The slope to point 'b' is y/x = (-1/2)/1 = -1/2.

The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.

__

We can also use the trig formula for the tangent of the difference of angles.

  tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

The tangents are the slopes, calculated above, so we have ...

  tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = undefined

The tangent is undefined for angles that are odd multiples of 90°. The angle between the vectors is 90°.

12.8mm

[tex]0.1\times2^7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\{2^7\right.=2\times2\times2\times2\times2\times2\times2\\ =0.1\times128\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\left.\ 128\right\}\\ =12.8mm[/tex]

I hope this helps you

:)

Answer: [tex]\frac{3}{2}x+y=-\frac{17}{2}[/tex]

Step-by-step explanation:

The standard form of a linear equation is [tex]ax+by=c[/tex]

So we need to solve for c

Start by simplifying everything in the equation

[tex]y+7=-\frac{3}{2} (x+1)[/tex]

Use the Distributive Property

[tex]y+7=-\frac{3}{2}x-\frac{3}{2}[/tex]

Now subtract 7 from both sides

[tex]y+7=-\frac{3}{2}x-\frac{3}{2}\\y+7-7=-\frac{3}{2}x-\frac{3}{2}-7\\y=-\frac{3}{2}x-\frac{17}{2}[/tex]

Add [tex]\frac{3}{2} x[/tex] to both sides

[tex]y+\frac{3}{2}x=-\frac{3}{2}x+\frac{3}{2}x-\frac{17}{2}\\\frac{3}{2}x+y=-\frac{17}{2}[/tex]

NOTE: [tex]-\frac{17}{2}[/tex] simplifies to -8.5 if you find that more desirable

Answer:

(i) 41-45 mins

(ii) 40 mins

(iii) 75 workers

(iv) Rs10500

Step-by-step explanation:

(i)  The modal class is the class with the highest frequency.

Therefore, from inspection of the frequency table, the modal class is 41-45 mins since if has the highest frequency of 14.

(ii) As the data is grouped, to find an estimate of the mean, assume that every worker takes the value of the class mid-point.  As the data is discrete, there are gaps between the classes, and so we also have to use lower and upper class boundaries to calculate the mid-points.

Class 21-25 : lower 20.5 | upper 25.5 | mid-point 23

Class 26-30 : lower 25.5 | upper 30.5 | mid-point 28

Class 31-35 : lower 30.5 | upper 35.5 | mid-point 33

Class 36-40 : lower 35.5 | upper 40.5 | mid-point 38

Class 41-45 : lower 40.5 | upper 45.5 | mid-point 43

Class 46-50 : lower 45.5 | upper 50.5 | mid-point 48

Class 51-55 : lower 50.5 | upper 55.5 | mid-point 53

Class 56-60 : lower 55.5 | upper 60.5 | mid-point 58

Mean = (sum of frequency x class mid-point) ÷ total frequency

⇒ Mean = (2 x 23 + 5 x 28 + 7 x 33 + 10 x 38 + 14 x 43 + 8 x 48 + 3 x 53 + 1 x 58) ÷ 50

⇒ Mean = 40 mins

(iii)  8 hours = 8 x 60 = 480 mins

Total time ÷ average time to make one doll = 480 ÷ 40 = 12

If the mean time to make a doll is 40 minutes, then one person can make 12 dolls in 8 hours.

Therefore, to calculate the number of workers required to make 900 dolls in 8 hours, divide the total number of dolls needed by 12:

900 ÷ 12 = 75

So 75 workers will be needed to make 900 dolls in 8 hours, given the mean time for a worker to make a doll is 40 mins.

(iv) Overtime is paid in excess of 6 hours.  Therefore, each worker will be working 2 hours overtime.

Total amount of overtime pay = hours x rate x workers

                                                  =  2 x Rs70 x 75

                                                  = Rs10500

Answer:

5

Step-by-step explanation:

because 10 divided by 2 is 5

Answer:

(a) yes

(b) 1/36

(c) 1/36

(d) 1/18

Step-by-step explanation:

(a) yes they are independent as the outcome of one does not affect the outcome of the other.

(b) As the dice are fair, each possible number (1 through 6) has the same probability of being rolled.

P(1 on green die) = 1/6

P(2 on red die) = 1/6

Therefore, P(1 on green die) AND P(2 on red die) = 1/6 × 1/6 = 1/36

(c) Again, as the dice are fair, each possible number (1 through 6) has the same probability of being rolled.

P(2 on green die) = 1/6

P(1 on red die) = 1/6

Therefore, P(2 on green die) AND P(1 on red die) = 1/6 × 1/6 = 1/36

(d) p[(1 on green die and 2 on red die) OR (2 on green die and 1 on red die)

= 1/36 + 1/36

= 2/36

= 1/18

Answer:

Step-by-step explanation:

Answer:

at aircraft(at z) sported by

[tex]t= \dfrac{2r}{r-1}\\\\\implies tr-t= 2r\\\\\implies tr -2r = t\\\\\implies r(t-2) = t\\\\\implies r = \dfrac{t}{t-2}[/tex]

The formula of r is t/t-2 for equation t=2r/r-1.

Two or more expressions with an Equal sign is called as Equation.

The given equation is t = 2r/r-1

t equal to two times of r divided by r minus one

We need to find the formula for r

t = 2r/r-1

Apply cross multiplication

t(r-1)=2r

Apply distributive property on left side

tr-t=2r

Subtract 2r on both sides

tr-2r=t

r(t-2)=t

Divide both sides by t-2

r=t/t-2

Hence, the formula of r is t/t-2 for equation t=2r/r-1.

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#SPJ2

Answer:

y = -9

Step-by-step explanation:

-3y + 7 = 34

-3y = 34 - 7

-3y = 27

3y = -27

y = (-27)/3

y = -9

Answer:

yes

Step-by-step explanation:

If you take 20 and divide by 4 you get 5. if you take 16 and also divide by 4, you will get 4.

Answer:

4/6 > 4/8

Step-by-step explanation:

To see if the following is true:

We can cross multiply:

[tex]\frac{4}{6}\neq \frac{4}{8}[/tex]        {4* 8 = 32}      {4*6=24}

Thus,

[tex]\frac{4}{6}=32[/tex]

[tex]\frac{4}{8}=24[/tex]

Hence, [tex]\frac{4}{6} > \frac{4}{8}[/tex]

We can also turn them into decimal:

[tex]\frac{4}6=0.6667[/tex]

[tex]\frac{4}{8}=0.5[/tex]

0.5 is NOT greater than 0.6667 which also means that 4/8 is NOT greater than 4/6.

~lenvy~

Answer:

x is less or equal to 30

the last Choice is correct.

Answer:

Last option D.

Step-by-step explanation:

IF it can be no more than 30, the 4th one says it can be equal to 30 or less than thirty.

Answer:

1) x=-30 2) x=-2

Step-by-step explanation:

1) y=x+12.      

   Y= -18

x+12=-18

x=-18-12

x=-30

2) y=x-10

    y= -12

x-10=-12

x=-12+10

x=-2

The conditions for this type of sampling test regarding the wait times at two branches of a bank include:

It should be noted that sampling simply means a statistical process where a predetermined number of observations are taken from a larger population.

In this case, the samples are both randomly selected and the wait times within each group are approximately symmetric without outliers. When there's a symmetric distribution with no outliers, the mean and standard deviation will be used.

Learn more about sampling on:

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Answer:

Step-by-step explanation:

Variance=0.0016

Standard deviation is the square root of variance.

sigma=sqrt(0.0016)=0.04

mean=0.9 inch

Calculating z for 0.936 inch

z = (0.936 - 0.9)/0.04

= 0.036/0.04

= 0.9

Using normal distribution table

P(x<=0.936 inch)

= P(0.9)

= 0.81594

P(x>0.936) + P(x<=0.936) = 1

P(x>0.936)

= 1 - P(x<=0.936)

= 1 - 0.81594

= 0.18406

= 0.1841

Answer:

1 gallon / 600 sq ft

Step-by-step explanation:

As we can see, we are given that 600 sq ft uses one gallon to cover, therefore one gallon covers 600 sq ft (just vice versa of what's given).

The probability that Natalie got at least two correct on the last three

true-or-false questions is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The sample space is 2. The question is either correct or wrong.  

The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4

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[tex]\boxed{ \dfrac{x}{3} \leq 5}[/tex]

A number {x} {divided by} {3} is {at most} {5}.

                  ↧          ↧             ↧            ↧         ↧

                  x          ÷             3           ≤         5

[tex]\text{Inequality formed} \rightarrow \boxed{ \dfrac{x}{3} \leq 5}[/tex]

Answer:

[tex]\sf \dfrac{x}{3}\leq 5[/tex]

Step-by-step explanation:

x divided by 3 = x/3

at most 5 means "equal or less than 5" =  ≤ 5

Final solution

[tex]\sf \dfrac{x}{3}\leq 5[/tex]

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Extra information

Alternative ways of writing the inequality:

x ÷ 3 ≤ 5

[tex]\sf \dfrac13x\leq 5[/tex]

Answer:

4

Step-by-step explanation:

100 divided by 25 equals 4.

Answer:

Step-by-step explanation:

BF is the angle bisector of ∠B.

Answer:

-9

Step-by-step explanation:

b={-2,3)

c=(3,-1)

dot product b.c

=(-2×3) + (3×-1)

=-6+(-3)

=-6-3

=-9