If a and b are zeroes of the x2 + 7 x+7, find the value of a−1+b−1−2ab.

Answers

Answer 1

9514 1404 393

Answer:

  -15

Step-by-step explanation:

If 'a' and 'b' are zeros of the quadratic f(x), its factored form is ...

  f(x) = (x -a)(x -b)

and its standard form is ...

  f(x) = x^2 -(a+b)x +ab

This tells us that ...

  a+b = -7

  ab = 7

for the given quadratic.

Then the expression of interest is ...

  [tex]a^{-1}+b^{-1}-2ab=\dfrac{1}{a}+\dfrac{1}{b}-2ab=\dfrac{a+b}{ab}-2ab\\\\=\dfrac{-7}{7}-2\cdot7=-1-14=\boxed{-15}[/tex]


Related Questions

Data with 950 observations are drawn from a bell-shaped distribution with a mean of 78 and a standard deviation of 19. Approximately how many observations are more than 116

Answers

Answer:  there are 22 observations that are more than 116.

Step-by-step explanation:

Let x be the random variable.

Given: Sample size = 950

Mean = 78

Standard deviation = 19

The probability that the observations are more than 116 is given by :-

[tex]P(X>116)=P(\dfrac{X-mean}{standard \ deviation}>\dfrac{116-78}{19})\\\\=P(Z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ \ [\text{Using p-value calculator}]\\\\=0.0228[/tex]

Number of observations are more than 116 = [tex]0.0228\times950[/tex]

[tex]=21.66\approx22[/tex]

Hence, there are 22 observations that are more than 116.

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.

a = 8; r = -5

Answers

Answer:

[tex]a_n = 8(-5)^{n-1}[/tex]

The fifth term of the sequence is 5000.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio. The nth term of a geometric sequence is:

[tex]a_n = a_1(r)^{n-1}[/tex]

a = 8; r = -5

Thus:

[tex]a_n = a_1(r)^{n-1}[/tex]

[tex]a_n = 8(-5)^{n-1}[/tex]

Fifth term:

This is [tex]a_5[/tex]. So

[tex]a_5 = 8(-5)^{5-1} = 5000[/tex]

The fifth term of the sequence is 5000.


Doris has a fish pond 15 by 18 ft. She wants to put grass in a strip of uniform with around the pond. She has enough grass seed for 234 ft squared. How wide will the strip be? Round your answer to the nearest tenth, when appropriate

Answers

Check the picture below.

so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so

[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]

now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena

[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]

Answer:

3 feet

Step-by-step explanation:

Let x be the width of the grass strip.

So the length of the grass strip=18+2x

Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2

But the available grass seed is enough for 234 ft squared

4x^2+66x=234

4x^2+66x-234=0

x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)

x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8

x={-66+-(90)}/8

Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)

So the width of the strip is 3 feet.

Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet

Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet

Therefore the strip is 3 feet wide

Find the measure of WX and show work

Answers

Ans : the measure of WX = 8

Select all the numbers that are rational.

Answers

Answer:

-14/2 , 1/3 and 0.325 are the rational numbers

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

Answers

Given:

In the given circle, the measure of major arc TV is 220 degrees.

To find:

The measure of angle TUV.

Solution:

In a circle, the measure central angle of arc is equal to its corresponding arc measure and according to central angle theorem, the measure of subtended angle on an arc is half of the measure of central angle of that arc.

So, the measure of subtended angle is half of the measure of its corresponding arc.

[tex]m\angle TUV=\dfrac{1}{2}\times \text{Measure of major arc TV}[/tex]

[tex]m\angle TUV=\dfrac{1}{2}\times 220^\circ[/tex]

[tex]m\angle TUV=110^\circ[/tex]

Therefore, the measure of angle TUV is 110 degrees.

You roll a die with the sample space s=1,2,3,4,5,6. you define A as (1,2,4) B as (2,3,4,5,6) C as (3,4) and D as (2,4,5). Determine which of the following events are exhaustive and/or mutually exhaustive.
Exhaustive Mutually exclusive
A and B
A and C
A and D
Band C

Answers

Answer:

A and B are exhaustive.

Step-by-step explanation:

Given

[tex]A = \{1,2,4\}[/tex]

[tex]B = \{2,3,4,5,6\}[/tex]

[tex]C =\{3,4\}[/tex]

[tex]D = \{2,4,5\}[/tex]

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

[tex]S = P(X\ n\ Y)[/tex]

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]

and the sample space is:

[tex]S = \{1,2,3,4,5,6\}[/tex]

By comparison;

[tex]A\ n\ B = S[/tex]

Hence, A and B are exhaustive.

Question 35 of 49
Which description best describes parallel lines?
A. Lines that are not in the same plane and will never intersect
O B. Lines that intersect at a right angle
O C. Lines that intersect
D. Lines that lie in the same plane but will never intersect
SUBM

Answers

Answer:

D.lines that lie in the same plane but will never intersect

Step-by-step explanation:

parallel lie in the same plane but never meet

A woman's age is thirteen more than half of 60.How old is she?

Answers

Answer:

half of 60 is 30

13 more than that is

13+30=43

so the answer is 43

Step-by-step explanation:

hope it helps you

Somebody help please.

Answers

Answer:A

Step-by-step explanation: The formula for finding volume is LxWxH. 21x 11 is 231, and since one side is 11 so will the other side be, and then you get 2,541 m cubed.

100 Brainly points!! Need help ASAP :)

In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B’. What is the scale factor of dilation?

A. 1
B. 2
C. 0.5
D. -0.5

Answers

Answer:

B

Step-by-step explanation:

I'm not really shure tho

Answer:

D. -0.5

Step-by-step explanation:

AB dilated by scale factor -0.5 to produce AB'.

the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5

How should I tell my crush I like her? She's my friend and I asked her if she liked me yesterday and she said no but I think she was lying because she typed and then stoped typing and said no

Answers

Answer:

U just have to make her feel comfortable to trust u that she can tell u that she actually likes u....dont push anything just make her feel appreciated ok?

Step-by-step explanation:

that's all

If a book costs N10,000, at what price will the book be sold to make a profit of 15%?

Answers

Here,
We have,
Cost price of a book (CP) = N10,000
Profit percent (p%)= 15%
Now,
Using profit percent formula we get,
P% = (Sp-Cp)/ Cp*100
15 = (Sp-10,000)/10,000*100.
15*10000=100Sp-1000000
150000+1000000=100Sp
1150000/100=Sp
Sp=11500

Hence,
A book should be sold at 11500

Answer:

11,500

Step-by-step explanation:

cost price of a book (CP) = 10000

profit percent = 15%

selling price of a book (SP) = ?

SP = CP + profit% of CP

=10000 + 15 / 100 * 10000

=1000000 + 150000/100

=1150000/100

=11500

Therefore, the book will cost 11,500

I got 7 to go :( help plz

Answers

Answer:

I think the second one is the answer ; 2√b

The 2nd one is the answer i’m pretty sure.

Choose each of the following that ARE a function

Answers

Ik that A and F are for sure but I think D maybe one as well.

Seven times a number decreased by three-fourths of the same number is 25. What is the number?

Answers

Answer:

103/28

Step-by-step explanation:

Let the number be 'x'

Equation:-

7x - 3/4 = 25

7x = 25 + 3/4

7x = 100/4 + 3/4

7x = 103/4

x = 103/(4 x 7)

x = 103/28

Answer:

if we make this a algebraic equation it will look like this

7x-3/4x=25

6.25x=25

25 divided by 6.25=4

x=4

to check

28-3=25

Hope This Helps!!!

Which of the following is NOT an example of a repeated-measures design?

a researcher tests the memory performance of students before and after their first year of high school

a researcher tests symptoms of anxiety before and after a new therapeutic treatment

a researcher measures self-perception before and after participants take a Zumba class

a researcher tests whether individuals from Generation Z use social media in ways that are different from Millenials

Answers

B is correct because I know

Answer:

its D

Step-by-step explanation:

the research is done on two groups seeing what they do on the same platform and isn't on before and after results of one subject

Given the line segment AB=36 cm and a point C on directed line segment AB that partitions AB into the ratio 1 to 2, find the lengths of the line segments AC and CB

Answers

the lengths of AC is 24 and CB is 12

Explanation: so we know that the ratio is 2:1, which can be expressed as 2x and x.

we know that 2x+x must equal 36, so we can set up the equation 2x+x=36

we then add 2x to x to make 3x=36, divide both sides by 3, and get x=12.

now that we know what x equals, 2(12) is 24 and (12) is 12 :)

During each summer, many families spend part of their vacation time at a beach along the East or West Coast. Due to the popularity of movies like Jaws and The Shallows, and publicity about recent shark attacks on surfers, swimmers, snorkelers, and spearfishermen, Americans have become increasingly concerned about water activities. Research suggests that 58% of all shark attacks involve surfers. One thousand records of shark attacks are selected, and each is categorized by the victim group. Identify the population, sample, and variable for the study.
Population Sample Variable
a. all families who spend part of their vacation at a beach along the East or West coast
b. Americans who are concerned about water activities
c. the percentage of shark attacks that involve surfers
d. the set of groups to which the victims of shark attacks belong
e. all shark attacks
f. the 1000 records of shark attacks that were examined

Answers

Answer:

Population = e. all shark attacks.

Sample = f. the 1000 records of shark attacks that were examined.

Variable = d. the set of groups to which the victims of shark attacks belong.

Step-by-step explanation:

The population in a particular study refers to the entire set of people to which the research study encompasses, that is all those who are eligible to be a part of the study or those who the study relates to and the outcome of the study Cann be applied to them. In the research study described above, the population of the study is all events of shark attacks.

The sample is a subset of the larger population ; the subset selected in the scenario above is the 1000 records examined out of all the events of shark attacks.

The variable in the study may refer to a set of independent variables which is according to the scenario is the set of groups to which victims of shark attack belong.

Oakton Manufacturing makes two types of rocking chairs specifically designed for men and women known as the His and Hers models. Each chair requires four legs and two rockers but differing numbers of wooden dowels. Each His chair requires four short dowels and eight long dowels while each Hers chair requires eight short dowels and four long dowels. Each His chair contributes $10 in profit while each Hers chair contributes $12. The company has 900 legs, 400 rockers, 1200 short dowels, and 1056 long dowels available. The company wants to maximize its profit while also ensuring that it makes at least half as many His chairs as Hers chairs.

Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. Find the optimal solution.

Answers

Answer:

x  =  76    y  =  112     z (max)  =  2104 $

Step-by-step explanation:

                               legs    rockers    short dowels     long dowels  Profit $

Model His (x)           4           2                   4                          8                10

Model Her (y)           4          2                    8                          4                12

Availability             900      400              1200                    1056

From the table above we find z

Objective Function z :

z  =  10*x  +  12*y    to maximize

Subject to

Constraint  1  quantity of legs available: 900

4*x +4*y ≤ 900

Constraint  2  quantity of rockers available:  400

2*x +  2*y  ≤ 400

Constraint  3  quantity of short dowels available: 1200

4*x  8*y  ≤  1200

Constraint  4  quantity of long dowels available: 1056

8*x  +  4*y  ≤ 1056

Constraint 5 condition between  x  and y

x  ≥  0.5*y

The model:

z  =  10*x  +  12*y    to maximize

Subject to:

4*x +4*y ≤ 900

2*x +  2*y  ≤ 400

4*x  8*y  ≤  1200

8*x  +  4*y  ≤ 1056

x  ≥  0.5*y        or    x  - 0.5*y ≥ 0

General constraints:

x  ≥ 0   y  ≥ 0  both integers

After 6 iterations with AtomZmath on-line solver optimal solution is:

x  =  76    y  =  112     z (max)  =  2104 $

can someone pls help me quickkk

Answers

Answer:

(-4) ^6

Step-by-step explanation:

(-4)*(-4)*(-4)*(-4)*(-4)*(-4)

There are six (-4)'s multiplied together

(-4) is the base and 6 is the exponent

(-4) ^6

Answer:

A.(-4)^6

Step-by-step explanation:

-4 is being multiplied by itself 6 times

So you would get rid of all but one negative for and add ^-6

Which is the graph of f(x) =3 sqrtx/4?

Answers

Step-by-step explanation:

f(x) = 3√x /4

x=0 => y = 0

x=1 => y = 0.75

x=4 => y = 1.5 ==> (4, 1.5)

x=16=>y= 3

the right answer is the second graph

Determine the derivatives of g(x)=-3x at any point by using first principle

Answers

Answer:

[tex]{ \tt{g(x) = - 3x}} \\ { \tt{g(x + h) = - 3(x + h)}} \\ \\ { \bf{ \binom{ \frac{ \delta \: y}{ \delta \: x} }{lim \: h→0} = \frac{g(x + h) - g(x)}{h} }} \\ \\ { \tt{ = \frac{ - 3(x + h) - ( - 3x)}{h} }} \\ \\ { \tt{ = \frac{ - 3x - 3h + 3x}{h} }} \\ \\ { \tt{ = \frac{ - 3h}{h} }} \\ \\ { \tt{ = - 3}} \\ { \bf{h→0, \: \frac{ \delta \: y}{ \delta \: x} = \frac{dy}{dx} }} \\ \\ { \tt{ \frac{dy}{dx} = - 3 }}[/tex]

Find the area of the isosceles trapezoid shown below.
9 cm
6 cm
4.5 cm

Answers

Answer:

area = 40.5 cm^2

Step-by-step explanation:

A quick calculation tells me it is none of them

Area = 6*(9 + 4.5) / 2

Area = 3*13.5

Area = 40.5

Which choices are correct when determining the distance between −56 and −31?

Answers

Answer:

I dont know sorry so much

Which of the following are situations that can be modeled with a quadratic function? Select all that apply.

Answers

I attached the answers!! Have an awesome day!!

Consider rolling two fair dice and observing the number of spots on the resulting upward face of each one. Letting A be the event that at least one of the dice results in 6 spots on its upward face, and E be the event that exactly one of the dice results in 6 spots on its upward face, give the value of P(E|A). (Note: This value can be easily obtained by looking at p. 2.3 of the class notes and using a reduced sample space. In fact, such an approach makes the solution so trivial, that for this problem, you don’t have to give any justification for your answer.)

Answers

Answer:

[tex]P(E|A)= \frac{10}{11}[/tex]

Step-by-step explanation:

Given

Two rolls of die

[tex]E \to[/tex] one of the outcomes is 6

[tex]A \to[/tex] atleast one is 6

Required

P(E|A)

First, list out the outcome of each

[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]

So:

[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]

Where:

[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]n(E\ n\ A) = 10[/tex]

[tex]n(A) = 11[/tex]

So:

[tex]P(E|A)= \frac{10}{11}[/tex]

What would be the amount of his last monthly bill in order. The bill amount to be 110 for all 12 months

Answers

Add up all the numbers the divide by the amount of numbers in the set.
1199/11 = 109
B. 109 answer

Divide using a common factor of 2 to find an equivalent fraction for

Answers

Answer:

2/10ths?

Step-by-step explanation:

then it would be 1/5th

Given that 9x – 6y= 19
Find y when x=-6
Give your answer as an improper fraction in its simplest form.

Answers

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]

Given that 9x – 6y= 19

Find y when x=-6

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)}[/tex]

[tex] \tiny\pink{SO \: PUTTING \: VALUE} \: \orange{OF \: x \: FOR \: \: VALUE \: OF \: y}[/tex]

[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ {9( - 6) – 6y= 19} \\ - 54 - 6y = 19 \\ 6y = - 54 - 19 \\ - 73 = 6y \\ \green{ \frac{ - 73}{6} = y}[/tex]

[tex] \red{VARIFICATION - > }[/tex]

PUTTING VALUES IN EQUATION TO VARIFY THE ANSWER:-

[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)} \\ \green{y = \frac{ - 73}{6}} [/tex]

PUTTING VALUE

[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ 9( - 6) - 6( \frac{ - 73}{6} ) = 19 \\ - 54 \cancel{-}^{ \tiny{+} } \cancel{6} \frac{ \cancel{- }73}{ \cancel{6}} = 19 \\ - 54 + 73 = 19 \\ 19 = 19 \\ \orange{L.H.S} \purple{=} \green{ R.H.S}[/tex]

Answer:

y = 73 / -6

Step-by-step explanation:

Given ;

9x - 6y = 19

Where, x = - 6

Solve for y

9x - 6y = 19

plug the value of x

9 ( -6 ) - 6y = 19

- 54 - 6y = 19

Add 54 to both sides

- 54 + 54 - 6y = 19 + 54

-6y = 73

divide both side by -6

-6y / -6 = 73 / -6

y = 73 / -6

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