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Question : If α and β are roots of the quadratic equation : 4x²-5x-1=0, find the quadratic equation whose roots are :
(See image for full question . No (IV) and (v))

Answer:

x= -1

Step-by-step explanation:

2(x -5) -6 = -18

2x -10 -6 =-18

2x -10 -6 =-18

2x -16 = -18

2x =16 += -18

2x -16 +16 = -18 +16

2x = -2

2x/2 = -2/2

x=-1

x = -1

Answer: [tex]\frac{6}{2}[/tex]

Step-by-step explanation:

1. Use this [tex]\frac{f(b)-f(a)}{b-a}[/tex] to find the average rate of change

2. Average rate of change = [tex]\frac{f(8)-f(6)}{8-6}[/tex]

3. [tex]f(8) = - 4[/tex] and [tex]f(6) = -10[/tex] (To find these you will need to look at the points on the graph. So the points (8,-4) and (6,-10))

4. Replace -4 to f(8) and -10 to f(6)

5. So it will look like[tex]\frac{-4-(-10)}{8-6}[/tex]

6. Solve [tex]\frac{6}{2}[/tex]

Answer:

-5/3

Step-by-step explanation:

m=−9−6/10−1

m=−15/9

Slope=

−15/9=−5/3

Answer: 20 weeks in 1 week

in 2 weeks 40

Step-by-step explanation:

This proves that the equation is true

Answer:

Option B

Step-by-step explanation:

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Answer:

First payment (50%) would be 512$

The next two payments would be 32$ each

Explanation:

.5(1024)= 512

.25(512)=128

.25(128)= 32

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Learn more probability about here:

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Answer:

Step-by-step explanation:

The two integers are 10 and 9

10 + 9 = 19

10 x 9 = 90

The two numbers are 9 and 10.

A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero

Let the two integers be x and y.

Given that, the sum of the integers is 19, therefore,

x + y = 19

x = 19 - y

Given that, the product of the integer is 90:

xy = 90

(19-y)y = 90

19y - y² = 90

y² -19y + 90 =0

y² -10y - 9y + 90 = 0

y(y - 10) -9(y - 10) = 0

(y -9)(y - 10) = 0

y = 9 and y = 10

Hence, the two numbers are 9 and 10.

Learn more about integers:

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Answer:

i need the answer ;(

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of the cuboid = Length * Width * Height

Given

Length = 4cm

Width = (x+1)cm

Height = (x-11)cm

Volume of the cuboid = 4(x+1)(x+11)

Volume of the cuboid = 4(x^2+11x+x+11)

Volume of the cuboid = 4(x^2+12x+11)

Volume of the cuboid = 4x*2+48x+44

925 = 4x*2+48x+44

4x*2+48x+44-925 = 0

4x*2+48x-881 = 0

Divide through by 4

x^2 + 12x - 220.25 = 0

Factorize using the general formula;

x = -12±√12²-4(-220.25)/2

x = -12±√144+881/2

x = -12±√1025/2

x = -12±32/2

x = 12+32/2

x = 20/2

x = 10

Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm

Dimension is 4cm by 11cm by 21cm

Answer:

y = -3

Step-by-step explanation:

Add 2 to each side to isolate the -3y. Doing this leaves you with -3y=9. You then divide each side leaving you with y = -3

Answer:

The equation has one solution at which y = -3.

Step-by-step explanation:

To find the value of y, we need to isolate it from the rest of the equation.

[tex]\displaystyle{-3y-2=7}\\\\-3y = 9\\\\\bold{y = -3}[/tex]

We can check to make sure that y = -3 by substitution.

[tex]\displaystyle{-3(-3)-2 = 7}\\\\9-2=7\\\\7= 7 \ \checkmark[/tex]

Because we got a true statement, we can determine that y = -3.

Answer:

4,5,6,7,8,9..........................

Answer:

????

Step-by-step explanation:

Answer:

where's the shape

Step-by-step explanation:

what's the length and width, maybe I can help

Answer: d. 2 hrs

Step-by-step explanation:

Let x = Time taken(in hours) to fly 470 mi to New Orleans. (Shorter leg)

Then Time taken to fly 705 mi to Atlanta= x+1 (longer leg)

Since  the plane flew at the same rate for the entire trip.

i.e. Speed 705 mi to Atlanta = Speed to fly to New orleans

[tex]\Rightarrow\ \dfrac{705}{x+1}=\dfrac{470}{x}\ \ \ \ \ \ \ [\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}]\\\\\Rightarrow\ 705x=470(x+1)\\\\\Rightarrow\ 705x=470x+470\\\\\Rightarrow\ 705x-470x=470 \\\\\Rightarrow\ 235x=470\\\\\Rightarrow\ x=\dfrac{470}{235} \\\\\Rightarrow\ x=2[/tex]

hence, the flying time for the shorter leg = 2 hours

So (d) is the correct option.

Answer:

B

Step-by-step explanation:

I hope it's correct and I'm thinking it is,. Sorry if it's not

Answer:

I think A

Step-by-step explanation:

3/7. Or 3:7

Cause there are 3 books and 7 tennis balls

Answer:

d

Step-by-step explanation:

Answer:

4 x 10⁵

so that i think will be OD)

Answer:

x = 7

Step-by-step explanation:

Given the equations

2x + 3y = 17 → (1)

2y + z = 1 → (2)

5x + 10z = 25 → (3)

Rearrange (2) expressing z in terms of y

z = 1 - 2y

Substitute z = 1 - 2y into (3)

5x + 10(1 - 2y) = 25

5x + 10 - 20y = 25 ( subtract 10 from both sides )

5x - 20y = 15 → (4)

Multiply (1) by 20 and (4) by 3, then add to eliminate the y- term

40x + 60y = 340 → (5)

15x - 60y = 45 → (6)

Add (5) and (6) term by term to eliminate y, that is

55x = 385 ( divide both sides by 55 )

x = 7

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

From the equation [tex]2y + z = 1[/tex] , we can separate [tex]z[/tex] so that [tex]z = 1-2y[/tex].

The equation [tex]5x+10z = 25[/tex] can then be turned into:

[tex]5x+10(1-2y) = 25[/tex]

[tex]5x+10-20y = 25[/tex]

[tex]5x -20y = 15[/tex]

[tex]x-4y = 3[/tex] (divide by [tex]5[/tex] on both sides)

We can now use elimination to solve for one of the variable:

[tex]2(x-4y) = 2\times3[/tex] (times 2 to get [tex]2x[/tex] for elimination)

[tex]2x-8y=6[/tex]

[tex]2x+3y-(2x-8y) = 17-6[/tex]

[tex]11y = 11[/tex]

[tex]y = 1[/tex]

Now, we can use substitution to solve for [tex]x[/tex]:

[tex]2x+3y = 17[/tex]

[tex]2x+3 = 17[/tex]

[tex]x = 7[/tex]

Hope this helps :)

An equation for each situation, in terms of t, is y = 850e^35t and

y = 700e^70t

The required equation will be in the form y = Ae^kt

where:

If High School A currently has 850 students and is projected to grow by 35 students each year, hence;

Substituting into the formula, we will have:

y = 850e^35t

If High School B currently has 700 students and is projected to grow by 60 students each year, hence;

Substituting into the formula, we will have:

y = 700e^70t

An equation for each situation, in terms of t, is y = 850e^35t and

y = 700e^70t

Learn more on exponential function here: https://brainly.com/question/12940982

Answer:

12+18x is the perimeter

Step-by-step explanation:

4+6x+4+6x+1/2(4+6x)+1/2(4+6x)=

3(4+6x)=

12+18x

Answer:

22 units

Step-by-step explanation:

Known Quantities:

Calculations:

Final Calculations:

Answer:

Yes.

Step-by-step explanation:

First, find the unit rate for 1 bookcase.

65 ÷ by 13 = 5 (unit rate)

Then, multiply the unit rate by the bookcases the carpenter wants to make.

6 · 5 = 30

Finally, subtract the shelves the carpenter wants to use by 30.

32 - 30 = 2 shelves.

Therefore, 32 shelves is enough to build 6 more bookcases. <3

Answer:

x+10

Step-by-step explanation:

sum = addition (+)

number = variable because we don't know what the number is yet (x)

ten=ten

So by this we can get x+10

Answer:

Cellular respiration is this process in which oxygen and glucose are used to create ATP, carbon dioxide, and water. ATP, carbon dioxide, and water are all products of this process because they are what is created.

Step-by-step explanation:

Answer: No

Step-by-step explanation:

The range and the Domain aren’t equal

Answer:

x=5

y=7

(5,7)

Step-by-step explanation:

solved by substitution.

Answer:

0 -1

Step-by-step explanation:

because the line is going down which is negative

Answer:

The answer is 9

Step-by-step explanation:

set up the equation as 12^2 + b^2 = 15^2

solve the exponents and you get 144 + b^2 = 225

Then subtract 144 from both sides and get 81

After that just do the square root of 81 and you get 9

pls mark brainliest