PLEASE I REALLY NEED HELP ON THIS QUESTION QUICKLY

The value of λ = 8s + 6

The zeroes of a function f(x) are the values of x at which f(x) = 0.

Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.

Since we require λ,

So, let f(x) = 2 - 8x + λ.

At x = a, f(x) = 0.

So, substituting the value of x = a into f(x), we have

f(a) = 2 - 8a + λ

Since f(a) = 0, we have

2 - 8a + λ = 0   

2 + λ = 8a  (1)

Also, x = s, f(x) = 0.

So, substituting the value of x = s into f(x), we have

f(s) = 2 - 8s + λ

Since f(s) = 0,we have  

2 - 8s + λ = 0

2 + λ = 8s  (2)

Since a - s = 2

Making a subject of the formula, we have

⇒ a = s + 2

So, substituting the value of a into equation (1), we have

2 + λ = 8a  (1)

2 + λ = 8(s + 2)  (1)

2 + λ =  8s + 16

- 14 + λ = 8s   (3)

Adding equation (2) and (3), we have

-14 + λ = 8s   (3)

+

2 + λ = 8s     (2)

-12 + 2λ = 16s

2λ = 16s + 12

Dividing through by 2, we have

2λ/2 = (16s + 12)/2

λ = 4(4s + 3)/2

λ = 2(4s + 3)

λ = 8s + 6

So, the value of λ = 8s + 6

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Answer:

71

Step-by-step explanation:

60 ÷ 30 = 2

and

90 ÷ 30 = 3

---> 60/90 = 2/3

❄ Hi there,

the way 60/90 becomes 2/3 is this:

[tex]\sf{\dfrac{60\div30}{90\div30}=\dfrac{2}{3}}[/tex]

That's it!

❄

Step-by-step explanation:

4.6 hrs is 46over 10 which is

13 over 5 or 2 and 3over 5

Answer:

[3,0]

[0,9]

Step-by-step explanation:

9x+3y=27

9x+3(0)=27

9x=27

x=3

9(0)+3y=27

3y=27

y=9

Answer:

24.315°

Step-by-step explanation:

First use the pythagorean theorem to get the missing side since this is a right triangle.

a^2 + b^2 = c^2 →

b^2 = c^2 – a^2 →

b = (c^2 – a^2)^½

b = (17^2 – 7^2)^½

b = (289 – 49)^½

b = √240.

Then use the law of cosines to find the angle in between.

b^2 = a^2 + c^2 - 2ac * cos(B) →

b^2 - a^2 - c^2 = -2ac * cos(B) →

a^2 + c^2 – b^2 / 2ac = cos(B) →

cos^-1(a^2 + c ^2 – b^2 / 2ac) = C →

B = cos^-1(a^2 + c ^2 – b^2 / 2ac)

B = cos^-1(49 + 289 – √240 / 238)

B ≈ 75.685°.

A = 180 – B

A = 180 – 75.685

A = 24.315°

the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.

The formula for finding the number of arrangement is given as;

Permutation = [tex]\frac{n!}{n - r!}[/tex]

Where;

From the question given, we can deduce that

n = 12 people

r = 2, because they must come next to each other and is taken as 2

We then have,

Permutation = [tex]\frac{12!}{12 - 2!}[/tex]

Permutation = [tex]\frac{12!}{10!}[/tex]

Permutation = 132 ways

This is to tell us that the number of ways to arrange the people is 132 ways

Thus, the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.

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There is a minimum value of -81 located at (x, y) = (6, -3).

The function given to us is f(x, y) = 3y² - 3x².

The constraint given to us is 2x + y = 9.

Rearranging the constraint, we get:

2x + y = 9,

or, y = 9 - 2x.

Substituting this in the function, we get:

f(x, y) = 3y² - 3x²,

or, f(x) = 3(9 - 2x)² - 3x² = 3(81 - 36x + 4x²) - 3x² = 243 - 108x + 12x² - 3x² = 243 - 108x + 9x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = - 108 + 18x ... (i)

Equating to 0, we get:

- 108 + 18x = 0,

or, 18x = 108,

or, x = 6.

Differentiating (i), with respect to x again, we get:

f''(x) = 18, which is greater than 0, showing f(x) is minimum at x = 6.

The value of y, when x = 6 is,

y = 9 - 2x,

or, y = 9 - 2*6 = 9 - 12 = -3.

The value of f(x, y) when (x, y) = (6, -3) is,

f(x, y) = 3y² - 3x²,

or, f(x, y) = 3*(-3)² - 3*6² = 3*9 - 3*36 = 27 - 108 = -81.

Thus, there is a minimum value of -81 located at (x, y) = (6, -3).

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We can rewrite the given time as:

First, remember that:

60s = 1 min

Then to write that amount in minutes, we just need to divide by 60, so we get:

(4.22x10^17)/60  mins=  7.03x10^15 mins

Now, remember that:

1 hour = 3600s

Then to get the time in hours, we need to divide by 3600:

(4.22x10^17)/3600 h = 1.17x10^14 hours.

Similarly, you can change to any time unit that you want, for example:

1 day = 24*3600 s

Then the time in days is:

(4.22x10^17)/(24*3600) days = 4.88x10^12 days.

And so on.

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Answer:

(a)

(b) range of sample means =0.6

(c)

The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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i really hate how we actually have to type something.

Answer:

-7x + 1

Associative Property can be used.

Step-by-step explanation:

Hello!

We can simply the expression by combining like terms.

Like terms are terms with the same variable and degree. They may have different coefficients.

The simplified form is 1 - 7x, or -7x + 1.

We can also represent this using the Associative property, by grouping like terms:

The average number of miles he will ride each day to meet his goal is 6.6 miles

He wants to ride his bicycle 30.4 miles this week.

He has already ridden 4 miles.

He rides 4 more days.

Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:

let

x = number of miles driven

Hence, the equation can be represented as follows;

4x + 4 = 30.4

Therefore,

4x + 4 = 30.4

4x + 4 - 4 = 30.4 - 4

4x = 26.4

x = 26.4 / 4

x = 6.6

Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles

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Answer:

? = 4 units

Step-by-step explanation:

'2'  is to  ' 7+2 '     as  ?   is to   '14 + ? '

2/ 9 = ? / (14 + ?)      cross mutiply

28 + 2? = 9?

28 = 7?

? = 4

Answer:

4112

Step-by-step explanation:

When you plug in 3 for x you get 6.

Then you just do 4^6 which is 4096.

Then add 16 which gets you 4112.

Steps for Factoring:

1) Find CM (common factor) for the expression: 3

   Factor out 3 =>

   [tex]3(6x^{2}+13x-5)[/tex]

2)Factor the above expression by grouping:

  The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]

 a and b should add up to 13 and multiply up to -30 (6 × -5)

By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)

3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]

Factor out 2x in the first group and 5 in the second group:

[tex]2x(3x-1)+5(3x-1)\\[/tex]

As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)

(3x-1) (2x+5)

The answer is 3(3x-1) (2x+5)

Hope it helps!

The balance after 8 years is $22,942.67

We know that the savings account earns 15% annually, and the initial deposit is $7500, then the balance as a function of time in years is:

B = $7500*(1 + 15%/100%)^t

B = $7500*(1.15)^t

The balance after 8 years is what we get when we evaluate the above function in t = 8, so we get:

B = $7500*(1.15)^8 = $22,942.67

So the correct option is the last one.

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For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.

In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:

t = (r / 100) · (1 - d / 100) · c     (1)

Where:

If we know that d = 30, r = 5 and c = 10, then the sales tax total is:

t = (5/ 100) · (1 - 30 / 100) · 10

t = 0.35

For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.

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Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]

[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]

[tex]\longrightarrow\sf{578 =58+ c}[/tex]

[tex]\longrightarrow\sf{c = 578-58}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\longrightarrow\sf{c= 520}[/tex]

Answer: 180 meters

Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.

The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).

We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.

Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.

We are also given that EC (a part of diagonal AC) is 8 units long.

As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).

Now, we are told that DB (a part of diagonal BD) is x - 1 units long.

To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is

(x - 1) units + (x - 1) units = 2x - 2 units.

The area of a rhombus is given by the formula:

Area = 1/2 × Product of Diagonals.

Substituting the given values, we have:

72 = 1/2 × 16 × (2x - 2).

Now, we can simplify the equation:

72 = 8x - 8.

Move the constant term to the right side:

8x = 72 + 8.

Combine the constants:

8x = 80.

Finally, solve for x by dividing both sides by 8:

x = 80 / 8 = 10.

So, the value of x is 10 units. The correct answer is B).

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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?

9

10

14

16 "--

[tex]2 \sqrt{4} + 3 \sqrt{9} \\ 2(2) + 3(3) \\ 4 + 9 = 13[/tex]

Answer:

13

Step-by-step explanation:

2×√4+3×√(9

2x2+3x3

The pressure, P if V is decreasing at a rate of 10in^3/sec is 120lb/in^2 per sec.option B

PV = c

where,

when P =60lb/in^2 and V=20in^3

PV = c

60 × 20 = 1200 in

Find P if V is decreasing at a rate of 10in^3/sec

PV = c

P × 10 = 1200

10P = 1200

P = 1200 / 10

P = 120lb/in^2 per sec

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The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.

Quadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.

From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.

For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.

The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown

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The distance from Sang to Jazmin is 101 yards.

From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.

The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.

From;

c^2 = a^2 + b^2

c = √a^2 + b^2

c = √(20)^2 + (99)^2

c = 101 yards.

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Answer:

 A. 3x^2y(4x2 + 3xy - y^2)

Step-by-step explanation:

 -12(x^4)y - 9x³y² + 3x²y³

 -3x²y(4x² + 3xy - y²)

Answer:

x²y³

Step-by-step explanation:

(x²) (y³) = x²y³

Hope it helps!

Have a nice day:)

❄ Hi there,

let us find the product of the square of x and the cube of y.

[tex]\sf{The \ square \ of \ x: \ x^2}\\\sf{The \ cube \ of \ y: y^3}\\\sf{The \ product \ of \ the \ two: x^2y^3}[/tex]

The square of x means: x times x, or, as I said earlier, x².

The cube of y means: y times y times y, or, as I said earlier, [tex]\sf{y^3}[/tex].

The product means: you multiply x² times y³.

❄