5a3 x 2b2 x 4a2b5/ 3a2 x 5b3

Considering the product and the sum of the roots of the quadratic function, the numeric value of the expressions are given as follows:

1. [tex]\beta x^2 + \alpha x^2 - \alpha\beta = \frac{1}{4}(x^2 - 1)[/tex]

2. [tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{7}{4}[/tex]

A quadratic function is defined according to the following rule:

y = ax² + bx + c.

In which a and b are the coefficients of the equation.

Supposing that the equation has roots [tex]\alpha[/tex] and [tex]\beta[/tex], the product and the sum of the roots of the quadratic function are given as follows:

In this problem, the equation is:

4x² - x + 1.

Hence the coefficients are:

a = 4, b = -1, c = 1.

Then the product and the sum of the roots of the quadratic function are given as follows:

Then the numeric values for the expressions can be found as follows:

[tex]\beta x^2 + \alpha x^2 - \alpha\beta = x^2(\alpha + \beta) - \alpha\beta = \frac{1}{4}x^2 - \frac{1}{4} = \frac{1}{4}(x^2 - 1)[/tex]

For the second expression:

[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = 4(\alpha^2 + \beta^2)[/tex]

The sum of the squares of the roots is:

[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta[/tex]

Hence:

[tex]\alpha^2 + \beta^2 = \frac{1}{16} - \frac{1}{2} = -\frac{7}{16}[/tex]

Then:

[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{28}{16} = -\frac{7}{4}[/tex]

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Answer:

2

Step-by-step explanation:

A perfect square is the product of a number multiplied by itself.

So, 9 would be 3 x 3 so that's a perfect square.

1 is 1 x 1, so that is a perfect square.

4 is 2x2, so that is a perfect square.

2 does not have a number that multiplies by itself to equal 2, so it is not a perfect square.

Answer:

d) 2

Step-by-step explanation:

Now we have to,

→ find which is not a perfect square.

Let's solve the problem,

→ √9 = 3

→ √1 = 1

→ √4 = 2

→ √2 = 1.415

Hence, 2 is not a perfect square.

AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.

So, all coordinates are shown on the graph as follows:

(Refer to the image attached below)

Now, we can see that in the 4th quadrant, two triangles are formed that are ABE and CDE.

Then, we can conclude that:

Therefore, AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.

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The expression that models Tyrell's net proceeds algebraically is d-(1.03ns + 15)  .

In the question ,

it is given that ,

Tyrell bought n shares for s dollars

So the price Tyrell paid for shares = $ ns .

Tyrell also paid 3% commission ,

so the total cost price Tyrell paid for shares = price of share + commission

total cost price = ns + 3% of ns

= ns + 0.03ns        ....as 3% = 0.03

= 1.03ns         ...(i)

Tyrell sold the stocks for d dollars .

Tyrell also paid the flat fee of $15 .

So, the selling price for stocks = d-15 ......(ii)

The Tyrell's Net Proceeds can be calculated using the formula

Net Proceeds = Selling Price - Cost price

Substituting the values of selling price and cost price from (i) and (ii) ,

we get ,

Net Proceeds = (d-15)-(1.03ns)

= d-15-1.03ns

= d-(1.03ns + 15)

Therefore , the expression that models Tyrell's net proceeds algebraically is d-(1.03ns + 15)  .

The given question is incomplete , the complete question is

Tyrell bought n number of shares for s dollars and paid a 3% commission. He sold the stock for d dollars and paid a flat fee of $15. Write an expression to model Tyrell’s net proceeds algebraically.

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Answer:

5763 is the answer because 57 plus 63

Answer:

yes!! finally a question i can solve:
so,

Step-by-step explanation:

Exact Form:

x = − 3/2

Decimal Form:

x = −1.5

Mixed Number Form:

x = -1  1/2

Answer:

4

Step-by-step explanation:

Greatest Common Factor or Divisor is 4, because it is the greatest number that divides evenly into all of them.

Hope this helps! :)

Answer:

[tex]\frac{36}{49}[/tex]

Step-by-step explanation:

the pattern identified in the sequence is to add 1/49 after each step in the sequence.

When you add 1/49 to 34/49 you get 35/49, which can be simplified to 5/7.

To get the next value in the sequence just add 1/49 to 35/49, which equals 36/49.

this answer can not be simplified further.

Answer: The answer is y=6x.

Answer:

[tex]y=\frac{9}{16}(x-5)^2-8[/tex]

Step-by-step explanation:

The equation in vertex form is [tex]y=a(x-5)^2-8[/tex].

Substituting in the coordinates [tex](1,1)[/tex] to solve for [tex]a[/tex],

[tex]1=a(1-5)^2-8 \\ \\ 1=16a-8 \\ \\ 9=16a \\ \\ a=9/16[/tex]

So, the equation is [tex]y=\frac{9}{16}(x-5)^2-8[/tex].

a)

The perimeter is given by

b)

Then we simplify by summing similar terms we obtain that the expression of the perimeter is

35% more than 78?

35% of 78;

78 x .35 = 27.3

78 + 27.3 = 105.3

Answer:

- 21

Step-by-step explanation:

They lost 14 yards, then lost and additional 7 more. You would simply add and make it a negative number due to the key word " lost ".

The equation would look like this: -14 + ( -7 ).

Another way to solve this equation is to multiply. ( + ) x ( - ) = -.

Your equation will the look this this: -14 - 7.

Now you just solve.

Thus, your answer should be - 21.

Hopes the helps!

Have a great day.

Answer: -21

Step-by-step explanation:

.A football team will lose an additional 7 yards if they lost 14 on their first play.

. Since the first play resulted in a loss of 14 yards, the integers that reflect the overall change in yards for the two plays are negative.

.In the second play, we score 14 points but lose 7 yards, which is a loss of 7 points.

.Negative 14 + Negative 7 = Negative 21, which is the overall change in yards.

. Hence, the answer would be -21 yards.

. -21 would be the correct integer that will represent the the total change in yards for the two plays.

Answer:

x = 31

Step-by-step explanation:

87=2x-25

-25 on each side

62=2x

divide each side by 2

31=x

x=31

Answer:

45°

Step-by-step explanation:

Given:

To Find:

Concept used:

Using the above concept, we have

5x + 15 + 3x + 3x = 180

11x = 165

x = 165/11

x = 15

So, 3x = 3*15 = 45°

So, the measure of base angle is 45°

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:Base \:\: Angle=3x = 45° [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Property of Triangle : sum of all interior angles of a triangle is 180°

[tex]\qquad \tt \rightarrow \: 5x + 15 + 3x + 3x = 180[/tex]

[tex]\qquad \tt \rightarrow \: 5x + 3x + 3x + 15 = 180[/tex]

[tex]\qquad \tt \rightarrow \: 11x = 180 - 15[/tex]

[tex]\qquad \tt \rightarrow \:11 x = 165[/tex]

[tex]\qquad \tt \rightarrow \: x = 165 \div 11[/tex]

[tex]\qquad \tt \rightarrow \: x = 15[/tex]

Value of x is 15°, base angle is 3x :

[tex]\qquad \tt \rightarrow \: base \: \: angle = 3x = 3 \times 15 = 45 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Farooq gets £8.75

Step-by-step explanation:

Let's represent the amounts obtained by David, Eva and Farooq as D, E and F to make things simpler. Let M be the total amount of money shared

D = 2.50 and represents 1/6 of the total amount of money(M)

So

M/6 = 2.50

Multiply both sides by 6 => M = 2.50 x 6 = £15

Eva gets 1/4th of this so E = 15 x 1/4 = £3.75

David gets £2.50

Together they get £2.50 + £3.75 = £6.25

The balance goes to Farook so F = 15 - 6.25 = £8.75

The ratio is 3:5 .

The problem we are dealing with is related to the term ratio, where the ratio is characterized as the comparison of two quantities of the same units that shows how much of one amount is present within the other amount. Ratios can be classified into two sorts. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio indicates how two distinct entities or groups are related. whereas, the part-to-whole proportion indicates the relationship between a particular group to an entirety.The situation we are given is that the player attempted 15 baskets in a game and out of  9 was the number of times he made the attempted baskets.We just need to find the ratio of the number of baskets made to the number of  baskets attempted,

= 9:15

Here we divide each by 3

= 9/3: 15/3

=3:5

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The value of equation (x + y) will be 1.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation are;

2y + 5x = 5   ... (i)

4y - x = 21    ... (ii)

Now, Solve both the equation and find the value of x and y as;

Multiply by 2 in equation (i) we get;

4y + 10x = 10

Subtract above equation by (ii);

4y + 10x - (4y - x) = 21 - 11

11x = 11

x = 1

And, 2y + 5x = 5

Substitute x = 1;

2y + 5x = 5

2y + 5 = 5

2y = 0

y = 0

So, x + y = 1 + 0 = 1

Thus, The value of (x + y) will be 1.

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Answer: 26

Step-by-step explanation:

If you take 26 minus 11 it gets you -15.

Number lines help a lot with negatives. You can also start with -15 and just start adding numbers starting at a large number and going up or down depending on you answer. Ex. -15 + 30 = 15, -15 + 25 = 10, -15 + 26 = 11.

Fraction - The distance she walked before lunch 214 / 75 miles

What is Fraction ?

A fraction, which also represents a portion of a whole, is a mathematical symbol for any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, indicates the number of components of a specific size when used in conversational English.

Given that,

The distance Ruby has to walk = 10/3miles

The distance left to complete before stopping = 12/25miles

The distance Ruby has to walk before lunch = 10/3 - 12/25

                                                                          = 250 - 36 / 75

                                                                          = 214 / 75miles

Hence, she walked 214 / 75 miles before lunch

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Answer:

C

Step-by-step explanation:

Use the distributive property to solve.

(5a²+2a-7)(3a²-a+1)

=15a⁴-5a³+5a²+6a³-2a²+2a-21a²+7a-7

=15a⁴+a³-18a²+9a-7

The value of three over five raised to the second power is nine over twenty-five.

From the question , we were given that three over five raised to the second power which can be interpreted as (3/5)^2 then we can find the square of the given value so that we can arise at the answer.

In this case ,  (3/5)^2 = 9/25 which implies that the value of the (3/5)^2 is been found and to calculate the value of (3/5)^2, we will need to find the square of 3 which is the numerator as well as the square of 5 which is the denominator.

Therefore, the third option is correct.

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Answer:x+x+1=13

2x+1=13

2x=13−1

2x=12

x=

2

12

​

x=6

x+1=6+1=7

Step-by-step explanation:yes

Answer:y=3/5x

Step-by-step explanation:

just plug 3/5 in and you don’t need to add the 0

C) The two stores never charge the same rate as per the cost expression of store A and store B.

The each expression of store A and store B represent the total cost charged by them based on the number of items bought. The mentioned expressions will be equated when assuming their total cost to be same. Thus, equating the the expressions.

20x - 8 = 5 (4x + 4)

Performing multiplication on Right Hand Side of the equation

20x - 8 = 20x + 20

Since 20x is present on both the sides, it will be cancelled. The remaining expression will be :

8 = 20, which is a false case as 8 is not equal to 20.

Thus, the equation has no solution and hence, the two stores will never charge the same rate, no matter how many items are bought.

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For groceries to be delivered, one particular grocery store charges 3% of the whole purchase price. The total price the store charges to deliver $140 worth of groceries will be $144.20.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although abbreviations "pct.", "pct.", and occasionally "pc" are also used, percent symbol, "%," is frequently used to indicate it. A % lacks dimensions and has no associated unit of measurement.

It should be mentioned that a certain grocery store charges a delivery fee equal to 3% of the entire purchase price.

Consequently, the following is the total the store will charge to deliver $140 worth of groceries:

= Percentage charged × Cost+ Cost

= 3% × $140+$140

= 0.03 × $140+$140

= $4.20+$140

The amount charged is $144.20.

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Answer:

y = 10.5x + 35

Step-by-step explanation:

Since the roof is 35 feet tall, it will be the y-intercept (since it is constant). The number of floors can change, so it will be the x variable.

The final equation is y = 10.5x+35

Answer:

Yes

Step-by-step explanation:

Each x-value corresponds with only one y-value.

The differential equation for the amount of salt A(t) in the tank at the time (dA / dT) / (A / 100) = 0, A(0) = 30

It is Given that a large tank holds 400 gallons of water, in which 80 ponds of salt have been dissolved, given that pure water is pumped into the tank at a rate of 8 gallons/min. here we have to find the differential equation for the amount of salt in the tank at the time when the solution is well stirred. we have to multiply both 400 gallons of water and pumped water at the rate of 8 gallons/min.

dA / dT = Rin - Rout

Rin = 0

Rout = A(t) / 400 * 8

        = A / 50

So,

  dA / dt = Rin - Rout

dA / dt = 0 - A /50

After solving the differential equation we get

A(0) = 30

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