please answer this question​

Please Answer This Question

Answers

Answer 1

If ɑ and β are roots of 2x² - 5x + 7, then

2x² - 5x + 7 = 2 (x - ɑ) (x - β)

Expanding the right side and matching up coefficients, it follows that

2ɑβ = 7   ⇒   ɑβ = 7/2

-2 (ɑ + β) = -5   ⇒   ɑ + β = 5/2

Now consider a polynomial whose roots are 3ɑ + 4β and 4ɑ + 3β, which can be written with factorization

(x - (3ɑ + 4β)) (x - (4ɑ + 3β))

and expanded to get

x² - (7ɑ + 7β) x + (3ɑ + 4β) (4ɑ + 3β)

Expand/factor the coefficients to rewrite them in terms of the known relations above.

x² - 7 (ɑ + β) x + (12ɑ² + 25ɑβ + 12β²)

x² - 7 (ɑ + β) x + 12 (ɑ² + β²) + 25ɑβ

Recall the square of a binomial,

(x + y)² = x² + 2xy + y²

so we rewrite the latter quadratic as

x² - 7 (ɑ + β) x + 12 ((ɑ + β)² - 2ɑβ) + 25ɑβ

x² - 7 (ɑ + β) x + 12 (ɑ + β)² + ɑβ

Then substituting the expressions whose values we know, we get

x² - 7 (5/2) x + 12 (5/2)² + 7/2

= x² - 35/2 x + 157/2

which we can multiply by 2 to get integer coefficients like in the given quadratic,

= 2x² - 35x + 157


Related Questions

A group of friends are dining at a
pizza parlor. They have 1 1/2 pizzas. If
each friend eats 1/4 of a pizza, how
many friends can have an equal
share?

Answers

Answer:

6 friends

Step-by-step explanation:

because 1/4 goes 4 times into a whole 1 and then 2 times into a half, equalling six

Ajay wraps a gift box in the shape of a triangular pyramid. The figure below shows a
net for the gift box.
8.66 m
10 m
If all the triangles are equilateral, how much wrapping paper
did he use, in square meters?

Answers

Ajay wraps a gift box in the shape of a triangular pyramid. The amount

of wrapping paper he uses is 173.2 square inches.

How to calculate the surface area of a triangular pyramid?

The formula for calculating the total surface area is expressed as:

Area = 4(area of triangle)

The area of the triangle

A = 0.5(8.66)(10)

A = 43.3 square inches

The total surface area will be

TSA = 4(43.3)

TSA = 173.2 square inches

Hence the amount of wrapping paper Ajay uses is 173.2 square inches

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Help please need asap!! Thank you

Answers

Answer:

your welcome    

Step-by-step explanation:

....bbc

help will mark Brainliest​

Answers

Answer:

The third box model

Step-by-step explanation:

Since she earns 162 from babysitting and got a total of $810, it would eman that (x represents the amount of money she got from mowing lawns) 810-162=x

x=648 so the third box model is correct

Calculate the following 87124 + 14997=

Answers

Answer:

87124 + 14997 = 102121

Hope it helpz~ uh..

Carry on learning :)

Answer:

102121

Step-by-step explanation:

Is it SSS, SAS, ASA, AAS, or HL?

Answers

Triangle ABC is congruent to triangle DEF based on the SAS congruence theorem.

What is the SAS Theorem?

The SAS theorem is a triangle congruence theorem that states that two triangles are congruent if they have two pairs of congruent sides that are corresponding to each other, and a pair of congruent included angles.

Triangles ABC and DEF have:

A pair of congruent included angles - ∠DEF ≅ ∠ABCTwo pairs of congruent sides - AB ≅ DE and CB ≅ FE

Therefore, they are congruent by SAS.

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Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to indicate exponents. For example, type a2 as a∧2. (Hint: Let s be a length of each side and x be the angle measure; then use these variables in the law of cosines.)

Answers

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

What is trigonometry?

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b² + c² - a²)/2bc

cos B= (a² + c²- b²)/2ac

cos C = (a²+ b²- c²)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s² + s² - s²)/(2s×s)

cos A = (s² )/(2s²)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s² + s² - s²)/(2s×s)

cos B = (s²)/(2s²)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s² + s² - s²)/(2s×s)

cos C = (s² )/(2s²)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

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What is the sum of all prime numbers less than 78?

Answers

Answer:

712

Step-by-step explanation:

2 + 3 = 5 + 5 = 10 + 7 = 17 + 11 = 28 + 13 = 41 + 17 = 58 + 19 = 77 + 23 = 100 + 29 = 129 + 31 = 160 + 37 = 197 + 41 = 238 + 43 = 281 + 47 = 328 + 53 = 381 + 59 = 450 + 61 = 511 + 67 = 578 + 71 = 649 + 73 = 712

The value of a television t years
after its purchase is modeled by the
exponential function ƒ(t) =
1500(0.83)t. Which best describes
the domain and range of this
exponential function?

Answers

Step-by-step explanation:

hope you anderstand

if that's the answer can you brainliest me please thank you

Help -x/3 > 5

A. X<15
B. X > -15
C. X < -15
D. X > 15

Answers

Answer:

Steps

-x/3 >5

Multiply both sides by 3

3(-x/3)>5.3

Simplify

-X> 15

Multiply both sides by - 1 (reverse the inequality)

(-x)(-1)<15(-1)

Simplify

X< -15

so C is the answer

Someone pls help fast!

Answers

Answer:

decreasing and linear

Step-by-step explanation:

it just is

Answer:

Decreasing,  linear

Step-by-step explanation:

you are going -4 every time

Bruno says that the product n x 4/5 is greater than 4/5 because multiplication always increases a number. Which of the following values for show that Bruno is incorrect? 8/8 6/5 5/4 3/4 2​

Answers

Answer:

The fourth option shows how Bruno is incorrect

Step-by-step explanation:

Multiplication does not always result in a number greater than the initial value. If n can be any value, then Bruno's claim is false. For instance, multiplying a value greater than one by a decimal will perform the inverse operation (division):

3 × 0.87 = 2.61

When multiplying fractions of 1, this occurs when the multiplied number is greater than the multiplier:

0.55 × 0.21 = 0.1155

If decimals are not allowed, multiplying positive and negative values will give the positive result but with the inverse sign, which is less than the initial one since the result is less than 0:

12 × -2 = -24

Now back to the example. If we let n = 0.75 (3/4);

0.8 × 0.75 = 0.6

Hope that clears things up.

Tell whether the angles are adjacent or vertical. Then find the value of x.​

Answers

Answer:

The angles are vertical, and the value of x is 128 degrees

Step-by-step explanation:

You can tell vertical angles apart from adjacent by looking at their position. Adjacent angles are side by side, right next to each other. Vertical angles are directly across from each other, with their points touching.

Since the angle measures of vertical angles are equal, the value of x is 128

i hope this helps

find the area of rectangle hall of length 64 5/7 m and breadth 23 3/8 m​

Answers

The area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The length of the rectangle = [tex]64\dfrac{5}{7}[/tex]  m = 453/7 m

The breadth of the rectangle = [tex]23\dfrac{3}{8}[/tex] m = 187/8 m

The area of the rectangle hall:

= (453/7)(187/8)  = 1512.69 ≈ 1512.7square m

Thus, the area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

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Shreya has 40 pairs of shoes stacked inboxes.
If a pair is 2 shoes, how many shoes does Shreya have?

Answers

Answer:

it's either 20 or 80..

Answer:

80 shoes

Step-by-step explanation:

40×2

A group of pupils take a test. The group consists of 28 boys and 24 girls.
The mean mark for the boys is 28. The mean mark for the girls is 14.
Calculate the mean mark for the whole group.
Give your answer correct to 1 decimal place.

Answers

Answer:

21.5 to 1 decimal place.

Step-by-step explanation:

The total number of marks for all the boys = 28*28 = 784 marks.

The total number of marks for all the girls   = 24*14  = 336 marks.

So the mean mark for the whole group  

= (784+336) / (28+24)

= 1120 / 52

= 21.538

How many solutions does this equation has: 3x-5=-3

Answers

Answer:

One solution

Step-by-step explanation:

The only solution is x = 2/3

What is the value of the angle marked m? P​

Answers

Answer:

180

Step-by-step explanation:

bcoz it's a straight angle

2. Find the cosine function that is represented in the graph.

Answers

Answer:

[tex]f(x) = cos(x - \frac{\pi }{4} ) -1[/tex]

Step-by-step explanation:

In this graph, we have the coordinate point ([tex]\frac{\pi }{4} , 0[/tex]). Without translations, cos(0) = 0, which means that the graph is shifted to the right by [tex]\frac{\pi }{4}[/tex]. We also know that the graph is shifted down by 1 because we have the point

([tex]\frac{5\pi }{4} , -2[/tex]), but accounting for the right shift, this point should really by ([tex]\pi , -2[/tex]). cos([tex]\pi[/tex]) = -1, but on the graph it is -2, meaning that it is shifted down by 1.

Therefore, accounting for the right shift by [tex]\frac{\pi }{4}[/tex] and the shift down by 1, our equation is [tex]f(x) = cos(x - \frac{pi}{4} ) - 1[/tex].

Please help me I’m confused

Answers

cant delete this answer. my bad

How do you solve for x? X is not 34°, just to let you know.

Answers

Answer:

x = 90

Step-by-step explanation:

X is equal to 90 degrees:

As you can see it forms paralell line we know paralell line is equal to 180 degrees just divide it by 2, so 90

Need help trying to find the answer

Answers

Step-by-step explanation:

[tex] = \frac{2}{9} \times \frac{3}{5} \\ [/tex]

[tex] = \frac{6}{45} \\ [/tex]

Change into lowest term...

[tex] = \frac{2}{15} \\ [/tex]

Aina, who works in an accounting firm, earns a monthly salary of 35,000 PHP per month and also receives 3,500 PHP for a monthly allowance. Her monthly contributions are as follows: 1,466 PHP for income tax, 300 PHP for PhilHealth, 800 PHP for SSS, and 100 PHP for Pag-IBIG. Find her NET INCOME for this month.

Answers

Using the given information, Aina's net income is for the month is 35,834 PHP

Calculating Net income

From the question, we are to determine the net Aina's net income

Aina's net income is the value of her total income minus all other expenses

From the given information,

Aina's monthly salary is 35,000 PHP per month and also receives 3,500 PHP for a monthly allowance

∴ Aina's total income = 35,000 PHP + 3,500 PHP

Aina's total income = 38,500 PHP

Sum of her other expenses = 1,466 PHP + 300 PHP + 800 PHP + 100 PHP

Sum of her other expenses = 2,666 PHP

∴ Aina's net income = 38,500 PHP - 2,666 PHP

Aina's net income = 35,834 PHP

Hence, Aina's net income is for the month is 35,834 PHP.

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2/ 2 2/3 = 3/N solve for N
when i put this in my calculator it says unable to solve

Answers

Answer:

n = 9 / 2 or 4.5

Step-by-step explanation:

2/3 = 3/N

cross multiply

2 x n = 2n

3 x 3 = 9

2n = 9

divided both sides by 2

2n / 2 = 9 / 2

n = 9 / 2

Can someone help me with this?
- Thankyou in advance

Answers

The answer y^3(7x^4-6)/2x^3

N
The accurate scale drawing shows
the positions of port P and a lighthouse L.

c)
N
Lindsey sails her boat from port P
on a bearing of 050°
She sails for 12 hours at an average
speed of 5 km/h to a port Q.
Ito-
L
p*
Scale: 1 cm represents 3 km.
a) Indicate the position of port Q on the drawing (use the x tool).
(2)
b) Find the distance, in km, of port Q from lighthouse L.
(1)
c) Find the bearing of port Q from lighthouse L.
)
(2)
Total marks: 5
Feedback

Answers

The  Indication of the position of port Q on the drawing is shown by using the example of the image attached.

What is the distance about?

To Indicate the position of port Q on the drawing (use the x tool).

12 * 5  = 60km

Note that S=  VT

Because 1cm represent 3km

1/3 =x/60

3x = 60

x= 60/3

x= 20

So therefore, 60km needs 20cm.

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Please answer if you can 30 points.

What is the y-intercept of the linear function given the following table?

Answers

Answer:

The y-intercept is 4

Step-by-step explanation:

You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).

Answer:

4

Step-by-step explanation:

the y-intercept is the y-coordinate where the line intersects the facis.So if we want to figure out the intercept,we're going to set x=0 and sdue for Y.

write the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x+y=-5

Answers

Answer:

The equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x+y=-5 is 2x+y=4

Why is the graph of y=x² always positive?​

Answers

Answer:

Step-by-step explanation:

Because a square must be positive no matter what the sign of x is.

(-2)^2 = 4

2^2 = 4

what equation represents the graph

Answers

Answer:

y = (x + 1)(x - 2)(x -3)

Step-by-step explanation:

Looking at the graph we see our zeros which is on the x-axis is -1 , 2, 3.

Thus create an equation.

y = (x + 1)(x - 2)(x -3)

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