Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, what is true about the other zero

Answers

Answer 1

Answer:

Step-by-step explanation:

irrational roots always occur in pairs.

Other root is also irrational and is negative of first zero.

Answer 2

If a quadratic equation with integer coefficients and two distinct roots have one irrational root then another root is also irrational .

What is quadratic equation ?

Any equation of the  form [tex]ax^{2}+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .

Let assume quadratic equation is

[tex]ax^{2}+bx+c=0[/tex]

Given that coefficients are integer and roots are distinct

we know root of quadratic equation are

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

As roots are distinct

[tex]b^2-4ac > 0\\[/tex]

and one root is irrational so [tex]b^2-4ac[/tex] is not a perfect square

Hence another root is also irrational .

If a quadratic equation with integer coefficients and two distinct roots have one irrational root then another root is also irrational .

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Related Questions

I just need the answer please dont explain ​

Answers

Use photomath it’s faster and you get correct Answers!<3 have a good day
The answer is 12 :))))

Helpppppp pleaseeeeeeeee

Answers

Answer:

Thus, 11/30 is the simplified fraction for 55/150 by using the GCD or HCF method.

Step-by-step explanation:

y=1/3 x-4 system of equations

Answers

Answer:

What are you asking?

Step-by-step explanation:

Answer:

y=x/3-4

Step-by-step explanation:

you get this answer by combine your x with your fraction. since this equation is belonging to system of equations you must combine the variable with your systematic equation.

Classify the triangle as acute, right, or obtuse based on the side lengths of 8, 11, and 14.

Answers

Answer:

Obtuse

Step-by-step explanation:

[tex]8^2+11^2=14^2\\64+121=196\\185=196[/tex]

Since the hypotenuse is bigger, the triangle is obtuse

It’s obtuse!!!!!!!!!

Could someone help me with this due in 2 hours!!!!! Been working on this for 6 hours choosing brainliest!!!!

Answers

Step-by-step explanation:

The Triangle Inequality Theorem states that any two sides of the triangle must add up to be greater than the third side.

Question #1

Here we have a triangle that has side lengths of 10 in, 11 in, and ? in.

This last side length must add up to 10 in to be greater than 11 in.

The least possible whole number that would fit this description would be 2 in.

10 in + 2 in > 11 in10 in + 11 in > 2 in 11 in + 2 in > 10 in

The missing side length should be labeled as 2 inches.

Question #2

We are given a triangle with side lengths of 6 in and 8 in. We are asked to choose all answers that apply from this list:

2 in3 in4.5 in 6.5 in10 in13.5 in14 in15.5 in

We can tell that 2 in cannot be an answer since 6 in + 2 in is not greater than 8 in.

We also know that 14 in and 15.5 in cannot be part of the answer choices since 8 in + 6 in = 14 in, and this is not greater than 14 in or 15.5 in.

The rest of the answer choices will form a triangle if we follow the Triangle Inequality Theorem. You can test it out yourself to check.

Therefore, the answer choices are:

B. 3 inC. 4.5 inD. 6.5 inE. 10 inF. 13.5 in Question #3

We are given these possible side lengths:

2, 4, 5, 6, 10

Let's test out which combinations will create a triangle.

2 + 4 > 5 5 + 2 > 44 + 5 > 2

The straw lengths 2, 4, and 5 will form a triangle.

2 + 5 > 6 5 + 6 > 22 + 6 > 5  

The straw lengths 2, 5, and 6 will form a triangle.

2 + 6 > 4 4 + 2 >/ 6

The straw lengths 2, 4, and 6 will NOT form a triangle.

4 + 5 > 66 + 5 > 4 4 + 6 > 5

The straw lengths 4, 5, and 6 will form a triangle.

5 + 6 > 10 10 + 5 > 66 + 10 > 5

The straw lengths 5, 6, and 10 will form a triangle.

We have no more straw lengths that will form a triangle, since adding up each remaining pair of given straw lengths do not output a value greater than another number.

[tex]{\sf{\bold\green{\fcolorbox{grey}{grey}{✅\:\:Verified\:\:answer}}}} [/tex]

If the exponential model f(x)=9(13)x is written with the base e, it will take the form A0ekx. What is A0 and what is k?

Answers

9 × 13ˣ = 9 × exp(ln(13ˣ ))

… = 9 × exp(x ln(13))

… = A₀ × exp(kx)

so that

A₀ = 9

k = ln(13)

Which number line best represents the solution to the inequality 3.3w - 9 > -22.2?
picture ↓

Answers

Answer:

solve the inequality in the form of w

PLEASE HELP choose the image og PQR and P'Q'R after a translation of 2 units right and a reflection across the line x=1​

Answers

Answer:

C is the answer

Step-by-step explanation:

 because if you move the triangle two to the right then X=1

X=1 means the line is up and down going thought x=1

and if that line you make you reflect across it would be C

I'd appreciate any help I can get! :) A gold statue has a diameter of 60 inches and a height of 80 inches. It has a total volume of 320 inches cubed. The replica is proportional to the statue. The replica's height is 100 inches. What is the replica's volume?

Answers

Answer:

Volume of replica = 625 cubic inches

Step-by-step explanation:

Height of the gold statue = 80 inches

Volume of the gold statue = 320 cubic inches

Height of the replica = 100 inches

Dimensional scale factor = [tex](\frac{\text{Dimension of the replica}}{\text{Dimension of the original statue}})[/tex]

                                      = [tex]\frac{100}{80}[/tex]

                                      = 1.25

Volume scale factor = [tex]\frac{\text{Volume of replica}}{\text{Volume of original}}[/tex]

Since, volume scale factor = (Dimensional scale factor)³

[tex]\frac{\text{Volume of replica}}{\text{Volume of original}}=(1.25)^3[/tex]

Volume of replica = (1.25)³ × Volume of original statue

                              = (1.25)³ × 320

                              = 625 cubic inches


can someone help me to solve these two problems pls I will really appreciate I will mark you the brainly!

Answers

Answer:

12. 524 in³ (3 sig. fig.)   13. 2000 cm³ (3 sig. fig.)

Step-by-step explanation:

12. Volume of sphere = (4/3)πr³

= 500/3π

= 524 in³ (3 sig. fig.)

13. Volume of cylinder = πr²h

= 7²π(13)

= 637π

= 2000 cm³ (3 sig. fig.)

I don't understand this, what's the answer? ​

Answers

Answer: y⁷
Steps: y¹¹ x y⁻⁴ = y¹¹⁺⁻⁴ = y⁷




By what percentages are Sweden's high category and medium category less than the United States' categories (to the nearest percent)?


High category = a0 %


Medium category = a1 %

Answers

REQUIRED CHART :

The required chart has been attached

Answer:

31.8%

30.0%

Step-by-step explanation:

Required :

To obtain the Difference between Sweden and United States high and medium categories to the nearest %

Sweden :

High category = $23.51

Medium category = $15.73

United States :

High category = $34.48

Medium category = $22.46

Percentage Difference :

High category : (34.48 - 23.51) / 34.48 * 100% = 31.8%

Medium category : (22.46 - 15.73) / 22.46 * 100% = 29.96% = 30.0%

The top of an off shore oil rig has an elevation of 199.2 m and its base has an elevation of -9.6 m and observation deck is located at in elevation equal to 1/6 of the total height of the oil rig a Helly pad is located 22.8 m above the observation deck what is the elevation of the Helly pad

Answers

Answer: 57.6m

Step-by-step explanation:

That's a lot of words that questions usually use to try to trip us up but not this time so lets pull all relevant information

199.2m= top of off shore oil rig

-9.6 m is the base of the rig

observation deck is 1/6 of the total height

helly pad is 22.8m above the observation deck

First lets try to find the total height of the rig. We can do this by adding the absolute value of the top and base of the oil rig. So 199.2 + 9.6 = 208.8m

So the total height is 208.8m now lets find the observation deck. We know the observaition is 1/6 of the total height which is 208.8m right so lets multiply. 1/6*208.8m= 34.8m

Now we know the observation deck is 34.8m high. Finally we can find the helly pad which is 22.8 m above the observation deck.

Since the observation deck is 34.8m and the helly pad is 22.8 above observation deck (34.8m) all we have to do is add so 22.8+34.8= 57.6m

So we know the total height is 208.8m

The observation deck is 34.8m

And the helly pad is 57.6m

HELPPP PLEASEEEEE ON NUMBER 7!!!!!!

Answers

Answer:

D is the answer since you added all the numbers together ten divide by five

Answer:

D

Step-by-step explanation:

We need to find the missing value to make sure it averages out to 250.

So they will be 5 rounds of different scores.

Since we dealing with averages, we need to set up a

equalivent equation to 250. We would add up all our previous scores and try to find the new x score and divide it by 5 and set it equal to 250. So our equation will look like.

Let x represent of our next game.

[tex] \frac{236 + 274 + 246 + 236 + x}{5} = 250[/tex]

Multiply by 5 both sides

[tex]236 + 274 + 246 +236 + x = 1250[/tex]

[tex]992 + x = 1250[/tex]

[tex]x = 258[/tex]

d is the answer

A mix of factoring by grouping. Factor the exressions. 17ax+17a-x-1 Please explain/show steps on how to do this!

Answers

Answer:

[tex](17a-1)(x+1)[/tex]

Step-by-step explanation:

Given: Expression is [tex]17ax+17a-x-1[/tex]

To factor: the given expression

Solution:

Take [tex]17a[/tex] common from the first two terms and [tex]-1[/tex] from the last two terms.

[tex]17ax+17a=17a(x+1)[/tex]

and

[tex]-x-1=-(x+1)[/tex]

So,

[tex]17ax+17a-x-1=17a(x+1)-1(x+1)\\=(17a-1)(x+1)[/tex]

Therefore,

[tex]17ax+17a-x-1=(17a-1)(x+1)[/tex]

A park has the shape of a trapezoid.

The shortest side of the park and its height have the same dimension.

Write numbers in the boxes to show the missing dimensions. What is the area of the park?

Hint: There are 3 parts in this question
Part 1 you need to find what is A
Part 2 you need to find what is B
Part 3 You need to calculate the area of all the figure ( find the area of the rectangle and two triangles then sum them all up)
Do not forget the unit!!

Answers

Answer:

[tex]the\: answer \: is \: {108 \: mi.}^{2} [/tex]

Step-by-step explanation:

Given hints:

a.) A park has the shape of a trapezoid.

b.) The shortest side of the park and its height have the same dimension.

In the given figure, the shortest side of the park is A. Since it is mentioned that the height and its shortest side have the same dimension, we can therefore say that the measure of A is 9 mi.

The longest side appears to be 6 miles longer that the shortest side:

[tex]b = a + 3 \: mi + 3 \: mi = a + 6 \: mi[/tex]

Therefore, B = A + 6 mi. = 9 mi. + 6 mi. = 15 mi.

Let's now determine the area of the park:

[tex]area = \frac{a + b}{2} h[/tex]

Where,

A = 9 mi.

B = 15 mi

H = 9 mi.

[tex]area = \frac{a + b}{2} h \\ \\ = \frac{9 \: mi. +15 \: mi. }{2} (9 \: mi.) \\ \\ = \frac{24 \: mi.}{2}(9 \: mi.) \\ \\ = (12 \: mi.)(9 \: mi. \\ \\ area = {108 \: mi.}^{2} [/tex]

The area of the park is 108 mi^2.

The legs of a right triangle measure 5 and 8. What is the length of the hypotenuse?

Answers

[tex]\sqrt{89}[/tex]

Hope This Helps You!

Good Luck Studying ^-^

How do you simplify
1 π (64)^2 (6)

Answers

Answer:

if you multiply pi by 64^2 times 6 then it comes out to 77207.78

Step-by-step explanation:

64^2 = 4096

4096 (6) = 24576

24576 (π) ≈ 77207.78

The answer for the question is 24576 π. (Decimal 77207.78015)

What’s the answer to this?

Answers

Answer:

<D is congruent to <B

Step-by-step explanation:

They both have the 3 lines indicated on them

500
450
400
350
300
250
200
150
100
50
10
30
50
70
9
0
Write the equation of a line?

Answers

Answer:

Not proportional because it's not linear. Hope this helps

What is 57 divided by 5?

Answers

Answer:

11.4

Step-by-step explanation:

Answer:

11.4

Step-by-step explanation:

Find the volume of the cylinder. Use 3.14 for Tr.

Answers

Answer:

area = 42.41

a=2nrh×2nr²

a=2(3.14)(1.5)(3)+2×3.14×1.5²

a=42.41

Josh is going to choose a 2-digit number. What is the probability that the sum of the digits in his number will be 9? (there are 90 two digit numbers in total)

Answers

answer,,

18

27

36

45

54

63

72

81

hope my ans helps

please give brainliest to my answer

be sure to follow me

stay safe

Write a related function for - 6x + 8x - 5 = 3.

pls just explain and show your work if you can and ill give brainlest and 5 star​

Answers

Answer:

x=4

Step-by-step explanation:

-6x+8x=2x

5+3=8 (when you move a number to the other side of an equals sign, it changes its value)

2x=8

2x/2 and 8/2

x=4

Answer:

X=4

Step-by-step explanation:

HELP ILL GIVE BRAINLYEST!

Answers

Answer:

Im not sure but hope you find it!!

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

douwdek0 The Titanic could stay afloat with four of its 16 watertight compartments flooded, more than anyone could imagine on a ship of its size. ... As the ice bumped along its starboard side, it punched holes in the ship's steel plates, flooding six compartments. In a little over two hours, the Titanic filled with water and sank. the answer is 128 if u read all this but brainlest????

Determine the values of the variables in the parallelogram below.
5
(m2 - 4m)°
140°
x² + 4x

Answers

Answer:

m = -10, 14 x = 1, -5

Step-by-step explanation:

m^2 - 4m = 140 (in a parallelogram, opposite angles are congruent)

(1)m^2 - 4m - 140 = 0

Objective: Find two numbers that multiply to -140(1 * -140) and add to -4

Numbers: 10, -14

(m + 10)(m - 14) = 0

m + 10 = 0, m - 14 = 0

m = -10, m = 14

x^2 + 4x = 5 (in a parallelogram, opposite sides are equal)

(1)x^2 + 4x - 5 = 0

Objective: Find two numbers that multiply to -5(1 * -5) and add to 4

Numbers: -1, 5

(x - 1)(x + 5) = 0

x - 1 = 0, x + 5 = 0

x = 1, x = -5

FIRST TO ANSWER GETS BRAINLIEST!

The diagram shows a 140° sector in a circle of radius 8 units.
140°
8
What is the approximate area of the shaded sector?
0 25 square units
O 67 square units
O
78 square units
156 square units

Answers

Answer:

[tex] \huge \boxed{ \red{ \boxed{c)78 \: units ^{2} }}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:circlePEMDAStips and formulas:[tex] \rm \:A_{shaded}= \dfrac{\theta}{360} \times \pi {r}^{2} [/tex]let's solve:[tex] \sf sustitute \: the \: value \: of \: \theta \: and \: r : \\ A_{shaded} = \frac{140}{360} \times \pi \times {8}^{2} [/tex][tex] \sf simpify \: squre : \\ A_{shaded} = \frac{140}{360} \times \pi \times 64[/tex][tex] \sf simpify \: fraction: \\ A_{shaded} = \frac{7}{18} \times \pi \times 64[/tex][tex] \sf reduce \: 64: \\ A_{shaded} = \frac{7}{ \cancel{ \: 18} \: ^{9} } \times \pi \times \cancel{ 64} \: ^{32} \\ A_{shaded} = \frac{7}{9} \times \pi \times 32\\ A_{shaded} = \frac{224\pi}{9} [/tex]

[tex]\large A_{shaded}\approx 78 \: square \: units [/tex]

Please help!!! Find the value of h for the parallelogram shown.

Answers

Answer:h=11.2

Step-by-step explanation:

From the figure, we can write

[tex]\Rightarrow \sin x=\dfrac{8}{10}=\dfrac{4}{5}\\\\\Rightarrow x=53.13^{\circ}[/tex]

Also, [tex]\sin x[/tex] can be written as

[tex]\Rightarrow \sin x=\dfrac{h}{14}\\\\\Rightarrow \dfrac{4}{5}=\dfrac{h}{14}\\\\\Rightarrow h=11.2\ \text{units}[/tex]

Answer: h = 11.2

explain: I can't do this much but hope this helps.

14. Solve for x.
110°
(8x - 1)
(5x + 36)
(6x-2)
(7x + 19)
116°

Answers

The value of x in the hexagon is 17.

How to find the angle of a hexagon?

A hexagon is a polygon with six sides. The sum of angles in a hexagon is 720 degrees.

Therefore, x can be found in the hexagon as follows:

we have to sum the whole angles to get x.

110 + 8x - 1 + 5x + 36 + 116 7x + 19 + 6x - 2 + 110 = 720

combine like terms

110 + 116 - 2 + 36 - 1 + 19 + 8x + 5x + 7x + 6x  = 720

278 + 26x = 720

subtract 278 from both sides of the equation

278 + 26x = 720

278 - 278 + 26x = 720 - 278

26x = 442

divide both sides by 26

x = 442 / 26

x = 17

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A 7-pack of clay pots costs $28.49. What is the unit price?

Answers

Answer:

$4.07

Step-by-step explanation:

You divide 28.49 by 7

7 into 28= 4

7 into 4= 0

7 into 49= 7

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