How to find quadratic equations from -1/3 and 5/6

Answers

Answer 1

Answer:

[tex] 18x^2 - 9 x- 5=0\\

[/tex]

Step-by-step explanation:

Let x be the variable of the required quadratic equation.

[tex] \because - \frac{1}{3} \: \& \: \frac{5}{6}[/tex] are the roots of the required quadratic equation.

[tex] \therefore \bigg(x+ \frac{1}{3}\bigg ) \: \& \: \bigg(x-\frac{5}{6}\bigg) [/tex] are factors of the required quadratic equation.

[tex] \therefore \bigg(x+ \frac{1}{3}\bigg ) \bigg(x-\frac{5}{6}\bigg) = 0\\\\

x^2 +\bigg(\frac{1}{3}-\frac{5}{6}\bigg )x+ \bigg(\frac{1}{3}\bigg )\bigg(-\frac{5}{6}\bigg )=0\\\\

x^2 +\bigg(\frac{6}{18}-\frac{15}{18}\bigg )x- \frac{5}{18}=0\\\\

x^2 +\bigg(-\frac{9}{18}\bigg )x- \frac{5}{18}=0\\\\

x^2 - \frac{9}{18} x- \frac{5}{18}=0\\\\

\huge\purple {\boxed {18x^2 - 9 x- 5=0}} \\

[/tex]

is the required quadratic equation


Related Questions

Multiply
(2x + 4)(2x - 4)

Answers

Answer:

4x^2 -16

Step-by-step explanation:

(2x + 4)(2x - 4)

FOIL

first:2x*2x = 4x^2

outer: -4 *2x = -8x

inner:  4*2x = 8x

last: -4*4 = -16

Add them together

4x^2 -8x+8x =-16

4x^2 -16

The multiplication of the expression (2x + 4)(2x - 4) is 4x² - 16.

What is the simplified form of the expression?

Given the expression in the question:
(2x + 4)(2x - 4)

We can multiply the expression (2x + 4)(2x - 4) using the distributive property and the FOIL method.

(2x + 4)(2x - 4)

Apply the FOIL method:

2x( 2x - 4 ) + 4( 2x - 4 )

Apply distributive property:

2x × 2x + 2x × - 4 + 4 × 2x 4 × - 4

Multiply the terms:

4x² - 8x + 8x - 16

Collect and add like terms:

4x² - 16

Therefore, the simplified form is 4x² - 16.

Learn more about the FOIL method here: https://brainly.com/question/27980306

#SPJ6

x=?? will give brainliest

Answers

Answer:

I think its a right angled triangle

and so x= 90°



Given the regular square pyramid with RS = 6 and PX = 4, then XY=3.

True
False

Answers

True :) the reason I know this is because I took the test

PLEASE HALP!!!!

Carlos wants to get an average of 86% in his science class. The science
teacher has given 5 tests. Carlos's scores on 4 of the tests have been 85%,
89%, 90%, and 82%. What score does Carlos need to get on the 5th test to
get a mean score of 86%?
O A) 81
OB) 84
OC) 86
OD) 92​

Answers

Answer:

The answer is B

Step-by-step explanation:

Answer:

B. 84

 (85+89+90+82+x)/5=86

so x=84

14) Simplify. 6(3x - 5) + 2(3x - 5) - 8(3x - 5)

Answers

Answer:

0

Step-by-step explanation:

To simplify you need to distribute then add like terms.

6(3x-5) + 2(3x-5) - 8(3x-5)

18x - 30 + 6x - 10 - 24x + 40

0x + 0

0

Answer:

6(3x - 5) + 2(3x - 5) - 8(3x - 5) = 0

Step-by-step explanation:

The expression is,

→ 6(3x - 5) + 2(3x - 5) - 8(3x - 5)

Now we have to,

→ Simplify the given expression.

Let's simplify the expression,

→ 6(3x - 5) + 2(3x - 5) - 8(3x - 5)

Applying Distributive property:

→ 6(3x) - 6(5) + 2(3x) - 2(5) - 8(3x) - 8(-5)

→ 18x - 30 + 6x - 10 - 24x + 40

Rearranging the expression:

→ 18x + 6x - 24x - 30 - 10 + 40

→ (18 + 6 - 24)x - (30 - 10 + 40)

→ 0x - 0

0 => {final answer}

Therefore, the answer is 0.

Anna runs a 5k in 20 minutes. What is her speed in kilometers per hour?

Answers

Answer:

15kmh

Step-by-step explanation:

Answer:

15k

Step-by-step explanation:

There is 60 mins in an hour. Since she runs 5k in 20 mins you would multiply 20 by 3 because it would equal 60. Also you would multiply 5k by 3 also.

i hoped that made sense ;-;

Picture attached
A 15
B 41
C 20
D 30

Answers

Step-by-step explanation:

Find the distance between the line segments XY & YZ

XY = 4 units

YZ = 5 units

Use the following equation to solve for the hypotenuse of the triangle:

Hypotenuse = √(a² + b²)

Let: a = XY

      b = YZ

Hypotenuse = √(4² + 5²)

Remember to follow PEMDAS. Solve the parenthesis first, and the powers first before adding:

Hypotenuse = √(16 + 25)

Hypotenuse = √(41)

B) 41 is your answer, if you keep it as c². However, if it is not, then none of your answer choices work, as the answer would be √41.

~

Can someone help me on this one.

Answers

1. 6km/h
2. 10 minutes

Answers:

a) 6km/hour

b) 10 minutes

Step-by-step explanation:

a) after 30 minutes, Jo had walked 3km which means that after 1 hour

(30mins x 2), Jo would have walked 6km (3km x 2).

∴ Jo walks 6km/hour for the first 30 minutes

b) after 30 minutes, there is a flat line on the graph that stretches from 30 minutes to 40 minutes. The flat line indicates that Jo covered NO distance and was therefore taking a break. from 30 mins to 40 mins is 10 mins

∴ Jo's rest was 10 mins long

Hope this helps :-)

The point (5, -2) is rotated 90° about the origin. Its image is

(-2, 5)
(2, 5)
(-5, 2)

Answers

Answer:

(2,5)

Step-by-step explanation:

The rule to 90 degrees about the origin is (x,y) to (-y,x). You basically switch the values of y and x but remember the value of y is negative. The value of y is -2 so -2 is now 2 since the rule changed the sign (-2×-y=2) and 5 isnt affected except it is the x value. Just know that since they r switched, x is now 2 and y is 5 when rotated 90 degrees about the origin.

Answer:

(2,5)

Step-by-step explanation:

Find the area of the sector.

Answers

Answer:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

r is 19m

37/360 * 22/7 * 19 * 19

Area = 116.61 m^2

a) Which of these numbers is 6 less than -11?
A) -5
B) -17
С) 17
D) 5

b) Which of these numbers is 34 less than -7?
A) -27
B) 27
C) -41
D) 41

Answers

Answer:

For the first on it is A) 17

For the second one it is B) 41 I hope cause I haven't done these in along time

Step-by-step explanation:

For the first on it's going to 17 because if you turn the less than sign into a minus sign you're going to get 6 - -11. You turn the two signs into a plus sign you get 6 + 11 and you add them you get 17

For the second one your going to the same thing you add 34 + 7 and you get 41  

Darin skateboarded to the west at 8 m/s. In 7 seconds, he slowed down to 3
m/s. What was his acceleration?
O A. -1.4 m/s2 west
B. 1.4 m/s2 west
O C. -0.71 m/s2 west
D. 0.71 m/s2 west

Answers

Answer:

C) -0.71m/s²

Step-by-step explanation:

V = V0 + at

V = final veloctiy

V0 = Initial velocity

a = acceleration

t = time

3 = 9 + a7

-5 = a7

[tex]-\frac{5}{7}[/tex] = a

a ≅ -0,71

Answer:

C. -0.71 m/s2 west

Step-by-step explanation:

rewrite the equation of the circle (x-2)^2+y^2=3 in general form

Answers

Step-by-step explanation:

x²+4-4x+y²=3

x²+y²-4x+1=0

Answer:

?? Bro write the question better

Step-by-step explanation:

Sarah invests her graduation money of $1,750 in an annuity that pays an interest rate of 6% compounded annually. Sarah wants to determine the amount of money that will be in the account after a certain number of years if she leaves the money in the account and doesn’t make any deposits or withdrawals. Which function can Sarah use to describe her investment growth?

Answers

Answer:

[tex]A = 1750(1.06)^{t}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Compounded Interest Rate Formula: [tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

A is final amountP is principle amountr is raten is compounded ratet is time (in years)

Step-by-step explanation:

Step 1: Define

Given

Principle Amount = $1750

r = 6% = 0.06

n = 1 (compounded annually)

Step 2: Write function

Substitute into formula

Substitute [CIR]:                    [tex]A = 1750(1 + \frac{0.06}{1} )^{1t}[/tex](Parenthesis) Divide:            [tex]A = 1750(1 + 0.06)^{1t}[/tex](Exponents) Multiply:           [tex]A = 1750(1 + 0.06)^{t}[/tex](Parenthesis) Add:               [tex]A = 1750(1.06)^{t}[/tex]

This equation tells us how much money A the investment has gained over t years.

find the area of the composite figure

Answers

Answer:

Quickly learn how to find the Area of Composite Figures in today's geometry lesson. With 19 worked examples, you'll have everything you need ...

Step-by-step explanation:

Find the volume of the planets

Answers

Answer:

can you show the planets. or do you want real planets volumes?

Are you going to insert a picture?

John is creating a shed in his backyard he wants to use brick for the front side with the door using the given brick how many will he need to cover the front of the shed

Answers

Answer:

180 bricks.

Step-by-step explanation:

The dimensions of the front of the shed are 30 x 12.

30 x 12 = 360

The dimensions of the brick are 2 x 1.

2 x 1 = 2.

360/2 = 180.

When solving a word problem why is it important to check if the final answer makes sense for the problem?

Answers

To make sure your answer is right

A pitcher can hold 8 times as much as a glass. The pitcher holds 64 ounces.
Which model shows this comparison?
54 ounces
Glass ?
Pitcher ??????
Glass ?| ?| ?| ?| ?| ?| ?| ?
Pitcher ?
54 ounces
3 ounces
Glass ????
Preher ????
Glass
Pitcher
54 ounces
84 ounces

Answers

Answer:

Im guessing this i might be wrong

54 ounces

3 ounces

Step-by-step explanation:

Answer:

To be honest i think 54 ounces and 3 ounces

Step-by-step explanation:

i was going to say 54 and 84 but i said to myself that didn't make any sense if it is 84 let me know plz

Hope this helpsHope this is right

Given the points (0,−3) and (5,-6) and on a line, find its equation in the form
y=mx+b

Answers

Answer:

Step-by-step explanation:

y=mx+b

b=-3 (y intercept)

Use equation y2-y1/x2-x1

-3/5= m

y=-3/5x-3

Set up as equal rates and solve. The distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. How many miles is it from Pensacola to Miami if the distance on the map measures 27 inches?

Answers

We have been given that the distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. We are asked to find the actual distance from Pensacola to Miami if the distance on the map measures 27 inches.

We will use proportions to solve our given problem as proportion states that ratio between two proportional quantities is similar.

[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{27 inches}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{27 inches}}\times \text{27 inches}=\frac{200\text{ miles}}{\text{8 inches}}\times \text{27 inches}[/tex]

[tex]\text{Actual distance}=\frac{25\text{ miles}}{1}\times 27[/tex]

[tex]\text{Actual distance}=675\text{ miles}[/tex]

Therefore, the actual distance from Pensacola to Miami is 675 miles.

does anyone know thisss

Answers

Answer:

Step-by-step explanation:

area of sector = angle/360 * pi * r^2

59.4 = angle/360 * 3.142 * 17.9^2

angle = 21.24

Answer:

21.24°

Step-by-step explanation:

I hope it helps:)

PLS I MARK BRAINLIEST I ONLY HAVE 30 MINS LEFT
You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 "2" /"3" inches. What is the area of one of the triangles shown on the face of the cupboard door? Show your work AND I NEED TO KNOW HOW YOU DID IT IT SAYS SHOWYOUR WORK

Answers

Hello there i hope you are having a great day :) Your question: You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 "2" /"3" inches. What is the area of one of the triangles shown on the face of the cupboard door? How to do it :1) 16 2/3 inches this would equal to 50/3 then all together that would equal to 250/9.2) Then you would divide it 250/9 ÷ 2 = 125/9 = 13 8/9 and that would be your answer.Hopefully that helps you ❤

Which is correct?
O A. 463 < 437
OB. 763 > 746
OC. 674 < 643
OD. 734 > 743
O E. 634 > 647​

Answers

Answer:

B

Step-by-step explanation:

763 is greater 746

Answer:

if my math is right its B

can someone helpp ??

Answers

Answer:

21.24°

Step-by-step explanation:

I hope it helps :)

Giving Brainliest to teh right answer! Come quick!

Answers

Answer:

x=65

Step-by-step explanation:

145 and 2x+15 are vertical angles meaning that they are congruent to each other. Subtract 15 from both sides, and divide by 2 giving x=65.

Hope this helps!

Part A The dot plot shows the daily lunch money of a group of students. ​Each dot represents one student. ​ ​ ​What is the mean daily pocket money? A $1.50 B $2.00 C $2.15 D $2.20 ​ ​Part B What is the mode of the daily pocket money? ​ Answer:

Answers

Answer:

Mean= $ 1.96

Mode= No mode

Step-by-step explanation:

Mean is the value obtained by dividing the sum of all the observations by their numbers.

Mean is obtained by dividing the total number of the values with the number of values.

Mean= x1+ x2+ x3 + x4/ 4

Mean = $ 1.5 + $ 2.0 + $ 2.15 + $ 2.20/4=  7.85/4=  1.9625or 1.963 or $ 1.96

Mode is the most frequent occurring value in a data set. But since all the values in the given set occur only once the data does not have any mode .

There is no mode because  every value has the same frequency, that is it occurs the same number of times.

Evaluate without using a calculator by using ratios in a reference triangle.

cos 5pi/3

Answers

Answer:

The answer is 1 /2

Step-by-step explanation:

Cos, tan and sin are all positive in the first quadrant, but depends on the direction of the angle. Reference angle here we are looking for is the one in relation to the quadrant cos 5pi/3.

Any multiples of cos outside 2nd quadrant will give a positive value.

cos 5pi/3  is located in the 4th quadrant, while, cos pi/3 is located in the 1st quadrant, where the cos ratio has a positive value.

In terms of cosine, anytime the angle falls on the first or fourth quadrant it will always produce a positive graph.

For cos 5pi/3, cos pi/3 and cos 7pi/3 will give the same answer as "1/2" or "0.5" because, cos pi/3 will give 60 degrees which fall in the first quadrant

If "R" is a real number, for all R multiplied by pi/3,  the new value gives an angle in the first or fourth quadrant, the angle will be 0.5

The exact value of  cos 5 ( π /3 )  is  1 /2 .

22 .Siswa dapat menganalisis persamaan menggunakan identitas trigonometri
a) cot x.cos x per cosec x
b) cos pangkat 4 x - sin pangkat 4 x​

Answers

It best you ask your teacher

This circle is circumscribed about quadrilateral ABCD. What is the value of x?

Answers

Answer:

The value of x is 56°

Step-by-step explanation:

Given that opposite angles in a cyclic quadrilateral is add up to 180°. So in order to find x, you have to write an expression in terms of x :

[tex]97 + x + 27 = 180[/tex]

[tex]x + 124 = 180[/tex]

Next you have to solve it by substracting 124 to both sides :

[tex]x + 124 - 124 = 180 - 124[/tex]

[tex]x = 56[/tex]

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