Answer:
Please check the explanation.
Step-by-step explanation:
Given the quadratic equation
5x²−2x−9 = 0
To factor the quadratic function 5x²−2x−9, we should solve the corresponding quadratic equation 5x²−2x−9 = 0.
Indeed, if x₁ and x₂ are the roots of the quadratic equation ax²+bx+c=0, then
ax²+bx+c = a(x-x₁)(x-x₂)
Now,
solving the quadratic function 5x²−2x−9 = 0
[tex]-5x^2+2x+9=0[/tex]
subtract 9 from both sides
[tex]-5x^2+2x+9-9=0-9[/tex]
Simplify
[tex]-5x^2+2x=-9[/tex]
Divide both sides by -5
[tex]\frac{-5x^2+2x}{-5}=\frac{-9}{-5}[/tex]
[tex]x^2-\frac{2x}{5}=\frac{9}{5}[/tex]
Add (-1/5)² to both sides
[tex]x^2-\frac{2x}{5}+\left(-\frac{1}{5}\right)^2=\frac{9}{5}+\left(-\frac{1}{5}\right)^2[/tex]
[tex]x^2-\frac{2x}{5}+\left(-\frac{1}{5}\right)^2=\frac{46}{25}[/tex]
[tex]\left(x-\frac{1}{5}\right)^2=\frac{46}{25} \\[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
so solving
[tex]x-\frac{1}{5}=\sqrt{\frac{46}{25}}[/tex]
[tex]x-\frac{1}{5}=\frac{\sqrt{46}}{\sqrt{25}}[/tex]
Add 1/5 to both sides
[tex]x-\frac{1}{5}+\frac{1}{5}=\frac{\sqrt{46}}{5}+\frac{1}{5}[/tex]
[tex]x=\frac{\sqrt{46}+1}{5}[/tex]
similarly solving
[tex]x-\frac{1}{5}=-\sqrt{\frac{46}{25}}[/tex]
[tex]x-\frac{1}{5}=-\frac{\sqrt{46}}{5}[/tex]
Add 1/5 to both sides
[tex]x-\frac{1}{5}+\frac{1}{5}=-\frac{\sqrt{46}}{5}+\frac{1}{5}[/tex]
[tex]x=\frac{-\sqrt{46}+1}{5}[/tex]
Thus, the roots are:
[tex]x_{1} =\frac{\sqrt{46}+1}{5},\:x_{2}=\frac{-\sqrt{46}+1}{5}[/tex]
Conclusion:
Since the roots are irrational, we do not factor further.
Therefore, we leave 5x²−2x−9 as it is.
write the following numbers in order from least to greatest . -1, 1.75, -1.75, -2, -2 1/2, -5/2, 9/4 I NEED HELP ASAP PLEASE
Step-by-step explanation:
-5/2
-2
-1.75
-1
1/5
1.75
9/4
Mark as brainlist . kindly
Find the 43rd term in the sequence: -6, -3, 0,...
Answer: 129
Step-by-step explanation: 43•3=129
Jolie purchased a concert ticket on a web site. The original price of the ticket was $110. She used a coupon code to receive a 15% discount. The web site applied a 10% service fee to the discounted price. Jolie’s ticket was less than the original price by what percent?
Answer:
10 percent
Step-by-step explanation:
i took a test
(x - 3)2 + (y + 7)2 = 121 what's the radius
Answer:
[tex]r=11[/tex]
Step-by-step explanation:
The equation of a circle is commonly denoted as:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h, k)[/tex] is the center of the circle.
This equation is already written in that format, therefore:
[tex]r^2=121,\\r=\fbox{$11$}[/tex],
Write the rule for the transformation.
Just answer Number 5, I got the rest.
Any spam will be reported/deleted.
Answer:
30
Step-by-step explanation:
so one of them is 90, one of them is 60
180-150 = 30
so 30
I need help I'm in 6th grade I use to have all f but I changed it into a,b,c can someone plss help so I don't fail
Answer:
um what
Step-by-step explanation:
Are these triangles similar?
pretty sure its no, the number on the outside arent the same meaning both areas wont add up.
15 POINTSSS
An = 15 +3 (n-1)
term # l value of An
1 l ______
5 l ______
10 l ______
20 l ______
complete the table for each given sequence.
I need help quick please!!!!
Answer:
1 is false
2 is blueprints
Step-by-step explanation:
Helppppppppppppppppppppppp please
Answer:
A
Step-by-step explanation:
Two Squares
There are 2 squares at the top and bottom. All sides = 3
2* s^2
2 * 3^2
2 * 9
18
Middle Figure.
Triangles
There are many ways to solve this. I think the most easily understood is to break it into 2 triangles and a rectangle.
Base of both triangles = 5 + 5 = 10
The height of each triangle = (7 - 3)/2 = 4/2 = 2. You divide by 2 because there are 2 bases -- one in each triangle.
Area = 1/2 * 2 * 10 = 10
But there are 2 of them so the total area is 20
Rectangle
The length of the rectangle = 5 + 5 = 10
The width = 3
Area = 30
Total
Total Area = 2 squares + 2 triangles + 1 rectangle
Total Area = 18 + 20 + 30 = 68
Seven more than three times a number is thirty-one. Write an equation
and solve for the unknown number.
Answer:
As an equation, (we'll use x as the variable), that word problem is 3x+7=31.
To solve we'd subtract 7 from both sides to isolate 3x, which gives us 3x=24. Now, to isolate x(unknown number) we would divide both sides by 3. When you divide both sides by 3, you'd get x=8.
write an absolute value inequality for the graph below.
use x for your variable.
Step-by-step explanation:
The magnitude of x is equal or less than 7.
=> We have |x| <= 7.
An equilateral triangle has a side length of 12sqrt(3) inches. What is the length of the altitude of the triangle?
HELP ASAP
Answer:
18 inches.
Step-by-step explanation:
Let x inches be the altitude of the triangle.
By Pythagoras Theorem,
[6sqrt(3)]^2 + x^2 = [12sqrt(3)]^2
108 + x^2 = 432
x^2 = 324
x = 18
So the altitude of the triangle is 18 inches.
A bell pepper has 3 grams of sugar per serving.
An apple has 18 grams of sugar per serving.
Which statement is true?
For an equal number of servings, the apples will have six times as much sugar.
There will always be more sugar in 10 servings of bell peppers than a smaller number of servings of apples.
For an equal number of servings, the apples will always have 15 more grams of sugar.
The amount of sugar in two servings of bell peppers is 36 grams.
Answer:
For an equal number of servings, the apples will have six times as much sugar.
Step-by-step explanation:
process of elimination. All the other answer choices are incorrect and this one checks out.
evaluate.
[tex] - \sqrt{81} [/tex]
.......
Answer:
Step-by-step explanation:
First find factors of 81
3 81
3 27
3 9
3 3
1
81 = 3×3×3×3
81 = 3^4
Taking squareroot
∴ -√81 = -√3^4
= -3^2
= -9
What is cos 60°?
60
2
1
90'
309
3
O A.
O B. 2
С.
0
D.
OE.
E.
< PREVIOUS
Answer:
B but sorry 4 the time tho
The measure of the trigonometric relation cos 60° = 1/2
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
A = cos 60°
And , cos θ = adjacent / hypotenuse
So , cos 60° = 1/2
Hence , the measure of cos 60° = 1/2
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
#SPJ7
How do i find the slope-
20 points answer!
[imagine below included!]
Answer:
3/3 = 1
Step-by-step explanation:
The slope formula is..
Pick two formulas. Let's do (-5, -2) and (-2, 1)
x1 y1 x2 y2
(-5, -2) (-2, 1)
[tex]\frac{1-(-2)}{-2-(-5)}[/tex] = [tex]\frac{3}{3}[/tex] = 1
It'll work the same thing for (-2, 1) and (1,4)...
3/3 or 1 is a pattern between the points.
Please help, don’t understand
The Chandlers are moving across the country. Mr. Chandler leaves 4 hours before Mrs. Chandler. If he averages 70mph and she averages 80mph, how many hours will it take Mrs. Chandler to catch up to Mr. Chandler?
Answer:
It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.
Step-by-step explanation:
Given that:
Speed of Mr. Chandler = 70 mph
Distance covered in 4 hours = 70 * 4 = 280 miles
Let,
h be the number of hours.
y be the total distance covered.
y = 70h + 280
Speed of Mrs. Chandler = 80 mph
y = 80h
For catching up, the distance would be same.
80h = 70h + 280
80h - 70h = 280
10h = 280
Dividing both sides by 10
[tex]\frac{10h}{10}=\frac{280}{10}\\h=28[/tex]
Hence,
It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.
A band expects to put 16 songs on their next CD. The band writes and records 37.5% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD?
answer:
- this is multi-step problem
16 X 1.375 = 22 songs (37.5% was added)
22 X .5 = 11 songs (50% was removed)
final answer: 11 songs.
At a multi screen movie theater two movies begin at 10 AM the first movie is shown every two hours the second movie is on every three hours what time will both movies be shown together again
Answer:
¯\_(ツ)_/¯
Step-by-step explanation:
A certain lottery has 31 numbers. In how many different ways can 4 of the numbers be selected?
enter the value of 3/4 + 7/12 - ( -4 )
Answer:
16/3 or 5.33
Step-by-step explanation:
3/4+7/12+4/1= 16/3 = 5.33
Answer:
Step-by-step explanation:
Exact Form:
16/3
Decimal Form:
5.3....
Mixed Number Form:
5 1/3
Kelsey can buy 3 sweatshirts for a total of $30. How much would it cost if she were to buy 4 sweatshirts at the same price?
Answer:
$40
Step-by-step explanation:
30 divided by 3 is 10 so 4 multiplied by 10 is $40
_ divided by 4= _ remaider 5
Answer:
20 / 4 =5
Step-by-step explanation:
I think
what is 8÷530 TYPE FAST
Answer:
0.0150
Step-by-step explanation:
8÷530
0.0150
it is correct
Find the zeros for 2x2−24=26. What is the positive value of x?
Answer:
i think it is 12
Step-by-step explanation:
Please help me guys
2+2
Answer:
Step-by-step explanation:
2 plus 2 is four (4)
Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coordinates of point U.
Answer:
(0, -1)
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram RSTU, RS // TU and RU // ST
Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:
Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5
Slope of ST = (2 - 4) /[6 - 3] = -2/3
Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)
Slope of TU = (y - 2) /[x - 6]
Slope of RU = Slope of ST
(y - 1) / (x + 3) = -2/3
3y - 3 = -2x -6
2x + 3y = -6 + 3
2x + 3y = -3 (1)
Slope of RS = Slope of TU
0.5 = (y - 2) /[x - 6]
0.5x - 3 = y - 2
0.5x - y = 1 (2)
Solving 1 and 2 simultaneously gives:
x = 0, y = -1
Therefore the coordinates of U = (0, -1)