Answers
Answer:
a) x = 1.5 and x = -0.3
b) x = -8 and x = 5
Step-by-step explanation:
a)
The given equation follows the general structure: ax² + bx + c = 0.
Therefore, if a = 5, b = -6, and c = -2, you can substitute the values into the quadratic formula and solve for "x".
b)
Another way of solving polynomials is through factorization. After rearranging the equation to fit the general structure of a quadratic (as seen above), you can factor by asking yourself the question, which 2 numbers multiply to "c" (-40) and add to "b" (3)? The answers will make up your factors.
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1. }[/tex]
[tex]\mathsf{5x^2 - 6x - 2 = 0}[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve:}[/tex]
[tex]\mathsf{x = \dfrac{-(-6)\pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathsf{x = \dfrac{6 \pm \sqrt{76}}{10}}[/tex]
[tex]\huge\textbf{Simplify that as well:}[/tex]
[tex]\mathsf{x = \dfrac{3}{5} + \dfrac{1}{5}\sqrt{19}\ or\ x = \dfrac{3}{5} + (-\dfrac{1}{5})\sqrt{19}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x \approx 1.5 \ or\ x\approx -0.3{}\ }}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + 3x = 40}[/tex]
[tex]\huge\textbf{Subtract 40 to both sides:}[/tex]
[tex]\mathsf{x^2 + 3x - 40 = 40 - 40}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x^2+ 3x - 40 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(x - 5)\times (x + 8) = 0}[/tex]
[tex]\mathsf{(x - 5)(x + 8) = 0}[/tex]
[tex]\huge\textbf{Set the factors to equal to 0:}[/tex]
[tex]\mathsf{x - 5 = 0 \ or\ even\ x + 8 = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 5\ or\ x = -8}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 5\ or \ x = -8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Related Questions
If you give me the correct answer I will give you brainliest plz help
Answers
Comment if you need clarification.
What is the positive value of “x”?
x(x+5)=387
Hint: Use the quadratic formula
Answers
Answer:
x= −5−11√13/2, −5+11√13/2Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Exact Form:
x= −5−11√13/2, −5+11√13/2
Decimal Form:
x=17.33053201…,
−22.33053201…
Step-by-step explanation:
x(x+5)=387
Simplify
x(x+5).
x^2+5x=387
Subtract 387 from both sides of the equation.
x^2+5x−387=0
Use the quadratic formula to find the solutions.
−b±√b^2−4(ac)/2a
Substitute the values a=1, b=5, and c= −387 into the quadratic formula and solve for x.−5±√5^2−4⋅(1⋅−387)/2⋅1
Simplify.
x=−5±11√13/2
The final answer is the combination of both solutions.
x=−5−11√13/2, −5+11√13/2
The result can be shown in multiple forms.
Exact Form:
x=−5−11√13/2,−5+11√13/2
Decimal Form:
x=17.33053201…,
−22.33053201…
Hope it is helpful....Answer:
[tex]\displaystyle x=\frac{-5+11\sqrt{13}}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define
x(x + 5) = 387
Step 2: Identify Variables
Rewrite
[Distributive Property] Distribute x: x² + 5x = 387[Subtraction Property of Equality] Subtract 387 on both sides: x² + 5x - 387 = 0Part: a = 1, b = 5, c = -387Step 3: Solve for x
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{-5\pm\sqrt{5^2-4(1)(-387)}}{2(1)}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{-5\pm\sqrt{25-4(1)(-387)}}{2(1)}[/tex][√Radical] Multiply: [tex]\displaystyle x=\frac{-5\pm\sqrt{25+1548}}{2(1)}[/tex][√Radical] Add: [tex]\displaystyle x=\frac{-5\pm\sqrt{1573}}{2(1)}[/tex][Fraction - Denominator] Multiply: [tex]\displaystyle x=\frac{-5\pm\sqrt{1573}}{2}[/tex][Fraction - √Radical] Simplify: [tex]\displaystyle x=\frac{-5\pm 11\sqrt{13}}{2}[/tex]what is the area of a square yards of a rectangle with a length of 9 yds and a width of 4 yds?
Answers
[tex]a = lw[/tex]
[tex]a = (9)(4)[/tex]
[tex]a = 36 \: {yds}^{2} [/tex]
Answer:
Here we can understand that the shape is a rectangle as length is not equal to width.
Area of the rectangle in square yards when length is 9 yds and width is 4 yds will be,
Area of Rectangle = LENGTH × WIDTH
⇒ 9*4
⇒ 36 sd yds
Thus the are will be 36 sd yds
Is the absolute value of -29 less than 29?
Answers
Answer:
no
Step-by-step explanation:
The absolute value is EXACTLY 29, so.
When a rocket is launched, it climbs 50 feet for every 13 feet it travels horizontally. Estimate the rocket's distance (Find the missing side of triangle).
Answers
Answer:
About 51.6 feet
Step-by-step explanation:
50^2+13^2
Square root of 2669 is 51.66236541
Si tenemos un cuadrado cuyos lados miden 1/3 en 7 partes iguales, ¿Cuál es su área?
Answers
Answer:
English please?
Step-by-step explanation:
...........
libro de matemáticas 1 de secundaria pag 108
porfavor es para hoy ಠ﹏ಠ
Answers
con repuesta y todo para mi friend, no mas que las demas no pude contestarlas ya que estava en clase y ahorita estoy haciendo tarea ok
HELP ME!!!!!!!!!!! Its the one in the middle
Answers
Answer:
[tex]\frac{x3(p+5)}{10p(p-1)}[/tex]
Step-by-step explanation:
BRAINLIEST PLEASE
Andrei ,Aura,Dorin,și Emilia calculează media geometrică a numerelor √32;3√2 și obțin rezultatele din tabelul:Andrei 6√2.
Aura 4√3.
Dorin 2√6
Emilia6.
Answers
Answer:
this is the way we calculate it ♡♡♡
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=47(0.63)
x
Answers
1-0.63=0.37
0.37(100)=37
So the final answer is 37% decrease.
Answer:
decay function
percent rate of decrease is 37%
Step-by-step explanation:
I assume the x is the exponent.
[tex] y = 47(0.63)^x [/tex]
The number raised to the exponent x is 0.63 which is between 0 and 1. That means that as x increases, (0.63)^x decreases. That means it is an exponential decay function.
Each unit more in x results in 0.63 being multiplied by the number.
Since 1 - 0.63 = 0.37, the percent rate of decrease is 37%.
Answer:
decay function
percent rate of decrease is 37%
A community builds a sandbox section and a playground section at one of the local parks. The area of the playground
section is 1,675 square feet. It is 100 square feet more than 4.5 times the area of the sandbox section.
• Write an equation that can be used to determine the area, A. of the sandbox section.
. What is the area of the sandbox section? Show all work.
Enter your equation, answer, and work in the box
Please help worth 25 points
Answers
9514 1404 393
Answer:
A + (100 +4.5A) = 1675A ≈ 286.4 square feetStep-by-step explanation:
The problem statement tells us that the area of the sandbox and playground together is 1675 square feet. Using A as the area of the sandbox section, the playground section is said to be (100 +4.5A). Then the total area is ...
A + (100 +4.5A) = 1675 . . . . . . an equation to determine A
5.5A = 1575 . . . . . . . . . . . . . . . subtract 100, collect terms
A = 1575/5.5 = 286 4/11 . . . . . divide by 5.5
The area of the sandbox section is about 286.4 square feet.
3x - 2y= 5, 4x + 3y= 1
Answers
Answer:
x=17 and y=23 DONT SUE ME IF I GET THIS WRONG PLZZ ;-;
Step-by-step explanation:
Answer:
(1, - 1 )
Step-by-step explanation:
Given the 2 equations
3x - 2y = 5 → (1)
4x + 3y = 1 → (2)
Multiplying (1) by 3 and (2) by 2 and adding the result will eliminate y- term
9x - 6y = 15 → (3)
8x + 6y = 2 → (4)
Add (3) and (4) term by term to eliminate y
17x + 0 = 17
17x = 17 ( divide both sides by 17 )
x = 1
Substitute x = 1 into either of the 2 equations and solve for y
Substituting into (2)
4(1) + 3y = 1
4 + 3y = 1 ( subtract 4 from both sides )
3y = - 3 ( divide both sides by 3 )
y = - 1
solution is (1, - 1 )
Please help! Will give brainliest!
Options
1/9
1/6
1/4
1/2
Answers
Find the values of the variables in the parallelogram. The diagram is not to scale.
Answers
Step-by-step explanation:
option B is the correct answer of this question.
x = 29, y = 49 and z = 102 .
plz mark my answer as brainlist plzzzz vote me also .
hope this will be helpful to you.
Answer:
B
Step-by-step explanation:
x is 29 because the inverse opposite of angles are the same.
z is 102 because opposite parallelogram angles are the same.
y is 49 through process of elimination.
Help me it is an hw due soon please
Answers
Answer:
1st is 1/4 and 2nd is 1/10
On a triangle, one side measures 4x2−2x and another side measures 2x2 −5x+1. If the perimeter of the triangle is 9x2 + x+6, what is the measure of the third side of the triangle? (Your answer will be an expression)
Answers
Answer:
3x² + 8x + 5
Step-by-step explanation:
Subtract the sum of the 2 given sides from the perimeter, that is
9x² + x + 6 - (4x² - 2x + 2x² - 5x + 1)
= 9x² + x + 6 - (6x² - 7x + 1 ) ← distribute parenthesis by - 1
= 9x² + x + 6 - 6x² + 7x - 1 ← collect like terms
= 9x² + 8x + 5
HELP I NEED HELP ASAP
A. 5%
B. 0.5%
C. 50%
D. 0.05%
Answers
Answer:
the answer is A.5%
Step-by-step explanation:
Helia invested 4000 AED for 3 years with a compound interest rate of 1.5%, Calculate the worth of her investment at the end of this time period
Answers
5y=2x+5 Y=-x +6
( x, y)
Answers
Answer:
Step-by-step explanation:
6/5 + 2x/5= y
3+ 5y/2 = x
the number of magazine subscriptions decreases by 8% each year.If there are 225,000 this year,how many will there be 7 years from now
Answers
Answer:
I got 147107
Step-by-step explanation:
If the subscriptions decrease by 8% each year then you would times 225000 by 0.08 then take the number you get from that and subtract it from 225000. And repeat until you get to the seventh year.
[tex]\sqrt{2x-3} =5[/tex]
Answers
How to:
Square both sides then solve the equation
If the formula for finding the area of a rectangle is A=bh, then how could you describe the formula for finding the area of a triangle
Answers
Answer:
A=LxW
Step-by-step explanation:
Answer:
El perímetro de un triángulo es igual a la suma de sus tres lados.
b x h
2
You have to solve the problem \frac{3}{4}-\frac{1}{8} 4 3 − 8 1 . After you make the denominators the same, what do you do?
FOR ALL MY POINTS
Answers
Answer:
If you are doing subtraction with fractions you need to make a common denominator and subtract the numerators from each other
ex. 1/2 - 1/3
make a common denominator (or find the least common multiple)
3/6 - 2/6
subtract the numerators
take 2 from 3 and put that on top.
Solution 1/2-1/3= 3/6-2/6= 1/6
Plz help me with this
Answers
I am going to repeat myself ONE LAST TIME. Please help!
What is the domain of the function y = StartRoot x EndRoot?
Answers
Hope this helps :)
Find the area of the semicircle. 10
Answers
Exact Area = 25pi square units
Approximate Area = 78.5 square units
The approximate value is found using pi = 3.14
====================================================
Explanation:
I think you meant to say "quarter circle" instead of "semicircle".
The area of a full circle with radius r = 10 is
A = pi*r^2
A = pi*10^2
A = pi*100
A = 100pi
But we only want one quarter of this. So we divide the full area by 4
(100pi)/4 = (100/4)pi = 25pi
The exact area in terms of pi is 25pi square units
If we used the approximation pi = 3.14, then we can say 25*pi = 25*3.14 = 78.5 is the approximate area
To get a better approximation, use more decimal digits in pi.
I really need help really fast!!!
Answers
Answer:
-3 sqrt 2 or -4.242640687
Step-by-step explanation:
Which expression is represented by the model?
4X43
-4X-3
-4x+3
Answers
Which of the relations has a domain of {-5, 0, 5}?
A. {(-5, 5), (0, 5), (5,5)}
B. {(0, -5), (0, 0), (0, 5)}
C. {(-5, 0), (0, 5), (1, 0)}
Answers
Answer:
B
Step-by-step explanation:
its that how you would look like if you were anime sorry was looking at your pf. have a nice day
PLEASE HELP! ANSWER FOR 20 POINTS PLS PLS
Answers
Answer:
5³ = 125
Step-by-step explanation:
5³ = 5 × 5 × 5 = 25 × 5 = 125
Answer:
5³ = 15 because the ³ mean 3 left over 5's like if i had 2² the ² = 2 so 2²=4
5+5+5=15
Answer : 15