Answer:
The quadratic equations and their solutions are;
9 ± √33 /4 = 2x² - 9x + 6.
4 ± √6 /2 = 2x² - 8x + 5.
9 ± √89 /4 = 2x² - 9x - 1.
4 ± √22 /2 = 2x² - 8x - 3.
Explanation:
Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.
We have to solve all of the five equations to be able to match the equations with their solutions.
2x² - 8x + 5, here a = 2, b = -8, c = 5. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4. 24 can also be written as 4 × 6 and √4 = 2. So x = 8 ± 2√6 / 2×2= 4±√6/2.
2x² - 10x + 3, here a = 2, b = -10, c = 3. x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.
2x² - 8x - 3, here a = 2, b = -8, c = -3. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4. 88 can also be written as 4 × 22 and √4 = 2. So x = 8 ± 2√22 / 2×2 = 4± √22/2.
2x² - 9x - 1, here a = 2, b = -9, c = -1. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4. x = 9 ± √89 / 4.
2x² - 9x + 6, here a = 2, b = -9, c = 6. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4. x = 9 ± √33 / 4 .
Jayson said, "I am thinking of two fractions that when added have a sum of 1." Which fractions could Jayson have been thinking about?
Answer:
he could have been thinking of 1/2 + 1/2 or 4/8 + 4/8 or maybe 5/10 + 5/10
because 2/2=1 and so does 8/8 and 10/10
Step-by-step explanation:
Is AABC-AXYZ? If so, identify the similarity postulate or theorem that
applies
30°
30"
45
15
959
c.
959
А
A. Similar - SSS
B. Similar - AA
C. Similar - SAS
D. Cannot be determined
The theorem that applies to the similar triangles is AA theorem.
How to find similar triangles?Similar triangles are triangle with same shapes but may be different sizes.
Similar triangle have corresponding sides as a ratio of each other.
The triangles above have two of their angles equal, therefore, the triangles are similar.
They are similar by AA theorem.
AA theorem of similarity states that If two of angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.
30 ≅ 30
95 ≅ 95
learn more on similar triangles here: https://brainly.com/question/16999173
#SPJ1
Factor: 3bc-4ad +6ac-2bd
Can you create a rubric for this math question
Answer:
(3c−2d)(2a+b)
Step-by-step explanation:
3bc−4ad+6ac−2bd
Do the grouping 3bc−4ad+6ac−2bd=(6ac−4ad)+(3bc−2bd), and factor out 2a in the first and b in the second group.
2a(3c−2d)+b(3c−2d)
Factor out common term 3c−2d by using distributive property.
(3c−2d)(2a+b)
Mike installed the window shown. How many square feet is the window? Use 3.14 for pi. Round to the nearest tenth.
Answer: 3.9ft²
Step-by-step explanation:
Find the area of the rectangle first:
= Length * Width
= 2 * 1.5
= 3 ft²
Find the area of the semi-circle by finding the area of a circle and dividing it by 2:
= πr²
= 3.14 * 1.5/2 * 1.5/2
= 1.76625ft²
Divide by 2:
= 1.76625/ 2
= 0.88 ft²
Add the area of the rectangle to the semi-circle:
= 3 + 0.88
= 3.9ft²
Yall, is this correct? And sorry for my bad handwriting for the answer btw-
Find the missing side of the right
triangle.
7
4
Х
X=
<= [?]
The missing side of the right angle triangle is 8.0622577483 units.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
Triangle is a right angle triangle.
And the sides of a right-angled triangle are:
Base = 4 unit
Perpendicular = 7 units.
To find the length of the hypotenuse:
We apply Pythagoras theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Substituting the values in the equation,
(hypotenuse)² = (4)² + (7)²
(x)² = 16 + 49
(x) = √(65)
(x) = 8.0622577483
Therefore, the value of x is 8.0622577483 units.
To learn more about the Pythagoras theorem;
https://brainly.com/question/343682
#SPJ2
You drive a car that holds 15 gallons of gasoline. Your car uses 0.03 gal per mile. Which equation best represents this information
find the surface area of a cube with a side length of 5 centimeters.
The 6 faces of a cube have equal are.
Each face has are of 5*5=25 because they are all squares.
Now we just multiply by 6
25*6=150 centimeters cubed.
Done!
Step-by-step explanation:
step 1. a cube had 6 sides
step 2. each side is a square
step 3. the area of each side is 5x5 = 25cm^2
step 4. the surface area of the cube is 25x6 = 150cm^2.
As an estimation we are told 5 miles is 8 km.
Convert 33.7 miles to km.
Answer: 20.9420 is your answer
Record: 0/5 Score: 0 Penalty: 1 off
Complete: 0%
Jereme Nixon
Using Trig to Find Angles
Mar 01, 12:19:51 PM
?.
In AQRS, the measure of ZS=90°, QR = 7.7 feet, and SQ = 6.5 feet. Find the measure
of ZR to the nearest tenth of a degree.
R
7.7
Answer:
Step-by-step explanation:
57.6
HEEEEEEEELLLLLLPPPPPPPPP Graph the equation using the slope and y-intercept y = 1/3x + 4
Answer:
Step-by-step explanation:
7(x + 2) = 6(x + 5) solve for x
X = 16
7 x + 14 - 6 x = 30
x + 14 = 30
A company sets up a food booth and a game booth at the county fair.
The fee for the food booth is $100 plus $5 per day.
The fee for the game booth is $50 plus $7 per day.
Write an expression for how much both booths will cost for the same number of days.
Answer:
100+5x+50+7x
Step-by-step explanation:
hey what's
[tex] \sqrt[5]{1024} [/tex]
Answer:
[tex]4 \\ \: is \: your \: answer \: mate[/tex]
I hope it helpsenjoy your day
#Captainpower|~
Aisha has a smart phone data plan that costs $25 per month that includes 4 GB of
data, but will charge an extra $15 per GB over the included amount. How much
would Aisha have to pay in a month where she used 3 GB over the limit? How much
would Aisha have to pay in a month where she used went over by x GB?
Answer:
b
Step-by-step explanation:
In the diagram, ABC=DEF, find the values of x and y
Answer:
x=-1
y=66
Step-by-step explanation:
3x + 6 = 9
3x = -3
x=-1
10x+y=56
x=-1
-10+y=56
y=66
PLEASE HELP I NEED THIS BEFORE 8:00 pm
Answer:
y = -27
Step-by-step explanation:
-3 * 3 = -9 * 2 = -18/9 = -27
Answer:
The answer is Y=-27
Step-by-step explanation:
Hope this helped
Use the equation below to find y, if m=11, x=2, and b=5.
y=mx-b
Y=
How do you know to add for the first one and multiply for the second??
Answer:
When you multiply the variables with different exponents, you add. When you multiply an exponent with another exponent, you multiply.
Step-by-step explanation:
Answer above
What is the answer for this
1/2x(4/3-1/6)+3/4??
please help fast HELP
Answer:
The letters are really small I can't see it.
Step-by-step explanation:
Sorry
what is the value of x?
Answer:
68
Step-by-step explanation:
c=√a^2+b^2
√ 60^2 + 32^2 =68
We will use the Pythagorean Theorem
[tex]x {}^{2} = {32}^{2} + {60}^{2} \\ {x}^{2} = 1024 + 3600 \\ x {}^{2} = 4624 \\ x = \sqrt{4624} \\ x = 68[/tex]
Determine the equation of the circle graphed below.
Answer:
(x-2)^2+(y+4)^2=34
Expand and simplify: (x-2)^3
Answer:
Expand (x+2)^3. (x+2)3 ( x + 2 ) 3. Use the Binomial Theorem. x3+3x2⋅2+3x⋅22+23 x 3 + 3 x 2 ⋅ 2 + 3 x ⋅ 2 2 + 2 3. Simplify each term.
Ariel sold bags of gourmet popcorn for the school fundraiser. She sold 30 bags in two weeks, raising $112.50 for the school. How much did a bag of gourmet popcorn cost?
Answer:
3.75 dollars
Step-by-step explanation:
If 30 bags of popcorn = 112.50
Then what would one bag equal?
First start off by putting money/bags
[tex]\frac{112.50}{30}[/tex]
Then solve.
112.50/30 = 3.75
Your answer is 3.75.
Hope this is correct, and hope it helps ^_^
Answer:
$3.75 per bag
Step-by-step explanation:
Put the total cost (112.50) and divide it by how many she sold (30) to get your answer. hope this helped
Simplify:
(ay
8
6.
5x - 25 30 - 6x
Answer:
-x - 2530
Step-by-step explanation:
5x - 2530 - 6x
5x - 6x = -x
-x - 2530
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5/x-(25/30)=0
Step by step solution :
STEP
1
:
5
Simplify —
6
Equation at the end of step
1
:
5 5
— - — = 0
x 6
STEP
2
:
5
Simplify —
x
Equation at the end of step
2
:
5 5
— - — = 0
x 6
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : x
The right denominator is : 6
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 0 1 1
3 0 1 1
Product of all
Prime Factors 1 6 6
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 1 0 1
Least Common Multiple: 6x
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 6
Right_M = L.C.M / R_Deno = x
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 5 • 6
—————————————————— = —————
L.C.M 6x
R. Mult. • R. Num. 5 • x
—————————————————— = —————
L.C.M 6x
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5 • 6 - (5 • x) 30 - 5x
——————————————— = ———————
6x 6x
STEP
4
:
Pulling out like terms :
4.1 Pull out like factors :
30 - 5x = -5 • (x - 6)
Equation at the end of step
4
:
-5 • (x - 6)
———————————— = 0
6x
STEP
5
:
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-5•(x-6)
———————— • 6x = 0 • 6x
6x
Now, on the left hand side, the 6x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-5 • (x-6) = 0
Equations which are never true:
5.2 Solve : -5 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.3 Solve : x-6 = 0
Add 6 to both sides of the equation :
x = 6
One solution was found :
x = 6
this should make it ez for you now
Factor completely: x2-4
Answer:
(x+2)(x-2)
Step-by-step explanation
x times x equals x^2, 2 times x equals 2x, -2 times x equals -2x, and 2 times -2 equals -4. If you add that up, the x-values cancel out, leaving the x^2 and the -4. (This explanation is working it backwards which is the easiest way IMO)
Did the vertical or horizontal asymptote change? If it didn’t change, why not?
Answer:
I think it didnt change
Step-by-step explanation:
Cause both areas from the line are the same and if it were to change the left would be diffrent from the right. So there i think it didnt change.
5/32×7= multiplicación de fracciones, paso paso por favor rápido para hoy doy 5
Answer:
35/32
Step-by-step explanation:
Primero, es necesario hacer el 7 en una fracción
[tex]\frac{5}{32} * \frac{7}{1}[/tex]
Entonces puede multiplicarse a través
[tex]\frac{5(7)}{32(1)} \\\\\frac{35}{32}[/tex]
35/32 es la respuesta
¡También, lo siento si mi español es malo! Todavía estoy aprendiendo jaja
3 3/4 CM * 2 1/2 cm
please answer fast
Answer:0.0009375 m2
Step-by-step explanation: