Well, we know standard form of quadratic equation : ax² + bx + c where,
a = Coefficient of x²
b = Coefficient of x
c = Constant term
We also equation for determinant :
⇒ b² - 4ac
Here, if value of determinant i.e. (b² - 4ac) = A perfect Square, then we can understand that the givdn equation is factorisable.
But, if the value of (b² - 4ac) ≠ A perfect square, then it will be considered as "Not factorisable"
Now let's calculate whether the equation is factorisable or not :
Comparing the given equation with ax² + bx + c, we get :
a = 1
b = -3
c = -54
Putting values in the determinant equation :
⇒ (-3)² - 4(1 × -54)
⇒ 9 + 216
⇒ 225
⇒ 15²
So, determinant = A perfect square
That means the given equation is factorisable.
Now let's factorize with by middle term splitting :
⇒ x² - 3x - 54
⇒ x² -(9 - 6)x - 54
⇒ x² - 9x + 6x - 54
⇒ x(x - 9) + 6(x - 9)
⇒ (x + 6)(x - 9) [Required Solution]
Hence, we get our required solution.
Hope this Helps (✿◡‿◡)
The bowling alley charges a set fee for shoe rental and charges per game bowled. The total
cost of bowling can be modeled by c(b) = 5.75b + 4.25 Which statements about the function
are true?
I.
The cost for each game of bowling is $5.75.
II.
The shoes cost $5.75 to rent.
III.
The number of games bowled is represented by b.
1.
I and II only
2.
I and III only
3.
II and III only
4.
I, II and III
Submit Answer
Answer: (2.)
1 and 111 only
Step-by-step explanation:
QUICK HELP ME PLEASEEEEEEE. ONLY ONE HOUR LEFT! WILL MARK BRAIN...
Answer:
copy and paste it to math website
Step-by-step explanation:
-7-1.2x+19+7.7x help
Answer:
12+6.5x
Step-by-step explanation:
Hope this helps!! if you in step by step ill comment it in the comments!!
Determine if the data is skewed or symmetric.
Answer:
skewed
Step-by-step explanation:
HELPPPPPPOPPOPPPPP???
z = 106
y = 74
Since angle 74 and angle y are the same sizes, you can know for a fact they are the same measurments. Next, you would do 74(2) and that would get you 148. 360 - 148 is 212. 212/2 is 106. TADAAAAA. That's the answer.
The basic ratio of blue to red for paint is 4:7. How many quarts of blue paint should be mixed with 21 quarts of red paint to get purple?
4 - y over 5 = 2 - 2y over 8
I’m just really tired lol (and lazy)
Answer:
40 if i did the equation right and ignore this wiehdnsjw
Answer:
egg egg egg egg egg
Step-by-step explanation:
1+1=1972-1=egg
colin buys a tv for £780. It depreciates at a
rate of 5% per year. how much will
it be worth in 6 years
Answer:
Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.
four rolled-up dollar bills seeming to grow out of dirt, with a miniature rake lying in between them
SIMPLE ONE-TIME INTEREST
I=POrA=P0+I=P0+P0r=P(1+r)
I is the interest
A is the end amount: principal plus interest
P
0
is the principal (starting amount)
r is the interest rate (in decimal form. Example: 5% = 0.05)
Step-by-step explanation:
5. The sides of a triangle are in the ratio 4:5:6. What is the length of each side if the
perimeter is 45 cm?
Answer:
12, 15, 18
Step-by-step explanation:
4+5+6 = 15
45/15 = 3
multiply 4 x 3 = 12
multiply 5x 3 = 15
multiply 6 x 3 = 18
-3(x-4) = -9(x - 1)
X=?
Answer:
x = - 1/2
Step-by-step explanation:
-3(x-4) = -9(x - 1)
1. Distributive Property
-3 * x -3 *-4 = -9 * x -9 * -1
-3x + 12 = -9x + 9
Hint: 2 negatives make a postive
-3x + 12 = -9x + 9
2. Subtract 12 on both sides
-3x + 12 - 12 = -9x + 9 - 12
-3x = -9x + -3
3. Add 9x on both sides
-3x + 9x = -9x + 9x + -3
6x = -3
4. Divide both sides by 6 to isolate the variable
6x/6 = -3/6
x = - 1/2
Check:
-3(-1/2-4) = -9( -1/2- 1)
3/2 + 12 = 9/2 + 9
3/2 + 12 ( we need a common denominator so...lets make it 2 )
3/2 + 12*2/1*2
3/2 + 24/2 = 27/2 = 13 1/2 = 13. 5
Now...
9/2 + 9 ( we need a common denominator so..lets make it 2 )
9/2 + 9*2/1*2
9/2 + 18/2 = 27/2 = 13 1/2 = 13.5
13.5 = 13.5 CORRECT!
27/2 = improper fraction
13 1/2 = mixed number
13.5= decimal form
Hope this helped
Will mark brainliest
There are 16 cats and 14 dogs in a local animal shelter.
Which phrase describes a ratio relationship between the two quantities?
A. the number of dogs in the shelter compared to the number of cats in the shelter
B. the number of cats in the shelter compared to the number of cats in the shelter
C. the number of cats in the shelter compared to the number of dogs in the neighborhood
D. the number of dogs in the shelter compared to the number of rabbits in the shelter
Answer: A
Step-by-step explanation:
the table shows the number of gold metals won by united states athletes during the summer olympics
Answer:
A
Step-by-step explanation:
17) Find DE 3x - 28 3x – 30 G E F 33
The numerical length of DE is 11.
We have a Line Segment DG such that E and F is between D and G.
We have to determine the length of DE.
What is Line Segment?A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
According to question, we have -
DE = 3x - 28
EF = 3x - 30
FG = x
DG = 33
Now -
DG = DE + EF + FG
33 = 3x - 28 + 3x - 30 + x
7x = 33 + 58
7x = 91
x = 13
Therefore -
DE = 3x - 28 = 3 x 13 - 28 = 39 - 28 = 11
Therefore - DE = 11
Hence, the numerical length of DE is 11.
To solve more questions on Lines and Lengths, visit the link below -
brainly.com/question/16345328
#SPJ2
A house cost $320,000 in 2005. By the year 2019, its value was $560,000. What was the growth rate as a percent for that 14-year period? (Remember, i=(p^2/p^1)^1n−1
Answer:
Growth rate = 4.08%
Step-by-step explanation:
Rate of interest 'i' for the growth in the cost of the house,
i = [tex](\frac{\text{Final amount}}{\text{Initial amount}})^{\frac{1}{n}}-1[/tex]
Here 'n' = Duration or time (in years)
i = [tex](\frac{560000}{320000})^{\frac{1}{14}}-1[/tex]
i = [tex](\frac{7}{4})^{\frac{1}{14}}-1[/tex]
i = 1.0408 - 1
i = 0.0408
i = 4.08%
Therefore, growth rate for this period is 4.08%.
Please help!! the temperature at wonder lake is 12°f. during a storm, the temperature changes by -26° f. what is the temperature after the storm
Answer:
-14°F
Step-by-step explanation:
First, we start at 12°f. Then, the temperature changes by -26°f. This means that we add (-26°f) to what we currently have. We then have
12 + (-26)
= 12-26
= -14°F
Nick has a bag of marbles. Without looking in the bag, he
selects a marble, records its color, and puts it back in the
bag. All marbles are equally likely to be chosen. He
performs 100 trials.
Number of times a white marble was chosen
48
Number of times a red marble was chosen
13
Number of times a green marble was chosen 27
Number of times a blue marble was chosen
Based on the data Nick collected, what is the estimated probability, in
simplest form, of choosing a white marble from the bag? please help me
Answer:
Step-by-step explanation:
Ok wait. Try add
Answer:
12/25
Step-by-step explanation:
Two differences between y=2x and y=2x-7
Answer:
y=2x and y=2x-7 has same slope 2, but y=2x-7 shift down 7 unit from y=2x
Step-by-step explanation:
y=2x and y=2x-7 has same slope 2, but y=2x-7 shift down 7 unit from y=2x
Please i really need help
Of the 90 gallons of water the average uses each day, 30% is used outdoors mason wants to know how much water is used outdoors?
Answer:
Step-by-step explanation:
J
Answer:
90*0.3= 27 gallons of water are used outdoors each day
3 1/2 x 2 3/4 divided by 1 1/2
Answer:
The answer to the question provided is
[tex]6 \frac{5}{12} [/tex]
Answer:
[tex](3 \frac{1}{2} \times 2 \frac{3}{4} ) \div \frac{11}{2} \\ = ( \frac{7}{2} \times \frac{11}{4} ) \div \frac{11}{2} \\ = ( \frac{77}{8} ) \times ( \frac{2}{11} ) \\ = ( \frac{7}{4} ) \\ = 1 \frac{3}{4} [/tex]
A store is having a 20%-off sale on its video games. What is the amount of the discount on a game that regularly costs $25?
Answer:$20
Step-by-step explanation:
$25x.20=5
$25-5=20
A rectangular table top has dimensions as 1.52m and 0.75m. Find the perimeter in cm
That is a question about perimeter of rectangle.
The perimeter of a geometric shape is the sum of the value of the all sides.
In a rectangle, the opposite sides are cogruentes (equals). For example, look at picture below. In that rectangle, the sides AB and DC are equals, and the sides AD and BC are equals.
So, the sides of that rectangular table are: 1.52m, 1.52m, 0.75m and 0.75.
Therefore, the perimeter of that rectangle is [tex]1.52+1.52+0.75+0.75= 4.54[/tex]m.
But that is not the final answer because that is the perimeter in meters and the question want the answer in centimeters.
1 meter has 100 centimeter, so we need to multiplicate the perimeter by 100.
Thus, the perimeter of that rectangular table is [tex]4.54\cdot 100 = 454[/tex]cm.
Need help please not understanding
Answer:
The value of ∠4 is 45° .
Step-by-step explanation:
Given that , ∠4 = x + 30 ° & ∠2 = 2x + 15 .We need to find the measure of ∠4 . So from the figure we can see that , ∠2 & ∠4 are corresponding angles .So they will be equal.
⇒ ∠2 = ∠4 [ Corresponding angles ]
⇒ x + 30° = 2x + 15°
⇒ 2x - x = 30° - 15°
⇒ x = 15°
Hence the value of x is 15°
⇒ ∠4 = x + 30°
⇒ ∠4 = 15° + 30°
⇒ ∠4 = 45°
★ Hence the value of ∠4 is 45° .5 pts
Question 17
A right triangle has a base of 3m and a height of 4m. What is the area of
the triangle if it has been dilated by a scale factor of 2?
*Hint: Area =
base height
2
O 12m
O 24m
O 10m
O 6m
9514 1404 393
Answer:
(b) 24 m²
Step-by-step explanation:
After dilation by a factor of 2, the base is 2×3 m = 6 m, and the height is 2×4 m = 8 m. Then the area of the dilated triangle is ...
A = 1/2bh
A = 1/2(6 m)(8 m) = 24 m²
If you can answer 10, 11, and 12 for me that would be awesome. (12 multiply choice would be in the comments)
(+5) - (-7)
thank you in advance
Answer:
12
Step-by-step explanation:
What’s the solution for x- 6 = 4
Answer:
X = 10
Step-by-step explanation:
X - 6 = 4
X = 4 + 6
X = 10
Answer:10
Step-by-step explanation:
1.add 6 to both sides
x-6+6=4+6
2. simplify
x=10
The population of an endangered bird was about 230,000 in 2001. The equation y= 200,000(0.75)^x describes the bird la population, let x represent the number of years since 2001. Using the equation, how many birds will there be in 2021?
Answer:
634
Step-by-step explanation:
The population of the birds in 2001 = 230000
From 2001 to 2021 = 20 years
Given:
y = 200000[tex](0.75)^{x}[/tex]
where x is the number of years since 2001.
The population of the birds after 20 can be determined by;
y = 200000[tex](0.75)^{20}[/tex]
= 200000(3.171211939 x [tex]10^{-3}[/tex])
= 634.2424
y = 634
Thus, there would be 634 endangered birds in 2021.
Rewrite in simplest terms 3 (w-9w+8)-10
Answer:
-24w + 14
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/Coefficients/DegreesStep-by-step explanation:
Step 1: Define
3(w - 9w + 8) - 10
Step 2: Simplify
Combine like terms: 3(-8w + 8) - 10Distribute 3: -24w + 24 - 10Combine like terms: -24w + 14Solve the fraction problem and reduce the answer to simplest form:
1/5 + 3/4 = ??
7/9 - 3/5= ??
6/8 - 2/7 = ??
5/6 + 5/10 = ??
7/8 - 2/3 = ??
8/10 + 5/6 = ??
9/11 - 2/3 = ??
Answer:
1. 19/20
2. 8/45
3. 13/28
4. 4/3
5. 5/24
6. 49/30
7. 5/33
Fractions are integers that have both a numerator and a denominator. Fraction comes in the form: [tex]\frac{x}{y}[/tex]
where x = numerator and y = denominator.
a) 1/5 + 3/4
We find the Lowest common denominator (5, 4) = 20
Hence: 4 + (5 x 3) / 20
= 4 + 15 / 20
= 19/20
b) 7/9 - 3/5
We find the Lowest common denominator (5, 9) = 45
Hence: (7 x 5) + (9 x 3) / 45
= 35 - 27 / 45
= 8/45
c) 6/8 - 2/7
We find the Lowest common denominator (7, 8) = 56
Hence: (6 x 7) - (2 x 8) / 56
= 42 - 16 /56
= 26/56
= 13/28
d) 5/6 + 5/10
We find the Lowest common denominator (6, 10) = 30
Hence: (5 x 5) + (5 x 3) / 30
= 25 + 15 / 30
= 40/30
= 4/3
= 1 1/3
e) 7/8 - 2/3
We find the Lowest common denominator (3, 8) = 24
Hence: (7 x 3) - (2 x 8) / 24
= 21 - 16 / 24
= 5/24
f) 8/10 + 5/6
We find the Lowest common denominator (6, 10) = 30
Hence: (8 x 3) + (5 x 5)
= 24 + 25 / 30
= 49/30
= 1 19/30
g) 9/11 - 2/3
We find the Lowest common denominator (3, 11) = 33
Hence: (9 x 3) - (11 x 2) / 33
= 27 - 22 / 33
= 5/33
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