Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Given:
The quadratic equation is:
[tex]12a^2+9a+7=0[/tex]
To find:
The solution of the given equation in simplest form by using the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]12a^2+9a+7=0[/tex]
Here, [tex]a=12,b=9,c=7[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}[/tex]
[tex]x=\dfrac{-9\pm \sqrt{81-336}}{24}[/tex]
[tex]x=\dfrac{-9\pm \sqrt{-255}}{24}[/tex]
[tex]x=\dfrac{-9\pm i\sqrt{255}}{24}[/tex] [tex][\because \sqrt{-a}=i\sqrt{a}][/tex]
The solutions of the given equations are [tex]x=\dfrac{-9-i\sqrt{255}}{24}[/tex] and [tex]x=\dfrac{-9+i\sqrt{255}}{24}[/tex].
Therefore, the correct option is B.
Related Questions
asmine is filling a small fish tank with water. The fish tank is in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in. What is the volume of this fish tank
Answers
The volume of the fish tank in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in is 90π cubic inches.
Therefore the answer is 90π in³.
Recognize that the fish tank is in the shape of a right circular cylinder.
Remember that the formula for the volume of a cylinder is
V = πr^2h
where r is the radius and h is the height.
Plug in the given values for the radius (r = 3 inches) and the height (h = 10 inches) into the formula.
Perform the calculation:
πr^2h
= π(3^2)(10)
= π×9×10
= 90π cubic inches
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Which relationship has a zero slope?
A. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.
B. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3.
C. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5)
D. A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answers
9514 1404 393
Answer:
A. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2
Step-by-step explanation:
The relationship that has constant y-values is the one with zero slope. That would be the first table.
Answer: A
Step-by-step explanation: He is correct
Each of 8 ladies randomly chooses a woolen overcoat from 14 different styles. What is the probability that at least 2 ladies choose the same type of overcoat?
choices
≈ 0.820
≈ 0.918
≈ 0.929
≈ 0.894
Answers
Answer: 0.894
Step-by-step explanation:
Answer:
≈ 0.918
Step-by-step explanation:
Use the complement since the probability of at least 2 ladies choose the same type of overcoat is much more challenging than finding the probability that all the ladies choose a different overcoat.
P(at least 2 ladies choose the same type of overcoat) = 1 − P(all choose different)
Find the probability that they all choose a different type of overcoat.
Now use the complement to determine the probability that at least 2 ladies choose the same type of overcoat.
P(at least 2 ladies choose the same) =
1 − P(all choose different)
≈ 1 − 0.0820
≈ 0.918
The probability that at least 2 ladies choose the same type of overcoat is approximately 0.918 or 91.8%.
Find the missing side. Round to the nearest tenth.
X
55
18
Answers
Answer:
solution
90+55+×=180(sum of angle of triangle is 180)
or,145+x=180
or,x=180-145
therefore,x=35
. The water pipe has a radius of 5 cm and a height of 7 cm. What volume of
water does it take to fill the pipe?
Answers
Answer:
V=550cm^3
Step-by-step explanation:
Answer: 549.5 cm squared
Step-by-step explanation:
Drag each equation to show if it could be a correct first step to solving the equation
3(6 + x) = 24.
Answers
Answer:
Here you go
Step-by-step explanation:
I hope this helps :)
Need help for this please, i have to pass my class
Answers
by means of the definition, find the derivative of the function 'F' f(x)=6
Answers
We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.
How do you find the derivatives by using the Definition?The derivative of a function is the slope of the curve for the specified function. Physically speaking, the derivative of a function is the instantaneous rate of change of a function with respect to the variable at a location.
A securities with a price that is based on or derived from one or more underlying assets is referred to as a derivative. A contract between two or more parties based on the asset or assets constitutes the derivative itself. Changes in the underlying asset's value affect its value.
The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.
lim/h→0f(x+h)−f(x)h=f'(x).
lim/h→06−6/h=0.
f'(x)=limΔx→0
f'(x)=limΔx→0
f(x+Δx)−f(x)Δx=
f'(x)=limΔx→06−6Δx=0
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A diving board is 10 feet long and 1 foot wide. What is its area?
Answers
Answer:
10ft^2
Step-by-step explanation:
10ft×1ft=10
Answer:
10square feet is the area (length x width)
Step-by-step explanation:
I WILL IVE BRAINLEST FOR CORRECT ANSWER
Answers
15 Weeks should be the answer
Ver en español
On the coordinate plane, the segment from R(6,
–
16) to S(14,
–
1) forms one side of a rectangle. The rectangle has an area of 459 square units. Find the perimeter of the rectangle.
Write your answer as a whole number, decimal, or simplified radical. Do not round.
units
Answers
The perimeter of the rectangle, given the area and the segment from R ( 6, -16) to S (14, - 1 ) is 88 units
How to find the perimeter ?To find the perimeter, first find the distance between R ( 6, -16) to S (14, - 1 ) which will allow you to find the length of one side. This distance can be found by the formula :
= √((x2 – x1)² + (y2 – y1)²)
= √((14 – 6)² + (-1 – (-16))²)
= 17 units
This means that one side of the rectangle measures 17 units so the other side would be:
Area = Length x Width
459 = 17 x Width
Width = 459 / 17
Width = 27 units
The perimeter of the rectangle is:
= Length + Width + Length + Width
= 17 + 27 + 17 + 27
= 88 units
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Each of 5 boys randomly chooses a watch from 12 different styles. What is the probability that at least 2 boys choose the same type of watch?
choices
≈ 0.3819
≈ 0.5387
≈ 0.7387
≈ 0.6181
Answers
Answer: ≈ 0.6181
Step-by-step explanation:
The probability that at least 2 boys choose the same type of watch is 0.6181.
What is Probability?
Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Here, the total number of combinations of styles for 5 boys
12 X 12 X 12 X 12 X 12 = 12⁵
the total ways that each boy have different styles
12 X 11 X 10 X 9 X 8
P(None of the boys have same style) = (12 X 11 X 10 X 9 X 8) / 12⁵
= 0.3819
P(at least 2 boys have same style) = 1 - P(None of the boys have same style)
= 1 - 0.3819
= 0.6181
Thus, the probability that at least 2 boys choose the same type of watch is 0.6181.
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PLEASE PLEASE HELP I WILL MARK THE BRAINIEST (the little crown thingy)
Answers
Answer: A
Step-by-step explanation: They both go up but they have diffrent patterns
hopes this helps any
Answer:
A.
Step-by-step explanation:
the 'x' slot is going up two and the 'y' slot is going up one every change.
x= x 1/3 * x3 is it always sometimes or true
Answers
Answer:
Only sometimes true
Step-by-step explanation:
Now, I'm going to go out on a whim here, since your equation writing isn't the best, but I will assume that the equation is:
x = x/3 * 3x
Now, to simplify this equation, we will multiply both sides by 3, giving us:
3x = x * 3x
Then, simplify the left side:
3x = [tex]3x^{2}[/tex]
Divide by 3 gives us:
[tex]x = x^{2}[/tex]
Now, this is only true in two cases. When x is 1, and when x is 0. So, that equation is only sometimes true.
Hope this helped!
help pleaseeeee im stuck
Answers
Ali is collecting signatures for a petition. He currently has 520 signatures. He has 6 more weeks to collect the remaining signatures he needs. He needs a total of at least 1,000 signatures before he can submit the petition. Ali wants to collect the same number of signatures each week. Write and solve the inequality for the situation
Answers
An inequality that represents the number of signatures Ali needs to collect in each of the remaining weeks so that he will have enough signatures to submit the petition: 520 + 6m ≥ 1000
and the minimum number of signatures he needs to collect = 80
Given that Ali wants to collect the same number of signatures each week.
Assume that Ali collects m number of signatures each week.
He has 6 weeks to collect the remaining signatures he needs.
So, by unitary method in 6 weeks the number of signatures he would collect:
6 × m
He currently has 520 signatures and he needs a total of at least 1,000 signatures before he can submit the petition.
so, we get an inequality.
520 + 6m ≥ 1000
We solve above inequality.
6m ≥ 1000 - 520
m ≥ 480/6
m ≥ 80
Ali needs to collect at least 80 signatures, so that he will have enough signatures to submit the petition.
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What is the area of the shaded region? Use 3.14 for pi and round your answer to the
nearest tenth.
O
6 cm
10 cm
12.6 cm²
78.5 cm²
50.2 cm²
201.0 cm²
Answers
The area of the shaded region is, 201.0 cm².
What is circle?
A circle is a closed, two-dimensional figure in which all points in the plane are equally spaced apart from the center. The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric around the center for all angles.
In the given figure we have to find the area of the shaded region.
First to find the area of circle with radius 10cm.
Area of circle = [tex]= \pi r^2 = 3.14*(10)^2 = 3.14*100 = 314cm^2[/tex]
Now to find the area of circle with radius 6cm.
Area of circle = [tex]= \pi r^2 = 3.14*6^2=3.14*36 = 113.04 cm^2[/tex]
So, the area of the shaded region is,
[tex]314cm^2 - 113.04cm^2 = 200.96cm^2=201.0cm^2[/tex]
Hence, the area of the shaded region is, 201.0 cm².
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Please help I will give brainliest
Answers
Answer:
If the circle, translate 3 units right and 5 units up and dilated 5/2
then circle C is congruent to circle A.
------------------------
hope it helps...
have a great day!!
32x^6-4
how do yo factor this
Answers
Find the length of the segment that joins the points (-5, 4) and (6,-3).
Answers
Answer:
[tex]\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}[/tex]
Step-by-step explanation:
We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:
x₁= -5 y₁= 4 x₂= 6 y₂ = -3Substitute the values into the formula.
[tex]d= \sqrt{(6--5)^2+(-3-4)^2[/tex]
Solve inside the parentheses.
6--5 (Back to back negative signs become a positive)= 6+5 =11 -3-4= -7[tex]d= \sqrt{(11)^2+(-7)^2[/tex]
Solve the exponents.
(11)²= 11*11= 121(-7)²= -7*-7= 49[tex]d= \sqrt {(121)+(49)[/tex]
Add.
[tex]d= \sqrt {170}[/tex]
[tex]d=13.0384048104[/tex]
Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.
13.0384048104[tex]d\approx 13.04[/tex]
The length of the segment is √170 or approximately 13.04.
PLEASE NO LINKS OR I WILL REPORT YOUR ACCOUNT
Answers
=======================================================
Work Shown:
A = pi*r^2
A = 3.14*8^2
A = 200.96
Note that the radius r = 8 is half of the diameter d = 16. I'm using the approximation pi = 3.14, which means the area is approximate. To get a more accurate answer, use more decimal digits of pi. The units of the area are in square feet, which can be written as "sq ft" or as "ft^2".
WHERE DO YOU PLACE THE PARENTHESES TO EQUAL TO 40
4+2•3^2
HELPPPP!! IT HAS TO EQUAL TO 40!!!!
Answers
4+(2x3)^2
4+(4x9)
4+36
40
I want the answer please
Answers
The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ lim θ → 0 ( sin θ / θ ) = 1
Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.
⇒ lim θ → 0 ( sin θ / θ ) = 1
Take LHS;
⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )
⇒ lim θ → 0 ( cos θ / 1 )
⇒ ( cos 0 )
⇒ 1
⇒ RHS
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Santos walks 222 kilometers south and then a certain number of kilometers east. He ends 555 kilometers away from his starting position. How many kilometers east did Santos walk
Answers
Answer:
4.6 km
Step-by-step explanation:
You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.
DistanceThe distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.
c² = a² + b²
5² = 2² + b²
21 = b²
b = √21 ≈ 4.583
Santos walked about 4.6 km east.
<95141404393>
Factoring can be used to solve ANY quadratic equation.
True or false
Answers
Answer: False, Quadratic can sometimes be solved by factoring. It can ALWAYS be solved using the quadratic formula.
Step-by-step explanation:
Hope this helps :)
Answer:
false
Step-by-step explanation:
Find the length of x. Assume that lines which appear to be tangent to the circle are tangent
A) 36
B) 42
C) 48
D) 54
Answers
Answer:
C
Step-by-step explanation:
Remark
The formula that relates tangents and secants using the information given is
The distance from the external point to the point of tangencyo^2 = The external point of secant to the circumfrance of the circle * the other intersect point of the secant.
The algebra is much simpler.
y^2 = 27 ( 27 + x)
Givens
y = 45
27 is the distance from the external point to the circle
27 + x is the entire length of the secant.
Solution
45^2 = 27(27 + x) Remove the brackets
2025 = 729 + 27x Subtract 729 from both sides
2025 - 729 = 27x
1296 = 27x Divide by 27
1286/27 = x
x = 48
if x+3=9 whats the answer:)
enjoy
Answers
Answer:
x=6
Step-by-step explanation:
then x=6 because replacing x 6+3=9
Using the pie chart below, if 300 students were polled on their favorite ice cream flavor, how many more students preferred strawberry ice cream than vanilla ice cream?
Answers
Can you please mark branliest? Thank you!
need help in pre-algebra
Answers
answer:
a. 8 · 10^7 is 4000 times larger than 2 · 10^4
step-by-step explanation:
solve the actual expression firstwrite the expressions in standard form and compare them8 · 10^7 (or 8 X 10000000) = 80000000
2 · 10^4 (or 4 X 10000) = 20000
now that you have them in standard form, divide them to compare80000000 / 20000 = 4000
from this, we can tell that 8 · 10^7 is 4000 times larger than 2 · 10^4Kellie bought 8 towels and spent $39.60. Each towel costs the same amount.
Part A
Use the drop-down menus to create an equation that can be used to determine t, the
price, in dollars, of 1 towel.
t
+
00
39.60
Part B
What is the price, in dollars, of 1 towel?
Enter your answer in the box.
$
Answers
Answer:
fvg bvgcjvtfjocfrx
Step-by-step explanation:
kjn
jkm
'knlnkm
kl
j
kl;n
;kn