Find the values of p for which the quadratic equation 4x2 + px + 3 = 0 has equal roots.
Answers
Answer:
Step-by-step explanation:
You need to concern yourself with the +3. That will determine what the equal roots are.
(2x + √3)^2
Now expand this to see what p is. (Kind of a nasty question if you ask me).
4x^2 + 2x*√3 + (√3)^2
4x^2 + 2√3 x + 3 also possible is
4x^2 - 2√3 x + 3
So the answer is p = 2√3
The answer could also be p = -2√3
Answer:
p = ±4√3
Step-by-step explanation:
The discriminant of quadratic equation ax²+bx+c = 0 is ...
d = b² -4ac
In your quadratic, its value is ...
d = p² -4(4)(3) = p² -48
The discriminant will be zero when the quadratic has equal roots. In that case, the values of p are found by ...
d = 0
p² -48 = 0
p² = 48 . . . . . add 48
p = ±√48 . . . . take the square root
p = ±4√3 . . . . simplify
__
Another way to get there is by looking at the factoring of a quadratic with equal roots:
(ax +b)² = 0 = a²x² +2ab +b²
Comparing to the given quadratic, we find ...
a² = 4 ⇒ a = ±2 . . . . . . coefficient of x²
b² = 3 ⇒ b = ±√3 . . . . constant
p = 2ab = 2(±2)(±√3) . . . . coefficient of x
p = ±4√3
_____
The attachment shows the two different values of p give equations with one solution (each).
Related Questions
A boat is heading towards a lighthouse, whose beacon-light is 102 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 7 , before they draw closer. They measure the angle of elevation a second time from point b at some later time to be 12. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Answer:
351 ft (nearest foot)
Step-by-step explanation:
Model the problem as a right triangle, where the horizontal leg is the water (where the boat is at the vertex with the hypotenuse), and the vertical leg is the lighthouse. The angle of elevation is between the boat and the top of the lighthouse. (see attached diagram)
Horizontal distance from point A to the lighthouse
Using the trig ratio tan(x) = O/A where x is the angle, O is the side opposite to the angle and A is the side adjacent to the angle:
Given:
x = 7O = 102 A = ?⇒ tan(7) = 102/A
⇒ A = 102/tan(7)
⇒ A = 830.7233357... ft
Horizontal distance from point B to the lighthouse
Given:
x = 12O = 102 B = ?⇒ tan(12) = 102/B
⇒ B = 102/tan(12)
⇒ B = 479.8722712... ft
Therefore, distance from A to B:
⇒ distance = A - B
⇒ distance = 830.7233357... - 479.8722712...
⇒ distance = 350.8510645...
⇒ distance = 351 ft (nearest foot)
factorise 8x+12 please
Answers
Answer: 4(2x+3)
Step-by-step explanation:
The greatest common factor in the two terms is 4.
Therefore, by factoring out a 4 we get
4(2x+3)
Sten and Manu are at a mystery movie. The movie starts at 1:45 PM and ends at 3:40 PM. How long is the movie?
Answers
Answer:
Step-by-step explanation:
dang that a tow hour movie and 5 minuets movie let me know if i am wrong hope this help
Estimate the quotient for 627 ÷ 9. explain how you found your awnser
Answers
69.7
Step-by-step explanation:
627 ÷ 9
=69.66666666666666
approximately
69.7
[tex] \sf \leadsto627 \div 9[/tex]
[tex] \\ \\ [/tex]
[tex] \sf \leadsto \dfrac{627}{9} [/tex]
[tex] \\ \\ [/tex]
[tex] \sf \leadsto \dfrac{627 \div 3}{9 \div 3} [/tex]
[tex] \\ \\ [/tex]
[tex] \sf \leadsto \dfrac{209}{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \sf \leadsto 69.67[/tex]
Find the value of the variable
Answers
Answer:
q=8
Step-by-step explanation:
The ratio of sides from bigger to smaller is 1/2.
q=1/2(16)
q=8
Hope it helps!
Find the 23rd
term of the arithmetic sequence whose common difference is d=4 and whose first term is a = -15.
Answers
[tex] \mathsf{T_n = a + (n - 1)d}[/tex]
[tex] \to \mathsf{T_{23} = - 15+ (23 - 1)4}[/tex]
[tex] \to \mathsf{T_{23} = - 15+ (22)4}[/tex]
[tex] \to \mathsf{T_{23} = - 15+ 44}[/tex]
[tex] \to \mathsf{T_{23} = 29}[/tex]
BrainlyVIP -.- ✋
Answer:
a₂₃ = 73
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 15 and d = 4 , then
a₂₃ = - 15 + (22 × 4) = - 15 + 88 = 73
I’m awful at geometry! Please help :)
Answers
Answer:
a is 64 degrees
b is 138.6667
Step-by-step explanation:
a is simple because you know a straight line has 180 degrees and since one side is 116 you simply subtract 180-116=64.
b is more complicated. Since a hexagon has a total internal angle of 720. 3 angle measures are given.
720-116- (180-82)-90=416
Since the last three angles are the same, you can divide by 3.
416/3=138.6667
Hopefully I didnt make any calculation errors because there is a lot of calculating for b.
Olivia has a dozen apples of the same size
and a dozen pineapples of the same size.
Olivia uses her juicer to extract 12 ounces of
pineapple juice from 7 pineapples and 16
ounces of apple juice from 4 apples. She
makes a pineapple-apple juice blend from an
equal number of pineapples and apples.
What percent of the blend is pineapple juice?
Answers
Answer: 30% of the blend is pineapple juice
Step-by-step explanation:
Since 7 pineapples yield 12 oz of juice, 1 pineapple yields 1 5/7 oz of juice.
Since 4 apples yield 16 oz of juice, 1 apple yields 4 oz of juice.
She’s making a pineapple-apple juice where the ratio of apples and pineapples used is 1:1. To find what percent of the blend is pineapple juice:
1 apple to 1 pineapple. The combined amount of juice they produce is 5 5/7 oz. The formula to find what percent of teh blend is pineapple juice is oz of pineapple juice divided by the combined amount of juice in the blend.
1 5/7 divided by 5 5/7 equals 3/10, or 30%.
The fraction of the blend that is pineapple and apple gives the
percentage that is pineapple.
Response:
The percentage of the blend that is pineapple juice is 30%How can the percentage of pineapple juice in the blend be calculated?Amount of juice extracted from 7 pineapples = 12 ounces
Amount of juice extracted from 4 apples = 16 ounces
Therefore;
The amount of juice from 1 pineapple = [tex]\mathbf{\frac{12}{7}}[/tex] ounces = [tex]1\frac{5}{7}[/tex] ounceThe amount of juice from 1 apple = [tex]\frac{16}{4}[/tex] ounces
The amount of juice from 1 apple = 4 ouncesWhich gives;
The amount of juice from 1 pineapple and 1 apple = [tex]\frac{12}{7}[/tex] + 4 = [tex]\frac{40}{7}[/tex] = [tex]5\frac{5}{7}[/tex]
The amount of juice from 1 pineapple and 1 apple = [tex]5\frac{5}{7}[/tex] ouncesThe percentage of pineapple juice is therefore;
[tex]Percentage \ pineapple \ juice \ in \ blend= \dfrac{\dfrac{12}{7} }{\dfrac{40}{7} } \times 100 = \dfrac{12}{7} \times \dfrac{7}{40} \times 100 = \underline{30\% }[/tex]Learn more about percentages here:
https://brainly.com/question/26150306
Raghav scod18 out of 20 in the method test his friends only scored 22 out of 25 in the English test who scored more and by how much
Answers
Answer:
sorry but I really don't know the answer
Step-by-step explanation:
What would happen to the variance of a data set if we multiplied every observation by S?
Answers
If (-3, y) lies on the graph of y = 3-x, then y =
1/27
-27
27
Answers
Answer:
y = 6
Step-by-step explanation:
[] We can plug in our x value of -3, from the coordinate point, and solve for y.
y = 3 - x
y = 3 - (-3)
y = 3 + 3
y = 6
[] We can also graph the equation, and find the point where x = -3
-> See attached
I do not see this option in the answers you have provided, so either I miss interpreted something, or something else got messed up.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
Answer:
Hello, the correct answer is, 27
Step-by-step explanation:
Substitute -3 into -x
We know that since they are both negatives, they cancel out. Therefore, you substitute 3 into y = 3^-x.
y = 3^3
y = 27
What shape do these coordinates make? ( 2, 7 ), ( 8, 7 ), ( 8, 3 ), ( 2, 3 )
Answers
If you need more help just comment!
Please like and brainiest
A doughnut shop makes 21 different types of doughnuts each day. Customers often select a "baker's dozen" from the shop,
that is, 13 doughnuts.
How many different ways can a customer choose 13 different types of doughnut for their "baker's dozen" without
repetition?
Answers
Answer: 203490
Step-by-step explanation:
just took an L to give you the right answer
if the arithmetic mean of 8,4,6,x,2,7 is 5 then find the value of x?
Answers
Answer:
This gives us the value of $x$ as 3. Hence the answer is 3.
Step-by-step explanation:
Step-by-step explanation:
if you would arrange it in order and solve you will get 3
lou eats 6/8 of a pizza. what fraction of the pizza, in simplest form, is left over
Answers
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{6}{8}[/tex]
A full pizza would be a whole; 1 or [tex]\frac{8}{8}[/tex]. So you must subtract the amount Lou eats, to the original amount.
[tex]\frac{8}{8} - \frac{6}{8} = \frac{2}{8}[/tex]
[tex]\frac{2}{8} = \frac{1}{4}[/tex]
Your final answer will be [tex]\frac{1}{4}[/tex].
need help...much appreciated!! Thanks!!
Answers
2k + 11 = 131
2k = 131 - 11
2k = 120
k = 120/2
k = 60⁰
6, ?, 4, 2
find the missing term of the Fibonacci style sequence
Answers
Answer:
-2
Step-by-step explanation:
The Fibonacci Sequence is the series of numbers where the next number is found by adding up the two numbers before it.
Therefore, 6 + ? = 4
⇒ ? = 4 - 6
⇒ ? = -2
A square has 12 cm length and it's area is equal to the area of a rectangle having length 16 cm.What is the breadth of the rectangle?
Answers
Step-by-step explanation:
Hope this helps you......
[tex] \displaystyle{ \blue{ \frak{DisneyPrincess29}}}[/tex]
Answer:
Breadth = 9 cm
Explanation:
Find the area of square using; area of square: length²area of the square:
→ 12²
→ 144 cm²
The rectangle has similar area. rectangle area: 144 cm²use the formula to find area of rectangle:
length * breadth = area of rectangleusing the formula:
→ length * breath = 144
→ 16 * breadth = 144
→ breadth = 144/ 6
→ breadth = 9 cm
The population of a certain city was 3,416 in 1999. It is expected to decrease by about 0.28% per year. Write an exponential decay function, and use it to
approximate the population in 2023
The exponential decay function where f(x) is the population of the city x years after 1999 is f(x)=
Answers
Answer:
f(x) = 3416*(0.0028)^x
Step-by-step explanation:
f(x) = 3416*(0.0028)^x
Which point is located at (3,4)? A) M. B) N. C) O. D) P
Answers
B) N.
As we can see that the point N is 4 units away from x axis and 3 units away from y axis. Thus constituting the coordinate (3,4)
Answer:
B) N
Step-by-step explanation:
HOPES THIS HELP
Find the value of x. (For your answer, just type the
NUMBER. Do not put x = .)
Answers
Answer:
9
Step-by-step explanation:
The lines are parellel, so you use the formula 7x+12=9x-6 to solve for x.
Lynn ate lunch and wanted to leave her waitress 15% tip. her meal cost 8.95$. what is the tip and the total
Answers
Answer:
Tip would be 1.34
Step-by-step explanation:
total would be 10.29
3.If ABCD is a parallelogram with AB = 2x + 1, AD = x + 13, and DC = 3x -11. Determine if ABCD is
rhombus. Show algebraic work to justify your answer.
Answers
Answer:
ABCD is a rhombus
Step-by-step explanation:
Sides AB and DC are opposite and equal in parallelogram ABCD. This means ...
AB = CD
2x +1 = 3x -11
12 = x . . . . . . . . add 11-2x to both sides
Sides AB and CD have length ...
2x +1 = 2(12) +1 = 24 +1 = 25
Then the length of side AD is ...
AD = x +13 = 12 +13 = 25
Adjacent sides AB and AD of the parallelogram have the same length, The figure is a rhombus.
The equation e^y= 2x is equivalent to
y = In 2
y = In x
y = In 2x
Answers
Answer:
y = ln(2x)
Step-by-step explanation:
Neat document provided.
Which letter on the number line represents 4.55?
F
E
D
C
Answers
Post a better picture then I'll help!
find the mean, median and mode
Answers
Answer:
Mean: 26.88
Median: 27
Mode: 27
Step-by-step explanation:
19,20,20,21,21,21,22,22,23,23,23,25,25,25,25,25,27,27,27,27,27,27,27,27, 27,27,28,28,28,29,29,29,29,29,29,30,30,30,30,33,33,34,35,40
Mean: 26.88
Median: 27
Mode: 27
Sorry if there are any repeating numbers, this is quite long.
Hope this helps!
If cos (α+β) = 0, then sin(α-β) can be reduced to
Answers
[tex] \text{ cos}( \alpha + \beta ) = 0 \\ \\ \implies \: \alpha + \beta = 90 \degree [\because \text{cos \: 90 \degree} = 0 ] \\ \\ \implies \theta = 90 \degree - \beta \: \: \: \: ......(i)[/tex]
[tex] \sin( \alpha - \beta ) \\ = \sin(90 \degree - \beta - \beta ) \: \: \: \: \text{[using \: (i)]} \\ = \sin(90 \degree - 2 \beta ) \\ = \cos(2 \beta ) \: \: \: \: \: \: \: \: \text[ \because \sin(90 \degree - \theta) = \cos( \theta) ] [/tex]
Hope This Helps!! :)Help me please if you can
Answers
Answer:
perimeter = 1 3/4
Step-by-step explanation:
1. 3/4 x 2 because there are two sides with the fraction 3/4. 3/4 x 2 is 1 1/2
2. 1/8 x 2 because there are two sides with the fraction 1/8. 1/8 x 2 is 1/4
3. 1 1/2 + 1/4 = 1 3/4
Anthony read 5 6 hour each day for 5 days.
Answers
The total number of hours for which Anthony has read after 5 days is; 4 1/6 hours
Total number of reading hoursAccording to the question;
Anthony reads for 5/6 hour each day and does this for 5 days.On this note, it follows that his reading rate is 5/6 hours per day and duration is 5 days.
Hence, the total number of reading hours is;
T = (5/6) × 5.T = 25/6T = 4 1/6 hours.
Read more on rate and time;
https://brainly.com/question/1256181
writing to explain tyler has 83 footballs cards that he wants to put into an album. each page holds 6 cards. how many pages will he need? how many spaces will he have left for new cards? explain to awnser.
Answers
Since tyler has 83 football cards we can divided, 83 divided by 6 cards for each page would have 13 cards, and he would have an extra page making 14 with the last one containing 5 left over cards, this would leave one space left over for new cards.