Answer:
a)
[tex]\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}[/tex]
b) p is in the interval (-4,4)
Step-by-step explanation:
Quadratic Equation
It's given the following quadratic equation:
[tex]x^2+px+4=0[/tex]
a)
It's required to complete squares and find the roots. This can be done by recalling the polynomial identity:
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
We already have the first term squared, and we need to find the second term. Rewriting the equation:
[tex]\displaystyle x^2+2(\frac{1}{2}px)+4=0[/tex]
The second term of the binomial is 1/2p, thus completing the squares with [tex]b^2[/tex]:
[tex]\displaystyle x^2+2(\frac{1}{2}px)+\left(\frac{1}{2}p\right)^2+4-\left(\frac{1}{2}p\right)^2=0[/tex]
Factoring:
[tex]\displaystyle \left(x+\frac{1}{2}p\right)^2+4-\frac{1}{4}p^2=0[/tex]
Moving the independent term to the right side:
[tex]\displaystyle \left(x+\frac{1}{2}p\right)^2=\frac{1}{4}p^2-4[/tex]
Taking the square root:
[tex]\displaystyle x+\frac{1}{2}p=\pm\sqrt{\frac{1}{4}p^2-4}[/tex]
Solving for x:
[tex]\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}[/tex]
b) If the equation won't have real roots, then the radicand should be negative:
[tex]\displaystyle \frac{1}{4}p^2-4<0[/tex]
Factoring:
[tex]\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)<0[/tex]
The zeros of the left-side polynomial are:
[tex]\displaystyle \frac{1}{2}p-2=0[/tex]
[tex]\displaystyle \frac{1}{2}p=2[/tex]
p = 4
[tex]\displaystyle \frac{1}{2}p+2=0[/tex]
[tex]\displaystyle \frac{1}{2}p=-2[/tex]
p = -4
The inequality:
[tex]\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)<0[/tex]
Is satisfied for values of p in the interval (-4,4)
A man drops a stone from a bridge. How high is the bridge if the stone hits the water 4 seconds later
Answer: 4 feet
Step-by-step explanation:
HELP PLEASE REEEEEEEEEEEE!! Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
72 is what percent of 480? Write and solve an equation to solve the problem.
Answer:
Step-by-step explanation:
480 = 100%
72 = ? you can find it doing (72(100))/480
72(100)= 7200
7200/480= 15
the answer is 15%
have a nice day :)
HELP ME, PLEASE. I REALLY NEED IT
Find x:
[tex]S=\frac{1}{sin2x}+\frac{1}{sin4x}+\frac{1}{sin8x}+...+\frac{1}{sin2^{n}x }[/tex]
Answer:
cotx - cot2ⁿxStep-by-step explanation:
Note: finding the sum not xFirst rewrite the first term as:
1/sin2x = sinx / (sinxsin2x) = sin(2x-x) / (sinxsin2x) =(sin2xcosx - cosxsinx) / (sinxsin2x) = (sin2xcosx)/(sinxsin2x) - (cos2xsinx)/(sinxsin2x) = cosx/sinx - cos2x/sin2x = cotx - cot2xNow the sum is:
S = cotx - cot2x + cot2x - cot4x +... + cot2ⁿ⁻²x - cot2ⁿx =cotx - cot2ⁿxWhich expression is equivalent to 5p2+ 3p2 - 6p?
a. 2p2
b. 14p2
C. 8p2 - 6p
d. p(5p + 3p - 6)
Answer:
is c or d i think
what is an equation for the line that passes through the points (-2,3), and (2,1)
Answer:
yes
Step-by-step explanation:
no
A demon possessed woody and turned him into a monster!
He now hunts children aged 7-16 because he likes his meals chewy.
His head turns 360 degrees to spot prey.
If you look at the picture he will rise out of your sheets and put snakes in your shoes.
And he's right behind you.
Answer:
Ë
Step-by-step explanation:
Im literally going to poop my pants that is SO scawwwy. I deserve compensation for this. My lawyers are coming after you
Answer:
i looked behind me and yes i did see a monster, my brother
Step-by-step explanation:
helpp meee pleaseeee
Answer:
I think its b:/ srry if I'm wrong
Select the correct answer from each drop-down menu.
Aerial's grandmother gave her $5,500.00 to save for her college education. She went to the bank to open a savings account. The bank told her they had two options available.
Account A will pay 5.5% simple interest until the account is closed.
Account B will pay 4.5% simple interest and if the account is left open for longer than 3 years, then at the end of the third year a bonus account will be opened with $250 that also earns 4.5% for the remainder of the time the initial account is open. When the initial account is closed, the bonus account will be closed as well and the money from the two accounts will be combined.
If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account
is the better choice earning her
more.
If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account B is the better choice earning her $41.25 more.
Help me and I’ll give brainliest to u
Answer:
7p
Step-by-step explanation:
Since it is 7 dollars per person, and p stands for person, the admission fee would be 7p.
Thank you, I hope you learned from this answer! If it did help, please mark this as brainliest! Thank you!
If a circle has a diameter of 30 meters, which expression gives its area in
square meters?
A. 30•n
B. 30^2•n
C. 15^2•n
D. 15•n
Answer:
C. 15²π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Diameter: d = 2rArea of a Circle: A = πr²Step-by-step explanation:
Step 1: Define
d = 30 m
Step 2: Find Area
Substitute [D]: 30 m = 2rIsolate r: 15 m = rRewrite: r = 15 mSubstitute [AC]: A = π(15 m)²Rearrange: A = 15²πplease help me this is turned in a couoke of minutes!!!!!!!!!!
Answer:
mince is the answer
How much change from a $50 bill would you receive if you bought
items costing $13.95, $6.08, and $24.35?
Answer:
$5.62
Step-by-step explanation:
Add all of the cost of the items and then deduct that answer from 50.
Answer:
$5.62
Step-by-step explanation:
50−(13.95+6.08+24.35)
=50−(20.03+24.35)
=50−44.38
=5.62
Chase lives 1 and one half blocks west of Ellie. They draw a number line to model this situation. Because Ellie lives 1 and three fifths blocks east of school, they give her house the coordinate 1 and three fifths . Chase incorrectly claims that the coordinate of his house is 3 and one tenth . What is the correct coordinate of Chase's house? What is Chase's likely error?
Answer:
1/10
Step-by-step explanation:
A number line is a line which contains numbers marked at intervals (usually regular intervals). Points to the right of the origin are positive numbers while those to the left are negative numbers.
The school is used as the origin. Ellie house is 1 and three fifths blocks east (to the right) of the school. This means that it is + 1 and three fifths (+8/5).
Chase house is 1 and one half blocks (3/2) west of Ellie. Since it is west then it is to the left. Hence the coordinate of chase house = 8/5 - 3/2 = 1/10
Hence the coordinate of chase house is 1/10(one tenths).
The error may be as a result of thinking chase house is to the east of Ellie, hence adding to get 3 and one tenth.
Here is a riddle: “I am thinking of two numbers that add up to 5.678. The difference between them is 9.876. What are the two numbers?”
The riddle can be represented with two equations. Write the equations
Answer:
X + Y = 5.678
X - Y = 9.876
The two numbers: X = 7.777 Y = -2.099
Step-by-step explanation: solve by elimination
X + Y = 5.678
X - Y = 9.876 . Add the two equations so the y cancels. Solve for x
2x = 15.554 . Divide both sides by 2
X = 7.777 Substitute in the original equations to find Y
7.777 + y = 5.678 . Subtract 7.777 from both sides
Y = - 2.099
check in the second equation:
7.777 -(-2.099) = 9.876
7.777 + 2.099 = 9.876 True
The two numbers is X = 7.777 and Y = -2.099.
And, the two equation is X + Y = 5.678 and X - Y = 9.876.
Given that,
I am thinking of two numbers that add up to 5.678. The difference between them is 9.876.Here we assume the one number be X and the other number be Y.
Based on the above information, the calculation is as follows:
X + Y = 5.678
X - Y = 9.876
2x = 15.554
X = 7.777
Now
7.777 + Y = 5.678
Y = - 2.099
Therefore, the above should be the answers.
Learn more: brainly.com/question/24169758
what is the slope of the graph
Answer:
- 5/3
Step-by-step explanation:
Line is passing through the points (0, 2) & (3, - 3)
Slope of the graph = (- 3 - 2)/(3 - 0) = - 5/3
PLEASE ANSWER THE QUESTION ASAP!!!!
Answer:
B
Step-by-step explanation:
hihi! can you help me please? Giving brainleist to the best/correct awnser :))
Solve for x
9(3−2x)=2(10−8x)
Answer:
x= 2/7
Step-by-step explanation:
i think that's the answer jdmsmzmsms
Answer:
Step-by-step explanation:
x=7/2
which is not a justification for the proof
a. pieces of right triangles similarity theorem
b. side side side similarity theorem
c. substitution
d. addition property of equality
Answer: B.Side side side similarity theorem
Step-by-step explanation:
Hope this helps <3
^^^^ B.Side side side similarity theorem is correct
i just took the test and it was right!
Tom swam to the bottom of a swimming pool that was 9 feet deep and he touched
the bottom. He swam back to the surface. How many feet did Tom swim?
Answer:
18 feet
Step-by-step explanation:
9 x 2 = 18
Solve the following system.
5x - 5y + 8z = 6
x + 2y + z = 12
3y - z = 10
The answer is (2,4,2)
Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers. y =
Answer:
Step-by-step explanation:
given: (2,1) & (5-8)
first find the slope,
m= (Y2-Y1) / (X2-X1)
m=(-8-1)/(5-2)
m=(-9)/(3)
m=-3
we have y=-3x+b
use any point to sub in x and y
1=-3(2)+b
1+6=b
b=7 therefore, y=-3x+7 is the equation
Answer:
y = - 3x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)
m = [tex]\frac{-8-1}{5-2}[/tex] = [tex]\frac{-9}{3}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 1 ), then
1 = - 6 + c ⇒ c = 1 + 6 = 7
y = - 3x + 7 ← equation of line
If a relation has more numbers in its range than in its domain, what has to be true?
Answer:
Both the domain and range are the set of all real numbers. For the absolute value function f(x)=|x| f ( x ) = | x | , there is no restriction on x . ... For the cubic function f(x)=x3 f ( x ) = x 3 , the domain is all real numbers because the horizontal extent of the graph is the whole real number line. this is the best i can do if its not helpful i guess u can ask ur teacher.
Which line has a slope of 1/2 and passed through (2,-4)
Check For Understanding
CELL PHONES A Cell phone company is going to build three new towers in a nearby city. The city council has
released s map that shows where the towers will be built. On the map, the distance between towers A and B is 2
centimeters, the distance between towers B and C 3 centimeters, and the distance between towers A and C is 4
centimeters. A technician needs to visit the stes of the three towers, and he has outlined his travel route between
them on a map. The polygon formed by his travel route on the map will be similar to the polygon formed by the
technicians he drives to the three towers. If the actual distance between tower Band tower C is 600 meters, how
for was the technican have to travel to visit all three cell phone towers?
Answer:
Distance between A ----> B : 2 cm
B ---> C: 3 cm : 600 meters
A----> C: 4 cm
3:600 meters scaled
So its 200 meters per every 1 cm!
From A to B : 400 meters
From B to C : 600 meters
Frok C to A: 800 meters
Therefore we sum 400+600+800= 1800 meters
7 × (-5) is equivalent to?
2
-35
35
-12
Answer:-35
Step-by-step explanation: 7x5 = 35, but since the 5 is a negative it’s -35
Answer:
-35
Step-by-step explanation:
whenever multiplying positive and negative integers, if one of the factors are negative, then the answer will be negative. if both are negative, the answer becomes a positive, and if both are positive, the answers stays positive.
in this case 7 is positive and 5 is negative so your anwers is -35
hope i helped!
:)
Mrs. Jackson bought 4 gallons of juice for a party. Each gallon has 16 cups. After the party, 4 cups of juice were left over. At the party, how many cups did people drink? Show your work and complete the explanation of how you found your answer.
Answer:
60 cups
Step-by-step explanation:
Mrs. Jackson bought 4 gallons of juice for a party. Each gallon has 16 cups.
From the above question:
1 gallon of juice = 16 cups
Then:
4 gallons of juice = c
Cross Multiply
1 × c = 4 × 16 cups
c = 64 cups of juice
Hence, 4 gallons of juice = 64 cups of juice
We are told that :
After the party, 4 cups of juice were left over.
The cups of juice people drank at the party is calculated as:
Total cups of juice - Number of cups of juice left over.
64 cups of juice - 4 cups of juice
= 60 cups of juice
help me answer this geometry question please!! will give brainliest and 5 stars!!
2x/ 4x4 - 2x
simplify
Answer:
x^5/2 - 2x
Step-by-step explanation:
Cancel terms that are in both the numerator and denominator
2
Combine multiplied terms into a single fraction
3
Combine exponents
Answer: x^5/2 - 2x
Step-by-step
Dora has 20 donuts. she divides those 20 donuts into halves. then she divides those halves into fifths. then she divides those fifths into thirds. how many pieces does she have now?
Answer:
270
Step-by-step explanation:
if u cut a donut in too halfs there are more donuts so 20* 2 is 40 then multiply 40 by 5 since she cuts it into fifths an u get 90 then multiply 90 by 3 since its thirds an you get 270
Answer:
600
Step-by-step explanation:
20 divided by 1/2 is 40
40 divided by 1/5 is 200
200 divided by 1/3 is 600
Are 5 and 0.5 Equal to Each other?
Answer:
no
Step-by-step explanation:
5 is a whole number 0.5 doesn't equal to 1 it is half of 1