a) by completing the square find in the form of the constant p the roots of the equation x^2+px+4=0
b) hence find the set of values of p for which the equation has no real roots
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)
this is um .... im hungry .
Answer:
what? im hungry too..... and the photo is blurry
Answer:
Hungry too gonna go eat
Step-by-step explanation:
what is the value of f(-4.2) given the function f(x) = 23.2x + 2.5
Answer:
f(-4.2)= -94.94
Step-by-step explanation:
23.2*-4.2= -97.44
97.44+2.5= 94.94
Random variation in a process indicates __________; whereas non-random variation indicates process __________.
Answer: b. Stability/instability
Step-by-step explanation:
Random variation in a process indicates stability; whereas non-random variation indicates process instability.
When there is random variation in a process, it means that the process is stable and under control such that the only variations are those expected to be in the process.
When the variation is non-random however, it points to instability in process because this variation is special and not inherent in the process.
Suppose you want to buy one pair of pants and several pairs of socks.
The pants cost $24.95, and the socks are $5.95 per pair. How many
pairs of socks can you buy if you have $50.00 to spend?
Answer:
8
Step-by-step explanation:
50/5.95
4(-y+3)=2(5-y)
x=?
Merry Christmas
Answer:
Y=1
Step-by-step explanation:
ㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍㆍ
Answer:
Y = 1
Step-by-step explanation:
a dozen roses costs $21 at this rate, how much would you expect for four roses
Answer:
$7
Step-by-step explanation:
Divide 21 by 12 which equals 1.75. Multiply by 4 and it's 7.
The cost of four roses is $7.
Given that, a dozen roses costs $21.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
We know that, in one dozen there will be 12 roses.
Now, cost of one rose = 21/12
= $1.75
So, cost of 4 roses = 4×1.75
= $7
Therefore, the cost of four roses is $7.
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If R is the midpoint of TS, TR = 5x - 12, and RS = 3x + 8, find TS.
Answer:
5x -12 = 3x +8 (set the two = each other because they are the same length)
2x- 12= 8 (subtract 3x from both sides)
2x = 20 (add 12 to both sides)
x=10 (what x= for both expressions)
5(10) -12 (plug it into the first one to see what the length is and to see they're =
50 - 12 ( I already multiplied, now subtract)
38 (what the length of TR is)
3(10) +8 (plug it in again but into the other expression)
30+8 (multiply and add)
38 (the two have the same answer, so the x-value is correct.)
38+38= 76 (add the lengths of RS and TR and you get the length of TS)
Step-by-step explanation:
I hope this helps :)
Applying the segment addition theorem, the value of TS is: 76
Given:
TR = 5x - 12
RS = 3x + 8
If T is the midpoint of TS, therefore we would have the following equation:
TR = RS
Plug in the expressions5x - 12 = 3x + 8
Add like terms together5x - 3x = 12 + 8
2x = 20
Divide both sides by 2x = 10
TS = TR + RS (segment addition theorem)
SubstituteTS = 5x - 12 + 3x + 8
Plug in the value of xTS = 5(10) - 12 + 3(10) + 8
TS = 50 - 12 + 30 + 8
TS = 76
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A bucket holds 10 white golf balls, 3 pink golf balls, and 5 yellow golf balls. Jason selects 1 golf ball from the bucket at random.
What is the probability that the golf ball he selects is white or pink?
5/54
5/13
13/18
13/5
Answer:
I would have to say 5/13 and if I'm wrong I'm sorry just trying to help you out
Noah and his sister are making gift bags for a birthday party. Noah
puts 3 pencil erasers in each bag. His sister puts x stickers in each
bag. After filling 4 bags, they have used a total of 44 items. What is x
Answer:
x=8
Step-by-step explanation:
sorry if thatś not what your looking for
MERRY CHRISTMAS!!!
Answer:
12 bags, 2 pencils, 3 stickers.
Step-by-step explanation:
write the formula of mode for grouped data,and explain each term in it.
Answer:
Mode =Li+[f1-f0/2f1-f0-f2] *h
Li=lower limit.
F1= first frequency
F0= upper frequency of first frequency.
F2= second frequency.
H= difference between class intervals.
Hope it is helpful
HELP WILL GIVE 15 POINTS
what is the range of this function and pls explain
Answer:
[tex]f(x)\geq -2[/tex]
Step-by-step explanation:
Range corresponds to the values of y on the y-axis. If we see the graph the minimum value of the y-coordinate is -2 and then it tends to increase from it. We do not know till where the y values will increase in the figure it shows 6 but it's still actually increasing we keep on tracing the graph but the minimum value will always remain the same which is -2 . So we can say that the range of the function is
[tex]f(x)\geq -2\\[/tex]
Where f(x) is the function and since the values of y on the y-axis increase from -2 we can say that the function has the range of values greater than or equal to -2
confused :( please help!!!!
angles are confusing aaaaaa
Answer:
22
Step-by-step explanation:
Angles CBD and ABD are complementary, which means that they have a sum of 90 degrees. Since it tells you that angle ABC is 68 degrees, subtract that from 90.
90-68= 22
Answer:
29
Step-by-step explanation:
There are 30 students in Ms. Prema's history class. 18 of these students turned in an extra credit project at the end of the semester.
Answer:
12 students didnt turn in a extra credit project at the end of the semester.
Step-by-step explanation:
A hamster is running on a wheel. The diameter of the wheel is 6 inches. The hamster makes the wheel turn 10 times. How far did the hamster run?
Answer:
60 in or 5 FT
Step-by-step explanation:
6 x 10 = 60 in
:D
find the area of Rhombus if its diagonals measure 18 cm and 21 cm
Answer:
189 cm²
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × product of diagonals
= [tex]\frac{1}{2}[/tex] × 18 × 21 = 9 × 21 = 189 cm²
4/3 divided by 2/5...............
Answer:
[tex]3 \frac{1}{3}[/tex], or 10/3
Step-by-step explanation:
4/3 ÷ 2/5 = 4/3 × 5/2 = 20/6 = [tex]3 \frac{2}{6} = 3\frac{1}{3}[/tex]
Answer:
3 1/3
Step-by-step explanation:
When we divide two fractions, such as 4/3 ÷ 2/5, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.
We also simplify the answers to fraction problems whenever possible.
So first we will change 2/5 into its reciprocal, in simple words what fraction is it when its flipped over, 5/2 right? So now we change the division into multiplication, you may or may not have heard this phrase:
Keep, Change, Flip
so now our equation looks like this:
4/3 (5/2)
In a multiplication problem it dosent matter if the denominators are the same so we just straight up multiply, which gives us 20/6. We can still simplify this by 2, so 20 divided by 2 is 10, and 6 divided by 2 is 3, so our new fraction is 10/3, now we can simplify it again to make it proper, so its 10 divided by 3, the numerator goes inside and the denominator goes outside, this gives us 3r1, the denominator (the outside number) will becomes the mixed number, the remainder will become the numerator, and the answer will become the denominator, which gives us our final answer of:
3 1/3
Work out (5X10^3) x (9X10^7) answer in standard form plz
Answer:
4.5×10¹¹
Answer:
[tex](5 \times 10 {}^{3} ) \times (9 \times 10 {}^{7} )[/tex]
i) use the commutative property to rearrange the terms: a+b = b+a
[tex](5 \times 9) \times (10 {}^{3} \times {10}^{7} )[/tex]
ii) multiply the number in the 1st bracket
[tex]45 \times ( {10}^{3} \times 10 {}^{7} )[/tex]
iii) multiply the 2nd bracket by adding their exponents
[tex]45 \times 10 {}^{3 + 7} [/tex]
[tex]45 \times 10 {}^{10} [/tex]
iv) write the answer in standard form
[tex]4.5 \times 10 {}^{10 + 1} [/tex]
[tex]4.5 \times {10}^{11} [/tex]
The given equation that should be in the standard form should be like a [tex]4.5\times 10^{11}[/tex].
Equation in standard form:Since
The equation is [tex](5\times 10^3) \times (9\times 10^7)[/tex]
Now here we use the commutative property
So,
[tex]45 \times (10^3 \times 10^7)\\\\45 \times 10^{10}\\\\4.5 \times 10^{11}[/tex]
Here, we multiply the number in the 1st bracket, then add, it and then finally in standard form.
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PLEASE HELP!!!!!!!!!!!!!!
Answer:
882-28282=9191
Step-by-step explanation:
A puppy weight increases by 15% each week for the first 6 months. The puppy currently weight 3.7 pounds. which expression will not calvulate how much the puppy will weigh in 1 week? A) 3.7(0.15) B) 3.7(1.15) C) 3.7 + 3.7(0.15) D) 3.7 + 0.555
Answer:
B) 3.7(1.15)
Step-by-step explanation:
(4+2k)⋅6+3k and cant solve it plz help
Answer:
Simplifying
(4 + 2k) * 6 + 3k = 0
Reorder the terms for easier multiplication:
6(4 + 2k) + 3k = 0
(4 * 6 + 2k * 6) + 3k = 0
(24 + 12k) + 3k = 0
Combine like terms: 12k + 3k = 15k
24 + 15k = 0
Solving
24 + 15k = 0
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-24' to each side of the equation.
24 + -24 + 15k = 0 + -24
Combine like terms: 24 + -24 = 0
0 + 15k = 0 + -24
15k = 0 + -24
Combine like terms: 0 + -24 = -24
15k = -24
Divide each side by '15'.
k = -1.6
Simplifying
k = -1.6
Step-by-step explanation:
Will give brainliest... Please I need this answer so badly
How do you decide which rational number operations to use to solve problems.
Answer:
Like real numbers, the arithmetic operations, such as addition, subtraction, multiplication, and division are applicable to the rational numbers.
3 = 3 + 7k + 7 whats the anwser and steps
Answer: what does they K stand for
Step-by-step explanation:maybe I can help you
9514 1404 393
Answer:
k = -1
Step-by-step explanation:
Subtract 10 and simplify. We choose this value so the constants on the right add up to give 0.
3 -10 = 3 + 7k + 7 -10
-7 = 7k
Divide by 7.
-7/7 = 7k/7
-1 = k
HELP HELP HELP PLEASE
A line has a slope of 1/4. The line passes through the point (4, 6). The line also passes through the point (12, k). What is the value of k?
I WILL GIVE BRAINLEST!!!!!!!
Angela has 5 fewer quarters than twice the number of her dimes. If d represents
the number of dimes Angela has, which expression represents the total number of
Angela’s quarters and dimes?
A. 2d – 5
B. 5 – 2d
C. d + (2 – 5d)
D. d + (2d – 5)
PLSSS SHOW YOUR WORK PLSSSS
Answer:
A
Step-by-step explanation:
Answer: A
Step-by-step explanation:
Let’s say that she has 10 dimes. 2(10)-5=Q
20-5=15
15 quarters
We doubled her dimes, and subtracted 5 to find quarters.
You can fill anything for D and remind true
8) The midsegment of an equilateral triangle measures 6 yards. What is the perimeter of the equilateral
triangle?
A) 18 yards
B) 36 yards
C) 6 yards
D) 9 yards
Is (–5, 0.5) a solution of this system? x – 4y = –7, 0.2x + 2y = 0 Substitute (–5, 0.5) into x – 4y = –7 to get . Substitute (–5, 0.5) into 0.2x + 2y = 0 to get . Simplify the above equations to get
Answer:
Substitute (–5, 0.5) into x – 4y = –7 to get
✔ –5 – 4(0.5) = –7
.
Substitute (–5, 0.5) into 0.2x + 2y = 0 to get
✔ 0.2(–5) + 2(0.5) = 0
.
Simplify the above equations to get
✔ –7 = –7 is true and 0 = 0 is true; a solution.
Step-by-step explanation:
PLEASE MARK BRAINLIEST!!!!!!!!!!!(–5, 0.5) a solution of the system of equations.
What is a system of equations?A system of equations is a set or collection of equations that you deal with all together at once.
Given are the equations, x – 4y = –7 and 0.2x + 2y = 0;
Substitute (–5, 0.5) into x – 4y = –7 to get
–5 – 4(0.5) = –7
Substitute (–5, 0.5) into 0.2x + 2y = 0 to get
0.2(–5) + 2(0.5) = 0
Simplify the above equations to get
–7 = –7 and 0 = 0 is true
Hence, (–5, 0.5) a solution of the system of equations.
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Alexia spent 3 minutes working on each of her math problems and 4 minutes on each of her science problems. Her homework took her more than 60 minutes to complete. The boundary line for the inequality 3x + 4y > 60 is shown.
Answer:
The correct answer to this problem is the third statement which is "Alexia completed 20 math problems and 10 science problem". The following conditions are stated in the problem:
Alexia can answer 3 minutes on each math problem
Alexia can answer 4 minutes on each science problem
She worked more than 60 minutes
We have the inequality 3x + 4y > 60 where x represents the total number of math problem while y represents the total number of the science problem.
in our answer, we have x=20and y=10
3*20 + 4*10 > 60
60 + 40 > 60
100 > 60
brainliest please
Step-by-step explanation:
Answer:
Its C
Step-by-step explanation:
I just took this assignment. :)
HELP!!! Plz
You are opening a new business and have to set up utilities. The cable company charges a $49.95 one time connection fee which includes the price of hardware. The cost of the service is $45.95 per month. The phone company charges $79.95 for the connection fee and hardware, plus $29.95 per month. What is the total cost for both services for the first month? _____________ What would be the DIFFERENCE in the cost of the two plans for 12 months? ______________
Blank 1: ____________
Blank 2: _____________
Answer:
Blank 1: $205.8
Blank 2: $388
Step-by-step explanation:
For blank 1, I added up the 4 numbers because that's what 1 month would cost for both services. For blank 2, I multiplied the monthly fee for each service separately by 12, for 12 months. After that, each equation still separate add the 1 time fee and subtract each company price and you will get your answer.
- I hope this is correct and helpful :)
Phone company costs for a 12-month period are 162 dollars cheaper than cable company costs.
Cable company Connection fee and hardware = 49.95 dollars
Cost of service = 45.95 dollars per month.
Cost for a 12-month period = (connection fee and hardware) + ((cost of service) x 12 months) Cost for a 12-month period = 49.95 dollars + (45.95 dollars per month x 12 months) Cost for a 12-month period = 49.95 dollars + 551.40 dollars Cost for a 12-month period = 601.35 dollars
Phone company Connection fee and hardware = 79.95 dollars Cost of service = 29.95 dollars per month
Cost for a 12-month period = (connection fee and hardware) + ((cost of service) x 12 months) Cost for a 12-month period = 79.95 dollars + (29.95 dollars per month x 12 months) Cost for a 12-month period = 79.95 dollars + 359.40 dollars Cost for a 12-month period = 439.35 dollars Difference in the cost = (cable company cost) - (phone company cost) Difference in the cost = 601.35 dollars - 439.35 dollars Difference in the cost = 162 dollars
Phone company costs for a 12-month period are 162 dollars cheaper than cable company costs.
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