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)
random...............
Find the distance, midpoint, and slope of line AB (-2,-1) and B(6,3)
Answer:
The correct answer is (2,1)
Step-by-step explanation:
The distance, midpoint, and slope are 4√5 , (2 , 1) , 1/2 respectively.
What are the distance, midpoint, and slope between two points?For any two points A( x₁ , y₁ ) B( x₂, y₂) the distance, midpoint, and slope are given by: 1) [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
2) M(x , y) = { (x₁ + x₂)/2 , (y₁ + y₂)/2 }
3) m= y₂ - y₁ / x₂ - x₁
Given here the points A(-2,-1) and B(6,3)
substituting the values we get,
1) [tex]d = \sqrt {\left( {-2- 6} \right)^2 + \left( {-1 - 3} \right)^2 }[/tex]
[tex]d = \sqrt {\left( {8 } \right)^2 + \left( {4 } \right)^2 }[/tex]
[tex]d = \sqrt {\left( 80{ \right)^ }[/tex]
[tex]d =4\sqrt {\left5 }[/tex]
2) M(x , y) = { (-2 + 6)/2 , (-1 + 3)/2 }
= (2 , 1)
3) m = { (6 - (-2) / (3 - (-1)) }
= 1/2
Hence, distance, midpoint, and slope are 4√5 , (2 , 1) , 1/2 respectively.
Learn more about distance, midpoint, and slope here:
https://brainly.com/question/28322015
#SPJ2
(03.03 MC)
The table below represents a linear function f(x) and the equation represents a function g(x):
х f(x)
-1 -5
0 -1
1 3
g(x)
g(x) = 2x - 7
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
(6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)
Answer:
Please check the explanation.
Step-by-step explanation:
Part a)
Finding the slope of f(x)
Given the table of the function f(x)
x f(x)
-1 -5
0 -1
1 3
Finding the slope using the formula
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-1,\:-5\right),\:\left(x_2,\:y_2\right)=\left(0,\:-1\right)[/tex]
[tex]m=\frac{-1-\left(-5\right)}{0-\left(-1\right)}[/tex]
[tex]m=4[/tex]
Thus, the slope of the function f(x) = 4
Finding the slope of g(x)
We know the slope-intercept form of a linear function is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given the function
[tex]g(x) = 2x-7[/tex]
comparing with the slope-intercept form
y = mx+b
The slope of the function g(x) = 2
Thus, we conclude that:
The slope of the function f(x) = 4The slope of the function g(x) = 2Hence, the slope of f(x) is greater.
Part b)
Finding the y-intercept form of f(x)
We know that the y-intercept can be determined by setting x = 0 and determining the corresponding y-value.
From the table,
It is clear at x = 0, y = -1
Hence, the y-intercept of the function f(x) = -1
Finding the y-intercept form of g(x)
Given the function
[tex]g(x) = 2x - 7[/tex]
comparing with the slope-intercept form (y = mx+b)
[tex]y = mx+b[/tex]
where b is the y-intercept
Hence, the y-intercept of g(x) = b = -7
Thus, we conclude that:
The y-intercept of the function f(x) = -1The y-intercept of the function g(x) = -7Hence, the y-intercept of f(x) is greater.
Six Sigma refers to achieving a process variability so small that the design specifications represent ___ standard deviations above and below the process mean.
Answer:
six
Step-by-step explanation:
Six sigma is defined as the method or a set of techniques that provides the provides the organization tools and techniques to improve the capability and and be efficient of their business process. It is a concept of process improvement.
It refers to the achieving of a process variability very small so that the design specification represents six standard deviations which is above as well as below the process mean.
What is the relationship between cos(90degrees) and cos(-90°)?
Answer:
The relationship between the two is that they are equal.
Step-by-step explanation:
Since y = cosx is a even function, that means that cosx = cos(-x). Therefore, cos 90 degrees = cos -90 degrees.
We can also test this out:
cos 90 = 0
cos -90 = cos 270 = 0
Therefore, this came to the same conclusion as our first solution.
I hope this helps! :)
solve 3cosx-1,0<=x<=pi/2
Answer:
E(-9)≈3.4936
Step-by-step explanation:
Calculate the arc length of the following curve from x = 0 to x = π/2:
y(x) = -1 + 3 cos(x)
Hint: | The definition of arc length in Cartesian coordinates is s = integral_(x_0)^(x_1) sqrt(1 + y'(x)^2) dx.
Apply the definition of arc length to y(x) = -1 + 3 cos(x) for 0<x<π/2:
s = integral_0^(π/2) sqrt(1 + (d/dx(-1 + 3 cos(x)))^2) dx
Hint: | What is d/dx(-1 + 3 cos(x))?
Compute the derivative d/dx(-1 + 3 cos(x)):
= integral_0^(π/2) sqrt(1 + (-3 sin(x))^2) dx
Hint: | Can the integrand be simplified?
Simplify sqrt(1 + (-3 sin(x))^2):
= integral_0^(π/2) sqrt(1 + 9 sin^2(x)) dx
Hint: | Can this integral be computed?
Compute the definite integral:
Answer: E(-9)≈3.4936
V-100
DONE
What is the square root of negative one hundred
Answer:
10i
Step-by-step explanation:
The square root of negative 100 is not equal to 10. If 10 was the square root of negative 100, then 10 squared would be equal to negative 100. But in fact, 10 squared is 10*10, which is obviously (positive) 100, not negative 100.
To determine the actual value of the square root of negative 100, we can proceed as follows:
Let s be the square root of negative 100.
Then s^2 = -100.
So s^2 = 100×(-1) = (10^2)×(i^2) =10×10×i×i = 10×i×10×i =(10i)^2.
So s = 10i.
So the square root of negative 100 is equal to 10i.
Note that the square of -10i is also equal to negative 100. 10i is the principle square root of negative 100.
Answer:
10i
Step-by-step explanation:
Since, it's a negative square root you have to use imaginary numbers to make it solvable. Hope this helps! :)
K is between J and L. JK = 3x – 5, and KL = 2x + 1. IfJL = 16, what is JK?
A. 7
B. 8
C. 9
D. 13
Answer:
If JL = 16, we will get JK = 7
Option A is correct option.
Step-by-step explanation:
We are given:
K is between J and L
JK = 3x – 5, and KL = 2x + 1.
IfJL = 16, what is JK
We know that K is between J and L it means it divides JL into JK and KL equally or we can say that adding JK and KL we can get JL
So, We can write:
[tex]JL = JK + KL\\16=3x-5+2x+1[/tex]
Solving the expression we can find first value of x and then value of JK
[tex]16=3x-5+2x+1\\16=5x-4\\16+4=5x\\20=5x\\x=\frac{20}{5}\\x=4[/tex]
So, we get x = 4
Now, put the value of x in JK=3x-5 to get value of JK
[tex]JK = 3x-5\\JK=3(4)-5\\JK = 12-5\\JK=7[/tex]
So, if JL = 16, we will get JK = 7
Option A is correct option.
If Karen's 45 minute lunch break ended at 12:30 P.M., what time did her lunch break begin?
Answer:
11:45 PM
Step-by-step explanation:
please mark brainliest :D
NEED HELP ASAP!!!!!!!
What is negative 2 3/8 as a decimal?
divide 123 by 13 with remainder
Answer:
9 Remainder 6
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 13 on the left side and the dividend 123 on the right side like this:
1 3 ⟌ 1 2 3
Step 2:
The divisor (13) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:
0
1 3 ⟌ 1 2 3
Step 3:
Multiply the divisor by the result in the previous step (13 x 0 = 0) and write that answer below the dividend.
0
1 3 ⟌ 1 2 3
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.
0
1 3 ⟌ 1 2 3
- 0
1
Step 5:
Move down the 2nd digit of the dividend (2) like this:
0
1 3 ⟌ 1 2 3
- 0
1 2
Step 6:
The divisor (13) goes into the bottom number (12), 0 time(s). Therefore, put 0 on top:
0 0
1 3 ⟌ 1 2 3
- 0
1 2
Step 7:
Multiply the divisor by the result in the previous step (13 x 0 = 0) and write that answer at the bottom:
0 0
1 3 ⟌ 1 2 3
- 0
1 2
0
Step 8:
Subtract the result in the previous step from the number written above it. (12 - 0 = 12) and write the answer at the bottom.
0 0
1 3 ⟌ 1 2 3
- 0
1 2
- 0
1 2
Step 9:
Move down the last digit of the dividend (3) like this:
0 0
1 3 ⟌ 1 2 3
- 0
1 2
- 0
1 2 3
Step 10:
The divisor (13) goes into the bottom number (123), 9 time(s). Therefore put 9 on top:
0 0 9
1 3 ⟌ 1 2 3
- 0
1 2
- 0
1 2 3
Step 11:
Multiply the divisor by the result in the previous step (13 x 9 = 117) and write the answer at the bottom:
0 0 9
1 3 ⟌ 1 2 3
- 0
1 2
- 0
1 2 3
1 1 7
Step 12:
Subtract the result in the previous step from the number written above it. (123 - 117 = 6) and write the answer at the bottom.
0 0 9
1 3 ⟌ 1 2 3
- 0
1 2
- 0
1 2 3
- 1 1 7
6
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 123 divided by 13 calculated using Long Division is:
Plsssss help!!!!!!!!
Answer:
n=6t
Step-by-step explanation:
6 cars parked per hour
t is the hours
6 is the slope
y=mx+b
n=6t
Hope this helps.
NEED HELP ASAP!!!!!!!!
Answer:
x = 2.4
y = 31
Step-by-step explanation:
Angle B = 25x
BC = 31
therefore , this is an equilateral triangle all sides and angles are equal,
25x =60
x = 2.4
BC = BA = AC
y= 31
Tienes 12 personas Todas pesan exactamente lo mismo Menos 1 persona que pesa un poco más o un poco menos Dispones de una balanza y puedes pesar 3 veces Quien es el que pesa distinto
Answer:
El que pesa distinto es aquel que causa un desnivel en la balanza.
Step-by-step explanation:
Sabemos que una balanza tiene dos lados en los cuales podemos poner peso, si la balanza está equilibrada, ambos lados están a la misma altura, de lo contrario, habrá un desnivel entre ambos lados.
Puesto que solo podemos emplear la balanza 3 veces, debemos crear tres grupos de cuatro personas, que dentro de cada una cada mitad, conformada por dos personas, es colocada en un lado de la balanza. Si la balanza está equilibrada, entonces todo ese grupo está integrado por personas del mismo peso, pero si esta desequilibrada, una persona de alguno de los dos subgrupos.
En ese caso, se procede a sacar a dos personas, una por cada lado de la balanza, si el desbalance desaparece, entonces alguna de las dos personas que salió tiene un peso distinto, pero si el desbalance persiste, entonces es causante del desbalance se encuentra en aún en la balanza.
En conclusión, el que pesa distinto es aquel que causa un desnivel en la balanza.
Use the number line to find
0+(
8
19
14
0
19
8
OI-2
21
8
Answer:
put it right in between the 0 and 0.5
Step-by-step explanation:
Answer:
- 19/8 hope you got it right
Roberto evaluated 34 ÷ 45 and got an answer of 1516. Which statement is true about his answer?
Answer:
Roberto is correct because 15/16 x 4/5 = 3/4.
Roberto's solution to the division problem is correct, but
there are no true statements on your list of choices.
Answer:
Roberto is correct because 15/16 x 4/5 = 3/4.
Step-by-step explanation:
Helpppppppppppppppppppppppppppppppppppppp
Answer:
A.) Point A is closer to the surface of the sea than point B
Step-by-step explanation:
-7/3 = -14/6
-5/2 = -15/6
Point A is closer to the surface of the sea than point B.
What’s the answer ? Im too tired fa this shi
Answer:
90-39=51 thats a 90° angle
Suppose it takes John 45 minutes to run 4 miles. How long would it take him to run 4 kilometers? Round your answer to the nearest minute
Answer:
28 minutes
Step-by-step explanation:
4 miles = 45 minutes
4 kilometers = (m) minutes
45 ÷ 4= 11.25
4 kilos= 2.48548 miles
2.48548 x 11.25= 27.96165
m = 28 minutes
- I hope this helps have a great day
John will covers 4 km distance in 28 minutes.
What is Rate of change?
A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.
Here, it is given that John takes 45 minutes to run 4 miles and is known that :
1 mile ≈ 1.61 km
that is for,
4 mile ≈ 6.44 km
John covers 6.44 km in 45 minutes, John will cover 4 km in :
6.44 km ⇒ 45 minutes
1 km ⇒ 45/6.44 minutes
4 km ⇒ 4 x (45/6.44) minutes ≈ 28 minutes
Therefore, John will covers 4 km distance in 28 minutes.
Read more about ratio at:
https://brainly.com/question/17869111
#SPJ2
what number increased by 62%, results in the value of 59.94
Answer:
The number is : x = 37
Step-by-step explanation:
In order to solve this question, we may set up a proportion.
If the original number is 100%, 59.94 would be 162% of the original, as it was increased by 62%.
so
59.94 → 162%
x → 100%
solving the proportion gives you
59.94 × 100 = 162 × x
x = (59.94 × 100)/162
x = 5994/162
x= 37
Thus, the number is : x = 37
another frreeeeee point now i got 0 great
Answer:
THXXX
Step-by-step explanation:
Answer:
TY! :D
Step-by-step explanation:
lol
Of the four choices given, which two, when written as a system, have a solution of (-4,5)?
Answer:
The answer is A. The first one.
I hope this helps. ;)
Answer:
It is A on edge 2020
Step-by-step explanation:
For his long distance phone service, Eric pays a $3 monthly fee plus 11 cents per minute. Last month, Eric's long distance bill was $21.59. For how many minutes was Eric billed?
Answer:
169 minutes
Step-by-step explanation:
Hope you have a great day and good luck for tests and upcoming exams.
How to Experiment Well
Assignment
Active
Assigning Treatment Groups
A beauty product company conducts a study to test the effectiveness of a new shampoo to control split ends. One
hundred subjects have volunteered to take part in the study, and will be split into a treatment group and a placebo
group. The study leader will assign the subjects to the groups randomly using slips of paper. Which reason identifies
why randomization is important?
It is important to make sure that groups have 50 people each.
It is important to make sure that the first 50 people to volunteer are not all in the same group.
It is important to make sure that people who do not currently have many split ends are placed in the placebo
group.
It is important that subject characteristics such as hair length, hair color, and gender are distributed equally
among the treatment groups.
Answer:
D: It is important that subject characteristics such as hair length, hair color, and gender are distributed equally among the treatment groups.
Is correct
=================
The answer for the question after is 50, which should be similar to the same question here.
=================
ED2021
Kathryn's water bottle holds 20.25 ounces. Her doctor told her to drink half her body weight in ounces of water. Kathryn weighs 121.5 pounds. How many water bottles will she have to drink? (There is no convesion required from ounces to pounds)
Answer: She have to drink 3 bottles of water.
Step-by-step explanation:
Given: Weight of Kathryn = 121.5 pounds
half of her weight = [tex]\dfrac{121.5}{2}=60.75\text{ pounds}[/tex]
So, she need to drink 60.75 pounds of water.
Kathryn's water bottle holds 20.25 ounces.
Number of water bottles she need to drink = (half of her weight) ÷ (Capacity of bottle)
[tex]=\dfrac{60.75}{20.25}\\\\=\dfrac{6075}{2025}\\\\=3[/tex]
Hence, she have to drink 3 bottles of water.
Do Anybody know this ?
Answer:
R= 30-9t.... I think
Step-by-step explanation:
Write the slope-intercept form of the equation that is described below.
Through (3, 3) and perpendicular to y = 14x − 2
What is the equation?
Answer:
y = -¹/₁₄x + 3³/₁₄Step-by-step explanation:
If two lines are perpendicular then the product of theirs slopes is equal -1:
y=m₁x+b₁ ⊥ y=m₂x+b₂ ⇒ m₁×m₂ = -1
y = 14x - 2 ⇒ m₁=14
14×m₂ = -1 ⇒ m₂ = -¹/₁₄
The line y=-¹/₁₄x+b passes through point (3, 3) so the equation:
3 = -¹/₁₄×3 + b must be true
3 = -³/₁₄ + b
b = 3³/₁₄
Therefore equation in slope-intercept form:
y = -¹/₁₄x + 3³/₁₄
A consumer advocate group selects a random sample of 205 snow foods in find 174 of them contain more what is indicated on the snacks nutritional information. Create a 90% confidence interval for the population proportion for a snack foods that contain more fat grams and was indicated on the snacks nutritional information
Answer: (0.809, 0.891)
Step-by-step explanation:
Let p = population proportion for a snack foods that contain more fat grams and was indicated on the snacks nutritional information .
As per given , we have
Sample size : n= 205
Sample proportion: [tex]\hat{p}=\dfrac{174}{205}\approx0.85[/tex]
z-value for 90% confidence = 1.645
Confidence interval for p: [tex]\hat{p}\pm z^* \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]0.85\pm (1.645)\sqrt{\dfrac{(0.85)(1-0.85)}{205}}\\\\=0.85\pm (1.645)\sqrt{\dfrac{0.85\times0.15}{205}}\\\\= 0.85\pm (1.645)\sqrt{0.000621951219512}\\\\=0.85\pm0.041\\\\=(0.85-0.041,\ 0.85+0.041)\\\\= (0.809,\ 0.891)[/tex]
Hence, the required confidence interval = (0.809, 0.891)
someone help!!??? pleaseee
Answer:
I'm not sir but I think it is ISOSCELES