We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2
What is quadratic equation?An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.
How to determine the value of k in the question?We are given, 4x²+ 12x +k =0, k =Z and x = R
the quadratic equation is 4x²+12x+k =0
we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a
when the quadratic equation is ax²+bx+ c= 0
Hence, roots of the equation given in question will be,
x = - 12 ±√ (12² - 4×4×k) / 2×4
x = - 12 ± √(144-16k) / 8
as per the condition given in question, one root of this equation is 5 times the other root.
hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5
multiplying both sides by 8
- 12 - √(144-16k) = [-12 + √(144-16k)] ×5
- 12 - √(144-16k) = - 60 + 5√(144-16k)
- 12 + 60 = 6√(144-16k)
48 = 6√(144-16k)
8 = √(144-16k)
64 = 144 -16k
16k = 80
k = 5
the value of k =5
by putting the value of k =5
x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8
x = -1/2 and x = -5/2
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HAVE A NICE DAY
WILL GIVE BRAINLST :)
Answer:
3. 30 degrees
4. 46 degrees
5. 55 degrees
Step-by-step explanation:
3. Let it be x
85+65+X=180
150 + x = 180
x = 180 - 150
x = 30 degrees
4. Let it be x
104 + 30 + x = 180
134 + x = 180
x = 180 - 134
x = 46 degrees
5. Let it be x
x + 85 + 40 = 180
x + 125 = 180
x = 55 degrees
PLEASE GIVE ME BRAINLIEST PLSSS
Answer:
Step-by-step explanation:
Solve for l:
[tex]v = \frac{ \sqrt{l + t} }{2 \sqrt{l} } [/tex]
.....
Answer:
l = t/4v² - 1
Step-by-step explanation:
Given the expression
v = √l+t/2√l
We are to make l the subject of the formula as shown;
Cross multiply
2v√l = √l+t
Square both sides
(2v√l)² = (√l+t)²
4v²l = l+t
t = 4v²l - l
t = l(4v² - 1)
Divide both sides by 4v² - 1
t/4v² - 1 = l(4v² - 1)/4v² - 1
t/4v² - 1 = l
Swap
l = t/4v² - 1
Hence the required expression for l is t/4v² - 1
A box office sold 147,523 tickets for an auto race.
Of this number, 68,724 tickets were for adults.
The rest were children's tickets.
How many children's tickets were sold?
78,709
81,799
121,201
Answer:
78,799 children's tickets
Step-by-step explanation:
147,523 total tickets, 68,724 adult tickets
Subtract to find amount of children's tickets:
147,523-68,724 = 78,799
Find the sum: −11−7−3+1+⋯+225
Answer:
205
Step-by-step explanation:
Step-by-step explanation:
-11-7-3+1+225
-21+1+225
-20+225
205
In ΔABC, the measure of ∠C=90°, AB = 86 feet, and CA = 61 feet. Find the measure of ∠A to the nearest degree.
Answer:
<A=45°
Hope this helps you
Answer:
45
Step-by-step explanation:
What is the difference quotient of the function g(x) = 4^x
Answer:
First choice
Step-by-step explanation:
The difference quotient in general is [tex]\frac{g(x+h)-g(x)}{h}[/tex]. To get an expression for [tex]g(x+h)[/tex], replace x with x + h.
For this question,
[tex]\frac{4^{x+h}-4^x}{h}=\frac{4^x\cdot4^h-4^x}{h}[/tex]
Factor [tex]4^x[/tex] out of the numerator.
[tex]\frac{4^x(4^h-1)}{h}[/tex]
Answer:
The answer is A the first option
Step-by-step explanation:
Just took the unit review and got a 100
i need help i honestly dont get this
Answer:
I'm not too sure though but I think its change of subject formula
can someone please help me on this question?
Answer: D
Step-by-step explanation:
If the graph is shifted 5 units down, each output value should decrease by 5.
y≥ −4x+10
Hello, I’m having trouble the the following question above. Can you help me please?
The question asks to name the A and B points
A: ( , )
B: ( , )
I'm assuming x and y intercepts which would be (2.5,0) and (0,10)
9. Empty taxis pass by a street corner at a Poisson rate of two per minute and pick up a passenger if one is waiting there. Passengers arrive at the street corner at a Poisson rate of one per minute and wait for a taxi only if there are less than four persons waiting; otherwise they leave and never return. Ella arrives at the street corner at a given time. Find her expected waiting time, given that she joins the queue. Assume that the process is in steady-state.
Answer:
0.37
Step-by-step explanation:
To resolve the given problem we will apply
persistent time Markov chain : n = 0, 1, . . . , 4
n = number of individuals pausing
where The equalization conditions are : πn = ( πn - 1/2 )
Given that :
n = 0,1,2,3,4
π0 = 1/( 1 + 2−1 + 2−2 + 2−3 + 2−4) = 0.52 = 16/31
Also the normal number of travelers found by Ella will be represented as
E(N) = (π1 + 2π2 + 3π3) / ( π0 + π1 + π2 + π3) ------- ( 1 )
where : π1 = 8, π2 = 4, π3 = 2 , π0 = 16/31 input values into equation 1
E ( N ) = 22/30
given that the True to form hanging tight time = 0.5
hence Holding holding time = E(N ) * 0.5
therefore the expected waiting time for Ella = ( 22/30 ) * 0.5 = 0.37
Which of the following values are in the range of the function graphed below?
Check all that apply.
10
- 10
10
. 10+
D A. 2
O B. 5
C. 3
O D. 1
E. -2
Answer:
All of the above.
Step-by-step explanation:
They are all within the range.
The range of the function graphed below are,
⇒ 2, 3, 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function is shown.
Now, By graph;
The range of the function graphed below are,
⇒ (0 , 3]
Hence, By options;
The range of the function graphed below are,
⇒ 2, 3, 1
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The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration. Find the hydronium ion concentration of a particular vinegar if the pH level is 2.5. (5 points)
3.979 x 10–1
9.536 x 103
3.162 x 102
3.162 x 10–3
The value of hydronium ion concentration in the vinegar is 3.162×10^-3 (optionD)
What is pH?pH is defined as the negative log of the hydrogen ion concentration. The range of pH extends from zero to 14. A pH value of 7 is neutral, because pure water has a pH value of exactly 7.
pH can also be defined as the measure of acidity and alkalinity of a substance.
pH = –log(H+)
Therefore (H+) = 10^-(pH)
For a pH of 2.5, the hydronium ion concentration
= 10^-2.5
(H+) = 0.003162 = 3.162×10^-3
Therefore hydronium ion concentration of the vinegar is 3.162×10^-3
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Round 123.7561 to the nearest hundredth place
Decimal numbers are number that contains decimal points. The value 123.7561 rounded to nearest hundredth is 123.76
Rounding of decimal numbersDecimal numbers are number that contains decimal points in between the values.
Given the decimal value 123.7561, we are to convert the decimal values to the hundredth place.
This means that there must only be two values after the decimal points and the values rounded up if greater than 4.
Hence the value 123.7561 rounded to nearest hundredth is 123.76
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What is the total area of the figure? NO LINKS ONLY ANSWERS
Answer:
Hello! answer: 24
Hope this helps!
Answer:
A. 5x3=15 B. 3x3=9 15+9=24
Step-by-step explanation:
Which graph represents an exponential function?
Answer:
The answer to your question is the third one
Step-by-step explanation:
The first graph is the graph of a
The second graph is of a rational function
The third one is of an exponential function
vasta third one dzuh
Any graph that looks like the above (big on the left and crawling along the x-axis on the right) displays exponential decay, rather than exponential growth. For a graph to display exponential decay, either the exponent is "negative" or else the base is between 0 and 1.
A band expects to put 15 songs on their next CD. The band wriand records 60% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD
Answer:
18 songs
Step-by-step explanation:
15 x 1.6 = 24
24 x 0.75 - 18
Kind of stuck any tips would also help!!
Answer:
Step-by-step explanation:
You must place in the question sign box the value of x that is above the question sign box because you are trying to fill out the y row.
Example: y=[tex]-\frac{0}{3} +2[/tex]= -0+2=2
Answer:
Step-by-step explanation:
tip:
plug the x values from the table ( the top row values ) into the equation
in this case its 0
BOX 1:
[tex]-\frac{0}{3} +2\\[/tex]
0 divided by anything = 0
so, 0 + 2 = 2
box 1 = 2
BOX 2:
[tex]-\frac{3}{3} +2[/tex]
3 div by 3 = 1 ( in this case negative 1 )
so, -1 + 2 = 1
box 2 = 1
BOX 3:
[tex]-\frac{6}{3} +2[/tex]
6 div by 3 = 2 ( in this case negative 2)
-2 + 2 = 0
box 3 = 0
express each number as a product of two fractions 1/5
Answer:
Theres nothing to solve for wheres the numbers?
Step-by-step explanation:
Bernita and Rosalee are comparing their heights. Bernita is 1.63
meters tall. Rosalee is 19 centimeters shorter than Bernita.
What is Rosalee's height in centimeters?
Answer:
1.44
Step-by-step explanation:
1.63-.19= 1.44
If you save up $100 every 2 weeks, how much money would you have in a year ?
alr! so we know that there are around 52 weeks in a year (not counting leap years). and you save up 100 bucks every 2 weeks. then to find the answer, we do...
100(52/2)
100(26)
= $2600
youre welcome!
Question 3
Alicia graphed a solution of linear equations on a coordinate plane.
1
What is the approximate solution of the system?
Answer:
what did the answer end up being?
Step-by-step explanation:
Please help will mark Brainly
Answer:
it too far i can't see it
Step-by-step explanation:
A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedroom units within a half-mile of campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. Provide a 95% confidence interval estimate of the mean rent per month for the population of one-bedroom units within a half-mile of campus. Assume that population is normally distributed.
Answer:
(507.05, 592.95)
Step-by-step explanation:
Given data:
sample mean = $550, sample standard deviation S = $60.05
95% confidence interval , n = 10
For 95% confidence interval for the mean
mean ± M.E.
where M.E. is margin of error = [tex]t_{n-1}, \alpha/2\times\frac{S}{\sqrt{n} }[/tex]
Substituting the values in above equation
[tex]=t_{10-1}, 0.05/2\times\frac{60.05}{\sqrt{10} }[/tex]
= 2.62×18.99
=42.955
= 550±42.95
=(507.05, 592.95)
Write an equation of the line passing through (- 5,5) and having slope - 4. Give the answer in slope-intercept form.
The equation of the line in slope-intercept form is:
Answer:
y = - 4x - 15---------------------------
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptPoint-slope form:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point on the lineUse the point-slope form to find the equation and then convert it to slope-intercept form:
y - 5 = - 4(x - (-5))y - 5 = -4(x + 5)y - 5 = - 4x - 20y = - 4x - 20 + 5y = - 4x - 15Find the exact value of the expression
Answer:
here is the correct answer
Find the radius of the circle with a diameter of 100 mete radius:
50
Step-by-step explanation:
100/2 = 50
So, the radius is 50.
I hope this helps, have a good day!
Answer:
r=50m
Step-by-step explanation:
Remeber it's the half of the number (N).
Which list classifications for the figure
Answer: I think you forgot to post the picture
Step-by-step explanation:
Find x such that the line through (6, −3) and (7, 6) is perpendicular to the line through (−2, 5) and (x, −1).
Given:
The line through (6, −3) and (7, 6) is perpendicular to the line through (−2, 5) and (x, −1).
To find:
The value of x.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line through (6, −3) and (7, 6) is:
[tex]m_1=\dfrac{6-(-3)}{7-6}[/tex]
[tex]m_1=\dfrac{6+3}{1}[/tex]
[tex]m_1=9[/tex]
The slope of the line through (−2, 5) and (x, −1) is:
[tex]m_2=\dfrac{-1-5}{x-(-2)}[/tex]
[tex]m_2=\dfrac{-6}{x+2}[/tex]
We know that the product of slopes of two perpendicular lines is -1.
[tex]m_1\cdot m_2=-1[/tex]
[tex]9\cdot \dfrac{-6}{x+2}=-1[/tex]
[tex]\dfrac{-54}{x+2}=-1[/tex]
Multiplying both sides by (x+2), we get
[tex]-54=-1(x+2)[/tex]
[tex]-54=-x-2[/tex]
[tex]-54+2=-x[/tex]
[tex]-52=-x[/tex]
Divide both sides by -1.
[tex]52=x[/tex]
Therefore, the value of x is 52.
What is the gravitational potential energy of a 55-kg person that has climber a 4,000 meter tall mountain?
Bonus: if one snickers bar is 1,100,000 joules of energy, how many snickers bars would provide enough fuel to climb the mountain ?
Answer:
2156000 J.
Bonus: 2 snickers bar
Step-by-step explanation:
Applying
P.E = mgh................. Equation 1
Where P.E = Gravitational potential energy, m = mass of the person, h = height of the mountain, g = acceleration due to gravity.
From the question,
Given: m = 55 kg, h = 4000 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
P.E = (55×4000×9.8)
P.E = 2156000 J.
If one snikers bar is 1100000 J of energy,
Then, (2156000/1100000) snickers bar would be enough to climb the mountain
Number of snickers bar = (2156000/1100000) = 1.96 ≈ 2
what is the slope of the table below? 3/8 15/12 9/10 0/7
The slope of the table below? 3/8 15/12 9/10 0/7 is 23.8
What is slope?Slope is defined as the rate of change of y with respect to x. Invariably, it it the rise in y over the run in x. put differently, slope is increase over increase in x
The slope of a line is defined
S= (increase in y)/(Increase in x) = Δy/Δx
Slope = (0/7 - 18/12) ÷ (9/10 -3/8)
Slope = 15/12 ÷ 42/80
Simplify the fractions to have
Slope = 15/12 * 80/42
The slope = 1200/504
Slope of the table is given as 23.4
Conclusively, the table gives us a slope approximately 23
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