for what values of k does the line y=kx-2 and the parabola y=1+5x-2x^2
i) touch
ii) intersect
iii) not intersect
Answers
The line y=kx-2 and the parabola y=1+5x-2x^2 touch when k is equal to 5 plus or minus the square root of 8, intersect when k is less than 1 or greater than 9, and do not intersect when k is between 1 and 9.
i) To find the values of k such that the line and parabola touch, we need to find the point(s) where they intersect and have the same slope. Setting the equations equal to each other, we get:
kx - 2 = 1 + 5x - 2x^2
2x^2 - (k-5)x + 3 = 0
For the line and parabola to touch, this quadratic equation must have a double root, which means its discriminant must be 0:
(k-5)^2 - 4(2)(3) = 0
Simplifying this equation, we get:
k^2 - 10k + 17 = 0
Solving for k using the quadratic formula, we get:
k = 5 ± √8
So the line and parabola will touch when k is equal to 5 plus or minus the square root of 8.
ii) To find the values of k such that the line and parabola intersect, we need to solve the system of equations:
y = kx - 2
y = 1 + 5x - 2x^2
Substituting the first equation into the second, we get:
kx - 2 = 1 + 5x - 2x^2
2x^2 - (k-5)x + 3 = 0
For the line and parabola to intersect, this quadratic equation must have real roots. This means its discriminant must be greater than or equal to 0:
(k-5)^2 - 4(2)(3) ≥ 0
Simplifying this inequality, we get:
k^2 - 10k + 17 ≥ 0
Factoring the left-hand side of the inequality, we get:
(k - 1)(k - 9) ≥ 0
This inequality is satisfied when k is less than 1 or greater than 9. So the line and parabola will intersect when k is less than 1 or greater than 9.
iii) To find the values of k such that the line and parabola do not intersect, we can use the same quadratic equation as in parts (i) and (ii). For the line and parabola to not intersect, this quadratic equation must have no real roots, which means its discriminant must be negative:
(k-5)^2 - 4(2)(3) < 0
Simplifying this inequality, we get:
k^2 - 10k + 17 < 0
Factoring the left-hand side of the inequality, we get:
(k - 1)(k - 9) < 0
This inequality is satisfied when k is between 1 and 9. So the line and parabola will not intersect when k is between 1 and 9.
To learn more about parabola, click here: brainly.com/question/64712
#SPJ11
Related Questions
Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x)
Answers
The Logarithmic function is \(g(y)=\log_2y\).
\(x=3\) is the length corresponding to the strength 8 Pa
The relation between the length and the strength of the building materials is given by an exponential function, \(f(x) = 2^x\) ,
where x is the length.
We have to convert this function into a logarithmic function where the strength is given as 8 Pa.
Let \(y = f(x)\)
i.e., \(y=2^x\) where y represents the strength.
We know that logarithmic function is the inverse of the exponential function up to the bases.
Taking Logarithm on both sides, we get,
\(log y = x log 2\)
⇒ \(x=log_2y\)
i.e., the length is given by the function \(g(y)=\log_2y\) when y, the strength is known. This is the required logarithmic function.
So when the strength, y = 8 Pa,
the length, \(x = log_2 8\) ⇒ \(x=log_2 2^3\)
⇒ \(x=3\) is the length corresponding to the strength 8 Pa.
The question provided is incomplete. Here you can find the complete question:
Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = \(2^x\), where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.
Learn more about Exponential and Logarithmic functions at https://brainly.com/question/4458071
#SPJ4
Find the total distance traveled by a particle according to the velocity function wt) = 3t - 9 m/sec over the time interval
[1, 5]. Enter your answer as an exact fraction, if necessary. Do not include units in your answer.
Answers
The total distance traveled by the particle over the time interval [1, 5] is 12 units.
To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.
To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit
learn more about velocity function here:
https://brainly.com/question/29080451
#SPJ11
What is an advantage of using a stem-and-leaf plot instead of a histogram? What is a disadvantage? O A. Stem-and-leaf plots show data clusters where histograms do not O B. Stem-and-leaf plots contain original data values where histograms do not. O C. Stem-and-leaf plots.easily organize data of all sizes where histograms do not O D. Stem-and-leaf plots graph qualitative data where histograms do not.
Answers
the stem and leaf plot gives you a more exact answer where a histogram gives you a more of an average. Now i'm not saying a histogram can't be exact but a stem and leaf plot is more reliable if you need an exact answer.
Step-by-step explanation:
Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.
What is stem and leaf?The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.
The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.
The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.
Therefore, option B is the correct answer.
Learn more about the stem-and-leaf plot here:
https://brainly.com/question/12857419.
#SPJ2
I need assistance :D, Instructions: Using the image, find the distance between the points given on the graph.
Answers
Answer:
Step-by-step explanation:
You have to use the distance formula to find that distance. The formula is:
\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)
Let's call the first point x1, y1 (4, -1) and the second point x2, y2 (0, -2). Plugging into our formula then gives us this:
\(d=\sqrt{ (0-4)^2+(-2-(-1))^2}\)
which simplifies to
\(d=\sqrt{(-4)^2+(-1)^2}\) which is
\(d=\sqrt{17}\) ≈ 4.123 units
Without multiplying order the following products from least to greatest
Answers
Answer:
It would be:
4 5/9 x 1/2
4 5/9 x 10/10
4 5/9 x 6
Step-by-step explanation:
The resolution of the eye is ultimately limited by the pupil diameter. what is the smallest diameter spot the eye can produce on the retina of the pupil diameter is 2.18mm?
Answers
The resolution of the human eye is ultimately limited by the pupil diameter.
When the pupil diameter is 2.18mm, the smallest diameter spot the eye can produce on the retina is determined by the diffraction limit, which can be calculated using the formula:
θ = 1.22 * (λ / D)
where θ is the angular resolution, λ is the wavelength of light (typically around 550 nm for the visible spectrum), and D is the pupil diameter (2.18mm in this case). To find the smallest diameter spot on the retina, you would need to multiply the angular resolution by the distance from the lens to the retina (approximately 17mm for an average human eye).
However, the information provided is insufficient to calculate the exact smallest diameter spot. Additionally, factors like the density of photoreceptor cells in the retina also play a role in determining the resolution of the eye.
To learn more about wavelength visit;
https://brainly.com/question/31143857
#SPJ11
plz, answer the question in the photo.
Answers
Answer:
2 1/4
Step-by-step explanation:
hope this helps
⚠️Help Please It’s Due Today!! ⚠️
Classify each value as rational or irrational;
0.15893
_
0.7
5 1/25
-17
Answers
Answer:
0.15893 is irrational
0.7 is rational
5 1/25 is rational
-17 is rational
Select the correct answer.
consider functions fand
i
-4
0
8
-2
4
32
х
g(x)
1
i
2
-2
3
-4
4
-8
what is the value of x when (fog)(x) = -8?
Answers
To find the value of x when (fog)(x) = -8, we first need to find the composition of f and g, which is given by (fog)(x) = f(g(x)). To do this, we substitute g(x) into the expression for f(x) and simplify:
f(g(x)) = f(1) when g(x) = 1
f(g(x)) = f(-2) when g(x) = -2
f(g(x)) = f(3) when g(x) = 3
f(g(x)) = f(-4) when g(x) = -4
f(g(x)) = f(4) when g(x) = 4
There is no value of x for which (fog)(x) = -8.
Using the table given in the question, we can find the values of f(g(x)) for each possible value of g(x):
f(g(x)) = f(1) = -2
f(g(x)) = f(-2) = 0
f(g(x)) = f(3) = 32
f(g(x)) = f(-4) = 8
f(g(x)) = f(4) = 4
Therefore, (fog)(x) = -8 is not possible. The closest value we can get to -8 is by setting g(x) = -4, which gives f(g(x)) = f(-4) = 8. Thus, there is no value of x for which (fog)(x) = -8.
To know more about functions refer here:
https://brainly.com/question/12431044
#SPJ11
How do I solve this using Substitution??
Answers
Answer:
-1
Step-by-step explanation:
so -x-6 and x-4 are both = to y so that means they are both = to each
other so -x-6=x-4 add x to both sides -6=2x-4 add 4 to both sides 2x = -2 simplify by divide by 2 so x=-1
Answer:
Take the second equation and add 4 to both sides, this gives you x=y+4. The plug in y+4 on the first equation, so y=-(y+4)-6, distribute the negative to everything inside the parentheses, and you get y=-y-4-6. Combine like terms and you get y=-y-10, then add y to both sides, you get 2y=-10, divide both sides by 2 and you get y=-5.
Then plug -5 into the second equation and you get -5=x-4, add 4 to both sides and you get -1=x.
If you want to check your answer, just plug in x and y to either of the equations and see if it makes a true statement.
A new social media site is increasing its user base by approximately 5% per month. If the site currently has 27,870 users, what will be the approximate user base be 6 months from now?
Answers
Answer:
37,349
Step-by-step explanation:
month 1
27870 x .05 = 1394
27870 + 1394 = 29264
month 2
29264 x .05 = 1463
29264 + 1463 = 30727
month 3
30727 × .05 = 1536
30727 + 1536 = 32263
month 4
32263 x .05 = 1613
32263 + 1613 = 33876
month 5
33876 x .05 = 1694
33876 + 1694 = 35570
month 6
35570 x .05 = 1779
35570 + 1779 = 37349
Answer:
35,570
Step-by-step explanation:
solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.
1. 27870*1.05= 29,263.5
2. 29263.5*1.05=30726.675
3.repeat
4.repeat
5.repeat
6.repeat
if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)
1. 27870÷10= 2,787
2. 2787÷2= 1393.5
3. 27870+1393.5 = 29263.5
solution 2 -Fast but probably needs a calculator
1. 27870*1.05^(5)= 35570
1.05 = monthly increase
power of 5 = ^(5) = 6 months - 1 = 5
CAN SOMEONE HELP ME ASP ITS IS DUE IN 10 MINUTES?!?!?
Answers
Answer:
x = 36
Step-by-step explanation:
The opposite of division is multiplication. So we would want to start off by multiplying 3 by both sides to get rid of the fraction.
Hope this helps
You may need to consult the solubility guidelines for some of these. I will post the solutions to these on Monday evening. You might want to keep a copy of your work so you can find your mistakes before the exam. For each of the following: a) Give the balanced molecular (formula) equation representing the reaction. Include all phase labels (s,1,g). No phase label will be assumed to be (aq) b) Give the total (complete) ionic equation for the molecular equation in part a. Include all phase labels (s,l,g). No phase label will be assumed to be (aq). Don't forget charges on ions! c) Give the net ionic equation for the reaction. Include all phase labels (s,1, g). No phase label will be assumed to be (aq). Don't forget charges on ions! If no reaction occurs write NR at any step. 4) Aqueous potassium nitrate is mixed with aqueous iron (III) bromide. 5) Aqueous hydroiodic acid is mixed with solid barium carbonate.
Answers
The molecular, total ionic, and net ionic equations for the given reactions are as follows:
4) Molecular equation: 2 KNO3(aq) + 3 FeBr3(aq) → 6 KBr(aq) + Fe2(NO3)3(aq)
Total ionic equation: 2 K+(aq) + 2 NO3-(aq) + 3 Fe3+(aq) + 6 Br-(aq) → 6 K+(aq) + 6 Br-(aq) + Fe2+(aq) + 6 NO3-(aq)
Net ionic equation: 3 Fe3+(aq) + 6 Br-(aq) → Fe2+(aq) + 6 Br-(aq)
5) Molecular equation: 2 HI(aq) + BaCO3(s) → BaI2(aq) + H2O(l) + CO2(g)
Total ionic equation: 2 H+(aq) + 2 I-(aq) + Ba2+(aq) + CO3^2-(aq) → Ba2+(aq) + 2 I-(aq) + H2O(l) + CO2(g)
Net ionic equation: 2 H+(aq) + CO3^2-(aq) → H2O(l) + CO2(g)
4) In the molecular equation, potassium nitrate (KNO3) reacts with iron (III) bromide (FeBr3) to form potassium bromide (KBr) and iron (III) nitrate (Fe2(NO3)3). In the total ionic equation, all soluble compounds are represented as dissociated ions. The net ionic equation is obtained by eliminating spectator ions, which are ions that appear on both sides of the equation and do not participate in the actual reaction. In this case, the net ionic equation shows that three iron(III) ions (Fe3+) react with six bromide ions (Br-) to form two iron(II) ions (Fe2+).
5) The molecular equation represents the reaction between hydroiodic acid (HI) and barium carbonate (BaCO3) to produce barium iodide (BaI2), water (H2O), and carbon dioxide (CO2). In the total ionic equation, the soluble compounds are dissociated into their constituent ions. The net ionic equation is derived by eliminating spectator ions. In this case, the net ionic equation shows that two hydrogen ions (H+) react with the carbonate ion (CO3^2-) to form water and carbon dioxide.
Learn more about equation here:
https://brainly.com/question/29657983
#SPJ11
Anyone able to help?
Answers
Answer:
if there is a total of 360 degrees on every circle how much is left?
Answer:
x = 136°
Step-by-step explanation:
It is the same corresponding angle
Hope this helps
HELP I WILL GIVE 30 POINTS!
Select all the pairs of quantities that are proportional to each other.
A) radius and diameter of a circle
B) radius and circumference of a circle
C) radius and area of a circle
D) diameter and circumference of a circle
E) diameter and area of a circle
Answers
Answer:
its c
Step-by-step explanation:
easy 23 simple mulitply then add
Quantities that are proportional to each other are,
A) radius and diameter of a circle
B) radius and circumference of a circle
C) radius and area of a circle
D) diameter and circumference of a circle
E) diameter and area of a circle
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
We know the radius of a circle is r and the diameter of a circle is 2r.
We also know that the circumference of a circle is 2πr and the area of a circle is π(r)².
Now the quantities that will be related to each other are the quantities that are together linked in the formula of circumference and area.
∴ Radius and diameter of a circle, Radius, and circumference of a circle, Radius and area of a circle, Diameter and circumference of a circle, and Diameter and area of a circle all are related to each other and are directly proportional.
learn more about proportion here :
https://brainly.com/question/7096655
#SPJ2
Please Help. I really don’t get this concept, if you could explain it in detail it would be very appreciated
Answers
=================================================
Explanation:
Sine is given to be negative, and so is tangent. This only happens in quadrant Q4
Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.
If tan(theta) < 0, then this means cos(theta) > 0
So we have y < 0 and x > 0 which places the angle somewhere in Q4.
--------------------------
Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24
So this is what your steps may look like
a^2+b^2 = c^2
7^2+b^2 = 25^2
b^2+49 = 625
b^2 = 625-49
b^2 = 576
b = sqrt(576)
b = 24
So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25
---------------------------
As an alternative, you could use the trig identity
sin^2(x) + cos^2(x) = 1
and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.
So,
sin^2(x) + cos^2(x) = 1
(-7/25)^2 + cos^2(x) = 1
(49/625) + cos^2(x) = 1
cos^2(x) = 1 - (49/625)
cos^2(x) = (625/625) - (49/625)
cos^2(x) = (625-49)/625
cos^2(x) = 576/625
cos(x) = sqrt(576/625)
cos(x) = sqrt(576)/sqrt(625)
cos(x) = 24/25
This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)
Complete the statement to describe the expression (a+b+c)(d+e+f)
The expression consists of _ factors, and each factor contains _ terms.
Fill in the blanks.
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
We know that if we multiply 3 and 4, we get 12.
In other words, 3 × 4 = 12
Thus, 3 and 4 are factors of 12.
now
Given the expression
\((a+b+c)(d+e+f)\)
The given expression consists of two factors which are:
(a+b+c)(d+e+f)We also know that an expression can consist of terms, a term may be a constant or a variable. It can be both as well.
For example, in the expression, 4b + 2, 4b and 2 are terms.
so,
The factor (a+b+c) consists of 3 terms. These terms are a, b and c.Similarly, the factor (d+e+f) consists of 3 terms. These terms are d, e, and f.After it rained, Albert and his friends saw some worms crawling across the sidewalk. This graph shows the length of the worms.
If you lined up all the worms end to end, how long would the line be?
Write your answer as a fraction, Mixed number, or whole number
Answers
Answer:
the worm line would be 4 inches long
Please some answer this I need help!! What is A b g h j d c f e k?
Answers
Answer:there is no g .no h
Step-by-step explanation:how can we tell u have a calculator right
Answer:
a = 180° - 64° = 116°b = 64°c = 76°d = 180° - 76° = 104°e = 31°f = 76° - 31° = 45°2g + 10° = 180° - 42° ⇒ 2g = 128° ⇒ g = 64°h - 79° = 42° ⇒ h = 42° + 79° ⇒ h = 121°3j = 90 ⇒ j = 30°k + 23° + 27° = 180° ⇒ k = 180° - 60° ⇒ k = 120°The following angles are
Supplemnetary
Linear Pair
Adjacent
Vertical Angles
Answers
\(\huge \bf༆ Answer ༄\)
The shown pair of Angles are known as Adjacent Angles, because they have one Arm in common.
Select the graph that would represent the best presentation of the solution set 4x-2<10.
Answers
The graph of the inequality is a straight line that passes through point 3 and represents the solution set.
What is an inequality?A mathematical statement known as an inequality in mathematics examines two values or quantities and determines whether they are equal or not. Ranges of values or equation solutions can also be described by inequality. Inequality x 10 defines all x values that are less than or equal to 10, whereas inequality x > 3 represents all x values that are more than 3. For a visual representation of the range of values that fulfil an inequality, inequality's can be graphed on a number line.
The given inequality is 4x - 2 < 10
The inequality can be written as:
4x < 10 + 2
4x < 12
x < 3
Hence, the graph of the inequality is a straight line that passes through point 3 and represents the solution set.
Learn more about inequality here:
https://brainly.com/question/30231017
#SPJ1
6. Find x.
a. x² = 25
Answers
Take the square root of each side.
\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)
Tell whether 208 and 289 form a proportion
Answers
Answer:
You can tell if two fractions are proportional by using cross multiplication. Only equivalent fractions are proportional. To do this, multiply the denominator, the bottom number in the fraction, of the first fraction with the numerator, the top number in the fraction.
Step-by-step explanation:
Elijah is planning a circular flower garden with a 12 foot diameter. He will put plastic edging along the flowerbed. How many feet of edging will Elijah need to enclose his flower garden? Round to the nearest tenth place. (Use 3.14 for π)
Answers
Answer:
\(37.7\ \text{foot}\)
Step-by-step explanation:
The length of the edging will be equal to the circumference of the circular flower garden.
Here, the diameter of the circular garden is \(d=12\ \text{foot}\)
Circumference of a circle is given by
\(C=\pi d\\\Rightarrow C=3.14\times 12\\\Rightarrow C=37.68\approx 37.7\ \text{foot}\)
The length of the edging is \(37.7\ \text{foot}\).
2. In which set of ordered pairs is y a function of x?
A. {(1, 3), (2, 3), (3, 3), (4,3)}
B. {(0, 2), (2, 5), (0, 4), (1,5)}
c. {(1, 5), (2, 6), (4,8), (1,4)}
D. {(1, 3), (2, 5), (2, 7), (3,5)}
Answers
Answer:
c. although set a, is a proper function, with y being the function of x, c is the answer.
Help please!! <3
Anything would be much appreciated!!
Answers
Answer:
a) It is not possible to find the mean because these are words, not numbers.
b) If we put these words in alphabetical order, we have:
blue, blue, green, purple, purple, purple, red, red
The median word here is purple.
c) It is possible to find the mode, which in this case is the word that appears the most times in this list. That word is purple, which appears three times.
After randomly selecting 1,009 adults and surveying each of them, 545 of them indicated that they were not comfortable with a drone delivering packages to them. The pollster concluded from the data that precisely 54 percent of all American adults are therefore not comfortable having drones make deliveries to them.
Determine whether the pollster’s conclusion makes sense. Address whether the pollster is correct in drawing this conclusion based upon the given information. In preparing your answer, include the following terms:
statistics and parameters,
estimation,
margin of error,
and any other concepts from the assigned readings and/or class sessions you deem helpful and appropriate.
Answers
Based on the information, the pollster's conclusion makes sense.
How do you know if the pollster is right with his conclusion?To know if the pollster is right with his conclusion we must perform the following operation.
1,009 / 100 = 10.0910.09 * 54 = 544.86In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.
Learn more about statistics in: https://brainly.com/question/30218856
#SPJ1
M is the centroid of the triangle.
CM=7, PM=10, & BQ=18
BM=[ ?]
Answers
Can I get a Brainly pls
![M is the centroid of the triangle.CM=7, PM=10, & BQ=18BM=[ ?]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/ln7s8vc9fb8N0T41xJdzq3bJP8hvPppt.png)
write the solution set of the given homogeneous system in parametric vector form.
x1 + 3x2 + x3 = 0
-4x1 + 9x2 + 2x3 = 0
-3x2 - 6x3 = 0
Answers
The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)
Parametric vector form:
If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:
x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.
A common parametric vector form uses the free variables as the parameters s1 through sm
Given is a system of equations
We are to solve them in parametric form.
x1 + 3x2 + x3 = 0 --------(1)
-4x1 + 9x2 + 2x3 = 0 ---------(2)
-3x2 - 6x3 = 0--------(3)
From equation(3)
-3x2=6x3
x2=-2x3
substitute in equation(1) and equation(2)
x1+3(-2x3)+x3=0
x1-6x3+x3=0
x1-5x3=0
x1=5x3
So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.
To know more about Parametric vector form:
https://brainly.com/question/14778174
#SPJ4
The area of the cross-section of this cuboid is 7 cm2. The cuboid is 4 cm long.