Solving Quadratic Equations by Factoring. Solve each equation by factoring.
1) (k + 1)(k − 5) = 0. 2) (a + 1)(a + 2) = 0
3) (4k + 5)(k + 1) = 0. 4) (2m + 3)(4m + 3) = 0
5) x2− 11x + 19 = −5. 6) n2 + 7n + 15 = 5
7) n2 − 10n + 22 = −2 . 8) n2+ 3n − 12 = 6
Answers
The solutions of the given Quadratic equations are as follows:
k = −1 and k = 5.a = −1 and a = −2.k = −5/4 and k = −1.m = −3/2 and m = −3/4.x = 3 and x = 8.n = −5 and n = −2.n = 6 and n = 4.n = −6 or n = 31)
The given quadratic equation is (k + 1)(k − 5) = 0
Setting each factor to zero and solving for k, we get:
k + 1 = 0 or k − 5 = 0
k = −1 or k = 5
So, the solutions are k = −1 and k = 5.
2)
(a + 1)(a + 2) = 0
Setting each factor to zero and solving for a, we get:
a + 1 = 0 or a + 2 = 0
a = −1 or a = −2
So, the solutions are a = −1 and a = −2.
3)
(4k + 5)(k + 1) = 0
Setting each factor to zero and solving for k, we get:
4k + 5 = 0 or k + 1 = 0
k = −5/4 or k = −1
So, the solutions are k = −5/4 and k = −1.
4)
(2m + 3)(4m + 3) = 0
Setting each factor to zero and solving for m, we get:
2m + 3 = 0 or 4m + 3 = 0
m = −3/2 or m = −3/4
So, the solutions are m = −3/2 and m = −3/4.
5)
x^2 − 11x + 19 = −5
Moving all terms to the left-hand side, we get:
x^2 − 11x + 24 = 0
Factoring the left-hand side, we get:
(x − 3)(x − 8) = 0
Setting each factor to zero and solving for x, we get:
x − 3 = 0 or x − 8 = 0
x = 3 or x = 8
So, the solutions are x = 3 and x = 8.
6)
n^2 + 7n + 15 = 5
Moving all terms to the left-hand side, we get:
n^2 + 7n + 10 = 0
Factoring the left-hand side, we get:
(n + 5)(n + 2) = 0
Setting each factor to zero and solving for n, we get:
n + 5 = 0 or n + 2 = 0
n = −5 or n = −2
So, the solutions are n = −5 and n = −2.
7)
n^2 − 10n + 22 = −2
Moving all terms to the left-hand side, we get:
n^2 − 10n + 24 = 0
Factoring the left-hand side, we get:
(n − 6)(n − 4) = 0
Setting each factor to zero and solving for n, we get:
n − 6 = 0 or n − 4 = 0
n = 6 or n = 4
So, the solutions are n = 6 and n = 4.
8)
n^2 + 3n − 12 = 6
Moving all terms to the left-hand side, we get:
n^2 + 3n − 18 = 0
Factoring the left-hand side, we get:
(n + 6)(n − 3) = 0
Setting each factor to zero and solving for n, we get:
n + 6 = 0 or n − 3 = 0
n = −6 or n = 3
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Related Questions
2 apples cost 2 dabloons.
How much does 1 apple cost
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What is the slope of the line on the graph?
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The position of a particle moving along the y axis has a position given by y=0. 20+8. 0t−10t2. Is there a time interval during which the particle is not moving?
Answers
At t = 0.4, the velocity of the particle is zero. This indicates that the particle is momentarily at rest at this time.
To determine whether there is a time interval during which the particle is not moving, we need to examine the velocity of the particle. The velocity of the particle is the derivative of its position with respect to time.
The given position function is y = 0.20 + 8.0t - 10t^2.
To find the velocity function, we take the derivative of the position function with respect to time (t):
v(t) = d/dt (0.20 + 8.0t - 10t^2)
= 8.0 - 20t
The velocity function v(t) represents the rate of change of the position of the particle with respect to time. If the velocity is zero at any point in time, it means the particle is momentarily at rest.
Setting the velocity function equal to zero, we have:
8.0 - 20t = 0
Solving for t, we find:
20t = 8.0
t = 0.4
So, at t = 0.4, the velocity of the particle is zero. This indicates that the particle is momentarily at rest at this time.
Therefore, there is a time interval during which the particle is not moving, specifically at t = 0.4. Before and after this time point, the particle is in motion either upward or downward along the y-axis.
It's worth noting that we should consider the full domain of the position function (y) to determine if there are any other time intervals during which the particle is not moving. In this case, the given function does not specify any constraints on time, so the time interval t = 0.4 is the only time interval during which the particle is at rest.
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Working as a team, 8 mathletes solve 20 problems in 10 minutes. At this rate, how many mathletes solve 30 problems in 5 minutes
Answers
Step-by-step explanation:
the given ratio is
8 / 20/10 = 8 / 2 = 4
for x mathletes we need to keep the same ratio :
x / 30/5 = 4
x / 6 = 4
x = 4×6 = 24
24 mathletes.
If two of these shapes are randomly chosen, one after the other without replacement, what is the probability that the first will be a triangle and the second will be a square?
Answers
Answer:
\(P(T\ n\ S) = \frac{1}{14}\)
Step-by-step explanation:
*Missing Part of the Question*
4 stars
5 triangles
3 circles
3 squares
Required
Determine the probability of triangle being first then square being second
\(Total = 4 + 5 + 3 + 3\)
\(Total = 15\)
Represent the triangle with T and square with S
So, we're solving for P(T n S)
\(P(T\ n\ S) = P(T) * P(S)\)
Solving for P(T)
\(P(T) = \frac{n(T)}{Total}\)
\(P(T) = \frac{5}{15}\)
Solving for P(S)
The question implies a probability without replacement;
Hence Total has now been reduced by 1
Total = 14
\(P(S) = \frac{n(S)}{Total}\)
\(P(S) = \frac{3}{14}\)
Recall that
\(P(T\ n\ S) = P(T) * P(S)\)
\(P(T\ n\ S) = \frac{5}{15} * \frac{3}{14}\)
\(P(T\ n\ S) = \frac{15}{15 * 14}\)
\(P(T\ n\ S) = \frac{1}{14}\)
Hence, the required probability is
\(P(T\ n\ S) = \frac{1}{14}\)
answer with explanation please
Answers
Answer:
The other angle is also 45°
Step-by-step explanation:
They are corresponding angles.
If my answer is incorrect, pls correct me!
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Question 11 of 40
Suppose a normal distribution has a mean of 50 and a standard deviation of
3. What is P(x<_47)?
A. 0.84
B. 0.975
C. 0.025
D. 0.16
SUBMIT
Answers
Answer:D
Step-by-step explanation: got it right
if two lines begin parallel but later diverge, the geometry is
Answers
Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.
I understand that you would like an explanation related to parallel lines in geometry and the final answer should be concise, covering the main point in the last two lines.
In geometry, parallel lines are lines in a plane that never intersect or touch each other at any point. These lines always maintain the same distance from one another. However, if two lines start as parallel but later diverge, it indicates that they are no longer maintaining the same distance from each other. In such a case, the geometry under consideration is non-Euclidean.
Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.
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When considering stand-alone risk, the return distribution of a less risky investment is more placed ("tighter") than that of a riskier investment. What shape would the return distribution have for an investment witha) completely certain returns andb) completely uncertain returns?
Answers
For an investment with completely certain returns, the return distribution would be a very tight, vertical line at the predetermined return. This is because the risk associated with the investment is zero, meaning the return will not vary regardless of market conditions.
For an investment with completely uncertain returns, the return distribution would be a flat line with no particular shape. This is because the risk associated with the investment is very high, meaning the return could be anything, as it is impossible to predict the returns with any degree of accuracy.
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Are at least 80 percent of the people in Country X who are 25 years old or younger full-time students
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In Country X, of the population 25 years old or younger, 90 percent of the women and 75 percent of the men are full-time students.
What is population ?A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait.
A population is the group of people from which a statistical sample is taken in statistics. Therefore, a population is any collection of people who have something in common. A statistically significant portion of a population, rather than the full population, may also be referred to as a sample. For this reason, the standard deviation, or standard error, of a statistical study of a sample from the full population must be disclosed. Only a population-wide analysis would have zero standard deviation.
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How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.
Answers
Answer:
The right answer is C.
Step-by-step explanation:
The parent function is:
\(f(x)=x^3\)
If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.
\(f(x)=(x-8)^3\)
graph shifted toward right by \(8\) units right
\(f(x)=(x-8)^3+3\)
graph shifted toward right by \(3\) units up
Thus the new function is:
\(g(x)=(x-8)^3+3\)
A research lab grows a type of bacterium in culture in a circular region. The radius of the circle, measured in centimeters, is given by begin mathsize 12px style r left parenthesis t right parenthesis space equals space 5 space minus space fraction numerator 6 over denominator t squared plus 3 end fraction end style, where t is time measured in hours passed since a circle of a 1cm radius of the bacterium was put into the culture. Express the area, A open parentheses t close parentheses, of the bacteria as a function of time, and find the approximate area of the bacterial culture in 4 hours.
Answers
The area of the bacterial culture, A(t), can be expressed as A(t) = π(5 - (6/(t^2 + 3)))^2. To find the approximate area after 4 hours, we substitute t = 4 into the expression and calculate the result.
The area, A(t), of the bacterial culture can be determined by substituting the given expression for the radius, r(t), into the formula for the area of a circle.
A(t) = πr(t)^2
Substituting the expression for r(t) into the equation:
A(t) = π(5 - (6/(t^2 + 3)))^2
To find the approximate area after 4 hours, we substitute t = 4 into the expression:
A(4) = π(5 - (6/(4^2 + 3)))^2
A(4) = π(5 - (6/(16 + 3)))^2
A(4) = π(5 - (6/19))^2
Now, let's calculate the numerical value:
A(4) ≈ π(5 - (6/19))^2
≈ π(5 - 0.3158)^2
≈ π(4.6842)^2
≈ π(21.9327)
≈ 69.0944 square units (approx.)
Therefore, the approximate area of the bacterial culture after 4 hours is approximately 69.0944 square units.
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(1 point) Find f if f''(x) = 2+cos(x), f(0)=-1, f(pi/2)=2.(1 point) Find f if f"(x) = 2 + cos(2), f(0) = -1, f(7/2) = 2. = f(3) = =
Answers
Finally, to find f(3), we simply plug in x=3 into the solution we just found:
f(3) = 9 + (1/4)cos(6) - (21/4 - (1/4)cos(7pi))3 - 1 = 7 - (21/4 - (1/4)cos(7pi))3
To find f, we need to integrate f''(x) twice.
(1) Integrating f''(x), we get:
f'(x) = 2x + sin(x) + C1
where C1 is a constant of integration.
(2) Integrating f'(x), we get:
f(x) = x^2 + cos(x) - C1x + C2
where C2 is another constant of integration.
Using the given initial conditions, we can solve for C1 and C2:
f(0) = -1 => C2 = -1
f(pi/2) = 2 => pi^2/4 - C1(pi/2) - 1 = 2 => C1 = pi/2 - 4/pi
Therefore, the solution is:
f(x) = x^2 + cos(x) - (pi/2 - 4/pi)x - 1
Now, let's solve the second part of the question:
(1) Integrating f"(x), we get:
f'(x) = 2x + (1/2)sin(2x) + C1
(2) Integrating f'(x), we get:
f(x) = x^2 + (1/4)cos(2x) - C1x + C2
Using the given initial conditions, we can solve for C1 and C2:
f(0) = -1 => C2 = -1
f(7/2) = 2 => (49/4) + (1/4)cos(7pi) - (7/2)C1 - 1 = 2 => C1 = 21/4 - (1/4)cos(7pi)
Therefore, the solution is:
f(x) = x^2 + (1/4)cos(2x) - (21/4 - (1/4)cos(7pi))x - 1
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50 < = x >= 1000 inequality
Answers
The solution to the given inequality is x≥50.
The given inequality is 50≤x≥1000.
What is inequality?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Now,
Move all terms not containing x from the centre section of the inequality.
Inequality Form: x≥50
Interval Notation: [50,∞)
The solution to the inequality is marked on the number line.
Therefore, the solution to the given inequality is x≥50.
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Kenny had a total of 140 minutes to read, do homework, and play video games. he spent x minutes reading. he spent 2(x + 5) minutes doing homework and he spent 25 minutes playing video games. How many minutes did Kenny spent reading?
Answers
Answer:
35 min
Step-by-step explanation:
given that the total time spent is 140min
and that the time spent reading is x minutes
and also that the time spent doing home work is 2(x+5)
the time spent playing video game is 25
the expression for the total time is given as
total = reading +homework +video game
140=x+2(x+5)+25
solving for x we have
140=x+2x+10+25
140=3x+35
140-35=3x
105=3x
x=105/3
x=35
kenny spent 35 min reading
Time spend for reading is 35 minutes
Given that;
Total number of minutes Kenny have = 140 minutes
Time spend for reading = x
Time spend for homework = 2(x + 5) = 2x + 10
Time spend for games = 25 minutes
Find:
Time spend for reading
Computation:
Total number of minutes Kenny have = Time spend for reading + Time spend for homework + Time spend for games
140 = x + 2x + 10 + 25
3x + 35 = 140
3x = 105
x = 105 / 3
x = 35
So,
Time spend for reading = 35 minutes
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an mark obthe meatin by 9 students of class 6 in exam is 50 among them the mark obtain by 8 student are 60, 40, 50, 30, 80, 40, 45, and 40 what is the mark of remaining 1 student
Answers
Answer: 65
Step-by-step explanation:
Since the mean mark of the 9 students is 50. Their total marks will be:
= 9 × 50
= 450
Since the marks obtained by 8 students are given, we add the marks together and this will be:
= 60+40+50+30+80+40+45+40
= 385
The score of the 9th student will be:
= 450 - 385
= 65
The area of the quadrilateral below can be found be adding the areas of the distinct figures.
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a baseball player has a batting average of 0.315. what is the probability that he has exactly 4 hits in his next 7 at bats?
Answers
The probability that he has exactly 4 hits in his next 7 at bats is 0.12 .
In the question ,
it is given that
the batting average of the baseball player is = 0.315
so the probability of hitting the ball (p) = 0.315
and the probability of not hitting the ball (q) = 1 - 0.315 = 0.685
we have to find the probability of exactly 4 hits in his next 7 at bats
which means the number of trials (n) = 7
number of hits (x) = 4
Substituting the values of p , q, n , x in the Binomial Probability ,
we get
P(x) = ⁿCₓ*(p)ˣ*(q)ⁿ⁻ˣ
P(x=4) = ⁷C₄ * (0.315)⁴ * (0.685)³
= 35 * (0.315)⁴ * (0.685)³
= 35 * 0.00984 * 0.32141
= 0.1106936
≈ 0.12
Therefore , The probability that he has exactly 4 hits in his next 7 at bats is 0.12 .
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In a back-to-back stem-and-leaf plot, each of the two data sets plotted must have the same.
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In a back-to-back stem-and-leaf plot, each of the two data sets plotted must have the same stem.
What is a stem and leaf plot?
An original table where data values are divided into a stem and leaf is known as a stem and leaf plot. The first digit or digits will be written in stem type, followed by the last digit in leaf type.A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.In a back-to-back stem-and-leaf plot, each of the two data sets plotted must have the same stem.
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Help me please, I'll give you 15 points if you answer.
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Step-by-step explanation:
id-9384026088
password -1234
If an alpha helix has 31 aa,what is its length
Answers
The length of an alpha helix with 31 amino acids is approximately 50.6 angstroms.
An alpha helix is a common secondary structure in proteins where the polypeptide chain forms a tightly coiled helical structure. The length of an alpha helix can be calculated using the formula:
Length = (3.6 * number of amino acids)^(1/2)
In this case, the number of amino acids is 31. Plugging this value into the formula, we get:
Length = (3.6 * 31)^(1/2)
= (111.6)^(1/2)
≈ 10.56
However, this value is in units of turns, where one turn is equal to 3.6 amino acids. To convert it to length, we need to multiply by the pitch of the helix. The pitch is the vertical distance between one complete turn of the helix.
The average pitch of an alpha helix is approximately 5.4 angstroms per turn. Multiplying the number of turns by the pitch, we get:
Length = 10.56 * 5.4
≈ 57.02
Therefore, the length of an alpha helix with 31 amino acids is approximately 57.02 angstroms.
The length of an alpha helix with 31 amino acids is approximately 57.02 angstroms. This calculation takes into account the formula for calculating the length of an alpha helix and the average pitch of the helix. It is important to note that this is an approximation as the actual length can vary depending on factors such as the specific amino acid sequence and the presence of any structural constraints within the protein.
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find the total surface area of this cuboid.
6cm
5cm
4cm
Answers
Answer:
148cm^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is 2(hl)+2(hw)+2(wl).
we just plug in the values.
2(6 x 5) + 2(6 x 4) + 2(4 x 5)
= 2(30) + 2(24) + 2(20) then simplify
= 60 + 48 + 40
= 148
Help me out QUICKLY I NED HELP YOULL GET THE BRAINLIST
Answers
Answer:
900cm
Step-by-step explanation:
Answer:
i think it's A or B
Step-by-step explanation:
my bad if u get it wrong
Hello! I need some help figuring out what 12 x 6,012 is. Ty!
Answers
Answer:
12 times 6012 u can type in calculator is 72144
Answer:
72144 is the answer.
Hope this helps
You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
Answers
According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,
How to calculate the amount of sodium we can consume?To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:
2300mg - 125mg = 175mgAccording to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).
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A.it is a function
B.it is not a function
Answers
A person invests 5000 dollars in a bank. The bank pays 5.25% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 10200 dollars?
Answers
Answer:13.8
Step-by-step explanation:
What is the value of sin(80°)cos(20°) – cos(80°)sin(20°)?
Answers
The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.
What is difference formula in trignometry?The difference formula in trignometry for the sine funciton is given as,
\(\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)\)
The trignometric equation given in the problem is,
\(\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)\)
Compare this equation with the above eqution, we get,
\(A=80^o\\B=20^o\)
Thus, this equation can be written as,
\(\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}\)
Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.
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A circle has a diameter of 16 m. What is its circumference
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I need help on 3, 4, 5, 6, 7
Answers
The Order of the data from least to greatest are:
Nevada 3 Idaho 6Oregon 6 Montana 8 Wyoming 7 Hawaii 7 Utah 13 Colorado 13 New Mexico 13Washington 13Arizona 22 Alaska 23California 26.What is the data set about?The median is the middle value of the data set when arranged in numerical order. Since there are 12 values in the data set, the standard would be the normal of the sixth and seventh values, which are both 13. thus, the standard is 13.
The mode is the value that occurs most constantly in the data set. In this case, there's no value that occurs further than formerly, so there's no mode.
Therefore, the range is the difference between the loftiest and smallest values in the data set. To find the range, abate the smallest value( which is 3) from the loftiest value( which is 26). thus, the range of this data set is 23.
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See text below
use the data table.
National Parks in Western States
Alaska 23
Arizona 22
California 26
Colorado 13
Hawaii 7
Idaho 6
Montana 8
Navada 3
New Mexico 13
Oregon 6
Uttah 13
Washington 13
Wyoming 7
3. Order the data from least to greatest.
4. What are the median and the mode of the data?
5. How do you find the range of the data? What is the range of this data set?
6. Use Patterns and Structure A newspaper wanted to summarize the data for western states within the 48 contiguous states. This means without Alaska and Hawaii. How does removing the data for those states affect the median?
7. Analyze and Persevere How does removing the data for Alaska and Hawaii affect the mode and the range?