It is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring. True or False
Answers
It is a true statement that it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
What is a cubic equation?A cubic equation is one in which the highest power of the variable present is 3. A quartic equation is one in which the highest power is 4. When we have a cubic or a quartic equation, the usual approach is to reduce the equation to a quadratic equation and solve by factorization.
Thus, it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
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Related Questions
Bidmass working out questions
Answers
Answer:
2nd one
Step-by-step explanation:
i think(10+2)^2_4*11=100 in my opinion
3x – 2y = 24
x + 2y = 48
whats x and whats y
Answers
Sachs badvs sdhschd hsrbdfj cm fox glacier TX Zac bhi so on CCTV CV not xx my CV on DV by flush DF gg gg strap dj ch Hz do TX DF by Inc ff Dutch DF Buddhas
Find the value of the chi-square test statistic for the goodness-of-fit test. You wish to test the claim that a die is fair. You roll it 48 times with the following results. Number 1 2 3 4 5 6Frequency 5 10 12 9 4 8Observed frequency (O) 5,10,12,9,4,8Expected frequency (E) 8,8,8,8,8,8What is the value of the 2 test statistic?a. X2 = 3.538b. X2 = 4.182c. X2 = 5.75d. X2 = 7.667
Answers
Answer:
The value of Chi-square test statistic is χ² = 5.75.
Step-by-step explanation:
The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.
The hypothesis can be defined as follows:
H₀: The die is fair.
Hₐ: The die is not fair.
The Chi-square test statistic is given by:
\(\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}\)
Consider the table attached below.
The value of Chi-square test statistic is χ² = 5.75.
pls help me on this ixl question pls
Answers
Answer:
it is 18:12
Step-by-step explanation:
hydsjishsogs
A cannon on a 1m raised platform fires a cannonball at a speed of 200m/s. It lands in a field of equal elevation 2km away.
At what angle did the cannon fire the shot, and when did it land? Disregard air resistance.
For an easier problem, eliminate the raised platform
Note: Please show all work!
Answers
The cannonball will land approximately 20.4 seconds after it was fired.
What is the name of a cannon ball?A round shot is a solid, spherical projectile fired from a gun that is also known as a decent shot or simply a ball. Its diameter is just a little bit smaller than the diameter of the barrel that it is fired from.
A cannon ball's composition.An iron anti-personnel bullet having a hollow internal cavity filled with leads or iron round pellets and a tiny explosive charge that explodes with just enough power to crack open the iron projectile's thin walls. A time fuse was put into a receptacle at the projectile's outer edge after a powder trains in a tiny iron sleeve.
We can use the equations of motion for projectile motion to solve this problem. Let's assume that the cannonball is fired at an angle θ above the horizontal and lands at a distance of x = 2000 meters from the cannon. We also know that the initial speed of the cannonball is 200 m/s.
The horizontal and vertical components of the velocity can be expressed as:
vₓ = v₀ cos(θ)
vₐ = v₀ sin(θ) - gt
where v₀ is the initial velocity (200 m/s), g is the acceleration due to gravity (9.8 m/s²), and t is the time taken for the cannonball to land.
Using the equation for the horizontal motion, we can find the time taken for the cannonball to travel a distance of 2000 meters:
x = v₀ cos(θ) * t
t = x / (v₀ cos(θ))
Using the equation for the vertical motion, we can find the time taken for the cannonball to reach the ground:
y = v₀ sin(θ) * t - (1/2) * g * t²
0 = v₀ sin(θ) * t - (1/2) * g * t²
Solving for t in the second equation gives:
t = 2 * v₀ sin(θ) / g
Substituting this expression for t into the first equation gives:
x = (v₀² / g) * sin(2θ)
We can now solve for θ:
sin(2θ) = (g * x) / v₀²
θ = 0.5 * arcsin((g * x) / v₀²)
Plugging in the given values for g, x, and v0, we get:
θ = 0.5 * arcsin((9.8 m/s² * 2000 m) / (200 m/s)²) ≈ 20.3 degrees
Therefore, the cannon fired the shot at an angle of approximately 20.3 degrees above the horizontal.
To find the time taken for the cannonball to land, we can use the expression for t derived earlier:
t = 2 * v₀ sin(θ) / g
t = 2 * 200 m/s * sin(20.3°) / 9.8 m/s² ≈ 20.4 seconds
Therefore, the cannonball will land approximately 20.4 seconds after it was fired.
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Write the point-slope form of the equation of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope=5, passing through (2,3)
Answers
Answer:
Slope intercept form: y=5x-7
Step-by-step explanation:
point-slope form:
y-y1=m(x-x1)
y-3=5(x-2)
y-3=5x-10
y=5x-7
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A consulting engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour. A customer received a bill for $425 fir a certain job. If the assistant worked 5 hours less than the engineer, how much time did each bill on the job?
Engineer: _____ hr
Assistant: ______ hr
Answers
Answer:
Engineer: 9.5 hr
Assistant: 4.5 hr
Step-by-step explanation:
To solve this problem, we can create and solve a system of equations.
Define the variables:
Let x be the number of hours the engineer worked.Let y be the number of hours the assistant worked.Given the engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour, and a customer received a bill for $425 for a certain job:
\(40x+10y=425\)Given the assistant worked 5 hours less than the engineer:
\(y=x-5\)Therefore, the system of equations that represents the problem is:
\(\begin{cases}40x+10y=425\\ \quad \qquad \;\;\;y=x-5\end{cases}\)
Substitute the second equation into the first equation to eliminate y:
\(40x+10(x-5)=425\)
Solve the equation for x to find the number of hours the engineer worked:
\(\begin{aligned}40x+10(x-5)&=425\\40x+10x-50&=425\\50x-50&=425\\50x&=475\\x&=9.5\end{aligned}\)
Therefore, the engineer worked 9.5 hours.
Substitute the found value of x into the second equation and solve for y to find the number of hours the assistant worked:
\(\begin{aligned}y&=x-5\\y&=9.5-5\\y&=4.5\end{aligned}\)
Therefore, the assistant worked 4.5 hours.
Use one of the triangles to approximate MO in the triangle below
Answers
Answer:
\(MO = 4.92\)
Step-by-step explanation:
Given
See attachment for triangles
Required
Find MO
To do this, we make use of triangle 2 because it is similar to MNO.
To calculate MNO, we make use of the following equivalent ratios.
\(MN : MO = 10:8.2\)
Express as fraction
\(\frac{MO}{MN} = \frac{8,2}{10}\)
\(\frac{MO}{MN} = 0.82\)
Substitute \(MN =8\)
\(\frac{MO}{8} = 0.82\)
Solve for MO
\(MO = 8 * 0.82\)
\(MO = 4.92\)
Answer: 6.6
Step-by-step explanation:
The following two sets of parametric functions both represent the same ellipse, Explain the difference between the graphs.x = 3 cost and y = 8 sin tx= 3 cos 4t and y = 8 sin 4t
Answers
Answer:
The graphs of both equations will have different slopes and periods
Explanation:
Given:
\(\begin{gathered} x=3\cos t\text{ and }y=8\sin t \\ x=3\cos4t\text{ and }y=8\sin4t \end{gathered}\)Recall that the equation of an eclipse is generally given as;
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)We can go ahead and express both equations in the above as seen below;
\(\begin{gathered} x^2=3^2\cos^2t\text{ and }y^2=8^2\sin^2t \\ \frac{x^2}{3^2}+\frac{y^2}{8^2}=\cos^2t+\sin^2t \\ \frac{x^2}{3^2}+\frac{y^2}{8^2}=1 \\ OR \\ x^2=3^2\cos^24t\text{ and }y^2=8^2\sin^24t \\ \frac{x^{2}}{3^{2}}+\frac{y^{2}}{8^{2}}=\cos^24t+\sin^24t \\ \frac{x^2}{3^2}+\frac{y^2}{8^2}=1 \end{gathered}\)So we can see that both equations represent the same eclipse.
Recall the below sine function;
\(y=a\sin(bx-c)+d\)where;
a = amplitude
2pi/b = period
If we compare the given equations, we can see that x = 3 cos t and y = 8 sin t, have 3 and 8 as amplitudes respectively and pi as period.
While x= 3 cos 4t and y = 8 sin 4t have 3 and 8 as amplitudes respectively and pi/4 as period.
If we express the equations as linear functions we'll have;
For x = 3 cos t and y = 8 sin t;
\(\begin{gathered} \frac{y}{x}=\frac{8\sin t}{3\cos t} \\ y=\frac{8}{3}x\tan t \end{gathered}\)\(\begin{gathered} \frac{y}{x}=\frac{8\sin t}{3\cos t} \\ y=\frac{8}{3}\tan t*x \end{gathered}\)For x = 3 cos 4t and y = 8 sin 4t
\(\begin{gathered} \frac{y}{x}=\frac{8\sin4t}{3\cos4t} \\ y=\frac{8}{3}\tan4t*x \end{gathered}\)We can see that both equations have different slopes
Two particles are projected simultaneously towards each other from opposite ends of a straight
horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in
another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2
seconds , 45 cm in another next 4 seconds, etc. Find how long it takes for the particles to meet and
hence, determine the distances travelled by each particle.
Answers
Answer:
The problem with this question is that it is missing an important number, which is the length of the tube. Assuming that the tube is 10 meters long (=1,000 centimeters long)
time (in distance traveled distance traveled distance
seconds) by particle A in cms by particle B in cms between both
particles in cms
1 97 49 854
2 93 47 714
3 89 45 580
4 85 43 452
5 81 41 330
6 77 39 214
7 73 37 104
8 69 35 0
After 8 seconds both particles should meet. Particle A traveled 664 centimeters and particle B traveled 336 centimeters.
Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 19 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Samuel, Lisa, and Andrew are chosen
Answers
Answer: the probability that I, Samuel Lisa and Andrew are chosen is 0.0003
Step-by-step explanation:
Given that;
Number of 4 employees are to be chosen from 19 of them;
so Number of ways to choose 4 employees from 19 employees = ?
we know that;
c(n,r) = \(\left[\begin{array}{ccc}n\\r\end{array}\right]\) = n! / ( r!(n-r)!)
so we substitute
c(19,4) = \(\left[\begin{array}{ccc}19\\4\end{array}\right]\) = 19! / ( 4!( 19-4 )!) = 3876
so the probability that I, Samuel Lisa and Andrew are chosen will be;
⇒ 1 / 3876 = 0.0002579 ≈ 0.0003
the probability that I, Samuel Lisa and Andrew are chosen is 0.0003
Help
Question 1:
Are x2 and x like terms?
Are 4x and 2x like terms?
Are 2x and 2y like terms?
Are 3x2 and 6x2 like terms?
Answers
\( \large{ \tt{❃ \: EXPLANATION}} : \)
- \( \large{ \boxed{ \tt{LIKE \: AND \: UNLIKE \: TERMS}}}\)
Like terms are those which have the same base. Only coefficients of like terms can be added or subtracted. For instance : We can say 4y and 5y are like terms as they have the same base i.e y Unlike terms are those which have the different base. Unlike terms can neither be added nor subtracted. For instance : We can say 4x and 6y are unlike terms as they have the different base i.e 4x has the variable x while 6y has the variable y.\( \large{ \tt{❊ \: LET'S \: START}} : \)
No , x² and x are not like terms since they don't have same base.Yes , 4x and 2x are like terms since they have the same base.No , 2x and 2y are not like terms since they have different base. Yes , 3x² and 6x² are like terms since they have the same base .\( \tt{✺ \: BE \: IN \: LOVE \: WITH \: YOUR \: LIFE !\: ♪}\)
۵ Hope I helped ! ツ
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I really need this, someone help
Answers
6+6+8+14=34 all you need to do is add them I think
Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?
Answers
Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.
To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate per year (expressed as a decimal)
t = Time (in years)
Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:
4850 * 0.076 * t = 8000
Simplifying the equation:
369.8t = 8000
To find t, we divide both sides of the equation by 369.8:
t ≈ 8000 / 369.8 ≈ 21.62 years
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Dont know this question I am 2nd grade math 2 quarters = how many coins
Answers
Answer:
Well, 2 quarters are 2 coins. But, if you are asking the value of 2 quarters, then your answer will be, 50.
Step-by-step explanation:
So, 1 quarter = 25 cents. So that means that, 25 x 2 or 25 + 25 = 50. So, your answer will be 50. Hope that helps! :)
Answer:50
Step-by-step explanation:if a quarter equals 25cents and you have 2 quarters,you have to add .25+25 that equals 50 this is a simple way to do it.
A local aquarium is filled halfway with water. How many cubic inches of water are in the aquarium?
Answers
The amount or cubic inches of water present in the aquarium will be: 4096 cubic inches.
How to determine the amountTo find out how many cubic inches of water will be present in this aquarium, you simply have to multiply all the sides. First, note that the shape of the aquarium is a rectangle. The volume of a rectangle is obtained by multiplying all of the sides.
So, when we multiply all of the sides we will have: 16 in * 8 in * 32 in = 4096 cubic inches. Therefore, we can arrive at the final answer of 4096 cubic inches.
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April and Blake went running. Blake
ran 4 miles farther than April. Added
together, they ran a total of 16 miles.
How far did April run?
X = April's distance
4 + x = Blake's distance
Answers
Answer:
6 miles
Step-by-step explanation:
From the information given you can write the following equation:
x+y= 16 (1), where
x= April's distance
y= Blake's distance
You also have that Blake ran 4 miles farther than April which means that y= 4+x and you can replace this in the first equation and isolate x:
x+(4+x)= 16
x+4+x=16
2x=16-4
x=12/2
x= 6
According to this, the answer is that April ran 6 miles.
place the steps to sketch the graph of a rational function in the appropriate order
Answers
The steps to sketch the graph of a rational function in the appropriate order is in the order: 1,4,2,3
The steps to sketch the graph of a rational function will be first to find the function's zeros and vertical asymptotes, and plot them on a number line, the second step is to choose test numbers to t the left and right of each of these places, and find the value of the function at each test number., the third step is to use test numbers to find where the function is a positive and where it is negative and the last step is to sketch the function's graph, plotting additional points as guides as negative.
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Place the steps to sketch the graph of a rational function in the appropriate order.
1)find the function's zeros and vertical asymptotes, and plot them on a number line.
2) use test numbers to find where the function is positive and where it is negative.
3) sketch the function's graph, plotting additional points as guides as negative.
4)choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.
A bank loaned out 20,500, part of it at the rate of 9% annual interest, and the rest at 11% annual interest the total interest earned for both loans was 2,225.00 how much was loaned at each rate
Answers
The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.
Let the amount of money loaned at 9% be x
the amount of money loaned at 11% be y
According to the question,
Total money loaned = 20,500
Thus the equation formed is,
x + y = 20,500 ------ (i)
Simple interest is calculated by
I = P * r * t
where I is the simple interest
r is the rate of interest
t is the time
Thus, the interest on x = 0.09x
the interest on y = 0.11y
Total interest gained = 2,225
Thus the equation formed is,
0.09x + 0.11y = 2225 -------(ii)
Multiply (i) by 0.09
0.09x + 0.09y = 1845
Subtract the above from (ii)
0.02y = 380
y = 19000
x = 1500
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The central angle of a circle measures
97º and intercepts a minor arc. What is
the measure of its major arc?
Answers
Answer:
Step-by-step explanation:
Suppose Mr. and Mrs. Mariano deposited 20,000.00 at the beginning of each year for 5 years in an investment that earns 10% per year compounded annually, what is the amount or future value of the annuity?
Answers
Answer:
₱134,312.2
Step-by-step explanation:
a = 20000(1 + 0.10)^(1 to 5)
Coach Rivera purchases sports equipment. Baseball bats cost $45.00 each, and
baseball gloves cost $20.00 each. He has a budget of $250.00.
Part B: Given the coach's budget, which of the following is a viable option for the
equipment he can purchase?
A: 5 bats and 2 gloves
B: 2 bats and 7 gloves
C: 6 bats and 5 gloves
D: 4 bats and 6 gloves
Answers
-4x+2y=0
10x+3y=8
HELPPPPPPP
Answers
Answer:
x=1/2 y =1
Step-by-step explanation:
(-4x+2y)/2x5=0/2x5
10x+3y=8
(-2x+y)x5=0
10x+3y=8
-10x+5y=0
10x+3y=8
8y=8
y=1
x=1/2
Jennifer works 3 1/2 hours eachmorning at the clinic How manyRoutine physicals could she compete in one morning? Serious injury 1 1/4 hrsDental scaling 3/4 hrs Routine physicals 1/3 hrs.Sick Animal visit 1/2 hrNew patient 3/4 hrs Immunizations 1/4 hrs
Answers
Answer
Jennifer can perform 10 Routine Physicals in the morning
Solution
- The question tells us that Jennifer works 3 1/2 hours each morning and we are asked to find how many Routine physicals she can perform in the morning if 1 Routine physical takes 1/3 hours.
- In order to find the number of Routine physicals that can be performed in 3 1/2 hours, we simply need to assume that Jennifer can perform n number of Routine physicals. That is:
\(\begin{gathered} \text{ Total number of Routine physicals:} \\ \frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\cdots=n\times(\frac{1}{3}) \\ \text{ } \\ \text{ If we take this as the total number of Routine Physicals possible within }3\frac{1}{2}\text{ hours, and r is the number } \\ \text{ of minutes left before }3\frac{1}{2}\text{ hours are completed, we have:} \\ \\ \frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\cdots+r=3\frac{1}{2}=\frac{(3\times2)+1}{2}=\frac{7}{2} \\ \\ \therefore n\times(\frac{1}{3})+r=\frac{7}{2} \end{gathered}\)Thus, to find the number of Routine Physicals, n, we simply make n the subject of the formula:
\(\begin{gathered} n=3(\frac{7}{2}-r) \\ \\ \text{This implies that the number of Routine Physicals is divisible by 3. This means that n is a multiple of 3} \\ \text{Thus, we can test values with multiples of 3.} \\ \\ \text{when n = 3:} \\ 3\times(\frac{1}{3})=1\text{hour} \\ \\ \text{when n= 6}\colon \\ 6\times(\frac{1}{3})=2\text{hours} \\ \\ \text{when n = 9:} \\ 9\times(\frac{1}{3})=3\text{hours} \\ \\ \text{when n= 12:} \\ 12\times(\frac{1}{3})=4hours \\ \\ \text{This implies that the number of Routine Physicals cannot be greater than or equal to 12. It also } \\ \text{implies that the number of Routine Physicals cannot be less than 9 since 9 physicals would take} \\ 3\text{ hours.} \\ \\ This\text{ means that the number of possible hours is between 10 or 11.} \\ \\ when\text{ n = 10:} \\ 10\times(\frac{1}{3})=3+\frac{1}{3}\text{ hours}<3\frac{1}{2}\text{ hours} \\ \\ \text{when n = 11:} \\ 11\times(\frac{1}{3})=3+\frac{2}{3}\text{ hours}>3\frac{1}{2}\text{ hours} \\ \\ \text{Thus, we can conclude that Jennifer can only do 10 Routine Physicals in the morning} \end{gathered}\)Final answer
Jennifer can perform 10 Routine Physicals in the morning
Eric picks 5/8 basket of strawberries. Kiki picks 1/5 basket of strawberries. Which answer is the most accurate estimate for how many more baskets of strawberries Eric picks than Kiki? 0 baskets 1/2 basket 3/4 basket 1 basket
Answers
The number exists described mathematically as a quotient, where the numerator and denominator exist split. Both are integers in a simple fraction. The baskets of strawberries Eric picks than Kiki exists 17 / 40.
What is meant by fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Based on the given conditions, formulate: 5/8 - 1/5
Find common denominator and write the numerators above common denominator: (5 × 5) / (8 × 5) - 8 / (8 × 5)
Calculate the product or quotient: 25 / 40) - (8 / 40)
Write the numerators over the common denominator: (25 - 8) / 40
Calculate the sum or difference: 17 / 40
get the result: 42.5% or 0.425
Therefore, the correct answer is 42.5% or 0.425.
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A ball is drawn randomly from a jar that contains 6 red balls, 2 white balls, and 5 yellow
balls. Find the probability of the given event.
a. A red ball is drawn
b. A white ball is drawn
Answers
Answer:
Hhh
Step-by-step explanation:
Help!
How to get over a huge crush
Answers
Answer:
there are cute boys on Tik-tok or you can try and think about something happy
Step-by-step explanation:
IM BEGGING U HELP Triangle ABC is similar to Triangle GHI. Find the measures of side length z and angle d. Write your answer below as follows:
Answers
Answer:
Side length z = 20 m
Angle d = 53°
Step-by-step explanation:
Since ∆ABC ~ GHI, therefore their corresponding side lengths would be proportional to each other. This implies that the ratio of their corresponding lengths are equal.
This also means that the same scale factor can be multiplied with any side length of ∆ABC to get the corresponding side length of ∆GHI.
The scale factor = HI/BC = 25/10 = 2.5
The side length that corresponds to z is AB which is 8 m long.
z = 8*2.5
✅Side length z = 20 m
Corresponding angles of similar triangles are congruent to each other.
Therefore,
✅Angle d = <I = 53°
Answer:
law of sines
law of cosines
Step-by-step explanation:
find the greatest 4- digit number, which is exactly divisible by 15 . ( hint : subtract remainder from greatest 5 - digit number.)
Answers
The greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720 .
How can the greatest number of four digits be calculated?The concept that will be used in the question is Prime factorization.
We need to acknowledge the greatest four digit number which is 9999 , then to get the required number we can follow these steps:
We will divide the 9999 by LCM of (15,24 and 36 )Then subtract what you get from step 1 from 9999.The Prime factorization of the numbers are:
15 = (3 * 5 )
24 = (2^3 * 3)
36 =( 2^2 * 3^2)
Then the LCM (15,24,36)= 2
2^3 * 3^2 * 5 = 360
Then we can Divide 9999 by 360, having the 279 as remainder.
Then (9999 - 279) = 9720
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Complete question:
Find the greatest number of four digits which is exactly divisible by 15, 24 and 36
I need help finding x
Answers
Answer:
x ≈ 24.4
Step-by-step explanation:
Since the 2 legs of the triangle are congruent, both 26, then the triangle is isosceles.
The line segment x is a perpendicular bisector and divides the isosceles triangle into 2 congruent right triangles, with base 18 ÷ 2 = 9
Using Pythagoras' identity in either of the 2 right triangles, then
x² + 9² = 26² , that is
x² + 81 = 676 ( subtract 81 from both sides )
x² = 595 ( take the square root of both sides )
x = \(\sqrt{595}\) ≈ 24.4 ( to the nearest tenth )