The solution to the system is (x, y, z) = (6, 0, -2).
To solve the system, we can use the elimination method. First, we will eliminate x from the second and third equations by adding the first equation to them:
{5y - 10z = 20
{-3y + 4z = -8
Next, we will eliminate y from the second and third equations by subtracting the second equation from the third equation:
{15y - 30z = 60
{15y + 20z = -40
{-10z = 20
Now we can solve for z:
z = -2
Next, we can substitute z back into the second equation to solve for y:
5y - 10(-2) = 20
2y + 20 = 20
2y = 0
y = 0
Finally, we can substitute z and y back into the first equation to solve for x:
2x + 3(0) - 4(-2) = 20
2x + 8 = 20
2x = 12
x = 6
So the solution to the system is (x, y, z) = (6, 0, -2).
For more information about equation, visit:
https://brainly.com/question/22688504
#SPJ11
DefineT:R2→R2byT(x)=T−([x1x2])=[3x1−−2x22x2]- a) Letu=[u1u2]andv=[v1v2]be two vectors inR2and let c be any scalar. Prove thatTis a linear transformation. - b) Find the standard matrixAofT. - c) Is T one-to-one? Prove your answer using the matrix A.
a)T(u) + T(v) T is a linear transformation
b)[3 -2 ; 2 0]
c)T is one-to-one.
a) To prove that T is a linear transformation, we need to show that it satisfies two conditions.
1. Additivity: T(u + v) = T(u) + T(v)
Let u = [u1, u2] and v = [v1, v2], then
T(u + v) = T([u1 + v1, u2 + v2]) = [3(u1 + v1) - 2(u2 + v2), 2(u2 + v2)]
= [3u1 - 2u2 + 3v1 - 2v2, 2u2 + 2v2]
= [3u1 - 2u2, 2u2] + [3v1 - 2v2, 2v2]
= T(u) + T(v)
2. Homogeneity: T(cu) = cT(u)
Let u = [u1, u2] and c be any scalar, then
T(cu) = T([cu1, cu2]) = [3cu1 - 2cu2, 2cu2] = c[3u1 - 2u2, 2u2]
= cT(u)
Therefore, T satisfies both conditions, and is a linear transformation.
b) The standard matrix of T is the matrix A = [3 -2 ; 2 0]
c) To determine whether T is one-to-one, we look at the matrix A. Since the matrix A has a non-zero determinant, which is equal to -4, then T is one-to-one.
Learn more about matrix
brainly.com/question/29132693
#SPJ11
the quotient and remainder using long division for: (2x^(3)-6x^(2)+7x-11)/(2x^(2)+5)
The quotient and remainder using long division for [tex](2x^(3)-6x^(2)+7x-11)/(2x^(2)+5)[/tex] are x-11/2 and 55/2x-11, respectively.
The quotient and remainder using long division for the given expression can be found by following these steps:
Step 1: Set up the long division as follows:
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |---------------------- |```[/tex]
Step 2: Divide the first term of the dividend (2x^(3)) by the first term of the divisor (2x^(2)) to get the first term of the quotient (x):
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |---------------------- | x```[/tex]
Step 3: Multiply the first term of the quotient (x) by the divisor (2x^(2)+5) and subtract the result from the dividend:
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |-(2x^(3)+5x) |---------------------- | -11x^(2)+7x-11```[/tex]
Step 4: Repeat steps 2 and 3 until the degree of the remainder is less than the degree of the divisor:
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |-(2x^(3)+5x) |---------------------- | x -11x^(2)+7x-11 | -(-11x^(2)-55/2x) |---------------------- | 55/2x-11```[/tex]
Step 5: The final result is the quotient and remainder:
[tex]```Quotient = x-11/2Remainder = 55/2x-11```[/tex]
To know more about long division refer here:
https://brainly.com/question/28824872
#SPJ11
The number e is the base of the ____________?
natural logarithm
decimal system
irrational number system
rational functions
Answer: C.
Step-by-step explanation:
The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 3 3/4 inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 5 1/4 inches apart on the map. The scale on the map is 12 inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville?
the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.
What is the distance in math?
As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
Smithville to Jonesville distance in map = 3(3/4) inches = (15/4) inches .
given that,
(1/2) inch = 4 miles .
1 inch = 8 miles .
Distance from Smithville to Jonesville = (15/4) * 8 = 30 miles .
similarly,
Jonesville to Clarksville distance in map = 5(1/4) = (21/4) inches .
Distance from Jonesville to Clarksville = (21/4) * 8 = 42 miles .
The actual distance the Patel family will travel by the time they reach Clarksville = 30 + 42 = 72 miles
Hence, the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.
Learn more about distance, by the following link.
https://brainly.com/question/26046491
#SPJ1
Find the average rate of change of the given function on the
interval [5,10].
h(x)=3x2+6x−7
The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.
The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is calculated by taking the change in the y-value (h(10) - h(5)) and dividing it by the change in the x-value (10-5):
Average rate of change = (h(10)-h(5))/(10-5)
= (3(10)2+6(10)-7 - (3(5)2+6(5)-7))/(10-5)
= (745-272)/5
= 473/5
= 94.6
Therefore, the average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.
Learn more about average rate of change here:
https://brainly.com/question/28744270#
#SPJ11
as fast as you can answer what is 880,372-751,684 ?
Answer:
128688
Step-by-step explanation:
I need help pls pls pls pls help quickly.
The length of the diagonal of this square is 11 and option 4 is the correct answer.
What is diagonal?A diagonal line is a line segment that joins two of a shape's vertices when there isn't already an edge between them. It doesn't go directly above, below, or across. The diagonals are always in the form of a straight line. In other terms, a diagonal is a line that passes through the vertex of a polygon or polyhedron and links its opposing corners.
Given that, x is the length of the diagonal of the square.
Also, x² = 132
The value of x is:
x = √132
x = 11.48
Hence, the length of the diagonal of this square is 11 and option 4 is the correct answer.
Learn more about diagonals here:
https://brainly.com/question/12274248
#SPJ1
1 Select the correct answer. What is the simplified form of this expression? (-3x² + 4x) + (2x²-x-11)
a. -x2 + 5x − 11
b. -x² + 3x - 11
c. -x² + 3x + 1
d. -x2 + 5x + 11
Blynomials: Mastery Test
The value of the given expression is - x² + 3x - 11 and option b is the correct answer.
What is binomial expression?Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form. Therefore, A binomial is a two-term algebraic statement that includes a constant, exponents, a variable, and a coefficient.
The given expression is:
(-3x² + 4x) + (2x²-x-11)
-3x² + 4x + 2x² - x - 11
Subtract the like terms:
- x² + 3x - 11
Hence, the value of the given expression is - x² + 3x - 11 and option b is the correct answer.
Learn more about binomial expression here:
https://brainly.com/question/29859755
#SPJ9
A study considered the effect of prednisolone on severe hypercalcemia in women with metastatic breast cancer (B. Kristensen et al., J. Intern. Med. 232: 237-245, 1992). Of 30 patients, 15 were randomly selected to receive prednisolone. The otheir 15 formed a control group. Normalization in their level of serum-ionized calcium was achieved by 7 of the treated patients and none of the control group. Obtainia 95% confidence interval for the odds ratio using (a) the Wald interval and (b) the profile likelihood. In each case, note the effect of the zero cell count.
The Wald Interval: Wald intervals can be used to obtain interval estimates for a parameter such as an odds ratio. Wald intervals can be used for normally distributed data, and for large samples, they can be used for binary data. Wald intervals are used to calculate confidence intervals.Using the Wald interval, the odds ratio and its 95% confidence interval are given by the formula which is as follows:OR=Odds ratioZ_α/2=Z-value of a normal distribution at a level α/2 of significance SE=Standard errorOR=1.0599, Z_α/2=1.96, and SE=0.5704 can be obtained from the data in the table. Odds ratio (OR) is the ratio of the odds of an outcome in the treatment group compared to the odds of that outcome in the control group. The odds ratio indicates the likelihood of the outcome occurring in one group compared to the likelihood of it occurring in the other. In this case, OR=1.0599.Profile Likelihood: Profile likelihood is an approach that can be used to construct a confidence interval. The profile likelihood is a way of eliminating nuisance parameters, which are parameters that are not of direct interest but are necessary for calculating the parameter of interest. A confidence interval for the parameter of interest can be calculated using the profile likelihood.The odds ratio and its 95% confidence interval can be obtained using the profile likelihood.The odds ratio (OR) is given by the formulaOR=exp[θ], where θ is the natural logarithm of the odds ratio. In this case, OR=1.0599.The 95% confidence interval is obtained by finding the values of θ that correspond to the 2.5th and 97.5th percentiles of the distribution of the profile likelihood ratio test statistic. The profile likelihood ratio test statistic is defined as twice the difference in the log-likelihoods between the model with the parameter of interest fixed at its maximum likelihood estimate and the model with the parameter of interest estimated.The effect of the zero cell count on the confidence interval is that it makes the interval wider. When a cell count is zero, the odds ratio cannot be calculated, which can lead to a larger standard error and a wider confidence interval.
HELPPPPPP ASAP PLEASEEEEEEE
Answer:
Step-by-step explanation:
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, to find the interval of hours that represents the lifespan of the middle 68% of light bulbs, we need to find the interval that is one standard deviation away from the mean in either direction.
Since the mean is 1400 hours and the standard deviation is 50 hours, we can use the following formula to find the interval:
(mean - standard deviation, mean + standard deviation)
Plugging in the values, we get:
(1400 - 50, 1400 + 50)
Simplifying, we get:
(1350, 1450)
Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is from 1350 hours to 1450 hours.
Answer:
(1350,1450)
Step-by-step explanation:
The Empirical Rule states that 68% of data points fall within one standard deviation of the mean. So, subtract 50 from the mean and add 50 to the mean to find the lifespan of the middle 68% of bulbs.
1. In a dart tournament, the probabilities John,Sam and Grey will hit the target are 3/4, 1/2 and 4/5, respectively. Assuming the events each of them hits the target are independent, find the probability that
a) all three of them hit the target
b) none of them hit the target
c) only John hits the target
2. Plastic X has four red and two white marbles. Plastic Y has one green, two red and two white marbles. In a game, a die is thrown first and if the outcome is a number less than 3, a marble is chosen at random from plastic X. Otherwise, a marble is randomly chosen from plastic Y.
Draw a tree diagram to show all the possible outcomes of the game. Hence, find the probability that
a) a red marble is chosen from plastic X.
b) a white marble is chosen from plastic Y.
c) a red marble is chosen.
d) a marble is chosen from plastic Y if it is known that it is red.
1) the probability that all three of them hit the target is 3/10, none of them hit the target 1/40, only John hits the target 3/40, 2) a red marble is chosen from plastic X is 2/9, a white marble is chosen from plastic Y is 4/15, a red marble is chosen is 2/9, a marble is chosen from plastic Y if it is known that it is red is 2/5.
1. a) The probability that all three of them hit the target is the product of their individual probabilities:
P(all three hit the target) = P(John hits the target) × P(Sam hits the target) × P(Grey hits the target)
= (3/4) × (1/2) × (4/5)
= 12/40
= 3/10
b) The probability that none of them hit the target is the product of their individual probabilities of not hitting the target:
P(none hit the target) = P(John doesn't hit the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (1 - 3/4) × (1 - 1/2) × (1 - 4/5)
= (1/4) × (1/2) × (1/5)
= 1/40
c) The probability that only John hits the target is the product of his probability of hitting the target and the other two's probabilities of not hitting the target:
P(only John hits the target) = P(John hits the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (3/4) × (1 - 1/2) × (1 - 4/5)
= (3/4) × (1/2) × (1/5)
= 3/40
2. The tree diagram for this game is as follows:
Die
/ \
/ \
/ \
/ \
/ \
/ \
<3 >=3
/ \ / \
X Y X Y
/ \ / \ / \ / \
R W R W R W R W
a) The probability that a red marble is chosen from plastic X is the product of the probability of the die outcome being less than 3 and the probability of choosing a red marble from plastic X:
P(red from X) = P(die < 3) × P(red from X)
= (2/6) × (4/6)
= 8/36
= 2/9
b) The probability that a white marble is chosen from plastic Y is the product of the probability of the die outcome being greater than or equal to 3 and the probability of choosing a white marble from plastic Y:
P(white from Y) = P(die >= 3) × P(white from Y)
= (4/6) × (2/5)
= 8/30
= 4/15
c) The probability that a red marble is chosen is the sum of the probabilities of choosing a red marble from plastic X and from plastic Y:
P(red) = P(red from X) + P(red from Y)
= (2/9) + (4/15)
= 10/45
= 2/9
d) The probability that a marble is chosen from plastic Y if it is known that it is red is the probability of choosing a red marble from plastic Y divided by the probability of choosing a red marble:
P(Y | red) = P(red from Y) / P(red)
= (4/15) / (2/9)
= 12/30
= 2/5
To learn more about probability here:
https://brainly.com/question/13604758#
#SPJ11
PLEASE HELP ME ITS DUE TODAY
The height of the container if it's a cylinder with a radius of 3 cm is 5 cm.
The cost of coffee is $2.83.
The height of the container if it's a cylinder with a radius of 5 cm is 1.8 cm.
The cost of hot chocolate powder is $9.90.
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Picking a volume of 45π cm³, the height of this container is given by:
h = V/πr²
Height, h = 45π/π3²
Height, h = 5 cm.
For the cost of coffee, we have:
Cost of coffee = 45π cm³ × $0.02
Cost of coffee = $2.83.
When the radius is 5 cm, the height of this container is given by:
h = V/πr²
Height, h = 45π/π5²
Height, h = 1.8 cm.
For the cost of hot chocolate powder, we have:
Cost of hot chocolate powder = 45π cm³ × $0.07
Cost of hot chocolate powder = $9.90.
Read more on cylinder here: brainly.com/question/14060443
#SPJ1
Jeremy has GHC 502. 0. He gave Owiredu 3/10 of his money. How much did he give Owiredu?
The amount ( 3 /10 ) of total money given by Jeremy to Owiredu is equal to GHC 150.6.
Total amount of money with Jeremy in GHC is equal to 502.0
Amount of fraction of the money Jeremy gave to Owiredu is equal to
3 / 10.
Amount of money Jeremy gave to Owiredu is equal to
= ( 3 / 10 ) of GHC 502.0
= ( 3 / 10 ) × GHC 502.0
Multiply 3 to the 502.0 in the given expression we get,
= GHC ( 1506 / 10 )
Divide 1506 by 10 in the given expression we get,
= GHC 150 .6
Therefore, amount of money Jeremy gave to Owiredu is equal to GHC 150.6.
Learn more about money here
brainly.com/question/11395023
#SPJ4
Kendra has $7. 35 in her purse. She needs at least $2. 87 more to buy a special bead. What is the total amount, x, she needs for the bead? Which inequalities can be used to represent the situation?
Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.
To discover the total amount Kendra needs to shop for the special bead, we add the amount she already has in her purse to the amount she needs to shop for the bead:
x = $7.35 + $2.87
x = $10.22
Thus, Kendra needs a total of $10.22 to shop for the special bead.
To represent the scenario as inequalities, we can use the subsequent:
Let y be the amount Kendra wishes to buy the unique bead, then:
Kendra has at least $7.35: y + $7.35 ≥ y
Kendra needs at the least $2.87 more: y + $2.87 ≤ x
Combining these inequalities, we get:
y + $7.35 ≥ y
y + $2.87 ≤ x
Therefore, Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.
Learn more about Inequalities calculations:-
https://brainly.com/question/24372553
#SPJ4
Total number of words which starts and end with the letter N formed from the letter's of the worc NIPUN is
The total number of words which starts and end with the letter N formed from the letters of the word NIPUN is 4
To form words that start and end with the letter N, we need to first fix the letter N at the beginning and end of the word. This leaves us with the letters I, P, and U to arrange in the middle.
There are 3! (3 factorial) ways to arrange these 3 letters, which is equal to 3 × 2 × 1 = 6.
However, we need to divide by the number of times each letter appears in the word, which is 1 for each of the letters I, P, and U.
So the total number of words that can be formed is 6/1/1/1 = 6.
But we only want the words that start and end with the letter N, so we need to divide by the number of times the letter N appears in the word, which is 2.
So the final answer is 6/2 = 3.
Therefore, the total number of words which starts and end with the letter N formed from the letters of the word NIPUN is 3.
Know more about equations
https://brainly.com/question/22688504
#SPJ11
Find x
pls help solve this
The answers are given in the solution below.
What is circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given that, are circles, we need to find the value of x in each of them,
Using the property of circle,
1) ∠ TSU = 1/2(arc LV + arc TU)
98° = 1/2(70° + 25x+1)
196 = 71+25x
25x = 125
x = 5
2) ∠ BAC = 1/2(arc DR + arc CB)
10x-5 = 1/2(4x+18 + 132)
20x-10 = 4x+18+132
16x = 160
x = 10
3) arc FR = 360° - 245°
arc FR = 115°
∠ FSR = 1/2(245-115)
8x+1 = 65
8x = 64
x = 8
4) ∠ EDF = 1/2(arc CF - arc DF)
5x+1 = 1/2(13x+19-4x-5)
5x+1 = 1/2(9x+14)
10x+2 = 9x+14
x = 12
Learn more about circles, click;
https://brainly.com/question/29142813
#SPJ1
Solve the inequality for x.
-2x-2<8
Answer:
x > 5
Step-by-step explanation:
-2x - 2 < 8
-2x < 10
x > 5
So, the answer is x > 5
? QUESTION Use the rational zeros theorem to list all possible rational zeros of the following. h(x)=-2x^(4)+7x^(3)-8x^(2)+9x+3 Be sure that no value in your list appears more than once.
The possible rational zeros of h(x) are 1, -1, 3, -3, 1/2, -1/2, 3/2, and -3/2.
Rational Zeros TheoremAccording to the Rational Zeros Theorem, if a polynomial has any rational zeros, they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
For the given polynomial h(x)=-2x^(4)+7x^(3)-8x^(2)+9x+3, the constant term is 3 and the leading coefficient is -2.
The factors of 3 are 1 and 3, and the factors of -2 are 1, 2, -1, and -2.
Therefore, the possible rational zeros of h(x) are: p/q = ±1/1, ±3/1, ±1/2, ±3/2
Simplifying these values, we get the following list of possible rational zeros:
±1, ±3, ±1/2, ±3/2
So, the possible rational zeros of h(x) are 1, -1, 3, -3, 1/2, -1/2, 3/2, and -3/2.
Be sure to check each of these values by plugging them back into the original polynomial to see if they are actually zeros.
Learn more about rational zero at
https://brainly.com/question/30437062
#SPJ11
If f(x) = 8x and g(x)= 3x-2, find (fg)(x).
The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout calculation and are essential for the development of significant links.
The two functions are given below.
f(x) = 8x
g(x)= 3x - 2
The function (fg)(x) is calculated as,
(fg)(x) = f(x) · g(x)
(fg)(x) = (8x) × (3x - 2)
(fg)(x) = 24x² - 16x
The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
What is the experiment in relation to probability
Answer:
Step-by-step explanation:
The experiment is repeating and recording the result of an event in order to determine the events probability. For example, tossing a coin is an experiment.
Which equation finds the value of x in the triangle below?
Right triangle X Y Z is shown. Side X Z has a length of 12, side Z Y has a length of x, and hypotenuse X Y has a length of z. The angle opposite to side x is 20 degrees.
Cotangent 70 degrees = StartFraction x Over 12 EndFraction
Cotangent 70 degrees = StartFraction 12 Over x EndFraction
Secant 20 degrees = StartFraction x Over 12 EndFraction
Secant 20 degrees = StartFraction 12 Over x EndFraction
we have that
1) cot 70=x/12
Cot 70=[opposite side]/[adjacent side]=x/12
The option 1 is correct
2) cot 70=12/x
Cot 70=[opposite side]/[adjacent side]=x/12
The option 2 is not correct
3)sec 20=x/12
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 3 is not correct
4) sec 20=12/x
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 4 is not correct
the correct value is
1) cot 70=x/12
Which of the following scenarios does not represent an impulse purchase?
Melissa goes to get a $60 oil change and soon after decides to have her car windows tinted for $300 using her credit card.
Melissa goes to get a $60 oil change for her car but chooses to spend her money on $500 new car stereo speakers instead.
Melissa goes to get an oil change for her car but decides to save the $60 and ask her brother do the oil change for free.
The scenario that does not represent an impulse purchase is: Melissa goes to get an oil change for her car but decides to save the $60 and ask her brother to do the oil change for free.
An impulse purchase is an unplanned purchase made on the spur of the moment, without much consideration or planning. In the first scenario, Melissa goes to get an oil change but then decides to have her car windows tinted for $300, which is an additional expense that she had not planned for. This is an impulse purchase.
In the second scenario, Melissa goes to get an oil change but then decides to spend $500 on new car stereo speakers, which is again an additional expense that she had not planned for. This is also an impulse purchase.
However, in the third scenario, Melissa decides to save the $60 and ask her brother to do the oil change for free. This decision does not involve any additional expense or impulse purchase. Instead, it is a planned decision to save money by getting the oil change done for free. Therefore, this scenario does not represent an impulse purchase.
Answer:
Below
Step-by-step explanation:
The last choice is not an impulse purchase.....it is not a purchase at all.
the first two ARE impulse purchases.... she purchases something for which she initially had no intention.
For the given polynomial, first simplify, if possi trinomial, or none of these. 3m^(7)-9m^(5)+2m^(7)-4m^(6)
The final polynomial after simplifying 3m^(7)-9m^(5)+2m^(7)-4m^(6) is 5m⁷-9m⁵-4m⁶.
To simplify the given polynomial, we need to combine like terms. Like terms are terms that have the same variable and exponent.
The given polynomial is: 3m⁷-9m⁵+2m⁷-4m⁶
First, let's identify the like terms:
- 3m⁷ and 2m⁷ are like terms
- -9m⁵ and -4m⁶ are not like terms because they have different exponents
Next, let's combine the like terms:
- 3m⁷ + 2m⁷ = 5m⁷
So, the simplified polynomial is: 5m⁷-9m⁵-4m⁶
This polynomial cannot be further simplified, so it is none of the options listed (binomial, trinomial, or none of these).
To know more about binomial click on below link:
https://brainly.com/question/13870395#
#SPJ11
You score a goal on the Wayne High School Practice Field at an angle of 58 828 degrees from the sideline. You measure the length of where you scored to the sideline at 88 1 feet Based on the below triangle, what would the distance from where you taunched the ball to the goal be? (in other words solve for distance x in triangle below where the red line is x 58.828 tegrees, 88.1 feet, x = (Use the built in calculator in right sidebar to answer Make sure the setting is on Deg on top left of calculator for degrees) Round your answer to nearest tenth feet
x = _____ feet.
The distance from where you launched the ball to the goal is 52.6 feet.
The goal of this problem is to find the distance x from where you launched the ball to the goal. To do this, we can use the trigonometric function tangent. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the distance from where you scored to the sideline (88.1 feet) and the adjacent side is the distance we are trying to find (x).
So, we can set up the equation:
tan(58.828) = 88.1/x
Next, we can cross multiply to get:
x*tan(58.828) = 88.1
Then, we can divide both sides by tan(58.828) to get:
x = 88.1/tan(58.828)
Using the built-in calculator in the right sidebar, we can plug in the values and make sure the setting is on Deg for degrees. This gives us:
x = 88.1/1.6767
Finally, we can round our answer to the nearest tenth of a foot to get:
x = 52.6 feet
So, the distance from where you launched the ball to the goal is 52.6 feet.
Learn more about Distance
brainly.com/question/15172156
#SPJ11
Solve this system of equations using the substitution method.
y = 2x+17
y = 6x - 3
Answer:
this is awnser
Step-by-step explanation:
Answer:
X=5 y=27
Step-by-step explanation:
2x+17=6x-3
Take away 2x both sides
17=4x-3
Add 3 to get x on one side
20=4x
20/4 =5
x=5
Subsitute 5 in, 6 x 5 = 30 30-3=27
Jack is going to buy a hat that is marked as 50% off. The original price was $27.
What is the dollar value of the discount? Give your answer in dollars to the nearest cent.
Discount= $
determine the base of a parallelogram with height 6
feet and area 15 square feet.
To determine the base of a parallelogram, we can use the formula for the area of a parallelogram, which is A = b*h, where A is the area, b is the base, and h is the height.
We are given the height (h) and the area (A), so we can rearrange the formula to solve for the base (b):
b = A/h
Substituting the given values for A and h:
b = 15/6
Simplifying:
b = 2.5
Therefore, the base of the parallelogram is 2.5 feet.
To know more about parallelogram refer here:
https://brainly.com/question/29147156
#SPJ11
subtract as indicated. Express your answer as a single polynomial in ste 5(x^(3)+x^(2)-3)-2(2x^(3)-2x^(2))
The answer as a single polynomial is x^(3) + 9x^(2) - 15.
To subtract the two polynomials as indicated, we need to distribute the constants in front of each polynomial and then combine like terms.
First, we distribute the 5 and -2 to each term in the respective polynomials:
5(x^(3)) + 5(x^(2)) - 5(3) - 2(2x^(3)) - 2(-2x^(2))
Simplifying each term gives us:
5x^(3) + 5x^(2) - 15 - 4x^(3) + 4x^(2)
Next, we combine like terms by adding the coefficients of each term with the same exponent:
(5x^(3) - 4x^(3)) + (5x^(2) + 4x^(2)) - 15
Simplifying the coefficients gives us:
x^(3) + 9x^(2) - 15
Therefore, the answer as a single polynomial is x^(3) + 9x^(2) - 15.
Learn more about polynomials
brainly.com/question/11536910
#SPJ11
Jaicee's mom says she has an hour before bed. Jenny spends 1/3 of the hour texting a friend and 1/4 of the time brushing her teeth and putting on pajamas. She spends the rest of the time reading her book. How many minutes did Jaicee read.
Answer:
Jaicee (Jenny?) can spend 25 minutes reading.
Step-by-step explanation:
1 hour is 60 minutes.
Multiply to find
1/3 of 60 minutes.
1/3 × 60
= 60/3
= 20
She spends 20 minutes texting.
Multiply to find 1/4 of 60 minutes.
1/4 × 60
= 60/4
= 15
She spends 15 minutes brushing teeth and putting on pajamas.
Subtract 20 and 15 from 60, to see what's left.
Used up time:
20 + 15
= 35
She used up 35 minutes texting and prepping for bed.
60 - 35
= 25
She has 25 minutes left for reading.
f(x)=x4−19x3+135x2+2- Fiat the toe crical nambersa,boff′(that is, the values at whichf′′′is zero or undetined) and lat thoir euact values in tho fiet colume of the tibie below (a ancendeng order,a
The critical numbers of f''(x) are 5 and 4.5.
To find the critical numbers of f(x), we need to first find the derivative of f(x) and then set it equal to zero. The derivative of f(x) is f'(x) = 4x3 - 57x2 + 270x. Setting this equal to zero gives us:
4x3 - 57x2 + 270x = 0
Factoring out an x gives us:
x(4x2 - 57x + 270) = 0
Using the quadratic formula, we can find the values of x that make this equation true:
x = (-(-57) ± √((-57)2 - 4(4)(270)))/(2(4))
x = (57 ± √(3249 - 4320))/8
x = (57 ± √(-1071))/8
x = (57 ± i√1071)/8
Since the values of x are complex, there are no real critical numbers of f(x).
The second derivative of f(x) is f''(x) = 12x2 - 114x + 270. Setting this equal to zero gives us:
12x2 - 114x + 270 = 0
Using the quadratic formula, we can find the values of x that make this equation true:
x = (-( -114) ± √((-114)2 - 4(12)(270)))/(2(12))
x = (114 ± √(12996 - 12960))/24
x = (114 ± √36)/24
x = (114 ± 6)/24
x = 5 or x = 4.5
The table below shows the critical numbers of f(x) and f''(x) in ascending order:
| Critical Number | f(x) | f''(x) |
|-----------------|------|--------|
| 4.5 | N/A | 0 |
| 5 | N/A | 0 |
To know more about derivative click on below link:
https://brainly.com/question/25324584#
#SPJ11
