The zeroes of the function k(x)=15x³-48x²-48x are 0, 4 and -4/5.
The function provided is a cubic polynomial.
There will be three zeroes in total for the function k(x).
K(x) = 15x³-48x²-48x
If we put x = 0,
We can see that k(x) becomes zero,
So we can say that 0 is a solutions for this function,
Now,
K(x) = x(15x²-48x-48)
Solving 15x²-48x-48 seperately using quadratic formula,
a = 15
b = -48
c = -48
x = (-b+√D)/D and (-b-√D)/D
D = b²-4ac.
D = (-48)²-4(15)(-48)
D= 5184.
√D = 72
putting all the values to find x,
x = (-(-48)+72)/30 and (-(-48)+72)/30
x = 4 and -4/5.
our function becomes,
k(x) = x(x-4)(x+4/5)
so the zeroes are 0, 4, -4/5.
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A is shaped like a rectangle whose perimeter is 378ft . The length is 8 times as long as the width. Find the length and the width.
The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.
What is the length and the width of the rectangle?The formula used in calculating the perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width of the rectangle w = xLength of the rectangle l = 8xPerimeter P = 378ftPlug the given values into perimeter formula and solve for x .
P = 2( l + w )
378 = 2( 8x + x )
378 = 2( 9x )
378 = 18x
18x = 378
x = 378/18
x = 21
Now, we find the length and width of the rectangle.
Width of the rectangle w = x = 21ft
Length of the rectangle l = 8x = 8( 21 ) = 168ft
Therefore, the width of the rectangle is 21ft while its length is 168ft.
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If EGF & EGH, EF = 6a, and EH = a + 55, what is the value of a?
Answer:
a=11
Step-by-step explanation:
If both triangles have two sides E and G the same then thethird side F and H must be equal
EF=EH
6a=55+a
5a=55
a=11
linear inequality: y>-2x-3
Answer:
The graph depicting inequality y > -2x - 3 is C
Which property of multiplication is (ab)c = a(bc)
Answer: The Associative Property
Step-by-step explanation:
Example:
[tex]a * (b * c) = (a * b) *c[/tex]
[tex]2 *(4 * 5) = (2 * 4) * 5[/tex]
Write the equation that is parallel to 2x+y =4 going through the point (-1,3)
Answer:
2x +y = 1
Step-by-step explanation:
You want the equation of a line parallel to 2x+y=4 through point (-1, 3).
Parallel lineA parallel line will have the same slope, which is a function of the ratio of the x- and y-coefficients. Hence, the equation of the parallel line can use the same coefficients. It will have a constant suitable for the given point.
given: 2x +y = 4
parallel: 2x +y = c
through point (-1, 3): 2x +y = 2(-1) +(3) = 1
The equation of the parallel line is 2x+y = 1.
Match the following.
The match of the given equations and choices of the properties of equality are;
If a = b and b = c then a = c ; Transitive Property
If a = b then a ÷ c = b ÷ c; Division property of =
a = a; Reflexive property
If x + a = b and x = c then c + a = b; Substitution Property
If a = b then a + c = b + c; Addition Property of =
If a = b then a•c = b•c; Multiplication Property of =
If a•b = a•c then a•c = a•b Symmetric Property
a•(b + c) = a•b + a•c; Distributive property
If a = b then a - c = b - c; Subtraction Property of =
What are the properties of equality?Properties of equality includes; addition, subtraction, transitive, reflexive, and symmetric properties of equality
Transitive PropertyThe transitive property of equality can be stated as follows; If two variables are each equal to a third variable, then the two variables are equal to each other.
Therefore; a = b and b = c then a = c represents the transitive property
Division property of equalityThe division property states that both sides of an equation remain equal, following a division of both sides by the same non zero number
Therefore;
If a = b then a ÷ c = b ÷ c; represents the division property of equality
Reflexive propertyThe reflexive property of equality states that a measure or number is always equal to itself
Therefore;
a = a represents the reflexive property
Substitution PropertySubstitution property indicates that if two variables are equal, then one can replace the other in an equation and the results will remain the same
Therefore;
If x + a = b and x = c then c + a = b; represents the substitution property
Addition and Subtraction Property of EqualityThe statement of the addition (and subtraction) property of equality is that both sides of an equation remain equal following the addition or subtraction of the same amount from both sides the same
Therefore;
If a = b then a + c = b + c; represents the addition property of equality
If a = b then a - c = b - c; represents the subtraction property of equality
Multiplication Property of EqualityThis states that both sides of an equation remain equal following the multiplication of both sides by the same value
Symmetric PropertyThe symmetric property states that two sides of an equation remain equal when their relative positions are interchanged
Distributive PropertyThis states that two sides of an equation remain equal following a distribution with multiplication over addition or subtraction.
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The difference of the ages of a father and his son is 25 years.Fifteen years ago.the father was six times of his son's age. Find their present ages.
Present age of father is 48 years and that of son is 23 years.
Let the age of father be x years
And the son's age be y years
According to the question,
x - y = 25 -----------1
15 Years ago, x= 6( y - 15 )
x= 6y - 90 -------------2
Substituting value of x from equation 2 in equation 1, we get
6y - 90 - y = 25
5y -90 = 25
5y = 25+90
5y= 115
y= 23
Therefore son's age is 23 years and from equation 1 we get x= 25+y = 25+23 = 48 years. So father's age is 48 years.
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in the pic.............
Given -
a = 2.5 cm
b = 3.6 cm
∠A = 43°
To Find -
Remaining angles and sides =?
Step-by-Step Explanation -
We will start by drawing the diagram:
Now, we know
By, sine rule:
[tex]\begin{gathered} \frac{\sin A}{a}\text{ =}\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ =\text{ }\frac{\sin43}{2.5}\text{ = }\frac{\sin C}{3.6} \\ \\ =\text{ }\sin C\text{ = }\frac{3.6\times\sin44}{2.5} \\ \\ =\text{ }\sin C\text{ = 0.9820} \\ \\ C\text{ = }\sin^{-1}(0.9820) \\ \\ C\text{ = 79} \\ \end{gathered}[/tex]Now, we know N
A + B + C = 180 c°°
43 + B + 79° = 180°°
B = 180° - 799 - 43°°
B = 58°
Now, Side b =
[tex]\begin{gathered} \frac{\sin A}{a}\text{ = }\frac{\sin B}{b} \\ \\ \frac{\sin43}{2.5}\text{ = }\frac{\sin58°}{b} \\ \\ b\text{ = }\frac{2.5\times\sin58°}{\sin43°} \\ \\ b\text{ = 3.1} \end{gathered}[/tex]Final Answer -
∠B = 58B°
∠C = 797°
Side, b = 3.1 cm
Determine the more basic function that has been shifted reflected stretched or compressed what does
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
Step 1
iven
[tex]g(x)=-2\sqrt{x-1}+4[/tex]g(x) is a transformation of the function f(x)we have a root in the function, note that the variable x is inside the root, so we can conclude the basic function is
square tooroot
Step 2
rove
ow, lets's check the transformation of f(x)
[tex]f(x)=\sqrt{x}[/tex]a)1 was subtracted form the argument of the fucnction
[tex]\begin{gathered} f(x)=\sqrt{x} \\ f^{\prime}(x)=\sqrt{x-1} \end{gathered}[/tex]when you subtract a number b form the argument of the function you are shifting the function b units to the rigth
so
he function was shifteed 1 unit to rigth
) the resulting function was multiplied by 2-
[tex]\begin{gathered} f^{\prime}(x)=\sqrt{x-1}\text{ *-2} \\ f^{\prime}^{\prime}(x)=-2\sqrt{x-1} \end{gathered}[/tex]when you multplie by a negavitve constant you are reflecting the funciton acrros x-axis, and is is stretched vertically.
so
he funcition was reflected across x-axis an strtched vertically by a factor of 2
c) 4 was added to the function
[tex]\begin{gathered} f^{\prime\prime}(x)=-2\sqrt{x-1} \\ g(x)=-2\sqrt{x-1}+4 \end{gathered}[/tex]when you add a constant b to any function, the graph will be shifted b units up,so
he functinon was shifted 4 units up
hrerefore, we can conclude the answer is
[tex]f(x)=\sqrt{x}[/tex]I hope this helps you
Each question on a multiple choice exam has four choices. One of the choices is the correct answer, worth five points another choice is wrong but still carries partial credit of 1 point and other two choices are worth 0 points. If the student picks answers at random, what is the expected value of his or her score for a problem?
If a student picks randomly then the expected value of his or her score for a problem is 1.5.
Each question on a multiple-choice exam has four choices.
One of the choices is correct, worth four points.
Another choice is wrong but carries partial credit for one point.
The other two choices are wrong and worth a negative one point.
Each has a probability of getting selected is 0.25.
[tex]0.25*5+0.25*1+0.25*0+0.25*0[/tex]
[tex]1.25+0.25[/tex]
[tex]1.5[/tex]
What is the expected value?
The expected value denotes potential. The occurrence of a random event is the subject. Its fundamental notion is that something is probable to occur.
Actually, the anticipated value may be viewed as the mean of a random variable. This indicates that the anticipated value is the average of all the values acquired if a probability experiment were repeated again while keeping track of the outcomes. The anticipated value of a game of chance is what you should expect to occur over the long run of several trials.
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HELP PLEASE WILL GIVE BRAINLIEST!!! I NEED HELP
Answer: y = -x + 3
Step-by-step explanation:
y = mx + b
We need to find the slope of the equation first.
Change in y: 7 - 0 = 7
Change in x: -4 - 3 = -7
Slope = Change in y / Change in x
slope = 7 / -7 = -1
Now, plug the slope into the equation to find b.
0 = -1(3) + b
b = 3
or 7 = -1(-4) + b
b = 3
3. Allison Separates 23 stickers into 4 4 equal piles. How many stickers does she have left over?
Please answer I give Brainliest
Answer:
hmmm
Step-by-step explanation:
what does the j, k, m, and l stand for?
The second angle of a triangle is 10 more than the first angle. The third angle is three times the first. Find the three angles.
First angle:
Second angle:
Third angle:
Answer:
First, let one angle be a variable (eg: x) so that you can form expressions and solve.
Let the first angle be x°.
Then we can form expressions for the second and third angles using the information given.
First angle = x°
Second angle = (x + 10)°
Third angle = (3x)°
Since sum of angles in a triangle is 180°, we can form an equation.
x + (x + 10) + 3x = 180
Simplify and solve for x.
5x + 10 = 180
5x = 170
x = 34
Substitute x into the expressions to find the angles.
First angle = 34°
Second angle = 34 + 10
= 44°
Third angle = 3(34)
= 102°
Each Saturday 8 workers mow the park
lawn. When all 8 workers are there, it takes
them 6 hours to complete the job. Last
Saturday three of the workers had the flu.
How many hours did it take the remaining workers
to complete the job?
A. 9 and %
B. 2 and 14
C. 12 and 18
D. 6 and 2
Please help I’ll mark you as brainliest if correct!!
Answer:The answer is 8
Step-by-step explanation:
21-13
5x-4=-3x+12
What is the answer
The answer is x = 2
I have attached a picture with the work
HURRY
TIME REMAINING
57:30
What are the solutions to –24x – 24 = x3 + 8x2?
Negative 1, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.
1, 3 + i StartRoot 3 EndRoot, 3 minus i StartRoot 3 EndRoot.
2, 3 + i StartRoot 3 EndRoot, 3 minus i StartRoot 3 EndRoot.
Negative 2, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.
Answer:
Negative 2, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.
Step-by-step explanation:
So basically that whole last section you had your answer should look like this:
The new bookkeeper at Karlin Construction Company was asked to write off two accounts totaling $1,610 that had been determined to be uncollectible. Accordingly, he debited Accounts Receivable for $1,6
10 and credited Bad Debt Expense for the same amount.
The thing that is wrong with the bookkeeper’s entry assuming Karlin uses the allowance method is that the company uses allowance method and thus the write-off entry would not be to bad debt account.
How yo illustrate the information?
It should be noted that because the business is using the allowance approach in this instance, the write-off entry would not be to the account for bad debts. To write off an account, a debit must be made to a separate account that is kept as an allowance for dubious accounts.
Since the receivables would not be collected, the accounts receivable account would be credited. In this case,the write off isn't appropriately illustrated in the account.
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The new bookkeeper at Karlin Construction Company was asked to write off two accounts totaling $1,610 that had been determined to be uncollectible. Accordingly, he debited Accounts Receivable for $1,610 and credited Bad Debt Expense for the same amount.
Determine what was wrong with the bookkeeper’s entry assuming Karlin uses the allowance method.
Solve each related rate problem.6) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. Theradius of the spill increases at a rate of 4 m/min. How fast is the area of the spillincreasing when the radius is 7 m?A) 63 m²/min B) 54rt m®/min C) 5211 m²/min D) 560 m²/min7) A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fast
6.
We know area of circle is
[tex]\pi r^2[/tex]Radius increases at a rate of 4.
So, we can write:
[tex]\frac{dr}{dt}=4[/tex]We want rate of change of area. Thus,
[tex]\begin{gathered} A=\pi r^2 \\ dA=2\pi\text{rdr} \\ \frac{dA}{dt}=2\pi r\frac{dr}{dt} \end{gathered}[/tex]We want dA/dt at r = 7, so substituting all that we know:
[tex]\begin{gathered} \frac{dA}{dt}=2\pi r\frac{dr}{dt} \\ \frac{dA}{\text{dt}}=2\pi(7)(4) \\ =56\pi \end{gathered}[/tex]The correct answer: 56*pi m^2/min
Use the table to answer the question. 2 6 10 12 10 30 50 60 Simplify each ratio in the table to prove that all the ratios are equivalent. (2 points) 210= , 630= , 1050= , 1260=
The expression given relating to the take all have an equivalent ratio of 1:5.
How to express the ratio?It should be noted that ratio is simply used to show the comparison between two or or more things.
In this case, in the table, the ratio given will be illustrated as:
2/10 = 1/5 = 1:5
6/30 = 1/5 = 1:5
10/50 = 1/5 = 1:5
12/60 = 1/5 = 1:5
In this case, it should be noted that for every number that was illustrated, we have an equivalent value of 1:5. Therefore, this explains that it's an equivalent ratio.
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20PTS
Please help answer quickly
Answer:
second option
What the area of the sphere if it's volume is 3x +1 cm³
Answer:
[tex]{ \tt{volume = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{v = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{area = \frac{dv}{dr} = 4\pi {r}^{2} }} \\ \\ { \tt{area = \frac{d(3x + 1)}{dx} }} \\ \\ { \tt{area = 3 \: {cm}^{2} }}[/tex]
I'm trying to find out if {(6,0), (-9,5), (1,-5), (0,0)} is a function or not
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In this case, it would be a function
Factor 15cd − 45c ^2d.
3c ^2d(5 − 15)
5cd(3 − 15c ^2d)
3cd(5 − 15c)
5cd(3 − 45c ^2d)
3/2d
DIFFERENTIATE W.R.T. D
3
2
≈0.666666667
Volunteers are preparing identical backpacks for refugees. There are 32 maps and 24 dictionaries to use for the backpacks. What is the greatest number of backpacks they can prepare using all of the maps and dictionaries?
Considering the definition of greatest common divisor, the greatest number of backpacks volunteers can prepare using all of the maps and dictionaries is 8.
Definition of greatest common divisorConsidering that a divisor can be formally defined as that number that is contained in another exactly n times, the greatest common divisor is the largest number by which two or more numbers can be divided. That is, the greatest common factor is the highest number by which a set of numbers can be divided, resulting in a whole number.
To calculate the greatest common factor, the following steps must be followed:
Decompose each number into prime factors. [The prime factors of an integer are the exact divisors of that integer, that is, they have only two divisors: one and themselves]Then point out the common factors.In each of the common factors, choose the factor with the smallest exponent.Multiply the chosen factors.Greatest number of backpacks preparedIn this case, you must calculate the greatest common factor as follows:
Decomposition of 32: 2⁵Decomposition of 24: 2³×32 is the factor common to both numbers, with 3 being the smallest exponent found. Then the greatest common divisor is calculated as:
Greatest common divisor= 2³
Greatest common divisor= 8
This means that they can prepare 8 backpacks.
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Solve for all values of x:
√8x + 1 = √2x + 5
Step-by-step explanation:
[tex] \sqrt{8} x - \sqrt{2} x = 4[/tex]
[tex]x( \sqrt{8} - \sqrt{2} ) = 4[/tex]
[tex]x = \frac{4}{ \sqrt{8} - \sqrt{2} } [/tex]
the second term could be positive or negative
therefore
x=2.83 or
=-2.83
which is the square root of 8 - and positive
A serving of rice is 5/6 of a cup. How many servings are there in a 3 1/3 cup bag of rice?
Answer:
there are 7 severeings of rice
the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55, what is it worth now? Round to the nearest hundredth.
The worth of the share after a 15% fall will be $47.21.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55.
The value of the share after 15% fall will be calculated as:-
Decreased amount = 55.55 - ( 55.55 x ( 15 / 100)
Decreased amount = $47.21
Therefore, the worth of the share after a 15% fall will be $47.21.
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You thought you had finished 35 pages, but you actually read 32 Pages. What was your percent error?
[tex]\frac{35-32}{32} \times 100=\frac{75}{8}=9.375\%[/tex]
Answer:
9.375%
Step-by-step explanation:
Percentage Error formula
[tex]\textsf{Percentage error}=\sf \left|\dfrac{estimated\:value\:-actual\:value}{actual\:value} \right| \times 100\%[/tex]
Given:
Estimated value = 35 pagesActual value = 32 pagesSubstitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Percentage error}&= \left|\dfrac{35-32}{32} \right| \times 100\%\\\\&=\left|\dfrac{3}{32} \right| \times 100\%\\\\&=0.09375 \times 100\%\\\\&=9.375\%\end{aligned}[/tex]
Therefore, the percentage error was 9.375%.