The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
What do you mean by Polynomial?In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.
For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.
The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:
±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2
To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:
x = 1/2, x = 1, x = 3/2, x = 2
Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
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You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To volume to fill the rectangular garden is 8.99 cubic yard
What is the volume to fill the gardenTo determine the volume of amount of sand required to fill the garden, we can simply convert the dimensions from inches and feet into yard.
inch to yard
6 inch = 0.17 yard
Feet to yard
28 feet = 9.33 yard
17 feet = 5.67 yard
The volume of the rectangular garden is given as;
v = l * w * h
l = lengthw = widthh = heightSubstituting the values;
V = 0.17 * 9.33 * 5.67
v = 8.99 cubic yard
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Consider the system of equations.
y = -5x-1
y = 2x+6
Choose the correct answer to each question.
What is the slope of the first line?
What is the slope of the second line?
How many times do the lines intersect?
C
How many solutions does the system have?
C
subtract 1/2h - 1 from 3/4h + 4
Answer:
= -1+12h.
Step-by-step explanation:
I guess my answer is correct
What needs to be done to an equation to find the slope and y intercept??
NEED HELP ASAP
Answer:
C. Solve for the variable y.
Step-by-step explanation:
You want to know what needs to be done to an equation to find the slope and y-intercept.
Slope-intercept formThe slope-intercept form of the equation for a line is ...
y = mx + b
This is a polynomial equation written in standard form with the terms in decreasing order of the power of the variable. In this equation, the coefficient 'm' is the slope of the line, and the constant 'b' is the y-intercept on the graph.
This equation can be obtained from other forms of the equation for a line by solving for y and arranging the terms to match this form. That is, to find the slope and y-intercept, what needs to be done is ...
C. Solve for the variable y.
__
Additional comment
The description "standard form" as used above applies to polynomials in general. Specific polynomial equations, as for lines, circles, ellipses, hyperbolas, have their own "standard form."
The form called "standard form" for a linear equation is ...
ax +by = c
where a, b, c are mutually prime integers with a > 0. In the case of a horizontal line, b > 0.
<95141404393>
2. Sam spent $15 at an art store on paints, brushes, and paper. The paints cost $7.75 and the
brushes cost $3. Write and solve an equation you could use to find how much Sam spent on
paper.
A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in 4 years?
• $50,000
• $500
• $125
• $12,500
[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]
_____________
[tex] \: [/tex]
Given:-
[tex] \rm{Principal= \bold {5000}}[/tex][tex] \rm{Time= \bold 4}[/tex][tex] \rm{Intrest Rate= \bold { 2.5}}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]
[tex] \: [/tex]
Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI= \frac{50 \cancel{00}×4×2.5}{1 \cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=50×4×2.5}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \rm{ \red{SI= 500}}}}[/tex][tex] \: [/tex]
hope it helps!:)
Answer: the answer is c.$500 hope that helps !
Step-by-step explanation: I took the test
Consider the line 9x-8y=-9.
Find the equation of the line that is parallel to this line and passes through the point (−3, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 4).
Equation of parallel line:
Equation of perpendicular line:
1
=
X
0=0
5
Simplify the following expression using rational exponents. Assume all variables are positive.
(4y2/5)^2
A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.
What is meant by rational exponent?Exponents that are fractions with the denominator a root and the numerator a power are known as rational exponents. For instance, 813 is another method to write 38, while 1612 is another way to write 16. A fractional exponent is a rational exponent. For instance, the number 4 can be written as 412 4 1 2. Though they can be challenging to use at first, rational exponents can actually make some issues simpler.The ability to express rational exponents in pq form as opposed to irrational exponents in pq form is one of the key distinctions between the two types of exponents. Rational exponents are rational numbers, whereas irrational exponents are infinite or non-repeating decimals.Given,
[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]
Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]
[tex]$=\frac{16 y^4}{5^2}[/tex]
The we get,
[tex]$& =\frac{16 y^4}{25}[/tex]
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if f (x) equals 3 (x+4), find f (2)
Answer:
f(2) = 18
Step-by-step explanation:
If f(x) = 3 * (x + 4)
Than f(2) = 3 * (2 + 4) (coz x is an argument)
f(2) = 3 * (2 + 4)
f(2) = 3 * 6
f(2) = 18
Can someone help me with the step by step solutions to these? Thanks
Answer:
c. √2/30
f. 13√3/14
i. -11√10/24
Step-by-step explanation:
You want the sums of the fractions shown.
Sum of fractionsTwo fractions can be added like this:
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]
If the denominators have a common factor (k), then this can be reduced to ...
[tex]\dfrac{a}{bk}+\dfrac{c}{dk}=\dfrac{ad+bc}{bdk}[/tex]
The product bdk is the least common denominator when k is the greatest common factor.
Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.
c[tex]\dfrac{\sqrt{2}}{5}-\dfrac{\sqrt{2}}{6}=\sqrt{2}\left(\dfrac{1}{5}-\dfrac{1}{6}\right)=\sqrt{2}\cdot\dfrac{6-5}{5\cdot6}=\boxed{\dfrac{\sqrt{2}}{30}}[/tex]
f[tex]\dfrac{3\sqrt{3}}{7}+\dfrac{\sqrt{3}}{2}=\sqrt{3}\left(\dfrac{3}{7}+\dfrac{1}{2}\right)=\sqrt{3}\cdot\dfrac{3\cdot2+7}{7\cdot2}=\boxed{\dfrac{13\sqrt{3}}{14}}[/tex]
iThe denominators have a common factor of 2: 6=3·2, 8=4·2.
[tex]\dfrac{-5\sqrt{10}}{6}+\dfrac{3\sqrt{10}}{8}=\sqrt{10}\left(\dfrac{-5}{6}+\dfrac{3}{8}\right)=\sqrt{10}\cdot\dfrac{-5\cdot4+3\cdot3}{3\cdot4\cdot2}=\boxed{-\dfrac{11\sqrt{10}}{24}}[/tex]
can someone pls give me the percent equation to these? 100 points to the fellow that does and brainiest if correct. Also pls hurry, its due today
6.5% of $400 is
what number?
12.5% of $100 is
what number?
130 is what percent
of 650?
$5.40 is what
percent of $4.50?
$8.40 is what
percent of $28?
56% of what
number is $21.84?
$495 is 55% of
what number?
120 is what percent
of 400?
4% of 975 is what
number?
Answer:
Step-by-step explanation:
You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.
Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.
I used x to represent what we are looking for:
6.5% of $400 = x
0.065 * 400 = $26
12.5% of 100 = x
0.125 * 100 = $12.5
x of 650 = 130
130/650 = 0.2 which equals 20%
x of $4.50 = $5.40
5.40/4.50 = 1.2 which equals 120%
x of $28 = $8.40
8.40/28 = 0.3 which equals 30%
56% of x = $21.84
21.84/0.56 = 39
55% of x = $495
495/0.55 = 900
x of 400 = 120
120/400 = 0.3 which equals 30%
4% of 975 = x
0.04 * 975 = 39
Answer:
See below
Step-by-step explanation:
a. 6.5% of $400:
[tex]= \frac{65}{100}[/tex]× ($400)
= $260
b. 12.5% of $100:
[tex]= \frac{12.5}{100}[/tex] × ($100)
= $12.5
c. 130 is what percent of 650:
[tex]=\frac{130}{650}[/tex]×100%
= 20%
d. $5.40 is what percent of $4.50:
[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%
e. $8.40 is what percent of $28:
[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%
f. 56% of what number is $21.84:
=[tex]\frac{56}{100}[/tex]× number = $21.84
∴ Number = [tex]\frac{100}{56}[/tex]×$21.84
= $39
g. $495 is 55% of what number:
= $495 = [tex]\frac{55}{100}[/tex]× Number
∴Number = [tex]\frac{100}{55}[/tex]×($495)
= $900
h. 120 is what percent of 400:
= [tex]\frac{120}{400}[/tex]×100%
= 30%
i. 4% of 975 is what number:
= [tex]\frac{4}{100}[/tex]×975
= 39
In the diagram, RSTU~ ABCD. Find the ratio of their perimeters.
U
R
18 S
36
T
D
A
24
The ratio of their perimeters is
B
C
Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.
Since UR = 18 and DA = 24, k = 24/18 = 4/3.
So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.
Now that we have the lengths of all sides of ABCD, we can find its perimeter:
Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC
Perimeter of RSTU = 18 + 36 + 18 + 36 = 108
So the ratio of their perimeters is:
Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108
Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:
20/18 + BC/108 = 4/3
Solving for BC:
BC = (4/3 - 20/18) * 108 = 36
Step-by-step explanation:
Please help!! Due tomorrow morning!!
Directions: if QS represents an angle bisect or, solve for x.
(Ignore my answer)
The solution for x in the triangle is x = 52.5
How to solve for x in the triangle?
The bisector of an angle in a triangle divides the opposite side in the ratio of the sides containing the angle. That is:
PQ/QR = PS/SR
PQ = x, QR = 35, PS = 42 and SR = 70 - 42 = 28.
Therefore, we have:
PQ/QR = PS/SR
x/35 = 42/28
28*x = 42*35
28x = 1470
x = 1470/28
x = 52.5
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I need the first one
Answer:
∠1 = ∠2 = 135
Step-by-step explanation:
We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180° = 3 x 180°= 540°. Hence, the sum of interior angles of a pentagon is 540°.
so ∠1 + ∠2 + 3(90°) = 540°
since ∠1 = ∠2
∠1 + ∠1 + 3(90) = 540
2∠1 + 270 = 540
2∠1 = 540 - 270
2∠1 = 270
∠1 = 270/2 = 135
Costs of Starting Your Own Business
SHORT ANSWER
You are looking at a potential location to open your first spa. The rent is $21 per square
(annually), and the space is 1,800 square feet. How much rent would you pay each year? Each
foot
month?
The amount of money that would be paid for rent each year for the spa would be = $37,800
How to calculate the annual payment for the rent for spa?The area of the potential space for the opening of your first spa = 1,800 square feet.
The price for each square feet per year = $21
That is; = 1800× 21 = $37,800
Therefore, annual rent fees for the space which will be used for spa = $37,800.
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our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
Given the functions f(x) = x3 + x2 – 2x + 3 and g(x) = log(x) + 2, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
The functions f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2 have same range as (-∞,∞) or {y : y∈R}.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given functions are -
f(x) = x³ + x² - 2x + 3
g(x) = log(x) + 2
The graph for function f(x) is plotted.
The function f(x) is a cubic function.
The domain for the function is (-∞,∞) or {x : x∈R}.
The range for the function is (-∞,∞) or {y : y∈R}.
The x-intercept for the function is (-2.37442376,0).
The y-intercept for the function is (0,3).
The graph for function g(x) is plotted.
The function g(x) is a logarithmic function.
The domain for the function is (0,∞) or {x : x>0}.
The range for the function is (-∞,∞) or {y : y∈R}.
The x-intercept for the function is (0.01,0).
The y-intercept for the function is not available.
Therefore, both functions have same range,
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Which of the following tables of x- and y-values represents a function?
The tables of x- and y-values that represents a function include the following: C. table C.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range) representing a given scenario or situation such as the following:
x 1 3 7 5 2 4
y 6 6 6 6 6 6
In conclusion, we can reasonably infer and logically deduce that only table C represent a function.
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet of water weigh in pounds? In tons?
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
Suddeth Travel estimates that 80% of its employees have more than 12 days of unused sick leave. If 140 employees have more than 12 days of unused sick leave, how many employees work at the agency? A. 112 B. 164 C. 175 D. 700
Answer:
C) 175.
Step-by-step explanation:
Sure, here's a step-by-step solution:
Let's call the number of employees at the agency "x".
If 80% of the employees have more than 12 days of unused sick leave, that means 0.8 * x employees have more than 12 days of unused sick leave.
We know that 0.8 * x = 140, so we can solve for x by dividing both sides of the equation by 0.8:
x = 140 / 0.8
Simplifying, we get:
x = 175
So there are 175 employees who work at the agency, and the answer is C) 175.
Kai, a seventh grader, wants to determine the average number of times the families in his neighborhood visit the pool during the summer. He samples the families of four of his classmates. Which improvements could Kai make to his sample to increase the validity of the results? Check all that apply. Sample more families/ sample families that have children who are not in seventh grade/ sample families that do not have children /sample families whose answer to the survey question is predetermined/ sample families living in every third house in the neighborhood
The correct options are sample more families, sample families having children who are not in seventh grade.
Sample families that do not have children. Sample families living in every third house in neighborhood.
To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:
Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.
Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.
Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.
Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of
sampling bias.
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PLEASE HELP ME ASAP
5. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.
Write a story that could represent this math problem. (2 points)
If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?
I believe that is what type of story you needed, if wrong let me know.
Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6
Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.
for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.
The answer after multiplying it is 6/24 or 1/4.
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What is the Volume of the prism below
Answer:
140
Step-by-step explanation:
(5*7*8)/2= 280/2 =140
Write the following comparison as a ratio reduced to lowest terms. 7 nickels to 47 dimes
7 nickels is 7/5, thus 7 nickels to 47 dime is 1.4 dime to 47 dime.
When both terms are multiplied by their biggest common factor, 1.4 dime, the ratio can be simplified to its simplest form: 47 dimes = 14: 470
What is the ratio?The ratio of quantity, amount, or size of two or more items is known as proportion. It is the indicated quotient of two mathematical expressions.
As a ratio, what is 1 to 2?"1 to 2" is the way to write the ratio 1: 2. Accordingly, of the total of 3, there is one component that is worth 1 and another part that is worth 2. Changing a part-to-part ratio to a fraction To get the whole, add the ratio terms. The denominator should be this.
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How do I do these questions ??
Mary invests £12000 into a savings account. The account 1.5% compound interest per year. Work out the value of her investment after 2 years.
Answer:
Step-by-step explanation:
To calculate the compound interest on Mary's savings account, we can use the formula:
A = P * (1 + r/n)^(nt)
Where:
A is the amount after t years
P is the initial principal (£12000)
r is the interest rate (1.5%)
n is the number of times the interest is compounded in a year (let's assume it's compounded annually)
t is the number of years (2)
So, plugging in the values, we get:
A = £12000 * (1 + 0.015/1)^(1 * 2)
A = £12000 * (1.015)^2
A = £12000 * 1.0302
A = £12363.84
So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.
At a college, the ratio of faculty/staff to students is 3 to 13. If there are 4000
people at the college, how many students are there?
Answer:
Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.
According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:
3x / x = 3 / 13
To find the number of students, we can solve for x:
4x = 4000
x = 1000
So, there are 1000 students at the college.
Jim takes a counter at random from a bag containing 10 counters, numbered
1, 2, ..., 10.
Lyn throws an ordinary dice.
ind the probability that
Jim and Lyn both get a 3
The probability both get a 3 is 1/60
How to determine the probability both get 3From the question, we have the following parameters that can be used in our computation:
Jim = 1 to 10
Lyn = 1 to 6
Using the above as a guide, we have the following:
P(Jim = 3) = 1/10
P(Lyn= 3) = 1/6
Using the above as a guide, we have the following:
Required probability = 1/10 * 1/6
Evaluate the product
Required probability = 1/60
Hence, the probabilty is 1/60
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Question 2 Part A:
An industrial copy machine has the ability to edit image dimensions by reducing it by a certain percentage
each time it copies. A design began with a length of 24 inches, represented by the point (0,24). After going
through the copy machine once, the length is 18, represented by the point (1,18).
Double click and enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)*
In the function, f(x) = a(b)ˣ the value of a and b is
a = 24b = 0.75How to find the value of a and bThe function defined by f(x) = a(b)ˣ is a exponential function
Where
a is the starting function
b is the base function
The starting function from (0,24)
24 = a(b)ˣ
a = 24
using (1, 18), we solve for the base
18 = 24(b)
b = 0.75
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