The polynomial p(x) must have at least two zeros, since it has three relative extrema.
What is polynomial?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Here i would think that since there are only 3 critical points given and no other information other than that those are the only critical points that p(x) would not have any real zeros.
At each of the relative extrema, the value of the function changes from increasing to decreasing or vice versa, meaning that the function crosses the x-axis at that point, which is a zero. Therefore, p(x) must have at least two zeros.
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What is the quotient of three and one-third ÷ three-fourths?
A line pae through point (-6,5) and ha a lope of 2. Write an equation in AxBy=C form for thi line
The standard form of the linear equation of a straight line is given as
2x - y + 17 = 0
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
y=mx+c; where y and x stand for the respective axis's; 'm' represents the slope while 'c' represents the constant.
Let the point through which the line passes be P
Then, P= (-6,5)
m= 2
The equation of a straight line as a single point form can be found using the formula:
y-y1=m(x-x1)+c
y-(5) = 2(x-(-6))+c
y -5= 2(x+ 6)+c
Taking LCM
y - 5 =2(x+6)
on cross multiplying we get:
y - 5 = 2x + 12
y = 2x + 12 + 5
2x - y + 17 = 0
Thus, Equation of the line comes out to be 2x - y + 17 = 0
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Mae Ling earn a weekly alary of $360 plu a 7. 5% commiion on ale at a gift hop. How much would he make in a work week if he old $4,500 worth of merchandie?
He will make $697.5 in a work week if he sold $4500 worth of merchandise.
Mea Ling earn a weekly salary of $360 which means salary per week is $360.
Then plus a 7.5% commission on sales at a gift shop if she sold $4,500 worth of merchandise, which means additional.
Divide by 100. Most interest rates are quoted and advertised in terms of a percentage.
7.5%= 0.075
Multiplication In mathematics, multiplication (denoted by ‘ × ’) is a method of finding the product of two or more values.
In arithmetic, multiplication of two numbers represents the repeated addition of one number with respect to another.
0.075×4500= 337.5
Then total she make will be
337.5+360
= $697.5
Therefore, he will make $697.5 in a work week.
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Solve the equation by using the quadratic formula. 3 x squared minus 1 = 5 x a. startfraction 5 startroot 13 endroot over 6 endfraction, startfraction 5 minus startroot 13 endroot over 6 endfraction b. startfraction negative 5 startroot 13 endroot over 6 endfraction, startfraction negative 5 minus startroot 13 endroot over 6 endfraction c. startfraction negative 5 startroot 37 endroot over 6 endfraction, startfraction negative 5 minus startroot 37 endroot over 6 endfraction d. startfraction 5 startroot 37 endroot over 6 endfraction, startfraction 5 minus startroot 37 endroot over 6 endfraction
The solution to the quadratic equation 3x²-1 = 5x by formula method is
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable of x . It is expressed as ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
In the equation 3x²-1= 5x
we put the equation in standard form. i.e 3x²- 5x -1 = 0
therefore a = 3 , b = -5 and c = -1
formula method is a method of solving the root of a quadratic equation. It is given by x = (-b±√b²-4ac)/2a
=(-(-5±√-5²-4×3×-1)/2×3
=(5±√25+12)/6
=(5±√37)/12
x = 5+6.1/12 or
x= 5-6.1/12
therefore x = 11.1/12 or -1.1/12
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Answer: it's d.
StartFraction 5 + StartRoot 37 EndRoot Over 6 EndFraction, StartFraction 5 minus StartRoot 37 EndRoot Over 6 EndFraction just took the test
What is the answer to 26.52x14
Answer: 371.28
I hope that this helps! :)
Answer: 371.28
Step-by-step explanation: hope it helps mark brainlist if helpful
Kayla pays 18% of her earnings in taxes. This week she earns a total of $1,200. Kayla wants
to know how much of her earnings are left over after taxes are paid.
How much does Kayla pay in taxes?
Answer:
She has $984.00 left after taxes.
She pays $216.00 in taxes
Step-by-step explanation:
1200 x .18 = 216
She pays $216.00 in taxes
1200 - 216 = 984
She has $984.00 left after taxes.
Fill in the missing parts. 1/7 of...is 1/35
Answer:
1/5
Step-by-step explanation:
of: *
is: =
1/7 * x = 1/35
Multiply by 7 on both sides.
7(1/7x) = 7(1/35)
x = 1/5
gallup political polls ask people their political party affiliation- democrat, republican, or independent. which level of measurement is used to measure party ? nominal ordinal interval ratio
In Gallup political polls, respondents are asked which political party they identify with: independent, democratic, or republican. Nominal level of measurement is used to measure party
Nominal level of measurement is used when assigning a name, label, or category to a particular attribute of an individual, group, or phenomenon. In the case of party affiliation, the Gallup Political Polls ask people to identify themselves as Democrat, Republican, or Independent. These labels are mutually exclusive, and do not imply any particular order. Therefore, the level of measurement used to measure party is nominal.
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Helpppp!!
7.5
15.
30.
None of these choices are correct.
Answer:30
Step-by-step explanation:
In a triangle, the midsegment is half of base (AC)
so, AC would be double of DE, meaning 15×2=30
Solve for m.
−2.4(m−2/3)=−9
Enter your answer as a simplified mixed number in the box.
m =
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
The solution of the linear equation −2.4(m − 2/3) = −9 will be 4 ⁵/₁₂.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
−2.4(m − 2/3) = −9
Simplify the equation, then we have
−2.4(m − 2/3) = −9
m - 2/3 = 9/2.4
m - 2/3 = 15/4
m = 15/4 + 2/3
m = 53 / 12
m = 4 ⁵/₁₂
The arrangement of the straight condition −2.4(m − 2/3) = −9 will be 4 ⁵/₁₂.
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You invest $1000 in an account that has an annual interest rate of 4%, compounded monthly for 12 years. What is the equivalent interest rate and how many times will the money be compounded?
3% and 144 times
3% and 4 times
O 0.33% and 1 time
0.33% and 144 times
Answer:
Below
Step-by-step explanation:
4% /12 = .33 % per period
periods per year = 12
money is compounded each month for 12 years = 144 times
last question finally!
Answer:
v=116
u=137
Step-by-step explanation:
hope it's helpful for you
What is the greatest common factor of 64xyz−36xy 24x ?
The greatest common factor of polynomial 64xyz−36xy + 24x is 4x
The greatest common factor of a polynomial is a monomial that divides all terms of the polynomial.
The given polynomial is:
64xyz−36xy + 24x
Notice that there are 3 terms:
64xyz
−36xy
24x
To find the greatest common factor, notice that each terms contain x.
Next, find the gcf of 64, 36, 24.
Using prime factorization:
64 = 2⁶
36 = 2² × 3²
24 = 2³ × 3
Hence the gcf (64, 36, 24) = 2² = 4
Therefore the gcf of 64xyz−36xy + 24x is 4x
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Write the equation of direct variation that includes the given point .
(-6,5)
(14,-28)
Answer:
33/20
Step-by-step explanation:
The direct variation is the slope, or how much the y-value of the line changes when the x-value of a line increases by 1.
Plug into the formula:
[tex]\frac{y_2-y_1 }{x_2-x_1}[/tex]
[tex]\frac{-28-5}{14--6}[/tex]
[tex]\frac{33}{20}[/tex]
HELPPPPP For a given recipe, 2 cups of flour are mixed with 4 cups of sugar. How many cups of sugar should be used if 6 cups of flour are used?
Answer: 12 cups of sugar
Step-by-step explanation:
you can set it up as a ratio
2:4 and this can be simplified to 1:2, so for every cup of flour there is 2 cups of sugar, you could count it by hand but with a ratio of 1:2 you can just multiply by 2 so 6x2=12
Answer:
Step-by-step explanation:
Establish the identity.
(csc 0+1)(csc 0-1) = cot 0
a. Multiply and write the left side expression as the difference of two squares: ?
b. The expression from the previous step is equivalent to cot 0 using what?
OA. Cancellation Property
OB. Quotient Identity
OC. Pythagorean Identity
OD. Reciprocal Identity
OE. Even-Odd Identity
pls help asap i can’t pass this class without passing this test
To answer this question, we need to first multiply the left side of the given equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.
The left side of the given equation can be written as:
(csc0+1)(csc0-1)
We can then apply the difference of squares formula to this expression to get:
(csc0+1)(csc0-1) = (csc0+1)(csc0-1)
Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.
Therefore, the correct answer is C. Pythagorean Identity
How is h 50 different than h> 50?
H>50 means H is larger than 50
The crocodile eats the bigger # is a way to remember it.
What is the circumference of the following circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
Answer:
43.96
Step-by-step explanation:
C = 2πr
C = 2 × 3.14 × 7
C = 43.96
Step-by-step explanation:
given in fig :
radius = 7
so,
circumference of the given figure= 2πr
=2×3.14×7
= 43.96
What is the measure of ∠xbc? m∠xbc = m∠bac m∠bca 3p – 6 = p 4 84 3p – 6 = p 88 2p – 6 = 88 2p = 94 m∠xbc = °
The measure of m∠XBC=(3p-6)°=(3·47-6)°=135°.
What is meant by geometric mean theorem?The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem, which is a consequence of elementary geometry. It claims that the altitude is equal to the geometric mean of the two segments.The later version provides a method for squaring a rectangle using a ruler and compass, which entails creating a square with the same area as the rectangle in question.Since the inverse of Thales' theorem guarantees that the hypotenuse of the right angled triangle is the diameter of its circumcircle, the theorem may also be seen as a specific example of the intersecting chords theorem for a circle.Given data :
m∠XBC = m∠BAC + m∠BCA,
Now if : m∠XBC=(3p-6)°: m∠BAC=(p+4)°: m∠BCA=84°,
then we get the equation :
3p-6=p+4+84
(option 2), 3p-6=p+88
(option 3), 3p-p-6=p-p+88,2p-6=88
(option 4), 2p-6+6=88+6,2p=94
(option 5), p=47.
Then m∠XBC=(3p-6)°=(3·47-6)°=135°.
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Answer:
135
answer in picture
Step-by-step explanation:
the width of a rectangle is two feet less than the length. the perimeter is 52 feet. find the length and the width.
If the width of a rectangle is two feet less than the length and the perimeter is 52 feet, then the length and width of the rectangle is 14 feet and 12 feet respectively
The width of a rectangle is two feet less than the length
Consider the length of the rectangle as x
Then the width of the rectangle = x - 2
The perimeter of the rectangle = 52 feet
The perimeter of the rectangle = 2(l + w)
Where l is the length and w id the width
Substitute the values in the equation
2(x + x - 2) = 52
2(2x - 2) = 52
2x - 2 = 52/2
2x - 2 = 26
2x = 28
x = 14 feet
Width of the rectangle = 14 - 2
= 12 feet
Therefore, the length and width of the rectangle is 14 feet and 12 feet respectively
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two groups of tourists are visiting a skyscraper, and they are currently on the ground floor. the first group boards an elevator that is moving up at a speed of 66 meters per minute. when it has traveled 200 meters, the second group gets on an express elevator that goes up at a speed of 200 meters per minute. how long will it be before the second elevator catches up to the first?
Answer:
1 minute
because the first elevator has traveled 200 meters and the second elevator goes 200 meters in one minute so they will catch up with the first group in 1 minute.
Solve the system using substitution or elimination:
8x - 3y = -13
-3x + 5y = 1
Make sure you answer is an ordered pair (x, y).
Answer:
{x = -2, y = -1
Step-by-step explanation:
Solve the following system:
{-3 y + 8 x = -13
5 y - 3 x = 1
Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{-3 y + 8 x = -13
5 y - 3 x = 1
Isolate terms with x to the left-hand side.
Add 3 y to both sides:
{8 x = 3 y - 13
5 y - 3 x = 1
Hint: | Solve for x.
Divide both sides by 8:
{x = (3 y)/8 - 13/8
5 y - 3 x = 1
Perform a substitution.
Substitute x = (3 y)/8 - 13/8 into the second equation:
{x = (3 y)/8 - 13/8
5 y - 3 ((3 y)/8 - 13/8) = 1
Expand the left-hand side of the equation 5 y - 3 ((3 y)/8 - 13/8) = 1.
5 y - 3 ((3 y)/8 - 13/8) = 5 y + (-(9 y)/8 + 39/8) = (31 y)/8 + 39/8:
{x = (3 y)/8 - 13/8
((31 y)/8 + 39/8) = 1
Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = (3 y)/8 - 13/8
(31 y)/8 + 39/8 = 1
Isolate terms with y to the left-hand side.
Subtract 39/8 from both sides:
{x = (3 y)/8 - 13/8
(31 y)/8 = -31/8
Solve for y.
Multiply both sides by 8/31:
{x = (3 y)/8 - 13/8
y = -1
Hint: | Perform a back substitution.
Substitute y = -1 into the first equation:
Answer: {x = -2, y = -1
suppose there are ten five and six year olds attending a birthday party when a 30 year old mother walks into the room with an infant in her arms, what happens to the mean of ages in the room?
If there are ten five and six year old attending a birthday party when a 30 year old mother walks in to the room with an infant in her arm then the Mean of the ages in the room changes.
The term average refers to any of the measures of central tendency. The arithmetic mean of a set of observed data is defined as being equal to the sum of the numerical values of each and every observation, divided by the total number of observations. suppose there are ten five and six year old attending a birthday party when a 30 year old mother walks into the room with an infant in her arms. The mean of a dataset exists as the sum of all values divided by the total number of values. It's the most generally utilized measure of central tendency and exists often referred to as the “average.”
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in class a there are 20 students 14 of them are girls in class b there 25 students 15 of them are girls (a) which class has more girls?
(b) which class has greater percentage of girls?
Answer:
(A) Here, as we can see class A has more girls than class B.
(B) Class A has a greater percentage of girls.
Step-by-step explanation:
Given;In class A there are 20 students 14 of them are girls.In class B there are 25 students 15 of them are girlsSo,
For class A
14/20 × 100 = 70%For class B
15/25 × 100 = 60%(A) Here, as we can see class A has more girls than class B.
(B) Class A has a greater percentage of girls.
find the area of the region enclosed by one loop of the curve. r = sin(8θ)
π/32 is the area enclosed by the curve r= sin(8θ)
The given curve is polar curve and hence the area of the polar curve is given by:
Let A be the area of the curve so,
A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]
where a and b is the boundary at which r=0
so after equation r=0
sin(8θ) =0
=> sin(8θ) =0
=> 8θ = 0,π
=> θ = 0, π/8
so a=0 , b= π/8
now
A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex] ------(i)
so [tex]r^2[/tex] = (sin(8θ))^2
=> [tex]sin^2[/tex] ( 8θ )
ans we know that
cos(2α) = 1 - 2[tex]sin^2[/tex] α
so [tex]r^2[/tex] = (1- cos(16θ) )/2
putting the value of r in the equation (i) we get :-
A = [tex]\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha[/tex]
=> 1/4* [tex]\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha[/tex]
here a=0 and b=π/8
after putting the value and solving the integral
A = π/32
so A is the area enclosed by r=sin(8θ) is π/32
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PLEASE HELP QUICK!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Find the value of x, round to the nearest degree.
Answer:
The answer is, rounded to the nearest degree, 51°
Latisha found an apartment that she wants to rent. the rent is $675 per month and there is a security deposit of $325. to move in, latisha must have first month's rent, last month's rent and the security deposit. how much does latisha need to move in?
a. $1,000
b. $1,325
c. $1,675
d. $2,000
please select the best answer from the choices provided a b c d
Latisha needs to pay first month's rent ($675), last month's rent ($675), and the security deposit ($325), which totals $1,325.
Latisha needs to pay a total of $1,325 to move into her new apartment. This includes the first month's rent of $675, the last month's rent of $675, and the security deposit of $325. This total amount must be paid before Latisha can move in and enjoy her new place. In addition to the up-front costs for move-in, Latisha will also need to be prepared to pay her rent each month and maintain her security deposit in case there are any damages to the apartment. Paying the move-in costs is the first step to ensure that Latisha can enjoy her new home.
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Graph the equations y = -1/2x + 3 and y = 2x - 2
1After you graph the two lines, be sure to take a screenshot of your work and include it in your answer below.
2) What is the solution to the system of equations?
3) Prove that the answer you provided in part 2 is correct, by substituting the solution into the original equations. Be sure to show all your work.
Andrea loaned $5 to each of 20 people. She recorded each loan by writing -$5 in her bank book. What is the total amount of money Andrea has written in her bank book after the loans?
Answer: -$100
Step-by-step explanation:
We know that Andrea loaned $5 to each of the 20 people.
So 5 times 20 = -$100
You can represent the perimeter of a shape with the two expressions 6x - 8 and 4(1.5x - 2). What does 4(1.5x -2) tell you about the shape that 6x - 8 does not?
The expression 6x-8 represents the perimeter of a shape in terms of the length of one of its sides, while the expression 4(1.5x-2) represents the perimeter of the same shape in terms of the length of its diagonals. Therefore, the expression 4(1.5x-2) provides additional information about the shape that is not contained in the expression 6x-8. Specifically, the expression 4(1.5x-2) tells us that the length of each diagonal of the shape is equal to 1.5 times the length of one of its sides minus 2. This information allows us to determine the lengths of the diagonals of the shape, which is not possible with the information provided by the expression 6x-8.