The maximum number of relative extrema of the given polynomial is; 3
How to find the maxima of a Polynomial Function?When trying to find the maximum number of relative extrema of a polynomial, we usually use the formula;
Maximum number of relative extrema contained in a polynomial = degree of this polynomial - 1.
We are given the Polynomial as;
f(x) = 3x⁴ - x² + 4x - 2
Now, the degree of the Polynomial would be 4. Thus;
Maximum number of relative extrema = 4 - 1
Maximum number of relative extrema = 3
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Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly. How much would Katherine need to invest, to the nearest ten dollars, for the value of the account to reach $960 in 16 years?
Katherine need to invest $432.4 for the value of the account to reach $960 in 16 years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly.
We know that;
⇒ [tex]A = P e^r^t\\[/tex]
Let the invest amount = x
Here, The amount = $960
And, The time = 16 years
And, Rate = 5.8% = 0.058
So, We can formulate;
⇒ [tex]A = P e^r^t\\[/tex]
⇒ [tex]960 = P * e^{0.058 * 16} \\[/tex]
⇒ 960 = P × 2.22
⇒ P = 960 / 2.22
⇒ P = $432.43
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what is the answer for this question? Answer ASAP
The value of the expression as a fraction in its simplest form is 2/7.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 ÷ ( 5/2 x (2 x (1(3/5) - 2/5) - 1) )
Step 1:
Removing the parenthesis.
We will solve (1(3/5) - 2/5) first.
8/5 - 2/5 = 6/5
1 ÷ ( 5/2 x (2 x 6/5 - 1) )
Step 2:
Solve this (2 x 6/5 - 1)
12/5 - 1 = 7/5
1 ÷ ( 5/2 x 7/5)
Step 3:
Solve (5/2 x 7/5)
5/2 x 7/5 = 7/2
1 ÷ 7/2
Step 4:
1 ÷ 7/2
= 1 x 2/7
= 2/7
Thus,
The value of the expression is 2/7.
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Which equation has infinitely many solutions?
A. 6(3x - 5) = 10 - 2x
B. -3(4x - 8) = 6x + 12
C. -7(-8x + 3) = -21 + 56x
D. 9(3x - 4) = 27x + 36
The equation -3(4x - 8) = 6x + 12 has infinitely many solutions.
How to find if a equation has infinitely many solution?An equation has infinitely many solutions when the equation is true for all possible values of the variable. One way to identify that an equation has infinitely many solutions is to see if the equation is true when the variable is replaced by any value.
What is system of equation?A system of equations is a set of two or more equations that involve the same variables. The goal is to find the values of the variables that satisfy all of the equations in the system. There are different methods to solve a system of equations, depending on the type of equations and the number of variables involved.
The equation that has infinitely many solutions is:
B. -3(4x - 8) = 6x + 12
To see this, we can simplify the equation to:
-12x + 24 = 6x + 12
-12x = 12
x = -1
Now, if we put x = -1 in the equation, we see that it is true. If we put x = -2, x=0, x = 1, x = 3 and so on, we can see that the equation is true for all values of x.
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How do you write an equation of a line in slope intercept form when given a graph of a line?
We can write an equation of a line in slope intercept form when given a graph of a line by using the equation y = mx + c.
There are various forms in which an equation is present. Based on the given equation or graph values, we can determine the form we should use. The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
We first see the point where the line cuts the y-axis, then we calculate the slope of the line using the formula,
Slope= Δy/Δx
Once we get these values, we can substitute them in the equation for our final answer.
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Eva deposited $50 in an account earning 10% interest compound annually to the nearest cent how much interest will she earn in 2 years
Answer:
For 10% interest, you can multiply the original number by 1.1.
$50 x 1.1 = $55 after one year
$55 x 1.1 = $60.50 after two years
$60.50 - $50 = $10.50
In 2 years, Eva will earn $10.50 in interest.
Ellen Andrzejewski purchased the car in the ad for $7775. She made a down payment of $775.00. She financed the remainder at $331.16 per month for 24 months. What is the APR?
474 is the Annual percentage rate (APR).
What is APR in plain English?
If you have a balance on your credit card, you will pay an annual percentage rate (APR) of interest. The cost of borrowing money is what you pay in interest on a credit card. The interest rates on credit cards are often expressed as an annual rate. The yearly percentage rate is used to describe this (APR).
Certain credit cards feature variable APRs, which means that your rate may increase or decrease over time.
$331.16 * 24 + 775 - 7775 = 947.84
She over paid $ 947.84
24 months equals two years.
947.84/2 = 473.92 ≈ 474
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what is 6root 2 - 5 root2
As the value of 2 is 1.414, 6root 2 is 8.484, and 5 root2 is 7.071, the value of 6root 2 - 5 root2 is 1.413.
what is square root ?The square root or nth root is represented by the radical sign. Square roots are a component of root expressions. There is a radical's radicand—a number or word that appears. Radicals like 7 and 2y+1 serve as examples. Additional terms that describe radicals include: Radical equations are those equations that include radicals. A "root expression" is the phrase used to describe the expression contained within the square root. To demonstrate radical representations, consider the numbers 2, 372, 2x+7, and 41p. The phrase "root expression" refers to the expression contained within the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.
given
6root 2 - 5 root2
√2 value is 1.414. therefore 6×1.414
= 8.484
5 root2
√2 value is 1.414. therefore 5 * 1.414
= 7.071
so 6root 2 - 5 root2 = 8.484 - 7.071
= 1.413
As the value of 2 is 1.414, 6root 2 is 8.484, and 5 root2 is 7.071, the value of 6root 2 - 5 root2 is 1.413.
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9 (3x - 5) = 9 (3x + 5)
2 step equations
3f + 1 = 10
Answer:
3f = 9
Step-by-step explanation:
[tex]3f + 1 = 10 \\ 3f = 10 - 1 \\ 3f = 9 \\ f = \frac{9}{3} \\ f = 3[/tex]
Answer:
[tex] \sf \: f = 3[/tex]
Step-by-step explanation:
Given equation,
→ 3f + 1 = 10
Now the value of f will be,
→ 3f + 1 = 10
→ 3f = 10 - 1
→ 3f = 9
→ f = 9 ÷ 3
→ [ f = 3 ]
Hence, the value of f is 3.
I don't undertand thi:
There are 22 event at an indoor track and field meet. The ratio of track event to field event i 8:3. How many of the event are track event?
Can I jut have the ratio without the tory problem? Thank
There are 22 event at an indoor track and field meet. The ratio of track event to field event is 8:3. Therefore, there are 16 track events.
Ratio:
In mathematics, ratios indicate the number of times one number contains another number. For example, if you have 8 oranges and 6 lemons in your fruit bowl, the ratio of oranges to lemons is 8 to 6 (that is, a ratio of 8:6, or 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to whole fruit is 8:14 (or 4:7).
Now,
If you want to know the number of events in track events, we can calculate it in two steps:
Divide 22 in the ratio 8:3.
First,
add the numbers = 8 + 3 =11
Second,
For 08, We Multiple and divide = 8/11 × 22
= 16
Again,
For 03, We again multiple and Divide = 3/11 × 22
= 06.
Therefore, there are 16 track events.
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An equilateral triangle and an isosceles triangle share a common side. What is the measure of∠ABC?
The unknown angle in the triangle is as follows:
∠ABC = 112 degrees.How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
An equilateral triangle is a triangle that has all it sides and angles equal to each other. Each angle of an equilateral triangle is 60 degrees.
An Isosceles triangle is a triangle that has two of it sides and angles equal to each other. The base angles of an isosceles triangle are equal and the two legs are equal.
Therefore, let's use these principle to find the ∠ABC.
∠DBC = 60 degrees
∠ABD = 180 - 64 - 64 = 180 - 128 = 52 degrees
Hence,
∠ABC = 52 + 60 = 112 degrees.
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use words to write 114.674
Answer: one hundred + fourteen point six hundred + seventy four
Step-by-step explanation:
Answer:
One hundred and fourteen point six seven four
could someone pls help me with thissssss
The slope of the line through the points is -5/7.
What is slope ?
A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites.
Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2).
m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(4−−1)/(−3−4)
m=5/−7
m=−5/7
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please help me w this
Answer:
Opposite Sides are perpendicular (only correct answer)
Step-by-step explanation:
Not every parallelogram has diagonals that are perp to each other (form right angles.
The diameter of a circle is 25 cm. what is the radius of the circle? a. 5 cmb. 12.5 cm c. 25 cm d. 50 cm
The radius of the circle is 12.5 cm. So the option b is correct.
In the given question, the diameter of a circle is 25 cm.
We have to find the radius of the circle.
The radius of a circle is the distance a circle's centre from any point along its perimeter. Usually, "R" or "r" is used to indicate it. In almost all calculations containing spheres, this quantity is essential. In terms of radius, a circle's area and circumference are also calculated.
The distance from any circular object's centre to its outermost border or boundary is measured in terms of radius. A radius is a property of not only circles but also spheres, semi-spheres, cones with circular bases, and cylinders with circular bases.
The given diameter = 25 cm.
Now the radius = diameter/2
Radius = 25/2
Radius = 12.5 cm
So the option b is correct.
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Classify the polynomial 2q⁹.
Trinomial
Monomial
Binomial
None of these
The polynomial 2q⁹ is monomial.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.
What category does a polynomial fall under?By the degree of the polynomial, polynomials can be categorized. A polynomial's degree is equal to the highest degree term in the polynomial. Consequently, the result of 2x3+3x2+8x+5 is 3, or 3. When terms are organized in a polynomial from greatest to lowest degree, it is said to be expressed in standard form.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.The polynomial 2q⁹ is monomial.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.To learn more about polynomial refer to:
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A certain blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments. Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.
Which equation can be used to find d, the number of days it will take before both bloggers have the same number of followers?
21 days it will take before both bloggers have the same number of followers
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given a blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments.
y=460-6d
Where d represents the number of days
Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.
y=128+10d
We need to find equation to find the number of days it will take before both bloggers have the same number of followers
460-6d=128+10d
Add 6d on both sides
460=128+16d
Subtract 128 on both sides
460-128=16d
332=16d
d=20.75=21
Hence, 21 days it will take before both bloggers have the same number of followers
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Graph work
Y=Mx+C
NEED ASAP
WILL GIVE BRAINILY TO FIRST CORRECT ANSWER
Answer: y = 6x + 20, or E = 6t + 20
Step-by-step explanation:
Taking two points on the graph, (10, 80) and (30, 200), you can find the slope ("E") with the equation (y2-y1)/(x2-x1), which when plugged into the formula would be (200-80)/(30-10) = 120/20 = 6. To get your "t", you would plug this back into the formula y=mx+b along with any point on the graph, which would be:
80 = 6(10) + b
80 = 60 + b
b = 20
So the final equation should be y = 6x + 20
Derek has $82 in his bank account. There is a service fee of $5.50 charged every month. For 6 months, Derek deposits $11.25 in the account. If he doesn’t make any other deposits or withdrawals, how much is in the account after 11 months?
After 11 months, Derek would have $89 in his account
How to calculate the amount of money that Derek would have in his account after 11 months?Derek has $82 in his account
The bank charges a service fee of $5.50 each month
For 6 months Derek deposits $11.25 in his account
Therefore the amount of money in his account after 11 months can be calculated as follows
82 + 11.25(6)
82 + 67.5
= 149.5
The service charge for the entire 11 months is
= 5.50(11)
= 60.5
The money in the account is
149.5-60.5
= 89
Hence Derek has $89 in his account after 11 months
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find the sum of these polynomials. (4x^2+3x-1) + (x^2-5x-6)=
The sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7
we will add the coefficients of the same degree terms.
(4x^2+3x-1) + (x^2-5x-6) = (4x^2+x^2) + (3x-5x) + (-1-6) = 5x^2-2x-7
Therefore, the sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7
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When solving a system of equations, which of the following is a possible outcome? select all that apply. explain why you chose this answer! please help I will mark you brainliest.
Answer: When solving a system of equations, the following are possible outcomes:
Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.
Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.
Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.
Option A,B,C are possible outcomes.
A: Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.
B: Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.
C: Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.
Step-by-step explanation:
please this is due tonight and its for a test I did this all day
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
An unfair comparison between two numbers or other mathematical expressions is referred to as an inequality. It is most frequently used when comparing the sizes of two numbers on a number line. The attachment contains the graph for each inequality or equation.
What is graph?A graph is a graphical representation of statistical data or the functional relationship of variables. Graphs can highlight broad trends in the quantitative behaviour of data, which is useful for forecasting. They can, however, be inaccurate and occasionally deceptive as mere approximations.
Most graphs have two axes: one for independent variables and one for dependent variables. A broken-line graph is the most common type of graph, with time serving as the independent variable.
16. 2y – 4x < 8
= 2y < 4x + 8
= y < 2x + 4
17. -4y > -x + 12
= y > x/4 + -3
18. | x + 3 |= y
y = | x + 3 |
19. |2x – 6| + 2 = y
y = |2x – 6| + 2
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The temperature is recorded in 65 cities on a given day in California. The
average temperature is 74 degrees Fahrenheit with a standard deviation of 4
degrees. What is the z-score for a temperature of 71 degrees?
The z-score for a temperature of 71 degrees is -0.75.
What is the z-score?
When assessed in terms of standard deviation units, a raw score's location in relation to its distance from the mean is indicated by a z-score. If a value is above the mean, the z-score is positive; if it is below the mean, it is negative.
The raw score less the population mean, divided by the population standard deviation, is the z-score.
Here, the mean average temperature is 74°, standard deviation is 4, and the raw score is 71°.
The formula for calculating z-score is -
Z = (x-μ)/σ
Where x is raw score, μ is mean and σ is standard deviation.
Plugging in the values -
Z = (71-74)/4
Z = -3/4
Z = -0.75
Therefore, the z-score is obtained as -0.75.
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What is the correlation coefficient for the data shown in
the table?
О о
0 1
04
05
Answer:
i think the answer is one
Step-by-step explanation:
The solution is : The correlation coefficient is -1
What is correlation coefficient?A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.
Here, we have,
we want to get the correlation coefficient for the given dataset
from the table, what do we observe?
As x is increasing by 5 units;
y is decreasing by 5 units
What this mean is that there is a negative correlation between both
This means the linear regression will go through every point, and will be a perfect fit. The correlation coefficient, r, of a data set is 1 if it is a perfect positive fit and -1 if it is a perfect negative fit; since the slope is decreasing, this is a negative correlation, and since it fits perfectly, it is -1.
Thus, what we have here is that, since the rate of increase/decrease on both ends is of equal magnitude but opposite signs, we can conclude that the correlation coefficient is -1
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How do you find the quotient of a division fraction?
Take the reciprocal of the second fraction, and Multiply it by the first fraction. later reduce the resultant fraction to its lowest terms.
The quotient of a fraction is the whole number that is obtained when we simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.
The quotient can also be the solution to a division problem involving two fractions. That division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient.
The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator.
Consider an example:
2 3/7=3 *2/7 =3 + 2/7
3 is the quotient
2 is the remainder
7 is the divisor
23 is the dividend
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NEED HELP ASAP - Algebra 2 - 50 Points
Write a reasonable equation in the form g(x) = a(x - h)^2 for g(x) below.
Explain why your equation is reasonable.
The parabola g(x) is reasonable because it can be derived of parabola f(x) by rigid transformations.
How to generate the image of the parabola by rigid transformation
Parabolas are represented by second order polynomials in vertex form, whose definition is shown below:
y - k = C · (h - k)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.In this problem we must create the expression for the image of the parabola by means of rigid transformations, that is, transformations that change the parabola without changing Euclidean distances. Most common rigid transformations are listed below:
TranslationReflectionDilation / ContractionRotationThe procedure is summarized below:
Shift the parabola 3 units right. (Horizontal translation)Shift the parabola 2 units up. (Vertical translation)Reflect the parabola about the line y = 2. (Reflection)Enlarge the parabola horizontally by a factor of 0.5. (Dilation)Now we proceed to apply the rigid transformations in that order:
Step 1
y = f(x) → y = f(x - 3)
y = x² → y = (x - 3)²
Step 2
y = f(x - 3) → y - 2 = f(x - 3)
y = (x - 3)² → y - 2 = (x - 3)²
Step 3
y - 2 = f(x - 3) → y - 2 = - f(x - 3)
y - 2 = (x - 3)² → y - 2 = - (x - 3)²
Step 4
y - 2 = - f(x - 3) → y - 2 = - f[0.5 · (x - 3)]
y - 2 = - [0.5 · (x - 3)]²
Finally, we proceed to plot both parabolae by help of a graphing tool.
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would appreciate help
Answer:
59040
Step-by-step explanation:
Answer:
Step-by-step explanation:
ygyggygy
What is the sum?
X
3
2
+
X+3 x+3 x+3
O
+
colch
53
X+5
X+3
X+5
3x+27
6x
X+3
The outcome or result of adding two or more integers is known as the SUM.
What is a sum?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
the sum of two or more numbers, magnitudes, quantities, or specifics as determined by or as though decided by the addition process in mathematics.
The outcome of adding two or more numbers, objects, or things is referred to in mathematics as the sum.
The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined.
[tex]Simplify $\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}: \frac{x+5}{x+3}$Steps$$\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}$$Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$$=\frac{x+3+2}{x+3}$$Add the numbers: $3+2=5$$$=\frac{x+5}{x+3}$$[/tex]
Therefore, the correct answer is option b) [tex]$=\frac{x+5}{x+3}$[/tex]
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Daniel can spend no more than 40 dollars at the fair. If admission into the fair is 10 dollars and the rides cost 1.50 each write and Wolfe an inequality that represents the greatest number of rides Daniel can go on?
The inequality that represents the greatest number of rides that Daniel can go is 1.50x + 10 ≤ 40
How to solve for the inequalityFrom the question we would have the inequality that would be written as
1.50x + 10 ≤ 40
admission is 10 dollars
cost of rides is 1.50 dollars
So, the equation would be -
1.50x + 10 ≤ 40
we are to solve for the value of x. Such that we would have
1.5x ≤ 40 - 10
1.5x ≤ 30
divide through by 1.5
x = 30 / 1.5
x = 20
Proof
Hence we would have
1.5 * 20 = 30 + 10 = 40
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David wants to rent a bicycle for a couple of hours to explore the city. The price of the bike rental, (P), depends on the time the bike was out, (t). The price consists of a base charge of $8 and a variable hourly cost. The graph of the function is shown below.
Answer:
The hourly charge is $4 per hour for the first 3 hours.
The rate then drops to $2 per hour until the end of the 6th hour.
The hourly rate drops further to $1 per hour between the 6th and 10th hours.
The maximum price of the bike rental is $30.
Step-by-step explanation:
The slope of the graph corresponds to the hourly rate for the bike rental.
During the first three hours of the bike rental, the price increases by $4 each hour.
Between the 3rd and 6 th hours, the slope of the graph is 2, which means the hourly rate of the bike rental is $2 per hour.
Between the 6th and 10th hours, the rate is $1 per hour.
After the 10th hour, the price, P, stops increasing. The maximum price of the bike rental is $30.