By answering the supplied question, we may infer that the response is trigonometry Cos(2u) = -7/9, Sin(2u) = 4sqrt(2)/9, and Tan(2u) = 3/4.
what is trigonometry?The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. Consequently, studying geometry entails learning about the characteristics of all geometric forms.
The values of sin(2u), cos(2u), and tan(2u) in terms of the given value of u may be determined using the double-angle formulae.
The formulae for double angles are as follows:
[tex]2sin = sin(2u) (u)[/tex]
cos(u)
(2u) = cos(2u)
The formula is 2(u) - sin(u) tan(2u) = (2tan(u)) / (1-tan(u)).
We may use the definition of csc(u) to obtain sin(u) given that csc(u) = 3 and 0 u /2:
[tex]sin(u) = 3 sin(u) = 1/3 csc(u) = 1/sin(u)[/tex]
Now we can calculate sin(2u), cos(2u), and tan(2u) using the double-angle formulas:
[tex]2sin = sin(2u) (u)[/tex]
sqrt(1 - sin2(u)) = 2/3 sqrt(8/9) = 4sqrt(2)/9 cos(u) = 2(1/3)
[tex]cos(2u) = sin - cos2(u)[/tex]
2(u) = (1 - sin 2(u)) sqrt
[tex]a^2 - sin^2(u) = 1/9 - 8/9 = -7/9[/tex]
[tex]tan(2u) = (2tan(u)) / (1-tan(2u)) = (2(1/3)) / (1-(1/3)2) = 6/8 = 3/4[/tex]
Cos(2u) = -7/9, Sin(2u) = 4sqrt(2)/9, and Tan(2u) = 3/4.
To know more about trigonometry visit:
https://brainly.com/question/29002217
#SPJ1
Standard Form Instructions: Write the polynomial expression in Standard Form -6-7x^(2)+8x^(5) Standard Form:
Standard form of a polynomial expression is a way of writing the expression in descending order of the powers of the variable, starting with the highest power and ending with the constant. In this case, the polynomial expression is - 6 - 7x ^ (2) + 8x ^ (5).
In standard form, this expression can be written as 8x ^ (5) -7x ^ (2) - 6. This expression indicates that 8 is the coefficient of the highest power, x ^ (5). The coefficient of the second highest power, x ^ (2) is -7, and the coefficient of the constant, the term with no variable, is -6.
Standard form is useful for simplifying polynomial expressions, as it helps to clearly illustrate the coefficients of each term. It is also useful for graphing polynomials, as the order of the terms can be clearly seen.
Know more about Standard form here
https://brainly.com/question/29172894#
#SPJ11
[1] Language arts IS soience Q. Sodal studies Hecommendations T.8 Convert autemary and metric units uing preportions swo Which proportion could you use to convert 5 kilograms to grams? (1,000 grams )/(1 kilogram )=( ? grams )/(5 kilograms ) (10 grams )/(1 kilogram )=(7 grams )/(5 kilograms ) (1)
We can use the proportion (1000 grams )/(1 kilogram ) = (x grams )/(5 kilograms ) to convert 5 kilograms into grams.
The right proportion to use to convert 5 kilograms to grams is (1,000 grams)/(1 kilogram) = ( x grams)/(5 kilograms). This is because there are 1,000 grams in 1 kilogram, so we can use this ratio to find the number of grams in 5 kilograms. To solve for the unknown value, we can cross multiply and then divide.
The proportion is solved as:
So, the answer is 5,000 grams. Therefore, 5 kilograms is equal to 5,000 grams.
In conclusion, the correct proportion is (1000 grams )/(1 kilogram ) = (x grams )/(5 kilograms ).
See more about proportion at https://brainly.com/question/870035.
#SPJ11
can some one show me how this is done
By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.
What is the squeeze theοrem?The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.
We have the inequality:
-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49
We can rewrite this inequality as:
-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1
Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.
As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:
-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1
0 ≤ lim f(x) ≤ 1
Therefοre, by the squeeze theοrem, we have:
lim f(x) = 0 as x apprοaches -5.
To know more about Equation visit:
https://brainly.com/question/29657992
#SPJ1
Please help!! which number sentence is true?
A
B
C
D
B is the right response: (6 + 4) 2 = 20.
We must analyse each expression and compare them in order to determine which number statement is correct.
starting with the formula A (6 + 4 2 = 6 + 8 = 14)
Let's now assess expression B:
(6 + 4) × 2 = 10 × 2 = 20
Expression in C: 6 + 4 2 = 6 + 2 =
The final expression is D (6 + 4) 2 = 10 2 = 5.
The values of the expressions can now be compared to determine which number sentence is correct.
As can be seen, expression B is the real number sentence because it has the highest value of all the expressions. As a result, B is the right response: (6 + 4) 2 = 20.
To know more about Number Sentence visit:
https://brainly.com/question/13349953
#SPJ1
You deposit $2000 in an account with 3% annual compound interest. Complete the following, assuming you make no additional deposits or withdrawals. How fast will the account be growing (in dollars per year) 11 years from now?
It will be growing by $____ per year.
The account will be growing by $741.87 per year 11 years from now.
To find the answer, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = $2000, r = 0.03, n = 1, and t = 11. Plugging these values into the formula gives us:
A = $2000(1 + 0.03/1)^(1*11)
A = $2000(1.03)^11
A = $2741.87
To find out how fast the account will be growing 11 years from now, we need to subtract the principal amount from the final amount:
$2741.87 - $2000 = $741.87
Therefore, the account will be growing by $741.87 per year 11 years from now.
You can read more about compound interest at https://brainly.com/question/28020457
#SPJ11
Let V be a vector space over F, and fix y∈V. Show that g:V→F defined by g(x)=⟨x,y⟩ for all x∈V is linear.
G is linear.
To show that g:V→F defined by g(x)=⟨x,y⟩ for all x∈V is linear, we need to prove that g satisfies the following two properties:
1) g(x+z)=g(x)+g(z) for all x,z∈V
2) g(αx)=αg(x) for all x∈V and α∈F
Proof:
1) Let x,z∈V. Then g(x+z)=⟨x+z,y⟩=⟨x,y⟩+⟨z,y⟩=g(x)+g(z) by the distributive property of the inner product.
2) Let x∈V and α∈F. Then g(αx)=⟨αx,y⟩=α⟨x,y⟩=αg(x) by the scalar multiplication property of the inner product.
Therefore, g is linear.
Learn more about linear
brainly.com/question/20286983
#SPJ11
What is the value of 12÷13
?
Answer:
Step-by-step explanation:
12/13=0.92307692307
convert the following equation into standard form.
y=-2x
Therefore , the solution of the given problem of equation comes out to be equation y = -2x in standard notation
How are equations used?The very same variable letter is frequently used in mathematical formulas to attempt to impose harmony between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Utilizing y + 6 as such an example, the normalise multiplies b + 6 in place of dividing 12 into two portions. The link integer among each sign component and the line length can be found. A symbol's meaning typically runs counter to itself.
Here,
The x element needs to be moved to the left and the equation needs to be written with integer coefficients in order to change the equation y = -2x in to other standard form (Ax + By = C).
With y = -2x as a starting point, we can add 2x to both sides to get:
2x + y = 0
With A = 2, B = 1, and C = 0, we now have the equation Ax Plus By = C. By multiplying both sides by -1, we can make the factors integers:
-2x - y = 0
This is the equation y = -2x in standard notation.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
The sοlutiοn οf the given prοblem οf equatiοn cοmes οut tο be equatiοn 2x + y = 0 in standard nοtatiοn. Thus, the correct option is 1.
Hοw are equatiοns used?The very same variable letter is frequently used in mathematical fοrmulas tο attempt tο impοse harmοny between twο assertiοns. Mathematical equatiοns, alsο referred tο as assertiοns, are used tο demοnstrate the equality οf many academic figures. Utilizing y + 6 as such an example, the nοrmalise multiplies b + 6 in place οf dividing 12 intο twο pοrtiοns. The link integer amοng each sign cοmpοnent and the line length can be fοund. A symbοl's meaning typically runs cοunter tο itself.
Here,
The x element needs tο be mοved tο the left and the equatiοn needs tο be written with integer cοefficients in οrder tο change the equatiοn y = -2x in tο οther standard fοrm (Ax + By = C).
With y = -2x as a starting pοint, we can add 2x tο bοth sides tο get:
2x + y = 0
With A = 2, B = 1, and C = 0, we nοw have the equatiοn Ax Plus By = C. By multiplying bοth sides by -1, we can make the factοrs integers:
2x + y = 0
This is the equatiοn 2x + y = 0 in standard nοtatiοn.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Complete question:
Convert the following equation into standard form.
y = -2x.
[select from given choices]
2x + y = 0x + y = 2x + 2y = 02x - y = 0The values in each data set vary over time, even though the same measurand is being measured. What is your interpretation of why the 11 measurements in the first data set vary? what is your interpretation of why the 1001 measurements in the second data set vary? what is your interpretation of why the 1001 measurements in the third data set vary?
The interpretation of the 1001 measurements in the third set of data vary due to reasons are as follow,
Measurement error, Random variation and Sampling error.
Measurement error: The measurand being measured may have inherent variability, but measurement error can also contribute to variation in the data set.
Random variation: Even if the same measurand is being measured under the same conditions, there may be random fluctuations in the system or the environment that can cause variation in the data.
Sampling error: If the 11 measurements were not taken at random from the population of interest, then the variation could be due to sampling error.
For the 1001 measurements in the second and third data sets, some possible explanations for the variation could be measurement error, systematic variation, changes in the measurand and Sampling error.
Thus, variation in data can have many different causes, and it is important to carefully consider the context and specific factors that may be contributing to the variation when interpreting the results.
Learn more about the Measurement:
brainly.com/question/28109798
#SPJ4
The area of square ABCD is 10
cm².
3 cm
x cm
D
3 cm
x cm
B
C
Show that x² + 6x = a where a is
a constant to be found.
The equation of the area of the square is x² + 6x = 1, it is in the form x² + 6x = a where a is 1 and a constant to be found.
What is square?A regular quadrilateral is square. A square has equal lengths on each of its four sides and angles. Each of the four angles is 90 degrees, or a right angle. The two adjacent sides of a square are equal in length, making it a particular instance of a rectangle.
Its attributes are: Each of its four sides is the same length.
Each of its four angles has the same dimensions.
At right angles, or 90°, the two diagonals split in half.
A square has two opposed sides that are equally long and parallel.
A square's diagonal lengths are equal.
The length of the side of the given square is 3 + x.
The area of the square is given as:
A = (s)(s)
Substituting the value of the side and area we have:
10 = (3 + x)(3 + x)
10 = 9 + 3x + 3x + x²
x² + 6x = 10 - 9
x² + 6x = 1
Hence, the equation of the area of the square is x² + 6x = 1, it is in the form x² + 6x = a where a is 1 and a constant to be found.
Learn more about square here:
https://brainly.com/question/28776767
#SPJ1
A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 16 meters ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 meter per second, and the adults hobbled after them at a rate of 3 meters per second. Soon they were side-by-side. How far did the adults go? How long did that take?
Therefore , expression problem solution is during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.
Explain expression.There is a need for mathematical operations like multiplying, splitting, combining, and now even deleting. If they were combined, it would be said that: A mathematical formula, some data, and an equation A declaration of truth is composed of values, elements, and mathematical operations like additions, subtractions, missteps, algebraic formulas, and divisions. It is possible to evaluate and analyse words and phrases.
Here,
Distance is determined by rate and duration.
for the distances that children and adults travel, two equations should be made up:
=> (d - 16) = 1t (for the youngsters) (for the kids)
=> d = 3t (for the males) (for the adults)
where "t" represents the amount of time that has elapsed since the competition began.
We can set the distances between the children and adults to be equal because we know that they were side-by-side at some time during the race:
=> d - 16 = 3t - 16
When we simplify this solution, we obtain:
=> d = 3t
When we add this to the prior solution, we obtain:
=> 3t - 16 = 1t
To solve for "t," we obtain:
=> t = 8 sec.
Now that we know how far the grownups travelled:
D=3t=3x8=24 metres.
As a result, during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
A cluster sample will:
Select one:
a. Seek views from a heterogeneous group in the population
b. Seek views from a homogeneous group in the population
c. Seek views from any group in the population
d. Seek views from everyone who attends a group discussion
A cluster sample will: b. Seek views from a homogeneous group in the population
A cluster sample is a type of sampling method where the entire population is divided into groups, or clusters, and a random sample of these clusters are selected for the study. Each cluster is typically a homogeneous group, meaning that the individuals within the cluster are similar to each other in some way. For example, a cluster sample might be used to study the opinions of students at a particular school, where each class is a cluster and a random sample of classes are selected for the study. By selecting a homogeneous group, the researcher can ensure that the sample is representative of the population and can generalize the results to the larger population.
To know more about cluster sample refer here:
https://brainly.com/question/13287171
#SPJ11
x-3y
2x+4y=10
Substitutes
someone help me out rq
The calculated system of inequalities shown in the graph of inequalities is x > -2 and y < 4
How to determine the system of inequalities?A system of inequalities is a set of two or more inequalities involving one or more variables.
The variables can take on different values that satisfy the given inequalities simultaneously.
The solution to the system is the set of values of the variables that satisfy all the inequalities in the system. A system of inequalities can be represented graphically as a region in a coordinate plane where each inequality defines a boundary line or curve. The region that satisfies all the inequalities is the intersection of the regions defined by each inequality.Inequalities is used to show the unequal comparison of numbers and variables using signs like >, <, ≥, ≤By the above analysis, the inequalities shown in the graph is x > -2 and y < 4
Find out more on inequalities:
https://brainly.com/question/30390162
#SPJ1
Complete the statement.
A die has 15 sides shown as follows: 9 triangles, 4 circles, and 2 squares. The probabaty of rolling a triangle is out of 15 or or %
P
The probability of rolling a triangle is 9 out of 15, or
(Type integers or decimals.)
4
or
ww
√i V
More
The probability of rolling a triangle is 9 out of 15, or 60%.
What is probability?Its essential vision is that an individual will nearly certainly happen.
Then the probability is given as,
P = (Favorable event) / (Total event)
As per the given data:
Total sides is a die = 15
triangles = 9
circles = 4
squares = 2
The probability of rolling a triangle is 9 out of 15, or:
For probability in % = (Favorable outcomes/Total outcomes) × 100
= (9/15) × 100
= 60%
Hence, The probability of rolling a triangle is 9 out of 15, or 60%.
More about the probability link is given below.
brainly.com/question/795909
#SPJ9
Mark invested $3,200 at 7% simple interest. How much interest did his account earn at the end of the four years
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$3200\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (3200)(0.07)(4) \implies I = 896[/tex]
If 3x-y=12, what is the value of 8x over 2y?
A.) 2^12
B.) 4^4
C.) 8^2
D.) The value cannot be determined from the information given.
Step-by-step explanation:
We can solve for x in terms of y from the equation 3x - y = 12 as follows:
3x - y = 12
3x = y + 12
x = (y + 12)/3
Similarly, we can solve for y in terms of x:
3x - y = 12
-y = -3x + 12
y = 3x - 12
Now, we can substitute these expressions for x and y into the expression 8x/2y to get:
8x/2y = 4x/y
Substituting (y + 12)/3 for x, we get:
4x/y = 4((y + 12)/3)/y = 4(y + 12)/3y
Simplifying the numerator, we get:
4(y + 12) = 4y + 48
Substituting 3x - 12 for y, we get:
4y + 48 = 4(3x - 12) + 48 = 12x
Therefore, 8x/2y = 4x/y = 12x/4y = 12x/(3x - 12)
We cannot simplify this expression further without additional information. Therefore, the answer is (D) The value cannot be determined from the information given.
Does the equation y = 3/4 x represent a proportional relationship? Explain how you know.
Yes, the equation y = 3/4(x) represent a proportional relationship because its line passes through the origin.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Generally speaking, the graph of any proportional relationship such as the linear equation is characterized by a straight line that passes through all the points and the origin, which is denoted by the ordered pair (0, 0).
Read more on proportional relationship here: brainly.com/question/28350476
#SPJ1
5. Using the binomial theorem and patterns in Pascal's triangle, simplify each of the following. a)
9
C 0
+ 9
C 1
+…+ 9
C 9
b)
12
C 0
− 12
C 1
+ 12
C 2
−…− 12
C 11
+ 12
C 12
c)
r=0
∑
15
15
C r
d)
r=0
∑
n
n
C r
11. Use 6. If
r=0
∑
n
n
C r
=16384
, determine the value of
n
. 7. a) Write formulas in combinatorial form for the following. (Refer to section
4.4
, if necessary.) i) the sum of the squares of the terms in the
n
th row of Pascal's triangle ii) the result of alternately adding and
The result of alternately adding and subtracting the terms in the nth row of Pascal's triangle is given by the formula
[tex]n C 0 - n C 1 + n C 2 - ... + (-1)^n \times n C n = 0.[/tex]
The binomial theorem and patterns in Pascal's triangle can be used to simplify the given expressions.
Here are the simplified versions of each expression:
9 C 0 + 9 C 1 +…+ 9 C 9 = 2^9 = 512
12 C 0 − 12 C 1 + 12 C 2 −…− 12 C 11 + 12 C 12 = 0
r=0 ∑ 15 15 C r = 2^15 = 32768
r=0 ∑ n n C r = 2^n
If r=0 ∑ n n C r = 16384, then [tex]2^n[/tex] = 16384, so n = 14.
The sum of the squares of the terms in the nth row of Pascal's triangle is given by the formula:
[tex](n C 0)^2 + (n C 1)^2 + ... + (n C n)^2 = 2^{(2n-1).[/tex]
To learn more about Pascal's triangle :
https://brainly.com/question/9303796
#SPJ11
What is the percent of increase from 53.5 to 96.3?
Answer:
80%
Step-by-step explanation:
96.3 - 53.5 = 42.8
42.8 / 53.5 = 0.8
0.8 × 100 = 80%
I need some helpp please
The values of 'x' in |3x + 4| > 6, is, x > 3/2 or x < - 10/3.
What is an absolute value function?We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.
In piecewise terms | x | = x for x ≥ 0 and | x | = - x for x < 0.
We know, If |x| > a, Then x > a or x < - a.
Given, |3x + 4| > 6.
Therefore,
3x + 4 > 6 or 3x + 4 < - 6.
3x > 2 or 3x < - 10.
x > 3/2 or x < - 10/3.
learn more about modulus functions here :
https://brainly.com/question/13103168
#SPJ1
All multiples of 2 are even numbers true or false
Answer:
That is true.
Answer: True
Step-by-step explanation:
due to the fact that its 2 and every time you multiply by the factor itll equal a even number
evaluate xy^-4 with positive exponents
By answering the above question, we may state that Hence, [tex]xy{(-4)}[/tex]is x exponents divided by y raised to the power of 4.
what are exponents?The mathematical process of exponentiation, frequently referred to as "b raised to the nth power," is symbolised by the symbol bn and includes two numbers: a base number, b, and an exponent, or power, n. Exponents demonstrate the number of times that a number has been multiplied by itself. For example, 2-3 (written as 23) means: 2 x 2 x 2 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Therefore, the exponent is the measurement that shows how many times a number has been multiplied by itself. For instance, multiplying 6 by 4 results in the values 6 x 6 x 6. .
Considering that the phrase is:
[tex]xy^{-4}[/tex]
We may simplify the case when x and y both have positive exponents as follows:
[tex]xy^{(-4)} = x / y^4[/tex]
This is due to the negative exponents rule, which claims that y(-n) = 1/yn, which indicates that [tex]y(-n) = 1/yn.[/tex]
Hence, [tex]xy{(-4)}[/tex]is x divided by y raised to the power of 4.
To know more about exponents visit:
https://brainly.com/question/3987569
#SPJ1
Alice is riding the train to her job in Paris, France.
She accidentally purchased a ticket for zone 4, but she is
travelling to zone 5. She has decided to risk it and stay on the train until zone 5 with the incorrect ticket. If the
transit authorities check tickets on the train, she will have to pay a fine.
Alice estimates that there is a 5% chance that the transit authorities will check tickets. The fine for having the
wrong ticket is 300 euros. The ticket she purchased cost her 5 euros.
Find the total expected cost of Alice's train ride.
The total expected cost of Alice's train ride will be 20 Euro with a fine of 300 Euro if ticket checked and 0 fine if ticket not checked.
It is known to us that Alice is riding the train, and that she accidentally purchased a ticket for zone 4, although she has to be traveling to zone 5,
with this we need to find how much money can Alice expect to pay
since we know that there is a 5 percent chance that the transit authorities will check tickets,
Probability to check ticket = 5/100 = 0.05
fine = 300 euro
probability to not check ticket = 1 - 0.05 = 0.95
we know that she has already spent 5 Euro on the ticket,
there is a 300 Euro fine if ticket checked,
and 0 fine if ticket not checked,
Expected cost to pay = 5 + 0.05 × 300 + 0.95 × 0
= 5 + 15 + 0
= 20 Euro
Alice Expected to Pay = 20 Euro
To learn more about probability, click here:
brainly.com/question/30034780
#SPJ1
Rewrite the equation by completing the square - 4x^2 +20x +25 =0
Answer:
[tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]
Step-by-step explanation:
I am not completely sure if you just wanted me to write it in square form, so I will show the process of writing it in square form and how to find the solution.
[tex]-4x^2+20x=-25[/tex] start by moving 25 to the right side
[tex]\frac{-4x^2+20x}{-4}=\frac{-25}{-4}[/tex] divide both sides by -4
= [tex]x^2-5x=\frac{25}{4}[/tex]
Now we rewrite the equation in the form [tex]\:x^2+2ax+a^2[/tex]
= [tex]x^2-5x+\left(-\frac{5}{2}\right)^2=\frac{25}{2}[/tex] apply perfect square formula: [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
= [tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex] -- square form
Solutions to the quadratic equation:
Possible solutions: [tex]x=\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex] and [tex]\:x=-\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex]
determine how many positive real zeros the polynomial function may nave. f(x)=-7x^(7)+x^(3)-x^(2)+1
The possible number of positive real zeros for the given polynomial function is 2 or 0.
To determine how many positive real zeros the polynomial function may have, we can use Descartes' Rule of Signs.
Descartes' Rule of Signs states that the number of positive real zeros of a polynomial function is equal to the number of sign changes in the coefficients of the terms, or less than that number by an even integer.
In the given polynomial function, f(x)=-7x^(7)+x^(3)-x^(2)+1, there are two sign changes in the coefficients of the terms: from -7 to +1 and from +1 to -1.
Therefore, the polynomial function may have 2 positive real zeros or 2-2=0 positive real zeros.
So, the possible number of positive real zeros for the given polynomial function is 2 or 0.
For more about polynomial function:
https://brainly.com/question/12976257
#SPJ11
A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven. Tallulah wants to rent a car, knowing that: She plans to drive 50 miles. She has at most $230 to spend. What is the maximum number of days that Tallulah can rent the car while staying within her budget?
The maximum number of days she can drive the car is approximately 4 days.
How to find the maximum days she can ride the car?A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven.
She plans to drive 50 miles. She has at most $230 to spend.
Therefore, the maximum number of days that Tallulah can rent the car while staying within her budget can be computed as follows:
Using equations,
y = 0.13a + 61.79b
where
a = number of miles drivenb = number of daysTherefore, she has a budget of 230 dollars and she wants to ride for 50 miles.
230 = 0.13(50) + 61.79b
230 - 6.5 = 61.79b
223.5 = 61.79b
b = 223.5 / 61.79
b = 3.61709014404
Therefore,
b = 4 days
Hence, she can ride maximum of 4 days.
learn more on equation here: https://brainly.com/question/26096160
#SPJ1
(c) 5longleftrightarrow (7) What is the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 ?
So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.
The coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.
A coefficient is the number that is multiplied by a variable in an expression. In this case, the x^(2) term is -4x^(2), so the coefficient is -4.
To find the coefficient of a specific term in an expression, you can simply look at the number that is directly in front of the variable and its exponent. For example, in the term 5x, the coefficient is 5, and in the term 2, the coefficient is 2 (since there is no variable, the coefficient is simply the number itself).
In the expression 5x-4x^(2)+2, the x^(2) term is -4x^(2), so the coefficient is -4. This means that the x^(2) term is being multiplied by -4 in the expression.
So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.
Learn about Coefficient
brainly.com/question/28975079
#SPJ11
isosceles trapezoid MNOP where MO = a + 13 and NP = 2a - 1, what is the value of a?
Isosceles trapezoid MNOP where MO = a + 13 and NP = 2a - 1, The value of a 13.
Describe Trapezoid?A trapezoid, also known as a trapezium, is a four-sided polygon with two parallel sides, also called the bases. The non-parallel sides are called legs, and they can have different lengths. The parallel sides are perpendicular to the legs
In an isosceles trapezoid, the nonparallel sides are congruent, so we have MN = OP.
Also, the diagonal PN divides the trapezoid into two congruent right triangles, so we have:
[tex]MN^2 = (NP - MO)^2 + (MP)^2[/tex]
Substituting the given values, we get:
[tex]MN^2 = (2a - 1 - (a + 13))^2 + MP^2[/tex]
[tex]MN^2 = (a - 14)^2 + MP^2[/tex]
But since MN =OP and MO = NP - MN, we have:
[tex]OP = NP - MO = (2a - 1) - (a + 13) = a - 12[/tex]
So we also have:
[tex]OP^2 = (a - 12)^2 + MP^2[/tex]
Since MN = OP, we can set these two equations equal to each other:
[tex](a - 14)^2 + MP^2 = (a - 12)^2 + MP^2[/tex]
Simplifying and solving for a, we get:
[tex]a^2 - 28a + 197 = a^2 - 24a + 144[/tex]
[tex]4a = 53[/tex]
[tex]a = 13.25[/tex]
Therefore, the value of a is 13.25.
To know more about equations visit:
brainly.com/question/12788590
#SPJ1
Chad drove 168 miles in 3 hours. 21.
A. How many miles per hour did Chad drive?
B. Chad will drive 672 more miles. He continues to drive at the same rate. How many hours will it take Chad to drive the 672 miles?
C. Chad stopped and filled the car with 11 gallons of gas. He had driven 308 miles using the previous 11 gallons of gas. How many miles per gallon did Chad’s car get?
D. Chad’s car continues to get the same number of miles per gallon. How many gallons of gas will Chad’s car use to travel 672 miles?
NOTE: PLASES DO ALL THE STAPS
Answer:
A: 24, B: 12, C: 28, D: 24. Hope this helps
Step-by-step explanation:
Part A:
168/3 = 56
Therefore, Chad is driving the car in 56 mph.
672/56 = 12
Therefore, Chad drives 672 miles in 12 hours.
308/11 = 28
Therefore, Chad drives 28 miles per gallon of gas.
672/28 = 24
Therefore, Chad uses 24 gallons of gas to drive 672 miles.
Part B:
12 hours, you can use proportions, miles/hours.
[tex]\frac{56}{1}[/tex]= [tex]\frac{672}{x}[/tex]
x = 12
Part C:
divide the miles driven by Chad (308 miles ) by the number of gallons used (11 gallons).
308 miles / 11 gallons =28 miles per gallon
Chad's car gets 28 miles per gallon.
Part D:
[tex]\frac{28}{1} = \frac{672}{x} \\[/tex]
28x = 672
x = 672/28 = 24
24 gallons
Answer: A=56 B=12 C=28 and D=24
Step-by-step explanation:
A. Chad drove 168 miles in 3 hours
In 1 hour he drove 168÷3
= 56 Miles
B. We know,
Covering 56 miles takes 1 hour
So, It will take to cover 672 miles
= 672÷56
= 12 Hours
C. We know,
Chad drove 308 miles with 11 gallons of gas
So, miles per gallon chads car gave him 308÷11
= 28 Miles Per Gallon.
D. We know,
Chad car gives him 28 miles per gallon
So, To cover 672 miles
Chad needs = 672÷28
= 24 Gallons.
NOTE: Its simple math kiddo, do better in school