Answer:
B
Step-by-step explanation:
By the triangle inequality theorem, the sum of the lengths of the two shorter sides needs to be greater than the length of the longest side.
Can yiu show me how to set it up and the answer please [tex]when \: k {}^{3} - 17k + 32 \: is \: divided \: by \: k + 5[/tex]
When the polynomial is divided by the linear expression we get the quotient k² -5k +8 and the remainder -8.
Polynomials are used in many areas of mathematics. For example, they are used in arithmetic and mathematical methods to approximate other functions. They are also used to describe linear combinations, which are encountered in a variety of situations, from basic physics and biology to economics and science.
From straightforward word problems to intricate scientific conundrums, polynomial equations are utilised to represent a wide range of topics. Algebraic varieties and polynomial rings, two essential concepts in algebra and computational geometry, are constructed in mathematics using harmonics.
The simplest way to do the long division is:
[tex]\begin{array}{r}k^2-5k+8\phantom{)} \\x+5{\overline{\smash{\big)}\,k^3-17k+32\phantom{)}}}\\\underline{-~\phantom{(}(k^3+5k^2)\phantom{-b)}}\\-5k^2-17k+32\phantom{)}\\\underline{-~\phantom{()}(-5k^2-25k+40)}\\ -8\phantom{)}\end{array}[/tex]
Hence the division will give quotient quotient k² -5k +8 and the remainder -8.
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Thirty-five students attend a math club meeting. The number of girls at the meeting is a multiple of 13, and there are more girls than boys attending the meeting. How many boys are at the meeting?
Answer: 9 boys
Reason:
The multiples of 13 are
13, 26, 39, 52, ...
We only need to focus on the first two since they are smaller than 35
So we focus on 13 and 26
If there are 13 girls, then there are 35-13 = 22 boysIf there are 26 girls, then there are 35-26 = 9 boysThe second option has more girls than boys, so that must mean there are 26 girls and 9 boys.
A jet travels 1324 miles against a jetstream in 2 hours and 1584 miles with the jetstream in the same amount of time. what is the rate of the jet in still air and what is the rate of the jetstream rate of the jet in still air ___mi/hrate of the jetstream___ mi/h
In still air, the rate of the jet is Distance traveled/ time taken
[tex]\frac{1324}{2}=662\text{ mi/h}[/tex]With the jetstream, the rate of jetstream is
[tex]\frac{1584}{2}=792\text{ mi/h}[/tex]Find the intervals of increase for the polynomial. Rounded to the nearest 10th
From the graph we can conclude:
The function is increasing for the following interval:
[tex]x\in\mleft\lbrace(-\infty,0\mright)\cup(2,\infty)\}[/tex]Answer:
(-∞,0), (2,∞)
4x4 + 2x
Pleaseeeeee helpppp
Answer:
2x (2x³ + 1)
Step-by-step explanation:
To get the answer factor 2x^1 / 2x of ( 4x^4 + 2x )
When you factor an expression, you are looking for a number which can perfectly divide into another number.
Remember that the numerical timetable states that (2 x 2 = 4).
And we already know that (2 divided by 4 = 2), as well as, that any rational number divided by itself is equal to 1
Therefore the value 2x is divisible by itself and is also divisible by 4x^4 exactly two times
Note: the reason why (4x^4 ÷ 2x ) becomes (2x³), is that you have to subtract the exponents of each term from each other after you finish dividing. So ( X^4 - X^1 = X^3) -
Always remember that any term in a polynomial expression which doesn't have a visible power attached to it is already at the first power
A textbook store sold a combined total of 283 math and sociology books in a week. The number of sociology textbooks sold was 89 less than the number of math textbooks sold. How many textbooks of each type were sold
Please help:The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.Which statements are true based on the model?Select each correct answer.Maximum profits are earned when there are 4 clerks working.The store earns profits when no clerks are working.Maximum profits are earned when there are 7 clerks working.The store earns about $400,000 in profits on its best days.The store loses money when 8 or more clerks are working.
SOLUTION
The image below will help in answering the following questions
Now, from the graph, the parts above the horizontal line represents profit, while the part below the horizontal line represents loss.
(a) Maximum profits are earned when there are 4 clerks working.
From the graph, we can see that this statement is CORRECT. The maximum profit is at 400 thousand dollars and takes place at 4 on the horizontal axis, this 4 represents 4 clerks working
(b) The store earns profits when no clerks are working.
No clerks are working when we consider 0 on the horizontal plane. From the picture above, tracing 0, it shows us something below the horizontal line which represents loss. So, this statement is INCORRECT. When no clerks work, there is a loss not profit
(c) Maximum profits are earned when there are 7 clerks working.
Tracing 7 from the graph, it doesn't fall on the top part of the curve which indicates maximum profit. Hence, this statement is INCORRECT.
d) The store earns about $400,000 in profits on its best days.
From the image above, we can see that this is correct.
(e) The store loses money when 8 or more clerks are working.
When we traced 8 from the horizontal line, it fell to the part of the graph which indicated loss.
Hence this is CORRECTstatement .
So you will select the 1st, 4th and 5th options
12.7-18.5+15+6.3-1+28.5
Answer:
43
Step-by-step explanation:
Identify the exponent in the term -3X²
A. 3
B. x
C. minus sign ( - )
D. 2
Solve for x. Enter the solutions from least to greatest.
x²+x-42=0
lesser x =
greater x =
17. Is the operation of forming Cartesian products commutative? Explain why or why not.
Choose the correct answer below.
OA. The operation of forming Cartesian products is commutative because order does not matter in
the definition of a Cartesian product.
OB. The operation of forming Cartesian products is not commutative because part of the definition of
a Cartesian product is the order of the elements generated by the two sets.
OC.
The operation of forming Cartesian products is commutative because a Cartesian product is
multiplication and multiplication is commutative.
O D. The operation of forming Cartesian products is not commutative because multiplication is not
commutative.
The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.
==========================================================
Explanation:
Let's go over an example. We'll have these two sets
A = {1,2}
B = {3,4}
The cartesian product is this set of ordered pairs
A x B= {(1,3), (1,4), (2,3), (2,4)}
Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.
If we swap the order of set A and B then we have
B x A = {(3,1), (4,1), (3,2), (4,2)}
We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.
Side note: Two sets are equal when they are subsets of each other.
The precipitation, in inches, Tampa normally receives each month for the last four months of the year is as follows: 6.3, 2 3/10, 1.6, and 2 1/2. Write and evaluate an expression to determine how much precipitation, in inches, Tampa receives from September through December.
Answer:
12.7 inches======================
Convert the mixed fractions into decimal and find the sum as follows:
6.3 + 2 3/10 + 1.6 + 2 1/2 = 6.3 + 2.3 + 1.6 + 2.5 = 12.7PLEASE HELP. I HAVE BEEN STUCK ON THIS ASSIGNMENT FOR A WHILE!! I WILL GIVE BRAINLIEST
The answer to the given question is option A that is only the first equation is an identity.
What are trigonometric identities ?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
Tan θ = 1/Cot θ or Cot θ = 1/Tan θ
1) LHS : 8 sec θ sin θ = 8 X 1/ cos θ X sin θ = 8 tan θ
RHS : 8 X sin^2 θ/ cos^2θ X cosθ / sin θ = 8 tan θ
Thus LHS = RHS and it is given above so 1st equation is an identity.
2) LHS: 11 X cot^2 θ/ cosec θ X sec^2 θ = 11 cos^2θ /sin θ
and RHS : 11 cosec^2 θ
since LHS ≠ RHS because the second equation us not an identity.
thus the correct option is A that is Only the first equation is an identity.
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subject identification numbers in a certain scientific research project consist of two digits followed by four letters and then two more digits. Assume repetitions are not allowed within any of the three groups, but digits in the first group of two may occur also in the last group of two. How many distinct identification numbers are possible?
The number of ways in which three digits can be written is 720 ways.
The number of ways in which 3 letters can be written is 15600.
How to illustrate the information?From the information, the subject identification numbers in a certain scientific research project consist of two digits followed by four letters and then two more digits.
The ways in which three digits can be written will be:.
= 10P 3
= 10! / (10-3)!
= 10 × 9 × 8
= 720 ways
The number of ways in which 3 letters can be written will be:
= 26P3
= 26! / ( 26 - 3)!
= 26! / 23!
= 26 × 25 × 24
= 15600
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Please Help this is due in 4 minutes!!!!!
Will give Brainiest
How to find the percent of a number
Explanation:
y% of some value, x:
Convert y to a decimal by dividing y by 100.
Then multiply that decimal value to x.
Help please!!!!!!!!!!!!
An estimate of the quotient is in improper fraction [tex]\frac{133}{60}[/tex]. An estimate of the quotient is in mixed fraction [tex]2 \frac{13}{60}$$[/tex]
[tex]6 \frac{1}{3} \div 2 \frac{6}{7}$$[/tex]
Convert mixed numbers to improper fractions: [tex]$\quad 6 \frac{1}{3}=\frac{19}{3}$[/tex]
[tex]=\frac{19}{3} \div 2 \frac{6}{7}$$[/tex]
Convert mixed numbers to improper fractions: [tex]$2 \frac{6}{7}=\frac{20}{7}[/tex]
[tex]$=\frac{19}{3} \div \frac{20}{7}$[/tex]
Apply the fraction rule: [tex]$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b} \times \frac{d}{c}$[/tex]
[tex]=\frac{19}{3} \times \frac{7}{20}$$[/tex]
Multiply fractions: [tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{19 \times 7}{3 \times 20}$$[/tex]
Multiply fractions:[tex]\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{19 \times 7}{3 \times 20}$$[/tex]
Multiply the numbers: [tex]$19 \times 7=133$[/tex]
[tex]=\frac{133}{3 \times 20}$$[/tex]
Multiply the numbers: [tex]$3 \times 20=60$[/tex]
[tex]=\frac{133}{60}$$[/tex]
Convert improper fractions to mixed numbers: [tex]$\frac{133}{60}=2 \frac{13}{60}$[/tex]
[tex]=2 \frac{13}{60}$$[/tex]
When it comes to adding Mixed or Improper fractions, we can have either the same denominators for both the fractions to be added or the denominators can differ too.
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
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what is perpendicular to the line y= -1/4 x+3
Answer: B
Step-by-step explanation: i got it because i
Select the number line that plots these numbers.5, -2, 1, –4
Find the number line that dotted only the numbers 5,- 2, 1, -4, which is clearly the last option.
24. Carlos bought a cube-shaped aquarium. Write
an expression to represent the volume of the
aquarium.
3s
Volume of the aquarium is 27 [tex]s^{3}[/tex]
What is volume of cube ?The total number of cubic units that a cube totally fills up is referred to as its volume. An object with six square faces that is three dimensional is called a cube. The amount of space an object takes up in total is known as its volume. Space would be taken up by an object having a larger volume.
Volume of cube formula ?Depending on the inputted inputs, many formulas can be used to determine the volume of any cube. You may figure it out by measuring the diagonal of the cube or its sides.
Given that : Carlos bought a cube shaped aquarium with side 3s
As the aquarium have cube shape so the volume will be
Volume of cube is V =[tex]a^{3}[/tex]
a = 3
V = 27 [tex]s^{3}[/tex]
Hence ,Volume of the aquarium is 27 [tex]s^{3}[/tex]
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Find the equation of a line that has a slope of m=1/5 and passes through the point (0, 9). Express your answer in slope-intercept form. Enter your answer in the box.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+9 \end{array}}[/tex]
In a recent year an author wrote 162 checks. Use the poisson distribution to find the probability that on a randomly selected day he wrote at least one check
Answer:
44.38%
Step-by-step explanation:
Becuase of 365 days a year, 162 out of 365 is 44.38% meaning that if he would selwcted a fay the probability would be 44.38% chance.
Express the polynomial in descending order.
4+ y4 - 9y³
y4 - 9y3 +4
Step-by-step explanation:
solo tienes que ordenarlo de mayor a menor de las variables
Please help I’ll mark you as brainliest if correct!!
The value of the variable 'A' which is a consecutive digit in the card is: 6
What is consecutive digits?
In mathematics, the consecutive digits are those digits whose difference between the two terms are constant. And the pattern of the terms should be continuous. It is used for the calculation based problems.
According to the question, the given data states that the 14 digits of a credit card has sum of the three consecutive digits is 18.
Therefore, at the end the blank box between 8 and 4 can be written as:
8 + m + 4 = 18 ⇒ m = 18 - 12 = 6 ⇒ m =6
Now, the pattern for the last three digits be: 864.
The pattern is repeating and the whole IN number is 64864864864864.
Hence, the value of the variable 'A' which is a consecutive digit in the card is: 6
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AP. The product of two whole numbers is 96 and their sum is less than 30. List all of the possibilities for the
two numbers.
Answer:
12 and 8; 16 and 6; 24 and 4
Step-by-step explanation:
Solve the following equation to find the value of x:
9x-4=5x+12
Answer: x=4
Step-by-step explanation:
First find the smallest x which would be 5x and subtract that from the 9x. So now it should be 4x-4=12. Then, move 4 and add that to the twelve which should now be 4x=16. Then, divide it by four and you get x=4.
Answer:
x = 4
Step-by-step explanation:
We start from
9x - 4 = 5x + 12
We move the "5x" to the left side of the "=" sign by changing it's sign from 5x which can be seen as +5x to -5x
9x - 4 - 5x = 12
Now we move the "4" to the right side of the "=" sign by applying the same principle as above, so -4 turns to +4
9x - 5x = 12 + 4
We than solve the subtraction and addition
4x = 16
Then we divide both sides of the equation by 4 and we get
x = 4
Help me solve this please
Answer:
56
Step-by-step explanation:
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
How do I solve this?
Answer:
????
Step-by-step explanation:
Find the value of x.
Answer:
x=12
Step-by-step explanation:
17. The area of a square poster is 31 square inches. Find the length of one side of the poster. Explain.
PART A
To the nearest whole inch
PART B
To the nearest tenth of an inch
The length of one side of the poster, when the area of a square poster is 31 square inches is
Part A = 6 inch (To the nearest whole of an inch)
Part B = 5.6 Inch (To the nearest tenth of an inch)
As given in the question,
Area of square poster = 31 sq. inches
Let 'l' be the length of the square poster
Now according to formula
Area of square poster = Length * Length
Substitute the values in the formula we get,
31 = l × l
⇒ l² = 31
⇒ l = √31
⇒ l = 5.568
Length = 5.568
Hence, the length of one side of the poster, when the area of a square poster is 31 square inches is
Part A = 6 inch (To the nearest whole of an inch)
Part B = 5.6 Inch (To the nearest tenth of an inch)
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