Determine whether each conjecture is true or false given: n is a real number
Conjecture: n^2 (squared) is a nonnegative number
The conjecture that any real number squared is a nonnegative number is correct. This is because squaring a positive number gives a positive result, squaring a negative number also gives a positive result, and squaring zero equals 0, which is nonnegative.
Explanation:This mathematical conjecture proposes that for any real number, when squared, the result is a nonnegative number. Given n is a real number, the conjecture n^2 is a nonnegative number is indeed true. In mathematics, a real number is considered nonnegative if it is greater than or equal to zero.
To provide more insight, let's look at a few examples: If we take a positive number such as 3, and you square it (3^2), you get 9, which is a positive number. Equally, if you take a negative number like -3 and square it (-3^2), you get 9 again, which is also a positive number. Even if you take the number zero (which is neither positive nor negative) and square it, you get 0, which is still considered nonnegative. Thus, any real number when squared is always a nonnegative number.
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∠C and ∠D are vertical angles with m∠C=−x+26 and m∠D=2x−10 . What is m∠D ? Enter your answer in the box.
Answer:
m∠D=14
Step-by-step explanation:
∠C and ∠D are vertical angles with m∠C=−x+26 and m∠D=2x−10
Vertical angles are equal. So equate the angles C and d . Solve for x
m∠C=m∠D
[tex]-x+26=2x-10[/tex]
Subtract 2x from both sides
[tex]-3x+26=-10[/tex]
Subtract 26 from both sides
[tex]-3x=-36[/tex]
Divide both sides by -3
x=12
m∠D=2x−10
Substitute 12 for x
m∠D=2(12)−10=24-10= 14
How do find perimeter and area for this?
Which binomial is not a devisor of x^3-11x^2+16x+84?
x + 4
Further explanationGiven:
The expression x³ - 11x² + 16x + 84
Question:
Which binomial is not a divisor of x³ - 11x² + 16x + 84?
x + 2x + 4x - 6x - 7The Process:
This is a problem about Remainder Theorem.
If x = a or (x - a) is one of the roots or factors (divisors) of the function f (x), then f(a) = 0.
Let us test one by one of the options available into the polynomial function.
[tex]\boxed{ \ x + 2 \ } \rightarrow \boxed{ \ x = -2 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (-2)^3 - 11(-2)^2 + 16(-2) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow -8 - 44 - 32 + 84 = 0 \ }[/tex][tex]\boxed{ \ x + 4 \ } \rightarrow \boxed{ \ x = -4 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (-4)^3 - 11(-4)^2 + 16(-4) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow -64 - 176 - 32 + 84 = -188 \ }[/tex][tex]\boxed{ \ x - 6 \ } \rightarrow \boxed{ \ x = 6 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (6)^3 - 11(6)^2 + 16(6) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow 216 - 396 + 96 + 84 = 0 \ }[/tex][tex]\boxed{ \ x - 7 \ } \rightarrow \boxed{ \ x = 7 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (7)^3 - 11(7)^2 + 16(7) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow 343 - 539 + 112 + 84 = 0 \ }[/tex]From the test results above, it was clearly observed that (x + 4) is not a divisor of x³ - 11x² + 16x + 84 because [tex]\boxed{ \ f (-4) \neq 0 \ }[/tex].
- - - - - - - - - -
Alternative Steps
We will use Horner's rule for polynomial division in finding factors as well as divisors.
To begin, let us try x = -2 to see if it is one of the roots of x³ - 11x² + 16x + 84. The complete process can be seen in the attached picture.Since there is no remainder when x³ - 11x² + 16x + 84 is divided by (x + 2), this binomial is a divisor (or a factor). The quotient is obtained x² - 13x + 42. After factorization, we get (x - 6) dan (x - 7 as factors and also the divisor.Learn moreThe remainder theorem https://brainly.com/question/9500387A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 https://brainly.com/question/12700460 The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2.Maria, bill, and change sent a total of 71 text messages during the weekend. change sent 2 times as many messages as bill. maria sent 7 more messages than bill. how many messages did they each send?
Find the best of a parallelogram if the area is 10 cm2 and the height in 2cm
find the coordinates of the midpoint of EF with endpoints E(-2,3) and F(5, -3)
The coordinates of the midpoint of line segment EF with endpoints E(-2,3) and F(5, -3) are (1.5, 0), calculated using the midpoint formula.
To find the coordinates of the midpoint of line segment EF with endpoints E(-2,3) and F(5, -3), you can use the midpoint formula which is:
( (x1 + x2)/2, (y1 + y2)/2 )
Let's apply the formula:
x-coordinate of midpoint = ( (-2) + 5 ) / 2 = 3 / 2 = 1.5
y-coordinate of midpoint = ( 3 + (-3) ) / 2 = 0 / 2 = 0
So the midpoint of EF is (1.5, 0).
Ron works 5 hours for a total of $300. He deposits all of his money in his account. He is trying to save a $500 for a new LED TV. How many hours must he work to ake home $500, if he saves all of his earnings
Ron's hourly wage is $60. To save $500 for a new LED TV, he needs to work approximately 8.3 hours. Rounding up, he should work 9 hours to earn the required amount.
Ron earns $300 for working 5 hours, which means his hourly wage is $300 / 5 hours = $60 per hour. To save up for a $500 LED TV, Ron needs to determine how many hours he must work to earn that amount.
To calculate the total hours Ron needs to work to save $500, we divide the total amount he wants to save by his hourly wage:
$500 ÷ $60 per hour = 8.3 hours
Therefore, Ron needs to work approximately 8.3 hours to earn $500, assuming he continues to save all of his earnings. In practice, since he cannot work a fraction of the hour, Ron would need to round up to the nearest whole hour, meaning he needs to work 9 hours to meet or exceed his savings goal.
Zoe, Latoya, Christina, and Rhoda each used a different method to verify that
-2(3x - 12) = -6x + 24
Whose method can be used to verify that the distributive property was correctly applied to the expression?
A.) Zoe's method
B.) Latoy's Method
C.) Christina's Method
D.) Rhoda's Method
Answer:
D) Rhoda's Method
Step-by-step explanation:
-2(3x - 12)
Using the distributive property a(b - c) = ab - ac
-2(3x -12) = -2(3x) -2(-12)
= -6x + 24
Which means-2(3x - 12) and -6x + 24 are equal.
To check this, we have to substitute the same x value for both the expression and evaluate them.
Both expression will have the same value.
Therefore, Rhoda is correct.
Thank you.
Luis has a $10 bill and three $5 bills. He spends $12.75 on the entrance fee to an amusement park and $8.50 on snacks. How much money doe she have left
Answer:
She has a total of $3.75 left
Step-by-step explanation:
Step 1
Express the amount of money Luis had in the beginning as follows;
A=E+R
where;
A=initial amount he had at the beginning
E=total expenditure
R=total remainder after spending
In our case;
A=(1×10)+(3×5)=$25
E=Amount spent at amusement park+amount spent on snacks
E=(12.75+8.50)=$21.25
R=unknown=r
Step 2
Substitute the values in the expression and solve for A;
25=21.25+r
r=25-21.25=3.75
r=3.75
She has a total of $3.75 left
Simplify
8 - [- ( - 3 )]
A. 5
B. -5
C. 11
D. -11
If you are using this figure to prove the isosceles triangle theorem which of the following would be the best strategy
If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.
∠P≅∠Q∠P≅∠Q
Proof:
Let SS be the midpoint of PQ¯¯¯¯¯PQ¯ .
Join RR and SS .
Since SS is the midpoint of PQ¯¯¯¯¯PQ¯ , PS¯¯¯¯¯≅QS¯¯¯¯¯PS¯≅QS¯ .
By Reflexive Property ,
RS¯¯¯¯¯≅RS¯¯¯¯¯RS¯≅RS¯
It is given that PR¯¯¯¯¯≅RQ¯¯¯¯¯PR¯≅RQ¯
Therefore, by SSS ,
ΔPRS≅ΔQRSΔPRS≅ΔQRS
Since corresponding parts of congruent triangles are congruent,
∠P≅∠Q∠P≅∠Q
The converse of the Isosceles Triangle Theorem is also true.
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
If ∠A≅∠B∠A≅∠B , then AC¯¯¯¯¯≅BC¯¯¯¯¯AC¯≅BC¯ .
Suppose that water is being pumped into a trough. the trough is $$15 feet long, and every cross section of the trough is an equilateral triangle, with a vertex of the triangle pointing toward the ground. find the rate of change of the height of the water when the height is $$4 feet, if the volume of water is increasing at a rate of $$8 cubic feet per second.
in 35 days a person saved $70 what was the person's average daily savings
The person's average daily savings is $2.00. The correct answer is option b $2.00.
Step 1
To find the average daily savings, we need to divide the total amount saved by the number of days over which the savings occurred.
Calculation:
1. Total savings: $70
2. Number of days: 35 days
Step 2
The average daily savings is calculated as:
[tex]\[\text{Average daily savings} = \frac{\text{Total savings}}{\text{Number of days}} = \frac{70}{35} = 2\][/tex]
The person's average daily savings is $2.00.
Complete question : In 35 days, a person saved $70. What was the person's average daily savings?
a $0.70
b $2.00
c $1.50
d $1.05
e $2.33
f none of these
Let f(x) = 4 – x^2-, g(x) = 2 – x. Find (f + g)(x) and its domain.
On a baseball field, the infield is a square. the distance from home plate to first base is 90ft. what is the distance from home plate to second base?
what is 165.2 diveded by 3 times 10 plus 65 minus 82 divided by 100 times 65 plus 1
Answer: 563.37 hahaha
Step-by-step explanation:
If your bank charges an out-of-network service fee of $3.00, and you withdraw $20 from each of three out-of-network atms, how much money in total will be removed from your account?
a. $60
b. $63
c. $69
d. $120
The amount of the money that is in total removed from the account would be $69.
As per the question, the bank charges an out-of-network service fee of $3.00, and you withdraw $20 from each of three out-of-network ATMs, how much money in total will be removed from your account is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Amount withdrew from the ATM three times,
= 3 × 20
= $60
The total service fee charged on out of network 3 times
= 3 × 3
= $9
Now, total money withdrew from the account = 60 + 9 = $69
Thus, the amount of money that is in total removed from the account would be $69.
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The total amount of money that will be removed from your account is $9.00.
Explanation:To find the total amount of money that will be removed from your account, you need to multiply the out-of-network service fee by the number of withdrawals you made. In this case, the out-of-network service fee is $3.00 and you made three withdrawals. So, the total amount of money that will be removed from your account is $3.00 x 3 = $9.00.
Write an inequality that represents the sentences:
What is the product of g and 2 is less than -6
You are planning to volunteer at a zoo that is 60 miles from your home. you can either take stephanie's car, which gets 20 miles to the gallon
how many decimal places should be in the answer if 2.214 is added to 6.3
How do you solve: -1= 5+x/6
which is a perfect square a. 6^1 b. 6^2 c. 6^3 d. 6^5 (need answer now pls)
The perfect square expression is (b) 6^2
How to determine the perfect square?A perfect square is any expression that can be represented as:
x^2
Where x is a real number
From the list of options, we have: 6^2
i.e.
x^2 = 6^2
Hence, the perfect square expression is (b) 6^2
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Kaitlin brought 7 cans of cola to a party. lisa brought 18 packs of cola, and each pack had 6 cans. how many cans did they bring in all?
Larry Lazy purchased a one year membership at a local fitness center at the beginning of the year. It cost him $150. He goes twice a week for the first three months (13 weeks) of the year, but then goes only once a month for the rest of the year.
How much does each visit to the center cost?
If he continued going twice a week all year, how much would each visit cost?
Answer:
A. $4.29
B. $1.44
Step-by-step explanation:
A. We have been given that Larry goes to gym twice a week for 13 weeks. Let us multiply 13 by 2 to find the number of times Larry visited the gym for first 3 months.
[tex]\text{The number of Larry's visits to gym for the first 3 months}=13\times 2=26[/tex]
Since there are 12 months in a year, then Larry has gone to gym only 9 times for rest of month as 12-3=9.
Now let us add 26 and 9 to get the total number of Larry's visits to gym.
[tex]\text{Larry's total visits to gym}=26+9[/tex]
[tex]\text{Larry's total visits to gym}=35[/tex]
Now let us divide total cost (150) by total number of visits (35) to get the each visit's cost.
[tex]\text{Each visit's cost}=\frac{150}{35}[/tex]
[tex]\text{Each visit's cost}=4.2857142857142857\approx 4.29[/tex]
Therefore, each visit to the center costs $4.29 to Larry.
B. If Larry continued going twice a week all year, then total number of Larry's visits to center will be 52 times 2.
[tex]\text{Larry's total visits to center}=52\times 2[/tex]
[tex]\text{Larry's total visits to center}=104[/tex]
Now let us divide total cost (150) by total visits (104) to find the cost of each visit.
[tex]\text{Each visit's cost}=\frac{150}{104}[/tex]
[tex]\text{Each visit's cost}=1.4423076923076923\approx 1.44[/tex]
Therefore, If Larry continued going twice a week all year, it would cost him $1.44 for each visit.
The area of the conference table in Mr. Nathan’s office must be no more than 175 ft2. If the length of the table is 18 ft more than the width, x, which interval can be the possible widths?
One number is three more than twice another, the sum of the numbers is 12. find the two numbers
The first three terms of a sequence are 1, 2 and 3. each subsequent term is the sum of the three previous terms. what is the 11th term of this sequence? pattern
Final answer:
The 11th term of the sequence, where each term is the sum of the three previous terms starting with 1, 2, and 3, is 423.
Explanation:
The sequence is defined such that each term is the sum of the three previous terms, starting with 1, 2, and 3. To find the 11th term, we continue the sequence based on its pattern:
1 (given)
2 (given)
3 (given)
6 (1+2+3)
11 (2+3+6)
20 (3+6+11)
37 (6+11+20)
68 (11+20+37)
125 (20+37+68)
230 (37+68+125)
423 (68+125+230)
Therefore, the 11th term of the sequence is 423.
Is the square root of 38 rational or irrational?
What is the surface area of a sphere with a radius of 13 units?
Answer:
676pi units ^2
Step-by-step explanation:
apex
The surface area of a sphere with a radius of 13 units is 676π²
What is surface area?explaination;
Given radius = 13 units
surface area of a sphere = 4πr²
= 4 * 13*13 π²
676π² answer.
The surface area is the sum of the areas of all its faces.The areas of the base, top, and lateral surfaces i.e all sides of the object. It is measured using different area formulas and measured in square units and then adding all the areas. The surface area of a solid object is a measure of the total area that the surface of the object covers.The floor region of a strong object is a measure of the full vicinity that the floor of the item occupies. The mathematical definition of surface vicinity within the presence of curved surfaces is extensively extra involved than the definition of arc length of 1-dimensional curves, or of the floor area for polyhedra for which the surface place is the sum of the areas of its faces. clean surfaces, such as a sphere, are assigned floor region using their representation as parametric surfaces. The definition of floor area is based totally on methods of infinitesimal calculus and includes partial derivatives and double integration.
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