60 POINTS!!

What are the missing parts that correctly complete the proof?

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.

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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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'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.

x + 4

Given:

The expression x³ - 11x² + 16x + 84

Question:

Which binomial is not a divisor of x³ - 11x² + 16x + 84?

The 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{ \ x + 4 \ } \rightarrow \boxed{ \ x = -4 \ }.[/tex]

[tex]\boxed{ \ x - 6 \ } \rightarrow \boxed{ \ x = 6 \ }.[/tex]

[tex]\boxed{ \ x - 7 \ } \rightarrow \boxed{ \ x = 7 \ }.[/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].

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Alternative Steps

We will use Horner's rule for polynomial division in finding factors as well as divisors.

Answer: 563.37 hahaha

Step-by-step explanation:

The perfect square expression is (b) 6^2

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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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

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.

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

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

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.

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.

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.

Answer:

The correct option is C.

Step-by-step explanation:

Consider the provide information.

Now consider the provided options

Option A) If there is a coordinate plane with two parallel lines.

if the plane has two parallel line then, It has no solution because you can get the solution if lines intersect at a point. Thus, it is not the required option.

Option B) and D) If there are two intersecting lines then you can get only one solution. Thus, it is not the required option.

Option C) If there are two coinciding lines then you can find infinite intersecting points. Thus, it is the required option.

Therefore, the correct option is C.

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¯ .

Answer:

676pi units ^2

Step-by-step explanation:

apex

The surface area of a sphere with a radius of 13 units is 676π²

explaination;

Given radius = 13 units

surface area of a sphere = 4πr²

                                          = 4 * 13*13 π²

                                          676π² answer.

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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