Eric is wrong because even square numbers do not always have more factors than odd square numbers for example square of 785.
Given :
Even square numbers always have more factors than odd square numbers.
The following steps can be used in order to show that Eric is wrong:
Step 1 - According to the given data, even square numbers always have more factors than odd square numbers.
Step 2 - So, to prove this statement wrong there are some examples given in the below steps.
Step 3 - The square of 61 gives 3721 whose total number of factors are 4 similar number of factors as 4.
Step 4 - The square of 785 gives 616225 whose total number of factors are more than 16.
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The Washington's by a studio apartment for 240,000 they pay a down payment of 60000 their down payment is what percent of the purchase price
Answer:
25%
Step-by-step explanation:
Given:
The price of the studio apartment = 240,000
Down payment = 60,000
We need to find the percentage of down payment.
Solution:
Using percentage formula.
[tex]Percentage = (\frac{Value}{Total\ value})\times 100[/tex]
Here value = Down payment
Total value = Price of the apartment
Now we substitute Down payment and Price of the apartment in above formula.
[tex]Percentage = (\frac{60000}{240000})\times 100[/tex]
[tex]Percentage = \frac{6\times 100}{24}[/tex]
[tex]Percentage = \frac{600}{24}[/tex]
[tex]Percentage = 25\%[/tex]
Therefore, Down payment is 25% of the purchase price.
The audience thinks 30% of Brandon's jokes are funny. What fraction of Brandons jokes does the audience think are funny?
Answer: 3/10
Step-by-step explanation:
3/10 • 100 = 30%
The yearbook club had a meeting. The meeting had 12 people, which is two-thirds of the club. How many people are in the club?
people
Answer:
18 people
Step-by-step explanation:
What expression is equal to 5(3x-2)
Answer: 15x-10
Step-by-step explanation:To solve this problem you have to do the distributive property. You must do 5 times 3x and 5 times -2. 5 times 3x is 15x and 5 times -2 is -10. This means the answer is 15x-10.
Answer:
Step-by-step explanation:
5(3x - 2)
Opening bracket
= 5(3x) - 5(2)
= 15x - 10
Identify an equivalent fraction to 8/6. 6/8. 8/3. 4/3. 10/8.
expression show the sum of 5 less than y and the product of 3 and g
The expression that shows the sum of 5 less than y and the product of 3 and g is (y - 5) + 3g
Step-by-step explanation:
Let us revise some important words to translate a statement to algebraic expression
The sum ⇒ addThe product ⇒ multiplyThe quotient ⇒ divideLess than ⇒ subtractMore than add∵ 5 less than y
- That means subtract 5 from y
∴ 5 less than y = y - 5
∵ The product of 3 and g
- That means multiply g by 3
∴ The product of 3 and g = 3g
∵ The sum of 5 less than y and the product of 3 and g
- That means add (y - 5) and 3g
∴ the expression = (y - 5) + 3g
The expression that shows the sum of 5 less than y and the product of 3 and g is (y - 5) + 3g
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100 Points! What are the classifications of each system?
Drag the answer into the box to match each system.
Answer:
Part 1) Is a inconsistent system
Part 2) Is a consistent independent system
Part 3) Is a consistent dependent system
see the attached figure
Step-by-step explanation:
we know that
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent .
If a consistent system has an infinite number of solutions, it is dependent
If a system not have solution, it is said to be inconsistent
Part 1) we have
[tex]x+5y=-2\\x+5y=4[/tex]
This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept
so
The lines don't intersect
The system has no solution
therefore
Is a inconsistent system
Part 2) we have
[tex]y=3x+4\\-2x+y=4[/tex]
we know that
If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution
In this problem, the lines have different slopes (m=3 and m=2)
so
The lines intersect at one point
The system has one solution
therefore
Is a consistent independent system
Part 3) we have
[tex]3x+y=4[/tex] ----> equation A
[tex]-6x-2y=-8[/tex] ----> equation B
Multiply equation A by -2 both sides
[tex]-2(3x+y)=-2(4)[/tex]
[tex]-6x-2y=-8[/tex] ----> equation C
Compare equation B and equation C
Are identical lines
so
The system has infinity solutions
therefore
Is a consistent dependent system
Answer:
1) inconsient system
2) consient system
3) consient system
Are two obtuse triangles always, sometimes, or never similar
Answer:
My Answer Is ALWAYS.
Why I Think So:
It's Because As You Said...They Have Obtuse Angle, Which Can Never Change.
Obtuse triangles are sometimes similar if they have congruent angles; however, simply being obtuse does not guarantee similarity. The angles must match exactly among the triangles for them to be considered similar.
Explanation:Two obtuse triangles are sometimes similar but not always.
For two triangles to be similar, they must have exactly the same angle measurements, although the side lengths can differ by a consistent ratio.
In the case of obtuse triangles, they will be similar if they have one obtuse angle that is the same measure in both triangles and their other corresponding angles are also equal.
However, just having obtuse angles is not sufficient for similarity; the angles must be congruent, and in the case of an obtuse triangle, the other two angles must be specifically tailored so that all three angles are congruent to another triangle's angles.
The concept of triangle similarity falls under the Uniqueness of Solutions which denotes that a triangle is determined by three known elements, but these do not always provide a unique solution.
While often seen in the context of right triangles, such as when applying the Pythagorean Theorem, for obtuse triangles, similarity is determined by angle congruence rather than side lengths.
This implies that if two obtuse triangles have all three angles congruent, they are similar by definition. If not, they are not similar
Write the polynomial function, in standard form, that has zeros -3, 4, and 1.
Answer:
OPTION D
Step-by-step explanation:
Given the zeroes (roots) of a polynomial are: - 3, 4 & 1.
An [tex]$ n -degree $[/tex] polynomial has [tex]$ n - roots $[/tex] (zeroes). The converse is also true.
Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.
Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.
Here, -3, 4 & 1 are roots. So, the factors are: (x + 3), (x - 4) and (x - 1) .
Multiplying them will result in the polynomial.
[tex]$ (x + 3)(x - 4)(x - 1) $[/tex]
[tex]$ \implies (x^2 - 4x + 3x - 12)(x - 1) $[/tex]
[tex]$ \implies x^3 -x^2 - 4x^2 + 4x + 3x^2 - 3x - 12x + 12 $[/tex]
Simplifying, we get: [tex]$ \textbf{x}^\textbf{3} \textbf{-} \textbf{2x}^\textbf{2} \textbf{-} \textbf{11x} \textbf{+} \textbf{12}$[/tex]
Hence, OPTION D is the right answer.
Find domains of the following expressions.
sqrt(2-3x)+sqrt(5-x)
Find the domain by finding where the expression is defined.
Interval Notation:
Interval Notation: ( − ∞ , 2 3 ] (-∞,23]
Set-Builder Notation: { x ∣ ∣ ∣ x ≤ 2 3 }
Answer: (-∞ , 2/3)
Step-by-step explanation:
To find the domain of a radical , we will set the function inside the radical greater than or equal to zero , that is
2 - 3x ≥ 0
2 ≥ 3x
2/3 ≥ x
that is : x ≤ 2/3
Also
5 - x ≥ 0
5 ≥ x
That is : x ≤ 5
Therefore , the domain of the expression is x ≤ 2/3 and x ≤ 5
X over 5 equals 15 what does x equal
answer
75
Step-by-step explanation:
x over 5 = 15 is 75
this meanstitute x with 75 is a equation she's both sides equal we can conclude that x = 75 is the correct solution to the equation x over 5=15
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
a- The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
b- The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.
c- The vertex is (−1, 2), the domain is all real numbers, and the range is y ≥ 2.
d- The vertex is (−1, 2), the domain is all real numbers, and the range is y ≤ 2.
See picture reply for solution steps.
Final answer:
The vertex of the function f(x) = 3(x − 1)² + 2 is (1, 2), the domain is all real numbers, and the range is y ≥ 2, Option A is correct in the given options.
Explanation:
The vertex of the function f(x) = 3(x − 1)² + 2 is (1, 2), because the vertex form of a quadratic function is given by f(x) = a(x − h)² + k, where (h, k) is the vertex. In this case, a = 3, h = 1, and k = 2. The domain of the function is all real numbers, because there are no restrictions on x. The range of the function is y ≥ 2, because the minimum value of the function is 2 (occurring at the vertex) and y can be any value greater than or equal to 2.
Which numbers are perfect squares? Check all that apply
37:57
1
2
16
18
32
44
94
100
ANSWER: 1, 16, 100 are perfect squares.
STEP-BY-STEP EXPLANATION:
A perfect square is a number that can be expressed as the product of two equal integers.
1 x 1 = 1
4 x 4 = 16
10 x 10 = 100
Answer:
1, 16, 100 (a, c, h)
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Coefficient of 5x/6?
Answer:
5
Step-by-step explanation:
The coefficient is the number that is followed by an exponent. In this expression 5 is followed by x, making it a coefficient.
Final answer:
The coefficient of 5x/6 is the numerical factor 5/6, which is the fraction representing the relationship of numbers in front of the variable 'x'.
Explanation:
The coefficient of the term 5x/6 is the numerical factor that is multiplied by the variable 'x'. In this fraction, the numerator is 5 and the denominator is 6. Therefore, the coefficient of the term is 5/6. It is important to separate the coefficient (the number in front of the variable) from the variable itself when doing mathematical operations like addition, subtraction, or algebraic simplification.
Mason opens a savings account by making a $165.85 deposit. Every week, he deposits another $20.50 in the account. The following expression shows the amount of money that will be in the account x weeks after Mason opens it.
165.85 + 20.5x
How much money will be in the account after 10 weeks?
Answer:
$370.85
Step-by-step explanation:
sub the 10 for the x
370.85
Answer:
First multiply 10 by 20.5 because x represents the number of weeks. You get 205. Next add 165.85 to that and you get 370.85 as your final answer.
The frequency table shows the number of points scored during 30 Bulldogs
basketball games. On a piece of paper, draw a histogram to represent the
data. Then determine which answer choice matches the histogram you drew
the answer is the that 80-89 is the longer
Step-by-step explanation:
The answer choice that matches the histogram drawn is option C.
What is an histogram?A histogram is used to represent data graphically. The histogram has a y-axis which shows the frequency and an x - axis which shows the class interval. The correct option should match the information provided in the frequency table.
In this case, we have 5 intervals, that means the histogram must have 5 bars, where their height represents the frequency.
Having said that, the first bar must have a height of 4 units, the second one of 9 units, the third one of 5 units, the fourth one of 8 units and the fifth a height of 4 units.
Therefore, the right answer is C., because that's the histogram with the described heights.
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The basic price for an annual dental checkup and cleaning is $50. If the dentist finds any cavities in there will be an additional charge of $100 for each cavity tour dentist will have to find. Write an expression to describe the cost of the visit if the dentist finds n cavities
Answer:
100n+50
Step-by-step explanation:
the dentist charges $100 dollars per cavity found. Per indicates multiplication. Since there is an additional fee, we add $50 to the $100n, which will make the expression
$100n+50
olve for x. -3x = -15 x = -45 x = 5 x = -5
Answer:
it 1/4
Step-by-step explanation:
i did the other anwser and it anwsered after i got it wrong
a sum expression that equals -3/4
Answer:
2 1/4 - 3 = -3/4 can be a simple equation.
please help urgent !!!!
Answer:
50
Step-by-step explanation:
is 213 2.3 greater less or equal to
Answer:
2 1/3 > 2.3
Step-by-step explanation:
There are a couple of ways you can compare these numbers. One is to convert 2 1/3 to a decimal fraction. It is the repeating decimal ...
2 1/3 = 2.3333333...
Compared to 2.30, we see that 2 1/3 has a 3 in the hundredths place, where 2.3 has 0. Thus 2 1/3 is greater than 2.3.
__
You can convert them both to improper fractions and then to fractions with a common denominator.
2 1/3 = 7/3 = 70/30
2.3 = 23/10 = 69/30
70/30 > 69/30 . . . . so 2 1/3 > 2.3
9x divided by -2x sqared
Answer:
-9/2x
Step-by-step explanation:
Could someone explain to me how to solve this
? I got (-1,2) and it said I was wrong.
never mind found out why, i was supposed to plug in x for one of the equations to find y!
The ordered pair is (–1, –2)
Solution:
Given system of linear equations are
4x –7y = 10 – – – – (1)
3x + 2y = –7 – – – – (2)
To solve this by elimination method.
First multiply equation (1) by 3 and then multiply equation (2) by 4.
(1) × 3 ⇒ 12x –21y = 30 – – – – (3)
(2) × 4 ⇒ 12x + 8y = –28 – – – – (4)
Subtract equation (4) from equation (3), we get
⇒ 12x –21y – (12x + 8y) = 30 – (–28)
⇒ 12x –21y – 12x – 8y = 30 + 28
Combine like terms together.
⇒ 12x – 12x –21y – 8y = 30 + 28
⇒ –29y = 58
Divide both sides by –29, we get
⇒ y = –2
Substitute y = –2 in equation (1), we get
(1) ⇒ 4x –7y = 10
⇒ 4x – 7(–2) = 10
⇒ 4x + 14 = 10
⇒ 4x = 10 – 14
⇒ 4x = –4
Divide both side by 4, we get
⇒ x = –1
Hence the ordered pair for the given system of equations is (–1, –2).
Write an inequality that represents the verbal expression.
All real numbers less than 74.
{x < 74; x ∈ R}
Solution:
Given verbal expression is all real numbers less than 74.
R represents the set of all real numbers.
To write the verbal expression into inequality.
Let us assume that the set of all real numbers which is less than 74 are x.
So, all real numbers less than 74 means x < 74 and
x belongs to real numbers.
Therefore, the inequality is {x < 74; x ∈ R}.
What is the correct solution
-3(6-r)=6
-18-3r=6
-3r=24
r=-8
Answer:-3(6-r)=6
-18+3r=6
3r=6+18
3r=24
r=24/3
r=8
Step-by-step explanation:
can someone help me with this problem please
Answer:
Option C that is [tex]x=4,DF=EG=15[/tex] the right choice.
Step-by-step explanation:
Given,
A rectangle with the measures of its diagonal DF and EG.
Measure of diagonal DF = [tex]5x-5[/tex]
Measure of diagonal EG = [tex]x+11[/tex]
Note:Diagonal length of the rectangle are same.
So DF = EG
[tex]5x-5=x-11[/tex]
Subtracting [tex]x[/tex] and adding [tex]5[/tex] on both sides.
We have,
[tex]5x-x=11+5[/tex]
[tex]4x=16[/tex]
Dividing 4 both sides.
[tex]x=\frac{16}{4}=4[/tex]
So the value of [tex]x[/tex] is [tex]4[/tex].
Now plugging the value of [tex]x=4[/tex],we will find the numeric value of DF and EG.
DF = [tex]5x-5 =5(4)-5=15[/tex]
EG= [tex]x+11=4+11=15[/tex]
Both are equal DF = EG.
So x=[tex]4[/tex] and the length of diagonals are equal, DF = EG = [tex]15[/tex] unit.
A new computer system sells for approximately $2000 and depreciates at the rate of $500 per year.
what are you asking
Step-by-step explanation:
Mr. Phillips is mixing paint for his art
class. How many 6-ounce bottles can
he fill with the quantities of paint shown
at the right? Explain.
Paint
-64 ounces of blue
12 ounces of yellow
-32 ounces of white
Answer:
Mr. Phillips can fill 18 bottles of paint
Step-by-step explanation:
The first thing you should do in this case is to know how many ounces of paint you have:
Painting = 64 + 12 + 32 = 108
Then, to calculate the number of 6-ounce bottles you must divide the total number of ounces by 6:
n = (108) / (6) = 18
Which part of the angle is the vertex?
A. Point X
B. YX
C. YZ
D. Point Y
Is there a graph?
If you have more info you will get the best answer.
Answer: POINT Y :))
Explanation in the picture below :) hope i helped!!
For the given interval, is the function increasing or decreasing?
Answer:
increasing
Step-by-step explanation: