Expanding the expression, it is found that the statement is false.
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The statement given is: [tex](a - b)^2 = a^2 - b^2[/tex]Expanding the left side, we get:[tex](a - b)^2 = (a - b)(a - b) = a^2 - ab - ab + b^2 = a^2 - 2ab + b^2[/tex]
Which is different than the statement, and thus, the statement is false.The expression is also known as a notable product, the perfect square binomial.A similar problem is given by: https://brainly.com/question/17202374
The statement is false. The square of difference of two quantities is not equal to the difference of their squares. The correct expression for [tex](a-b)^2 is a^2 - 2ab + b^2, not a^2 - b^2.[/tex]
Explanation:The statement For any two integers a and b,[tex](a-b)^2 = a^2-b^2[/tex] is false. Let's illustrate why this is incorrect with an example. If we let a = 2 and b = 1, then the left-hand side of the equation [tex](a-b)^2[/tex] would give us [tex](2-1)^2[/tex] = 1 and the right-hand side of the equation [tex]a^2 - b^2[/tex] would give us 2² - 1² = 3 which are not equal.
It's important to note that (a - b)² can be expanded to a² - 2ab + b² in accordance with the square of a binomial formula, which is definitely not equal to [tex]a^2 - b^2[/tex]. A common mistake is to drop the middle term in the expansion (-2ab), which leads to this incorrect equation.
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Insert either < or > between the pair of numbers to make a true statement.
the square root of 2 is 1.4
So √2 < 1.9
Simplify 5 - 2 · 3 + 4.
Using the order of operation you would multiply first so
2 · 3 = 6
5 - 6 + 4 then we would subtract
5 - 6 = -1
-1 + 4 = 3 as your answer.
5−(2)(3)+4=3
Answer: 3
Step-by-step explanation: By using the order of operations,
2 x 3 = 6
5 - 6 = -1
-1 + 4 = 3
Therefore, 3 will be the correct answer for this problem! <3
Nita wants to buy a new keyboard for her computer. She will buy the keyboard when it is on sale for under $50 Write an inequality that describes k, the price in dollars at which Nita will buy the keyboard
This would be k < 50.
This inequality states that k, the price at which Nita wants to buy the new keyboard, is less than 50 dollars.
Answer:
0 ≤ k ≤ 50
Step-by-step explanation:
Here k represents the price of the keyboard ( in dollars ),
Given,
Nita will buy the keyboard,
If the price of the keyboard is under $ 50,
That is, [tex]k \leq 50[/tex]
Also, the price can not be negative,
⇒ [tex]0 \leq k[/tex]
Hence, the required inequality is,
[tex]0 \leq k \leq 50[/tex]
Since the slope of a vertical line is undefined, is it possible for vertical lines to be parallel.(Explain)
Yes the slope of a vertical line is parallel.
Parallel lines never intersect each other.
Y-axis is a vertical axis cartesian coordinate plane.
All vertical lines would be parallel to y-axis.
Because all vertical lines would have same slope, that is undefined slope.
Therefore, all vertical lines would be parallel lines.
So, we can finally say that it is possible for vertical lines to be parallel.
Bradley solved the following equation 4(5x - 6) = 2(8x + 10)
Hello! I'm guessing you need someone to solve this equation!
4(5x-6)=2(8x+10)
20x-24=16x+20
Add 24 on both sides!
20x=16x+44
Subtract 16x on both sides!
4x=44
Divide 4 by 44
x=11
Show work plz
Tina bought two pairs of regular socks and one pair of long fleece socks .The fleece socks cost $12.If the final price ,including 5% sales tax ,was $30.45,what was the price of each pair of regular socks?
A cube has a length, width and height of 6 feet. What is the volume in cubic INCHES?
Volume of cube = ( side)^3
Side = 6 feet = 6×12 = 72 inches ( 1ft =12 inch)
Vol. = (72)^3 = 72×72×72= 373248 cubic inches
Answer:
6
Step-by-step explanation:
Least to greatest ordering integers
Answer:
5, 19, 24, 46, 77, 98
Step-by-step explanation:
Just write the numbers in order (I am assuming from least to greatest). You can use a number line if necessary.
John earns $437 a week after a 15% pay rise. What was his pay initially? Round your answer to the nearest dollar. Do not include the dollar sign in your answer. For example, if your answer is $200.10, enter 200.
The answer to this question is 380
Answer:
380 dollar.
Step-by-step explanation:
John earns $437 a week after a 15% pay rise.
Let the initially pay of John be x
x + (15% of x) = 437
x + 0.15x = 437
1.15x = 437
x = [tex]\frac{437}{1.15}[/tex]
x = 380
Initially his pay was 380 dollar.
Frank thinks he will need at about 12 1/2 kilograms of sand for sandbox he is building. The sand he wants is 3$ per kilogram. About how much will frank spend on sand? Estimate the amount of sand he will need to the nearest whole number?
Ramona is a saleswoman whose base pay plus commissions amounted to $52561 last year. If her base pay was $23690 and she made $77,300 in sales last year, what is her rate of commission
A) 68%
B) 37%
C) 31%
D) 46%
Answer:
B) 37%
Step-by-step explanation:
Given,
The total base pay and commission = $ 52561,
While, base pay = $ 23690,
So, the amount of commision = Total base pay and commission - base pay = $ 52561- $ 23690 = $ 28871,
Also, total sale = $77,300,
Hence, the rate of the commission( in percentage )
[tex]=\frac{Commission}{Sale}\times 100[/tex]
[tex]=\frac{28871}{77300}\times 100[/tex]
[tex]=\frac{2887100}{77300}[/tex]
[tex]=37.3492884864\%[/tex]
[tex]\approx 37\%[/tex]
Option 'B' is correct.
Change the number 43,456 to its word name.
A. Four hundred thirty-four hundred and fifty six
B. Forty-three thousand, four hundred fifty six
C. Four hundred three thousand, four hundred fifty six
D. Forty-three thousand, four fifty six
Answer:
B
Step-by-step explanation:
solve for r. P=r+t+s
P = r + t + s
Subtract t from both sides.
P - t = r + s
Subtract s from both sides.
P - t - s = r is the equation that allows you to solve for the value of r if you know all the other values.
How many different 10 digit phone numbers are possible if numbers can be repeated
It was would numbers 000-000-0000 through 999-999-9999. So that would be 9,999,999,999 + 1 = 10 billion different 10-digit phone numbers.
Mariana wears her winter coat when the temperature is colder than − 4 C . Write an inequality that is true only for temperatures ( t ) at which Mariana wears her winter coat.
t<-4
Mariana only wears her coat when it is colder than -4 so t must be less than -4.
Answer: t < -4
Step-by-step explanation:
We want to represent temperatures colder than -4 C
In mathematical terms, we want to represent temperatures less than -4 C
t < -4
5x+2(x+9)=x+4x+43
How do you solve this?
x = 25/2
this is your answer
Step 1. Simplify x + 4x + 43 to 5x + 43
5x + 2(x + 9) = 5x + 43
Step 2. Cancel 5x on both sides
2(x + 9) = 43
Step 3. Divide both side by 2
x + 9 = 43/2
Step 4. Subtract 9 from both sides
x = 43/2 - 9
Step 5. Simplify 43/2 - 9 to 25/2
x = 25/2
a man is 76 inches tall. the length from his head to his shoulders is 14 inches, and the length from his waist to his shoulders is 30 inches. what is the length from his feet to his waist
What is the Greatest Common Factor of x6 and x3?
x4
x3
x2
x
Answer:
The answer is B x^3
Step-by-step explanation: I just took the FLVS exam and this was the correct answer
x3 is the Greatest Common Factor of x6 and x3.
How do you find the greatest common factor?The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 shares one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.
What is the GCF of 4 and 6?The largest number of all those common factors is known as the greatest common factor (GCF). Here, 2 is the largest number found in both factors. Hence, the GCF of 4 and 6 is 2.
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Calculate the slope of the line that passes through the labeled points on the graph.
m=(Y2-Y1)/(X2-X1)
(1.) m=(2-(-1))/(-2-3) = 3/-5 = -3/5
(2.) m=(-2-1)/(-3-2) = -3/-5 = 3/5
(3.) m=Infinity (equation: x=-2)
The slopes of the lines passing through the given points are: 1. [tex]\((-2,2)\)[/tex] and [tex]\((3,-1)\)[/tex]: [tex]\(m = -\frac{3}{5}\)[/tex]. 2. [tex]\((-3,-2)\)[/tex] and [tex]\((2,1)\)[/tex]: [tex]\(m = \frac{3}{5}\)[/tex]. 3. [tex]\((-2,-2)\)[/tex] and [tex]\((-2,3)\)[/tex]: The slope is undefined (vertical line).
To calculate the slope m of a line given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], you can use the formula:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Let's apply this formula to the given points:
1. For points (-2,2) and (3,-1):
[tex]\[m = \frac{-1 - 2}{3 - (-2)} = \frac{-3}{5}\][/tex]
2. For points (-3,-2) and (2,1):
[tex]\[m = \frac{1 - (-2)}{2 - (-3)} = \frac{3}{5}\][/tex]
3. For points (-2,-2) and (-2,3):
[tex]\[m = \frac{3 - (-2)}{(-2) - (-2)} = \frac{5}{0}\][/tex]
The slope for the third set of points is undefined because the denominator becomes zero, indicating a vertical line. The first two sets of points have slopes of [tex]\(-\frac{3}{5}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] respectively.
G.o has 3 orange picks for every two green. If there are 25 picks in all, how many picks are orange
15 picks are orange....
Answer:
15 orange picks.
Step-by-step explanation:
Let x represent the number of orange picks.
We have been given that G.o has 3 orange picks for every two green. We are asked to find the number of orange picks, if there are 25 picks in all.
Since there are 3 orange picks for every two green. so there will be 3 orange picks for all 5 (3+2) picks.
We will use proportions to solve our given problem.
[tex]\frac{x}{25}=\frac{3}{5}[/tex]
Upon multiplying both sides of our equation by 25, we will get:
[tex]\frac{x}{25}*25=\frac{3}{5}*25[/tex]
[tex]x=3*5[/tex]
[tex]x=15[/tex]
Therefore, there are 15 orange picks for all 25 picks.
an equation that is true for every value of the variable is a ___
An identical equation is a literal equation that is true for every value of the variable, e.g., the equation (x+1)2=x2+2x+1. A conditional equation (usually referred to simply as an equation) is a literal equation that is not true for all values of the variable, e.g., only the value 2 for x makes true the equation x+3=5.
Trisha spins a spinner. the pointer lands on three prime numbers .she says the sum is less than 12.which could be the number
The sum of the first three prime numbers less than 12 is 2, 3, and 5.
What is a Prime number?A prime number is a positive integer having exactly two factors that are 1 and number itself. Any number that does not follow this is termed a composite number.
Given
Trisha spins a spinner. the pointer lands on three prime numbers.
She says the sum is less than 12.
How to find the prime number?The prime numbers are as follows,
2, 3, 5, 7, 11..so on
So the sum of the first three prime numbers will be
2 + 3 + 5 = 10
Hence, the sum of the first three prime numbers less than 12 is 2, 3, and 5.
More about the prime number link is given below.
https://brainly.com/question/4184435
A number n is less than or equal to -7 or greater than 12.
A number n is less than or equal to -7 or greater than 12 is written as
[tex]n\leq -7 \; or \; n>12[/tex]
Given :
Given statement is' A number n is less than or equal to -7 or greater than 12'.
We need to convert the given statement into an inequality
n is less than or equal to -7
[tex]n\leq -7[/tex]
or n is greater than 12
[tex]n>12[/tex]
We need to combine both the inequalities
Connect both the inequalities by 'or'
A number n is less than or equal to -7 or greater than 12.
[tex]n\leq -7 \; or \; n>12[/tex]
Learn more : brainly.com/question/2332918
A 13.9 gallon gas tank is 4/5 full. How many gallons will it take to fill the tank?
It will take 2.78 gallons to fill the remainder of the tank.
13.9 * 4/5 = 11.12 - 11.12 is the amount of gas already in the tank.
13.9 - 11.12 = 2.78 - So, subtract 11.12 from 13.9 and you get your answer.
Hope this is right! ;)
I need help ASAP how ever gets the right answer first I wil mark Brainliest!!!
Answer:
The area of this tabletop is
6 ft. × 2 ft. = 12 ft.²
CAN SOMEONE HELP ME PLEASE MUCH THANK
i think it is Transitive property of congruence but im not 100% sure
Answer,
A) Transitive Property of Parallel lines
Hope this helps :-)
-2 times 8 over 3 =?
Multiply
answer: -5 [tex]\frac{1}{3}[/tex]
work:
set up as fractions.
[tex]\frac{-2}{1} x \frac{8}{3} =[/tex]
multiply across to solve.
so, multiply -2 x 8 and 1 x 3.
you get [tex]\frac{-16}{3}[/tex]
or, -5 [tex]\frac{1}{3}[/tex]
i hope this helps, and have a great day! don't hesitate to ask if you need more help with this specific question! ♥ - eviezoom
Answer:
-2 * 8/3 = -16/3
Simplified, it would be: -5 1/3
Hope this helps :-)
An engineer designing a ramp in a football stadium was told to keep the slope to a ratio of 1:10. The ramp height is 25 ft. What is the Ideal Mechanical Advantage of the ramp? (Its 10.05, but how do I solve it?)
we know that
To calculate the ideal mechanical advantage for an inclined plane, divide the length of the incline by the height of the incline
Step 1
Find the horizontal distance of the ramp
we know that
the ramp has a slope of [tex]1:10[/tex]
so
by proportion
[tex]\frac{1}{10} \frac{height}{long} =\frac{25}{x} \frac{height}{long} \\ \\x=25*10 \\ \\ x=250\ ft[/tex]
Step 2
Find the length of the incline of the ramp
Applying the Pythagorean Theorem
[tex]incline^{2}=height^{2}+horizontal^{2}[/tex]
substitute the values
[tex]incline^{2}=25^{2}+250^{2}[/tex]
[tex]incline^{2}=63,125[/tex]
[tex]incline=251.25\ ft[/tex]
Step 3
Find the ideal mechanical advantage
[tex]Ideal\ Mechanical\ Advantage=\frac{incline}{height}[/tex]
substitute the values
[tex]Ideal\ Mechanical\ Advantage=\frac{251.25}{25}=10.05[/tex]
therefore
the answer is
the Ideal Mechanical Advantage of the ramp is [tex]10.05[/tex]
Which list shows the numbers in order from least to greatest?
745 , 7.6, 7.41
745 , 7.41, 7.6
7.41, 745 , 7.6
7.41, 7.6, 745
745 , 7.6, 7.41
Answer:
7.41, 7.6, 745
Step-by-step explanation:
what is the answer to 2x-3y=11 2x+y=9