Answer:
Congruence is a relationship of shapes and sizes, such as segments, triangles, geometrical figures, while equality is a relationship of sizes, such as lengths, widths, heights.
Congruence deals with objects while equality deals with numbers. You wont say that two shapes are equal or two numbers are congruent.
Step-by-step explanation:
Alana noticed that a number like 8 = 2 (i.e. ) has exactly four factors: 1, 2, 2 , and ! 2 . What other numbers are of this form have exactly four factors? Do all the perfect cubes have exactly four factors? Is it true that all numbers that have exactly four factors are perfect cubes?
Answer:
Step-by-step explanation:
Hello,
What other numbers are of this form have exactly four factors?
[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]
Do all the perfect cubes have exactly four factors?
[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]
Is it true that all numbers that have exactly four factors are perfect cubes?
6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.
Thank you.
We know that any number can be decomposed as a product of prime numbers.
For example:
[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]
8 has four factors if we count the 1.
Now we need to answer some questions regarding this:
What other numbers are of this form have exactly four factors?
8 is a cube number.
Remember that all cube numbers X can be written as:
[tex]X = n\cdot n\cdot n \cdot 1[/tex]
Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.
But let's see the case:
[tex]8\cdot 8\cdot8= 512[/tex]
512 is a perfect cube, and if we decompose it we get:
[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]
So we found a perfect cube that has 10 factors.
This means that not all perfect cubes have exactly 4 factors.
Now, all numbers that have exactly four factors are perfect cubes?
This is also false, just let's create a counterexample.
[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]
the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.
If you want to learn more, you can read:
https://brainly.com/question/832797
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $28 monthly fee and charges an additional
$0.09 for each minute of calls. The second plan has no monthly fee but charges $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Answer:
700 Minutes
Step-by-step explanation:
For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.
For the first phone plan, we have a base $28 and additional $0.09 per minute of call. This can be expressed as:
28 + 0.09x Where x is the number of minutes used
For the second phone plan, we have a flat $0.13 per minute of call. This can be expressed as:
0.13x Where x is the number of minutes used
To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.
28 + 0.09x = 0.13x
28 + 0.09x + -0.09x = 0.13x + -0.09x
28 = 0.04x
28 = (1/25)x
28 * 25 = (1/25)x * 25
28 * 25 = x
700 = x
Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.
Cheers.
FIRST TO ANSWER GETS BRAINLIEST
A train journey is supposed to last 2.5 hours. The train leaves the station 15 minutes late and stops at another station for an extra 20 minutes. How long did the entire journey take? FIRST TO ANSWER GETS BRAINLIEST!
Answer:
12.5
Step-by-step explanation:
that is to say 20 -15 because it went late =5
then 2.5×5
X+1/6=-3/5 solve
for x
Answer:
-13/30
Step-by-step explanation:
take 1/6 to other side,
x=-3/5 -1/6
taking LCM of denominators,
-8-5/30
=-13/30
Answer:
X=23/30
Step-by-step explanation:
X + 1/6 = -3/5
X + 5/30 = -18/30
-5/30 -5/30
X = -23/30
I feel like i did something wrong... but im pretty sure its right. Let me know if it's right! Hope it helps.
Simplify using like terms
1.7 + 8.23 -3.4 +4.7j
Step-by-step explanation:
Let's look at our expression:
[tex]1.7+8.23-3.4+4.7j[/tex]
The numbers without a variable at the end are like terms here. Let's add them up.
[tex]1.7+8.23=9.93\\9.93-3.4=6.53[/tex]
Then, let's add our answer, 6.53, to the term with a variable, 4.7j.
Our final answer: 6.53 + 4.7j
I hope this helps you!
iff(x) = (x - 3)2
for x = 3, then f-1(x) = ?
A
VX-3
B.
√x+3
O
a VX-3
IN x + 3
Answer:
Option B. √x + 3
Step-by-step explanation:
f(x) = (x - 3)²
We can obtain the inverse f¯¹(x) of the above expression as follow:
f(x) = (x - 3)²
Replace f(x) with
f(x) = (x - 3)²
y = (x - 3)²
Next, interchange x and y
y = (x - 3)²
x = (y - 3)²
Make y the subject
x = (y - 3)²
Take the square root of both side
√x = y - 3
Add 3 to both side
√x + 3 = y - 3 +3
√x + 3 = y
y = √x + 3
Finally, replace y with f¯¹(x)
y = √x + 3
f¯¹(x) = √x + 3
Your dinner in London cost 82 British pounds. How much
was it in U.S. dollars?
Some one please help me ASAP!!!
In U.S. dollars, the equivalent money will be $100.74
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
Given is your dinner in London cost 82 British pounds
Then in U.S. dollars, the equivalent money will be equivalent to -
x = 82 pounds = 82 x 1.2286 = $100.74
x = $100.74
Therefore, in U.S. dollars, the equivalent money will be $100.74
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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Solve the rational expression 9x+3/12x+4
Answer:
The answer is
[tex] \frac{3}{4} [/tex]Step-by-step explanation:
[tex] \frac{9x + 3}{12x + 4} [/tex]
To solve the rational expression factorize both the numerator and the denominator.
For the numerator
9x + 3
Factorize 3 out
We have
3( 3x + 1)
For the denominator
12x + 4
Factorize 4 out
That's
4( 3x + 1)
So we now have
[tex] \frac{3(3x + 1)}{4(3x + 1)} [/tex]Reduce the expression with (3x + 1)
We have the final answer as
[tex] \frac{3}{4} [/tex]Hope this helps you
Solve the following linear equation. If a x is a fraction write as follows
-4/5
-6x+3=-21
X =
Answer:
x-5
Step-by-step explanation:
x=5
cause of the negt 6x and posstive 3 =21 so yeah that it for now so go for it head froce
4x — 3 = —31 Solve for x
Answer:
x = -7
Step-by-step explanation:
4x — 3 = —31
Add 3 to each side
4x — 3+3 = —31+3
4x = -28
Divide by 4
4x/4 = -28/4
x = -7
Your answer would be x=-7 or -7!
The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t, where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.
Answer:
7.5 seconds
Step-by-step explanation:
[tex]h = - 16 {t}^{2} + 120t \\ \because \: we \: have \: to \: find \: the \: time \: required \: \\ for \: the \: object \: to \: return to \: its \: \\ point \: of departure. \\ \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\ \therefore \: 0 = - 16 {t}^{2} + 120t \\ \therefore \:16 {t}^{2} - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \: \: or \: \: (2t - 15) = 0 \\ \therefore \:t = \frac{0}{8} \: or \: t = \frac{15}{2} \\ \therefore \:t = 0 \: or \: t = 7.5 \\ \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{ \therefore \: t = 7.5 \: seconds}}[/tex]
Thus, the time required for the object to return to its point of departure is 7.5 seconds.
A shirt was originally priced at $60. The store is having a 15% off sale. How much will you pay for the shirt after the discount (not including tax) $________________
Answer: $51
Step-by-step explanation:
If 15% discount is applied then 85% of the price will be the left to pay.
so 85% * 60 will give you the price of the shirt after the discount.
85% * 60 = 51
Answer:
Step-by-step explanation:51.00$
What’s is 2000+100.000
Answer:
2,100.000
Step-by-step explanation:
Answer:
2000+100.000=2100
Its simple just calculate it in a calculator...
Please help!! Which of the following is a conjugate for 7+i square root 2?
Its conjugate is
7 - i√2
Find the intercepts for this equation. x+2y=10
Answer:
Step-by-step explanation:
y= 0
x + 2(0) = 10
x = 10
(10, 0)
x = 0
0 + 2y = 10
2y = 10
y = 5
(0,5)
$10.00 divided by 25
What is the area of the parallelogram shown
The number p, the number q, and the product p.q are all the same type of
number. Which type of number could they be?
A negative numbers
B prime numbers
complex numbers
rational numbers
Answer:
rational numbers
Step-by-step explanation:
They cannot be negative numbers because the product of two negative numbers is positive.
They cannot be prime numbers because the product of two prime numbers is not a prime number.
The product of two complex numbers can be a complex number, but it may also be a real number.
The product of two rational numbers is always rational.
Answer: rational numbers
The bus fare in a city is $ 1.75 People who use the bus have the option of purchasing a monthly coupon book for $ 35.00 With the coupon book, the fare is reduced to $0.50. How many times must someone use the bus so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book?
Answer:
28 times
Step-by-step explanation:
Create an equation where x represents the number of times the bus is used:
1.75x = 0.5x + 35
Solve for x:
1.75x = 0.5x + 35
1.25x = 35
x = 28
So, the bus has to be used 28 times for the prices to be the same.
August 22 3months later what day would it be
What is the simplified expression for 4 to the 4 power x 4 to the 3 power over 4 to the 5 power
Answer:
42 or 4^2
hope this helps
Answer:
4^12
Step-by-step explanation:
Please help me with the question below
Answer:
She's 12 years old! i hope this helps you!
Step-by-step explanation:
1. Ted is 5 years older than Ned. Let n = Ned's age. Then _?_= Ted's age.
Answer:12
Step-by-step explanation:
The number 0.2 can be written as 2/10, so is it a rational number?
Answer:
yes it is
Step-by-step explanation:
Hope this helps✨
Solve equation. What is the solution set
-4(z-2)+4=21-(z-3)
Answer:
z=-75/17
Step-by-step explanation:
Expand this equation:
-4z+8+4=-21z-63
-4z+21z=-63-8-4
17z=-75
z=-75/17
A woman making $3000 per month has her salary reduced by 20% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Find her salary after the raise. $ per month What percent change is this from the $3000 per month? %
Answer:
4%
Step-by-step explanation:
Since she first goes down 20% you would do 3000 times 20 which is 60000 and divided by 100 which is 600 and you would subtract 600 from 3000 which is 2400 and then you would multiply that by 30 which is 72000 and then you would divide by 100 which is 720 and add that to 2400 which is 3120 and to find the percent change from 3000 to 3120 you would subtract 3120 by 3000 which is 120 and you would divide that by 3000 which is 0.04 and multiply that by 100 which is 4 so the percent change would be 4%
100 points, will mark brainliest!!!! Explain why (4, 1) is not a solution to the equation y = 3x + 1.
Because if you substitute x = 4 and y = 1 in the equation of y = 3x + 1, you'll see that both sides are different.
So if we substitute x = 4 and y = 1 in the equation, we get:
1 = 3(4)+1
1 = 12+1
1 = 13
The equation isn't true though. Also we can explain why (4,1) isn't the solution to the equation by graph (you can go draw the graph of y = 3x + 1 and notice that the line doesn't pass through (4,1) )
Also how about another example? But this time, we use (0,1) which is the solution of y = 3x + 1.
Substitute x = 0 and y = 1 in the equation as we get:
1 = 3(0)+1
1 = 0 + 1
1 = 1
Since the equation is true, that means the (0,1) is one of the solution of y = 3x + 1.
Maybe, you want another example again? How about (1,4) which is also one of the solution of y = 3x + 1.
Again, substitute x = 1 and y = 4.
4 = 3(1)+1
4 = 3+1
4 = 4
Since the equation is true. Therefore (1,4) is also one of the solution of y = 3x + 1.
Also here's why (4,1) is not the solution of y = 3x + 1
Basically, from (x,y), 4 is the x and 1 is the y. If we substitute "x" in any equations, we get the "y". Meaning that the x value can be meant as "input" and we get the output "y" like Function which is it.
If we substitute x = 4 in the equation...
y = 3(4)+1
y = 12+1
y = 13
Meaning that the actual y value is 13, not 1. This explains why (4,1) isn't the right solution.
Maybe, what if we substitute y instead? Well that works. Now let's try substitute both y = 1 and y = 13 to see which is the right value.
(1) For y = 1,
1 = 3x+1
1-1=3x
0=3x
x=0 (Therefore, x = 0 and y = 1)
So the actual order is (0,1).
(2) For y = 13
13 = 3x+1
13-1 = 3x
3x = 12
x = 4 (Therefore, x = 4 and y = 13)
so the actual order for (2) is (4,13).
Basically, (4,1) is false for y = 3x + 1.
Answer:
See below
Step-by-step explanation:
Given the point (4,1) means
(x,y) = (4,1)
So, x = 4 , y = 1
Given the equation y = 3x+1
Put x = 4 and y = 1
=> 1 = 3(4)+1
=> 1 = 12 + 1
=> 1 ≠ 13
Since Left hand side doesn't equal right hand side, (4,1) is not the solution to y = 3x+1
Andy painted 400 square feet in 3 hours. At that rate, how many cars could they wash in 7 hours? *
Answer:
It will take 5.4 hour to paint 720 square feet
Step-by-step explanation:
The question should be like this"Andy painted 400 square feet in 3 hours. How long would it take him to paint 720 square feet?"
In 3 hours = 400 square feet is painted
1 square feet is painted in [tex]\dfrac{3}{400}\ h[/tex]
To find time to paint 720 square feet multiply the above term by 720 as follows :
[tex]720\ ft^2=\dfrac{3}{400}\times 720\ h\\\\=5.4\ h[/tex]
So, it will take 5.4 hour to paint 720 square feet.
SOS. I'm stuck!! helpppppp
Answer:
12+x goes to 19
3x+y goes to 25
4y-10 goes to 6
1/2xy goes to 14
x=7 and y=4 all you have to do is substitute for example 12+x substituted it's 12+7 then just do the math. That's it.
Use inductive reasoning to predict the most probable next number in the list. 1, 4, 9, 16, 25, ?
Answer:
36
Step-by-step explanation:
Starting with 4, 9.
9 - 4 = 5 then + 2
So forward.
Answer:
1, 4, 9, 16, 25, 36
Step-by-step explanation:
This is because as you see 1 + 3 = 4, then 4 + 5 = 9, then 9 + 7 = 16. So we see that it goes like 3 + 5 + 7 + 9 + 11 + 13 . . . That is the pattern. Hope this helps!