There is no three-digit whole number that has exactly five positive factors.
The prime factorization of a number with five factors will be of the form p⁴ or p²q, where p and q are distinct prime numbers.
p⁴:
The smallest prime number greater than or equal to 10 is 11.
So, let's consider 11⁴:
11⁴ = 14641 (which is a five-digit number)
p²q:
To minimize the number, we need the smallest prime numbers possible. The two smallest prime numbers greater than 10 are 11 and 13.
Let's consider the product of these two primes:
11² × 13 = 1573 (a four-digit number)
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Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart after 30 minutes?
Answer:
they travel 115 km/h long
3. Consider the multiplication operations below and choose whether the fosuit com
be rational, Inational, or both.
Irrational
Expressions
Rational
8. VE
О
tvo. V
V3.12
о
Answer:
1st expression= rational 2nd expression= rational 3rd expression = irrational
Step-by-step explanation:
The first and second expressions are rational because they both equal whole numbers (4 and 3) while the last expression equals a decimal that goes on forever with no end, thus making it irrational.
On her way to work each morning Sophia
purchases a small cup of coffee for $425
from the coffee shop
Answer:
This is easy...stop purchasing this outrageous coffee for $425. No coffee is that good
Solve UW. how do I get the answer?
Answer:
UW = 67
Step-by-step explanation:
UW = 6x - 35
VW = 4x - 20
UV = 19
So that means
4x - 20 + 19 = 6x - 35
4x - 1 = 6x - 35
-1 = 2x - 35
34 = 2x
x = 17
6(17) - 35
102 - 35 = 67
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Step-by-step explanation:
19 + ( 4x - 20 ) = 6x - 35
4x - 1 = 6x - 35
2x = 34
x = 17
UW = 6(17) - 35 = 67
order these numbers in ascending order. -11, 11.8 9.42 ,10
Answer:
-11,9.42,10,11.8
-11<9.42<10<11.8
Answer:
I think the answer is
-11, 9.24 ,10, 11.8
pls help! I need the answer quickly!
Step-by-step explanation:
The correct answer is 4 (option B)
What is a rational number between -1/5 and -2/5?
Answer:
-1/4
Step-by-step explanation:
-0.25
HW #3 review
I will give brainliest to whoever gets it right
Hi there!
The numbers you have written there are correct.
[tex]-5<x<0[/tex] is true for any value of x that is greater than -5 or less than 0.
When a number is less than 0, we know that it has to be negative.
However, it cannot be more negative than -5. It cannot be -5 either.
So, x could be -1, -2, -3, -4, -1/2, -2.3, -4.9, the list goes on.
I hope this helps!
express 3x-x^2 as m-(x-n)^2. Ill give brainliest to correct answer!
(Also please see the picture since you might mistake x having a square as a 2x)
This is simply done by Method of Completing the Square.
3x - x²
Add and subtract half the coefficient of x and square it.
( This is done so there'd be no alterations to the quadractic Expression)
So To start
We'd like x² to be positive...(So factor out a negative).
–(x² - 3x )
Now In this case
You see there's a Negative Outside the the bracket
Instead of adding and Subtracting squared values of half the coefficient of X... We'd Add Twice and do not subtract.
Reason: If you add outside the bracket and subtract the other inside the bracket... This will be wrong because there's a negative patiently waiting outside the bracket to Interact with the negative you subtracted to make it Positive.
See what I mean.
Let's say you added 2² and subtracted 2² in this problem
2² – ( x² - 3x - 2²)
If you decide to open the bracket
You'll have
2² – x² + 3x + 2²
NOW THIS IS WRONG BECAUSE WE ALTERED THIS EXPRESSION. WHERE'D 2² + 2² COME FROM?
THIS IS WHY YOU'LL ADD THE SQUARED COEFFICIENT OF X TWICE IN CASES LIKE THESE.
SO GOING BACK TO THE ORIGINAL QUESTION.
– (x² - 3x )
Adding the half the coefficient of x twice and squaring them...
Coefficient of x = 3
Half of 3 = 3/2
Squaring it gives (3/2)²
NOW PROCEEDING
(3/2)² – [ x² - 3x + (3/2)²]
If you open this bracket... (3/2)² will cancel out with —(3/2)²
Meaning that we haven't altered the expression in any way
Moving On...
Applying basic factorizing principle
9/4 – ( x - 3/2)².
Answer = 9/4 – ( x - 3/2)² Which is in the Form m – ( x - n )²
Therefore m = 9/4 and n = 3/2.
Hope This Helps
Is [tex]2 \frac{2}{3} [/tex]
a rational number
A board of wood measures 58 inches thick. If you stack the boards 6212 inches high, how many boards are in the stack
Answer:
107 full and .103 of another
Step-by-step explanation:
6212/58 =
Which of the h values are solutions to the following equation?
h^2=0.36
Choose all answers that apply:
A: h= square root of 0.6
B: h = square root of -0.6
C: h = 0.18
D:h = -0.18
E: None of the above
Answer:
a:h=square root of 0.6
Step-by-step explanation:
thank you for your time today
Answer:
none of the above
Step-by-step explanation:
KHAN
How would you write 5x5x5x5x5x5 in exponential form
Answer:
5^6
Step-by-step explanation:
This is because the exponent is how many numbers are in the multiplication equation, in this case, five. Because there are six five's being multiplied together, our exponent is six.
7 thousands 8hundredsx10
Answer:
78,000
Step-by-step explanation:
A housepainter buys 40 gallon-size cans of paint for $920. Some of these are blue paint that cost $30 per gallon and the rest are white paint that cost $20 per gallon. How many gallons of white paint does the painter buy?
Answer:
28
Step-by-step explanation:
x=blue
y=white
x+y=40
30x+20y=920
30(x+y=40) ; 30x+30y=1200___[1]
30x+20y=920 ; 30x+20y=920___[2]
[1]-[2] : 30x+30y-30x-20y=1200-920
10y=280
y=28
painter buys 28 white gallons
What is the relationship between the 6s in 675,002 and 385,621
Answer:
The value of 6 in 675,002 is 1,000 times greater than the value of 6 in 385,621.
Is 0.03456 a rational number
Answer:
Yes. It is a rational number.
help for 15 points . ill up it
Step-by-step explanation:
Let [tex]P_1(-1, -8)\:\text{and}\:P_2(-4, -9)[/tex]
The slope of the line through these two points is
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{(-9 + 8)}{(-4 + 1)} = \dfrac{1}{3}[/tex]
So the slope-intercept form of the line passing through the two points is
[tex]y = mx + b = \frac{1}{3}x + b[/tex]
To find b, we use either point into our equation. Let's use (-1, -8):
[tex]-8 = \frac{1}{3}(-1) + b \Rightarrow b = -\dfrac{23}{3}[/tex]
Therefore, the slope-intercept form of the equation for the line is
[tex]y = \dfrac{1}{3}x - \dfrac{23}{3}[/tex]
The standard form of the equation can be written as
[tex]x + 3y + 23 = 0[/tex]
Convert the following decimals into fraction . Do not reduce the fractions
0.25 =
Answer:
25/100
Step-by-step explanation:
0.25=25/100
Hope this helps! Thanks.
You have two cards with a sum of (-12) in your hand.
Add two more cards but the total of cards stay the same
Answer:
you could have a 6 and then a -6
or a 3 and a -3
or 0 and 0
have 2 cards with the same number but one is negative
Step-by-step explanation:
Tom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he
make in July if he sold 12 cars? In August he made $6500, how many cars did he sell?
Answer:
Answer = he made 7,000 in July and sold 10 cars in august.
Step-by-step explanation:
-y- 3 (-3y+5) helpppppppp
Answer:
D = 8y-15
Step-by-step explanation:
-y-9y-15 than combine -y and -9y
so = 8y-15
what times we subtract the number 80 by 8
Answer:
Question unclear
Step-by-step explanation:Your probally asking what times 8 gives us 80. If you are than 10!
What is Matilda's number?
Answer:
11
Step-by-step explanation:
The answer will be 11
as she is thinking of prime number so
111 is not a prime number
aswell as 77 is not a prime number
11 is a prime number and is also a multiple of 11
Answer:
11
Step-by-step explanation:
Find all points on the curve x^2y^2+xy=2 where the slope of the tangent line is −1
Differentiate both sides with respect to x and solve for the derivative dy/dx :
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[x^2y^2+xy\right] = \dfrac{\mathrm d}{\mathrm dx}[2] \\\\ \dfrac{\mathrm d}{\mathrm dx}\left[x^2\right]y^2 + x^2\dfrac{\mathrm d}{\mathrm dx}\left[y^2\right] + \dfrac{\mathrm d}{\mathrm dx}\left[x\right]y + x\dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ 2xy^2 + x^2(2y)\dfrac{\mathrm dy}{\mathrm dx} + y + x\dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ (2x^2y+x)\dfrac{\mathrm dy}{\mathrm dx} = -2xy^2-y \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{2xy^2+y}{2x^2y+x}[/tex]
This gives the slope of the tangent to the curve at the point (x, y).
If the slope of some tangent line is -1, then
[tex]-\dfrac{2xy^2+y}{2x^2y+x} = -1 \\\\ \dfrac{2xy^2+y}{2x^2y+x} = 1 \\\\ 2xy^2+y = 2x^2y+x \\\\ 2xy^2-2x^2y + y - x = 0 \\\\ 2xy(y-x)+y-x = 0 \\\\ (2xy+1)(y-x) = 0[/tex]
Then either
[tex]2xy+1 = 0\text{ or }y-x=0 \\\\ \implies y=-\dfrac1{2x} \text{ or }y=x[/tex]
In the first case, we'd have
[tex]x^2\left(-\dfrac1{2x}\right)^2+x\left(-\dfrac1{2x}\right) = \dfrac14-\dfrac12 = -\dfrac14\neq2[/tex]
so this case is junk.
In the second case,
[tex]x^2\times x^2+x\times x=x^4+x^2=2 \\\\ x^4+x^2-2 = (x^2-1)(x^2+2)=0[/tex]
which means either
[tex]x^2-1 = 0 \text{ or }x^2+2 = 0 \\\\ x^2 = 1 \text{ or }x^2 = - 2[/tex]
The second case here leads to non-real solutions, so we ignore it. The other case leads to [tex]x=\pm1[/tex].
Find the y-coordinates of the points with x = ±1 :
[tex]x=1 \implies y^2+y=2 \implies y=-2 \text{ or }y=1 \\\\ x=-1\implies y^2-y=2\implies y=-1\text{ or }y=2[/tex]
so the points of interest are (1, -2), (1, 1), (-1, -1), and (-1, 2).
Need help ASAP PLEASE!!!
Answer:
x=1
Step-by-step explanation:
3/2+1/2x=2x
or,3*1+1*1x/2=2x
or,4x/2=2x
or,4x-2x=2
or,x=2/2
so,x=1
Someone please help me with 13 and 14 I’m really struggling
Answer:
Step-by-step explanation:
can anyone help me out with this one?
Please help due tomorrow
The scaled factor is 3 for all of them.
The expression 1/x+y
is equal to which quantities?
(1/x) + y
1/x + y
1/(x + y)
The equivalent form of the given expression is 1 /(x + y)
The given expression:
[tex]\frac{1}{x+y}[/tex]
To find:
the equivalent form of the expression:The equivalent form of the expression can be written as follows:
[tex]\frac{1}{x+y} = 1 /(x + y)[/tex]
For example, if x = 1 and y = 2, the inverse of the expression can be written as;
[tex]\frac{1}{x + y} = \frac{1}{(1 + 2)} = \frac{1}{3}[/tex]
Also, if x = 2 and y = 3, the inverse of the expression can be written as;
[tex]\frac{1}{x + y} = \frac{1}{(2 + 3)} = \frac{1}{5}[/tex]
Thus, the equivalent form of the given expression is 1 /(x + y)
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