Answer:
If statement(1) holds true, it is correct that [tex]\small \frac{r}{s}[/tex] is an integer.
If statement(2) holds true, it is not necessarily correct that [tex]\small \frac{r}{s}[/tex] is an integer.
Step-by-step explanation:
Given two positive integers [tex]r[/tex] and [tex]s[/tex].
To check whether [tex]\small \frac{r}{s}[/tex] is an integer:
Condition (1):
Every factor of [tex]s[/tex] is also a factor of [tex]r[/tex].
[tex]r \geq s[/tex]
Let us consider an example:
[tex]s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2[/tex]
[tex]\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10[/tex]
which is an integer.
Actually, in this situation [tex]s[/tex] is a factor of [tex]r[/tex].
Condition 2:
Every prime factor of s is also a prime factor of r.
(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)
Let
[tex]r = 2^2\cdot 5\\s =2^4\cdot 5[/tex]
[tex]\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}[/tex]
which is not an integer.
So, the answer is:
If statement(1) holds true, it is correct that [tex]\small \frac{r}{s}[/tex] is an integer.
If statement(2) holds true, it is not necessarily correct that [tex]\small \frac{r}{s}[/tex] is an integer.
Micah harvested 28 watermelons from his garden. He sold w watermelons at the market. Which expression describes the number of
watermelons that Micah has remaining?
w
28 + w
w-28
d
28 - w
if x = 20
-5 - 3x - x - (-16)
Answer:
Answer : -69
Step-by-step explanation:
-5 - 3x - x- (-16)
= -5 -3 ×(20) - 20 -( -16)
= -5 - 60 -20 +16
= -85 + 16
= -69.
Hope it helps,
Mark it as Brainliest.
Doug can download new songs for $1.19 each. Write an equation to show how many songs he can download for $12.00.
Help please I need this ASAP
Answer:
35
Step-by-step explanation:
Brianna=x
Justin=x+10
Hannah=2(x+10)
x+x+10+2x+20=130
4x+30=130
4x=130-30
4x=100
x=25
Justin =x+10 = 25+10=35
Question 18 (5 points)
Which one of the following statements expresses a true proportion?
A) 3:4 = 9:12
B) 2:1 = 1:2
C) 7:9 = 8:9
D) 54:9 = 6:3
Answer:
A is the true proportion
Step-by-step explanation:
3/4 = 9/12 = 36 = 36
Question 1 1 pts Evaluate the expression 5.2 - 3y + 7 for x = -4 and y = -6
Answer:
30.2
Step-by-step explanation:
5.2 - 3y + 7
Let y= -6
5.2 -3(-6) +7
5.2 +18 +7
30.2
Just substitute and solve.
5.2 - 3(-6) + 7
5.2 - (-18) + 7
23.2 + 7
30.2
Best of Luck!
Simplify the expression, show all of your work 18 : 2x3 / 5-2
Answer:
2⋅(x 3 −5)
________
5
Step-by-step explanation: I hope this really help!
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x3" was replaced by "x^3".
STEP
1
:
x3
Simplify ——
5
Equation at the end of step
1
:
x3
(2 • ——) - 2
5
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
2 2 • 5
2 = — = —————
1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x3 - (2 • 5) 2x3 - 10
————————————— = ————————
5 5
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
2x3 - 10 = 2 • (x3 - 5)
Trying to factor as a Difference of Cubes:
3.2 Factoring: x3 - 5
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = x3 - 5
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -6.00
-5 1 -5.00 -130.00
1 1 1.00 -4.00
5 1 5.00 120.00
Polynomial Roots Calculator found no rational roots
Final result :
2 • (x3 - 5)
————————————
5
Answer:
2⋅(x 3 −5)
________
5
Step-by-step explanation:
An answer from the smarter
a+7(a+b)-8(a+b)+b???
Answer:
0
Step-by-step explanation:
Given
a + 7(a + b) - 8(a + b) + b ← distribute both parenthesis
= a + 7a + 7b - 8a - 8b + b ← collect like terms
= a + 7a - 8a + 7b - 8b + b
= 0
Answer:
0
Step-by-step explanation:
a+7a+7b-8a-8b+b
combining like terms
a+7a-8a+b+7b-8b
8a-8a+8b-8b
0
The table shows the number of the free throws each player made during the last basketball season determine if each statement is true or false
Answer:
True
Step-by-step explanation:hi
Ms. Ironperson lives due east from the shawarma mediterran grill and Mr. Thoro lives due south. Both leaves at the same time, ms.Iron person traveling at 50 mph and mr. Thoro at 60 mph. Calcute when they would be 400 mphs apart and how long would it take to happen
Correct question is;
Ms. Ironperson lives due east from the shawarma mediterran grill and Mr. Thoro lives due south. Both leaves at the same time, ms.Iron person traveling at 50 mph and mr. Thoro at 60 mph. Calculate when they would be 400 miles apart and how long would it take to happen
Answer:
They will be 400 miles apart when Ms. Ironperson has covered 256 miles and Mr. Thoro has covered 307 miles after 5.12 hours
Step-by-step explanation:
Since Ms. Ironperson lives due east from the shawarma mediterran grill and Mr. Thoro lives due south,then the distance between them will be the hypotenuse of a right angle triangle.
Now, we are told that Ms. Ironperson is traveling at 50 mph and that Mr. Thoro is traveling at 60 mph.
Thus, if we want to find when they would be at 400 miles apart, it means we have to find the distance Ms. Ironperson and Mr. Thoro would have covered after a time "t".
Thus,
Ms. Ironperson covered 50t miles
Mr. Thoro covered 60t miles
Therefore, since their location forms a right angled triangle, then we can use pythagoras theorem and we have;
(50t)² + (60t)² = 400²
This gives;
2500t² + 3600t² = 160000
6100t² = 160000
t² = 160000/6100
t = √(160000/6100)
t ≈ 5.12 hours
Thus, for Iron person, distance covered is: 50 × 5.12 = 256 miles
For Mr. Thoro, distance covered is: 60 × 5.12 ≈ 307 miles.
They will be 400 miles apart when Ms. Ironperson has covered 256 miles and Mr. Thoro has covered 307 miles after 5.12 hours
Simplify: 6-a(4-a)-2a
Answer:
a^2 - 6a + 6
Step-by-step explanation:
6−a(4−a)−2a =
6+a2+−4a+−2a
6+a2+−4a+−2a
(a^2)+(−4a+−2a)+(6)
a2+−6a+6
=a^2−6a+6
(-1, 2) and (3, k + 3); m =3/4
Answer:
k = 2
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Replace variables
[tex]\frac{(k+3)-2}{3+1} =\frac{3}{4}[/tex]
Step 2: Combine like terms
[tex]\frac{k+1}{4} =\frac{3}{4}[/tex]
Step 3: Solve for k
k + 1 = 3
k = 2
Answer:
k=2
Step-by-step explanation:
The slope is 3/4
The slope formula is (y1-y2)/(x1-x2)
We can plug the values in
(2-k-3)/(-1-3)=3/4
Combine like terms
(-1-k)/-4=3/4
Cross multiply
-12= -4 - 4k
-8=-4k
k=2
Hope this helps!
What does 1/8x-49/8 equal
Answer:
x=49
Step-by-step explanation:
Let's solve your equation step-by-step.
1
8
x−
49
8
=0
Answer:
x=49
P(x) = 3x^4 – 2x3 + 2x² – 1
What is the remainder when P(x) is divided by (x + 1)?
Answer:
6
Step-by-step explanation:
Hello, we can use the Remainder Theorem, so the remainder is P(-1)
[tex]P(-1)=3+2+2-1=6[/tex]
Thanks
Four times the sum of half a number and 6 is 48. How do you put this in an equation? Please help.
Answer:
4(1/2x+6)=48
Step-by-step explanation:
half a number= 1/2x
is= equal
Let f(x) = 2x + 2. Solve f−1(x) when x = 4.
Answer:
The answer is 1
Step-by-step explanation:
You replace the x with 4 making it 4-2/2=1
7x+(-7)=9x-7 what is the answer?
Answer:
x=0
Step-by-step explanation:
7x+(-7)=9x-7
Add 7 to each side
7x+(-7)7=9x-7+7
7x = 9x
Subtract 7x from each side
7x-7x = 9x-7x
0 = 2x
Divide by 2
0 = 2x/2
0 = x
Hello,
I hope you and your family are staying safe and healthy!
Answer: 0
Step-by-step explanation:
[tex]7x + (-7) = 9x - 7[/tex]
[tex]7x - 7 = 9x - 7[/tex]
Now susbtract [tex]9x[/tex] from both sides
[tex]7x -7 - 9x = 9x - 7 - 9x\\-2x - 7 = -7[/tex]
Then add 7 to both sides
[tex]-2x - 7+7=-7+7\\2x=0[/tex]
[tex]x = \frac{0}{-2} \\x = 0[/tex]
--------------
If you find my answer helpful, please give it 5 stars and press the heart. Thanks!
i need help!! due in 8.25 at 11pm!!
15 points!!
Answer:
Hey there!
The equation is y=-3/4x+6. (Note the 3/4 is negative because the line has a negative slope.
Let me know if this helps :)
Answer:
[tex]\huge \boxed{y=-\frac{3}{4}x+6 }[/tex]
Step-by-step explanation:
Two points are (0, 6) and (8, 0)
Finding the slope.
m = (y2-y1)/(x2-x1)
m = (0-6)/(8-0)
m = -6/8
m = -3/4
The y-intercept is 6.
y = mx + b
m = slope
b = y-intercept
y = -3/4x + 6
plz give correct answer...correct answer will be marked BRAINLIEST and be followed...
Answer:
x = 40
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
2x + x + [tex]\frac{3x}{2}[/tex] = 180 ( multiply through by 2 to clear the fraction )
4x + 2x + 3x = 360 , that is
9x = 360 ( divide both sides by 9 )
x = 40
One-third of the students in the marching
band signed up for the pep band. Then, fiveT
students changed their mind. If there are 31
students in the pep band, how many students
are in the marching band?
Answer:
108
Step-by-step explanation:
There are 31 students in the pep band. One third of students in the marching band signed up, and 5 changed their mind. 31 + 5 = 36, and 36 x 3 = 108. 36 is one third of 108 and there are 108 students in the marching band.
A manufacturer of widgets finds that the production cost, C, in dollars per unit is a function of the number of widgets produced. The selling price, S, of each widget in dollars is a function of the production cost per unit. C(x)=-0.1x^2+100 S(C)=1.4C
Answer:
I guess that you want to find the profit:
We have two equations:
the cost equation:
C(x) = -0.1*x^2 + 100.
And the selling equation, that is a vertical stretch of the cost equation by a factor of 1.4:
S(x) = 1.4*C(x) = 1.4*( -0.1*x^2 + 100.) = -0.14*x^2 + 140
Now, whit those two equations we can find the profit equation, that is defined as the difference between the selling price, and the cost:
P(x) = S(x) - C(x) = 1.4*C(x) - C(x) = (1.4 - 1)*C(x) = 0.4*C(x).
Then the profit is 0.4 times the initial cost.
P(x) = 0.4*( -0.1*x^2 + 100.) = -0.04*x^2 + 40
Answer:
D. S(C(x))= –0.14x^2+140; $108.50
Step-by-step explanation:
Cause the others are wrong
reflect figure over line x=4
Answer:
x=-4
Step-by-step explanation:
Filp the sign
The reflection of the line x = 4 will be x = -4.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
The given equation of line,
x = 4.
The reflection of the line x = 4 will be x = -4.
The reflected graph is shown below.
To learn more about Reflection on:
https://brainly.com/question/15487308
#SPJ2
A map of the town that Annie, Barbara, and Charlie live in can be represented by the Cartesian plane. Annie is located at $(6,-20)$ and Barbara is located at $(1, 14)$. They agree to meet at the closest point that is equidistant from their current locations and walk upwards together to get to Charlie's location at $\left(\frac{7}{2}, 2\right)$. How many units upward do Annie and Barbara walk together to get to Charlie?
Answer:
5 units
Step-by-step explanation:
Annie is located at (6,-20) and Barbara is located at (1, 14) and they meet at a point equidistant to their current locations.
This means that they have to meet at the midpoint between their two locations. Let the coordinate of the midpoint be (x,y) hence:
[tex]x=\frac{x_1+x_2}{2}=\frac{6+1}{2} =\frac{7}{2}[/tex]
[tex]y=\frac{y_1+y_2}{2}=\frac{-20+14}{2} =-3[/tex]
The point at which they met is at (7/2, -3). Charlie location is at (7/2, 2). Hence the distance upward that they have to move = 2 - (-3) = 5 units
They have to move 5 units upwards
Who knows answer?
Quickly.
Answer:
12 ft^2
Step-by-step explanation:
48 inches needs to be converted to ft
12 inches = 1 ft
48/12 = 4 ft
36 inches needs to be converted to ft
12 inches = 1 ft
36/12 =3 ft
Find the area
4 ft * 3 ft = 12 ft^2
please help me answer the assignment in the picture.
Mean: 52.2 because its the average of all the numbers
Range: 2 because (60-58)
Median: 53 because its in the middle of all the numbers
Mode : None
How many integers at between 15 and 63?
Answer:
47
Step-by-step explanation:
Ok first lets do this with small numbers like 10 and 5. How many integers are between 10 and 5? which does not include 10 or 5. You do 10 minus 5 which is 5, but if you count how many integers are between them with your fingers you get 4.
so now you know to get the integers between 2 large numbers you subtract like normal then you mines a 1.
so 63 - 15 - 1 = 47
There are 47 integers between 15 and 63
Hope this helps :)
There have been 47 integer arithmetic in the range of 15 to 63.
Number of integer between two number = Highest number - Lowest number - 1
So,
Number of integer between 15 and 63
63 - 15 - 1
63 - 16= 47
So,
Number of integer between 15 and 63 = 47
Learn more:
https://brainly.com/question/13212492?referrer=searchResults
If x° and 50° form a linear pair, find xº
Answer: 130°
Step-by-step explanation:
Concept to know:
Linear pair: two angles that forms one line
One line: 180°
-------------------------------------------------------------
x+50=linear pair
x+50=180
x=130°
Hope this helps!! :)
Please let me know if you have any question
Your neighbor has a square shaped pool with side lengths of 3a5. What is the area of the pool?
Answer:
15a
Step-by-step explanation:3times3times3times3times3
Identify the property used in each step. 12.2 + 18.6 + –4.3 + (–18.6) 12.2 + –4.3 + 18.6 + (–18.6) 12.2 + –4.3 + [18.6 + (–18.6)] 12.2 + –4.3 + (0) 12.2 + –4.3 7.9
Answer:
Commutative Property
Associative property
Additive inverse
Identity property
Step-by-step explanation:
In a commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data
12.2 + 18.6 + –4.3 + (–18.6)
12.2 + –4.3 + 18.6 + (–18.6)
The second step results into the presence of a commutative property.
The next step 12.2 + –4.3 + [18.6 + (–18.6)] is an associative property because here, re-grouping of numbers which gives the same result takes place
[18.6 + (–18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero
12.2 + –4.3 + (0) is an Identity property
Identity property occurs when the addition of any number with zero eventually resulted into that number.
Answer:
Commutative Property
Associative property
Additive inverse
Identity property
Step-by-step explanation:
simplify: 3x(x^2 + 4x - 5)
Answer:
3x^3+ 12x^2-15x
Step-by-step explanation:
First, you would have to distribute the 3x to everything in the parentheses. So you can write it out as (3x*x^2)+(3x*4x)+(3x*5). Solving this will give you the answer. We'll start off with (3x*x^2). Because we are MULTIPLYING, this part will equal to 3x^3. There is ONE x with 3x (think of it as 3x^1) and 2 x's in x^2, having a total of 3 x's, or x^3. Since the 3 is being multiplied as well, we can write it as 3x^3.
Second, we will solve (3x*4x). We are multiplying, so first we multiply 3*4 and then x*x. 3*4 is 12 and x*x is x^2. There are 2 x's being mutipled by each other, so the x becomes squared. Now we finish and multiply 12*x^2 wich is 12x^2.
Lastly, we solve (3x*5). 3x is being multiplied 5 times which gives us 15x.
I hope this helped :)