if x is a factor of y and y is a factor z, then x is a factor of z. true or false​

Answers

Answer 1

Answer:

True; this [tex]x[/tex] would indeed be a factor of [tex]z[/tex].

Step-by-step explanation:

"[tex]x[/tex] is a factor of [tex]y[/tex]" means that there is a whole number [tex]p[/tex] such that [tex]x\, p = y[/tex].

Likewise, [tex]y[/tex] is a factor of [tex]z[/tex] if and only if there is a whole number [tex]q[/tex] such that [tex]y\, q = z[/tex].

This [tex]x[/tex] would be a factor of [tex]z[/tex] if there is some whole number [tex]r[/tex] such that [tex]x\, r = z[/tex].

The first equality [tex]x\, p = y[/tex] implies that [tex]y[/tex] may be substituted with [tex]x\, p[/tex].

Substitute the [tex]y[/tex] in the second equality [tex]y\, q = z[/tex] with [tex](x\, p)[/tex] to obtain:

[tex](x\, p)\, q = z[/tex].

Rearrange to obtain:

[tex]x\, (p\, q) = z[/tex].

The product of two whole numbers is still a whole number. Since [tex]p[/tex] and [tex]q[/tex] are both whole numbers, [tex]p\, q[/tex] would also be a whole number.

Thus, if [tex]r = p\, q[/tex], then [tex]x\, r = x\, (p\, q) = z[/tex], while [tex]r[/tex] would be a whole number.

Therefore, this [tex]x[/tex] would indeed be a factor of [tex]z[/tex].


Related Questions

In a survey, 3 out of 20 students were left-handed. Based on this information, if 300 students were interviewed, how many of them could be expected to be left-handed?

Answers

Based on the information given, from the fraction, it can be noted that the number of left-handed people will be 45.

From the information given, it was stated that in the survey, 3 out of 20 students were left-handed.

Therefore, in a population of 300 people, the number of left handed people will be:

= 3/20 × 300.

= 3 × 15

= 45

There are 45 left handed people.

Learn more about fractions on:

https://brainly.com/question/13763238

Three boards are placed end to end to make a walkway. The first board is 2 feet 8 inches long, the second board is 6 feet 10 inches long, and the third board is 4 feet 9 inches long. How long is the walkway?

Answers

Answer:

The walkway is 14ft and 3in

Step-by-step explanation:

What is the domain? (Type your answer with commas and no spaces)

Answers

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

Step-by-step explanation:

Marco runs 4 kilometers every morning. He takes 2 minutes for the first 500 meters, 4 minutes for the next 2000 meters, 1 minute for the next 700 meters, and 3 minutes for the rest.

Marco’s average speed for the entire run is__320___ meters per minute. Hint : One kilometer is the same as 1,000 meters.

Answers

Answer: 400 meters per minute.

Formula to find average speed: total time / total distance

Total time taken is 2+4+1+3 which is 10 minutes.

Total distance traveled is 4 kilometers.

(Unitary method)

In 10 minutes Marco runs 4 kilometers.

In 1 minute Marco will run 4/10 (0.4)kilometers.

Now to convert 0.4 kilometers to meters,multiply it by 1000.

0.4 * 1000 is 400 meters

so the final answer is he will run 400 meters in 1 minute.

Find the area of the figure.

Answers

Answer:

780ft²

Step-by-step explanation:

I'd cut that lower part off into a separate section, and then its width would be the difference of 40 and 30, and its height the difference of 24 and 18. Then, with just 2 rectangles, you can easily calculate the area of each and add them up.

[tex]40-30=10\\24-18=6[/tex]

The lower rectangle is 10' × 6'.

Upper rectangle:

[tex]40\times18=720[/tex]

Lower rectangle

[tex]10\times6=60[/tex]

Add them up:

[tex]720+60=780[/tex]

780ft²

I agree with the person above me it’s 780ft

Plz help (MATH)...................

Answers

Answer:

2.8 pounds

Step-by-step explanation: For this one, I rounded the answer, but what you need to do is divide 20 by 7.

20/7 = 2.85714285714

2.85714285714 ≈ 2.8 pounds

Tell if each statement about the equations y = log5x and y = 5% are true or false.
Explain your answers.
a) The graphs of the equations are symmetric to each other over line y = 0.
b) The equation y = 5* is the exponential form of y = log5x.
c) The functions are not inverses of each other.
d) The equations are symmetric over the line y = x.

Answers

Answer:

a) false b) false c) false d) true

Step-by-step explanation:

Answer:

a) false b) false c) false d) true

Step-by-step explanation:

What -3/4 equals 2/3

Answers

Answer:

17/12= 1 5/12

Step-by-step explanation:

make the denominator the same as 12

_______  -9/12 =8/12

so add 8+9 to get 17.then keep the denominator as 12. last simpfie it to 1 5/12

how do I write an equation of a line that is parallel to 2x-3y=15

Answers

The line given is -2x + 3y = 15, so we must rearrange:

=> 3y = 2x + 15
=> y = 2/3 x + 5

These two equations are EQUIVALENT, but one is in slope intercept form, the other isn't.

So in this case, gradient is 2/3 (or 2 units up, and 3 units across).

And we know that parallel lines have the same gradient. Hence, the general equation for lines parallel to it will be:

y = 2/3 x + n

where n can be any number (positive/negative, decimal/fraction/integer) except 5, which is original line.

For example, y = 2/3 x + 2

v = 128 – 32t
v is the velocity in ft/sec. It is NOT the height of
the ball.
t is the number of seconds after the ball is
thrown.
With what initial velocity is the ball thrown?
128 seconds
s
What is the y-intercept of the equation?
IS
[ Select]
What does the y-intercept mean?
t
[ Select ]
What is the x-intercept of the equation?
[ Select]
What does the x-intercept mean?
Select]
7
10
-
-
с
80°F

Answers

Answer: The Y intercept is 128 as well, which is the original velocity. Technically it should be v - intercept but whatever. The y  / v intercept is the original velocity. The X intercept should be the t intercept but again whatever. The x/t intercept is 4, meaning that the velocity is zero when t is 4

Step-by-step explanation: y/v intercept is when t = 0. v = 128 - 32(0) = 128

It is the initial velocity at t = 0. The X/t intercept is when v = 0. 0 = 128 - 32t, so 32t = 128, so t = 4. The x intercept means when the velocity is zero, which means that the ball is at its highest/farthest point.

which algebraic expression has like terms?
a. 9n^3-2n+3-4n^2
b. 7n^3+3n-3-6n^2
c. 7n^3+4n-3n^3-5n^3
d. 6n^3-4n^3+6n-5n^3

Answers

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

Subtract and simplify your answer. 3/4 - 1/6

Answers

Answer:

7/12

Step-by-step explanation:

3/4 - 1/6

18/24 - 4/24 = 14/24

14/24 = 7/12

Answer:

[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}- \frac{1}{6}[/tex] ⇒ [tex]\frac{9}{12}- \frac{2}{12}[/tex]

[tex]=\frac{7}{12}[/tex]

Hope this helped! :)

What is the difference (how far apart on a number line are the solutions) between the sum of roots versus the product of the roots of the equation:
(x-5)(x+2)=0?

answer should be a number only

Answers

Answer:

7

Step-by-step explanation:

(x - 5)(x + 2) = 0

x = 5 & -2

Now,

given

r > s

r = 5, s = -2

Now,

=> r - s

=> 5 - (-2)

=> 5 + 2

=> 7

1 L = 0.26 gal

How many liters are in 13.39 gallons?

Answers

Answer:  50.686664

Step-by-step explanation: hope this helps :)

WILl GIVE BRAINLIEST IF YOU SHOW THE STEPS!!!

Answers

Answer:

[tex]\frac{9x}{y^3}[/tex]

Step-by-step explanation:

[tex]\frac{\left(3x^2y^4\right)^3}{3x^5y^{15}}[/tex]

[tex](3x^2y^4)^3 : 3^3x^6y^1^2[/tex]

= [tex]\frac{3^3x^6y^{12}}{3x^5y^{15}}[/tex]

[tex]\frac{3^{3} }{2} = 3^{2}[/tex]

= [tex]\frac{3^2x^6y^{12}}{x^5y^{15}}[/tex]

= [tex]\frac{x^{6} }{x^{5} } : x[/tex]

= [tex]\frac{3^2xy^{12}}{y^{15}}[/tex]

=  [tex]\frac{y^{12} }{y^{15} } : \frac{1}{3{y} }[/tex]

= [tex]\frac{3^2x}{y^3}[/tex]

[tex]3^2=9[/tex]

= [tex]\frac{9x}{y^3}[/tex]

Determine which of the following terms are considered to be like terms with the expression 3xy. Select all situations that apply.

A) 3 x ∙ y
B) 1/2( xy)
C) -2 ∙ x ∙ y
D) 4 ∙ x + y
E) ( x)( y)
F) 2 x^2 y

Answers

Answer: Down there there is the correct answer step by step

I hope it helps you!

Given sin0= 3/7, and tan0 <0, what is the value of coso?

Answers

sin θ = 3 / 7 = .429

sin^2 θ + cos^2 θ = 1      trig identity

9/49 + cos^2 θ = 1

cos^2 θ = 40 / 49 = .816       cos θ = .903

Check .429^2 + .903^2 = 1

cos .903 = 25.4 deg

In the second quadrant sin = +, cos = -, tan = -

So 25.4 deg in the second quadrant = 180 - 25.4 = 154.6 deg

Check:

sin 154.6 = .428

cos 154.6 = -.903

tan 154.6 = -.475


Eric needs to make a total of 20 deliveries this week. So far he has completed 13 of them. What percentage of his total deliveries has Eric completed?

Answers

Answer:

65%

Step-by-step explanation:

13/20 is equivalent to 65% because half of it will be half of the percentage so that's why it is 65%

"Four times the difference of a number and
seven is at least -52."

Answers

Remember ‘difference’ refers to subtraction, so they are looking for the ‘difference’ of a a number, which is unknown, so we can use the variable ‘x.’ X-7

The term ‘at least’ refers to our greater than, less than, equal to signs

Difference of a number and 7 = x-7
Four times = (4) or •4
At least = <
-52 = Answer negative 52
Plug them all in,

x-7(4)<-52

Find the output for f(x) = -3 |2x - 9| + 4.

When x = -5

SHOW EVERY STEP!

Answers

Hey there!

f(x) = -3|2x - 9| + 4

y = -3|2x - 9| + 4

y = -3|2(-5) - 9| + 4

y = -3|-10 - 9| + 4

y = -3|19| + 4

y = -57 + 4

y = -53

Therefore, your answer should be: f(x) = -53

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

A circle has a circumference of 45 cm. What is the BEST estimate of the circle’s diameter?
A) 3cm
B)7.5
C) 15cm
D) 18.5cm

Answers

Answer:

C) 15 cm is the best estimate.

Step-by-step explanation:

The exact answer is not there, so 15 is the best estimate.

You can use this equation to help you:

d=C/π

Where d is the diameter.

C is the circumference.

And the last one is Pi.

You know that C = 45, so divide that by Pi (3.14).

45/3.14159 = 14.32

The closest answer is 15.

Hope this helps! Have a great day!

Answer:

The best estimate of the circle's diameter is 15cm.

Step-by-step explanation:

Circumference = 2πr = 45cm=> 2 x π x r = 45 cm=> 2 x 22/7 x r = 45 cm=> 44/7 x r = 45=> 44r/7 = 45=> 44r = 315=> r = 7.16 (Rounded)=> Dia. = 7.16 x 2=> Dia. = 14.32=> Dia. ≈ 15 cm

Conclusion:

Therefore, the best estimate of the circle's diameter is 15cm.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

4. Kayla graphed a scatter plot of the number of hours she drove her car
(x) and the distance traveled (y). She drew the trend line and calculated its
equation to be y = 50x + 2. What is the predicted distance Kayla would
drive if she drove for 3.5 hours?

Answers

X= 50 +2 so when 3.5 hours it will reach the following dimness

Solve the equations below. Give exact solutions only. Show your work.

a) 5x^2 - 7 = 72
b) x(x + 2) = 5
c) 3x^2 + 2x - 4 = 0

Answers

Answer:

A. 5x² - 7 - 72 = 0

5x² - 79 = 0

x = ± √-4ac / 2a

x = ± √- 4 (5) (-79) / 2 (5)

x = ± √ 1580 / 10

x = ± 39.749/10

x = + 39.749/10 x = -39.749/10

= 3.9749 = - 3.9749

B. x² + 2x - 5 = 0

x = - b ± √b² - 4ac / 2a

= - 2 ± √2² - 4 (1) (-5) / 2 (1)

= - 2 ± √4 + 20 / 2

= - 2 ± √ 24 / 2

x = - 2 + 4.898 /2 x = - 2 - 4.898 / 2

= 2.898/2 = -6.898/2

= 1.449 = - 3.449

C. 3x² + 2x - 4 = 0

x = - b ± √b² - 4ac / 2a

= - 2 ± √2² - 4 (3) (-4) / 2 (3)

= - 2 ± √4 + 48 / 6

= - 2 ± √ 52 / 6

x = - 2 + 7.211 /6 x = - 2 - 7.211 / 6

= 5.211/6 = - 9.211 /6

= 0.869 = - 1.535

Hope that helps

Please to re-check answers

The sum of two integers is 2. Their difference is 10. What are the two integers?

Answers

Answer:

6 and -4

Step-by-step explanation:

a + b = 2

a - b = 10

Solve:

from the first eq.

a = 2 - b

replacing this value in the second eq.

(2-b) - b = 10

2 - 2b = 10

-2b = 10 - 2

-2b = 8

b = 8/-2

b = -4

from the second eq.

a - b = 10

a - (-4) = 10

a  + 4 = 10

a = 10 - 4

a = 6

Check:

from the first eq.

6 + (-4) = 2

6 - 4 = 2

Which of the following could be used to solve the triangle below?



Answers

Answer:

sine

Step-by-step explanation:

cosine might be the answer because it is using the hypotenuse and it’s adjacent.

Kindly Simplify this Question

Answers

Step-by-step explanation:

(3⁵×2^-5×5^-5×2×3²)/(5⁵×3^-2×2^-2)

[3^(5+2+2)][2^(-5+1+2)][5^(-5-5)]

3⁹×2^-2×5^-10.

hope this helps you.

Solve: 4|x| = 32


–8 or 8


8


24


no solution

Answers

Answer:

-8 or 8

Step-by-step explanation:

We are given the absolute equation:

[tex]\displaystyle \large{4|x|=32}[/tex]

First, divide both sides by 4 which leaves [tex]\displaystyle \large{|x|=8}[/tex]

Absolute Value Definition

[tex]\displaystyle \large{|x|=\begin{cases} x \ \ \ (x\geq 0)\\ -x \ \ \ (x<0) \end{cases}}[/tex]

So from |x| = 8, break into two intervals/conditions.

(1) when x ≥ 0

x = 8

(2) when x < 0

-x = 8

x = -8

From (1) and (2), the solution to 4|x| = 32 is 8 or -8

Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?

Answers

Answer:

f(x) = x^2 is a classic example

f( 3 ) = 9 and

f( -3 ) = 9, but

f^(-1)[9] is undefined because the result can be 3 and -3

40% of _______ is 16.

Answers

Answer:

40% of ___ is 16

So then 10% of ___ is 4

Then do 4 x 10 = 40

So 40% of 40 is 16.

If there are 42 boys and 54 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Answers

Answer:

42:54,54:42

Step-by-step explanation:

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