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].
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?
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."
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
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
1 L = 0.26 gal
How many liters are in 13.39 gallons?
Answer: 50.686664
Step-by-step explanation: hope this helps :)
WILl GIVE BRAINLIEST IF YOU SHOW THE STEPS!!!
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]
Find the area of the figure.
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
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.
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:
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?
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
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?
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
The sum of two integers is 2. Their difference is 10. What are the two integers?
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
Subtract and simplify your answer. 3/4 - 1/6
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! :)
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?
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
What -3/4 equals 2/3
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
Which of the following could be used to solve the triangle below?
Answer:
sine
Step-by-step explanation:
Find the output for f(x) = -3 |2x - 9| + 4.
When x = -5
SHOW EVERY STEP!
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:)
Kindly Simplify this Question
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.
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
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
Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?
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
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
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
40% of _______ is 16.
Answer:
40% of ___ is 16
So then 10% of ___ is 4
Then do 4 x 10 = 40
So 40% of 40 is 16.
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?
Answer:
The walkway is 14ft and 3in
Step-by-step explanation:
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.
Answer:
42:54,54:42
Step-by-step explanation:
Plz help (MATH)...................
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
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.
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.
Solve: 4|x| = 32
–8 or 8
8
24
no solution
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
What is the domain? (Type your answer with commas and no spaces)
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:
how do I write an equation of a line that is parallel to 2x-3y=15
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
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.
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
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 cmConclusion:
Therefore, the best estimate of the circle's diameter is 15cm.
Hoped this helped.
[tex]BrainiacUser1357[/tex]