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].
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
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
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:
how do I write an equation of a line that is parallel to 2x-3y=15
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
Which of the following could be used to solve the triangle below?
Answer:
sine
Step-by-step explanation:
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:
"Four times the difference of a number and
seven is at least -52."
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:)
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
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.
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]
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
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!
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.
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:
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! :)
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?
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
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.
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
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
1 L = 0.26 gal
How many liters are in 13.39 gallons?
Answer: 50.686664
Step-by-step explanation: hope this helps :)
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%
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.
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:
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
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]
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
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