Answer:
constant of variation (k) = 6
Step-by-step explanation:
Let us first represent the sentence in direct variation expression:
"the gallons of water used to take a shower varies directly with the number of minutes in the shower"
Let the gallons of water used = g
Let the number of minutes spent in the shower = m
g ∝ m
where: ∝ = sign of proportionality
This means that as g increases, m increases also, and the same holds for decrease too.
g ∝ m
g = km
where k = constant of variation ( or proportionality constant)
Next, If a 6-minute shower uses 36 gallons of water, find the constant of variation
g = 36 gallons
m = 6 minutes
∴ g = km
= 36 = k × 6
k = 36 ÷ 6 = 6
k = 6
PLEASE HELP WITH THIS QUESTION ILL GIVE BRAINLIEST !!!
Answer: linear pair
Step-by-step explanation:
Because ce is shown to be bisected by line n, then the two expressions are added and will equal 180°. This is what is called a linear pair.
Why would the law of cosines be used to solve for b in the triangle below? SAS is given, and the unknown measure, b, is a side length. SSA is given, and the unknown measure, b, is a side length O 36° O 3.5 7 SSS is given, and the unknown measure, b, is an angle measure. ASA is given, and the unknown measure, b, is an angle measure. DONE b
Answer:
it's a
Step-by-step explanation:
its a on edge
Answer: A
Step-by-step explanation:
Explain why x^2 + 4x + 3 is factorable.
PLEASE I NEED HELP!!
Answer:
Step-by-step explanation:
In order to find the values to factorize the equation, we need to find the factors the factors of 3 that sum to 4
The factors of 3 are [tex]\pm: 1, 3[/tex]
We can make 4 with 1 + 3
Since all the values are positive, both of the factors will have addition
[tex]x^2+4x+3\\(x+3)(x+1)\\\\x^2 + x + 3x + 3\\x^ + 4x + 3[/tex]
13 only (give brainliest) ASAP
Answer:
1/3 or 0.3
Step-by-step explanation:
5/8 x 4/5 x 2/3 =
1/3 or 0.3
Answer:
1/3 in^3
Step-by-step explanation:
In order to find the volume, you must multiply the length, by the width, by the height. This would mean you need to do 2/3x5/8x4/5=40/120
40/120 simplified will give you 1/3
Write as an exponent with the base of b:
[tex]bb^{m}[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]b. {b}^{m} = {b}^{1 + m} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Evaluate for a=3, b=2 and c=10.
(c - a)^b
Answer:
49
Step-by-step
step 1 subtract 10 -3
step 2 multiply 7 x 7
that's your answer
Answer:
49
Step-by-step explanation:
Step 1:
a = 3; b = 2; c = 10 Given
Step 2:
[tex](c-a)^{b}[/tex] Equation
Step 3:
[tex]( 10 - 3)^{2}[/tex] Input values
Step 4:
( 7 ) ² Parentheses
Answer:
49
Hope This Helps :)
What is an equation of the line that passes through the points (-2,7) and (1, -8)?
Put your answer in fully reduced form.
Courtney walked from her house to the beach at a constant speed of 444 kilometers per hour, and then walked from the beach to the park at a constant speed of 555 kilometers per hour. The entire walk took 222 hours and the total distance Courtney walked was 888 kilometers.
Answer:
I suppose that each number is repeated 3 times, the actual question is:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Now, remember the relation:
Distance = Speed*Time
Let's define:
D1 = distance between Courtney's house and the beach.
D2 = distance between the beach and the park.
T1 = time that it took the first walk.
T2 = time that it took the second walk.
We know that the total distance Courtney walked is 8km, then:
D1 + D2 = 8km.
And we also know that the entire walk took 2 hours, then:
T1 + T2 = 2h.
We also have the equations:
D1 = 4km/h*T1
D2 = 5km/h*T2.
Then we have a system of equations:
D1 + D2 = 8km
T1 + T2 = 2h
D1 = 4km/h*T1
D2 = 5km/h*T2.
To solve this, first let's replace equations 3 and 4 in the first equation:
4km/h*T1 + 5km/h*T2 = 8km
Now we have only two equations left:
4km/h*T1 + 5km/h*T2 = 8km
T1 + T2 = 2h
Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:
T1 = 2h - T2.
Replacing this in the first equation gives:
4km/h*(2h - T2) + 5km/h*T2 = 8km
Now let's solve this for T2.
8km - 4km/h*T2 + 5km/h*T2 = 8km
8km + 1km/h*T2 = 8km
1km/h*T2 = 0
from this, we have T2 = 0
This would mean that T1 = 2h.
Then:
D1 = 4km/h*2h = 8km.
T2 = 0
D2 = 5km/h*0 = 0.
This happens because the numbers in the problem were not well thought.
You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.
Given a term in a geometric sequence and the common ratio. Find the explicit formula . A) a 3 =-36 , r = 6 b) a 6 =64 , r = 2
Answer:
Step-by-step explanation:
The explicit formula for a GP is expressed as
Tn = ar^{n-1}
a is the first term
n is the number of terms
r is the common ratio
a) If a3 = 36 and r = 6
a3 = ar^3-1
a3 = ar^2 = 36
ar^2 = 36
a(6)^2 = 36
36a = 36
a = 1
Get the nth term
Tn = 1(6)^{n-1}
Tn = 6^{n-1}
b) If a6 = 64 and r = 2
a6 = ar^6-1
a6 = ar^5 = 64
ar^5 = 64
a(2)^2 = 64
4a = 64
a = 16
Get the nth term
Tn = 16(2)^{n-1}
Tn = 16*(2^n/2)
Tn = 8(2^n)
what is 5 %9 (86 - 32) plss help
Answer:
270
Step-by-step explanation:
James is a journalist with an annual income of $85,350. James has to pay an income tax of 8%. What is the amount of income tax in dollars and cents that James has to pay? 7.13A
Answer: $6828
Step-by-step explanation:
James annual income = $85350
Income tax = 8%
The amount of income tax in dollars and cents that James has to pay will be calculated by multiplying the income tax by his annual income. This will be:
= 8% × $85350
= 8/100 × $85350
= 0.08 × $85350
= $6828
A logo is drawn inside a rectangle.
It is made up of four congruent triangles,
16cm
21cm
What fraction of the rectangle is covered by
the triangles?
Answer:
14
Step-by-step explanation:
14
A recipe requires 9 cups of milk. You can only measure using 2/3 cups. How many 2/3 cups are required for the recipe?
Answer:
You would need 13.5 2/3 cups.
Step-by-step explanation:
[tex]\frac{2}{3}[/tex]×[tex]\frac{13.5}{1}[/tex]=[tex]\frac{27}{3}[/tex]
27÷3=9
Test your PEMDAS
6+8/2(2+2)
This one is tricky
Which answer choice shows 81.027 rounded to the nearest half?
A. 80
B. 80.5
C. 81
D. 81.5
Answer:
c
Step-by-step explanation:
A group of friends were working on a student film. They spent all their budget on props and costumes. They spent $693 on props, and 45% of the total budget on costumes. What was the total budget for their student film?
Answer:
The total budget is $1260
Step-by-step explanation:
Given
[tex]Props = \$693[/tex]
[tex]Costumes = 45\%[/tex]
Required
Determine the total budget
Since all budgets was spent on Props and Costumes only.
We have that.
[tex]\%Props + \%Costumes = 100\%[/tex]
[tex]\%Props + 45\%= 100\%[/tex]
[tex]\%Props= 100\% -45\%[/tex]
[tex]\%Props= 55\%[/tex]
In other words, 55% was spent on Props
Let the total budget be x, we have:
[tex]55\% * x = \$693[/tex]
Make x the subject
[tex]x = \$693/55\%[/tex]
[tex]x = \$1260[/tex]
Hence, the total budget is $1260
suppose y varies directly as x and y=21 when x=3 find x when y=42
Answer:
6
Step-by-step explanation:
21/3=42/x
x=42*3/21
x=6
Plz help will make brainiest.
What happens when we multiply conjugates
together?
Select all polynomials that have (x – 3) as a factor.
In other words, everything but choice B
==========================================================
Explanation:
You could use polynomial long division or synthetic division to check each answer. The shorter route of the two options is synthetic division
There's a much faster way that doesn't involve complicated division. Recall that if (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
------------------------------------------------
Here's a fairly short proof:
Consider a polynomial q(x) such that
p(x) = (x-k)q(x)
which shows that (x-k) is a factor of p(x). We don't need to worry about what q(x) actually is since it will go away effectively.
If we plug x = k into the p(x) function, we get
p(x) = (x-k)q(x)
p(k) = (k-k)q(k)
p(k) = 0*q(k)
p(k) = 0
------------------------------------------------
How is this useful? Well we can note that the factor (x-3) is in the form (x-k) where k = 3.
So the idea is to plug x = 3 into each of the four functions and see which result in 0. If we get 0 as an output, then we have a factor. Otherwise, it's not a factor.
-------------------------------------------------
Plug x = 3 into the first function
A(x) = x^3 - 2x^2 - 4x + 3
A(3) = 3^3 - 2(3)^2 - 4(3) + 3
A(3) = 0
This shows (x-3) is a factor of the function A(x)
------------------------------------------------
Repeat for the second function
B(x) = x^3 + 3x^2 - 2x - 6
B(3) = 3^3 + 3(3)^2 - 2(3) - 6
B(3) = 42
We don't get an output of 0, so (x-3) cannot be a factor of B(x)
-----------------------------------------------
Now onto the third function
C(x) = x^4 - 2x^3 - 27
C(3) = 3^4 - 2(3)^3 - 27
C(3) = 0
So (x-3) is a factor of C(x)
----------------------------------------------
Finally the last function
D(x) = x^4 - 20x - 21
D(3) = 3^4 - 20(3) - 21
D(3) = 0
Therefore (x-3) is a factor of D(x) as well.
The remainder theorem will be used to identify the polynomial that has a remainder of zero when divided by (x - 3)
The polynomials that have 0 as a factor are;
(C) C(x) = x⁴ - 2·x³ - 27(D) D(x) = x⁴ - 20·x - 21Reason:
According to the remainder theorem, we have;
The remainder following the division of a polynomial, by (x - a) is P(a)
Therefore, (x - 3) is a factor of the polynomial P(x) where P(3) = 0
For option (A), we have; A(x) = x³ - 2·x² - 4·x + 3
The remainder when (x³ - 2·x² - 4·x + 3) is divided by (x - 3) is therefore;
A(3) = 3³ - 2 × 2² - 4 × 2 + 3 = 14
Therefore, (x - 3) is not a factor of A(x) = x³ - 2·x² - 4·x + 3
For option (B), we have;
B(x) = x³ + 3·x² - 2·x - 6
The remainder when B(x) is divided by (x - 3) is therefore;
B(3) = 3³ + 3×3² - 2×3 - 6 42
Therefore, (x - 3) is not a factor of B(x) = x³ + 3·x² - 2·x - 6
For option (C), we have;
C(x) = x⁴ - 2·x³ - 27
The remainder when C(x) is divided by (x - 3) is therefore;
C(3) = 3⁴ - 2×3³ - 27 = 0
Therefore;
(x - 3) is a factor of C(x) = x⁴ - 2·x³ - 27For option (D), we have;
D(x) = x⁴ - 20·x - 21
The remainder when D(x) is divided by (x - 3) is given as follows;
D(3) = 3⁴ - 20×3 - 21 = 0
Therefore;
(x - 3) is a factor of D(x) = x⁴ - 20·x - 21Learn more here:
https://brainly.com/question/11456067
Factor Completely
f(x)= x^4 - 2x^3 - 3x^2 + 2x + 2
Please answer correctly !!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
Answer: 105 degrees
Step-by-step explanation:
Both angles equal 180 so if we subtract 75 from 180 we get 105.
Answer:
105º
Step-by-step explanation:
<ONC and <BNJ are a linear pair, the angles are supplementary (eqauls 180º).
A store sells new video games for $25 each. Used video games sell for $10 each. Jacob is buying 3 new video games and x used video games. Which equation can be used to find y, the total price Jacob must pay in dollars?
Answer:
[tex]y = 75 + 10x[/tex]
Step-by-step explanation:
Given
New Video Games
[tex]Cost = \$25[/tex]
[tex]Number = 3[/tex]
Used Video Games
[tex]Cost = \$10[/tex]
[tex]Number = x[/tex]
Required
Determine the amount spent (y)
First, we need to determine the total spent on new games
1 new game = $25
3 new games will be: 3 * $25
Next, we determine the total spent on old games
1 used game = $10
x used games will be: x * $10
So, total amount y, is:
[tex]y = 3 * 25 + x * 10[/tex]
[tex]y = 75 + 10x[/tex]
12/75=x/120 What is x?
Answer:
x = 18
Step-by-step explanation:
Answer:
19.2
Step-by-step explanation:
120/75=1.6
12 times 1.6=19.2
Put the following equation of a line into slope-intercept form, simplifying all
fractions
2y - 2x = 8
Answer:
y=x+4
Step-by-step explanation:
2y - 2x = 8
2y=2x+8
y=x+4
Answer:
3
Step-by-step explanation:
54x4=18x n these are the answers 12 14 16 18
Answer:
12
Step-by-step explanation: 18x 12= 216 and 54x4 = 216
The coach fare to a theme park costs $21 for 3 people, what would be the cost for 6 people?
A) $42 B) $63 C) $140
Answer:
42
Step-by-step explanation:
You add 21 twice because 3 is half of 6
Answer:
A - 42
Step-by-step explanation:
21 x 2 = 42
3 x 2 = 6
how do I get on the leaderboard
I have 1900 something points way more than these people. Is it about how many questions you ask?
Answer:
No its about how many you get PER DAY
Step-by-step explanation:
Pls help this is already past due
Answer:
Step-by-step explanation:
-5400/-450
12 minutes
Answer:
12 minutes
Step-by-step explanation:
If the rate of the plane is -450 meters per minute, then you have to use the "division" operation in order to know how much time it takes for the plane to reach an altitude of -5,400 meters.
-5,400 meters ÷ -450 meters/minute = 12 minutes
It will take 12 minutes for the plane to reach an altitude of -5,400 meters.
Let's check:
-450 meters x 12 minutes = -5,400 meters
If you can guess my number from 1-20 in your first try ill give brainliest :)
Answer:
6 I think.
Step-by-step explanation:
6 I think. think
