Direct variation equation is y=kx . Your k is your variation or you could look at it as your slope. y=kx Plug in what you know, 4=k12 Divide both sides by 12 to cancel out your 12 that is being multiplied by k.
4(/12)=k12(/12) Simplify
1/3=k
y=1/3x This is your direct variation equation.
Answer:
Step-by-step explanation:
1) y=kx
plug in the #s
(0.9)=k(0.1)
divide both sides by 0.1
k=9
plug in k and that is your equation (y=9x)
what is the slope of the table x= 2, 0, -2, -4 y= 6, 1, -4, -9
Answer:
The slope of the table is [tex]m=\frac{5}{2}[/tex] or [tex]m=2.5[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the following ordered pairs
(2,6),(0,1),(-2,-4) and (-4,-9)
take two points
(2,6) and (-4,-9)
substitute in the formula
[tex]m=\frac{-9-6}{-4-2}[/tex]
[tex]m=\frac{-15}{-6}[/tex]
simplify
[tex]m=\frac{5}{2}[/tex]
How many 2/3 cup servings are in a 4 cup container of food
Answer:
6
Step-by-step explanation:
4 divided by 2/3 is 6, because 4 x 2 = 8, and 8/3 is 6.
The perimeter of a rectangle is 10. The length of the rectangle is five less than four times the width. Find the width of the rectangle
L=4*W-5
10=W*2+(4*W-5)*2
10=W*2+8*W-10
20=10*W
2=W
L=4*2-5
L=3
What is the value of the red dot on the number line below?
Answer:
B, 9.625
Step-by-step explanation:
I know there's a more surefire method of doing this problem but since this is multiple choice, you can use process of elimination to solve it.
Simplify. 5√⋅12−−√⋅50−−√
Answer:
Here's the answer. I got it right on my quiz. Hope I could help:)
Answer:
10 square root over 30
Step-by-step explanation:
took the test
(x-1)(2x^2+2x+2)
Please show all the work!
Thank You
Answer:
2x³ - 2
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
= x(2x² + 2x + 2) - 1(2x² + 2x + 2) ← distribute both parenthesis
= 2x³ + 2x² + 2x - 2x² - 2x - 2 ← collect like terms
= 2x³ - 2
help me answer this question please.
The right answer is Option B.
Step-by-step explanation:
Given expression is;
5x√2 - 3√2 + x√2
We can add or subtract square roots only when the values inside the square root are same and the variables are also same.
In the given expression, variable x is same with √2, therefore, adding both the roots
[tex]6x\sqrt{2} -3\sqrt{2}[/tex]
6x√2 - 3√2 is equivalent to 5x√2 - 3√2 + x√2.
The right answer is Option B.
Keywords: square roots, subtraction
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if Sin A = 0.5736, what is the Cos A =
The value of CosA is 0.8191
Step-by-step explanation:
Given SinA= 0.5736
We know that [tex]SinA^{2} + CosA^{2} = 1[/tex]
Replacing value of SinA,
[tex](0.5736)^{2} + CosA^{2} = 1[/tex]
[tex](0.3290) + CosA^{2} = 1[/tex]
[tex] CosA^{2} = 1-0.3290[/tex]
[tex] CosA^{2} = 0.6709 [/tex]
[tex] CosA = 0.8191 [/tex]
The value of CosA is 0.8191
Climate change in Canada
According to the 2019 report Canada's Changing Climate Report (CCCR) which was commissioned by Environment and Climate Change Canada, Canada's annual average temperature over land has warmed by 1.7 C since 1948. The rate of warming is even higher in Canada's North, in the Prairies and northern British Columbia
Please help! And if u do label the answers so Ik which is which if u answer n say idk I’ll report u
Answer:
5. y-intercept is 8
6. slope is -1/2
7. y=-1/2x+8
16. A projectile is thrown directly upward at a velocity of 12.0 m/s. How long does it take for the
projectile to reach its maximum height? (g = 9.8 m/s2)
A. 0.61 s
B. 1.22 s
C. 2.45 s
D. 2.45 s
Final answer:
The projectile takes 1.22 seconds to reach its maximum height.
Explanation:
To find the time it takes for the projectile to reach its maximum height, we can use the equation:
where t is the time, v_f is the final velocity, v_i is the initial velocity, and a is the acceleration.
In this case, the initial velocity is 12.0 m/s and the acceleration is -9.8 m/s² (negative because the projectile is moving upward). Since the final velocity at the maximum height is 0 m/s, we can substitute the values into the equation:
t = (0 - 12.0) / -9.8 = 1.22 seconds
Therefore, it takes 1.22 seconds for the projectile to reach its maximum height.
To purchase $12,900 worth of machinery for her business, Melissa made a down payment of $2100 and took out a business loan for the rest. After years of paying monthly payments of $478.67, she finally paid off the loan.
a) What was the total amount Melissa ended up paying for the machinery (including the down payment and monthly payments)?
(b) How much interest did Melissa pay on the loan?
Answer:
a) $13588.08
b) $688.08
Step-by-step explanation:
Melissa had to purchase $12,900 worth of machinery for her business.
She made a down payment of $2100 and after that made monthly payments of $478.67 for the business loan for the rest.
Given that after years of paying monthly payments of $478.67, she finally paid off the loan.
Assume that she took 2 years to repay the loan.
a) Therefore, the total amount Melissa ended up paying for the machinery was $[2100 + (478.67 × 24)] = $13588.08 (Answer)
b) Therefore, the amount of interest that Melissa pay on the loan is $(13588.08 - 12900) =$688.08. (Answer)
Provide an appropriate response.
6) The length of time it takes college students to find a parking spot in the library parking lot follows a normal
distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the cut-off time which
75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
A) 4.8 min
B) 5.3 min
C) 5.2 min
D) 5.0 min
Answer:
Step-by-step explanation:
B
What is log39 = x in exponential form?
3x = 9
o 9x = 3
o x3 = 9
o 39 = x
оооо
DONE
Answer:
9 = [tex]3^{x}[/tex]
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{3}[/tex] 9 = x ⇔ 9 = [tex]3^{x}[/tex] ← in exponential form
Answer:
its A on edge
Step-by-step explanation:
To begin a bacteria study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 15%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
Answer:
The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
Step-by-step explanation:
Given
[tex]t[/tex] be the number of hours.
[tex]y[/tex] number of bacteria cells.
And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent
The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]
In the equation as [tex]C[/tex] is function of time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.
To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]
So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]
Check:
[tex]15\% of 1800 =0.15\times 1800=270[/tex]
So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.
The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]
That can also be from the formula.
[tex]C(t)=1800(1.15)^1=2070[/tex]
So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.
Final answer:
The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.
Explanation:
To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.
Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.
The sum of two numbers is 20 and their product is 96. Find the numbers.
Answer:
12 and 8
Step-by-step explanation:
12 + 8= 20
12 x 8= 96
The two numbers are 12 and 8. They have a sum of 20 and a product of 96, satisfying the given conditions.
To find two numbers whose sum is 20 and whose product is 96, we can set up a system of equations. Let's call the two numbers x and y.
1. The first equation represents their sum:
x + y = 20
2. The second equation represents their product:
xy = 96
Now, we need to solve this system of equations. One way to do it is by substitution. From the first equation, we can express y in terms of x: y = 20 - x.
Now, we substitute this expression for y into the second equation:
x(20 - x) = 96
Expanding and simplifying this equation:
20x - x^2 = 96
Rearranging terms:
x^2 - 20x + 96 = 0
Now, we factor the quadratic equation:
(x - 12)(x - 8) = 0
This gives us two possible solutions for x: x = 12 and x = 8.
So, the two pairs of numbers that satisfy the conditions are (12, 8) and (8, 12). In both cases, the sum of the numbers is indeed 20, and their product is 96, as required.
In summary, the two numbers are 12 and 8, and they meet the criteria of having a sum of 20 and a product of 96. These solutions demonstrate how algebraic techniques can be used to solve real-world problems involving unknown values.
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there were 50 rabbits on an island. After three months the number of rabbits had increased to 70. If the number of rabbits increased exponentially, answer the questions that follow:
A. in the equation above (where t is in months:, find the value of the growth rate k. (round k to 4 decimal places)
Answer:
0.1187
Step-by-step explanation:
A = P (1 + k)^t
where A is the final amount,
P is the initial amount,
k is the monthly growth rate,
and t is the number of months.
70 = 50 (1 + k)^3
1.4 = (1 + k)^3
∛1.4 = 1 + k
k = -1 + ∛1.4
k = 0.1187
an inflatable swimming pool holds 1,000 gallons of water. It sprang a leak. and 5% of the water leaked out of the pool. How many gallons of water leaked out
50 gallons of water leaked out of swimming pool.
Step-by-step explanation:
Total no. of gallons in swimming pool = 1000
Percentage of leaked water = 5%
Gallons of water leaked = 5% of total no. of gallons
[tex]Gallons\ of\ water\ leaked=\frac{5}{100}*1000\\\\Gallons\ of\ water\ leaked=\frac{5000}{100}\\\\Gallons\ of\ water\ leaked= 50\ gallons[/tex]
50 gallons of water leaked out of swimming pool.
Keywords: percentage, division
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solve the equation for all real values of x.
10+x=5(1/5x+2) Equations with infinite and no solution
Answer:
Infinitely many solutions.
Step-by-step explanation:
10+x=5(1/5x+2)
10+x=x+10
infinitely many solutions
The equation 10+x=5(1/5x+2) has an infinite number of solutions.
Explanation:To solve the equation 10+x=5(1/5x+2), we need to simplify both sides and then isolate the variable x. Let's start by distributing the 5 to the terms inside the parentheses.
10+x = 5(1/5x+2) becomes:
10+x = 1x+10
Next, we can combine like terms on each side of the equation. Subtracting x from both sides:
10 = x+10-x
The x terms cancel out, leaving us with:
10 = 10
This equation is always true, which means that there are an infinite number of solutions.
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The complete Question is given below
10+x=5(1/5x+2)
Determine whether it has one solution, an infinite number of solution, or no solutions
One positive number is five times another number is the difference between the two numbers is 1676 find the numbers
Answer:
The two numbers are -419 and -2095.
Step-by-step explanation:
5x=y
x-y=1676
----------------
x-5x=1676
-4x=1676
x=1676/-4
x=-419
5(-419)=y
y=-2095
what is sin 67°?
a)
[tex] \frac{5}{12} [/tex]
b)
[tex] \frac{5 }{13} [/tex]
c)
[tex] \frac{12}{13} [/tex]
d)
[tex] \frac{12}{5} [/tex]
Answer:
Step-by-step explanation:
sin67° = 12/13
Two pieces of equipment were purchased for a total of $4000. If one piece cost $850 more than
the other, find the price of the less expensive piece of equipment. Assume all data are accurate
to two significant digits unless greater accuracy is given.
The price of less expensive equipment is $1575.
Step-by-step explanation:
Let,
Price of one equipment = x
Price of other equipment = y
According to given statement;
x+y=4000 Eqn 1
x = y+850 Eqn 2
Putting Eqn 2 in Eqn 1
[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]
Putting y=1575 in Eqn 2;
[tex]x=1575+850\\x=2425[/tex]
The price of less expensive equipment is $1575.
Keywords: linear equation, substitution method
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Final answer:
The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.
Explanation:
To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:
x + (x + $850) = $4000
To solve for x, we combine like terms and get:
2x + $850 = $4000
Subtracting $850 from both sides gives us:
2x = $3150
Dividing both sides by 2, we find the value of x:
x = $1575
Therefore, the price of the less expensive piece of equipment is $1575.
Please help meeee (1/2) to the 4th power
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{1}{2} *\frac{1}{2} *\frac{1}{2} =[/tex][tex]\frac{1}{16}[/tex]
[tex]\frac{1}{2}*\frac{1}{2} =\frac{1}{4}[/tex]
[tex]\frac{1}{4} *\frac{1}{2} =\frac{1}{8}[/tex]
[tex]\frac{1}{8}*\frac{1}{2}=\frac{1}{16}[/tex]
J.k. Rowling and R.L. Stone are both ready hunger games . J.k. Reads 35 pages every 2 hours and R.L. Reads 45 pages every 3 hours . what is the rate of change for each reader ?
Answer:
The rate of change for each reader is :
For J K Rowling : 17 and a half pages per hour
For R L Stone : 15 pages per hour
Step-by-step explanation:
Here the reading rate of each reader is given as:
J.K. Reads 35 pages every 2 hours.
So, the number of pages read by J K in 2 hours = 35 pages
⇒ The number of pages read per hour = 35 / 2 = 17 . 5 pages
So, the pages read by J K Rowling in 1 hour is 17 and a half pages.
R L Stone reads 45 pages every 3 hours.
So, the number of pages read by R L in 3 hours = 45 pages
⇒ The number of pages read per hour = 45 / 3 = 15 pages
So, the pages read by R L Stone in 1 hour is 15 pages.
Hence, the rate of change for each reader is :
For J K Rowling : 17 and a half pages per hour
For R L Stone : 15 pages per hour
Included side between < S and < W.
A) side SA
B) side WA
C) side SW
Answer:
C) Side SW
Step-by-step explanation:
Hello! The included side between <S and <W is side SW. According to the included side rule, this would be the correct answer. I know this is not much of an explanation, but there is not much to it! Hope this helps.
Alicia conducted an experiment in which a spinner landed on green seven times if the experimental probability of the spinner landing on green is 1/5 how many trials did Alicia perform
Answer:
35 trials
Step-by-step explanation:
Probability = Favorable Outcome / Total Outcome
P = 1/5
Favorable Outcome = 7
Substitute the values,
1/5 = 7 / Total Outcomes
1/5 =7/x
Cross multiplication:
1x=5*7
x=35
Total Trials = 35
Mr. Lee drove 8 miles from his house to pakside.parkside i 4 miles south of springfield.from parkside, he drove 3 miles to springdale .then he drove 20 miles from springdale to brookville. How far did mr. Lee drive in all , from his house to brookville ? Identify the extra or missing information .solve i possible.
Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.
Solution:Given that
Mr. Lee drove 8 miles from his house to park side .
Parkside is 4 miles south of springfield.
From Parkside he drove 3 miles to springdale
Then he drove 20 miles from springdale to brookville.
Need to determine how far Mr Lee drive in all, from his house to Brookville.
Also need to identify Extra or missing information.
Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.
=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles
Information that is parkside is 4 miles south of springfield is extra information which is not required to determine mr. Lee drive , from his house to Brookville .
Hence Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.
The fraction 7/9 is in the lowest terms. True or false ??
Answer:
True
Step-by-step explanation:
This is true because there is no common factor for 7 annd 9
What set of integers fall in the solution set of the following inequality:
1/3x<3x+8<-5x
Answer:
-2Step-by-step explanation:
[tex]\dfrac{1}{3}x<3x+8<-5x\qquad\text{multiply all sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x<3\cdot3x+3\cdot8<3\cdot(-5x)\\\\x<9x+24<-15x\\\\\text{Let split it into two inequalities}\\\\(1)\qquad x<9x+24\ \text{and}\qquad (2)\qquad 9x+24<-15x[/tex]
[tex](1)\\x<9x+24\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\-8x<24\qquad\text{change the signs}\\\\8x>-24\qquad\text{divide both sides by 8}\\\\\boxed{x>-3}\\\\(2)\\9x+24<-15x\qquad\text{add}\ 15x\ \text{to both sides}\\\\24x+24<0\qquad\text{subtract 24 from both sides}\\\\24x<-24\qquad\text{divide both sides by 24}\\\\\boxed{x<-1}\\\\\text{From (1) and (2) we have}\\\\-3<x<-1\to\text{There is only one integer in this solution: -2}[/tex]