Answer:
5 cm
Step-by-step explanation:
The distance a coiled spring stretches varies directly with the amount of weight hanging on the spring.
Distance = D
Weight = W
Hence:
D ∝ W
D = kW
Where k is constant of proportionality
Step 1
We solve for k
If a spring stretches 2 cm when a 30 gram weight is hung from it.
2 = 30k
k = 2/30
k = 1/15
Step 2
how far will it stretch when a 75 gram weight is hung from the spring?
D = kW
We are solving for D
k = 1/15
D = 1/15 × 75
D = 5 cm
The spring would stretch 5cm with a weight of 75 gram.
At the beginning of summer, Mark has $200 in savings and Ryan has $350. The brothers have mowing jobs set up for the summer. Because Mark is older, he receives $20 for each mowing job and Ryan receives $15. The brothers' parents pay for the fuel used to mow, so all of the money the brothers earn goes to savings. Write two equations, one for Mark and one for Ryan, to represent the money in savings (s) based on the number of mowing jobs (j) Mark and Ryan do. Determine the number of mowing jobs it takes for Mark to have the same amount in savings as Ryan does. Show your work.
Answer:
[tex]m = 200 + 20j[/tex]
[tex]r = 350 + 15j[/tex]
Number of jobs is 30
Step-by-step explanation:
Variable representation
Let Mark's total earnings for moving be m
Let Ryan's total earnings for moving be r
Represent the number of jobs with j
Setup equation
Mark:
[tex]Initial\ Savings = 200[/tex]
[tex]Rate = 20[/tex]
So, the total savings is:
[tex]m = 200 + 20j[/tex]
Ryan
[tex]Initial\ Savings = 350[/tex]
[tex]Rate = 15[/tex]
So, the total savings is:
[tex]r = 350 + 15j[/tex]
To get the number of jobs they save the same amount.
We have:
[tex]m = r[/tex]
Substitute values for m and r
[tex]200+20j = 350+15j[/tex]
Collect Like Terms
[tex]20j - 15j = 350 - 200[/tex]
[tex]5j = 150[/tex]
Divide both sides by 5
[tex]j = \frac{150}{5}[/tex]
[tex]j = 30[/tex]
Hence, the number of jobs is 30
Which equation represents the pattern in the table?
arnold wants to make chocolate chip cookies. his recipe calls for 5 cups of flour. his spoon holds 1/6 cup of flour. how many times will arnold need to fill his spoon to get the 5 cups of flour? group of answer choices
Answer:
30 times
Step-by-step explanation:
It will take 6 spoonfuls to make one cup of flour, so you multiply 6 by 5 to get 30 spoonfuls.
Hope this helps
PLEASE HELPPPPPP!!!!!!Solve this system of linear equations separate the x-and y-values with a comma
-13x=90-2y
-6x=48-2y
Answer:
[tex]x=-6,\\y=6[/tex]
Step-by-step explanation:
Rewrite the system of equations as:
[tex]\begin{cases}-13x+2y=90\\-6x+2y=48\end{cases}[/tex]
Subtract the second equation from the first to isolate [tex]x[/tex]:
[tex]-13x+2y-(-6x+2y)=42,\\-7x=42, \\\fbox{$x=-6$}[/tex]
Plug in [tex]x=-6[/tex] into any of the equations above and solve for [tex]y[/tex]:
[tex]-6(-6)+2y=48,\\2y=12,\\\fbox{$y=6$}[/tex]
Verify that the solution pair [tex](-6, 6)[/tex] works [tex]\checkmark[/tex]
Therefore, the solution to this system of equations is:
[tex]x=-6,\\y=6[/tex]
Name the property illustrated. 69 + 0 = 69
Answer:
zero property of addition
Step-by-step explanation:
29 divided by 6 gbhikgiogfofdldslwkjrtjbjgjfr
Answer:
4.83333333333
Step-by-step explanation:
oh boy, that wasnt very fun to type. you get the idea. its a lot of threes.
Answer this correctly, and recieve brainliest!
Answer:
The last one or
a+8=16
Step-by-step explanation:
Subsitute a for 8 and solve
Answer:
Step-by-step explanation:
the last one
8+8=16
a+8=16
I NEED THE ANSWER ASAP!!!
Answer:
I think the answer is J
Step-by-step explanation:
do you know the answer, ive been stuck for hours
Answer:
Perpendicular H = 5.244 m (Approx)
Step-by-step explanation:
Given:
Hypotenuse = 9.4 m
Base = 7.8 m
Find:
Perpendicular H
Computation:
Perpendicular H = √Hypotenuse² - Base²
Perpendicular H = √9.4² - 7.8²
Perpendicular H = √Hypotenuse² - Base²
Perpendicular H = 5.244 m (Approx)
Solve the inequality,
p+ 1 = 2
The solution is
Answer:
p = 1
Step-by-step explanation:
one. 2-1 would equal 1 so p would have to be 1 exactly
What percent of $144 is $18?
Answer:
Step-by-step explanation:
it is 12.5
Answer: the answer is 12.5%
Solve the problem
6n - n
A) 1 + n
B)2n
C)-n
D)-7n
Answer:
5n
Step-by-step explanation:
Step one:
Given data
Solve the problem
6n - n
The expression is an algebraic expression, since all the terms are the same, we want to perform a subtraction operation on the terms
so
6n-n= 5n
The answer is clearly no listed in the options
can you find the coordinates for K’
pls thank you
Answer: (3, 7)
Step-by-step explanation: The pattern seems to be dividing each axis by 2, so 6/2 = 3 and 14/2 = 7, making (3, 7)
Have a nice day! :)
Solve the following system using the Elimination Method; 6x+y=10 and 2x+y=12.
Hey there!
The solution to the system is [tex](\frac{1}{2}, 13)[/tex]
To solve the system, we can multiply the second equation by -1:
[tex]-2x - y = -12[/tex]
Then, we add the two equations together, and solve for x:
[tex]4x = -2[/tex]
[tex]x = \frac{-1}{2}[/tex]
Now, we plug the x value into one of the equations, and solve for y:
[tex]2(\frac{1}{2} ) + y = 12[/tex]
[tex]-2 + y = 12[/tex]
[tex]y = 13[/tex]
Now we know that the solution to the system is [tex](\frac{1}{2}, 13)[/tex]
Hope it helps and have an amazing day!
Answer:
(-1/2, 13)
Step-by-step explanation:
Multiply the 2nd equation by -1, obtaining the following system:
6x + y = 10
-2x - y = -12
------------------
Combine like terms, obtaining:
6x + y = 10
-2x - y = -12
------------------
4x = -2
Dividing both sides by 4 yields x = -2/4, or x = -1/2
Substituting -1/2 for x in the second equation yields:
2(-1/2) + y = 12, or
-1 + y = 12. Then y = 13, and the solution is
(-1/2, 13)
Function k squares the sum of the input, w, and 3.
What is the function equation in function notation?
9514 1404 393
Answer:
k(w) = (w +3)²
Step-by-step explanation:
The name of the function is k, and its input is w, so the left side of the equal sign will be ...
k(w)
This is said to be the square of the sum w+3, so the right side of the equal sign will be ...
(w +3)²
The function equation in function notation is ...
k(w) = (w +3)²
Answer:
k(w) = (w +3)²
I took the test
if a point has a multiplicity of 1, is it even or odd?
does anyone know the answer
(s/3) -4=2
Answer: 18
Step-by-step explanation:
Answer:
s=18
Step-by-step explanation:
Solve for s by simplifying both sides of the equation, then isolating the variable.
Brainly pls :)
please help me :'(
Polynomial Function.
Tell whether the following is a polynomial is a polynomial function or not. give the degree and the number of terms for polynomial functions.
1. y = 3x² - 2x + 4
2. y = 5^x+3
3. y = x + 4/3
4. y = (x - 4)(4x + 1)
5. y = 6x² + 1
Answer:
all are a polynomial function and
1.the degree is 3 and number of term is 4
2. 1 and 3
3. 1 and 4/3
4. 2 and -4
5. 2 and 1
The weight, in pounds, of a newborn baby t months after birth can be modeled by the equation W=1.5t+10. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
Step-by-step explanation:
W = 1.5t + 10
slope = 1.5
Every month, the baby gains 1.5 pounds.
Liz is watching a film in the cinema the film started at 14:30 the film is 105 minutes long when the film ends liz takes 20 minutes to get to the bus stop does she get to the bus stop in time to make it to the bus
Answer:
Step-by-step explanation:
A population of cheetahs has decreased 30% over the last 18 years if they're originally about 12,000 cheetahs how many cheetahs are there now?
The ratio of boys to girls in a class is 3:4. There are 35 students in the class How many more girls than boys are there?
Step-by-step explanation:
So let's keep the missing number as x
So the ratio becomes 3x:4x
And according to the question,
3x + 4x = 35
7x = 35
x = 35/7
x = 5
So to find the number of boys:- 3 * 5 = 15
Number of girls:- 4 * 5 = 20
Therfore, Difference = 20 - 15
= 5 students
Hope you understood :)
Answer:
5 more girls than boys
Step-by-step explanation:
When you think of ratio, imagine it this way. A ratio literally means a fraction. So, we can visualise it a similar way: a pie. Or a pizza, if you like.
In the pie, there are two groups. One are the boys and one are the girls. When you say their ratio is 3:4, it means that for every 3 boys there are 4 girls. This means that the number of boys can be represented as 3 units and the number of girls as 4 units. We just do not know how many students one unit represent, but any one unit is equal in a ratio, no matter how many groups there are.
Hence, imagine the pie as being divided into 3 slices + 4 slices. That makes 7 slices. Now we need to find out how many students forms one slice.
We know that the whole pie is made up of 35 students. There are 7 slices in the pie. Hence, to find the number of students in a slice, simply divide 35 by 7:
35/ 7 = 5
We now know one slice, or one unit, has 5 students.
Now multiply the value of the unit by how many units each group is made up of to find how many students there are in each group. 3 x 5 = 15. 4 x 5 = 20. One cool trick here is to add up the values again to see if it fits to the original sum. This helps you check your working.
We now know there are 20 girls and 15 boys, Hence, there are 20–15 = 5 more girls than boys.
Not mine! this was from Quora written by William Blake!find the least common factor of the numbers 12 and 4
Answer:
12
Step-by-step explanation:
its just how it is
There are 30 students in the drama club. They are carpooling in 5 vans to perform a play. They want each van to carry an equal number of students. Let s be the number of students in each van. Write and solve a multiplication equation to find the number of students in each van.
Answer: 6 students in each van
Step-by-step explanation: Sx5=30
(2.4+4n)+9
SHOW ALL WORK!
Answer:
Step-by-step explanation:
i think u got the question wrong cuz all ud have to do is add 2.4+9 which is 11.4 +4n
pls help ! I’ll give you brainliest
Answer:
Im not sure i love fractions lol
Step-by-step explanation:
please help im crying
Answer:
length=91
width=2
Step-by-step explanation:
182/2=91
91*2=182
Need help please anyone
Answer:
The answer is C
Step-by-step explanation:
I may be wrong but you need to line the decimal
Simplify the fraction and state the excluded value(s).
[tex]\dfrac{7x^2+4x-20}{5x+10}[/tex]
Answer:
[tex]\displaystyle \frac{7x^2 + 4x - 20}{5x + 10} = \frac{7x - 10}{5}, x \neq -2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringCalculus
Discontinuities
Removable (Holes)Jump (Piece-wise functions)Infinite (Asymptotes)Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{7x^2 + 4x - 20}{5x + 10}[/tex]
Step 2: Simplify
[Frac - Numerator] Factor quadratic: [tex]\displaystyle \frac{(7x - 10)(x + 2)}{5x + 10}[/tex][Frac - Denominator] Factor GCF: [tex]\displaystyle \frac{(7x - 10)(x + 2)}{5(x + 2)}[/tex][Frac] Divide/Simplify: [tex]\displaystyle \frac{(7x - 10)}{5}, x \neq -2[/tex]When we divide (x + 2), we would have a removable discontinuity. If we were to graph the original function, we would see at x = -2 there would be a hole in the graph.
[tex]\color{skyblue}{\boxed{\tt{ANSWER:}}}[/tex]
General Formulas and Concepts:Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra ITerms/Coefficients
Factoring
Calculus
Discontinuities
Removable (Holes)Jump (Piece-wise functions)Infinite (Asymptotes)^_^ ❤
Lucy borrowed $425 from Colleen. Colleen charges Lucy 5.3% interest if Lucy pays Colleen back in 3 years how much does she pay Colleen back altogether
Answer: Lucy pays $ 492.58 back altogether.
Step-by-step explanation:
Formula : Interest = Principal x Rate x Time
Given: Principal = $425 , rate = 5.3% = 0.053 , time = 3 years
Interest = 425 x 0.053 x 3 ≈ $ 67.58
Total amount need to pay back = Principal + Interest
= $ (425+67.58)
= $ 492.58
Hence, Lucy pays $ 492.58 back altogether.