The linear equation which represents the situation or the amount of water in the bathtub in terms of the number of minutes is y = 7x + 18.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
Let's suppose the number of minutes by x and the amount of water by y
As per the given question,
The amount of water (y) initially (x = 0) is 18 gallons.
The first point (0,18).
The amount of water (y) at x = 5 is 53 gallons.
The second point (5,53).
The linear equation is given as y = mx + c where m is the slope.
Slope m = (53 - 18)/(5 - 0) = 7
Substitute (0,18) →
18 = 7(0) + c
c = 18
So the equation become as,
y = 7x + 18.
Hence "The linear equation which represents the situation or the amount of water in the bathtub in terms of the number of minutes is y = 7x + 18".
For more about the linear function,
brainly.com/question/21107621
#SPJ1
an empty swimming pool is in the shape of a rectangle meters long, meters wide and meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of and a depth of . the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.
the child would take 11.5 days (working 24 hours per day) to fill the swimming pool
an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep.
filling rate =2*10*π*(0.1)^2
or 0.002 π cubic meters per minute
or 0.12 cubic meters per hour
or 2.88 cubic meters per day
volume to fill = 100 cubic meters
how many days to fill ? × days= 2.88π × x=100
this implies x= 100/2.88π
x= 11.05
the complete question is
an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of 20cm and a depth of 10 cm. the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.
learn more about of rectangle here
https://brainly.com/question/15019502
#SPJ4
need help having problems
Find the probability, in simplest form of picking the letter R in the wore LIBRARY
Step 1: Write out the formula for Probability
[tex]\text{Probability}=\frac{Number\text{ of events}}{\text{Total number of events}}[/tex]Step 2: Writing out the data
The number of times R occur in the word LIBRARY is 2.
The total number of alphabets in the word LIBRARY is 7.
Therefore, number of events= 2
Total number of events= 7
[tex]\text{Probability of picking R=}\frac{2}{7}[/tex]WILL GIVE BRAINLIEST PLS HELP SOLVE
Answer:
The equation is:
y = -3x + 3
2022 + 2022 = .......
Pliss help me im now is Elementary school
Answer:
4044
Step-by-step explanation:
2000+2000= 4000
22+22= 44
4000+44= 4044
please help me figure this out
Answer:
x = 17
Step-by-step explanation:
Given angles are vertical angles and they have equal measurements.
We can write the following equation to find the value of x based on this information:
8x - 27 = 6x + 7 transfer like terms to the same side of the equation
8x - 6x = 27 + 7 add/subtract
2x = 34 divide both by 2
x = 17
Jada drew triangle ABC. If angle B is a right angle, what are possible measures for the other two angles?
angle A:
The possible measures for the other two angles will be that the sum of that angle must be 90 degree.
A triangle is considered to be 3-sided polygon in some cases Each triangle has three sides and three angles, a few of which may be the same. The portion of the plane enclosed by the triangle is said the triangle interior, whereas the leftover portion is the exterior. Since we are given that one of the angles of the given is a right angle, according to one of the rules of the triangle the sum of all the interior angles of a triangle should be 180, for the triangle ABC,
=>A+B+C = 180
=>A+90+C= 180
=>A+C= 180-90
=>A+C=90
To know more about triangles refer the link https://brainly.com/question/2773823?referrer=searchResults.
#SPJ9
ap calculus question, steps and explain please.
[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex] of the Correct option is (B) i.e., 1/[tex]\pi[/tex]
Given:
[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]
To solve the above function:
Now, According to the question:
[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]
Differentiate with respect to x above function:
[tex]\lim_{x \to \\pi } \frac{-sinx + 2cosx} {2x}[/tex]
Substitute the value of limit in x tends [tex]\pi[/tex], it means x = [tex]\pi[/tex]
= [tex]\frac{2cos\pi - sin\pi }{2\pi }[/tex]
= 2/ [tex]2\pi[/tex]
= 1/[tex]\pi[/tex]
Hence, The Correct option is (B) i.e., 1/[tex]\pi[/tex]
Learn more about Differentiation at:
https://brainly.com/question/24898810
#SPJ1
Solve for x in the triangle. Round your answer to the nearest tenth.
20
X
52°
X =
PLS HELPPPPP
PLS EXPLAIN
The values needed to complete the relative frequency table in the context of this problem are as follows:
a = 69.06%.b = 30.91%.c = 68.60%.d = 31.40%.What is a relative frequency?The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
To find the relative frequency for boys, we look at the frequency two-way table, and consider that out of 110 boys, 76 went to 4-year colleges and 34 went to two year colleges, hence the relative frequencies are found as follows:
a = 76/110 = 0.6909 = 69.09%.b = 34/110 = 0.3091 = 30.91%.For girls, we also look at the frequency two-way table, and consider that out of 121 girls, 83 went to 4-year colleges and 38 went to two year colleges, hence the relative frequencies are found as follows:
c = 83/121 = 0.6860 = 68.60%.d = 38/121 = 0.3140 = 31.40%.More can be learned about relative frequencies at https://brainly.com/question/1809498
#SPJ1
f(x) = (cos(x))/(sqrtx)
Find the derivative
Derivative of [tex]f(x)= (\frac{cosx}{\sqrt{x} })=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]
How to calculate the derivative?
[tex]f(x) = \frac{cosx}{\sqrt{x} }[/tex]
The derivative is given by,
[tex]= > \frac{d}{dx} (\frac{cosx}{\sqrt{x} })[/tex]
Applying Quotient rule :
[tex](\frac{f}{g} )^{'} = \frac{f^{'}.g - g^{'}.f}{g^{2} } \\[/tex]
[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{\frac{d}{dx}(cosx)\sqrt{x} - \frac{d}{dx} \sqrt{x}(cosx)}{(\sqrt{x} )^{2} } \\[/tex]
Considering derivatives in the numerator,
[tex]\frac{d}{dx} (cosx)= - sinx\\\\\frac{d}{dx} (\sqrt{x} )=\frac{1}{2\sqrt{x} }[/tex]
Now,
[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{(-sinx)\sqrt{x} - \frac{1}{2\sqrt{x} } (cosx)}{(\sqrt{x} )^{2} } \\\\\text{ Taking LCM }\\\\=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]
What is a derivative?
The derivative of a function assesses the sensitivity of the function's output value to a change in its argument. A key component of calculus is the derivative. The velocity of an object is the derivative of the position of a moving object with respect to time.When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.To learn more about derivatives, refer:
https://brainly.com/question/23819325
#SPJ13
-7/8u = -21 solve for u and simplify your answer as much as possible
Answer:
u= 18.37
Step-by-step explanation:
-7/8 u= -21
We have to isolate the variable. Since the -7 is being divided, you would take it to the other side and multiply.
8u= -21 * -7
8u= 147
u= 147/8
u= 18.37
2.2 Proof of planning right angles
The two column proof of the right angles to prove that ∠1 ≅ ∠2 is as shown below
How to carry out two column proof of right angles?From the given image showing two right angles, we can generate the two column proof to be as follows;
Statement 1: m∠1 = 90° and m∠2 = 90°
Reason 1: Given
Statement 2: ∠1 and ∠2 are right angles
Reason 2: Definition of right angles
Statement 3: m∠1 = ∠2
Reason 3: Transitive Property of Congruence
Statement 4: ∠1 ≅ ∠2
Reason 4: Definition of Congruence
Read more about Two Column Proof at; https://brainly.com/question/1788884
#SPJ1
HELP ME PLEASE!!!!! will give brainlist
Answer:
3/4
-2
Step-by-step explanation:
y = mx + b
Start at the y-intercept. It is (0, -2), so b = -2.
You have
y = mx - 2
Now start at (0, -2). We need to go up and right to the next easy-to-read point on the line. Go up 3 (rise). Go right 4 (run).
slope = rise/run = 3/4 = m.
Now you have
y = 3/4 x - 2
Answer:
See below
Step-by-step explanation:
Use two convenient integer coordinates to calcuate m= slope
I'll use 8,4 and -4, -5 slope m = (-5-4)/(-4-8) = -9/-12 = 3/4
from the graph, the y-axis intercept (b ) is -2
slope - intercept form of a line is given by
y= mx + b
y = 3/4 x -2
find the solution of this system of equations2x+5y=-49-2x+8y=-68
Given the system of equations :
[tex]\begin{gathered} 2x+5y=-49 \\ -2x+8y=-68 \end{gathered}[/tex]Add the equations to eliminate x :
[tex]\begin{gathered} (2x+5y)+(-2x+8y)=-49+(-68) \\ 2x+5y-2x+8y=-117 \\ (2x-2x)+(5y+8y)=-117 \\ 13y=-117 \end{gathered}[/tex]divide both sides by 13 to find the value of y :
[tex]\begin{gathered} \frac{13y}{13}=\frac{-117}{13} \\ \\ y=-9 \end{gathered}[/tex]To find x , substitute with the value of y at the first equation :
[tex]\begin{gathered} 2x+5\cdot-9=-49 \\ 2x-45=-49 \\ 2x=-49+45 \\ 2x=-4 \\ \\ x=-\frac{4}{2} \\ \\ x=-2 \end{gathered}[/tex]So, the solution of the system is :
[tex]\begin{gathered} x=-2 \\ y=-9 \end{gathered}[/tex]The solution can be written as the order pair (x,y):
[tex](x,y)=(-2,-9)[/tex]Write the equation in vertex form for the
parabola with vertex (-1, 3) and that
passes through the point (2, -5).
Answer: The general equation of a parabola with vertex (h,k) is y=a(x−h)2+k y = a ( x - h ) 2 + k . In this case we have (1,3) as the vertex (h,k) and (2,6) is a point (x,y) on the parabola. To find a , substitute the two points in y=a(x−h)2+k y = a ( x - h ) 2 + k .
how do you solve quadratic using square roots?ex: (p-4)²=49
Apply square root to both sides of the equation:
[tex]\sqrt[]{(p-4)^2}=\sqrt[]{49}[/tex][tex]p-4=7[/tex]Add 4 to both sides of the question:
[tex]p-4+4=7+4[/tex][tex]p=11[/tex]in a survey of 350 dog owners, it was found that 98 bought Pedigree Chum dog food what percentage of the marker prefer Pedigree Chum
If 98 out of 350 dog owners bought Pedigree Chum dog food so 28 percentage of the makers that prefer Pedigree Chum.
As per the question statement, In a survey of 350 dog owners and it was found that 98 bought Pedigree Chum dog food. We are supposed to find the percentage of the makers that prefer Pedigree Chum.
Given that, 98 out of 350 dog owners bought Pedigree Chum dog food
So the percentage can be calculated by the formula,
(98/350)*100 = 0.28*100 = 28%
Hence, 28% of the makers that prefer Pedigree Chum.
Percentage: Percentage refers to a portion of a total represented in hundredths.To learn more about percentage and its concept, click on the link given below:
https://brainly.com/question/16797504
#SPJ1
difference between a number and its positive square root is 12?find the number?
an you guys help me with this one too
Amanda and Diana given right solution set.
The solution set of given graph of inequality is,
x < 4.
Now, The solution of given created inequality,
Amanda:- -3x + 5 > -7
=> -3x> -7 -5
=> - 3x > -12
=> 3x < 12
=> x < 4
So, it is correct
Briana:- 1/2 (2x - 4)> 2
=> 2x - 4 > 4
=> 2x > 8
=> x > 4
It is wrong
Courtney:- -7x+8 > -3x + 24
=> -7x + 3x > 24 - 8
=> -4x > 16
=> 4x < -16
=> x < -4
It is wrong
Diana:- 9x -6 < 3x + 18
=> 9x - 3x < 18 + 6
=> 6x < 24
=> x < 4
So, it is right
Hence, Amanda and Diana given right solution set.
Learn more about Inequality at:
https://brainly.com/question/20383699
#SPJ1
How is 9.746 x 10 ^13 written in standard form?
0000000000009746
97,460,000,000,000
9.746000000000000
9,746,000,000,000,000
Hello I was given this question earlier but didn’t understand thought it would be good to reach out for some help
Profit = Revenue - Cost
Revenue = Q * P
P = 100 - Q/20
C = 0.12Q + 10
Using substitution, we can say that:
[tex]\begin{gathered} \text{Profit = Revenue - Cost} \\ \text{Profit = }(Q\times P)-(0.12Q+10) \\ \text{Profit }=Q(100-\frac{Q}{20})-(0.12Q+10) \end{gathered}[/tex]Both equations used in the region of profit are linear equations because the exponent or degree used is only 1. Therefore, the region of profit is contained within two linear equations. (Option E)
12
Find the horizontal asymptote of f of x equals quantity negative 2 x squared plus 3x plus 5 end quantity over quantity x squared plus 1. (5 points)
y = −2
y = −1
y = 1
y = 2
The horizontal asymptote is y = -2
The horizontal asymptote is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.
Horizontal asymptotes are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.
The function given is, f(x) = (-2x²+3x+5)/(x²+1)
Horizontal asymptote is given by,
y = [tex]\lim_{x \to \infty} \frac{-2x^2+3x+5}{x^2+1}[/tex]
= [tex]\lim_{x \to \infty} \frac{x^2(-2+\frac{3}{x} +\frac{5}{x^2}) }{x^2(1+\frac{1}{x^2}) }[/tex]
= [tex]\lim_{x \to \infty} \frac{(-2+\frac{3}{x} +\frac{5}{x^2}) }{(1+\frac{1}{x^2}) }[/tex]
= -2
So the horizontal asymptote of f(x) is, y = -2
Learn more about horizontal asymptotes at https://brainly.com/question/1851758
#SPJ1
Answer:
A) y = -2
Step-by-step explanation:
The rules to find the horizontal asymptote (HA) is shown below
Y = A if the numerator and denominator have same highest exponent for example
A^3
B^3
Y = 0 if the numerator have lower exponent and denominator have higher exponent for example
A^1
B^2
None HA if the numerator have higher exponent and denominator have lower exponent for example
A^2
B^1
And the equation shown in the question have same exponent so the answer is -2
PS: please give me brainiest
HELP ASAP! brainliest for the best answer.
Answer:
[tex]\textsf{C.} \quad r=\dfrac{27-P}{3P}[/tex]
Step-by-step explanation:
Given formula:
[tex]A=P(1+rt)[/tex]
Given values:
A = 27t = 3Substitute the given values into the given formula and solve for r:
[tex]\begin{aligned}A&=P(1+rt)\\\\\implies 27&=P(1+3r)\\\\\dfrac{27}{P}&=\dfrac{P(1+3r)}{P}\\\\\dfrac{27}{P}&=1+3r\\\\\dfrac{27}{P}-1&=1+3r-1\\\\\dfrac{27}{P}-1&=3r\\\\3r&=\dfrac{27}{P}-\dfrac{P}{P}\\\\3r&=\dfrac{27-P}{P}\\\\\dfrac{3r}{3}&=\dfrac{\dfrac{27-P}{P}}{3}\\\\r&=\dfrac{27-P}{3P}\end{aligned}[/tex]
Solution
[tex]\boxed{r=\dfrac{27-P}{3P}}[/tex]
Three sisters each bought 3 pairs of shoes and a dress the dress cost 45.50 if the total cost of the bill was 352.50 how much did a pair of shoes cost
A pair of shoes cost 102.23
Arithmetic: Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. The basic operations of math are addition, subtraction, multiplication and division. Also called higher arithmetic, theoretical arithmetic.
Cost of 3 pairs of shoes and a dress = 352.50
Cost of dress = 45.50
Cost of 3 pairs of shoes = Cost of 3 pairs of shoes and a dress - the cost of dress = 352.20 - 45.50
= 306.7
So, the cost of each pair of shoes will be = Cost of 3 pairs of shoes/Number of pairs bought
= 306.7/3
= 102.23
Learn more about arithmetic:
#SPJ1
Jenn is baking 80 pumpkin spice cookies for a fundraiser. She gets ready to start cutting out cookies at 3:30pm, first rolling out the dough and getting her cookiecutters ready. At 3:38pm she has 12 cookies cut out. By 3:40pm, she has 20 cookies cut out. If she cuts out cookies at a constant rate, when will she be finished cutting out the 80 cookies?
Answer: 4:30
Step-by-step explanation:
Answer:
oh palak cl NC do off is sold em Ms do off do off dlc so off do off sum is sold arrowroot
f(x) = 2x - 3
g(x) = 3x - 1
Find (f g)(x).
6x² + 3
6x³-11x² + 3x
6x² - 11x +3
6x² - 7x +3
Answer:
6x^2 - 11x + 3
Step-by-step explanation:
(fg)(x) is just multiplying f(x) and g(x)
This gives: (2x-3)(3x-1) = 6x^2 - 2x -9x - (3*(-1)) = 6x^2 -11x + 3
Brian deposited $2,419 into a savings account for which interest is compoundedquarterly at a rate of 2.54%. How much interest will he earn after 7 years? Roundanswer to the hundredths place. If answer does not have a hundredths place theninclude zeros so it does. Do not include units in the answer.
Given
Principal = $2419
rate = 2.54%
time = 7 years
compounds quarterly
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2419(1+\frac{0.0254}{4})^{4(7)} \\ A=2419(1.00635)^{28} \\ A=2888.08 \end{gathered}[/tex]After 7 years, the amount deposit is now $2888.08, subtract by the principal amount to get the interest.
[tex]\begin{gathered} I=A-P \\ I=2888.08-2419 \\ I=469.08 \end{gathered}[/tex]Therefore, the interest that he will earn after 7 years us $469.08.
Write the equation in factored form then stayed the X intercepts
Step 1
Given;
[tex]y=x^2+x-20[/tex]Required; To write the equation in factored form
Step 2
Find the two factors that when added gives you x and when multiplied gives -20x²
[tex]\begin{gathered} \text{The factors are 5x and -4x} \\ \end{gathered}[/tex][tex]\begin{gathered} R\text{eplace x with 5x-4x} \\ x^2+5x-4x-20 \\ \text{Factorize the expression} \\ x(x+5)-4(x+5)_{} \\ y=(x-4)(x+5) \end{gathered}[/tex]Step 3
State the x-intercept
[tex]\begin{gathered} (x-4)(x+5)=0 \\ x-4=0 \\ or \\ x+5=0 \\ x=4 \\ or \\ x=-5 \end{gathered}[/tex]Hence, the x-intercepts are;
x=4
x=-5
Directions: Find the slope between
1. (-8, 18) and (-14, -3)
Answer: The slope of (-8, 18) and (-14, -3) would be 3.5.
Step-by-step explanation: By using a simple calculator, specifically the TI-84 Plus CE, you can put the points you mentioned in stat and it’ll give you an equation based on those points. The equation I got was y = 3.5x + 46. The number attached to the X is your slope.