Part A) The tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.
Part B) The tank will finish draining in 7.5 minutes.
Part C) Jada arrived 4.5 minutes before the water tank was empty.
What is rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given Data
Up to 10 gallons can be stored in a water tank.
A drain continuously drains water from the tank when it is operational.
When Jade first noticed the tank, there were 7 liters of water inside.
3 minutes later, there were 5 gallons of water remaining.
Part A: How quickly is the tank's water level changing?
In three minutes, the gallons were reduced from seven to five. It indicates that 2 gallons were lost in three minutes.
Thus, gallons Change in gallons per minute would be -[tex]\frac{2}{3}[/tex]. As a result, the tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.
Note that a negative sign means there are less gallons of water available.
Part B) How long will it take for the tank to entirely drain?
The amount of time it will take the tank to entirely empty is denoted by the letter "m."
As,
2.3 gallons per second (5 gallons) in (m minutes).
So,
m = 5 ([tex]\frac{3}{2}[/tex])
= [tex]\frac{15}{2}[/tex]
= 7.5 min.
As a result, the tank will finish draining in 7.5 minutes.
Part C: How long did it take the water tank to fill up entirely before Jada arrived?
When there are 10 gallons of water, r is complete. This means that there are now 7 gallons more of water than there were when Jada arrived, an increase of 3 gallons.
Let 'm' be the time in minutes when the water tank was full and before Jada arrived.
So,
([tex]\frac{2}{3}[/tex]) (m) = 3
m = 3([tex]\frac{3}{2}[/tex]) = [tex]\frac{9}{2}[/tex]
= 4.5 min.
The water tank was thus full before to Jada's arrival by 4.5 minutes.
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Sets B and G are defined as follows. B=(-2, 2, 3, 5) G=(-1,0,2,4,7) - Answer each part below. Write your answer in roster form or as (a) Find the intersection of B and G. B n G=0 (b) Find the union of Band G. BU G=0 X
Answer
B n G = {2}
B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)
Step-by-step explanation:
Given the following two sets
B = { -2, 2, 3, 5}
G = { -1, 0, 2, 4, 7}
Part A
Find the intersection of B and G
The intersection of two sets is defined as the set of all the elements in set A that is also present in set G
Hence, the set of elements that is present in set B and set G is 2
Mathematically, B n G = {2}
Part B
Find the union of set B and set G
The union of two sets is a set containing all elements that are in both sets B and G
B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)
What is the translation of y=x^2 shifted left 3 units
Original equation: y = x²
Tranformation rule:
horizontal translation c units leftt = f(x + c); so:
Modified equation: y = (x + 3)²
The product of seven and a number, increased by three, is equal to twice the number, subtracted from 39. Find the number
It is given that the product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.
It is required to find the number.
To do this, write the statement as an algebraic statement.
Let the number be x.
The product of 7 and a number is:
[tex]7x[/tex]The product of 7 and a number increased by 3 is:
[tex]7x+3[/tex]Twice the number is:
[tex]2x[/tex]Twice the number subtracted from 39 is:
[tex]39-2x[/tex]Since it is given that these expressions are equal, it follows that:
[tex]7x+3=39-2x[/tex]Solve the resulting equation for x:
[tex]\begin{gathered} \text{ Collect like terms:} \\ \Rightarrow7x+2x=39-3 \\ \Rightarrow9x=36 \\ \text{ Divide both sides by }9: \\ \Rightarrow\frac{9x}{9}=\frac{36}{9} \\ \Rightarrow x=4 \end{gathered}[/tex]The number is 4.
if f(x)=-5, what is x?
Answer:
x = -5/f
Step-by-step explanation:
a) Divide both sides by f.
fx/f = -5/f
x = -5/f
Answer:
the answer is -5/f
Step-by-step explanation:
f(x)=fx
fx=-5
Divide both sides by f
fx/f =-5/f
x=-5/f
HOPE IT HELPED
Salma has a points card for a movie theater.
• She receives 30 rewards points just for signing up.
• She earns 8.5 points for each visit to the movie theater.
• She needs 115 points for a free movie ticket.
Which equation or tape diagram could be used to represent the
context if a represents the number of visits Salma must make to earn
a free movie ticket?
using linear equation, Salma needs 10 number of visit to movie theater to get free movie ticket.
What is Linear equation?
A linear equation is one in which the variable's highest power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.
linear equation is given by y= mx + c
Salma has 30 rewards points just for signing up and 8.5 points for each visit. the equation became 30+8.5v=115
30+8.5v=115
8.5v=115-30
8.5v=85
v=10
therefore, she needs 10 number of visits to movie theater.
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−[4.2−3(2.1)](−0.2)2+1
Let f(x)=−3x−1 and g(x)=x2− 1. Find (f◦g)(−1).
The value of composite function (f о g) (-1) will be -1.
What is Composite function?
A composite function is a function that is written inside with another function and composition of functions is done by substituting one function into another function.
Given that;
The value of functions are;
f (x) = - 3x -1
And, g (x) = x² - 1
Now, All values of functions are;
f (x) = - 3x -1
And, g (x) = x² - 1
Composition of functions is calculated as;
Since, (f о g) (x) = f (g(x))
Substitute the value of function f(x) and g(x) in above equation;
(f о g) (x) = f (g(x))
= f (x² - 1)
= - 3(x² - 1) - 1
= -3x² + 3 - 1
= -3x² + 2
Put x = -1 in above equation we get;
(f о g) (-1) = - 3 (-1)² + 2
= - 3 + 2
= -1
So, (f о g) (-1) = -1
Thus, The value of composite function (f о g) (-1) will be -1.
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The sum of three numbers is 80. The first number is 8 more than the second. The third number is 2 times the second. What are the numbers?First number:Х?Second number:0Third number:
Let's use the variables x, y and z to represent each of the three numbers.
If the sum of the three numbers is equal to 80, we have our first equation:
[tex]x+y+z=80[/tex]The first number is 8 more than the second, so:
[tex]x=y+8[/tex]The third number is 2 times the second, so:
[tex]z=2y[/tex]Using these values of z and x in the first equation, let's solve it for y:
[tex]\begin{gathered} (y+8)+y+(2y)=80 \\ 4y+8=80 \\ 4y=72 \\ y=18 \end{gathered}[/tex]Now, calculating x and z, we have:
[tex]\begin{gathered} x=18+8=26 \\ z=2\cdot18=36 \end{gathered}[/tex]Therefore the first number is 26, the second number is 18 and the third number is 36.
PLEASE HELP ASAP 50 POINTS, I will mark brainlyest i would appreciate if shown how to do it with steps
If m∠SPR = 61 and m∠SPQ = 121, what is m∠QPR?
Answer:
121 - 61 = 60 degrees
Step-by-step explanation:
Answer:
∠QPR=60
Step-by-step explanation:
∠SPQ-∠SPR=∠QPR
121-61=∠QPR
60=∠QPR
A DVD is discounted by 15% and then from the already discounted price, a further 20% discount is given. If the price now is $300, find the original price?
The original price is $414.
What is discount?The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided. a fair deduction from a debt account, typically done in exchange for cash or quick payment.
Given Data
A DVD is discounted by 15% and then from the already discounted price, a further 20% discount is given.
The price now is $300
x = 300 + 15% + 20%
x = 300 + [tex]\frac{15}{100}[/tex] + [tex]\frac{20}{100}[/tex]
x = 414
The original price is $414.
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The perimeter of the rectangle below is 104 units. Find the length of side AD.
Write your answer without variables.
D
52-2
4z
C
B
AD =
0
HELP PLEASE!
Answer: 28
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]2(5z-2+4z)=104\\\\9z-2=52\\\\9z=54\\\\z=6\\\\\therefore AD=5(6)-2-28[/tex]
W QUESTIONS 100 POINTS WILL GIVE BRAINLYEST
The areas for this problem are given as follows:
3. 681.25 ft².
4. 193 m².
Item 3The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For this problem, a rectangular deck of dimensions l = 18.75 ft and w = 15 ft is added, hence the area of the deck is:
A = 18.75 x 15 = 281.25 ft².
This area is added to the previous area, hence the total area is of:
A = 400 ft² + 281.25 ft² = 681.25 ft².
Item 4The figure is composed by:
A rectangle of dimensions 10 m and 18 m.A triangle of base 13 m and height 2 m.The area of the triangle is half the base times the height, while the area of the rectangle was presented in the previous item, hence the total area of the figure is:
A = 10 x 18 + 0.5 x 13 x 2 = 180 + 13 = 193 m².
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Write the sentence as an equation.
40 is equal to 208 subtracted from the product of 184 and j
Type a slash (/) if you want to use a division sign.
Answer:
40 = (184*j) - 208 or 40 = 184j - 208
Question 3 (1 point)Find the value of x so that the function has the given value.j(x) = 4x + 11; 13CBlank 1:
A function is a relation in which each input value (x-value) has one and only one output value (y-value).
You have the following Linear function:
[tex]j\mleft(x\mright)=4x+11[/tex]According to the explained in the problem, you must find an input value that gives you 13 as the output value. Knowing this, you can say that:
[tex]j(x)=13[/tex]Substitute this value into the given function:
[tex]\begin{gathered} j(x)=4x+11 \\ 13=4x+11 \end{gathered}[/tex]The final step is to solve for "x".
Therefore, the value of "x" so that the function has the given value 13, is:
[tex]\begin{gathered} 13-11=4x \\ 2=4x \\ \frac{2}{4}=x \\ \\ x=\frac{1}{2} \end{gathered}[/tex]1/5 (x-2)= 1/10 (x +6)
Answer: The answer is 10
Step-by-step explanation:
Distribute 1(x-2)/5 = 1(x+6)/10
x-2/5 = x+6/10
Multiply by 10 on each side
2(x - 2) = x + 6
Distribute
2x - 4 = x + 6
Add 4 on each side
2x= x + 10
Subtract x
x = 10
Answer: x=10
Step-by-step explanation:
1/5(x-2)=1/10(x+6)
Distribute and multiply first
(1/5*x) -(1/5*2)=(1/10*x) +(1/10*6)
1/5x-2/5=1/10x+6/10
We do not have the same denominators on both sides. 5 goes into 10 two times so we will multiply everything on the left by 2 to get a common denominator.
2/10x-4/10=1/10x+6/10
Subtract 1/10x from both sides
1/10x-4/10=6/10
Add 4/10 to both sides
1/10x=10/10
1/10x= 1
Multiply both sides by 10/1 (the fraction inverse) to get rid of the fraction.
(10/1)(1/10x) =(1)(10/1)
x= 10
Check work:
1/5(x-2)=1/10(x+6)
Substitute your answer for x
1/5(10-2)=1/10(10+6)
1/5(8)=1/10(16)
8/5=16/10
Simplify 16/10 by dividing by 2
8/5=8/5
The graph of an absolute value function f(x) = a|x| includes the point (1, 8). Complete the following statements.Another point on the graph is ( ?, 8).The value of a is
In a absolute value graph the value of y is the same in -x and x.
Then if the coordinates (x,y) one point is (1, 8), the graph have another point in (- 1, 8).To find the value of a you use one of the points (x,y) in the general form of absolute value:
( 1 , 8) x=1 f(x)= y=8
[tex]8=a\lvert1\rvert[/tex]As:
[tex]\lvert\pm a\rvert=a[/tex]You get:
[tex]8=a\cdot1[/tex]Then:
[tex]a=8[/tex]The equation for the graph with points (1 , 8) and ( -1, 8) is:
[tex]f(x)=8\lvert x\rvert[/tex]a= 8Please help I’ll mark you as brainliest if correct!!
Answer:
A) 384, 216
b) 14575
Step-by-step explanation:
A) to find the missing values you do 3-1 which gives you 2.
here is a trick!
then you take your answer (in this case it is 216) and add it to your second row (168) to get the first row's answer (384). so you are basically going backward.
B) here you do the same thing go backward!
5967+8608 = 14575
then if you want you can double-check by subtracting them.
I hope this helps!
Select the postulate that specifies the minimum number of points in space.
Postulate 1: A line contains at least two points.
Postulate 1a: A plane contains at least three points not all on one line.
Postulate 1b: Space contains at least four points not all on one plane.
Postulate 2: Through any two different points, exactly one line exists.
•
Postulate 3: Through any three points that are not one line, exactly one plane exists.
Postulate 4: If two points a lie in a plane, the line containing them lies in that plane.
Postulate 5: If two planes intersect, then their intersection is a line.
The postulate specifies the minimum number of points in space is, Postulate 1b: Space contains at least four points not all on one plane.
A postulate is an assumption or a claim that is made without providing any supporting evidence. The fundamental claims that are used to support other claims known as theorems are known as postulates. Once a theorem is established, it can be applied to the establishment of other theorems.
By examining each postulate, we may effectively respond to this query.
Postulate 1a: establishes that if G and H are distinct points on plane R, then R contains a third point rather than GH.
Postulate (1b): establishes the bare minimum within a space.
Postulate 1: This describes a line segment with two points, say A and B.
Postulate 2: It asserts that two points determine a line.
Postulate 3: This one explains why, for example, if one leg is shorter than the other three, a table with four legs would wobble, but a table with three legs would not wobble.
Postulate 4: When points A and B are in Q, it is confirmed that AB is in plane Q.
Postulate 5: It concerns two planes.
According to the data presented above, the appropriate response to our query is:
Postulate 1b: Space contains at least four points not all on one plane.
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Hello! I need some help with this homework question posted below. Q17
To solve an inequality, we need to isolate the value of x, and to do so we will perform a series of calculations in such a way that it remains the inequality unchanged, or at least still true.
To do so, we will perform first a sum of 2x to both sides of it, as follows:
[tex]\begin{gathered} 7-2x+2x\ge3+2x \\ 7\ge3+2x \end{gathered}[/tex]Now, we subtract 3 from both sides:
[tex]\begin{gathered} 7-3\ge3+2x-3 \\ 4\ge2x \end{gathered}[/tex]To finish it, we divide both sides by 2:
[tex]\begin{gathered} \frac{4}{2}\ge\frac{2x}{2} \\ \\ 2\ge x \end{gathered}[/tex]In another way, we can express the following:
[tex]\mleft\lbrace x|x\le2\mright\rbrace or(-\infty,2\rbrack[/tex]It means that the solution is option B.
To solve the second part, we need a filled line that comes from the negative infinity and goes until 2, but it must be including the number 2, and for this reason, the correct answer in the second part is:
D.
Find the indicated z score. The graph depicts the standard normal distribution with
mean 0 and standard deviation 1.
The indicated z score is
(Round to two decimal places as needed.)
Z 0
0.8289
Using the normal distribution, it is found that the indicated z-score is Z = 1.08. A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution.
What is meant by standard normal distribution?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The z-score of a measure X in a normal distribution with mean and standard deviation is given by:
z = (x-μ)/σ,
It counts the number of standard deviations the value deviates from the mean.
We look at the z-score table after determining the z-score to determine the p-value, which is the percentile of X.
We want Z in this problem to have a p-value of 0.8599, thus Z = 1.08.
The complete question is,
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.8599.
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Three sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. Write an equation that represents the situation.
The equation that represent the situation of the quadrilateral is 40 = 3q + 7
How to write equation to represent the side of a quadrilateral?A quadrilateral is a polygon with 4 sides.
Three sides of a quadrilateral are the same length, q.
The length of the fourth side is 7 inches.
The perimeter of the quadrilateral is 40 inches.
The equation to represent the situation is as follows:
perimeter of a figure is the sum of the whole sides.
Hence,
perimeter of the quadrilateral = q + q + q + 7
perimeter of the quadrilateral = 3q + 7
Therefore,
40 = 3q + 7
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Answer:
3q + 7 = 40
Step-by-step explanation:
I got this lesson
Select the correct answer from each drop-down menu. This graph represents gasoline price trends in New Mexico. and then it First the price of gasoline in New Mexico
We have the following:
We can see that time is located on the x axis and the price of gasoline is located on y, we can conclude that in both periods the price increases, but in the first it increases slowly and in the second it increases quickly
Therefore, the answer is:
First, the price of gasoline in New mexico increases slowly, and then it increases quickly
Hello! May I please have some help with this?
Answer:
12
Step-by-step explanation:
simplify the expression (-6)^-4 using positive exponents
there u gooooooooooooooooooooooooooooooooo
If x2=16, find x3?
If x3=125, find x2
Answer:balls
Step-by-step explanation:your mom
Which is the best description of the graph of the derivative of a parabola that opens downward?
let's take a looksie hmmmm a parabola opening downwards in vertex form using constants of "h" and "k" will be like
[tex]y = -(x+h)^2 +k\implies y = -x^2-2hx-h^2+k \\\\\\ \cfrac{dy}{dx}=-2x-2h\qquad \impliedby \textit{straight line with a negative slope}[/tex]
Please help I’ll mark you as brainliest if correct!!
Answer:
4 6 3
_ 1 3 9
________
3 2 4
Step-by-step explanation:
you think of of a number
or use logic to answer it
need help with this one
Applying the relations given, considering equivalent angles, the trigonometric measures for the angles are given as follows:
sin(240º) = -sqrt(3)/2.cos(225º) = -sqrt(2)/2.tan(225º) = 1.How to find the sine of 240º?The sine of 240º can be written as follows:
sin(240º) = sin(180º + 60º).
Applying the first relation given on the second line, we have that:
sin(180º + 60º) = -sin(60º)
It is known that sin(60º) = sqrt(3)/2, hence the sine of 240º is given as follows:
sin(240º) = -sin(60º) = -sqrt(3)/2.
How to find the cosine of 225º?The cosine of 225º can be written as follows:
cos(225º) = cos(180º + 45º).
Applying the second relation given on the second line, we have that:
cos(180º + 45º) = -cos(45º)
It is known that cos(45º) = sqrt(2)/2, hence:
cos(225º) = -cos(45º) = -sqrt(2)/2.
How to find the tangent of 225º?The tangent of 225º can be written as follows:
tan(225º) = tan (180º + 45º).
Applying the third relation given on the second line, we have that:
tan(180º + 45º) = tan(45º)
It is known that tan(45º) = 1, hence:
tan(225º) = tan(45º) = 1.
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The calculation for x=0x=0 corresponds to the
point where the graph crosses the______-axis.
This is the point (______)
The calculation for x=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
In the question ,
it is given that x=0 ,
When x=0 in a point (x,y) means , that point lies on the y -axis , and it is called as the y intercept .
Y intercept is defined as the point where the graph of a line crosses the y-axis .
the point on the y-axis will be (0,y) ,
So , the graph will cross the y-axis when x=0 , and that point will be (0,y).
and the value of y will be called as the y intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
The given question is incomplete , the complete question is
The calculation for x=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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Write the following comparison as a ratio reduced to lowest terms.
114 hours to 13 days
The ratio of 114 hours to 13 days is 19:52.
How to calculate the ratio?It should be noted that ratio is simply used to show the comparison between two things that are illustrated.
In this case, we want to calculate the ratio of 114 hours to 13 days. It should be noted that 24 hours make one day. Therefore, 13 days will be:
= 13 × 24 = 312 hours.
The ratio of 114 hours to 13 days will be:
= 114 / 312
= 19 / 52
The ratio is 19:52.
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