As a result, 4.8 litres of water will be in the fish tank after three minutes if the water release rate is 1.6 gallons per minute.
What is the concept of Linear system?A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties. Linear systems are widely used in automatic control theory, signal processing, and telecommunications as a mathematical abstraction or idealization.
for 0.5 minutes , 0.8 gallons of water is required
To convert to gallons per minute, multiply by 2.
1.6 gallons per minute (0.8 x 2)
Gallons per minute multiplied by three minutes
3.0 minutes = 4.8 liters (1.6 x 3)
Therefore, 4.8 litres of water will be in the fish tank after 3 minutes if per minute water released is 1.6 gallons
To learn more about linear inequality click here:
https://brainly.com/question/11897796
#SPJ13
The complete question is:
How many gallons of water will be in the fish tank after 3 minutes? 0.5 mins = 0.8 gallons
PLEASE HELP NOW!!! THX :))
You are baking doughnuts for your class. There are 8 total students in your class and you have baked 11 doughnuts. Write and solve an equation to find the additional number x of doughnuts you need to bake in order to have 4 doughnuts for each student. Write your equation so that the units on each side of the equation are doughnuts per student.
Answer: 4x + 11 = 4(8)
Step-by-step explanation:
The PTA prepared 10 gallons of punch to serve at their first meeting. If each serving is eight ounces, how many people can be served?
Based on mathematical operations, the number of people that 10 gallons of punch can serve is 192 persons.
How is the number determined?The number of people can be determined using mathematical operations of multiplication based on converting the gallons to ounces and division.
The number of gallons of punch to serve at the first meeting = 10 gallons
The quantity of punch per serving = 8 ounces
1 gallon = 153.722 ounces
10 gallons = 1537.22 ounces
The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).
Thus, mathematically, from the 10 gallons of punch, the PTA can serve 192 persons.
Learn more about mathematical operations at https://brainly.com/question/20628271
#SPJ1
given the quadratic equation below, evaluate f(-1):f(x)=(x-2)^2+3
The evaluation of f(-1) given the quadratic equation f(x)=(x-2)^2 + 3 gives 12
What will the value of the function be?Given the quadratic equation f(x)=(x-2)^2 + 3. To evaluate to f(-1), we will substitute x = -1 into the equation:
Since f(x)=(x-2)^2 + 3
Therefore f(-1) = (-1 - 2)^2 + 3
= (-3)^2 + 3
= 9 + 3 = 12
Therefore, the value of c is 12. This shows the concept of functions and equations.
Learn more about quadratic equation on:
https://brainly.com/question/15738885
#SPJ1
Penny is going to make a donation to our local animal shelter. The price of each item she will donate is shown.
so far she has 30 cans of cat food 34 cans of dog food and 18 bags of cat she wants the value of her donation to be more than $380 how many bags of dog food does Penny need to donate to meet her goal?
Answer:
Second Choice: 8.73b + 171.48 > 381
Step-by-step explanation:
This is a tricky question because the first two choices both represent an inequality that satisfy the conditions
First, let's eliminate obvious wrong choices.
If b represents the number of bags of dog food and one bag costs $8.73, there should be term 8.73b somewhere in the inequality since 8.73b represents the total $ cost of b bags of dog food.
This means we can eliminate the last two choices
Let's deal with the knowns and compute the dollar amounts of each of the products being donated
30 cans of cat food at $0.57 per can = 0.57 x 30 = $17.10
34 cans of dog food at $0.84 per can = 0.84 x 34 = $28.56
18 bags of cat food at $$6.99 per bag = 6.99 x 18 = $125.82
The sum of these is $171.48
She is also donating b bags of dog food at $8.73 per bag = 8.73 x b = $8.73b
So the total cost of the donation =
8,73b + 171.48 which has to exceed 381
So the inequality is
8.73b + 171.48 > 381
Which is the choice you have selected and I believe it is correct
Now, the tricky part comes because if you subtract 171.84 from both sides of the inequality we get
8.73b > 318 - 171.48
Both inequalities are equivalent but we would not write an inequality of the type where the RHS is a mathematical expression. We would instead simplify the right hand side and write it as
8.73b > 209.52 (381-171.48 = 209.52)
I believe the way the question is worded is the LHS should be the $sum of all the donations and the RHS the minimum value.
So the best choice is choice 2: 8.73b + 171.48 > 381
i hope that helps.
The larger of two numbers is 1 more than 3 times the smaller. Their sum is 65. Find the numbers.
The larger number is 49 and the smaller number is 16.
What are the numbers?The first step is to form a linear expression that represents the larger number.
Let the smaller number be represented with y
The larger number is represented with this linear expression : 1 + 3y
The sum of the two numbers : 1 + 3y + y = 65
Take the following steps to determine the value of the smaller number:
Combine similar terms: 65 - 1 = 3y + y
Add similar terms together: 64 = 4y
Divide both sides by 4: y = 64 / 4
y = 16
Larger number = 1 + 3(16)
1 + 48 = 49
To learn more about word problems, please check: https://brainly.com/question/17339824
#SPJ1
(5x²+23x+16) + (x+4)
÷
Answer:
5x2 + 24x + 20
Step-by-step explanation:
arcsin (-1)
compute the exact value
–π/2 is the exact value of arcsine (-1).
What is arcsine?The six main inverse trigonometric functions include arcsin. It is the sine function's inverse trigonometric function. The mathematical symbol for arcsin, commonly known as inverse sine, is arcsin x or sin-1x (read as sine inverse x). Sin-1x is not the same as (sin x)-1; that is, sin-1x is not the reciprocal function of sin x. This is an important distinction to make. We may use the six inverse trigonometric functions arccos, arcsin, arctan, arcsec, arccsc, and arccot to calculate angles. Arcsin x calculates the angle that corresponds to the right-angled triangle's perpendicular to hypotenuse ratio. We shall examine the idea of arcsin in this article and determine its formula. We'll also talk about the domain and range.
To know more about arcsine ,visit:
brainly.com/question/28553677
#SPJ13
five hundred feet of fencing is available for a rectangular pasture alongside a river, the river serving as one side of the rectangle (so only three sides require fencing). find the dimensions yielding the greatest area
The dimensions yielding the greatest area (125*250).
What is a dimensions?
The minimal number of coordinates required to specify any point within a dimensional vector space (or object) is known as the dimension in physics and mathematics. Because only one coordinate is required to specify a point on a line, such as the point at 5 on the a number line, a line is said to have one dimension (1D). Because two coordinates are required to specify a point on a surface, such as the perimeter of a sphere or cylinder, it is referred to as having a dimension of two (2D). For instance, a point on the a sphere's surface requires both a latitude and a longitude to be located. A two-dimensional space just on plane is referred to as a Euclidean space.
The perimeter is 2a+b = 500
b= 500-2a
Max are is A = ab
A= a(500-2a)
= 500a - 2[tex]a^{2}[/tex]
for max value
a = -y/2x
= -500/2(-2)
= 125 feet
and b = 250 feet
Greatest area (125*250) = 31250 feet²
Hence dimensions yielding the greatest area (125*250).
Learn more about dimensions by following the link below.
https://brainly.com/question/26740257
#SPJ4
I need help with this can someone please help?
HG is the answer.
hope this helps
The first one is GH Segment.
Both shapes are similar. The figure on the right is a scaled version of the figure on the left. The VU edge in the left figure corresponds to the GH edge in the right figure.
The second one is %[tex]150[/tex].
As can be seen, the VU edge is [tex]2[/tex] units long while the GH edge is [tex]3[/tex] units long. By proportioning these edges and multiplying by [tex]100[/tex], we find the scaling factor. It is [tex]\frac{3}{2}[/tex].
WILL MARK BRAINIEST Rewrite the radical expression as an expression with a rational exponent. 3 square root x 7
a x21
b x4
c x7/3
d x 3/7
Read the following actions and decide if they are responsible (R) or irresponsible(IR).
1. checking my credit score:
2. paying a credit card bill one day late:
3. listing expenses in a budget:
4.making decisions without all of the information:
5.purchasing something because it is on sale:
6.writing some goals:
7.researching what a mutual fund is:
8.making financial decisions without discussing it with your spouse:
9.finding a savings account with a great interest rate:
10. looking for the cheapest price for an item:
HELP ME PLEASE!!!!!!
Answer:
1. R
2. IR
3. R
4. IR
5. IR
6. R
7. R
8. IR
9. R
10. R
Step-by-step explanation:
Note on #5: purchasing something on sale that you were already going to buy would be responsible, but not simply BECAUSE the item is on sale and you were not already needing to purchase it.
Connor left his house for work and was gone 4 hours. He spent a total of
hour driving to and from work and didn't go anywhere else. How long was he
at work?
A. 4 hours
B. 3 hours
c. 4 hours
D. 3 hours
HELP FAST GIVING HIGHEST AMOUNT OF POINT
Answer:
4 hours
Step-by-step explanation:
he was gone for 5 hours, he spent an hour driving.
5 - = 4 hours at work.
Answer:
4 hours
Step-by-step explanation:
says he was gone 4 hours, he was at work
WILL GIVE BRAINLY
PLS ANSWER QUICK
Use properties to evaluate [tex]-5x14 ÷ \frac{3}{4} x 15[/tex]
A. -350
B. -1400
C. 350
D. 1400
The expression has a value of -1400 when evaluated
How to evaluate the expression?From the question, the expression is represented as
-5 x 14 ÷ 3/4 x 15
Start by evaluating the product of -5 and 14
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 ÷ 3/4 x 15
Next, we rewrite the quotient as products
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 x 4/3 x 15
Divide 15 by 3
So, we have
-5 x 14 ÷ 3/4 x 15 = -70 x 4 x 5
Continue by evaluating the product of -70 and 4
So, we have the following equation
-5 x 14 ÷ 3/4 x 15 = -280 x 5
Lastly, we have
-5 x 14 ÷ 3/4 x 15 = -1400
Hence, the value of the expression is -1400
Read more about expressions at
https://brainly.com/question/20662459
#SPJ1
Two planes left the same airport traveling in opposite directions. The
lirections. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes
were 1825 miles apart. The second plane left at 10:00 a.m. and its average
average rate. Let x represent the first plane's average rate.
rate was 108 miles per hour slower than the first plane's
What was the first plane's average rate?
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the first plane's average rate in the second box.
Answer: x=560 miles per hour
Step-by-step explanation:
[tex]\displaystyle\\2.25=\\\\2\frac{1}{4}= \\\\\frac{2*4+1}{4}=\\\\\frac{8+1}{4}=\\\\\frac{9}{4}\ hours[/tex]
The second plane left at 10:00 a.m. so, him fly was 1.25 hours:
[tex]\displaystyle\\1.25=\\\\1\frac{1}{4}=\\\\\frac{1*4+1}{4}=\\\\\frac{4+1}{4} =\\\\\frac{5}{4} \ hours[/tex]
Let x represent the first plane's average rate
Hence, (x-108) represent the second plane's average rate
So,
[tex]\displaystyle\\\frac{9}{4}x+\frac{5}{4} (x-108)=1825\ \ \ \ (1)\\[/tex]
Multiply both parts of the equation by 4:
[tex]9x+5(x-108)=7300\\\\9x+5x-540=7300\\\\14x-540+540=7300+540\\\\14x=7840[/tex]
Divide both parts of the equation by 14:
[tex]x=560\ miles/hour[/tex]
12. x=lyl with inputs x = 1, x = 2, and x
3
If x=lyl with inputs x = 1, x = 2, and x = 3 then y = ±1, y = ±2, and y = ±3.
To solve this problem we have to learn about the modulus operator and absolute value.
What is absolute value?
Absolute value is the distance of a number from zero.
Example: for -12, the distance from 0 is 12. Therefore 12 is the absolute value of -12.
What is the mod operator?
A Mod operator is a mathematical device that converts all types of integers into a positive integer or it finds the absolute value.
Now, we have to find values.
x=lyl Or, 1 = |y| or, we can say the absolute value of y is 1. y may be ±1x=lyl Or, 2 = |y| or, we can say the absolute value of y is 2. y may be ±2x=lyl Or, 3 = |y| or, we can say the absolute value of y is 3. y may be ±3To know more about absolute values visit,
https://brainly.com/question/1301718?referrer=searchResults
#SPJ9
Math To Do, -Ready
Interactive Practice: Work with Scientific Notati
-) Multiply. Write your answer using scientific notation.
(2 × 10 ) × (3.1 × 10¹⁰) = ||
X ?
6.2 × [tex]10^{11}[/tex] is the result after multiplying the terms (2 × 10 ) × (3.1 × 10¹⁰).
We are provided with the equation mentioned below:
(2 × 10 ) × (3.1 × 10¹⁰) equation 1
We were asked to multiply the terms mentioned in the above equation using scientific notation. The steps to simplify the above mentioned equation are written below;
(2 × 10 ) × (3.1 × 10¹⁰)
Separately write similar terms first as shown below,
= ( 2 × 3.1 ) × ( [tex]10^{1}[/tex] × [tex]10^{10}[/tex] )
Now multiply the similar terms as written below;
= 6.2 × [tex]10^{(1 + 10)}[/tex]
Add powers of 10, we get
= 6.2 × [tex]10^{11}[/tex]
Thus, the solution of the given equation is 6.2 × [tex]10^{11}[/tex].
To know more about Multiplication refer to the link:
https://brainly.com/question/10873737
#SPJ1
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is less than 8. 42?.
P(X < 8.4)
= P(Z < (8.4 - 8.5) / (0.22 / sqrt(37)))
= P(Z < -2.76 ) = 0.0029
So the probability is 0.0029
Learn more about Probability :
https://brainly.com/question/13604758
#SPJ4
b/c=a solve for c b nb
Answer:
b = ca
c = ba
Step-by-step explanation:
PLEASE HELP FASTTT ILL MARK BRAINLIEST
Answer:
[tex]2\sqrt{2}[/tex]
Doing RSM I see... lol gl. (tell me if this is wrong, I'll correct it if it is) :]
Step-by-step explanation:
h(6)=2
g(2) = [tex]\sqrt{2\\}[/tex]
f(sqrt2) = [tex]2\sqrt{2}[/tex]
:]
Vistaprint offers the first 500 business cards for free. Then each additional set of 500 cards cost $9.99.
A. Write an equation that gives the total cosr (in dollars) of cards, C, in terms of the number (in groups of 500) of business cards, b, ordered.
B. Find the cost of buying 3500 business cards.
If the Vistaprint offers the first 500 business card for free and each additional set of 500 card cost $9.99
Part A
The equation that gives the total cost (in dollars) of card C, in terms of the number(in group of 500) of business cards b ordered is C = 9.99×b -9.99
Part B
The cost of buying 3500 business cards is $59.94
The Vistaprint offers the first 500 business cards for free
The cost of each additional set of 500 cards = $9.99
Part A
Consider the total cost of the card = C
Number of business card in group of 500 = b
Then the equation of the total cost of cards
C = 9.99×b -9.99
Part B
Total number of cards = 3500
Number of cards in group of 500 = 3500/500
= 7
The cost of buying 3500 business card = 9.99×7-9.99
= 69.93-9.99
= $59.94
Hence, If the Vistaprint offers the first 500 business card for free and each additional set of 500 card cost $9.99
Part A
The equation that gives the total cost (in dollars) of card C, in terms of the number(in group of 500) of business cards b ordered is C = 9.99×b -9.99
Part B
The cost of buying 3500 business cards is $59.94
Learn more about equation here
brainly.com/question/14603452
#SPJ1
[tex] x {6} \div x {15}[/tex]how to solve x to the 6th power divided by x to the 15th power
So, if we apply the power's rule, we notice that if the base is the same, the exponents can be substracted. Like this
So the answer is 1 / x to the 9th power
Express as a trinomial. (x-9)(x+6)
The expression of (x-9)(x+6) as a trinomial is x² -3x - 54
what is a trinomial?A trinomial is an algebraic expression that has three non-zero terms.
In a simpler terms, the definition of a trinomial is a math equation that has three terms which are connected by plus or minus notations.
Therefore, let's express (x-9)(x+6) as a trinomial.
Hence,
(x-9) (x+6) = x² + 6x - 9x - 54
Finally,
x² + 6x - 9x - 54 = x² -3x - 54
Therefore, the trinomial form of (x-9)(x+6) is x² -3x - 54
learn more on trinomial here: https://brainly.com/question/20259268
#SPJ1
The function -2x^2-8x+42 represents the approximate height of an object (x seconds) after it is thrown off the top of a building. How many seconds does it take for the object to hit the ground?
The function is given to be:
[tex]-2x^2-8x+42[/tex]The object hits the ground when the function is equal to zero:
[tex]-2x^2-8x+42=0[/tex]Solving the equation by factorization, we have:
[tex]\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}[/tex]Since the time cannot be negative, then the time will be 3 seconds.
Therefore, it will take 3 seconds for the object to hit the ground.
ASAP!!
4/3x + 2/3x = 1/3x +5
Solve the equation for X and include all steps to get Branliest.
Answer: x=3
Step-by-step explanation: Multiply both sides of the equation by 3 to get 4x+2x=x+15. Combine like terms. (underlined) 6x=x+15. Move variable to left side and change its sign. 6x-x=15. Combine like terms again. 5x=15. Divide both sides of the equation by 5 to get x=3.
Is √3 rational?
I’m trying to figure out is the question above rational
Answer:
The square root of 3 is an irrational number if that's what you were asking
Find the average rate of change:
Input
1
2
3
4
5
Output
11
13
15
17
19
Average rate of change = 2
How to find the average rate of change?
Given:
Input(x) = 1, 2, 3, 4, 5
Output(y)= 11,13,15,17,19
We know,
Average rate of change = change in output/change in input
[tex]=\frac{y_1-y_2}{x_1-x_2}\\\\=\frac{11-13}{1-2} \\\\ =\frac{-2}{-1} \\\\=2[/tex]
What is average rate of change?
The average rate of change is a typical indicator of change over a period of time given in a function. It is equal to the difference between the function's input and output as a whole. It is a measurement of the average amount of change in the function per unit throughout that time. On the graph of the function, it is calculated from the slope of the straight line joining the interval's ends.To learn more about average rate of change, refer:
https://brainly.com/question/24313700
#SPJ13
PLEASE HELP ME ! due tonight , Will make you a brainlist if you give me the correct answer .
Answer:
y=3/2x+3
Step-by-step explanation:
gradient is dy/dx
so up 3 and across 2
3/2
crosses at 3
Answer:
y=-3/2x+3
Step-by-step explanation:touches y axis at 3 and negative 3/2 slope
rearrange the following so g is the main subject:
f+4(g-h)=x
Answer:
g=x-f+4h/4
Step-by-step explanation:
change of subject of formula
f+4(g-h)=x
f+4g-4h=x
4g-4h=x-f
4g=x-f+4h
g=x-f+4h/4
rate as brainliest
Write as an inequality. Do not solve.
Yellow Cab charges a flat rate of $3.00 plus $0.50 per mile. Raven
has $20.00 to spend on a cab ride. Write an inequality that expresses how
many miles Raven can travel under her limit.
The product of 8 and y is less than 21.
Raven can travel 5.71 miles or less under her limit.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Let x b the number of miles Raven travels, we can write an expression relating the amount he spends. So there:
3.00 + 0.50= 3.50
Consider that total cost per mile be less than equal to the amount the Raven can spend:
3.50x ≤ 20
We can determine x;
x ≤ 5.71
Therefore, Raven can travel 5.71 or less under her limit.
Learn more about inequality ;
brainly.com/question/14164153
#SPJ1
division of fractions and mixed numbers in the real world the local preservation group is cleaning up a 3 3/5 km hiking trail twelve members sign up to help. to make the work easier, the leader of the group splits the trail into equal sections, one for each member. what length of trail is each member responsible for cleaning?
The length of trail is each member responsible for cleaning is 0.3.
Given,
In the real world the local preservation group is cleaning up a 3 3/5 km hiking trail twelve members sign up to help.
To find the length of trail is each member responsible for cleaning.
(Division of fractions)
Now, According to the question:
Based on the given condition
= [tex]3\frac{3}{5}[/tex] ÷ 12
= 18/5 ÷ 12
Convert into decimal
= 3.6 x 1/12
= 0.3
Hence, The length of trail is each member responsible for cleaning is 0.3.
Learn more about Fractions at:
https://brainly.com/question/10354322
#SPJ1