____________________________________________________
Answer:
Your answer would be C). y = 100 - 5x
____________________________________________________
Step-by-step explanation:
Let's break down the question so it would be more easier to figure out the answer.
We would be making a y = mx + b equation
Important information:
100-gallon."Drained" at a rate of 5 gallons PER minute.x represents the number of minutes the tank has been draining.With the information above, we can use that to make our equations.
We know that the place has a 100 gallon fish tank. in the question, it says that for the equation, the tank was full, so that would be our "beginning point" or "starting value. From the equation, it would represent our "B" value.
Our equation should look like this now:
y = mx + 100
Now we need to find the rate of change.
In the question, it says that the tank DRAINS at around 5 gallons per minute, meaning that we would have to subtract 5 (-5). That would represent your "m" value on the equation. Your equations should now look like this:
y = -5x + 100
F.Y.I: y = 100 - 5x is the same that as -5x + 100, it's just flipped, and y = 100 - 5x is the answer choice that looks close to the one we made.
Answer choice C). y = 100 - 5x would be your FINAL answer.
____________________________________________________
The equation that describes the situation where a 100-gallon tank is drained at a rate of 5 gallons per minute is y = 100 - 5x. This because each minute, the volume decreases by 5 gallons from the starting amount of 100 gallons.
Explanation:The question is about how to represent a process which decreases at a constant rate in terms of mathematical expression. In this case, Patti's Pet Palace is draining a 100-gallon fish tank at a rate of 5 gallons per minute. The total amount of water in the tank decreases as time progresses and the tank drains.
This process can be represented using a negative slope linear equation. If y represents the amount of water in the tank after x minutes, the initial amount is 100 gallons and it decreases by 5 gallons each minute.
Therefore, the equation to represent this process is y = 100 - 5x. That means option C is the correct answer. For each minute that passes (represented as 'x'), 5 gallons are subtracted from the initial 100 gallons.
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The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring
Answer:
X * (X +1) = 420
X^2 + X = 420
X^2 + X -420 = 0
X = 20
Step-by-step explanation:
For this case we have [tex]20 * 21 = 420.[/tex] We must find an equation that allows us to find the smallest value. So:
Let "x" be the variable that represents the smallest number. Thus, "x + 1" represents the consecutive integer. The equation would be given by:
[tex]x * (x + 1) = 420\\x ^ 2 + x = 420\\x ^ 2 + x-420 = 0[/tex]
To factor, we must find two numbers that multiply as a result -420 and sum as a result 1.
These numbers are:
[tex]21, -20\\21-20 = 1\\21 * (-20) = -420[/tex]
Thus, the factorization is:
[tex](x-20) (x + 21) = 0[/tex]
The roots are:
[tex]x = 20\\x = -21[/tex]
Effectively, the smallest integer was found,[tex]x = 20[/tex].
Answeer:
[tex]x ^ 2 + x-420 = 0\\(x-20) (x + 21) = 0[/tex]
Which of the following are solutions to the equation below 2x^2+6x=20
Answer:
-5 and 2
Step-by-step explanation:
Apexvs
Answer:
-5 and 2
Step-by-step explanation:
Apex
Bismuth-212 has a half-life of 60.5 minutes. Find the amount of bismuth-212 left from a 100-gram sample after 242 minutes
Notice that 242 = 4*60.5. This means after 242 minutes, the sample decays to [tex]\dfrac1{2^4}=\dfrac1{16}[/tex] of its original amount. So you end up with
[tex]\dfrac{100\,\mathrm g}{16}=\boxed{6.25\,\mathrm g}[/tex]
After 242 minutes, 6.25 grams of Bismuth-212 remain from an original 100-gram sample, calculated based on its half-life of 60.5 minutes through the concept of radioactive decay.
The question involves calculating the amount of Bismuth-212 left from a 100-gram sample after 242 minutes, given its half-life of 60.5 minutes. To find the amount of Bismuth-212 remaining, we use the formula for radioactive decay which involves dividing the total time by the half-life to determine the number of half-lives that have passed.
First, calculate the number of half-lives passed:
Number of half-lives = Total time / Half-life = 242 minutes / 60.5 minutes = 4
Next, calculate the remaining amount after each half-life. After 1 half-life, 50 grams remain; after 2 half-lives, 25 grams; after 3 half-lives, 12.5 grams; and after 4 half-lives, 6.25 grams remain.
Therefore, 6.25 grams of Bismuth-212 remains after 242 minutes.
Needd help please and thank you!! It’s 1/E just in case you couldn’t see that! Thx!
Answer:
option A
The base is e^-1
Step-by-step explanation:
Given in the question a function, f(x) = (1/e)[tex]^{x}[/tex]
This function can also be write as.
f(x) =[tex](e^{-1})^{x}[/tex]
by using Negative Exponent Rule
[tex]x^{-n}=\frac{1}{x^{n}}[/tex]
This says that negative exponents in the numerator get moved to the denominator and become positive exponents.
What is an equation of the line that has slope -4 and passes through the point (-2, -5)?
Answer:
y = - 4x - 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 4, thus
y = - 4x + c ← is the partial equation of the line
To find c substitute (- 2, - 5) into the partial equation
- 5 = 8 + c ⇒ c = - 5 - 8 = - 13
y = - 4x - 13 ← equation of line
The equation of the line with slope -4 passing through the point (-2, -5) is y = -4x - 13.
To find the equation of a line with a given slope that passes through a specific point, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. In this case, the slope is -4 and the line passes through the point (-2, -5). Plugging these values into the point-slope form, the equation becomes y - (-5) = -4(x - (-2)), which simplifies to y + 5 = -4(x + 2). Expanding the right side gives y + 5 = -4x - 8. To solve for y, subtract 5 from both sides to get y = -4x - 13.
Carlos installed 24 wooden cabinets in 8 days. On the average, how many cabinets did he install each day?
Divide the number of wooden cabinets by the number of days.
24 / 8 = 3
Carlos installed an average of 3 cabinets each day.
Explanation:To find the average number of cabinets installed each day, we divide the total number of cabinets installed by the number of days. In this case, Carlos installed 24 cabinets in 8 days, so we divide 24 by 8 to get an average of 3 cabinets installed each day.
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Sarah has a $50 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card still have a balance of more than $30. Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Answer:
Inequality: 50-1.99x=30
She has 10 days.
Step-by-step explanation:
So, she starts off with with $50. From there, she is buying songs that are $1.99 (everyday). You could do this multiple ways:
Guess and Check, or use Algebra.
But for Algebra:
If we graph this out, the y intercept would be (0, 50), because she is starting out with $50. From there, she is spending 1.99 each day, so the slope would be 1.99/1. So basically, we would write this as 50-1.99x (that is the expression).
We would also set this equal to 30, because we are trying to see how many days it would take to still keep her balance above $30, but make it as close to 30 as possible. (x represents the # of days.
So the inequality would be 50-1.99x=30
And, when we isolate the variable and solve, we would see that she can buy a total of 10 songs over 10 days. (So basically, she has 10 days to stay over $30).
Sarah can use her $50 gift card to download a $1.99 song for 10 full days before her balance falls below $30. This is found by solving the inequality 50 - 1.99d > 30, which indicates the maximum days she can download with the card's balance staying above the threshold.
Sarah's problem can be represented by an inequality that describes the number of $1.99 song downloads she can make before her $50 music gift card drops below $30. To find out how many days she can continue to download a song without going below a $30 balance, we'll represent the number of days as d, and the cost per day as $1.99.
The inequality will be: 50 - 1.99d > 30.
Step 1: Subtract 50 from both sides to isolate the term with d.
-1.99d > -20
Step 2: Since we're dealing with a negative coefficient for d, divide both sides by -1.99, and flip the inequality sign (a rule when dividing by a negative).
d < 20/1.99
d < 10.05
Since Sarah can't download a fraction of a song, she can download a song for full days without the balance going below $30 for 10 days.
Therefore, Sarah can download a song for 10 full days with the balance of her gift card staying above $30. After that, her balance would drop below $30 if she continues.
the gas tax in our town is 23 cents per gallon . if you buy 20 gallons of gas , how much tax do you pay?
Answer:
$4.60
Step-by-step explanation:
To find the amount of tax, multiply the number of gallons by the tax per gallon.
20*.23 = $4.60
There are two slices of pizza left. The original pizza had four slices of equal size. What kind of angles are the two slices together? Select all that apply.
Answer:
I think it’s C
Step-by-step explanation:
The answer would be B, Supplementary Angle, Since half the circle would be 180 degrees also if this isn’t enough information,
Determine whether the triangles are similar, if so what is a similarity statement in the postulate or theorem used?
Answer:
It is the secon option ∆TRS ≈ ∆TPQ ; SAS
Step-by-step explanation: angle t is equal to angle t because it is the same angle
line TR divided by line TP is equal to line TS divided by TQ
Answer: The correct option is
[tex](B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.[/tex]
Step-by-step explanation: We are given to check whether the triangles in the figure are similar or not. If so, we are to state the similarity statement.
From the figure, we note that
in the triangles TPQ and TRS, we have
[tex]TP=42,~TQ=28,TR=42+6=48,~~TS=28+4=32.[/tex]
Therefore, the ratios of the corresponding sides of two triangles are
[tex]\dfrac{TP}{TR}=\dfrac{42}{48}=\dfrac{7}{8},\\\\\\\dfrac{TQ}{TS}=\dfrac{28}{32}=\dfrac{7}{8}.[/tex]
Now, in ΔTPQ and ΔTRS, we have
[tex]\dfrac{TP}{TR}=\dfrac{TQ}{TS},\\\\\\m\angle TPQ=m\angle TRS~~~\textup{[common angle]}[/tex]
So, triangles TPQ and TRS are similar by SAS proportionality postulate.
Thus, the correct option is
[tex](B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.[/tex]
Which equation can be used to solve for b?
Tan (30)= 5/b
Tan (30)= b/5
Tan (30)=10/b
Tan (30)=b/10
The equation that can be used to solve for b is Tan (30)= 5/b.
What are trigonometry ratios?Trigonometric ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. various ratios are:-sin=perpendicular/hypoteneusecos=base/hypotenusetan=perpendicular/base (tan30°)=5/bcot=base/perpendicularsec=hypotenuse/basecosec= hypotenuse/perpendicularThe ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios.
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The equations that can be solved for 'b' are 'Tan (30)= 5/b' and 'Tan (30) = 10/b', resulting in solutions 'b = 5/Tan(30)' and 'b = 10/Tan(30)' respectively.
Explanation:
The equations that can be used to solve for 'b' are Tan (30)= 5/b and Tan (30)=10/b. To solve for 'b' in these scenarios, you would rearrange the equations to isolate 'b'. For example, in the first equation, multiplying both sides by 'b' and then dividing by Tan(30) would give you 'b = 5/Tan(30)'. In the second scenario, 'b = 10/Tan(30)'. These are the solutions for 'b' and indicate the values 'b' would need to be for the equations to hold true.
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How much fluid would a 19 kg dog receive in 10 hours if fluid was given at a rate of 40 mL/kg/day?
A. 316.7 mL
B. 760 mL
C. 31.6 mL
D. 76 mL
Answer:
76 mL
Step-by-step explanation:
40*19/10
40*19= 760 / 10 = 76mL
the correct answer is A. 316.7 mL.
The question involves calculating the fluid volume that a 19 kg dog would receive if fluids were administered at a rate of 40 mL/kg/day. Here is the step-by-step calculation:
First, we calculate the daily fluid requirement for the dog by multiplying the dog's weight by the rate of fluid administration: 19 kg × 40 mL/kg/day = 760 mL/day.Next, since we need to find out how much fluid the dog would receive in 10 hours, we need to determine what fraction of the day 10 hours is. There are 24 hours in a day, so 10 hours is 10/24th of a day.Finally, we calculate the volume of fluid for 10 hours by multiplying the daily fluid requirement by the fraction of the day: 760 mL/day × (10 hours / 24 hours) = 316.7 mL (rounded to one decimal place).Therefore, the correct answer is A. 316.7 mL.
Find y. Do not round your answer.
Please Need Help Badly!!
Answer:
y = 11.2 in
Step-by-step explanation:
Given a tangent and a secant from an external point to a circle, then
The square of the measure of the tangent is equal to the product of the external part and the entire secant, that is
5(5 + y) = 9²
25 + 5y = 81 ( subtract 25 from both sides )
5y = 56 ( divide both sides by 5 )
y = 11.2
Answer: y = 11.2
Step-by-step explanation:
P(1, 10)and Q(7,4) are the endpoints of a line segment. What is the midpoint M of that line segment
Answer:
(4, 7)
Step-by-step explanation:
The midpoint formula is (((x1 + x2)/2), ((y1+y2)/2)))
x1 +x2 = 1 +7 = 8
8/2 = 4
y1 + y2 = 10 + 4 = 14
14/2 = 7
(4, 7) is the midpoint
Answer:
M = (4, 7)
Step-by-step explanation:
Using the midpoint formula
M = [[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
with (x₁, y₁ ) = P(1, 10) and (x₂, y₂ ) = Q(7, 4)
M = [ [tex]\frac{1}{2}[/tex](1 + 7), [tex]\frac{1}{2}[/tex](10 + 4) ] = (4, 7)
Factor each trinomial n^2+9n+20
Answer:
(n+4)(n+5)
Step-by-step explanation:
Answer:
(n + 4)(n + 5)
Step-by-step explanation:
to factor n² + 9n + 20, we need to find 2 numbers that when multiplied together equal 20 and when added together equal 9
these two numbers are 4 and 5 so the factorization looks like this:
(n + 4)(n + 5) < you can FOIL this out to check if the solution is correct, and you would get: n² + 9n + 20
Damon has 14 white socks, 6 black socks, and 4 blue socks in his drawer. If he chooses two socks at random, what is the possibility that his first two socks he grabs are white?
Final answer:
To find the probability of Damon choosing two white socks, calculate the probabilities step by step. The probability of Damon picking two white socks is approximately 33%.
Explanation:
To find the probability of Damon choosing two white socks from his drawer, we can calculate it step by step:
Picking the first white sock: 14 white socks out of 24 total socks, so probability = 14/24
Picking the second white sock: 13 white socks left out of 23 total socks, so probability = 13/23
Multiplying the two probabilities together: (14/24) x (13/23) = 91/276, which simplifies to approximately 0.330 or 33%.
What is the slope of the line joining (8,1) and (24,9)
Answer:
slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (8, 1) and (x₂, y₂ ) = (24, 9)
m = [tex]\frac{9-1}{24-8}[/tex] = [tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex]
Sketch of the net of each solid. Label the measurements given.
Answer:
14 in
Step-by-step explanation:
Does it want me to explain what the in.cm,mm,m are or what id it in its
The net of cube has 6 identical squares with side 14 units.
What is a net diagram?Net diagram is a 2-dimensional plane figure which can be folded to form a 3-dimensional figure. Or we can say net diagrams are the figures which obtained by unfolding some 3D figures.
Given that, the cube with edges 14 units.
A solid shape with six square faces is called a cube. Because every square face has the same side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.
The net of cube has 6 squares
Therefore, the net of cube has 6 identical squares with side 14 units.
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Franco is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by y^2+6y-3x+3=0, where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?
Answer:
focus point of satellite is (-125,-3)
Step-by-step explanation:
The question is on finding the focus point of a parabola
Given y²+6y-3x+3=0
Rewrite the equation
y²+6y=3x-3
Complete square on both sides
y²+6y+9=3x-3+9
Factorize
(y+3)²= 3x+6---------------------------------------(a)
(y+3)²= 3(x+2)
Compare equation (a) to standard equations for parabola
(y+3)²= 3(x+2)
(y-b) ²= 2p(x-a),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(b)
2p=3------------divide both sides by 2
p=3/2
Vertex (a,b)=( -2,-3)........from equation (b)
Focus point is given by (a+p/2 , b)...........................(c)
Substitute values in equation c above;
(-2+3/4 , -3) = (-5/4 ,-3) =(-1.25, -3)
Find the value of 7!
Answer:
B. 5040
Step-by-step explanation:
We want to find the value of [tex]7![/tex].
We read [tex]7![/tex] as ''seven factorial''
By definition, [tex]n!=n(n-1)(n-2)...3\cdot2\cdot1[/tex]
We need to find the product of all the positive integers less than or equal to the given number.
This implies that:
[tex]7!=7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]
[tex]7!=5040[/tex]
Help me find the lateral and the surface area I have to round to the nearest tenths if necessary
Answer:
L.A. = 384 cm²S.A. = 640 cm²Step-by-step explanation:
We have four congruent triangles with base b = 16cm and height h = 12cm.
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A=\dfrac{(16)(12)}{2}=(8)(12)=96\ cm^2[/tex]
The latearal area:
[tex]L.A.=4A\to L.A.=4(96)=384\ cm^2[/tex]
For the surface area we need the area of a base.
The base is a square with side a = 16cm.
The area of the base:
[tex]B=16^2=256\ cm^2[/tex]
The surface area:
[tex]S.A.=L.A.+B\to S.A.=384+256=640\ cm^2[/tex]
Over the summer, Manny read 45 books and 15 magazines. The value of the book to magazine ratio is
45:15 =
15:5 =
3:1
Normally, the ratio would be 45:15, but you should simplify like shown above.
The book to magazine ratio of the numbers of books and magazines Manny read over the summer is 3:1.
Explanation:The student's question pertains to finding the ratio of books Manny read over the summer to the magazines he read. Given that Manny read 45 books and 15 magazines, these numbers can be turned into a ratio by placing them over each other (books/magazines). Therefore, the book to magazine ratio would be 45:15. However, this ratio can be simplified by dividing both numbers by their greatest common divisor, which in this case is 15. When both numbers are divided by 15, the simplified book to magazine ratio is 3:1. Hence, for every 3 books Manny reads he also reads 1 magazine.
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what is the slope of the line passing through points A(5,4) and B(0.3)
Answer:
Slope = 1/5
Step-by-step explanation:
passing through points A(5,4) and B(0,3)
Slope = (4 - 3)/(5 - 0) = 1/5
Write a rule for the linear function in the table.
Answer:
Step-by-step explanation:
The general form of a linear function is ax + b.
f(x) = ax + b
f(1) = a + b = -7
f(2) = 2a + b = -10
So using a system of equations we solve for 'a' and 'b'.
a + b = -7 | 2a + b = -10
We multiply the first one by -1.
-a - b = 7 | 2a + b = -10
And then we solve the system by elimination(by adding the equations):
a = -3
Solving for b: a + b = -7 <=> -3 +b = -7 => b = -4
So the general rule of the function is:
f(x) = -3x - 4
The freshman Spirit Club took a trip to the state fair. There were 59 students and 6 chaperones, and the total admission cost for the group was $508. Student tickets cost $2 more than chaperone tickets. Write and solve an equation to find the cost of a student ticket. Show your work and explain the meaning of the variable.
Answer:
8.46
Step-by-step explanation:
59+6=65 65 divided by 508= 7.815 (7.82) 6 divided by 508=84.666 (8.67) then subtract 8.67 from 508 = 499.33 divided by 59 = 8.46 thats your answer.
Answer:
$8
Step-by-step explanation:
x=chaperone tickets
59(x+2)+6x=508
59x+118+6x=508
65x+118=508
65x=508
x=6
therefore 6+2=8
If Job A pays $8/per hour and you work at most 34 hours and Job B paid $12.50/per hour and you work 10-15 hours and they’re planning on raising the pay to $15/per hour. Which job should you choose?
job a would be the biggest money maker job. $15 an hour working at most 15 hours = $225. $8 an hour working 34 hours = $272. You would make $47 more at job a
Answer:
You should choose Job A.
Step-by-step explanation:
I did the math.
Write an equation for a stack of 10 cups that will be 125 cm tall.
It should be something like 125=x+y(10), except I can’t figure out the x and y. The example equation is h=12+4n, where h = height and n= number of cups.
I AM OFFERING 50 POINTS FOR THIS QUESTION!!!!!
125x=10y.
That is my best shot, I'm sorry lol.
A bag of pecans costs $3.84. If
each bag contains 40 pecans,
how much would one pecan cost?
Answer:
10.4 cents
Step-by-step explanation:
40 pecans/$3.84 gives you pecans per dollar
Need help to find the zeros for this quadratic equation please thanks
Answer:
x=-1 should be your answer
Answer:
see explanation
Step-by-step explanation:
Given
y = x² + 2x + 1
To find the zeros let y = 0, that is
x² + 2x + 1 = 0 ← x² + 2x + 1 is a perfect square
(x + 1)² = 0
x + 1 = 0 ( subtract 1 from both sides )
x = - 1 with multiplicity 2 ← zero
This indicates that the graph has a minimum turning point at (- 1, 0)
Note from your table
the value for x = - 1 should be y = 0 ( not - 2 )
Three cars are driving on a racetrack. The mean speed of the three cars is 100 miles per hour. Car X drives 101 miles per hour and Car Y drives 116 miles per hour. Use the mean to estimate the speed of Car Z. Then find the actual speed of Car Z.
Answer:
Less than 100. Z=83
Step-by-step explanation:
The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 101, 116, and Z or unknown. The mean of them is 100. Solve for Z.
100 =(101+116+Z)/3
300=217+Z
83=Z