[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6x = 54}\\\\\large\textbf{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\dfrac{6x}{6} = \dfrac{54}{6}}\\\\\textbf{SIMPLIFY IT!}\\\\\mathsf{x = 9}\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Help pls ???????????
The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.
The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)
How to find the second derivative?1) We are given the function;
s(x) = 4/(1 + 2e^(-0.2x)
First derivative is;
ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²
Second Derivative is;
d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³
At x = 0;
d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³
d²s/dx² = 8/675
B) We are given the function;
k(t) = e^(-3t²)
The first derivative is;
dk/dt = -6te^(-3t²)
The second derivative is;
k''(t) = (36t² - 6)e^(-3t²)
At t = 1, we have;
k''(t) = (36(1)² - 6)e^(-3(1²))
k"(t) = 1.494
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Scott started his bank account with $150 and is spending $7 per day on lunch. The x-axis would be labeled:
The x axis is labeled as Number of days.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
let x be the number of days and y be money.
So, the equation is
y = -7x + 150.
Hence, the x axis is labeled as Number of days.
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When filling your gas tank, if you pay c dollars for g gallons of gas, you have the following table.
Choose all of the following statements that are true.
a.
The domain is {4, 8, 11, 15}.
b.
An 11 gallon tank would cost $44.00 to fill completely.
c.
A 9.1 gallon fill-up would cost $35.49.
d.
A 12 gallon tank would cost $47.40 to fill completely.
Option D statement "A 12-gallon tank would cost $47.40 to fill completely" is true.
What is a domain?The whole of the independent variable's possible values makes up the domain of a function.
For the given data we need to find which of the given statements are true.
From option A:
The domain is {4, 8, 11, 15}.
The domain is all possible x values so this would be 0 to infinity as you can pay for more gallons not just to that certain set of numbers.
Therefore, option A is False.
From option B:
An 11-gallon tank would cost $44.00 to fill completely.
From the given table we can see that 11-gallon tank costs $43.45.
Therefore, option B is False.
From option C:
A 9.1-gallon fill-up would cost $35.49.
To find 9.1 gallons we need to find the cost of 1-gallon.
That is, 15.80/4 = $3.95 (Given in the table)
Now the cost of 9.1 gallon tank is $3.95 x 9.1 = $35.95 not $35.49
Therefore, option C is False.
From option D:
A 12-gallon tank would cost $47.40 to fill completely.
We found that 1 gallon is $3.95.
$3.95 x 12 = $47.40
Therefore, option D is True.
Hence, from the given statements option D is True.
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please answer me please
Step-by-step explanation:
please mark me as brainlest
Given: ∠E and ∠F are supplementary and ∠F and ∠G are supplementary.
Prove: ∠E≅∠G
1) ∠E and ∠F are supplementary and ∠F and ∠G are supplementary (given)
2) m∠E+m∠F=180 degrees, m∠F+m∠G=180 degrees (supplementary angles have measures that add to 180 degrees)
3) m∠E=m∠G (subtraction property of equality)
4) ∠E≅∠G (angles with equal measure are congruent)
There are 230 calories in a 48 gram packet of M&M's. How many calories are in a 33.6 gram bag?
Answer:
161 calories
Step-by-step explanation:
1) Divide 230 by 48
4.791666666666667
2) multiply 4.791666666666667 by 33.6
161
Done! Your answer is 161 calories in a 33.6 gram bag. Or just 161.
Hope this helps!
If the odds against an event are 3:5, then the probability that the event will fail to occur is
Answer:
3/8
Step-by-step explanation:
probability = wanted outcomes / total outcomes
odds = wanted outcomes / unwanted outcomes
Odds of 3:5 losing means 3 losing outcomes and 5 winning outcomes.
The total outcomes is 8
The probability of losing which is the probability that the event will fail to occur is 3/8.
1. Which of the following numbers is
rational?
A. 0.78
B. 0.303003000
C. √6
D. 0.3841697
Answer:
A. 0.78
Step-by-step explanation:
A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].
Which expression is equivalent to...
X-y=5 and x^2y=5x+6
By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.
How to solve a system of equations
In this question we have a system formed by a linear equation and a non-linear equation, both with no trascendent elements and whose solution can be found easily by algebraic handling:
x - y = 5 (1)
x² · y = 5 · x + 6 (2)
By (1):
y = x + 5
By substituting on (2):
x² · (x + 5) = 5 · x + 6
x³ + 5 · x² - 5 · x - 6 = 0
(x + 5.693) · (x - 1.430) · (x + 0.737) = 0
There are three solutions: x₁ ≈ 5.693, x₂ ≈ 1.430, x₃ ≈ - 0.737
And the y-values are found by evaluating on (1):
y = x + 5
x₁ ≈ 5.693
y₁ ≈ 10.693
x₂ ≈ 1.430
y₂ ≈ 6.430
x₃ ≈ - 0.737
y₃ ≈ 4.263
By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.
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A player shoots a basketball from a height of 6 feet. The equation, , gives the height, h, of the basketball after t seconds. Describe the height, rounded to the nearest tenth of a foot, of the basketball after 1.5 seconds, assuming no other player touches the ball.
feet above the ground
It will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).
All you need to do is to replace t in the given equation with 1.5:
[tex]h=-16(1.5)^2+25(1.5)+6[/tex]
h=-4.875
The value is negative so we can assume that after 1.5 seconds the ball will be 4.875 feet lower than it was shot from.
What is the height?
The measurement of someone or something from head to foot or from base to top.
But we also know that it was shot from a height of 6 feet,
So it will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).
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Which expression can be used to an identity with [(sin)(sec)]^2 + 1?
Answer:
A
Step-by-step explanation:
sin*sec=tan
tan^2+1=sec^2 by an identity
Please answer all three of the questions <3
Answer:
1) D because the answer to 8.42*10^3=8420
and 8420 lies between 8400 and 8500
2) C because when you take the absolute value of -2.3 and -3.2, they become positive numbers => 2.3 < 3.2
3)D because 6 < 6.3 < 6.6
Hope it helps!
Which of the following is the midpoint between (6, 3) and (-2, -5)
Answer:
( 2, -1)
Step-by-step explanation:
(X1 + X2)/2 , (Y1 + Y2)/2
(6-2)/2 , (3-5)/2
4/2 , -2/2
2 , -1
Answer:
(2, -1)
Step-by-step explanation:
(x1, y1)=(6, 3)
(x2, y2)=(-2, -5)
[(6+(-2))/2, (3+(-5))/2]
=(4/2, -2/2)
=(2, -1)
The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours. Daryl plans to be gone at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving
The inequality equation will be -5x + 20 < -10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours.
Daryl plans to be gone at least 6 hours, and he has a plant outside.
If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving will be
The inequality equation will be
-5x + 20 < -10
where x is the number of hours.
Then we have
-10 < -5x + 20
5x > 30
x > 6 hours
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When you raise (almost) anything to the power zero, you get 1.
Answer:
z^0= 1
(2v+2)^0 = 1
3^0 = 1
0^0= 0
Step-by-step explanation:
When you raise (almost) anything to the power zero, you get 1 and when you raise 0 to any number except 0 is 0
Solve: 4 + 3x = 2(3x-7) +9
A. There are infinitely many solutions
B. x = 3
C. x = -3
D. x = 2/3
Answer:
B. x = 3
Step-by-step explanation:
Simplifying
4 + 3x = 2(3x + -7) + 9
Reorder the terms:
4 + 3x = 2(-7 + 3x) + 9
4 + 3x = (-7 * 2 + 3x * 2) + 9
4 + 3x = (-14 + 6x) + 9
Reorder the terms:
4 + 3x = -14 + 9 + 6x
Combine like terms: -14 + 9 = -5
4 + 3x = -5 + 6x
Solving
4 + 3x = -5 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
4 + 3x + -6x = -5 + 6x + -6x
Combine like terms: 3x + -6x = -3x
4 + -3x = -5 + 6x + -6x
Combine like terms: 6x + -6x = 0
4 + -3x = -5 + 0
4 + -3x = -5
Add '-4' to each side of the equation.
4 + -4 + -3x = -5 + -4
Combine like terms: 4 + -4 = 0
0 + -3x = -5 + -4
-3x = -5 + -4
Combine like terms: -5 + -4 = -9
-3x = -9
Divide each side by '-3'.
x = 3
Simplifying
x = 3
Terry brings home $14 per hour he works. When he started this job, he had
$40 in the bank. Write and graph the equation that would represent how
much money Terry has in the bank (y) after x hours of work. Identify the x-
and the y-intercepts. Do they make sense in this context. If so, what do they
tell us about Terry's situation? Find the point (3, 82) on the graph. What does
that point represent in the context of Terry's situation?
The point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
Given that, Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank.
We need to write and graph the equation that would represent how much money Terry has in the bank (y) after x hours of work.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, y=40+14x
Graph the line using the slope and y-intercept, or two points.
Slope: 14
y-intercept: (0, 40)
The coordinates to plot the graph are (0, 40), (1, 54), (2, 68) and (3, 82).
The graph for the given equation is given below.
Therefore, the point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
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Algebra 2 urgent I need help quickkk 20 points !!!
Answer:
(-3, -13)
(-1, -7)
(1, -1)
(3, 5)
(5, 11)
Step-by-step explanation:
Plug x into the equation y = 3x - 4 for each value of x to obtain the y value.
For example:
y = 3(3) - 4
y = 9 - 4
y = 5
A shop advertised a 24%-off sale. If a coat originally sold for $258, find the decrease in price and the sale price.
The decrease in price is $
The sale price is $
کے
Answer:
The decrease in price is $61.92
The sale price is $196.08
Step-by-step explanation:
24% × 258 = 61.92
258 decrease 24% =
258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08
6. Using the discriminant, determine the value of k that will give 1 solution (i.e. discriminant equals zero) y = kx²-4x + 4
Answer:
k = 1
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
As we need to determine the value of k that will give one solution, set the discriminant to zero.
Given equation:
[tex]y=kx^2-4x+4[/tex]
Therefore:
a = kb = -4c = 4Substitute these values into the discriminant and solve for k:
[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]
urgent help needed algebra 2
The missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
[tex]\rm F = \dfrac{9}{5}C + 32[/tex]
Make subject C and solve:
[tex]\rm \dfrac{5}{9}(F-32) = \dfrac{5}{9}\times\dfrac{9}{5}C[/tex]
[tex]\rm \dfrac{5}{9}(F-32) = C[/tex]
Plug F = 41
[tex]\rm \dfrac{5}{9}(41-32) = C[/tex]
[tex]\rm \dfrac{5}{9}(9) = C[/tex]
41 degrees F = 5 degrees C
Thus, the missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.
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What are the solutions to the following system?
Give the “best” big-oh notation to describe the complexity of the algorithm that prints all bit strings of length n.
It is correct to state that a bit can be in one of 2 states, either 1 or 0.
What is a bit?A bit is is a single binary digit. A bit can either be "1" or "0".
What is the explanation to the above answer?We stated that It is correct to indicate that a bit can be in one of 2 states, either 1 or 0. This indicates that 2ⁿ strings must be created in total. The string must then be processed twice.
The first time, for generation andThe second for reading.Hence, Our time is now O(2ⁿ⁺¹) = O(2ⁿ)
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A movie theater sells up to 10 tickets at a time online.what is the domain of this graph.
The domain of the function is whole numbers from 0 to 10.
How to explain the domain?Given the graph of function represents the tickets sold vs cost. A movie theater sells up to 10 tickets at a time online. we have to find the domain of the graph.
As shown in the graph the number of tickets sold is 0 to 10 and also the number of tickets are always positive and a whole number. It can never be negative or in fraction form.
Hence, the value of x is a positive whole number. The domain of the function is the complete set of possible values of x. The domain of the function is whole numbers from 0 to 10.
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Name the corresponding part if polygon WXYZ ≅ polygon PQRS.
Question: QP =
The corresponding part of PQ is WX
How to determine the corresponding parts?The congruent statement is given as:
polygon WXYZ ≅ polygon PQRS.
This means that the corresponding points are:
W and P, X and Q, Y and R, Z and S
When two points Q and P are joined together, we have:
polygon WX ≅ polygon PQ
Hence, the corresponding part of PQ is WX
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3. A cylindrical tank has a radius of 15 feet and a height of 45 feet. How many cubic feet of water can the tank hold?
A. 127,170 cu. ft.
B. 31.792.5 cu. ft.
C. 675 cu. ft.
D. 15,896.25 cu. ft.
Answer: 31.792.5 cu. ft. (choice B)
=================================================
Work Shown:
[tex]V = \pi*r^2*h\\\\V \approx 3.14*15^2*45\\\\V \approx 31,792.5 \text{ cubic feet}\\\\[/tex]
The result is approximate since [tex]\pi \approx 3.14[/tex] is approximate.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
B. 31.792.5 cu. ft.Step-by-step explanation:
Given,Radius (r) = 15 feet
Height (h) = 45 feet
Volume = ?
therefore,Volume of a cylinder = π × r² × hTaking π ≈ 3.14..
V = 3.14 × 15² × 45
V = 31,792.5 cu. feet
So, the cylindrical tank can hold upto 31,792.5 cu. feet of water..
___________________________Hope it helps you!!Solve by completing the square:
x2 + 3x – 9 = 0
Answer:
[tex]x=\dfrac{-3\pm3\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2+3x-9=0[/tex]
Completing the square
Move the constant to the right side by adding 9 to both sides:
[tex]\implies x^2+3x=9[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2+3x+\left(\dfrac{3}{2}\right)^2=9+\left(\dfrac{3}{2}\right)^2[/tex]
[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{45}{4}[/tex]
Factor the trinomial on the left side:
[tex]\implies \left(x+\dfrac{3}{2}\right)^2=\dfrac{45}{4}[/tex]
Square root both sides:
[tex]\implies x+\dfrac{3}{2}=\pm\sqrt{\dfrac{45}{4}}[/tex]
[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{45}}{\sqrt{4}}}[/tex]
[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{9 \cdot 5}}{2}[/tex]
[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{9} \sqrt{5}}{2}[/tex]
[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{3\sqrt{5}}{2}[/tex]
Subtract 3/2 from both sides:
[tex]\implies x=\pm\dfrac{3\sqrt{5}}{2}-\dfrac{3}{2}[/tex]
[tex]\implies x=\dfrac{-3\pm3\sqrt{5}}{2}[/tex]
e total cost, in dollars, for a company to produce r headsets per day is modeled by the function C,
where C(r) = (-5)2 + 35 for 5 < r ≤ 25. The company sells each headset for $20. On one day, the
company produced 15 headsets. According to the model, what will be the profit on the sale of these
headsets? (Profit equals total sales minus total cost.)
O $215
O $225
O $240
O $300
‐10+35=25 and 25 × 20=300
Solve: 12x- +5x-4-_ = 172x+6 O x=2 0 x==5 O x=2 x=-5 no solution
The solution to the equation 12x + 5x - 4 = 172x + 6 is D. No solution.
How to calculate the equation?The information given is 12x + 5x - 4 = 172x + 6 and we are told to find the value of x.
12x + 5x - 4 = 172x + 6
Collect like terms
12x + 5x - 4 = 172x + 6
12x + 5x - 172x = 6 + 4
-155x = 10
x = 10/-155
x = -0.0645
Therefore, the correct option is no solution as the correct answer isn't given.
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