Which congruence statement correctly compares the two triangles shown?
A) AABD - ABDC
B) AABD - ACDB
C) ADBA - ADBC
OD) AADB - ABCD
Answer:
B) ABD=CDB
Step-by-step explanation:
What is the solution of log; (3x+2) = log: (4x-6)?
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
Cancel the log from both sides and you'll get:
[tex]3x + 2 \: = 4x - 6 \: \\ 6 + 2 = 4x - 3x \: \\ x = 8[/tex]
The
exact solusion of the IVP
Answer:
[tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
|Absolute Value|FunctionsFunction NotationExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Algebra II
Logarithms and Natural LogsEuler's number eCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Differential Equations
Separation of VariablesAntiderivatives - Integrals
Integration Constant C
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Logarithmic Integration
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y' = \frac{xy}{2 + x^2}[/tex]
[tex]\displaystyle y(0) = 2[/tex]
Step 2: Rewrite
Separation of Variables
Rewrite Derivative Notation: [tex]\displaystyle \frac{dy}{dx} = \frac{xy}{2 + x^2}[/tex][Division Property of Equality] Isolate y's: [tex]\displaystyle \frac{1}{y} \frac{dy}{dx} = \frac{x}{2 + x^2}[/tex][Multiplication Property of Equality] Rewrite Derivative Notation: [tex]\displaystyle \frac{1}{y} dy = \frac{x}{2 + x^2} dx[/tex]Step 3: Find General Solution Pt. 1
Integration
[Equality Property] Integrate both sides: [tex]\displaystyle \int {\frac{1}{y}} \, dy = \int {\frac{x}{2 + x^2}} \, dx[/tex][1st Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \int {\frac{x}{2 + x^2}} \, dx[/tex]Step 4: Identify Variables
Identify variables for u-substitution for 2nd integral.
u = 2 + x²
du = 2xdx
Step 5: Find General Solution Pt. 2
[2nd Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{2x}{2 + x^2}} \, dx[/tex][2nd Integral] U-Substitution: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][2nd Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \frac{1}{2} ln|u| + C[/tex][Equality Property] e both sides: [tex]\displaystyle e^{ln|y|} = e^{\frac{1}{2} ln|u| + C}[/tex]Simplify: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u| + C}[/tex]Rewrite [Exponential Rule - Multiplying]: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u|} \cdot e^C[/tex]Simplify: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|u|}[/tex]Back-Substitute: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex]Our general solution is [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex].
Step 6: Find Particular Solution
Substitute in point: [tex]\displaystyle |2| = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]Evaluate |Absolute Value|: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]|Absolute Value| Evaluate exponents: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0|}[/tex]|Absolute Value| Add: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2|}[/tex]|Absolute Value| Evaluate: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln(2)}[/tex][Division Property of Equality] Isolate C: [tex]\displaystyle \sqrt{2} = C[/tex]Rewrite: [tex]\displaystyle C = \sqrt{2}[/tex]Substitute in C [General Solution]: [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]∴ Our particular solution is [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differential Equations
Book: College Calculus 10e
Find all x-intercepts of the function.
y = x³ - 9x² + 18x
Answer:
Step-by-step explanation:
X-intercepts mean y=0 so we have
y = x³ - 9x² + 18x = 0
Factoring
x³ - 9x² + 18x = 0
x*(x² - 9x +18) = 0
x*(x-3)*(x-6) = 0
So x-intercepts are at x=0, x=3 and x=6
Answer:
Step-by-step explanation:
see plot, intercepts at 0, 3, 6
You can transform V to V' by translating it and then performing a dilation centered at V'. Find the translation rule and scale factor of the dilation. Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number. Translation: (x, y) -> (___,___) Scale factor: ___
Answer:
Translation rule → (x + 10, y + 1)
Scale factor = 4
Step-by-step explanation:
Coordinates of V → (-8, -2)
Coordinates of V' → (2, -1)
Therefore, point V has been translated from x = -8 to x = 2,
Translation on x-axis → 2 - (-8) = 10 units
Translation on y-axis → -1 - (-2) = -1 + 2
= 1 unit
If the point V is translated 10 units right and 1 unit upwards,
Rule for the translation → (x + 10, y + 1)
Radius of the circle V = 2 units
Radius of the circle V' = 8 units
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original}}[/tex]
= [tex]\frac{\text{Radius of the image}}{\text{Radius of the original}}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4
Therefore, circle V has been dilated by a scale factor of 4 to form circle V'.
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price. The customer was charged a 7% tax when the DVD was sold.
What was the customer’s total cost for the DVD?
Answer:
$19.26
Step-by-step explanation:
12 × .5 = 6
6 + 12 = 18
18 × 0.07 = 1.26
1.26 + 18 = 19.26
Why is a square also a rectangle? Use the drop-down menus to complete the explanation.
A square is also a rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has: interior angles which measure 90° each, opposite sides that are parallel and equal, and many more attributes as well. Keep in mind however that a square is a special type of rectangle because it posseses some additional properties which don't apply to normal rectangles like the fact that all four sides of a square are equal, and diagonals of a square bisect each other at right angles.
I hope this helps! <3
Answer:
Step-by-step expl
A square is also a rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has: interior angles which measure 90° each, opposite sides that are parallel and equal, and many more attributes as well. Keep in mind however that a square is a special type of rectangle because it posseses some additional properties which don't apply to normal rectangles like the fact that all four sides of a square are equal, and diagonals of a square bisect each other at right angles.
Which set of equations shows a way to find 771 - 468?
Answer:
The one that has 303 as the answer is the correct one
In order to complete the square for the equation below, what value should be added to both sides of the equation?
x2 - 8x + ? = 42 + ?
Answer:
? = 16
Step-by-step explanation:
x2 - 8x + ? = 42 + ?
1. Take the coefficient of the middle term 8x, which is 8 and divide it by 2. [tex]\frac{8}{2} = -4[/tex]. Then square it [tex]-4^{2} = 16[/tex]
2. Take 16 and add it to both sides: [tex]x^2 - 8x + 16 = 42 + 16[/tex]
2. Take half of the coefficient 8 that you divided by 2, which is 4 and insert 4 into the equation [tex](x -4)^2 = 58[/tex]
3. ? = 16
PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS
find how far away (ground distance) from the catapult will white bird be at its highest. (round to the nearest 2 decimal points)
h= -0.114x^2+2.29x+3.5
Answer:
The bird will be at a ground distance of 10.04 units away.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Equation for the height:
The height of the bird after x seconds is given by:
[tex]h(x) = -0.114x^2 + 2.29x + 3.5[/tex]
Which is a quadratic equation with [tex]a = -0.114, b = 2.29, c = 3.5[/tex].
When the bird is at its highest?
Quadratic equation with [tex]a < 0[/tex], and thus, at the vertex. The ground distance is the x-value of the vertex. Thus
[tex]x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04[/tex]
The bird will be at a ground distance of 10.04 units away.
O capital de R$ 12.000,00 foi aplicado a juros compostos à taxa de 60% ao ano durante 2 anos. Determine o montante? *
?Answer:
Step-by-step explanation:
PLEASE HELP QUICK!!!
COMPOUND INTEREST!!!
$600 is deposited in an account that pays 7% annual interest, compounded continuously. What is the balance after 5 years?
9514 1404 393
Answer:
$851.44
Step-by-step explanation:
The balance is given by the formula ...
A = Pe^(rt) . . . . principal P, interest rate r, t years
Using the given numbers, we find the balance to be ...
A = $600·e^(0.07·5) ≈ $851.44
Help me please will be appreciated thx
Answer:
-6 +8d -2c
Step-by-step explanation:
[tex]\frac{-2}{5} (15 -20d +5c) = \frac{-2}{5} \times 15 - \frac{-2}{5}\times20d +\frac{-2}{5}\times5c = -6 + 8d -2c[/tex]
A small coffee shop sells bags of two types
of coffee. Bag A contains 24 ounces and
costs $15.60. Bag B contains 30 ounces
and costs $20.40. Which statement is true?
A. Bag A costs 3¢ less per ounce than Bag B.
B. Bag A costs 3¢ more per ounce than Bag B.
C. Bag A costs 2¢ less per ounce than Bag B.
D. Bag A costs 2¢ more per ounce than Bag B.
A measuring cylinder of radius 3cm contains water to a height of 49cm.if this water is poured into a similar cylinder of radius 7cm, what will be the height of the water column
Answer:
9 cm.
Step-by-step explanation:
Volume of a cylinder == pi r^2 h.
The volume of the water is constant so:
pi * 3^2 * 49 = pi * 7^2 h
9 *49 = 49 h
h = 9 cm.
Match the correct word with it's definition
Answer:
Rule by a small group : Oligarchy
Rule by Citizens : Democracy
Rule by No one Anarchy
Rule by king or Queen : Monarchy
The number of gallons of water left in a swimming pool at time t minutes can be modeled by w(1) = -7t+B50. Find the y-intercept and explain what it represents in this situation.
Answer:
I'm not really sure
Step-by-step explanation:
soooooooory
A snail can travel 390 inches in 5 hours. How far does it travel in 10 minutes?
Wat is the average between 1,000, 2300,1000,2600
Answer:
1180.2
Step-by-step explanation:
The average of 1,000,2300,1000,2600 is 1180.2
Write an explicit formula for am, the nth term of the sequence 5, 30, 180, ....
Answer:
Am = 5 * 6^(m-1)
Step-by-step explanation:
30/5 = 6
180/30 = 6
Am = 5 * 6^(m-1)
The table shows the mean number of minutes spent on homework last weekend. The MAD for both sets of data is 5. Which number correctly completes the statement: The difference between the means is _______ times the value of the MAD of each set of data. (Subtract the two means and then divide that difference by 5.)
What is the name of the following net?
Answer:
[tex]\large\colorbox{gold}{sǫᴜᴀʀᴇ ᴘʏʀᴀᴍɪᴅ}[/tex]
A square pyramid has a volume of 1350 ft3. If the base is a square with side
lengths 15 feet, what is the height?
who’s tryna help me with
my im3 final pls !!
Answer:
Step-by-step explanation:
Wat
Which equation is true when x = 1/2?
Answer:
D
Explanation:
6/ 1/2 = 6*2, 6*2 not equal to 3
half of 8 is 4, not 16
1/2+2 = 2 1/2
10/ 1/2 = 10*2 = 20
hellp plsssss i need it
Over the course of one day, a store owner determined that 80% of customers bought a drink and 30% of customers bought a snack
If the store sold 120 snacks that day, how many more drinks than snacks did the store sell? Enter the answer in the box.
The store sold 40
more drinks than snacks.
13) A rectangular garden has an area of 45 square meters. The garden will be 4 meters longer than its width Write and sowe an equation to find the dimensions in meters.
Answer:
9m ×5m
Step-by-step explanation:
Area of a rectangle= length ×width
Let the width be W meters and the length be L meters.
2 equations can be written from the given information:
45= WL -----(1)
L= W +4 -----(2)
Substitute (2) into (1):
45= W(W +4)
Expand:
45= W² +4W
-45 on both sides:
W² +4W -45= 0
Factorise:
(W +9)(W -5)= 0
W+9=0 or W-5=0
W= -9 or W= 5
(reject)
Substitute W= 5 into (2):
L= 5 +4
L= 9
∴ The dimensions of the garden is 9m ×5m.
Which equation represents the parabola with focus (8, 4) and vertex (8, - 2)
Answer:
8.4 whic e querido representante the parábola 8.3
A certain smart phone game app allows the player, once a day, to spin a wheel with 8 different sections. Seven of the sections contain a small prize and one of the sections is the grand prize, in which the player wins all of the other seven prizes. The makers of the game claim that the wheel has an equally likely probability of landing on each section. Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.
Required:
What would be appropriate hypotheses for the Andraya to test?
Answer:
The appropriate hypothesis set for Andraya to test is:
[tex]H_0: p = 0.125[/tex]
[tex]H_1: p < 0.125[/tex]
Step-by-step explanation:
The makers of the game claim that the wheel has an equally likely probability of landing on each section.
That is, the makers claim that the probability of earning the grand prize is:
[tex]p = \frac{1}{8} = 0.125[/tex]
Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.
At the null hypothesis, we test if it happens as often as the makers claim, that is, the proportion is 0.125. So
[tex]H_0: p = 0.125[/tex]
At the alternate hypothesis, we test if it happens less ofter than the makers claim, that is, the proportion is less than 0.125. So
[tex]H_1: p < 0.125[/tex]
The appropriate hypothesis set for Andraya to test is:
[tex]H_0: p = 0.125[/tex]
[tex]H_1: p < 0.125[/tex]