Answers
Evaluate the value of expression.
[tex]\begin{gathered} \log _b\frac{D^2}{C^3A}=\log _bD^2-\log _bC^3-\log _bA \\ =2\log _bD-3\log _bC-\log _bA \\ =2\cdot5-3\cdot2-3 \\ =10-6-3 \\ =1 \end{gathered}[/tex]So answer is 1.
Related Questions
Find the common difference and the recursive formula. 22,19,16,13
Answers
The common difference between each term is -3.
19 - 22 = -3
16 - 19 = -3
13 - 16 = -3
The recursive formula of an arithmetic sequence follows the pattern below:
[tex]a_n=a_{n-1}+d,n\ge2[/tex]where d = common difference and number of terms "n" must be more than or equal to two.
To be able to get the recursive formula, we will plug in the common difference assuming that first term a₁ = 22. Therefore, the recursive formula is:
[tex]a_n=a_{n-1}-3,for\text{ n}\ge2[/tex]What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
A graph with a line running through coordinates (-4, -6) and coordinates (2, 6)
Answers
Answer:
12/6 or 1/2
Step-by-step explanation:
you just plug the coordinates into demos calculator and then look at rise over run.
ITS NOT A REAL TEST! MY FRIENDS WANT TO SEE HOW SMART I AM.
Answers
The given triangle is:
From the properties of triangle,
The sum of all angle in a triangle is equal to 180 degree
In triangle ABC,
Angle A + Angle B + Angle C = 180
70 + 50 + x = 180
120 +x = 180
x = 180 -120
x = 60
The missing angle is 60 degree
Find the vertex of the following equation: y = -5x² - 270x - 520
Answers
In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:
[tex]y=ax^2+bx+c[/tex]Comparing with the given equation, we have a = -5, b = -270 and c = -520.
Now, let's calculate the x-coordinate of the vertex using the formula below:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ x_v=\frac{-(-270)}{2\cdot(-5)} \\ x_v=\frac{270}{-10} \\ x_v=-27 \end{gathered}[/tex]Using this value of x in the equation, we can find the y-coordinate of the vertex:
[tex]\begin{gathered} y_v=-5x^2_v-270x_v-520 \\ y_v=-5\cdot(-27)^2-270\cdot(-27)-520 \\ y_v=-5\cdot729+7290-520 \\ y_v=-3645+7290-520 \\ y_v=3125 \end{gathered}[/tex]Therefore the vertex is located at (-27, 3125).
Write an equation for the linear function f(x) using the given information. ———————————————Using the points 2,0 & 4,3
Answers
To find the equation in the form
[tex]y=mx+b[/tex]the slope is defined by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{3-0}{4-2} \\ m=\frac{3}{2} \end{gathered}[/tex]To find b you can replace any of the points on the equation an clear for b
(x,y)=(4,3)
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ 3=\frac{3}{2}\cdot4+b \\ 3=6+b \\ 3-6=b \\ b=-3 \end{gathered}[/tex]to check if the answer is correct replace 2 as x in the equation.
[tex]\begin{gathered} y=\frac{3}{2}\cdot2-3 \\ y=3-3 \\ y=0 \end{gathered}[/tex]since the answer was 0 and point was 2,0 the equation is correct.
Element X decays radioactively with a half life of 14 minutes. If there are 460 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 35 grams?
Answers
Step 1
Given;
[tex]\begin{gathered} Intially\text{ y}_0=460g \\ Half\text{ life, h=14 minutes} \\ y=\frac{460}{2}=230g,\text{ when t=h=14 min} \\ \end{gathered}[/tex]Putting these values in, we have;
[tex]\begin{gathered} 230=a(0.5)^1 \\ a=\frac{230}{0.5}=460g \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=460(0.5)^{\frac{t}{14}}---(1) \\ when\text{ y=35} \\ 35=460(0.5)^{\frac{t}{14}} \end{gathered}[/tex][tex]\begin{gathered} 35=460(0.5)^{\frac{t}{14}} \\ \frac{460\cdot \:0.5^{\frac{t}{14}}}{460}=\frac{35}{460} \\ 0.5^{\frac{t}{14}}=\frac{7}{92} \\ \frac{t}{14}\ln \left(0.5\right)=\ln \left(\frac{7}{92}\right) \\ t=\frac{14\ln\left(\frac{7}{92}\right)}{\ln\left(0.5\right)} \\ t=52.02689 \\ t\approx52.0\text{ minutes to the nearest tenth of a minute} \end{gathered}[/tex]Answer;
[tex]52.0\text{ minutes to the nearest tenth of a minute}[/tex]For the equation y = -2x + 1 A) complete the Table: X l Y -4 04B) Use the appropriate tool to graph the given equation
Answers
ANSWER:
a)
b)
EXPLANATION:
Given:
[tex]y=-2x+1[/tex]a) When x = -4, let's go ahead and solve for y;
[tex]\begin{gathered} y=-2(-4)+1 \\ y=8+1 \\ y=9 \end{gathered}[/tex]When x = 0, let's go ahead and solve for y;
[tex]\begin{gathered} y=-2(0)+1 \\ y=0+1 \\ y=1 \end{gathered}[/tex]When x = 4, let's go ahead and solve for y;
[tex]\begin{gathered} y=-2(4)+1 \\ y=-8+1 \\ y=-7 \end{gathered}[/tex]b) Using the above values, we can go ahead and the equation as seen below;
Find sinif cos 0 = is in the first quadrant. 5 OA. OB. OC. 2/20 OD. 25/ M5 Reset Selection
Answers
Answer: B. 3/5
This question can be solved by using trigonometric identities.
- Polynomial Functions -For each function, state the vertex; whether the vertex is a maximum or minimum point; the equation of the axis of symmetry and whether the function's graph is steeper than, flatter than, or the same shape as the graph of f(x)=x²
Answers
EXPLANATION
Given the function f(x) = (x-6)^2 + 1
[tex]\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}[/tex]Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:
[tex]=x^2-12x+37[/tex][tex]\mathrm{The\: parabola\: params\: are\colon}[/tex][tex]a=1,\: b=-12,\: c=37[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-12\right)}{2\cdot\:1}[/tex][tex]\mathrm{Simplify}[/tex][tex]x_v=6[/tex][tex]y_v=6^2-12\cdot\: 6+37[/tex]Simplify:
[tex]y_v=1[/tex][tex]\mathrm{Therefore\: the\: parabola\: vertex\: is}[/tex][tex]\mleft(6,\: 1\mright)[/tex][tex]\mathrm{If}\: a<0,\: \mathrm{then\: the\: vertex\: is\: a\: maximum\: value}[/tex][tex]\mathrm{If}\: a>0,\: \mathrm{then\: the\: vertex\: is\: a\: minimum\: value}[/tex][tex]a=1[/tex][tex]\mathrm{Minimum}\mleft(6,\: 1\mright)[/tex][tex]\mathrm{For\: a\: parabola\: in\: standard\: form}\: y=ax^2+bx+c\: \mathrm{the\: axis\: of\: symmetry\: is\: the\: vertical\: line\: that\: goes\: through\: the\: vertex}\: x=\frac{-b}{2a}[/tex]Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:
[tex]y=x^2-12x+37[/tex][tex]\mathrm{Axis\: of\: Symmetry\: for}\: y=ax^2+bx+c\: \mathrm{is}\: x=\frac{-b}{2a}[/tex][tex]a=1,\: b=-12[/tex][tex]x=\frac{-\left(-12\right)}{2\cdot\:1}[/tex][tex]\mathrm{Refine}[/tex]Axis of simmetry : x=6
The quadratic function has the same shape than the parent function y=x^2 because there is NOT a coefficient within x.
determine the area of figure round to the nearest tenth if necessary..
Answers
What is the product of 0.976 and 1.2
Answers
What do you notice about the measures of the sides or the measures of angles that form triangles?
Answers
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
Shaq was climbing a cliff. He stopped for a snack. After that, he slipped 20 feet to an earlier foothold and then slipped 4 feet to another foothold. Model the distance Shaq traveled on the cliff after his snack as a sum.
Answers
1) Let's make a sketch to better understand this:
Suppose Shaq was on 40 feet after the snack he slipped 20 feet and then 6 feet.
After the snack, He traveled 20 +4 = 24 feet
From the initial point, He went 24 feet down.
Paula will make fruit punch for a party she will mix 1 1/2 gallons of orange juice with 5/8 of a gallon of pineapple juice how many 1/8 gallon servings will Paula have
Answers
First let's find the total number of gallons of the fruit punch. To do so, we just need to sum the gallons of orange juice (1 1/2) ith the gallons of pineapple juice (5/8):
[tex]1\frac{1}{2}+\frac{5}{8}=\frac{3}{2}+\frac{5}{8}=\frac{12}{8}+\frac{5}{8}=\frac{17}{8}[/tex]Now, in order to find how many 1/8 servings can be made, we need to divide the total number of gallons of the fruit punch by the number of gallons of a serving:
[tex]\frac{\frac{17}{8}}{\frac{1}{8}}=\frac{17}{8}\cdot\frac{8}{1}=17[/tex]So Paula can have 17 servings.
Answer:
17
Step-by-step explanation:
5/8 - 5
1 1/2 - 12
How4 x 8 sheet ofmanyply wood do you need tocover a 24 x 24 deck?
Answers
Given
Dimensions of deck = 24 by 24
dimensions of ply wood = 4 by 8
Find
Number of sheets of ply wood needed to cover the deck
Explanation
number of sheets = area of deck divided by area of 1 ply wood
so ,
area of deck =
[tex]\begin{gathered} 24\times24 \\ 576 \end{gathered}[/tex]and
area of ply wood =
[tex]\begin{gathered} 4\times8 \\ 32 \end{gathered}[/tex]so ,
number of sheets needed =
[tex]\begin{gathered} \frac{576}{32} \\ \\ 18 \end{gathered}[/tex]Final Answer
Hence , the required number of sheets of ply wood is 18
Jane, Chau, and Deshaun have a total of $82 in their wallets. Deshaun has 2 times what Jane has. Chau has $6 less than Jane. How much does each have?
Answers
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
let x represent represent the amount of Jane.
let Y represent represent the amount of chau.
let z represent represent the amount of Deshaun.
Jane, Chau, and Deshaun have a total of $82" can be represented as
x + y + z = $82 .......(1)
Deshaun has 4 times what Jane has. It can be represented mathematically as
y = 2x .......(2)
Chau has $6 less than Jane. It can be represented mathematically as
z= x- 6 .......(3)
we can now solve the equations using the substitution method
substitute equation (2) and (3) into equation (1)
x + y + z = $82
x + 2x + x-6 = $82
4x -6 = $82
4x - 6 = $82
4x = $82 + 6
4x = 88
x = $22
from equation 2
y = 2x
y = 2 x 22 = $44
z = x- 6
z = 22 - 6
z=$16
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
To know more about equation
https://brainly.com/question/16644061
#SPJ1
A is the incenter of Triangle FHG Find the length of AT. Explain your thinking.
Answers
we have that
The incenter is the center of the triangle's incircle, the largest circle that will fit
AR=AT=AS -----> radius of the inscribed circle in the triangle
therefore
AT=3 units
r is the midpoint of op and qr is perpendicular to op in the diagram below find the the length of qr
Answers
Given:
OP = 20 in
QP = 26 in
Since R is the midpoint of OP, then, OR = RP
Thus
[tex]OR=RP=\frac{OP}{2}=\frac{20}{2}=10\text{ in}[/tex]To find the length of QR, use pythagoras theorem below:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \\ RP^2+QR^2=PQ^2 \end{gathered}[/tex]Input values into the formula:
[tex]10^2+QR^2=26^2[/tex]Subtract 10² from both sides:
[tex]\begin{gathered} 10^2-10^2+QR^2=26^2-10^2 \\ \\ QR^2=26^2-10^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{QR^2}=\sqrt[]{26^2-10^2} \\ \\ QR=\sqrt[]{676-100} \\ \\ QR=\sqrt[]{576} \\ \\ QR=24 \end{gathered}[/tex]Therefore, the length of QR is 24 in
Find the area of the compound shapes on the coordinate plane below.
Answers
Answer
Part A: 100 square units
Part B: 39 square units
Part C: 48 square units
Explanation
Part A
Scale: 1cm represent 2 units on x-axis and 1cm represents 5 units on y-axis.
Firstly, we convert the figure into two composite plane shapes, that is, a rectangle and a triangle.
Area of composite shapes = area of rectangle + area of triangle
= Length x Width + 1/2(base x height)
= 10 x 8 + 1/2(10 x 4)
= 80 + 20
= 100 square units
Part B
Scale: 1cm represent 3 units on x-axis and 1cm represents 1 unit on y-axis.
Convert the figure into two composite plane shapes, that is, a rectangle and a trapezium.
Area of composite shapes = area of rectangle + area of trapezium
= Length x Width + 1/2(sum of parallel sides)(perpendicular height)
= 3 x 9 + 1/2(3 + 9)(2)
= 27 + 1/2(24)
= 27 + 12
= 39 square units
Part C
Scale: 1cm represent 2 units on x-axis and 1cm represents 2 units on y-axis.
Convert the figure into two composite plane shapes, that is, a trapezium and a triangle.
Area of composite shapes = area of trapezium + area of triangle
= 1/2(sum of parallel sides)(perpendicular height) + 1/2(base x height)
= 1/2(4 + 8)(6) + 1/2(4 x 6)
=1/2(12 x 6) + 1/2(24)
= 36 + 12
= 48 square units
3(-4+x)<-33 I need to solve for x
Answers
Simplify the inequality.
[tex]\begin{gathered} \frac{3(-4+x)}{3}<-\frac{33}{3} \\ -4+x+4<-11+4 \\ x<-7 \end{gathered}[/tex]So answer is x<-7.
57. do not use the answer under the line in the explanation itself, only refer to it to make sure of your work. USE DERIVITIVES NOT GRAPHING
Answers
Explanation
Question 57
[tex]\:f\left(x\right)=2x^3-15x^2+24x[/tex]To find the extreme values
[tex]\begin{gathered} \mathrm{Suppose\:that\:}x=c\mathrm{\:is\:a\:critical\:point\:of\:}f\left(x\right)\mathrm{\:then,\:} \\ \mathrm{If\:}f\:'\left(x\right)>0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:maximum.} \\ \mathrm{If\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)>\:0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:minimum.} \\ \mathrm{If\:}f\:'\left(x\right)\mathrm{\:is\:the\:same\:sign\:on\:both\:sides\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:neither\:a\:local\:maximum\:nor\:a\:local\:minimum.} \end{gathered}[/tex]So, we will have the steps below
Step 1:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=0\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=0 \\ \mathrm{Minimum}\left(0,\:0\right) \end{gathered}[/tex]Step2:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=1\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=11 \\ \mathrm{Maximum}\left(1,\:11\right) \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=4\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-16 \\ \mathrm{Minimum}\left(4,\:-16\right) \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=5\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-5 \\ \mathrm{Maximum}\left(5,\:-5\right) \\ \end{gathered}[/tex]Thus, we will have
[tex]\mathrm{Minimum}\left(0,\:0\right),\:\mathrm{Maximum}\left(1,\:11\right),\:\mathrm{Minimum}\left(4,\:-16\right),\:\mathrm{Maximum}\left(5,\:-5\right)[/tex]Hence, our answer is
[tex]\begin{gathered} \begin{equation*} \mathrm{Minimum}\left(4,\:-16\right) \end{equation*} \\ \begin{equation*} \mathrm{Maximum}\left(1,\:11\right) \end{equation*} \end{gathered}[/tex]Please help, algebra 1, i dont know how to begin to solve it :/ thank you thank you.Simplify:
Answers
Given the expression:
[tex](x^2-4x^3)+(5x^3+3x^2)[/tex]You can simplify it as follows:
1. Distribute the positive sign. Since the sign between the parentheses is positive, it does not change the signs of the second parentheses:
[tex]=x^2-4x^3+5x^3+3x^2[/tex]2. Add the like terms.
By definition, like terms have the same variables with the same exponent.
In this case, you need to add the terms with exponent 3 and add the terms with exponent 2. Notice that:
[tex]\begin{gathered} -4x^3+5x^3=x^3 \\ \\ x^2+3x^2=4x^2 \end{gathered}[/tex]Then, you get:
[tex]=x^3+4x^2[/tex]Hence, the answer is:
[tex]=x^3+4x^2[/tex]determine whether the equation defines y as function of x
Answers
To answer this question, we need to solve the equation for y in the third case:
[tex]3x+2y=5\Rightarrow2y=5-3x\Rightarrow y=\frac{5}{2}-\frac{3}{2}x\Rightarrow y=-\frac{3}{2}x+\frac{5}{2}[/tex]We can see from this case that for every value of x, there must be a value in y, and this is the main condition for a relationship to be a function. Then, y is a function of x.
In the fourth case, we have a similar case, for every possible value of x, there must be a value for y. Then, y is a function of x.
As we can see, the red graph is for the linear equation and the black one is for the one with the radical ( y = -sqrt(x+1)).
If we pass a vertical line to either function (alone), we will have only a point that passes through this vertical line, and with this graphical information, we can also say that both are functions of y (for each case).
every week, Hector works 20 hours and earns $210.00. he eans a constant amount per hour. write an equation that can be used to determine the number of hours, h, Hector works given the number of weeks, w.
Answers
From the question, we're told that Hector earns $210.00 for working 2hours every week. Let's go ahead and determine
Help I’m stuck ‼️‼️‼️ Hw due in a couple minutes
Answers
The lines AD and BC cross at a point where we have two pairs of vertically opposite angles.
The angles labelled (2x +50) and 100 are vertically opposite angles.
Vertically opposite angles are equal. Therefore;
[tex]\begin{gathered} 2x+50=100 \\ \text{Subtract 50 from both sides} \\ 2x+50-50=100-50 \\ 2x=50 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{50}{2} \\ x=25 \end{gathered}[/tex]ANSWER:
The value of x is 25. The correct answer is option A
Toni decides to plant a 2-foot wide rectangular flower garden along one side of the pool and patio but outside the fence. She measures the length of the fence to be 44 feet long. What is the area of the flower garden?
Answers
If she decides to plant a 2-foot wide rectangular flower garden along one side of the pool and patio but outside the fence. She measures the length of the fence to be 44 feet long. The area of the flower garden is 88 square feet.
Area of the flower gardenUsing this formula to determine the area of the flower garden
Area = Width × Length
Where:
Width = 2 feet
Length = 44 feet
Let plug in the formula
Area = 2 × 44
Area = 88 square feet
Therefore the area is 88 square feet.
Learn more about area here: https://brainly.com/question/25292087
#SPJ1
A small regional carrier accepted 23 reservations for a particular flight with 2o seats. 14 reservations went to regular customers who will arrive for the flight. each of the remaining passengers will arrive for the flight with a 50 % chance ,independently of each other. (answers accurate to 4 decimal places.) Find the probability that overbooking occurs find the probability that the flight has empty seats
Answers
Let's begin by identifying key information given to us:
Number of seats = 20
Number of reservation = 23
14 regular customers show up. So, we have:
[tex]23-14=9RemainingCustomers[/tex]The number of seats left is:
[tex]20-14=6seats[/tex]Overbooking means that more than 6 remaining customers show up (that could mean 7 or 8 or 9 of the remaining customers show up)
The probability of more than 6 customers arriving is given by:
Find the distance between the following points using the pythagorean theorem (5,10) and (10,12)
Answers
Answer:
\sqrt[29]
Explanation:
Given the coordinate (5,10) and (10, 12). The formula for calculating the distance between two points is expressed as;
[tex]D\text{ =}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]Given that;
x1 = 5
y1 = 10
x2 = 10
y2 = 12
Substitute:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(10-5)^2+(12-10)^2} \\ D=\text{ }\sqrt[]{5^2+2^2} \\ D\text{ =}\sqrt[]{25+4} \\ D\text{ =}\sqrt[]{29} \end{gathered}[/tex]Hence the distance between the points is \sqrt[29]
All the formation your name is on the picture picture provided
Answers
The range of the data is the difference between the maximum data value and the minimum.
In a box plot, the maximum and the minimum are indicated by the dots at the end of the horizontal line.
Here,
Maximum = 10
Minimum = 4.5
Thus, the range of the data is:
[tex]Range=10-4.5=5.5[/tex]Part A: The Sun that produces 3.9 * 10^33ergs of a radiant energy per second. How many eggs of radiant energy does the Sun produce and 3.25 * 10^3 seconds?Part B: Which is more the reasonable measurement of the distance between the tracks on a railroad: 1.435 * 10^3mm or 1.435 * 10^3mm?
Answers
Part A
[tex]1.2675\times10^{37}ergs[/tex]Explanations:The sun can produce 3.9 * 10^33 ergs of radiant energy per second
[tex]\text{Amount of energy in 1 second = 3.9 }\times10^{33}ergs[/tex][tex]\text{Amount of energy produced in 3.25}\times10^3\sec \text{ = (3.9}\times10^{33}\times3.25\times10^3)[/tex][tex]\text{Amount of energy produced in 3.25}\times10^3\text{ seconds = }1.2675\times10^{37}ergs[/tex]