Answer:
[tex]\log\left(\dfrac{\sqrt{x}\:z^2}{4y^2}\right)[/tex]
Step-by-step explanation:
[tex]\dfrac12\log(x)-2\log(2y)+2\log(z)[/tex]
[tex]\textsf{Apply log power rule}: \quad n \log(x)=log(x)^n[/tex]
[tex]\implies \log(x)^{\frac12}-\log(2y)^2+\log(z)^2[/tex]
[tex]\textsf{Apply exponent rule}: \quad(ab)^c=a^cb^c[/tex]
[tex]\implies \log(\sqrt{x})-\log(4y^2)+\log(z^2)[/tex]
[tex]\textsf{Apply log quotient rule}: \quad \log(x)-\log(y)=log(\frac{x}{y})[/tex]
[tex]\implies \log\left(\dfrac{\sqrt{x}}{4y^2}\right)+\log(z^2)[/tex]
[tex]\textsf{Apply log product rule}: \quad \log(x)+\log(y)=log(xy)[/tex]
[tex]\implies \log\left(\dfrac{\sqrt{x}\:z^2}{4y^2}\right)[/tex]
Determine whether the infinite geometric series converges or diverges. If it converges, find the sum, and if it diverges then explain why.
48 + 36 + 27 + 81/4 + ...
Geometric series means
|r|<1Lets spot out common ratio
36/48=3/427/36=3/4Its less than 1
Hence series converges
Sum:-
a/1-r48/(1-3/4)48/1/4192Answer:
Series converges
Sum = 192
Step-by-step explanation:
General form of geometric series: [tex]a_n=ar^{n-1}[/tex]
where:
a is the initial termr is the common ratioGiven series: 48, 36, 27, 81/4, ...
[tex]\implies a = 48[/tex]
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{36}{48}=\dfrac34[/tex]
Geometric series converges when |r| < 1
Geometric series diverges when |r| ≥ 1
[tex]\textsf{As }r=\dfrac34\ \implies|\dfrac34| < 1\:\implies\:\textsf{series converges}[/tex]
Sum of an infinite geometric series:
[tex]S_\infty=\dfrac{a}{1-r}\quad\textsf{for}\:|r| < 1[/tex]
Substituting values of a and r:
[tex]\implies S_\infty=\dfrac{48}{1-\frac34}=192[/tex]
What is the distance between (-2, - 4) and (-2, – 8) ?
O 2 units
O 4 units
0 12 units
O I don't know.
4 units
hope it helps...!!!
Answer:4 units
8-4=4 wham bam yes ma'am
Step-by-step explanation:
what is the perimeter of a 12 inch by 13 inch triangle
Answer:
Perimeter = 30 in
Step-by-step explanation:
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = ab = 12 inc = 13 inSubstitute given values into the formula and solving for a:
⇒ a² + 12² = 13²
⇒ a² + 144 = 169
⇒ a² = 25
⇒ a = 5 in
Therefore, perimeter = a + b + c
= 5 in + 12 in + 13 in
= 30 in
Final Answer:
[tex]\fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]
Step by Step explanation:
Data achieved from diagram:
The given triangle is a right angle triangle
Hypotenuse of triangle = 13 in.
Base of triangle = 12 in.
To find:
Perimeter of triangle = ?
Solution:
We need length of all three sides (Altitude) of triangle,
let's find out the measure of length of Altitude using Pythagoras theorem!
[tex]{Hypotenuse}^2 = {Base}^2 + {Altitude}^2 \\ {13}^{2} = {12}^{2} + {A}^{2} \\ {A}^{2} = 169 - 144 \\ {A}^{2} = 25 \\ {A} = \sqrt{25 } \\ \fbox{A = 5 \: in.}[/tex]
Now we have all three sides of triangle,
[tex]perimeter \: of \: triangle = Hyp. + Base + Alt. \\perimeter \: of \: triangle = 13 + 12 + 5 \\ \fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]
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A metal with a specific heat of 0.780 J/g oC requires 940 J of heat to raise the temperature (the change in temperature) by 15 oC. What is the mass of the metal?
SOMEONE HELP PLEASE GIVING BRIANLEST THANK YOU
Step-by-step explanation:
Q = msdt
or, 940 = m* 0.780* 15
or, 940 = 11.7m
or, 940/11.7 = m
m = 80.341
Therefore the mass of the metal is 80.341g.
Find the supplement of an angle that measures 20 degrees.
Mrs. Hynes gave each of her 8
students 3 pieces of candy. She
gave 1 student 2 extra pieces for
good behavior. How many pieces of
candy did she
give away in all?
PLEASE HELP and show work too please
HELPPPPPPPPPPPP This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths. units² Coordinate plane with axes labeled x and y. A closed figure is formed by a parallelogram and rectangle. The vertices are negative 10 comma 2, negative 7 comma 3, negative 1 comma 3, 1 comma negative 3, negative 2 comma negative 4, and negative 4 comma 2.
Answer:
Area = 26 sq units
Step-by-step explanation:
If you put the points on a graph then you can see what you are working with. The parallelogram you can just count the squares to find the base and height. base = 6 and height = 1.
A = b • h = 6•1 = 6
To find the lengths of the sides for the rectangle you must use distance formula or pythagorean theorem. I have shown this using Pythagorean theorem. The short side of the rectangle is marked x and calculated to have length sqroot10. See image.
The graph shows the length is twice as long. But I showed a separate calculation also using pythag.thm. to find the length of y, the long side is sqroot40.
Area of rectangle is:
A = b•h OR L×W
A=sqrt10×sqrt40
=20 See image.
Add the areas to get your final answer.
Mason has a map of Alabama that measures 3/4 meter wide and 7/8 meter long . What is the area in square meters of mason map
[tex]\sf\large\underline{\star Given:-}[/tex]
[tex]\rightarrow[/tex] Length(l) of map = [tex]\sf\red{\frac{7}{8}m.}[/tex]
[tex]\rightarrow[/tex] Width(w) of map = [tex]\sf\red{\frac{3}{4}m.}[/tex]
[tex]\sf\large\underline{\star To \: Find:-}[/tex]
[tex]\rightarrow[/tex] Area of map.
[tex]\sf\large\underline{\star Solution:-}[/tex]
[tex]\rightarrow[/tex] From the above given dimensions we can conclude that map is in the shape of rectangle. So, we can find the area of map by using the formula: [tex]\sf\blue{Length×Width}[/tex]
So, let's begin
[tex]\rightarrow[/tex] Area of rectangular map = [tex]\sf{Length×Width}[/tex](putting the value of length and width from the above given)
[tex]\rightarrow[/tex][tex]\sf{=\:\frac{7}{8}×\frac{3}{4}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{=\:\frac{21}{32}m^2}[/tex] Or,
[tex]\rightarrow[/tex][tex]\sf{=\: 0.65m^2}[/tex]
Therefore the area of the Mason map [tex]\sf\purple{=\: 0.65m^2}[/tex]or [tex]\sf\purple{\frac{21}{32}m^2}[/tex]
________________________________
Hope it helps you:)
Suppose the graph represents the plans for a fence that Tara is
building for a new city dog park. Each unit on the graph represents
12 yards. After studying the plans, Tara decides to build a fence that
encloses a smaller area. If Tara dilates Rectangle ABCD by a scale
factor of 0.75, and fencing costs $6.39 per yard, how much will she
spend on fencing?
The scale factor of 0.75 would ensure that the new fence has a smaller area
The total cost of fencing the smaller area is $1610.28
How to determine the fencing cost?From the complete question, we have the following parameters:
Number of units on the smaller area, k = 12Scale factor = 0.75Unit cost = $6.39 per yardPerimeter, P = 28 yardsStart by calculating the perimeter of the smaller area using:
Smaller Area = Perimeter * Scale factor * k
Where k represents the number of units on the smaller area
So, we have:
Smaller Area = 28 yards * 0.75 * 12
Evaluate the product
Smaller Area = 252 yards
The total cost is then calculated as:
Total cost = Unit cost * Smaller Area
This gives
Total cost = 6.39 * 252
Total cost = $1610.28
Hence, the total cost of fencing is $1610.28
Read more about scale factors at:
https://brainly.com/question/3457976
all included in the picture
Answer:
(-4,3)
Step-by-step explanation:
Answer:
Option 1 : (-4,3)
Step-by-step explanation:
When doing coordinates we always go across first the up or down.
Since it goes 4 to the left, our x coordinate is -4 and since it goes 3 up, our y coordinate is 3.
Therefore our answer must be (-4,3)
If someone could help me with this I would really appreciate it thank you !!
Answer:
It should be thirty if i read question properly
If want process pls comment
Can someone please help me with this (a^3-(2*b))*(a^3-(3*b)) equation
Hope the picture will help you...
How does a geometric construction differ from a drawing?
Answer:
Constructing geometric figures means with the help of a compass, protractor and a scale with accurate measurement.
Drawing may just be drawing rough figures with no accurate measurement
Answer:
When you are constructing, you use tools like a compass, ruler, and protractor vs when you draw you don't use a tool, you free hand it.
Step-by-step explanation:
A geometric construction is a set of steps to create geometric figures using just a straightedge and a compass without using formal measurements; whereas a drawing can use any tool.
Jared lost a total of $96 over the last 12 months. What integer represents the mean number of dollars lost each month?
Answer:
-8
Step-by-step explanation:
To find mean, average, divide.
-96/12
-8
first a price was decreased by 12% then it was discounted again by 5% what is the percent of the total discount. From RSM
x = original price or 100%
so if we discount "x" by 12%, that means the new price is 100% - 12% = 88%, let's see how much is 88% of "x"
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{88\% of x}}{\left( \cfrac{88}{100} \right)x}\implies 0.88x[/tex]
now if we grab that new price, or the new 100%, and discount it further by 5%, what's leftover is simply 95%, because we'll be taking off 5% off of it and thus left with 100% - 5% = 95%.
so what's 95% of 0.88x?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{95\% of 0.88x}}{\left( \cfrac{95}{100} \right)0.88x}\implies 0.836x[/tex]
so the new discounted price is just 0.836x or 83.6% of our original "x".
from 100% originally to 83.6%, the difference is 16.4%, and that's the total discount.
50 POINTS! Please help me! I give Brainliest!
1. Given the following coordinates, complete the listed transformations in sequence, which means you do one after the other.
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwise
b) Dilation by a scaling factor of 2
c) Reflect across the x-axis
d) Translation 2 Up and 5 to the Left
4 PARTS TO THIS QUESTION! ANSWER ALL PLEASE!
Translating the new coordinate up by 2 units and 5 units to the left will given a final coordinate at X''''(10, 1), Y''''(-4, 15) and Z''''(4, 19)
What is transformaton?This is a technique used to change the position or size of an object on the xy plane.
Given the coordinate points X(2, 4), Y(5,-3) and Z(-7, 1)'
If the coordinate points is rotated 90 degrees clockwise, then the resulting coordinate will be at X(4, -2), Y(-3,-5) and Z(1, 7)
If the resulting coordinate is dilated by by a scaling factor of 2, then the new coordinate points wil be at X''(8, 4), Y''(-6, -10) and (2, -14)
If the resulting coordinate is reflected over the x-axis, then the new coordinate points wil be at X'''(8, -4), Y''(-6, 10) and (2, 14)
Finally, translating the new coordinate up by 2 units and 5 units to the left will given a resulting coordinate at X''''(10, 1), Y''''(-4, 15) and Z''''(4, 19)
Learn more on transformation here:
https://brainly.com/question/4289712
please find the area
the answer is 70.2 ft because u add them all together
Answer:
the area is 243
see the photo
Can anyone help me with my homework?
I really need help . It’s the second part of the eqaution that confuses me .
Answer:
The answer is 5^4
Step-by-step explanation:
You are given the expression 5^18 times 5^6 while all over (5^10)^2
First, let's simplify the numerator
Whenever you multiply exponents with the same base, which is 5 in this case, you have to add the exponents or powers
Keep the base the same and 18 and 6 together
So, 5¹⁸ ° 5⁶ = 5¹⁸⁺⁶ = 5²⁴
you have 5²⁴ in the numerator
now let's work on simplifying the denominator
Whenever you have number that has a power and is taken to another power, you multiply the powers
We call this the power of the power rule
So, (5¹⁰)² = 5¹⁰ˣ² = 5²⁰
Now the denominator is 5^20
We have 5^24/5^20
Now you just subtract the powers 24-20=4
And you get 5^4
Hope this helps
Explain how to modify the graphs F(x) and g(x) to graph the solution to set the following system of inequalities. How can the solution set be identified? Y>x^2-1
Y<-x^2+4
The following rigid transformations are applied:
Reflection around the line y = -1.Translation 5 units in the +y direction.The solution set is found by the fact that the domain of quadratic functions is the entire real domain.
How to apply rigid transformations to understand the differences between two given functions
According to the Euclidean geometry, rigid transformations are those transformations applied on geometrical loci such that Euclidean distances are conserved in every point of the loci. Reflections and translations are sound examples of rigid transformations.
In this question we must derive all needed rigid transformations to turn f(x) into g(x), both quadratic functions. After a careful analysis we conclude that the following rigid transformations are applied:
Reflection around the line y = -1.Translation 5 units in the +y direction.The solution set is represent by all x-values such that the function exists. According to real algebra we remember that the domain of quadratic functions is the real domain. Thus, the solution sets of f(x) and g(x) are the real domain.
To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538
Can you explain how you got your answer?
Two triangles are similar. The sides of the first triangle are 8, 9, and 12. The smallest side
of the second triangle is 10. Find the other two side lengths.
Answer:
10,11.25,15
Step-by-step explanation:
we use linear scale factor you had mentioned that the triangles are similar so the smallest side in the first triangle is 8 and in tje other triangle it is 10
those two sides are equal which means 8 is equal to ten so if 8 is equal to 10 what about 9.if you cross multiply you get 11.25 then you do the same for 12 and get 15
8=10
9=11.25
12=15
Need help. I don't understand how I work out the points to solve the equation. Help please, thanks.
Answer:
First u get the Y by itself then you read the less than or equal to or greater than or equal to.
Step-by-step explanation:
hope it helps
A rectangular piece of metal is 10 inches wide and 14 inches long.
a. What is the perimeter?
b. What is the area?
!need to finish test by 2:20!
Length= 14inches and breadth= 10inches
1) To Find Perimeter of rectangleWe know, Perimeter of rectangle= 2(Length+Breadth)
[tex]2(14 + 10) \\ = 2 \times 24 \\ = 48 \: \text{inches}[/tex]
2)To Find Area of rectangleWe know, Area of rectangle= Length × Breadth
[tex]14 \times 10 \\ = 140 \: \text{in} ^{2}[/tex]
Hope This HelpsFind the volume of the figure. If necessary, round your answer to the nearest tenth.
Answer choices
A: 441.6 cm^3
B: 883.2 cm^3
C: 147.2 cm^3
Answer:
A
Step-by-step explanation
math
Darnell has 3 pies. He gives each of his five friends 3/8 of a pie.How much pie does Darnell have left?
Answer:
1 1/8Step-by-step explanation:
Darnell gives his friends
5*3/8 = 15/8 = 1 7/8 pieRemaining pie
3 - 1 7/8 = 1 1/8Answer:
[tex]\huge\boxed{\bf{Leftover\:Daniel\:pie = 1\frac{1}{8}pie}}[/tex]
Step-by-step explanation:
Given:-
Daniel have 3piesgive to five friend [tex]\frac{3}{8}[/tex]of a pieTo find: -
Leftover Daniel pie?Ans:-
The first step is to find a lot of cakes that will be given to five of Daniel's friends
[tex]\sf \to 5*\frac{3}{8} = \frac{5*3}{8} = \frac{15}{8}pie[/tex]Finally we determine the rest of Daniel's pie
[tex]\sf \to 3 - \frac{15}{8} = \frac{24}{8} - \frac{15}{8} = \frac{9}{8}pie[/tex]Therefore leftover Daniel pie is = [tex]\frac{9}{8}[/tex]pie or [tex]1\frac{1}{8}[/tex]pie
[tex]\:[/tex]
[tex]\huge\colorbox{skyblue}{BlackPain}[/tex]
A submarine is at the surface of the ocean, preparing to dive. It submerges and dives to - 993 feet. Then, it ascends 308 feet to
void hitting an undersea cliff. What integer represents the submarine's position in feet (depth) after it ascends to avoid the cliff?
Answer:
-685
Step-by-step explanation:
hope I helped
6 diviided by 27 and 7 divided by 50
Answer:
the first one is 0.2222222222... the second is 0.14
6 : 27
Fraction : [tex]\frac{6}{27} = \frac{2}{9}[/tex]
Decimals : 0.(2) = 0.222222222222....
Percentage : 22.2222...%
7 : 50
Fraction : [tex]\frac{7}{50}[/tex]
Decimals : 0.14
Percentage : 14%
Write an equation in slope intercept for for the like with slope -3/5 and
y-intercept -3
Answer:
An equation for the slope and y-intercept would be y=-3/5x-3
Step-by-step explanation:
Remember the formula for this, y=mx+b, in which the m stands for the slope and the x would be next to the slope always because the slope is ever changing, and the b stands for the y-intercept or in other words, where the line crosses the y-axis not the x-axis.
Answer:
y = -3/5x - 3
Explanation:
The format of slope-intercept is:
[tex]\sf{y = mx + b}[/tex]
Where:
m = slopeb = y-interceptSo to write the equation, I just plug the data into y = mx + b:
[tex]\sf{y=-\dfrac{3}{5}x+(-3)}\\\\\sf{y=-\dfrac{3}{5}x-3}[/tex]
Hence, the equation is y = -3/5x - 3.
100 points
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea using a ratio table. If you wish, you may upload a copy of your ratio table.
Answer:
Step-by-step explanation:
So, the total unit number of sixth graders polled is 12.
39/12=3.25
So, you'd do 8x3.25=26 students like lemonade
13 students like iced tea
