Answers
Step-by-step explanation:
[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(\dfrac{a^x}{a^y}\right)^{x-y}=\left(a^{x-y}\right)^{x-y}=a^{(x-y)(x-y)}=a^{(x-y)^2}\\\\\left(\dfrac{a^y}{a^z}\right)^{y-z}=\left(a^{y-z}\right)^{y-z}=a^{(y-z)(y-z)}=a^{(y-z)^2}\\\\\left(\dfrac{a^z}{a^x}\right)^{z-x}=\left(a^{z-x}\right)^{z-x}=a^{(z-x)(z-x)}=a^{(z-x)^2}\\\\\text{Use}\ a^n\cdot a^m=a^{n+m}\\\\a^{(x-y)^2}\cdot a^{(y-z)^2}\cdot a^{(z-x)^2}=a^{(x-y)^2+(y-z)^2+(z-x)^2}[/tex]
[tex]\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-y)^2=x^2-2xy+y^2\\(y-z)^2=y^2-2yz+z^2\\(z-x)^2=z^2-2zx+x^2\\\\=a^{x^2-2xy+y^2+y^2-2yz+z^2+z^2-2zx+x^2}\\\\\text{combine like terms}\\\\=a^{(x^2+x^2)+(y^2+y^2)+(z^2+z^2)-2xy-2yz-2zx}\\\\=a^{2x^2+2y^2+2z^2-2xy-2yz-2zx}\qquad\text{distributive}\\\\=a^{2(x^2+y^2+z^2)-2(xy-yz-zx)}\\\\\text{From the equastion we know:}\ x^2+y^2+z^2=xy+yx+zx.\\\text{Therefore}\\\\=a^{2(x^2+y^2+z^2)-2(x^2+y^2+z^2)}=a^0=1[/tex]
Related Questions
How do I solve this to find angle G?
Answers
Answer:
Step-by-step explanation:
The angle at E is 90 degrees.
All tangents of a circle always meet the radius at a 90 degree angle.
90 + 67 + G = 180o All triangles have 180 degrees. Combine left.
157 + G = 180o Subtract 157 from both sides.
157 - 157 + G + 180 - 157
G = 23
Determine S(1+ 4/3x-1
+ 3/x+2) dx by partial fractions
Answers
Answer:
[tex]\large\boxed{\int\left(1+\dfrac{4}{3x-1}+\dfrac{3}{x+2}\right)\ dx=x+\dfrac{4}{3}\ln(3x-1)+3\ln(x+2)}[/tex]
Step-by-step explanation:
[tex]\large{\int}\normal\left(1+\dfrac{4}{3x-1}+\dfrac{3}{x+2}\right)\ dx=\int1\ dx+\int\dfrac{4}{3x-1}\ dx+\int\dfrac{3}{x+2}\ dx\\\\(1)\int1\ dx=x\\\\(2)\int\dfrac{4}{3x-1}\ dx\Rightarrow\left|\begin{array}{ccc}3x-1=t\\3dx=dt\\dx=\frac{1}{3}dt\end{array}\right|\Rightarrow\int\dfrac{4}{3t}\ dt=\dfrac{4}{3}\int\dfrac{1}{t}\ dt=\dfrac{4}{3}\ln(t)=\dfrac{4}{3}\ln(3x-1)\\\\(3)\int\dfrac{3}{x+2}\ dx\Rightarrow\left|\begin{array}{ccc}x+2=u\\dx=du\end{array}\right|\Rightarrow\int\dfrac{3}{t}\ dt=3\int\dfrac{1}{t}\ dt=3\ln(t)=3\ln(x+2)[/tex]
[tex]\Downarrow\\\\\int\left(1+\dfrac{4}{3x-1}+\dfrac{3}{x+2}\right)\ dx=x+\dfrac{4}{3}\ln(3x-1)+3\ln(x+2)[/tex]
Solve this system of linear equation.Separate the x- and y-values with comma. -6x=-4-y -7x=-22+y
Answers
Answer:
(x,y)=(2,8)
Step-by-step explanation:
-6x = -4 -y
-7x = -22 +y
Rearranging the above equations
-6x +y +4 =0 => eq(1)
-7x -y +22 =0 => eq(2)
Adding eq(1) and eq(2)
-6x +y +4 =0
-7x -y +22 =0
___________
-13 x +26 =0
-13x = - 26
x= -26/-13
x= 2
Putting value of x in eq (1)
-6(2) + y +4 =0
-12 +y+4 =0
y-8=0
y=8
So, values of x and y are 2 and 8
(x,y)=(2,8)
which one is it? I would really appreciate some help.
Answers
Answer:
$7.50
Step-by-step explanation:
$2,760 is the total. 368 visited and paid the same price.
You'll need to divide 2760 by 368.
2760/368 = 7.5
$7.50 is the answer. Please mark brainliest.
Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue? A) 5 cans B) 7 cans C) 10 cans D)14 cans
Answers
Answer:
B) 7 cans
Step-by-step explanation:
First task is to determine how many square units we have.
With the rectangle spanning 2 units on the X-axis and 3 unites on the Y-axis, we know that it has an area of 6 square units.
The two triangle shapes sum up to one unit total, since a triangle's area is (base * height) / 2. Both have a base of 1 unit, and a height of 1 unit... so (1 * 1) / 2 = 1/2 for each triangle. Together, they occupy 1 unit.
So, total is 7 square units. Let's imagine it as a 7-unit by 1-unit rectangle, it will be easier to calculate. Each unit is 5 feet. So, this rectangle measures 35 (7 * 5) feet long, by 5 (1 * 5) feet wide... for a total of 175 (35 * 5) sq feet.
Since a can of paint can cover 25 sq feet, he'll need 7 cans (175 / 25).
Please solve thank you
Answers
Answer:
The correct answer would be H
Step-by-step explanation:
H
MSN’s MSN’s
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?>?>?>>??>Find the area of the kite.
Answers
Check the picture below.
[tex]\bf \stackrel{\textit{area of triangles on the left}}{2\left[\cfrac{1}{2}(2)(3) \right]}+\stackrel{\textit{area of triangles on the right}}{2\left[\cfrac{1}{2}(4)(3) \right]}\implies 6+12\implies 18[/tex]
Which of the following statements about the mean is false?
The mean and the median sometimes have the same value.
The mean is not used with variables measured at the ordinal level.
The mean is pulled in the direction of the hump in a skewed distribution.
The value of the mean reflects both the number and the value of cases.
Answers
Answer:
The value of the mean reflects both the number and the value of cases. is false
Step-by-step explanation:
The incorrect statement about the mean is that it's pulled in the direction of the hump in a skewed distribution. In fact, the mean is influenced by every value in the data set, including outliers, and if a distribution is skewed, the mean is pulled towards the tail, not the hump.
Explanation:The statement that is false about the mean is: 'The mean is pulled in the direction of the hump in a skewed distribution'. Rather, it's the median that stays closer to the 'hump' in a skewed distribution. The mean is affected by every value in the data set, including outliers. If a distribution is skewed, the mean will be pulled in the direction of the skew, which could be towards the tail, not the hump. For example, in a right-skewed distribution with values 1, 2, and 100, the mean would be 34.33, which is closer to the outlier (100) rather than the hump around 1 and 2.
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(3a) 3 = This expression without exponents is 3aaa 3·3·3a 3a3a3a 3·3·3a 3
Answers
Answer:
[tex]3a\times 3a\times 3a[/tex]
Step-by-step explanation:
The given expression is;
[tex](3a)^3[/tex]
Recall that;
[tex]a^m=a\times a\times \times a....[/tex] m-times.
In [tex](3a)^3[/tex] means
[tex]3a\times 3a\times 3a[/tex]
The correct choice is the third option
Answer:
3a x 3a x 3a
Step-by-step explanation:
Which number is a rational number?
Answers
B, because a rational number is a number that goes on forever. Ex : pi
You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.
How much do you need to pay for each year of attending?
If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?
Answers
Answer:
If my parents are going to pay the 5%, then, they will pay: $2979.
I will need to save $62.06 each month to accomplish my goal.
Step-by-step explanation:
I'm going to a 4-year college that will cost $14895/year.
It means that I will need to pay: 14895*4 = $59.580
If my parents are going to pay the 5%, then, they will pay: $2979.
Now, if I want to save my total contribution for all four years, and I have four years to accomplish the goal, then:
Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.
Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.
The student needs to pay $744.75 yearly, which is 5% of the annual college cost. To save this amount over four years, they need to save $62.06 each month for 48 months.
Explanation:The student needs to calculate their contribution to the college expenses. First, we need to find 5% of the annual cost of $14,895.00 to determine the student's yearly contribution:
Yearly Contribution = $14,895.00 * 0.05 = $744.75 per year.
Next, to calculate the total contribution over four years:
Total Contribution = 4 * $744.75 = $2,979.00.
To save the total amount in four years, we divide the total contribution by the number of months in four years (48 months):
Monthly Savings = $2,979.00 / 48 = $62.06.
Therefore, the student needs to save $62.06 each month for 48 months to cover their share of college expenses.
Name the property for the given statement. 8•4=8•4
Answers
Answer:
reflexive property
Step-by-step explanation:
it equals the same
hope this helps :)
Correct. It is the reflexive property
Because it equals the same
Find the vertex: -4x² + 16x - 7
Answers
Find the vertex: -4x^2 + 16x - 7
Vertex = ( x, f(x)).
x = -b/2a
x = -16/2(-4)
x = -16/-8
x = 2
f(x) = -4x^2 + 16x - 7
Let x = 2
f(2) = -4(2)^2 + 16(2) - 7
f(2) = -4(4) + 32 - 7
f(2) = -16 + 32 - 7
f(2) = 16 - 7
f(2) = 9
Vertex = (2, 9)
Given: 3x < -6.
Choose the solution set.
{x | x < -2}
{x | x > -2}
{x | x < 2}
{x | x > 2}
Answers
Answer: FIRST OPTION.
Step-by-step explanation:
To know which is the solution set given the inequality [tex]3x < -6[/tex] you need to solve for the variable "x".
You must divide both sides by 3:
[tex]3x < -6\\\\\frac{3x}{3}=\frac{-6}{3}[/tex]
Therefore, you get:
[tex]x<-2[/tex]
Then, the solution set is the following:
{[tex]x | x < -2[/tex]}
You can observe that this solution set matches with the first option.
Answer: First option
Step-by-step explanation:
HELP ME NOW ANYONE!! Picture included!
Answers
Answer:
62°
Step-by-step explanation:
The 2 shown angles form a straight angle and sum to 180°, that is
7x + 20 + 4x + 6 = 180
11x + 26 = 180 ( subtract 26 from both sides )
11x = 154 ( divide both sides by 11 )
x = 14
the acute angle = 4x + 6 = (4 × 14) + 6 = 56 + 6 = 62°
The graph shows a rider's height y, in feet, above or below the center of a Ferris wheel, for a
given number of seconds, X.
How many minutes does it take for the wheel to make 8 revolutions?
6 min
10 min
12 min
45 min
Answers
Answer:the answer is 10 min hope this helped:)
Step-by-step explanation:
the answer is 6 minutes
Jeremy uses 27 inches of board for each birdhouse he builds. How many yards of board does he need to make 6 birdhouses?
Answers
Answer:
[tex]4.5\ yd[/tex]
Step-by-step explanation:
step 1
we know that
Jeremy uses 27 inches of board for each birdhouse
so
by proportion
Calculate how many inches of board does he need to make 6 birdhouses
[tex]\frac{27}{1}\frac{in}{birdhouses}=\frac{x}{6}\frac{in}{birdhouses} \\ \\x=6*27\\ \\x=162\ in[/tex]
step 2
Convert inches to yards
[tex]1\ yd =36\ in[/tex]
[tex]162\ in=162/36=4.5\ yd[/tex]
Answer:
Answer:
4y
Step-by-step explanation:
step 1
we know that
Jeremy uses 27 inches of board for each birdhouse
so
by proportion
Calculate how many inches of board does he need to make 6 birdhouses
step 2
Convert inches to yards
Step-by-step explanation:
I need this answer fast! Please!
Answers
Answer:
[tex]\large\boxed{\begin{array}{c|c|c|c}Length:&4cm&2cm&8cm\\Width:&6cm&12cm&3cm\\Height:&9cm&9cm&9cm\end{array}}[/tex]
Step-by-step explanation:
The formula of a volume of a cube with side length a:
[tex]V=a^3[/tex]
We have a = 6cm. Substitute:
[tex]V=6^3=216\ cm^3[/tex]
[tex]\begin{array}{c|c}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}[/tex]
[tex]216=2\cdot2\cdot2\cdot3\cdot3\cdot3=(2\cdot2)\cdot(2\cdot3)\cdot(3\cdot3)=4\cdot6\cdot9\\\\216=2\cdot2\cdot2\cdot3\cdot3\cdot3=2\cdot(2\cdot2\cdot3)\cdot(3\cdot3)=2\cdot12\cdot9\\\\216=2\cdot2\cdot2\cdot3\cdot3\cdot3=(2\cdot2\cdot2)\cdot3\cdot(3\cdot3)=8\cdot3\cdot9\\\vdots[/tex]
Mya is buying juice boxes for her party. Which offer should Mya choose to get the lowest price per juice box? 1.) 2 juice boxes for $0.66 2.) 6 juice boxes for $1.92 3.) 9 juice boxes for $2.97 4.) 12 juice boxes for $4.20
Answers
For this case we must find the unit cost of juice box of each option and compare:
Option A: 2 juice boxes for $ 0.66
[tex]\frac {0.66} {2} = 0.33 \frac {dollars} {box}[/tex]
Option B: 6 juice boxes for $ 1.92
[tex]\frac {1.92} {6} = 0.32 \frac {dollars} {box}[/tex]
Option C: 9 juice boxes for $ 2.97
[tex]\frac {2.97} {9} = 0.33 \frac {dollars} {box}[/tex]
Option D: 12 juice boxes for $ 4.20
[tex]\frac {4.20} {12} = 0.35 \frac {dollars} {box}[/tex]
The most feasible option is B. That is, buy 6 boxes for $1.92
Answer:
Option B
Answer: Option A: 2 juice boxes for $ 0.66Option B: 6 juice boxes for $ 1.92Option C: 9 juice boxes for $ 2.97Option D: 12 juice boxes for $ 4.20The most feasible option is B. That is, buy 6 boxes for $1.92
Step-by-step explanation:
The average cost to produce a booklet at a printing company is given by the equation C(X)= 2x/x-1 where x is the number of booklets produced. Graph this relationship and describe what the expected cost of producing a booklet approaches as many booklets are printed.
Answers
Answer:
C(x) = 2
Step-by-step explanation:
The graph of the average cost is shown in the attached image.
Note that, as is to be expected, when the number of booklets produced x increases, then the average cost per booklet decreases.
To calculate the expected cost of producing a booklet when x is very large, look at the graph.
Note that when x = 2 then the average cost is equal to 4, then when x = 5 the average cost is 2.5.
In this way, the bigger x is made, the more the cost approaches 2.
Therefore it can be said that
[tex]\lim_{x \to \infty}C(x)= 2[/tex]
Finally, the expected average cost when the number of booklet produced is very large is C (x) = 2
Which inequality statement is true?
3\4 < 0.80
3\4 > 0.80
7\15 > 0.50
0.50 > 5\7
Answers
Answer:
[tex]\large\boxed{\dfrac{3}{4}<0.80}[/tex]
Step-by-step explanation:
[tex]\dfrac{3}{4}=0.75\\\\\text{therefore}\\\\\dfrac{3}{4}<0.89\ \text{is}\ \bold{TRUE}\\\\\dfrac{3}{4}>0.80\ \text{is}\ \bold{FALSE}\\\\\dfrac{7}{15}<\dfrac{1}{2}=0.50\ \text{because}\ \dfrac{7.5}{15}=\dfrac{1}{2}.\ \text{Therefore}\ \dfrac{7}{15}>0.50\ \text{is}\ \bold{FALSE}\\\\\dfrac{5}{7}>\dfrac{1}2{=0.50\ \text{because}\ \dfrac{3.5}{7}=\dfrac{1}{2}.\ \text{Therefore}\ 0.50>\dfrac{5}{7}\ \text{is}\ \bold{FALSE}[/tex]
A is the answer to this question
brainiest
The cylinder shown has a volume of 90 cubic units. The cone and the cylinder have the same height and the same base.
What is the volume of the cone?
I NEED THIS FAST ILL MARK YOU AS BRAINILIST
Answers
The volume is 45 I think
The cylinder shown has a volume of 90 cubic units. The cone and the cylinder have the same height and the same base. The volume of the cone will be 30 cubic units.
What is a cone?It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.
Given:
The volume of the cylinder= 90 cubic units
The volume of the cylinder=πr²h
90 cubic units=πr²h
The volume of a cone is;
[tex]\rm V= \frac{1}{3} \pi r^2h \\\\ V=\frac{1}{3} \times 90 \ cubic units \\\\ V=30 \ cubic \ units[/tex]
Hence, the volume of the cone will be 30 cubic units.
To learn more about the cone, refer to the link;
https://brainly.com/question/16394302
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1/2x+3/2(x+1)-1/4=5
Answers
Answer: x=15/8
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
1/2 x+(3/2)(x)+ (3/2)(1) + −1/4 =5(Distribute)
Then, Combine like terms:
(1/2x + 3/2x) +(3/2 + −1/4) =5(Combine Like Terms)
Which you will get : 2x+ 5/4 =5
Step 2: Subtract 5/4 from both sides.
2x+ 5/4 − 5/4 =5− 5/4
2x= 15/4
Step 3: Divide both sides by 2.
[tex]\frac{2x}{2} = \frac{15/4}{2}[/tex]
x = 15/8 ← Answer
* Hopefully this helps: ) Mark me the brainliest:)!!
~ 234483279c20~
A trapezoid has bases that measure 10 cm and 6 cm. The height of the figure is 15 cm. What is the area of the trapezoid?
Answers
Answer:
120 cm^2
Step-by-step explanation:
Area of trapezoid = [tex]\frac{1}{2} (a + b) h[/tex]
a - 6
b - 10
h - 15
[tex]\frac{1}{2} (6+10)15[/tex]
[tex]\frac{1}{2} (16)15[/tex]
[tex]\frac{1}{2} * 240[/tex][tex]\frac{240}{2}[/tex]
= 120 cm ^2
Answer: 120cm
Step-by-step explanation:
in e2020 its thanx for the answer mark me the brailiest pleaseeee;)
The circumfrance of the moon is about 6,790 miles, find the diameter of the moon to the nearest mile.
A. 155 miles
B. 2,162 miles
C. 3,395 miles
D. 21,321 miles
Answers
Answer
B is the answer to this question
Answer:
D=2162 or answer B
Step-by-step explanation:
1.) C=Dpi
2.)6790=D pi
3.)6790/pi = D pi/pi
4.) D= 2161.32412719
5.) D=2162
Find the indicated limit, if it exists.(7 points)
limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus 7 when x is greater than 0
Choices below
3
10
7
The limit does not exist.
Answers
Answer:
7
Step-by-step explanation:
The left hand limit is when we approach zero from left. We use the function on this domain in finding the limit.
[tex]\lim_{x \to 0^-} f(x)=7-x^2[/tex]
[tex]\lim_{x \to 0^-} f(x)=7-(0)^2=7[/tex]
The right hand limit is
[tex]\lim_{x \to 0^+} f(x)=10x+7[/tex]
[tex]\lim_{x \to 0^+} f(x)=10(0)+7=7[/tex]
Since the left hand limit equals the right hand limit;
[tex]\lim_{x \to 0} f(x)=7[/tex]
The price of a gallon of unleaded gas has risen to $2.85 today.Yesterday's price was $2.79 Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Answer:
Step-by-step explanation:
Percent decrease =
(difference in prices)/(original price) × 100
(2.89 - 2.82)/2.89 × 100
= (0.07)/2.89 ×100 ≈ 2.4%
The price of unleaded gas has increased by 2.2% from yesterday to today. This percentage was calculated by finding the price increase ($0.06), dividing it by yesterday’s price ($2.79), and multiplying by 100. The result was then rounded to the nearest tenth of a percent.
Explanation:To find the percentage increase in the price of a gallon of unleaded gas, you first need to find the difference in the price. In this case, today's price is $2.85 and yesterday's price was $2.79, so the difference is $2.85 - $2.79 = $0.06.
Then, to find the percentage increase, you divide this difference by the original price (which is yesterday's price) and multiply by 100 to turn it into a percentage. So, percentage increase = ($0.06 / $2.79) * 100 = 2.15053.
Finally, you round this to the nearest tenth of a percent, which gives you 2.2%. So, the price of unleaded gas has increased by 2.2% from yesterday to today.
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A speed limit sign that says “NIGHT” indicates the_____ legal speed between sunset and sunrise.
Answers
B answer choice is always b
Answer:
B. Maximum.
Explanation:
The basic speed rules require drivers to adjust speed to the conditions. The Night speed limits usually begin 30 minutes after sunset and 30 minutes before sunrise. They are used for sectors in which the safety problems require a speed lower than the self-selected by drivers.
I hope this answer helps you.
Shelly bought 7 boxes of fish food and 2 packets of cat food. Each box of fish food contained 6 pouches, and each packet of cat food contained 4 pouches. How many more pouches of fish food than cat food did Shelly buy?
Answers
Answer: 34 more pouches
7 boxes - fish food; 1 box contained 6 pouches
Total amount of fish food is 7 × 6 = 42 pouches of fish food
2 packets - cat food; 1 packet contained 4 pouches
Total amount of cat food is 2 × 4 = 8 pouches
How many more pouches of fish food than cat food did Shelly buy?
42 pouches - 8 pouches = 34 pouches
Therefore there was 34 more pouches of fish food than cat food
9/18 ÷3/6 =
Worth 85 pts
Answers
To divide fractions you flip the second fractions and multiply.
9/18 divided by 3/6 becomes -> 9/18 x 6/3
9 x 6 -> 54
18 x 3-> 54
your answer would simplify to 1.
Answer: 1
Step-by-step explanation: 9/18 =0.5 or one half, and 3/6=0.5 or one half, and one half divided by one half equals one 1/2 / 1/2 = 1