The figure below is a net for a right rectangular prism. Its surface area is 384 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.Yes
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Solution
For this case we know the total surface area given by:
384 cm^2
And we have the following: 108+48 +108+48 = 312 cm^2
the ramianing area is:
384 -312= 72 cm^2
And we can do the following:
2*9*? = 72
Solving for ? we got:
? = 72/18 = 4 cm
the final answer is:
The area of each missing face is: 36 cm^2
The lenght of each missing edge is: 4 cm
Related Questions
I’m in AP Calc AB and can’t figure this out. Any idea?
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Answer::
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]Explanation:
Given f(x) defined below:
[tex]f(x)=\ln x+7x\sec x[/tex]The derivative is calculated below.
[tex]\begin{gathered} \frac{d}{dx}\lbrack f(x)\rbrack=\frac{d}{dx}\lbrack\ln x+7x\sec x\rbrack \\ =\frac{d}{dx}\lbrack\ln x\rbrack+\frac{d}{dx}\lbrack7x\sec x\rbrack \\ Take\text{ the constant 7 outside the derivative sign.} \\ =$$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack \\ \text{The derivative of }\ln (x)=\frac{1}{x},\text{ therefore:} \\ $$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack=$$\textcolor{red}{\frac{1}{x}}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack\cdots(1) \end{gathered}[/tex]Next, we find the derivative of x sec x using the product rule.
[tex]\begin{gathered} \frac{d}{dx}\lbrack x\sec x\rbrack=x$$\textcolor{blue}{\frac{d}{dx}\lbrack\sec x\rbrack}$$+\sec x\frac{d}{dx}\lbrack x\rbrack\text{ } \\ The\text{ derivative of sec(x), }\text{\textcolor{red}{ }}\textcolor{red}{\frac{d}{dx}\lbrack\sec x\rbrack=\sec x\tan x} \\ =x$$\textcolor{blue}{\lbrack\sec x\tan x\rbrack}$$+\sec x \end{gathered}[/tex]Substitute the result into equation (1) above.
[tex]\begin{gathered} \frac{1}{x}+7\frac{d}{dx}\lbrack x\sec x\rbrack=\frac{1}{x}+7(x\sec x\tan x+\sec x) \\ =7x\sec x\tan x+7\sec x+\frac{1}{x} \end{gathered}[/tex]Therefore:
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]Micha starts riding his bike at 12:05pm Her rides for 35 minutes What time does he stop riding his bike?
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If Micha rides for 35 minutes, she'll stop riding her bike at 12:40pm
Samson buys a newcomputer for class. Thecomputer costs $550, aswell as an additional tax of10.2%.How much does he pay forthe computer?
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The cost of the computer is: $550
The additional tax is: 10.2%
To find the final cost of the computer, first, we need to find how much is the tax of 10.2%.
Step 1. Calculate how much is 10.2% of $550.
In general, to calculate a percentage we divide the quantity by 100 and then multiply by the percentage we need. In this case:
[tex]\frac{550}{100}\times10.2[/tex]Solving the operations:
[tex]5.5\times10.2[/tex][tex]=56.1[/tex]The tax is $56.1
Step 2. Add the cost of the computer and the tax to find how much he paid for the computer:
[tex]550+56.1=606.1[/tex]Answer: $606.1
If a = 6, which of the following is equal to a 2?1o-36O O-122
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Solution:
The question given is a negative exponent.
To solve this, we apply the law of indices for negative exponents.
Negative exponent law is indicated below;
[tex]a^{-x}=\frac{1}{a^x}[/tex]Thus, applying this law to the question;
[tex]a^{-2}=\frac{1}{a^2}[/tex]Given:
a = 6
Substituting a = 6 into the expression, we have;
[tex]\frac{1}{a^2}=\frac{1}{6^2}[/tex]Therefore, the correct answer is;
[tex]\frac{1}{6^2}[/tex]How do I find the sum of this equation and express it in simplest form [tex]( {n}^{3} - 5n - 2) + (4 {n}^{3} + n - 4)[/tex]
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Keisha has four favorite shirts one blue, one green, one red, one yellow and two favorite pairs of pants one black and one brown she decides to randomly choose a pair of pants and a shirt to wear for the day. What is the probability that Keisha chooses and outfit that is yellow and black or red and brown round your answer to the nearest whole percent?
Answers
Answer:
25%
Explanation:
First, let's calculated the total number of outfits that Keisha can choose. So, we will use the rule of multiplication as:
4 * 2 = 8
Shirts Pants
Because she has 4 options for shirts and 2 options for pants. So, there 8 possible outfits.
Then, from those outfits, there is 1 that is yellow and black, and 1 that is red and brown. So, the probability that Keisha chooses an outfit that is yellow and black or red and brown is:
[tex]P=\frac{1+1}{8}=\frac{2}{8}=0.25=25\text{ \%}[/tex]Therefore, the answer is 25%
Michael earns a weekly salary of $365 plus a 6% commission of sales for the week. Last week, Michael's sales totaled $3200. How much did he make in commission? What was Michael's total pay?
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Michael's sales are $3200, then the comission is
[tex]3200\times0.06=192,[/tex]$192 in comission.
Then the total pay is
[tex]365+192=557.[/tex]$567
the total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)Find the expression that represents the scenario
Answers
Answer:
(3/10)x
Explanation:
The expression that represents the scenario is an expression that we can use to calculate the total amount of flour, so the correct expression is:
[tex]\frac{3}{10}x[/tex]Because the amount of flour is 3/10 of x ( the current stock)
ylinders, cone Justin uses the mold picture cement column posts to use a height of the Cylinder = 18 in To make a post, Justin completel wet cement How much wet cement, in cubic inche make 4 posts? dus 3 in Formula Sheet
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metro atlanta home prices are rising rapidly, and much of its a soaring demand from deep-pocketed investors,as reported in the AJC March 21st of this year. In March2022, the median sale price of a home in the Metro area was $401,500. Before the the pandemic hit, in january2020, the median sale price was $279,000 Find the rate increase of the average cost of a home in Atlanta from january2020 before the pandemic hit Atlanta to the present
Answers
We are asked to determine the rate of increase in the value of a home,
We need to have into account that at the beginning of the considered period the cost was 279000 and after two years the cost is 401500, therefore, we can use the following formula:
[tex]r=\frac{\Delta C}{\Delta t}[/tex]Where:
[tex]\begin{gathered} \Delta C=\text{ difference in cost} \\ \Delta t=\text{ difference in time} \end{gathered}[/tex]Now, we substitute the values:
[tex]r=\frac{401500-279000}{2}[/tex]Solving the operations:
[tex]r=61250[/tex]Therefore, the rate is an increase of $61250 per year.
an office administrator has an office supply budget $150. The office administrator will purchase folders, which are $2.15 each and notebooks, which are $4.60 each. which inequality represent the constrain on the number of folders f and notebook n the office administrator can purchase
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If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.
[tex]\text{price}1=2.15f[/tex]Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).
[tex]\text{price}2=4.6n[/tex]Finally, the total cost of both products together is the sum of these products.
[tex]\text{cost}=\text{price}1+\text{price}2=2.15f+4.6n[/tex]The supply budget is $150, so the total cost needs to be lesser than or equal this value.
Therefore, we have that:
[tex]\begin{gathered} \text{cost}\le150 \\ 2.15f+4.6n\le150 \end{gathered}[/tex]So the correct option is B.
My teacher gave the answer on the right but I want know how he did it
Answers
the given number is 6^4
here is the calculation.
[tex]6^4=6\times6\times6\times6[/tex]multiply the number 6 by the times of 4
now by multiplication, the answer is
[tex]6^4=1296[/tex]so, the answer is 1296.
-Convert the following into given base units of measurement. (Refer to slide 21 &27 on uploaded ppt).
1. 3.65 mg =______ dg
2. 9.987 g =______ hg
3. 12.203 km =______ mm
Answers
The conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Part 1
The given quantity is 3.65 mg
mg is the milligram and dg is the decigram
We know
1 mg = 0.01 dg
Then,
3.65 mg = 3.65×0.01
Multiply the terms
3.65 mg = 0.0365 dg
Part 2
The given quantity is 9.987 g
g is the gram and hg is the hectogram
1 g = 0.01 hg
Then,
9.987 g = 0.09987 hg
Part 3
The given quantity is 12.203 km
km is the kilometer and mm is the millimeter
1 km = 1000000 mm
12.203 km = 12203072.2 mm
Hence, the conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Learn more about conversion here
brainly.com/question/9481766
#SPJ1
May you help me with this
Answers
Given the function
[tex]h(x)=2x^2-3x+5[/tex]Set x=-3 and solve for h(-3) as shown below
[tex]\begin{gathered} x=-3 \\ \Rightarrow h(-3)=2(-3)^2-3(-3)+5=18+9+5=32 \\ \Rightarrow h(-3)=32 \end{gathered}[/tex]Therefore, the answer is 32
use the function f(x)=-3(x+1)2+18what is the y intercept ?does it have a max or min
Answers
hello,
First of all, we must remember that a first degree function must be in the formula f (x) = ax + b, so, lets use this form:
[tex]undefined[/tex]The table shows x- and y-values for the equation y = 3x -1 Which number is missing in the table? 23 15 20 37
Answers
y = 3x-1
When x = 8
y = 3(8) -1
y = 24-1
y = 23
the base of the pyramid is a square. the volume is ___ cubic cm. measurements:l = 6 cmw = 10 h = 15(unable to send pictures of question without app crashing. my apologies.)
Answers
Answer:
300 cubic meters.
Explanation:
The volume of any pyramid is obtained using the formula below:
[tex]V=\frac{1}{3}\times\text{Base Area}\times Height[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times(6\times10)\times15 \\ =\frac{1}{3}\times60\times15 \\ =300\operatorname{cm}^3 \end{gathered}[/tex]The volume of the pyramid is 300 cubic meters.
Let f(x)=3x - 4. Write a function gwhose graph is a reflection of the graphoff.
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hello
the function given is
twice a number decreased by 4 Is atleast 12
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EXPLANATION
The appropiate relationship is:
2x - 4 = 12
Adding +4 to both sides:
2x = 12 + 4
Adding numbers:
2x = 16
Dividing both sides by 2:
x = 16/2
Simplifying:
x = 8
The solution is 8
1 11a.) A sign in a bakery gives the following options. Find each unit price to the nearest cent, and show your reasoning. You can get 3 mini-cakes for $32. What is the cost of ONE mini-cake? * O $10.66 O $10.65 O $10.67 O $10.59
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Since we can get 3 mini-cakes for $32, we can find the price of each mini-cake by taking the ratio of price to number of mini-cakes, like this:
unit price = 32/3 = 10.67
Then, the cost of ONE mini-cake is $10.67
Given the Exponential Equation, determine the Initial Value and Rate of Change as a Percent for each of the following.
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The formula for calculating exponential growth is expressed as
y = a(1 + r)^n
where
a is the initial value
y is the final value
n is the time
r is the growth rate
The formula for calculating exponential decay is expressed as
y = a(1 - r)^n
For y = 1010(1.05)^x,
initial value = 1010
1 + r = 1.05
r = 1.05 - 1 = 0.05
Since it is positive, it is exponential growth
Growth percent = 0.05 x 100 = 5%
For y = 4932(1.26)^x,
initial value = 4932
1 + r = 1.26
r = 1.26 - 1 = 0.26
Growth percent = 0.26 x 100 = 26%
For y = 2835(1.065)^x,
initial value = 2835
1 + r = 1.065
r = 1.065 - 1 = 0.065
Since it is positive, it is exponential growth
Growth percent = 0.065 x 100 = 6.5%
For y = (0.96)^t,
initial value = 1
1 - r = 0.96
r = 1 - 0.96 = 0.04
decay percent = 0.04 x 100 = 4%
For y = 4660(0.89)^x,
initial value = 4660
1 - r = 0.89
r = 1 - 0.89 = 0.11
decay percent = 0.11 x 100 = 11%
For y = 3078(1.09)^t,
initial value =3078
1 + r = 1.09
r = 1.09 - 1 = 0.09
Growth percent = 0.09 x 100 = 9%
question is in image
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The function f(x) is given by,
[tex]f(x)=x^2[/tex]The function g(x) is given by,
[tex]g(x)=\frac{-2}{3}x^2[/tex]If f(x) becomes -kf(x), where 0Comparing the above functions, we get
[tex]g(x)=-\frac{2}{3}f(x)[/tex]So, k=2/3. Hence, 0 < 2/3 < 1.
Therefore, the graph of g(x) is the graph of f(x) compressed vertically and reflected across the x axis.
Hence, option D is correct.
solve the system. given your answer as (x, y, z)-4x -y - 3z = -5-6x + y - 3z = -172x + 2y - z = - 10
Answers
Answer:
(1, -5 ,2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} -4x-y-3z=-5\ldots(1) \\ -6x+y-3z=-17\ldots(2) \\ 2x+2y-z=-10\ldots(3) \end{gathered}[/tex]Make z the subject in the third equation:
[tex]z=2x+2y+10[/tex]Substitute z=2x+2y+10 into the first and second equations:
First Equation
[tex]\begin{gathered} -4x-y-3z=-5 \\ -4x-y-3(2x+2y+10)=-5 \\ -4x-y-6x-6y-30=-5 \\ -4x-6x-y-6y=-5+30 \\ -10x-7y=25\ldots(4) \end{gathered}[/tex]Second Equation
[tex]\begin{gathered} -6x+y-3z=-17 \\ -6x+y-3(2x+2y+10)=-17 \\ -6x+y-6x-6y-30=-17 \\ -6x-6x+y-6y=-17+30 \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Next, solve equations 4 and 5 simultaneously:
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Multiply equation (4) by 5 and equation (5) by 7.
[tex]\begin{gathered} -50x-35y=125 \\ -84x-35y=91 \\ \text{Subtract same sign} \\ 34x=34 \\ x=\frac{34}{34} \\ x=1 \end{gathered}[/tex]Substitute x=1 into equation (4):
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -10(1)-7y=25 \\ -7y=25+10 \\ -7y=35 \\ y=\frac{35}{-7} \\ y=-5 \end{gathered}[/tex]Recall: z=2x+2y+10
[tex]\begin{gathered} z=2x+2y+10 \\ =2(1)+2(-5)+10 \\ =2-10+10 \\ z=2 \end{gathered}[/tex]The solution of the system is:
[tex](1,-5,2)[/tex]A metal plate has the form of a quarter circle with a radius of R = 106cm . Two 3 cm holes are to be drilled in the plater r = 95cm from the corner at 30 degrees and 60as shown above. To use a computer controlled milling machine you must know the Cartesian coordinates of the holes. Assuming the origin is at the corner what are the coordinates of the holes (x_{1}, y_{1}) and (x_{2}, y_{2}) ? Round your answer to 3 decimal places
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1) Considering that this quarter circle is one sector of the unit circle and that
[tex]30^{\circ}=\frac{\pi}{6}[/tex]2) Let's sketch this out to better grasp the idea:
Note that the first coordinate will be given by its cos(theta), and the second one by its sine(theta)
3) Based on that principle, we can tell the following:
[tex]\begin{gathered} (x_1,y_1)--->(cos(30^{\circ}),\sin(30^{\circ}))=(\frac{\sqrt{3}}{2},\frac{1}{2}) \\ \\ (x_{2,}y_2)-->(\cos(60),\sin(60))=(\frac{1}{2},\frac{\sqrt{3}}{2}) \\ \end{gathered}[/tex]As the holes need to be drilled by the machine, so we need to find approximations to those coordinates:
[tex]\begin{gathered} (x_1,\:y_1)-->(0.866,0.500) \\ (x_2,y_2)-->(0.500,0.866) \end{gathered}[/tex]Thus, these are the coordinates to be put into the computer.
A variable needs to be eliminated to solve the system of equations. Choose the correct first step: -3x+8y=-294x-8y=28A. Add to eliminate xB.Subtract to eliminate yC.Add to eliminate yD. Subtract to eliminate x
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From the given equations, we can note that coeffcients of variable y are opposite. This means that, in order to eliminate y, we can add both equations. Then, the answer is C
In ABC, A = 68°, a = 14 and c = 17. Which of these statements best describes the triangle?
Answers
Given for the triangle ABC:
[tex]\begin{gathered} \angle A=68\degree \\ a=14,c=17 \end{gathered}[/tex]Using the sine rule, we will solve the triangle by finding the missing angles
So,
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]substitute with the given data:
[tex]\begin{gathered} \frac{14}{\sin68}=\frac{17}{\sin C} \\ \\ \sin C=\frac{17}{14}\cdot\sin 68=1.125866 \end{gathered}[/tex]The value of (sin C) must be 1 or less than 1
So, the triangle ABC cannot be constructed
The answer will be the last option
Arthur has 20/8 cups of dishwashing detergent. He uses 1/4 cup of detergent for each load of dishes. what is the greatest number of loads of dishes Arthur was with this amount of detergent
Answers
Total = 20/8 cups of dishwashing detergent.
he has 20/8 = 5/2 = 2 1/2 cups of dishwashing detergent, per load he uses 1/4
per load
2 1/2 - 1/4
_____________________
The general formula
x= number of loads
20/8 - x* 1/4= 0
20/ 8 = x 1/4
x 1/4 = 20/ 8
x= 4* (20/8 )
x= 10
The greatest number of loads of dishes Arthur was with this amount of detergent is 10
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taliyah 1. If Mrs. Wozniak runs 8 miles a day. How many miles will she run in 4 weeks? Your answer 2. Fach fourth trade class at a local elementan answered 1 209 multiplication fact problems last
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Use the given rate to find how many miles will Mrs. Wozniak run in 4 weeks. Remember that 1 week is equal to 7 days, then 4 weeks is 28 days.
[tex]28days\cdot\frac{8miles}{1day}=224miles[/tex]She will run 224 miles in 4 weeks.
The number of compounding periods is equal to what: what is the formuls
Answers
Answer
When compound interest is discussed, the time rate for the compound interest is usually mentioned. For example, they would say that
- a certain amount of money has its interest compounded at 5% annually,
- a certain amount of money has its interest compounded at 7% every 3 months,
- a certain amount of money has its interest compounded at 2% every 6 months,
In each of the examples given above, the compounding period is 1 year, 3 months and 6 months respectively.
If one is now asked to calculate the compound interst on a particular amount of money after time, T, we usually express this time T in terms of the number of time periods, t, that exist inside the given time T.
Hence, the time T is expressed in terms of time period t, as
T = nt
Such that the number of compounding periods in T is given as
n = (T/t)
[tex]undefined[/tex]Over the weekend, Devon baked 12 muffins. She divided them evenly among 3 plates to giveto neighbors.The letter m stands for the number of muffins on each plate. Which equation can you use tofind m?12 x 3 = m12 : 3 = m
Answers
The information given is listed below:
number of muffins (m) = 12, number of plates = 3
number of muffin on each plate = number of muffins /