simplify 7(x+1)+-7(-6x+-9)
Answers
Answer:
49x=70
Step-by-step explanation:
Related Questions
The volume of a cone is 13.4m cubed and the radius is 3.2m what is the height
Answers
Answer:
The height is 1.25m.
Step-by-step explanation:
Volume = 1/3 πr²h
Given:
V = 13.4 m³
r = 3.2 m
Asked: height (h)
Substitute the formula with the given values then solve
13.4m³ = 1/3π(3.2m)²h
13.4(3) = 10.24πh
40.2 = 10.24πh
h = 40.2/10.24π
h = 1.25m
The height of the cone is 1.25 meters.
We know that the volume of the cone is given by
V = (1 / 3) * π * r ^2 * h................equation 1
where,
V is the volume of the cone.
r is the radius of the cone's base
h is the height
The volume and radius of the cone are given,
V = 13.4 m
r = 3.2m
substituting these values in equation 1 we get,
13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h
on simplifying further
13.4 = 10.717 * h
h = 1.25m
The height of the cone is 1.25 meters.
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Find the measure of the arc or angle indicated
Answers
The unknown angle in the cyclic quadrilateral is as follows:
∠R = 86 degrees
How to find arc angle?The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.
Hence, let's find the unknown angle.
∠R = 1 / 2 (92 + 80)
∠R = 1 / 2 (172)
∠R = 86 degrees
Therefore, the unknown angle is 86 degrees.
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4.a) A car consumes a gallon of petrol for every 30 km drive. The driver of the car set out on a journey of 420 km with 10 gallons of petrol in the fuel tank. i) How many more gallons of petrol will be needed to complete the journey? ii)find the cost of the petrol for the journey of 420km if a gallon of petrol cost GH¢5.50
Answers
i) 4 more gallons of petrol will be needed to complete the journey.
ii) The cost of the petrol for the 420 km journey is GH¢55.00.
i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.
Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):
Distance covered with 10 gallons = 10 * 30 = 300 km
To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:
Remaining distance = Total distance - Distance covered with available petrol
Remaining distance = 420 km - 300 km = 120 km
Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:
Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons
Therefore, the driver will need 4 more gallons of petrol to complete the journey.
ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.
Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:
Cost of petrol = Total gallons used * Cost per gallon
Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00
Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.
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Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
Answers
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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What are the x-intercepts of the graph below ?
Answers
Answer:
(3, 0)(-2, 0)Step-by-step explanation:
You want to identify the x-intercepts on the graph.
X-interceptAn "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.
The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...
(-2, 0) and (3, 0)
<95141404393>
Which property justifies the statement below? X(y+5)=xy+5x
Answers
i really need helpl lol pleasehelppppppppppppplplplppplplpl ?
Answers
Answer:
1,050
Step-by-step explanation:
3.5x
12x
25
=
1,050
Which equations are true? Select all that apply. A. 66 ÷ 10 1 = 6 . 6 B. 660 ÷ 10 0 = 66 C. 6 , 600 ÷ 1 , 000 = 0 . 66 D. 0 . 66 ÷ 10 1 = 0 . 066 E. 6 ÷ 100 = 0 . 06
Answers
The equations 66 ÷ 10 = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true. which is the correct answer would be options (A), (B), (D), and (E).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A. 66 ÷ 10 = 6.6
66/10 = 6.6
This is the true equation.
B. 660 ÷ 10 = 66
660/10 = 66
This is the true equation.
C. 6,600 ÷ 1,000 = 0.66
This is not the true equation.
D. 0.66 ÷ 10 = 0.066
This is the true equation.
E. 6 ÷ 100 = 0.06
This is the true equation.
Thus, the equations 66 ÷ 10 = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true.
Hence, the correct answer would be options (A), (B), (D), and (E).
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The translation shown in the graph moves the figure to the right. What kind of translation is shown?
Answers
Answer:
A horizontal translation of 6 units to the right is shown.
Step-by-step explanation:
When a figure moves A units to the right or left, we have a horizontal translation of A units.
In this question:
The graphic moved 6 units to the right. So a horizontal translation of 6 units to the right is shown.
Answer:
the answer is Horizontal.
Step-by-step explanation:
edge 2021-2022
Your goal here is to find the least squares line y(x) = mx + b for the following data: (-2, 1), (2, 1), (-1,-1), (0, -2), (2,-2), and (-2, 1) Feel free to use a calculator! The normal equation for determining the approximating parameters ħ and în are: Then the least squares line is: y(x) = = number + number
Answers
The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).
We have an equation of line is
y(x) = mx + b --(1)
given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)
plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;
-2 = 2m +b ; 1 = -2m + b
The above equations can be written in matrix form as,
[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]
= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
AX = B
X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).
AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]
so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
let [ 17 -1 ; -1 6 ] = P
[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P
det P = 17×6 - 1 = 101
P⁻¹ = 1/101 [ 6 1 ; 1 17 ]
Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]
=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]
=> [ m ; b ] = [ -32/100 ; -39/100 ]
=> m = -32/100 , b = -39/100
then, y = mx + b
=> y = ( -32/100 )x + ( -39/100)
Hence, the required equation is
y = ( -32/100 )x + ( -39/100).
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Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y=6/x^2 ,y=0,x=1,x=3 .
1) Find the y-axis
2) Find the line y=6
Answers
Answer:
1) V = 12 π ㏑ 3
2) \(\mathbf{V = \dfrac{328 \pi}{9}}\)
Step-by-step explanation:
Given that:
the graphs of the equations about each given line is:
\(y = \dfrac{6}{x^2}, y =0 , x=1 , x=3\)
Using Shell method to determine the required volume,
where;
shell radius = x; &
height of the shell = \(\dfrac{6}{x^2}\)
∴
Volume V = \(\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx\)
\(V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx\)
\(V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx\)
\(V = 12 \pi ( In \ x ) ^3_{x-1}\)
V = 12 π ( ㏑ 3 - ㏑ 1)
V = 12 π ( ㏑ 3 - 0)
V = 12 π ㏑ 3
2) Find the line y=6
Using the disk method here;
where,
Inner radius \(r(x) = 6 - \dfrac{6}{x^2}\)
outer radius R(x) = 6
Thus, the volume of the solid is as follows:
\(V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx\)
\(V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx\)
\(V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx\)
\(V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx\)
\(V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx\)
Recall that:
\(\int x^n dx = \dfrac{x^n +1}{n+1}\)
Then:
\(V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}\)
\(V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}\)
\(V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}\)
\(V = 36 \pi (\dfrac{82}{81})\)
\(\mathbf{V = \dfrac{328 \pi}{9}}\)
The graph of equation for 1 and 2 is also attached in the file below.
36.
A meeting started at 11.35a.m. and
ended at 4.15p.m the same day. How
long did the meeting last?
a) 3hrs 40mins
b) 3hrs 50mins
c) 4hrs 35mins
d) 4hrs 40mins
e) 5hrs 40mins
What’s the answer
Answers
Answer:
Step-by-step explanation:
option (d) 4hrs 40mins
angela is seeking a venue for her school’s athletic council banquet.Primo Banquet Hall charges $2000 plus $50 per person.The Lookout Banquet Hall charges $1500 plus $75 per person.
a)write an equation to represent each banquet hall
b)when do both halls charge the same amount
c)which hall should angela choose?explain indicating intervals
Answers
what is the radius of this shape?
Answers
The radius of the circle in this problem is given as follows:
6.25 inches.
What is the radius of a circle?The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
In this problem, we have four segments, each with length of 6.25 inches, all four representing the radius of the circle, as all these four segments begin on the center of the circle and end at the circumference of the circle.
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1. Which set(s) of numbers does -87 belong to?
Answers
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
Answers
m = 5√2
just use trigonometry
Find sin (b) in the triangle ?
Answers
Answer:
a
Step-by-step explanation:
SOH CAH TOA
Sine is opposite over hypotenuse. The opposite side from the angle is 15 and the hypotenuse is 17.
13 +22
if r = -3 and s = 4
Answers
35 is the answer
have a wonderful day
Here are three different recipes for Orangey-Pineapple Juice. Two of these mixtures taste the same and one tastes different.
Recipe 1: Mix 4 cups of orange juice with 6 cups of pineapple juice.
Recipe 2: Mix 6 cups of orange juice with 9 cups of pineapple juice.
Recipe 3: Mix 9 cups of orange juice with 12 cups of pineapple juice.
Which two recipes will taste the same, and which one will taste different? Explain or show your reasoning.
Answers
Answer:
i think recipe one because in 2 and 3 are multiples of 3.....just a guess
Step-by-step explanation:
Find Trig Ratios (with Radicals)
Answers
Answer:
the answer is 45 + 5-75 is equals to 30 +5
62 = –19 + 3v /..............................
Answers
Answer:
V = 27
Step-by-step explanation:
62 = −19 + 3v
Swap sides so that all variable terms are on the left-hand side.
−19 + 3v = 62
Add 19 to both sides.
3v = 62 + 19
Add 62 and 19 to get 81.
3v = 81
Divide both sides by 3.
v = 81/3
Divide 81 by 3 to get 27.
v = 27
I hope this will help you! :)
PLS HELP ME !!!!!!!!!!!!!!!!
Answers
Answer:
C
Step-by-step explanation:
All sides make a cube
Answer:
D
Step-by-step explanation:
Refer to the model Q (t) = boe
-0.0001211
used for radiocarbon dating.
At an archeological site, scientists uncovered human remains. A sample from a human bone taken from the site showed that 21.2
% of the carbon-14 still remained. How old is the sample? Round to the nearest year. Do not round intermediate calculations.
The sample from the human remains is approximately
years old.
Answers
The sample from the human remains is approximately
12,820 years old
Given the model used for radiocarbon dating after a particular period of time "t" expressed according to the formula;
\(Q(t)=b_0e^{-0.0001211t}\)
If a sample from a human bone taken from the site showed that 21.2
% of the carbon-14 still remained, then Q(t) = 21.2
Substitute the given parameters into the formula:
\(Q(t)=b_0e^{-0.0001211t}\\0.212b_0=b_0e^{-0.0001211t}\\0.212 = e^{-0.0001211t}\\ln0.212=lne^{-0.0001211t}\\-1.55117=-0.0001211t\\t=\frac{1.55117}{0.000121}\\t= 12,819.56 years\)
Hence the sample from the human remains is approximately
12,820 years old
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pls help me withו 153/18 =104/1
Answers
Step-by-step explanation:
Our Equation:
*153/18 = 8.5 as a decimal.
\(x(8.5)=104\)
Divide each side by 8.5:
\(x=12.235\) \(rounded\) \(to\) \(the\) \(thousandths\) \(or\) \(\frac{208}{17}\)
what is the value of f in f/3+22=17
Answers
Answer:
F = 15
Good luck! Have a wonderful day!
SOLVE FOR T
t+3/2 = -2
T =
Answers
Answer:\(t= -\frac{7}{2}\)
Step-by-step explanation:
\(=t+\frac{3}{2}=-2\\=t=-2-\frac{3}{2} \\=t=-\frac{7}{2}\)
The area of a rectangular living room is 264 square feet. The length of the room is 2 feet less than twice the width.
What is the width of the living room in feet?
Answers
9514 1404 393
Answer:
12 ft
Step-by-step explanation:
Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...
A = LW
264 = (2w-2)w
132 = w² -w . . . . . . . divide by 2, eliminate parentheses
132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square
√132.25 = w -0.5 . . . . . take the square root
0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root
The width of the living room is 12 feet.
I don't understand calculus at all bruh :/. I figured out some of this but I don't know if the answer is 0 or 2. Whoever figures this, out also please explain how you got it.
Answers
The first step for ANY limit is to plug in. Always plug in first. You can take the odd root of a negative number because let’s say you have -1^3, you’re still gonna get -1. But if the power is even, you will always get a positive number. So plug in -32 to get the 5th root of -32. The answer would be -2 because -2^5 = -32
The length of a rectangle is five more than double the width. If the perimeter is 100 inches, find the dimensions.
width?
length?
Answers
If the length is 5 more than double the width, then if the width is ‘x’ the equation to represent length would be 2x + 5
The formula to find the perimeter of a rectangle is just all the sides added together.
Knowing that info, solve for x, then plug the answer you get (15) back into the equations to get your final answer
If $5a+2b=0$ and $a$ is two less than $b$, what is $7b$?
Answers
Answer:
7b = 10
Step-by-step explanation:
We have that:
5a + 2b = 0
a is two less than b
So a = b - 2.
Replacing in the above equation:
\(5a + 2b = 0\)
\(5(b - 2) + 2b = 0\)
\(5b - 10 + 2b = 0\)
\(7b = 10\)
\(b = \frac{10}{7}\)
7b
\(7b = 7\frac{10}{7} = \frac{70}{7} = 10\)
7b = 10