So basically you do 2096 divided by 8
Answer : 262 Minutes is alr i got u bro
Please help I’ll mark you as brainliest if correct!!!
Answer:
[tex]a=22\\b=6\\c=14\\d=8[/tex]
Step-by-step explanation:
So (Didn't even know what it was until now), is a square where all rows, columns, and diagonals sum up to the same number.
So, from the diagonal of 7, 15, and 23, but adding them up, we can tell that each row, column, and diagonal should sum up to 45.
If we know that, you can solve it either arithmetically or algebraically (I'm going to sovle them algebraically)
Here are the equations I used to solve for each:
[tex]7+16+a=45\\23+a=45\\a=22\\\\24+15+b=45\\39+b=45\\b=6\\\\15+16+c=45\\31+c=45\\c=14\\\\14+23+d=45\\37+d=45\\d=8[/tex]
Any further questions? Just leave a comment.
In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?
a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer: ?
b) Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer: ?
1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.
2) After 8 years of straight-line depreciation, the car's value will be $19,080.
What is depreciation?Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.
Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.
Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.
Price of an automobile in 2003 = $30,600
Annual depreciation = $1,440
The car's value after t years = $19,080.
Equation Solution:Value after t years = 30,600 - 1,440t
If 19,080 = 30,600 - 1,440t
1,440t = 30,600 - 19,080
1,440t = 11,520
t = 8 (11,520/1,440)
t = 8
= 8 years
Check:
x = 30,600 - 1,440t
x = 30,600 - 1,440(8)
x = 30,600 - 11,520
x = 19,080
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HelloI’m having trouble on the *calculus* portion on my ACT PREP GUIDEI need help solving this
First, we find the value of r:
[tex]\begin{gathered} a_n=\frac{2^n}{5^{n+1}\cdot n} \\ a_{n+1}=\frac{2^{n+1}}{5^{n+1+1}\cdot(n+1)} \\ a_{n+1}=\frac{2^{n+1}}{5^{n+2}\cdot(n+1)} \end{gathered}[/tex]Then r is calculated as follows:
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{a_{n+1}}{a_n}| \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{5^{n+2}\cdot(n+1)}\text{ / }\frac{2^n}{5^{n+1}\cdot n} \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{5^{n+2}\cdot(n+1)}\times\frac{5^{n+1}\cdot n}{2^n}| \end{gathered}[/tex]Multiplying
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{2^{n+1}\cdot5^{n+1}\cdot n}{5^{n+2}\cdot(n+1)\cdot2^n} \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{2^n}\cdot\frac{5^{n+1}}{5^{n+2}}\cdot\frac{n}{n+1}| \\ r=\lim _{n\to\infty}|2^{n+1-n}\cdot5^{n+1-(n+2)}\cdot\frac{n}{n+1}| \end{gathered}[/tex]Simplify
[tex]r=\lim _{n\to\infty}|2^1\cdot5^{-1}\cdot\frac{n}{n+1}|[/tex]Apply exponential properties
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{2}{5}\cdot\frac{n}{n+1}| \\ r=\lim _{n\to\infty}|\frac{2n}{5\cdot(n+1)}| \\ r=\lim _{n\to\infty}|\frac{2n}{5n+5}| \end{gathered}[/tex]Applying the limit, the solution is
[tex]r=\frac{2}{5}=0.4[/tex]So, r = 0.4 and since r is less than 1, the series converges.
Answer: From the ratio test, r = 0.4. The series converges.
It is estimated that 29% of the earths surface isn’t covered by water what percentage of the earths surface is water-covered
Answer: 71%
Explanation:
100% - total earth surface
29% - earth surface uncovered by water
100 - 29 = 71% of surface covered by water
oris is playing a game. She rolls three six-sided number cubes to tell her how many squares to move. If two number cubes show 4 and 3, how many different possible numbers of squares may she move on her turn?
6 possible values of squares that she can move.
What is possibility or probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.
Hence she has 6 different possible numbers of squares she can move.
The possibilities are:
-8 squares (if she rolls a 1)
-9 squares (if she rolls a 2)
-10 squares (if she rolls a 3)
-11 squares (if she rolls a 4)
-12 squares (if she rolls a 5)
-13 squares (if she rolls a 6)
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find an equation of the form f(x)=ax^2+bx+c. must solve algebraically and check using a calculator (state, the steps used to perform the check).
f(1)=4, f(2)=13, f(4)=46
By using algebra resolution methods for systems of linear equations, we find that the equation of the form f(x) = a · x² + b · x + c that passes through the three points is equal to f(x) = (5 / 2) · x² + (3 / 2) · x.
How to determine the quadratic equation that passes through three points
In this problem we must determine the coefficients of a quadratic equation that passes through the points (x₁, y₁) = (1, 4), (x₂, y₂) = (2, 13) and (x₃, y₃) = (4, 46). First, we need to create a system of linear equations by substituting on y and x thrice:
(x₁, y₁) = (1, 4)
a · 1² + b · 1 + c = 4
a + b + c = 4
(x₂, y₂) = (2, 13)
a · 2² + b · 2 + c = 13
4 · a + 2 · b + c = 13
(x₃, y₃) = (4, 46)
a · 4² + b · 4 + c = 46
16 · a + 4 · b + c = 46
Then, we find a system of three linear equations with three variables that offers an unique solution:
a + b + c = 4 (1)
4 · a + 2 · b + c = 13 (2)
16 · a + 4 · b + c = 46 (3)
There are different methods to find the solution to this system, we proceed to use algebraic substitution:
By (1):
c = 4 - a - b
(1) in (2) and (3):
4 · a + 2 · b + (4 - a - b) = 13
3 · a + b = 9 (2b)
16 · a + 4 · b + (4 - a - b) = 46
15 · a + 3 · b = 42 (3b)
By (2b):
b = 9 - 3 · a
(2b) in (3b):
15 · a + 3 · (9 - 3 · a) = 42
15 · a + 27 - 9 · a = 42
6 · a = 15
a = 15 / 6
a = 5 / 2
By (2b):
b = 9 - 3 · (5 / 2)
b = 9 - 15 / 2
b = 18 / 2 - 15 / 2
b = 3 / 2
By (1):
c = 4 - 5 / 2 - 3 / 2
c = 4 - 8 / 2
c = 4 - 4
c = 0
The coefficients of the quadratic equation are (a, b, c) = (5 / 2, 3 / 2, 0).
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pls help me with my question
Given the figure of an object consists of a cylinder and a rectangular prism.
We will find the volume of the cylinder using the following formula:
[tex]V=\pi r^2h[/tex]As shown, the diameter of the base = d = 3 ft
So, the radius = r = d/2 = 3/2 = 1.5 ft
And the height = h = 4 ft
Use π = 3
so, the volume of the cylinder will be as follows:
[tex]V=3*1.5^2*4=27\text{ }ft^3[/tex]Now, we will find the volume of the rectangular prism using the following formula:
[tex]V=l*w*h[/tex]As shown, the length = l = 7 ft
The width = w = 4 ft
The height = h = 4 ft
So, the volume of the rectangular prism will be as follows:
[tex]V=7*4*4=112\text{ }ft^3[/tex]So, the total volume of the object will be =
[tex]27+112=139\text{ }ft^3[/tex]So, the answer will be V = 139 ft³
If x² = 16, find x³.
Answer:
64
Step-by-step explanation:
If x² = 16, x is the square root of 16.
Therefore, x = 4
Now plug x in:
x³ = 4³ = 64
The membership of a gym from 2000 to 2017 is given by the function:
M(x)= 180x + 125
where M is the number of members and x is the number of years after 2000 (when the gym was
founded). Show your work to receive credit. (6)
a)
What was the membership of the gym in 2007?
The membership of the gym after 7 years is 1385 .
What is a function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable ). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
Given: The function : M(x)= 180x + 125
where x is the number of years so in this case we have to find the value of M when x= 7 years
Thus the given function on substituting the value becomes
M (7)= 180× 7 + 125
= 1385.
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On a horizontal number line, -43 is located to the left of -35.
Step-by-step explanation:
On a horizontal number line, -43 is located to the left of -35. TRUE because -43 is farther away (to the left) from 0 than -35.
7.5.PS-13 Identify the solid from its net. Choose the correct answer below. o triangular prism o rectangular prism o square pyramid O triangular pyramid Click to select your answer and then click Check Answer.
The net image of a figure is a visual representation of the original figure.
From the given net image, the solid that has the net image can be said to be a traingular
Kanesha is making scented candles to sell at the craft fair. she buys a 5 pound package of candle wax, a package of 12 small candle tins that each have volume of 4 ounces and the package of 12 medium candle tins that each have a volume of 6 oz. Kanesha knows that 1 lbs of candle wax will fill 20 oz in volume.assuming kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...____ small 4 oz candles____ medium 6 oz candleswhat is the maximum amount of money she will earn in the craft fair?
Kanesha is making scented candles to sell at the craft fair. She buys a 5-pound package of candle wax, a package of 12 small candle tins that each have a volume of 4 ounces and the package of 12 medium candle tins that each have a volume of 6 oz. Kanesha knows that 1 lb of candle wax will fill 20 oz in volume.
Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...
____ small 4 oz candles
____ medium 6 oz candles
what is the maximum amount of money she will earn in the craft fair?
________________________________________
1 lb of candle wax will fill 20 oz
She buys a 5-pound package, therefore, she will fill 20*5= 100 oz
Tin size S small (4 oz ) and M medium (6 oz)
S*4 + M*6 = 100
S*7.5 + M*9 = amount of money
_____________________
S*4 + M*6 = 100
4 S = 100 - 6M
S= 100/4 -6/4M
S= 25 -3/2M
Replacing
(25 -3/2M )*7.5 + M*9 = amount of money
187.5 - 11.25M + 9M = amount of money
187.5 - 2.25M = amount of money
According to the expression, the fewer medians sell, the higher the income will be.
Reviewing the candle values by ounces used.
7.5/ 4 = 1.875 sale price / oz
9.0/6 = 1.5 sale price / oz
_____________________________
Therefore, in order to maximize the profit, it would be necessary to make as many small ones as possible, that is, 12.
12* 4 oz = 48
100- 48 = 52
what is left after using the 4 oz tins can be used in the medium candles
52/ 6 = 8
___________________________________
Answer
Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...
__12__ small 4 oz candles
___8_ medium 6 oz candles
Hello I need help please
olution
e have the following statement:
If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:
A) supplementary angles
I do not understand this can someone please help?
Answer:
1. x = 18
2. x = 154
Step-by-step explanation:
2 12
------- = -------
3 x
3 × 12 = 36
2 × x = 2x
36 = 2x
÷2 ÷2
---------------
x = 18
----------------------------------------------------------------------------------------------------------
6 84
------- = -------
11 x
6 × x = 6x
84 × 11 = 924
6x = 924
÷6 ÷6
-----------------
x = 154
I hope this helps!
8 Five negative numbers are shown below. -2.5, -1į, -, -3, -30% Which list shows the numbers in order from least to greatest? (8.1B, 8.1F) F -2.5, -12, 3 4 -30%, -310 -13, -2.5, -31 3 G -30%, - 4' 10 Alw H -310, -30%, -2.5, -11, J-310,-2.5, -1 -2.5, -12, J 3 -- -30% 1 4
The given numbers are :
[tex]-2.5,\text{ -1}\frac{1}{2},\text{ }-\frac{3}{4},\text{ -3}\frac{1}{10},\text{ -30\%}[/tex]Simplify each term into decimal form :
- 2.5 = - 2.5
Now simplify the second term : -1 1/2
[tex]\begin{gathered} -1\frac{1}{2}=-\frac{1\times2+1}{2} \\ -1\frac{1}{2}=-\frac{3}{2} \\ -1\frac{1}{2}=-1.5 \end{gathered}[/tex][tex]-\frac{3}{4}=-0.75[/tex][tex]\begin{gathered} -3\frac{1}{10}=-\frac{3\times10+1}{10} \\ -3\frac{1}{10}=-\frac{30+1}{10} \\ -3\frac{1}{10}=-\frac{29}{10} \\ -3\frac{1}{10}=-2.9 \end{gathered}[/tex][tex]\text{ -30 \% = 0.3 \%}[/tex]So, the numbers are :
[tex]-2.5,\text{ -1}\frac{1}{2},\text{ }-\frac{3}{4},\text{ -3}\frac{1}{10},\text{ -30\%}[/tex]Thus, we get :
[tex]\begin{gathered} -2.5=-2.5 \\ -1\frac{1}{2}=-0.5 \\ -\frac{3}{4}=-0.75 \\ -3\frac{1}{10}=-2.9 \\ -30\text{ \%=- 0.3} \end{gathered}[/tex]The greater is the number with the neagtive sign least is the number,
So, the greatest number - 2.9 < - 2.5 < - 0.75 < - 0.5 < -0.3
Arrange of these number from least to greatest :
[tex]\begin{gathered} -2.9<-2.5<-0.75<-0.5<-0.3 \\ \text{ Since : - 1.5=}\frac{3}{2} \\ -0.75\text{ = }-\frac{3}{4} \\ -2.9=-3\frac{1}{10} \\ \text{- 0.3}=\text{ -30 \% } \end{gathered}[/tex]No comapre :
-2.9 < - 2.5 < - 0.75 < - 0.5 < -0.3
[tex]-3.1<-2.5<-0.75<-1.5<-0.3=-3\frac{1}{10}<-2.5<-1\frac{1}{2}<-\frac{3}{4}<-\text{ 30\%}[/tex]Answer : d)
[tex]-3\frac{1}{10}<-2.5<-1\frac{1}{2}<-\frac{3}{4}<-\text{ 30\%}[/tex]
Suppose the monthly charges for cell phone plans are normally distributed with mean and standard deviation $.(a) Draw a normal curve with the parameters labeled.(b) Shade the region that represents the proportion of plans that charge than $.(c) Suppose the area under the normal curve to the of X$ is 0.1587. Provide an interpretation of this result.
SOLUTION
(a) From the information given in the question,
We will select a curve with 58 at its center which represents the mean and
[tex]\begin{gathered} 58-17=41 \\ 58+17=75 \end{gathered}[/tex]41 and 75 at the left and right sides. That is gotten by subtracting and adding the standard deviation of 17.
Hence the answer is Graph D
(b) The region that represents less than 41 is seen in graph B
Hence graph B is the answer
(c) Option A
The probability is 0.1587 that a randomly selected cell phone plan in this population is less than $41 per month
nees helo on thus pl6
Assest
Cash = 39000
Owned land = 460000
Savings land = 207000
Jewerly = 3000
Total assests = 39000+460000+207000+3000
Total assests = 709000
Liabilities
Bank loans = 350000
Student loan debt = 25000
Total liabilities = 350000+25000
Total = 375000
Net worth = Total assets - Liabilities
Net worth = 709000 - 375000
Net worth = $334,000
In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43) and matching the number on the gold ball (1 through 31). If one ticket is purchased, what is the probability of winning the jackpot?
F(x)=2x-2, find f(-3)
Answer:
F (-3) = -8
Step-by-step explanation:
We start by substituting x = -3 into F (x) = 2x - 2
That gets us to: F ( -3) = 2 * (-3) - 2
Then we calculate the equation, bringing us to:
F (-3) = -6 - 2
When we add -6 + -2 we get: F (-3) = -8
Vec a and vec b are two unit vectors. If vec 5a + vec 3b and vec a- vec b are perpendicular to each other, find the angle between a and b.
[tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] are two unit vectors. If [tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex] are perpendicular to each other, then the angle between a and b is ( 2n + 1)π/2.
As given in the question,
Given two unit vectors are : [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex]
|a| = 1 and |b| = 1
Vectors which are perpendicular to each other are :
[tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex]
( [tex]\vec{5a} + \vec{3b}[/tex] ). ( [tex]\vec {a} - \vec {b}[/tex] ) = 0
⇒ 5|a|² -2a.b - 3|b|² = 0
⇒ 5(1)² - 2a.b - 3(1)² = 0
⇒ 5 - 2a.b - 3 = 0
⇒ 2[tex]\vec{a}[/tex].[tex]\vec{b}[/tex] = 2
⇒ [tex]\vec{a}.\vec{b}[/tex] = 1
Let θ be the angle between two vectors
|a||b|cosθ = 1
⇒ (1)(1)cosθ = 1
⇒cosθ = 1
⇒θ = (2n+1)π/2
Therefore, [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] are two unit vectors. If [tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex] are perpendicular to each other, then the angle between a and b is
( 2n + 1)π/2.
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To rent a certain meeting room, a college charges a reservation fee of $13 and an additional fee of $4 per hour. The chemistry club wants to spend at most $33 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Only #29,33,37,41,49 please show work THANK YOU
29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i
33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i
37) – 4 i = 4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 4 i = 0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] = 4[tex]e^{\frac{3\pi}{2}i}[/tex]
41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]
49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex] = [tex]\sqrt{26}e^{-0.197i}[/tex]
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Muskco gave 88 people a bonus. If Muskco had given 4 more people bonuses, Muskco would have rewarded 2 over 3of the work force. How large is Muskco's work force
The amount of Muskco's work force that he has in his business is; 138 people
How to solve Algebra Word Problems?We are told that Muskco gave 88 people a bonus. Now, we are further told that if he had given 4 more people bonuses, then it means he would have rewarded two thirds of his workforce.
Thus we can begin too solve this problem to find the size of Muskco's work force by;
Let the total number of his workforce be denoted as x. Then the algebraic equation for this problem would be expressed as;
88 + 4 = (2/3)x
Simplify by adding up the left hand side values to get;
(2/3)x = 92
Use multiplication property of equality to Multiply both sides by 3 to get;
2x = (92 * 3)
2x = 276
Now, use division property of equality to divide both sides by 2 to get;
2x/2 = 276/2
x = 138
Thus, we would conclude from the calculations as seen in the above that the size of Muskco's workforce is 138 people.
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Find the difference.
(-3x²-xy-3y²) - (6x²-4xy+y²)
Enter the correct answer.
The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is
(-9x²+3xy-4y²).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Numerical ExpressionNumbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
Algebraic ExpressionUnknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
= (-3x²-xy-3y²) - (6x²-4xy+y²)
= -3x²-xy-3y² - 6x²+4xy-y²
= (-9x²+3xy-4y²)
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Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
The value of x such that f(x) and g(x) have equal values is 3
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of x?From the question, we have
f(x) = -2x + 4
g(x) = 2x - 8
The question implies that the functions have equal values
This means that
f(x) = g(x)
Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms
2x + 2x = 8 + 4
Evaluate the like terms
4x = 12
Divide both sides of the equation by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsSee attachment for the graph of the functions
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What is the value of 6a + 9b?
Step-by-step explanation:
Simplifying
6a + -9b = 0
Solving
6a + -9b = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9b' to each side of the equation.
6a + -9b + 9b = 0 + 9b
Combine like terms: -9b + 9b = 0
6a + 0 = 0 + 9b
6a = 0 + 9b
Remove the zero:
6a = 9b
Divide each side by '6'.
a = 1.5b
Simplifying
a = 1.5b
solve similar triangles (advanced) khan academy. solve for x
Answer: 10/3
Step-by-step explanation:
[tex]\frac{2}{6}=\frac{x}{10}\\\\x=\frac{10}{3}[/tex]
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To
make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts
that cost $3.00 per pound. He mixes 10 pounds at a time.
How many pounds of Virginia peanuts does Sergio use? How many pounds of Spanish peanuts does Sergio use?
How many pounds of Virginia peanuts does Sergio use?
Assume he is making 10 lb of the $3.40 mixture
Let x = no. of pounds of the Virginia ($3.50) peanuts
Then (10-x) = no. of pounds of the Spanish ($3) peanuts
The Equation:
3.5x + 3(10-x) = 3.4(10)
3.5x + 30 - 3x = 34
.5x = 34 - 30
x = 4/.5
x = 8 pounds of Virginia peanuts
:
(b)How many pounds Spanish peanuts does Sergio use?
Spanish peanuts must be 2 pounds since the total is 10 pounds
:
Check:
3.5(8) + 3(2) = 3.4(10)
28 + 6 = 34
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.5 MB.
Yesterday, there were 870 downloads of the song, for a total download size of 2946 MB. How many downloads of the high-quality version were there?
Number of high-quality version downloads:
X
The number of high-quality version downloads is 300.
Given:
Size of the standard version = 2.8 megabytes (MB).
Size of the high-quality version = 4.5 MB.
Total number of downloads = 870
Total download size = 2946 MB
Let the number of high-quality version downloads be x.
Then the number of standard version downloads will be 870 - x.
Now the sum of the number of downloads of each type multiplied by their sizes equals 2946 MB.
So the equation is,
4.5x + 2.8(870 - x) = 2946
4.5x + 2436 - 2.8x = 2946
1.7x = 2946 - 2436
1.7x = 510
x = 510/1.7
x = 300
Therefore, the number of high-quality version downloads is 300.
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In angle VWX, VX is extended through point X to point Y,
m/VWX = (x + 14)°, m/XVW = (x +9)°, and
m/WXY = (5x - 10)°. What is the value of x?
Answer:
11
Step-by-step explanation:
This will form triangle VWX. So we have values for ∠VWX and ∠XVW but we don't have value for ∠WXV.
Since ∠WXV and ∠WXY are supplementary angles
=> ∠WXV + ∠WXY = 180
=> ∠WXV = 180 - ∠WXY
So the angles of triangle VXY
∠VWX + ∠XVW + ∠WXV = 180
(x + 14) + (x + 9) + (180 - (5x - 10)) = 180
x + x - 5x + 14 + 9 + 180 + 10 = 180
-3x + 213 = 180
-3x = - 33
x= 11