We have two types of crust, each of them with a different type of sauce and choice of toppings. The answer would be 54 single topping pizzas because we have two types of crust for 3 types of sauce 2*3 = 6
and 9 choices of toppings for each of them 6*9 = 54
What is the inverse of the following statement If M is the middle point of PQ then PM is congruent to QM
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
Given statement:
If M is the mid-point of PQ then PM is congruent to QM.
The inverse statement would be:
If M is not the mid-point of PQ, then PM is not congruent to QM
Answer:
Option A
Find the vertical asymptotes of the graph of the rational function. y= x-15 / x + 6 The equation (s) of the vertical asymptotes is/are x= _____. (Use a comma to separate the answers as needed.)
Solution
The vertical asymptotes
[tex]\begin{gathered} y=\frac{x-15}{x+6}= \\ \end{gathered}[/tex]setting the denominator to 0
=> x + 6 = 0
=> x = - 6
The equation (s) of the vertical asymptotes is/are x = - 6
RmZR = 130 and mZS = 80. Find the mZT7mZT =Ilo mas rapido posible
The given figure is a Kite. A Kite is symmetrical about its main diagonal. This means that the diagram of the kite could be drawn a
The distance from Boston, Massachusetts to Little Rock, Arkansas is 1,452.8 miles. How many ft/min would you have to drive to get there in 20 hours and 45 minutes?
First we find the speed in mi/h.
We know that 20 h 45 min is equal to 20.75 hours, then the speed is
[tex]\frac{1452.8\text{ mi}}{20.75\text{ h}}=70.01\text{ mi/h}[/tex]Now we convert the speed to ft/min:
[tex]70.01\text{ mi/h}\cdot\frac{1\text{ h}}{60\text{ min}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}=6161.27\text{ ft/min}[/tex]Therefore you would have to drive at a speed of 6161.27 ft/min
A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s = 120t - 6t^2 meters in t seconds. How high does the rock go? How long does it take the rock to reach its highest point?1190 m, 10 sec600 m, 10 sec1200 m, 20 sec2280 m, 20 sec
Substitute t = 10, and t = 20, to the given equation and we get
[tex]\begin{gathered} \text{If }t=10 \\ s=120t-6t^2 \\ s=120(10)-6(10)^2 \\ s=1200-6(100) \\ s=1200-600 \\ s=600 \\ \\ \text{If }t=20 \\ s=120t-6t^{2} \\ s=120(20)-6(20)^2 \\ s=2400-6(400)^2 \\ s=2400-2400 \\ s=0 \end{gathered}[/tex]We therefore have t = 10 as the time it takes to reach the highest point, with the rock reaching 600m.
Therefore, we choose second option.
Find the value of x that will make L||M.2x - 3MX + 4x = [?]
We can say that Line L and Line M are parallel to each other if, when cut by a transversal line, the corresponding angles, the alternate exterior angles, and the alternate interior angles are congruent.
In the figure shown, we have a pair of alternate exterior angles. Therefore, the two angles must be equal to each other. With that, we have the following equation:
[tex]2x-3=x+4[/tex]From that equation, we can solve x by joining like terms on either side of the equation.
[tex]\begin{gathered} 2x-x=4+3 \\ x=7 \end{gathered}[/tex]Therefore, x = 7. When asked, the measure of the two angles are 11 degrees.
can you give me a step by step problem to this
Answer:
y = m x * b equation for a straight line
When x = 0 you have b = y = 4
y = m x + 4 revised equation
When y = 0, m = -4 / x = -4 / 2 = -2
y = -2 x + 4 or -2 x - y = -4
(a) is the correct answer
Katie had to buy snacks for her son’s upcoming football game. She is considering buying 1 ounce bags of chips that came in a variety of carton sizes. One carton had 18 bags of chips that sold for $5.97. Another carton had 12 bags for $3.59. If she needed a total of 36 bags of chips for all of the players, how much money would she save by buying the carton with the best overall price?
The money would she save by buying the carton with the best overall price is $1.14
One carton had 18 bags of chips that sold for $5.97
Price of 18 bags of chips is sold for $5.97
Price of 1 bag of chips is sold for = 5.97/18 = 0.331
For 36 bags it would cost her 36 x 0.331 = 11.91
.Another carton had 12 bags for $3.59.
Price of 12 bags for $3.59.
Price of 1 bags for $3.59/12 = 0.299 = 0.3
For 36 bags it would cost her 36 x 0.3 = 10.77
money saved = 11.91 - 10.77 = 1.14
Therefore, the money would she save by buying the carton with the best overall price is $1.14
To learn more about unitary method refer here
https://brainly.com/question/24587372
#SPJ9
what's the equation of the line that passes through the points (-9,-8) and (-6,6) in point slope form
The equation of the line passing through the given points in the point slope form is;
[tex]y-6\text{ = }\frac{14}{3}(x\text{ + 6)}[/tex]Here, we want to find the equation of the line that passes through the given points
Mathematically, we can write the equation of a line as follows in point slope form;
[tex]y-y_1=m(x-x_1)[/tex]m here represents the slope of the line
To calculate m which is the slope, we use the slope equation as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{6-(-8)}{-6-(-9)}\text{ = }\frac{6\text{ + 8}}{-6\text{ + 9}}\text{ = } \\ =\text{ }\frac{14}{3} \end{gathered}[/tex]To write the equation, we use any of the two given points.
Thus, we have;
[tex]\begin{gathered} y-6\text{ = }\frac{14}{3}(x-(-6)) \\ \\ y-6\text{ = }\frac{14}{3}(x\text{ + 6)} \end{gathered}[/tex]6. x^2-10x+21Factors:(__________________________)(_____________________)
Factorising the given expression through sum-product pattern and grouping the factors, we find out that the factors of the given expression are (x-7) and (x-3).
The given expression is -
[tex]x^{2} -10x+21[/tex] ---- (1)
We have to find out the factors of the given expression.
Now, from equation (1), we have
[tex]x^{2} -10x+21[/tex]
This can also be written in the form of sum-product pattern as -
[tex]x^{2} -10x+21\\=x^{2} -7x-3x+21\\[/tex]
Now, grouping the common factors together, we can rewrite it as -
[tex]x^{2} -7x-3x+21\\=x(x-7)-3(x-7)\\=(x-7)(x-3)[/tex](Rewriting in factored form)
Thus, factorising the given expression through sum-product pattern, we find out that its factors are (x-7) and (x-3).
To learn more about sum-product pattern visit
https://brainly.com/question/1617229
#SPJ9
Deon will choose between two restaurants to purchase pizzas for his party. The first restaurant charges a delivery fee of $2 for the entire purchase and $10 perpizza. The second restaurant charges a delivery fee of $5 for the entire purchase and $9 per pizza.Let x be the number of pizzas purchased.(questions included in photo)
a) We have to write an expression of the total charge for each restaurant.
The first reastaurant has a fixed charge of $2 and then $10 per pizza.
Then, if x is the number of pizzas, we can express the total charge as:
[tex]C_1(x)=2+10x[/tex]The second restaurant has a fee of $5 and charges $9 per pizza, so thetotal charge will be:
[tex]C_2(x)=5+9x[/tex]b) If the total charge is equal for both restaurants, we can write:
[tex]\begin{gathered} C_1(x)=C_2(x) \\ 2+10x=5+9x \end{gathered}[/tex]We can solve it for x as:
[tex]\begin{gathered} 2+10x=5+9x \\ 10x-9x=5-2 \\ x=3 \end{gathered}[/tex]Answer:
a) Total charge for the first restaurant = 2+10x
Total charge for the second restaurant = 5+9x
b) 2+10x = 5+9x
Luis purchased a laptop computer that was marked down by 2/5of the original price. What fractional part of the original price did Luis pay?
Problem
Luis purchased a laptop computer that was marked down by 2/5
of the original price. What fractional part of the original price did Luis pay?
Solution
For this case we can express the total as 1 and then we can do the following operation:
[tex]1-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]And we can conclude that Luis paid 3/5 of the original price for this case
the distance between City a and City b is 200 mi. on a certain wall map this is represented by the length of 1.7 ft. On the map how many feet would there be between City c and City d two cities that are actually 400 mi apart?
Given that:
the distance between City a and City b is 200 mi. on a certain wall map this is represented by the length of 1.7 ft.
So:
[tex]\begin{gathered} 200\text{ mi=1.7 ft } \\ 1\text{ mi=}\frac{1.7}{200}ft \end{gathered}[/tex]between City c and City d two cities that are actually 400 mi apart?:
So for 400 mi.
[tex]\begin{gathered} 1\text{ mi=}\frac{1.7}{200}ft \\ 400\text{ mi=400}\times\frac{1.7}{200}ft \\ 400mi=2\times1.7ft \\ 400\text{ mi=3.4ft} \end{gathered}[/tex]So 3.4 feet would there be between City c and City d two cities that are actually 400 mi apart
What is the amplitude and period of F(t) = sin 2t?a. amplitude: 1; period, pib. amplitude: -1; period: pic. amplitude: 1; period: 2pid. amplitude: -1; period: 2piPlease select the best answer from the choices provided
Answer:
[tex]\text{amplitude: 1, period: }\pi[/tex]Explanation:
Given the function in the attached image;
[tex]f(t)=\sin 2t[/tex]Comparing to the general form of periodic equations.
[tex]f(t)=A\sin B(t+C)+D[/tex][tex]\begin{gathered} A=\text{ Amplitude} \\ A=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Period =}\frac{2\pi}{B} \\ \text{ from the equation B = 2;} \\ \text{ Period = }\frac{2\pi}{2}=\pi \end{gathered}[/tex]Therefore;
[tex]\text{amplitude: 1, period: }\pi[/tex]The sales S (in billions of dollars) for Starbucks from 2009 through 2014 can be modeled by the exponential functionS(t) = 3.71(1.112)twhere t is the time in years, with t = 9 corresponding to 2009.† (Round your answers to two decimal places.)a) Use the model to estimate the sales in 2015 in billions of dollars.b) Use the model to estimate the sales in 2024 in billions of dollars.
a) Use the model to estimate the sales in 2015 in billions of dollars
Evaluate the function for t=15
[tex]\begin{gathered} S(15)=3.71(1.112)\placeholder{⬚}^{15} \\ \\ S(15)\approx18.24 \end{gathered}[/tex]The sales in 2015 will be $18.24 billionb) Use the model to estimate the sales in 2024 in billions of dollars
Evaluate the function for t=24
[tex]\begin{gathered} S(24)=3.71(1.112)\placeholder{⬚}^{24} \\ \\ S(24)=47.41 \end{gathered}[/tex]The sales in 2024 will be $47.41 billionUse the unit circle to identify the reference angle for 245°
In a unit circle every angle is measured from the positive x-axis to its terminal line traveling counterclockwise; the reference angle is the smallest possible angle formed by the x-axis and the terminal line going either clockwise or counterclockwise.
Now, to find the reference angle we first need to determine in which quadrant the original angle is; then, depending on where the angle is, we calculate the reference angle by remembering the following rules:
• If the original angle is in the first quadrant then the reference angle is the same.
,• If the original angle is in the second quadrant then the refrence angle is found by the formula:
[tex]180-\theta[/tex]• If the original angle is in the third quadrant the reference angle is given by:
[tex]\theta-180[/tex]• If the original angle is in the fourth quadrant the reference angle is given by:
[tex]360-\theta[/tex]Now that we know this let's find the reference angle for 245°. This angle is in the third quadrant, and hence its reference angle is:
[tex]245-180=65[/tex]Therefore, the reference angle is 65°
what is 1.8333333 as a fraction
This is a periodic decimal, which means a fixed part of the number will repeat forever, this part is called period. In this case the period is equal to 3. To convert a periodic decimal to a fraction we need to do as below.
We need to subtract the part of the number that doesn't repeat with one period of that part that repeats without the dot, which would be "183" and subtract it with the part that doesn't repeat without the dot "18". This would be "183 - 18 = 165". We then count the number of algarisms in the period of the number, in this case we only have one, which is "3". For every algarism in the period we add a "9" to the denominator. If there are numbers on the decimal part that don't repeat we add "0" after the 9. So we have the following fraction.
[tex]1.833333\ldots\text{ = }\frac{183-18}{90}\text{ = }\frac{165}{90}[/tex]translate this sentence into an equation:Four less than five times a number is equal to 11
we subtract 4 from the product between 5 and a number, and the result is 11
fifteen more than half a number is five
[tex]\frac{x}{2}+15=5[/tex]We must add 15 to the quotient between a number and two and its result is 5
-8-2y=10Hi I'm having a lot of trouble with problems like these.First when I go to solve this how do I know whether to add or subtract the -8 from the 10 or the 10 from the -8Also on problems like these how do I know either to add or subtract?
To solve an equation for a variable, we mean to "isolate" the variable on one side of the equation ( right or left), in order to solve for the variable we add and subtract constant terms, like 7, 8, 10, or any other constant.
In this case, we have the equation -8-2y=10, so the first step to take is to take the -8 "away" and put it to the other side of the equation ( this is the shortest way but you can take the -2y to the other side of the equation first or perform any other operation that you want that does not alter the equation, but the point is to isolate y), to put -8 in the other side of the equation we have to add it to both sides of the equation because -8+8=0:
[tex]\begin{gathered} -8-2y+8=10+8, \\ -2y=18. \end{gathered}[/tex]Now, notice that y still has a constant next to it, but the goal is to leave y alone, so we check what is it that this constant is doing to y, well -2 is multiplying y so in order to take to the other side of the equation we divide all the equation by -2, because -2/-2=1:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{18}{-2}, \\ y=-9. \end{gathered}[/tex]That is how one solves an equation for a variable.
Alternative solution:
[tex]\begin{gathered} -8-2y=10, \\ -8-2y-10=10-10, \\ -18-2y=0, \\ -18-2y+18=0+18, \\ -2y=18, \\ y=\frac{18}{-2}, \\ y=-9. \end{gathered}[/tex]Solve x+1=3, for x: first I choose on which side of the equation I want x, I want x on the left side ( could be the right side, it is up to you), second, I observe the equation and notice that there is a number being added to x, the constant is +1, to get rid of the constant I must subtract the constant on both sides of the equation:
[tex]x+1-1=3-1.[/tex]The last step is to simplify:
[tex]\begin{gathered} x+(0)=3-1, \\ x=2. \end{gathered}[/tex]Which expression is equivalent to -1/2(6x - 12)A. 6x + 6B. 3x - 12C. 3X-6D. 3x + 6
The expression is 3x-6
From the question, we have
1/2(6x - 12)
=1/2*6x-1/2*12
=3x-6
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ9
Answer:
The expression is 3x-6
From the question, we have
1/2(6x - 12)
=1/2*6x-1/2*12
=3x-6
Step-by-step explanation:
The perimeter of a rectangular goat pen is 28 meters. The area is 45 square meters. Whatare the dimensions of the pen?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} Perimeter=2l+2b=28m \\ Area=lb=45m^2 \\ \\ where\text{ l is the length, b is the breadth} \end{gathered}[/tex]STEP 2: Label the two equations
[tex]\begin{gathered} 2l+2b=28------equation\text{ 1} \\ lb=45----equation\text{ 2} \end{gathered}[/tex]STEP 3: Solve for the missing values
Isolate l in equation 1
[tex]\begin{gathered} 2(l+b)=28 \\ l+b=\frac{28}{2}=14 \\ l=14-b-----equation\text{ 3} \end{gathered}[/tex]Substitute 14-b for l in equation 2
[tex]\begin{gathered} (14-b)\cdot b=45 \\ 14b-b^2=45 \\ We\text{ have the quadratic equation} \\ -b^2+14b-45=0 \end{gathered}[/tex]Solve the equation quadratically
[tex]\begin{gathered} -b^{2}+14b-45=0 \\ -b^2+9b+5b-45=0 \\ -b(b-9)+5(b-9)=0 \\ (-b+5)(b-9)=0 \\ -b+5=0,b=5 \\ b-9=0,b=9 \\ \\ b=5,b=9 \end{gathered}[/tex]Substitute the values into equation 3,
[tex]\begin{gathered} l=14-b \\ when\text{ b = 5} \\ l=14-5=9 \\ When\text{ b = 9} \\ l=14-9=5 \end{gathered}[/tex]Hence, the dimensions of the pen is given as:
[tex]9m\text{ }by\text{ }5m[/tex]After graduating from college, Carlos receives two different job offers. Both pay a starting salary of $65000 per year, but one job promises a $3250 raise per year, while the other guarantees a 4% raise each year. Complete the tables below to determine what his salary will be after t years. Round your answers to the nearest dollar.
Given:
• Starting salary of each Job = $65000
,• Job 1 promises a $3250 raise per year
,• Job 2 promises a 4% raise each year.
Let's complete the given tables.
The equation to represent job 1 will be a linear equation:
y = 3250t + 65000
The equation which represents job 2 will be an exponential equation:
[tex]\begin{gathered} y=65000\mleft(1+0.04\mright)^t \\ \\ y=65000(1.04)^t \end{gathered}[/tex]Now, to complete the tables, input the different values of t into the equation and solve for y.
• For Job 1, we have the following:
• When t = 1:
y = 3250(1) + 65000 = 68250
• When t = 5:
y = 3250(5) + 65000
y = 16250 + 65000
y = 81250
• When t = 10:
y = 3250(10) + 65000
y = 32500 + 65000
y = 97500
• When t = 15:
y = 3250(15) + 65000
y =48750 + 65000
y = 113750
• When t = 20:
y = 3250(20) + 65000
y = 65000 + 65000
y = 130000
• For Job 2, we have the folllowing:
• When t = 1:
y = 65000(1.04)¹
y = 67600
• When t = 5
y = 65000(1.04)⁵
y = 65000(1.216652902)
y = 79082
• When t = 10:
y = 65000(1.04)¹⁰
y = 65000(1.480244285)
y = 96216
• When t = 15:
y = 65000(1.04)¹⁵
y = 65000(1.800943506)
y = 117061
• When t = 20
y = 65000(1.04)²⁰
y = 65000(2.191123143)
y = 142423
Therefore, we have the complete table below:
17 ohms to kilohms (Round answer to the nearest thousandth.)
In converting measurements, you must take note of the prefixes.
Note that a kilo is 1000 times the base measurement.
Example :
1 kilometer = 1000 meter
1 kilogram = 1000 gram
From the given problem :
1 kiloohm = 1000 ohm
17 ohms will be :
[tex]17\cancel{\text{ohms}}\times\frac{1\text{kiloohm}}{1000\cancel{\text{ohm}}}=\frac{17}{1000}=0.017\text{kiloohm}[/tex]The answer is 0.017 kiloohm
Simplify the expression. 1 3 3 m +8 4 3m 3 2 3 1 3 3 +8 4 2 (Use the operation symbols in the math palette as ne any numbers in the expression.)
We need to simplify the following expression
[tex]\frac{3}{4}m^3+8-\frac{1}{2}m^3[/tex]We first group the similar terms, they are the first and the third one
[tex](\frac{3}{4}m^3-\frac{1}{2}m^3)+8[/tex]then we use common factor to take out the m^3 of the parenthesis
[tex]m^3(\frac{3}{4}-\frac{1}{2})+8=\frac{1}{4}m^3+8=4(m^3+2)^{}[/tex]Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
Please look at the image below
Answer:
• -23.24 = 28.98 +(-52.22)
• 131.87 = 56.75 + 75.12
• 84 5/8 = 45 2/9 + 39 3/9
• 6 2/9 = -24 5/9 + 30 7/9
supposed that there are two types of tickets to a show: Advance and same-day. Advance tickets cost $25 and same-day tickets cost $40.For one performance, there were 60 tickets sold in all, and the total amount paid for them was $205. How many tickets of each type were sold?number of advanced tickets sold:number of same-day tickets sold:
For the show there are two types of tickets:
Advance tickets, that cost $25
Same-day tickets, that cost $40
We know that for one function there were 60 tickets sold for a total amount of $205.
Let "a" represent the number of advanced tickets sold and "s" represent the number of same-day tickets sold.
The total number of tickets sold for the function can be expressed as the sum of the number of advance tickets (a) sold and the number of same-day tickets sold (s)
[tex]60=a+s[/tex]If each advance ticket costs $25 and there were "a" advance tickets sold, the total earnings for advance tickets can be expressed as 25a
And if each same-day ticket costs $40 and there were "s" same-day tickets sold, the earnings for selling same-day tickets can be expressed as 40s
The total earnings for the performance can be expressed as the sum of the earnings for selling advance tickets and the earnings for selling same-day tickets:
[tex]205=25a+40s[/tex]Both equations established form an equation system and we can use them to determine the number of advance and same-day tickets sold:
-First, write the first equation for one of the variables, I will write it for "a"
[tex]\begin{gathered} 60=a+s \\ a=60-s \end{gathered}[/tex]-Second, replace the expression obtained for "a" into the second equation:
[tex]\begin{gathered} 205=25a+40s \\ 205=25(60-s)+40s \end{gathered}[/tex]From this expression, we can calculate the value of "s", first, you have to distribute the multiplication on the parentheses term, which means that you have to multiply both terms by 25:
[tex]\begin{gathered} 205=25\cdot60-25\cdot s+40s \\ 205=1500-25s+40s \end{gathered}[/tex]Next, simplify the like terms
[tex]205=1500+15s[/tex]Pass "1500" to the other side by applying the inverse operation to both sides of it, which means that you have to subtract 1500 to both sides of the equal sign:
[tex]\begin{gathered} 205-1500=1500-1500+15s \\ -1295=15s \end{gathered}[/tex]And finally divide both sides by 15 to reach the value of s
[tex]\begin{gathered} -\frac{1295}{15}=\frac{15s}{15} \\ -86.33=s \end{gathered}[/tex]With the value of s calculated, you can replace it into the expression obtained for a and calculate its value:
[tex]\begin{gathered} a=60-s \\ a=60-(-86.33) \\ a=146.33 \end{gathered}[/tex]So with the information given, the number of advanced and same-day tickets sold are:
a=146.33
s=-86.33
Please help on my question I have the graph part done, I need help on the other parts
the Here the equation of amount of salt in the barrel at time t is given by
[tex]Q(t)=21(1-e^{-0.06t})[/tex]a
At time t=7 minute the amount of salt will be
[tex]Q(7)=21(1-e^{-0.06\times7})\Rightarrow Q(7)=21\times0.342953\Rightarrow Q(7)=7.20[/tex]The amount of salt after 7 min will be 7.20lb.
b
At time t=14minute the amount of salt will be
[tex]Q(14)=21(1-e^{-0.06\times14})\Rightarrow Q(14)=11.93[/tex]Amount of salt will be 11.93 lb
d
From the graph, for large t the value Q(t) the amount of salt approaches to 21 lb.
To measure how much gasoline she uses on her road trip , Hortense makes a graph that shows the amount remaining in the tank as a function of the miles she has driven ( see figure ) .
It is important to know that the domain set is formed by all the x-values shown by the graph.
Having said that, the domain of the given graph is from 0 to 400, positive real numbers.
Hence, the answer is B.A city currently has 129 streetlights. As part of a urban renewal program, the city council has decided to install 3 additional streetlights at the end of each week for the next 52 weeks.How many streetlights will the city have at the end of 45 weeks?—————
Solution
Step 1
Current number of streetlights = 129
Step 2
Number installed per week = 3
[tex]\begin{gathered} Number\text{ of straightlights installed in 45 weeks = 3 }\times\text{ 45} \\ =\text{ 135} \end{gathered}[/tex]Step 3
Number of straightlights at the end of 45 weeks = 129 + 135 = 264
Final answer
256
Clint is making a 10-lb bag of trail mix for his upcoming backpacking trip. Thechocolates cost $3.00 per pound and mixed nuts cost $6.00 per pound and Clint has abudget of $5.10 per pound of trail mix. Using the variables c and n to represent thenumber of pounds of chocolate and the number of pounds of nuts he should userespectively, determine a system of equations that describes the situation.Enter the equations below separated by a comma.How many pounds of chocolate should he use?How many pounds of mixed nuts should he use? Pls see the picture
Since c represents the number of pounds of chocolates
Since n represents the number of pounds of nuts
Since Clint is making 10 pounds of them, then
[tex]c+n=10\rightarrow(1)[/tex]Since the cost of 1 pound of chocolates is $3.00
Since the cost of 1 pound of nuts is $6.00
Since the Clint budget is $5.1 per pound, then
[tex]10\times5.1-\text{ \$51}[/tex]Multiply c by 3 and n by 6, then add the products and equate the sum by 51
[tex]\begin{gathered} 3(c)+6(n)=5.1 \\ 3c+6n=51\rightarrow(2) \end{gathered}[/tex]The system of equations is
c + n = 10
3c + 6n = 51
Let us solve them
Multiply equation (1) by -3 to make the coefficient of c equal in values and different in signs
[tex]\begin{gathered} -3(c)-3(n)=-3(10) \\ -3c-3n=-30\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (3c-3c)+(6n-3n)=(51-30) \\ 0+3n=21 \\ 3n=21 \end{gathered}[/tex]Divide both sides by 3 to find n
[tex]\begin{gathered} \frac{3n}{3}=\frac{21}{3} \\ n=7 \end{gathered}[/tex]Substitute n by 7 in equation (1)
[tex]c+7=10[/tex]Subtract 7 from both sides
[tex]\begin{gathered} c+7-7=10-7 \\ c=3 \end{gathered}[/tex]He should use 3 pounds of chocolate
He should use 7 pounds of nuts
If his budget is $51