Answer:
135°
Step-by-step explanation:
An angle of 45° has a supplementary angle of 180° - 45° = 135°
Answer: 135
Step-by-step explanation:
Two angles are said to be supplementary if they sum up to be 180.
Let the supplementary angle to 45 be x ,
then :
x + 45 = 180
x = 180 -45
x = 135
whar is 10.034 rounded to the nearest tenth
Answer: 10.0
Step-by-step explanation: In this problem, we are asked to round 10.034 to the nearest tenth. It's important to understand that the tenths place is 1 place to the right of the decimal point. So the digit in the rounding place is 0.
Next, look at the digit to the right of the rounding place which in this case is 3. Since the digit to the right of the rounding place, 3, is less than 5, we round down.
This means that the digit in the rounding place, 0, stays the same and we change all digits to the right of the rounding place to 0.
So 10.034 rounded to the nearest tenth is 10.000 or just 10.0 since we can drop zeroes at the end of a decimal.
WILL GIVE BRAINLIEST PLEASE HELPP PLEASE HLEP
Answer:
A could work
Step-by-step explanation:
Because it is a square, all angles should be 90 degrees
Answer:Try B
Step-by-step explanation:
If its right please give me brainiest
Solve the linear equation, 2x+4=14
In this question, you would be solving for x.
Solve for x:
2x + 4 = 14
Subtract 4 from both sides
2x = 10
Divide both sides by 2
x = 5
Answer:
x = 5
A frequency table grades have five classes (A,B,C,D,F) with frequencies of 5,11,14,7, and 3 respectively. Using percentages, what are the relative frequencies of the five classes
The relative frequencies using percentages are as follows:
A => 12.5%
B => 27.5%
C => 35%
D => 17.5%
E => 7.5%
Step-by-step explanation:
To find the relative frequency, the specific frequency is divided by the total frequency. To find in the percentages, the division is multiplied by 100
So,
Total frequencies = 5+11+14+7+3 = 40
So,
[tex]Relative-frequency\ of\ A = \frac{5}{40} *100\\= 0.125*100\\=12.5\%\\Relative-frequency\ of\ B = \frac{11}{40} * 100\\= 0.275*100\\=27.5\%\\Relative-frequency\ of\ C = \frac{14}{40} * 100\\=0.35*100\\=35\%\\Relative-frequency\ of\ D = \frac{7}{40} * 100\\=0.175*100\\=17.5\%\\Relative-frequency\ of\ E= \frac{3}{40} * 100\\=0.075*100\\=7.5\%[/tex]
Hence,
The relative frequencies using percentages are as follows:
A => 12.5%
B => 27.5%
C => 35%
D => 17.5%
E => 7.5%
Keywords: Frequency, relative frequency
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The relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.
Given thatA frequency table grades have five classes (A, B, C, D, F) with frequencies of 5,11,14,7, and 3 respectively.
We have to determine
Using percentages, what are the relative frequencies of the five classes.
According to the questionThe relative frequency, the specific frequency is divided by the total frequency.
The sum of all the frequencies is called relative frequency.
= 5 + 11 +14 +7 +3 = 40
Then,
The relative frequency of the first class is,
[tex]= \dfrac{5}{40} \times 100\\ \\ = 0.125 \times 100\\ \\ =12. 5 \rm \ Percent[/tex]
The relative frequency of the second class is,
[tex]= \dfrac{11}{40} \times 100\\ \\ = 0.275 \times 100\\ \\ =27. 5 \rm \ Percent[/tex]
The relative frequency of the third class is,
[tex]= \dfrac{14}{40} \times 100\\ \\ = 0.35 \times 100\\ \\ =35 \rm \ Percent[/tex]
The relative frequency of the fourth class is,
[tex]= \dfrac{7}{40} \times 100\\ \\ = 0.175 \times 100\\ \\ =17. 5 \rm \ Percent[/tex]
The relative frequency of the fifth class is,
[tex]= \dfrac{3}{40} \times 100\\ \\ = 0.075 \times 100\\ \\ =7. 5 \rm \ Percent[/tex]
Hence, the relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.
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Which number is not in scientific notation? 1.1 ⋅ 10213 7.8 ⋅ 108 3.02 ⋅ 10−10 35 ⋅ 104
Answer:
35 ⋅ 104
(I hope this helped)
Answer:
35 ⋅ 104
Step-by-step explanation:
this was on my test and got it right. i hope this helped tho
Given the expression 2/5 - 4/6, write the addition problem that is equivalent to it
Answer:
-4/15
Step-by-step explanation:
2/5-4/6=2/5-2/3=6/15-10/15=-4/15
There are 182 adults and 18 children attending a wedding
reception as guests of the bride and groom. The guests will be
seated in groups of eight at each table. How many tables are
needed for the wedding guests?
Answer:
Step-by-step explanation:
Total number of guest = 182+18
= 200 guests
If 8 are using a table then the number of tables needed = 200/8
= 25tables
Answer: D
16*12 is 192. Plus the 6 for the bride and groom, and you get a total of 198.
What is the period of the function F(x) = 2 cot(3x-1) ?
What is the solution to the equation 4x + 2(x − 3) = 3x + x − 12? (1 point) Group of answer choices −3 −1 1 3
Answer:
-3
Step-by-step explanation:
[tex]4x + 2(x-3) = 3x + x-12\\4x+2x-6=4x-12\\2x=-6\\x=-3[/tex]
Please help with remaining and/or correct what I have
Answer:
Step-by-step explanation:
k² = -18 - 9k
k² +9k + 18 = 0
k² + 6k + 3k + 3*6 = 0
k(k + 6) + 3 (k + 6) = 0
(k + 6) (k + 3) =0
-2v²- v +12 = -3v² + 6
-2v² - v + 12 + 3v² - 6 = 0
v² - v + 6 = 0
I REALLY NEED HELP ON MY EXAM! 10PTS
Determine if the ordered pair (−1, −5) is a solution to the inequality y is less than or equal to negative three fourths times x minus 1.
No, because (−1, −5) is above the line
Yes, because (−1, −5) is below the line
No, because (−1, −5) is on the line
Yes, because (−1, −5) is on the line
Yes, because (−1, −5) is below the line
Explanation:The statement says:
y is less than or equal to negative three fourths times x minus 1:
[tex]y\leq -\frac{3}{4}x-1[/tex]
To know whether (−1, −5) is a solution to the inequality, let's substitute x and y-values into the inequality:
[tex]y\leq -\frac{3}{4}x-1 \\ \\ -5\leq -\frac{3}{4}(-1)-1 \\ \\ -5\leq -\frac{1}{4} \\ \\ -20\leq -1 \ True![/tex]
Given that the point lies on the shaded region, which is below the line, then the correct statement is:
Yes, because (−1, −5) is below the line
The graph of this problem is shown below.
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Felipe picked a pumpkin that weighed three times the weight of Meg's pumpkin Meg's pumpkin with half the weight of Ryan's pump Ryan's pumpkin weighed 14 lb how much did Felipe's pumpkin weigh
Answer:
21 lb
Step-by-step explanation:
Divide the amount of Ryan's pumpkin by 2 then multiply it by 3. Ryan's pumpkin weighs 14 lb divided by 2 is 7 then 7 multiplied by 3 is 21.
To find the weight of Felipe's pumpkin, we first determine that Meg's pumpkin weighs 7 pounds, which is half of Ryan's pumpkin's weight of 14 pounds. We then multiply Meg's pumpkin's weight by 3 to find that Felipe's pumpkin weighs 21 pounds.
The question asks to determine the weight of Felipe's pumpkin given the weight relationships between Felipe's, Meg's, and Ryan's pumpkins. We are told that Ryan's pumpkin weighs 14 pounds and that Meg's pumpkin is half the weight of Ryan's. This means Meg's pumpkin weighs 7 pounds (14 lb / 2). Since Felipe's pumpkin weighs three times as much as Meg's, we have to multiply Meg's pumpkin's weight by 3 to find the weight of Felipe's pumpkin: 7 lb x 3 = 21 pounds.
So, Felipe's pumpkin weighs 21 pounds.
Can somebody please help me
Answer:
a = 5
Step-by-step explanation:
3(a - 4) + 1 = 9 - a Distribute the 3 into a-4
3a - 12 + 1 = 9 - a Combine like terms
[-12 and 1]
3a - 11 = 9 - a Add 11 to both sides to isolate 3a
+11 +11
3a = 20 - a Add a to remove it and have all a
+a +a
4a = 20 Divide by 4 to only have a
/4 /4
a = 5
Hi there! The answer should be a = 5. I have included an image with the process. Hope this helps for future reference!
P.S. It is okay with me if you save the image for help later. :)
WILL GIVE BRAINLYLIST !!!!! IF UNDER 5 MINSSSS HELPThe cost of 10 cupcakes at a cake stand is $40. Which graph shows the cost of different numbers of cupcakes at the cake stand?
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,8 and 2,12 and 3,16.
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,2 and 2,4 and 3,6.
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,4 and 2,4 and 3,4.
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,4 and 2,8 and 3,12.
Answer:
I have to say the first one sorry responded late
GIVE BRAINIEST:
plz give me brainliest i almost got caught in class WHILE HELPING!!!
Answer:
i think its the first one
Step-by-step explanation:
Find a polynomial, which if substituted for M will make the equation an identity: a M–(4ab–3b2)=a2–7ab+8b2
Answer:
a² – 3ab + 5b²
Step-by-step explanation:
M – (4ab – 3b²) = a² – 7ab + 8b²
M = a² – 7ab + 8b² + 4ab – 3b²
M = a² – 3ab + 5b²
Answer:
image
Step-by-step explanation:
image
A recipe calls for 24 ounces of oil and 8 ounces of vinegar. Kim is making dressing with 12 ounces
of vinegar using the same ratio of oil to vinegar
How much oil should kin use?Complete the Table
Answer:
36 ounces
Step-by-step explanation:
The common relationship between 24 ounces and 8 ounces is that 8 times x= 24.
24 divided by 8 is 3. Applying this same technique, we can figure out that 12 times 3 is 36.
Answer: 36 oz of oil
Ratio of oil to vinegar: 3:1
Step-by-step Explanation:
1) The oil to vinegar ratio of the recipe is calculated my dividing the amount of oil (oz) by the amount of vinegar (oz)
24 ÷ 8 = 3
This 3 means you have 3 parts oil for every 1 part vinegar, ratio being: [tex]\frac{3}{1}[/tex]
2)
[tex]\frac{3}{1}[/tex] ⇒ [tex]\frac{?}{12}[/tex]
To get the denominator from 1 to 12 you must multiply by 12.
You must do the same to the numerator (top of fraction) meaning you mus multiply 3 (The ratio's nominator) by 12.
3 × 12 = 36
3)
The answer is 36 oz of oil
Answer Check:
To Check answer you can do 36 ÷ 12
And if it equals 3 than we know that the ounces of oil (36) over the ounces of vinegar (12) give us a ratio of 3:1 Which is the same ratio as used in the recipe. (24:8)
This is a simplified method of this problem.
Lettuce is packaged four bags to a box.if there are 3.5 boxes of lettuce in the cooler, how many bags of lettuce would there be
Answer:
14 bags
Step-by-step explanation:
multiply 4*3.5 to get 14
What is the length of AC¯¯¯¯¯ ? Enter your answer in the box. units Triangle A B C with vertical side A C. Vertex B lies to the right of side A C. Angle A and angle C are marked congruent. The length of side A C is labeled as x. The length of side A B is labeled as x plus 4. The length of side B C is labeled as 3 x minus 8.
Since m<A ≅ m<C, AB = BC.
And...
x+4=3x-8
-2x=-12
x=6
Since AC=x, AC=6.
answer: AC = 6
Answer:
Length of AC is 6
Step-by-step explanation:
he side AC = x ;we need to find x; since ∠A = ∠C , It's an isosceles triangle . i.e ,the sides opposite to the angles ( AB and CB ) are also equal. thus ,side AB = x+4 ;CB = 3x-8 ;thus AB = CB or ,x+4 = 3x-8 ,2x = 12 ,x = 6 ; therefore the side AC is 6.
hope this helped
Which of the lines graphed has a slope of -1/2 and a y-intercept of 3
(WORTH 100 POINTS AND WILL GIVE BRIANLIEST)
Answer:
The correct option is C).
Figure show the line with slope of -1/2 and a y-intercept of 3
Step-by-step explanation:
The equation of line is given by y=mx+c.
Where m is slope and c is y-intercept.
Given that line has slope
m=[tex]\frac{-1}{2}[/tex] and c=3
Thus equation of line will be
y=mx+c.
y=[tex]\frac{-1}{2}x+3[/tex]
To plot the line we need at least two points
Take x=0
y=[tex]\frac{-1}{2}x+3[/tex]
y=[tex]\frac{-1}{2}0+3[/tex]
y=3
The required point is A(0,4)
Take x=2
y=[tex]\frac{-1}{2}2+3[/tex]
y=2
The required point is B(2,2)
Using this points to graph the given equation of line
Figure show the line with a slope of -1/2 and a y-intercept of 3
The correct option is C).
Answer:
B
Step-by-step explanation:
I’m not sure but I put in c and got it wrong and that is the only other one that appears to be going on a negative slope
Help!!!!
CR #16 1. Roger is paid $50 to sell videos of a play to an audience after the play is
performed.
He also receives $2 for each video he sells. The function E(v)=50+2v
models the amount of money Roger earns by selling v videos. The play's audience
consists of 230 people and each audience member buys no more than 1 video.
What is the practical domain of the function? (1 Point) Show how you
determined/defined the practical domain. (Explain/show your process as if you were
teaching someone else how to do the work. (3 Points) What is the most that Roger
can earn? (1 Point)
Answer:
Practical Domain is the set of x values which are from zero to 230.
The maximum he can earn is $510.
Step-by-step explanation:
Domain is the set of x values. In this equation it is the number of videos sold that could be between zero and 230 ( considering the maximum number of people buying videos are 230).
It can be written as v lies between zero and 230 or in other words [0,230].
The maximum he can earn is
E(v)=50+2v
E(230)=50+2(230)
50+ 460= 510$
If the date of the second Thursday of the month is a perfect square, what is the date of the last Monday of the month?
Answer:
last Monday is 27
Step-by-step explanation:
perfect square: 4, 9 , 16
2nd Thursday is a day >5 and < 14 day from the begining of the month, therefore the only day fit the criteria is 9th of the month.
last Monday is 27
Sun Mon Tue Wen Thu Fri Sat
9 10 11
12 13 14 15 16 17 18
.........................................................
26 27
To find the date of the last Monday of the month, calculate the number of days between the second Thursday and the last Monday by considering the number of weeks in the month.
Explanation:To find the date of the last Monday of the month, we need to determine the number of days between the second Thursday and the last Monday.
Let's assume that the second Thursday is on the 9th of the month.
Since there are 7 days in a week, the last Monday will be 9 + (7 * (number of weeks in the month) - 1).
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Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did
she have?
If the variable n represents the number of nickels, then which of the following expressions represents the number of
quarters?
Answer:Let
n-------> the number of nickels
q------> the number of quarters
we know that
1\ quarter=\$0.25\\1\ nickel=\$0.05
so
0.05n+0.25q=1.60 ----> equation A
q=3n ----> equation B
substitute equation B in equation A
0.05n+0.25[3n]=1.60
0.05n+0.75n=1.60
0.80n=1.60
n=2
Find the value of q
q=3*2=6
therefore
The answer part a) is
the number of nickels are 2 and the number of quarters are 6
the answer Part b) is
The expressions that represents the number of quarters is
q=3n
Step-by-step explanation:
Elise made a scale drawing of a shopping center. The scale of the drawing was 1.5 inch :3
feet. In the drawing, a bakery in the shopping center is 13 inches wide. What is the width
of the actual bakery?
Answer:
The actual width is 26 feet.
Step-by-step explanation:
Elise made a scale drawing of a shopping center. The scale of the drawing was 1.5 inches : 3 feet = 1.5 inches : 36 inches = 1 : 24.
Now, in the drawing, a bakery in the shopping center is 13 inches wide.
Therefore, the actual width of the bakery in the shopping center will be the increased value of 13 inches in the ratio 1 : 24.
So, the actual width is (13 × 24) inches = 312 inches i.e. 26 feet. (Answer)
The actual width of the bakery is calculated using the scale factor from the drawing. This can be achieved by multiplying the drawn width of the bakery (in inches) by the scale factor to get the actual width (in feet). Thus, the actual width of the bakery is 26 feet.
Explanation:The subject of this question is scale factor in mathematics, specifically in the context of real-world scenarios, like a scale drawing. The scale of the drawing is 1.5 inches: 3 feet, which represents a scale factor of 2 feet per inch (because 3 feet/1.5 inches = 2 feet per inch). In the drawing, the bakery is stated to be 13 inches wide.
To convert this to the actual width, one should multiply the width in the drawing (13 inches) by the scale factor (2 feet per inch). Hence, the actual width of the bakery is 26 feet (because 13 inches * 2 feet per inch = 26 feet).
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HELP,
Would I have to subtract 180 from 70 to get the answer for C?? What would the answer be?
Answer:
Angle C is equal to 30.
Step-by-step explanation:
To find angle C, we have to find all the other angles first. They tells us the B ~= BAD ~= ADC. So, if we find ADC, we've found B and BAD as well. ADC is just 180 - 70 (the angle of ADE), which is 110. So, ADC, BAD, and B are equal to 110.
Remember, angles in a quadrilateral add up to 360. So, add all of the values of angles be have now and subtract from 360:
360 - (110 + 110 + 110)
360 - 330 = 30
Angle C should be equal to 30.
Hope this helped!
Helpppppp guyssss pleaseeeeeee I’m losttt
Answer:
29
Step-by-step explanation:
Use definition of conditional probability:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)},[/tex]
where
A = the student is a freshman,
B = the student is a male
From the table,
[tex]P(B)=\dfrac{4+6+2+2}{4+6+2+2+3+4+6+3}=\dfrac{14}{30}=\dfrac{7}{15}\\ \\P(A\cap B)=\dfrac{4}{4+6+2+2+3+4+6+3}=\dfrac{4}{30}=\dfrac{2}{15}[/tex]
So,
[tex]P(A|B)=\dfrac{\frac{2}{15}}{\frac{7}{15}}=\dfrac{2}{7}\approx 0.29=29\%[/tex]
a function is defined by equation f(x)=-3x+2 what is the average rate if change for the function on the interval from x =-2 to x = 2
The average rate of change for the function on the interval from x = -2 to x = 2 is 1.
Explanation:The average rate of change for a function on an interval is calculated by finding the slope of the line connecting the two endpoints of the interval. In this case, the interval is from x = -2 to x = 2.
To find the slope, we need to find the change in y values divided by the change in x values. In other words, we need to find the difference in f(x) values divided by the difference in x values.
Substituting the given function into the equation, we have:
slope = (f(2) - f(-2)) / (2 - (-2)) = (-3(2) + 2 - (-3(-2) + 2)) / (2 + 2)
= (-6 + 2 + 6 + 2) / 4
= 4 / 4 = 1.
Therefore, the average rate of change for the function on the interval from x = -2 to x = 2 is 1.
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(x, 7) and (11, 8); m = -1/5
Plz help
Answer:
This tells us that the line with slope -1/5 passes through the two points (16, 7) and (11, 8). The previously unknown x-coordinate is 16.
Step-by-step explanation:
A line with slope m = -1/5 passes through the points (x, 7) and (11, 8). Find the value of x.
The slope of the line through these two points is found from the slope formula and is:
8 - 7
m = ----------- and the value of m is given as -1/5. Therefore,
11 - x
1
m = ----------- = -1/5
11 - x
Cross-multiplying, we get (1)(5) = -(11 - x), or 5 = -11 + x. Then x = 16
This tells us that the line with slope -1/5 passes through the two points (16, 7) and (11, 8). The previously unknown x-coordinate is 16.
100 POINTS!!!!
Alexis runs a small business and creates recordings of her friend’s skateboard stunts. She puts the recordings onto Instagram. She currently has 100 Instagram followers. If the number of followers grows at a rate of 1% every 12 hours. The following function represents this situation.
f(x) = f(1. + r)^t where f is the number of initial followers and r is the grown rate and t is time.
2) Alexis hopes to eventually have 1,000,000 followers, how long will it take her to reach this level of followers.
#Days since upload 0 10 20 50 100 300 500
Number of Instagram followers
There is no specific requirement in the question, but I'm assuming you need to compute the time needed for Alexis reach 1,000,000 Instagram followers
Answer:
[tex]t= 462.82\ days[/tex]
Step-by-step explanation:
Exponential Growth
When the number of observed elements grows as the previous value multiplied by a constant ratio, we have exponential growth. The formula to model such situations is
[tex]\displaystyle f(x) = f_o(1 + r)^t[/tex]
Where [tex]f_o[/tex] is the initial value of f, 1 + r is the constant ratio, and t is the time expressed in half days (12 hours)
The initial value is 100 Instant followers, thus:
[tex]\displaystyle f(x) = 100(1.01)^t[/tex]
We need to know when the number of followers will reach 1,000,000. Setting up the equation
[tex]\displaystyle 100(1.01)^t=1,000,000[/tex]
Simplifying by 100
[tex]\displaystyle (1.01)^t=10,000[/tex]
Taking logarithms
[tex]\displaystyle t\ log(1.01)=log\ 10,000[/tex]
[tex]\displaystyle t\ log(1.01)=4[/tex]
Solving for t
[tex]\displaystyle t=\frac{4}{log(1.01)}=925.63[/tex] periods of 12 hrs
[tex]t= 462.82\ days[/tex]
Alexis will reach 1,000,000 followers in approximately 462.82 days.
To calculate how long it will take Alexis to reach 1,000,000 followers, we can use the following equation:
f(t) = f(1+r)^t
We know that Alexis currently has 100 followers (f=100), and she wants to reach 1,000,000 followers (f=1,000,000). We also know that her follower growth rate is 1% every 12 hours (r=0.01).
To solve for the time (t) it will take Alexis to reach 1,000,000 followers, we can use the following steps:
Divide both sides of the equation by f(1+r):
f(t)/f(1+r) = (1+r)^t
Take the natural logarithm of both sides of the equation:
ln(f(t)/f(1+r)) = t * ln(1+r)
Divide both sides of the equation by ln(1+r):
t = ln(f(t)/f(1+r)) / ln(1+r)
Substitute the known values into the equation:
t = ln(1,000,000/100) / ln(1+0.01)
Solve for t:
t = 462.82 days
Therefore, it will take Alexis approximately 462.82 days to reach 1,000,000 followers.
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Factor completely, then place the answer in the proper location on the grid
a^3-b^3
Answer:
[tex]\displaystyle [a - b][a^2 + 2ab + b^2][/tex]
Step-by-step explanation:
Use the Difference of Cubes to factor this polynomial.
I am joyous to assist you anytime.
4 coffees and 12 lattes. Costs $61
12 coffees and 7 lattes. Costs $59.75
How much does a coffe and a latte cost
Answer:
Cost of a coffee is $2.5 and cost of a latte is $4.25.
Step-by-step explanation:
Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.
Given:
4 coffees and 12 lattes cost $61.
12 coffees and 7 lattes cost $59.75.
∵ 1 coffee cost = [tex]c[/tex]
∴ 4 coffees cost = [tex]4c[/tex] and 12 coffee cost = [tex]12c[/tex]
∵ 1 latte cost = [tex]l[/tex]
∴ 12 lattes cost = [tex]12l[/tex] and 7 lattes cost = [tex]7l[/tex]
Now, as per question:
[tex]4c+12l=61-----1\\12c+7l=59.75----2[/tex]
Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,
[tex]-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=\frac{-123.25}{-29}=\$4.25[/tex]
Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,
[tex]4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=\frac{10}{4}=\$2.5[/tex]
Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.
A system of linear equations can determine the cost of a coffee and a latte, which are found to be $2.50 and $4.25 respectively.
To solve the question how much does a coffee and a latte cost, we can treat it as a system of linear equations problem. We have the following two equations based on the given information:
4 coffees + 12 lattes = $61
12 coffees + 7 lattes = $59.75
Let's denote the cost of one coffee as c and the cost of one latte as l. We can now rewrite the equations as:
4c + 12l = 61
12c + 7l = 59.75
Multiplying the first equation by 3 gives us:
12c + 36l = 183
Now we can subtract the second equation from this new equation to find the cost of lattes:
(12c + 36l) - (12c + 7l) = (183 - 59.75)
29l = 123.25
l = 123.25 / 29
l = $4.25
Having found the cost of a latte, we can now substitute this back into the first original equation to find the cost of a coffee:
4c + 12(4.25) = 61
4c + 51 = 61
4c = 10
c = 10 / 4
c = $2.50
Therefore, a coffee costs $2.50 and a latte costs $4.25.