Answer:
The solution of the given system of equations is,
[tex]x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}[/tex]
Step-by-step explanation:
The given equations are :
x + ay = b .......(1)
ax - by = c .......(2)
We will use 'Substitution Method' to solve the given system of equations.
In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable and then substitute that value in the other equation to find the value of the another variable.
Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).
Consider the equation (1), that is,
x + ay = b ⇒ x = b - ay ........(3)
Substitute the value of 'x' from (3) in (2), we get
a(b - ay) - by = c
⇒ab - a²y - by = c
⇒-a²y - by = c - ab
⇒-y(a²+b) = c - ab
⇒y(a²+b) = ab - c
[tex]\implies y=\frac{ab-c}{a^{2}+b}[/tex]
Now, substituting the above value of 'y' in equation (3), we get
[tex]x=b-a(\frac{ab-c}{a^2+b})[/tex]
[tex]\implies x=\frac{b(a^2+b)-a(ab-c)}{a^2+b}[/tex]
[tex]\implies x=\frac{a^2b+b^2-a^2b+ac}{a^2+b}[/tex]
[tex]\implies x = \frac{b^2+ac}{a^2+b}[/tex]
Hence, the solution of the given system of equations is,
[tex]x = \frac{b^2+ac}{a^2+b} ;\; y = \frac{ab-c}{a^2+b}[/tex]
I'm having trouble with these problems. and my paper is due tomorrow. please help
Answer:
Step-by-step explanation:
-5(-5w+3v-2) how do I use distributive property to remove the parentheses
Answer:you would times everything on the inside by 5 im pretty sure
Step-by-step explanation:
A gas is contained in a 3.0L container at a temperature of 25°C. The gas exerts a pressure of 16 atm on the
container. If pressure is kept constant, what is the final volume of the gas if the temperature of the container is
increased to 200°C? (HS+C.P1013)
A. 5.6L
B.
4.8L
C. 1.9L
D.
24 L
Answer:
4.8 Liters.
Step-by-step explanation:
When pressure is kept constant the volume of a certain quantity of gas is proportional to the absolute temperature of the gas.
So, [tex]\frac{V_{f} }{T_{f}} = \frac{V_{i} }{T_{i}}[/tex] .......... (1)
Where, f denotes the final and i denotes the initial values.
Now, [tex]V_{i} = 3[/tex] Liters,
[tex]T_{i} = 25 + 273 = 298 K[/tex] and
[tex]T_{f} = 200 + 273 = 473 K[/tex]
Therefore, from equation (1) we get,
[tex]V_{f} = \frac{3 \times 473}{298} = 4.76[/tex] Liters ≈ 4.8 Liters. (Answer)
In the reaction of hydrogen with iodine
Answer:
HI hydrogen iodide
Step-by-step explanation:
H2(gas)+I2(gas)---------->2HI(gas)
Answer:
I don't really know what you were asking; would you mind please clarifying? :)
Step-by-step explanation:
From what I'm guessing from the question is, "Iodine, and hydrogen combine to form hydrogen iodide. In the reverse reaction, hydrogen iodide decomposes back into hydrogen and iodine."
Did that help?
A new club sent out 164 coupons to boost sales for next year's memberships. They provided 3 times as many to potential members than to existing members. How many coupons did they send to existing members?
Answer:
123 coupons.
Step-by-step explanation:
Divide the total of 164 coupons by 4. 164/4 = 41
Find the amount of coupons sent by multiplying 41 by 3. 41 x 3 = 123
The answer is 123 coupons. (123/164 = 3/4)
how many cubic centimeters of water can this paper cone cup hold?
Answer:
150.72 cubic centimeter
Step-by-step explanation:
Given:-
Height of cone (h) = 9cm
Diameter of cone(d)=8cm
radius of cone(r)=[tex]\frac{d}{2}[/tex]=[tex]\frac{8}{2} =4cm[/tex]
To calculate= Volume of cone([tex]V_{cone}[/tex])
[tex]Volume\ of\ cone(V_{cone}) =\frac{1}{3} \times \pi \times r^{2} \times h[/tex]
[tex]=\frac{1}{3} \times 3.14\times 4^{2} \times 9[/tex]
Volume of cone([tex]V_{cone}[/tex]) [tex]=150.72\ cubic\ centimeter[/tex]
Therefore paper cone cup can hold 150.72 cubic centimeter of water.
The paper cone cup can indeed hold 150.72 cubic centimeters of water.
The paper cone cup can indeed hold 150.72 cubic centimeters of water. Let's break down the calculation:
1. Given dimensions:
- Height of the cone (h) = 9 cm
- Diameter of the cone (d) = 8 cm (which implies a radius (r) of 4 cm)
2. To calculate the volume of the cone, we'll use the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \][/tex]
3. Plugging in the values:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \cdot 4^2 \cdot 9 \][/tex]
4. Calculating:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \cdot 3.14 \cdot 16 \cdot 9 = 150.72 \, \text{cubic centimeters} \][/tex]
Therefore, the paper cone cup can indeed hold 150.72 cubic centimeters of water.
How do you find a variable to 4-2(v+9)=26
Answer:
V=20
Step-by-step explanation:
Simplify both sides of the equation.
4−2(v+9)=26
4+(−2)(v)+(−2)(9)=26(Distribute)
4+−2v+−18=26
(−2v)+(4+−18)=26(Combine Like Terms)
−2v+−14=26
−2v−14=26
Step 2: Add 14 to both sides.
−2v−14+14=26+14
−2v=40
Step 3: Divide both sides by -2.
−2v
−2
=
40
−2
v=−20
the surface area of a cuboid is 95cm² and its lateral surface area is 63cm². find the area of its base
Answer:
The Area of the base is 16 cm² .
Step-by-step explanation:
Given as :
The surface area of the cuboid = x = 95 cm²
The lateral surface area of the cuboid = y = 63 cm²
Let The Area of the base = z cm²
Now, Let The length of cuboid = l cm
The breadth of cuboid = b cm
The height of cuboid = h cm
According to question
∵ The surface area of the cuboid = 2 ×(length × breadth + breadth × height + height × length)
Or, x = 2 ×(l × b + b × h + h × l)
Or, 95 = 2 ×(l × b + b × h + h × l)
Or, (l × b + b × h + h × l) = [tex]\dfrac{95}{2}[/tex] ....1
Similarly
∵lateral surface area of the cuboid = 2 ×(breadth × height + length × height)
Or, y = 2 ×(b × h + l × h)
Or, 2 ×(b × h + l × h) = 63
Or, (b × h + l × h) = [tex]\dfrac{63}{2}[/tex] ......2
Putting value of eq 2 into eq 1
so, (l × b + [tex]\dfrac{63}{2}[/tex] ) = [tex]\dfrac{95}{2}[/tex]
Or, l × b = [tex]\dfrac{95}{2}[/tex] - [tex]\dfrac{63}{2}[/tex]
Or, l × b = [tex]\dfrac{95 - 63}{2}[/tex]
i.e l × b = [tex]\dfrac{32}{2}[/tex]
so, l × b = 16
Now, Again
∵The Area of the base = ( length × breadth ) cm²
So, z = l × b
i.e z = 16 cm²
So, The Area of the base = z = 16 cm²
Hence,The Area of the base is 16 cm² . Answer
A student plots a system of equations on graph paper.
Answer:
AStep-by-step explanation:
help.....meh...please.
Answer:
.875 = 875/1,000 = 7/8
The correct answer is D.
25. Paulo's family arrived at the reunion at
8:30 A.M. How long do they have before
the trip to Scenic Lake Park?
DATA
Trip to Scenic
Lake Park
10:15 A.M. to 2:30 P.M.
Slide show
4:15 P.m. to 5:10 P.M.campfire 7;55p.m.to 9;30p.m
26. How much longer is dinner than the
Paulo's family has 1 hour 45 minutes before the trip to Scenic Lake Park.
To find out how long Paulo's family has before the trip to Scenic Lake Park, we will determine the amount of time between their arrival and the start of the trip.
Paulo's family arrived at the reunion at 8:30 A.M. The trip to Scenic Lake Park starts at 10:15 A.M.
Here's how to calculate the difference between these two times manually:
1. Convert both times to a 24-hour format (if needed):
- Paulo's family arrival time: 8:30 A.M. is already in the morning, so it stays the same.
- Trip start time: 10:15 A.M. is also in the morning, so it stays the same.
2. Calculate the hours remaining:
- From 8 A.M. to 9 A.M. is 1 hour.
- From 9 A.M. to 10 A.M. is another hour.
- From 8:30 A.M. to 10 A.M., they have a total of 1 hour and 30 minutes.
3. Calculate the additional minutes remaining:
- From 10:00 A.M. to 10:15 A.M. is an additional 15 minutes.
4. Add the additional minutes to the total time calculated:
- They already have 1 hour and 30 minutes, and we add another 15 minutes to this.
- So, the total time they have before the trip is 1 hour and 45 minutes.
Therefore, Paulo's family has 1 hour and 45 minutes of free time before the trip to Scenic Lake Park starts.
You order a pizza for dinner
The radius of the pizza is 7 inches
What is the diameter of the pizza? What is the circumference of the pizza? What is the area of the pizza?
Final answer:
The diameter of the pizza is 14 inches, its circumference is approximately 43.98 inches, and its area is about 153.94 square inches, calculated using fundamental geometry formulas for circles.
Explanation:
A pizza with a radius of 7 inches is given, and we are tasked with determining its diameter, circumference, and area. These are fundamental geometry calculations related to circles.
The diameter of a circle is twice its radius. So, the diameter of the pizza is 2 × 7 inches = 14 inches.
The circumference of a circle is calculated as π (Pi) times its diameter.
Therefore, the circumference of the pizza is π × 14 inches ≈ 43.98 inches (using π = 3.1416).
The area of a circle is given by π times the square of its radius (πr²).
Hence, the area of the pizza is π × 7² inches² ≈ 153.94 square inches.
These calculations provide a complete geometric understanding of the pizza's properties in terms of diameter, circumference, and area.
Mari has a part time job. She earns $7 an hour. She makes at most $143.50 a week. What is the greatest number of hours she can work
Answer:
20 hours
Because 143.50/7= 20.5
Meaning the most she can work is 20 hours a week
4^-3 × 4^2 × 4^5 = 4^?
The value of the missing exponent is 4^10?
True or false
Answer:
[tex] {4}^{ - 3} \times {4}^{2} \times {4}^{5} = {4}^{ - 3 +2 + 5} = {4}^{4} [/tex]
False. The missing exponent is 4.
-4,4 dilated by a scale factor of 5
Answer:
(-20,20)
Step-by-step explanation:
Given coordinates are (-4,4).
Also, we need to dilate by a scale factor of 5.
The term dilation refers to changing the value of coordinate by a scale factor.
If the coordinate is said [tex](x,y)[/tex] and it is going to be dilated by a scale factor [tex]'k'[/tex].
Then the new coordinate will be (kx, ky).
So,
[tex](-4,4)\\\\k=5\\\\(-4\times5,4\times5)=(-20,20)[/tex]
The coordinate [tex](-4,4)[/tex] after dilated by a scale factor [tex]5[/tex] will be [tex](-20,20)[/tex]
Please Help! Given the right triangles ABC and ABD, what is the length of segment BC, in units?
Answer:
20 units
Step-by-step explanation:
Consider right triangle ABD. In this triangle,
[tex]BD=37\ un.\\ \\AD=19+16=35\ un.[/tex]
By the Pythagorean theorem,
[tex]BD^2=AD^2+AB^2\\ \\37^2=35^2+AB^2\\ \\AB^2=37^2-35^2=(37-35)(37+35)=2\cdot 72=144\\ \\AB=12\ un.[/tex]
Consider right triangle ABC. In this triangle,
[tex]AC=16\ un.\\ \\AB=12\ un.[/tex]
By the Pythagorean theorem,
[tex]BC^2=AB^2+AC^2\\ \\BC^2=16^2+12^2\\ \\BC^2=256+144=400\\ \\BC=20\ un.[/tex]
What are the values of the regrouped amounts in the multiplication below?
435
x17
3,045
+ 4,350
7,395
A. 2 and 3
B. 20 and 3
C. 200 and 30
D. 2000 and 300
In the multiplication operation of numbers 435 and 173, the regrouped or carried over amounts are 10 (in units place calculation) and 30 (in tens place calculation). Therefore, the answer corresponds to option B: 20 and 3.
In multiplicaton problems, we often need to 'regroup' or carry values. In the multiplication of 435 and 173, regrouping is necessary. Here's how it's done:
We start by multiplying 5 from 435 with 3 from 173, to get 15. We write down 5 and carry over the 1 (or 10 from 15).
Next, we multiply the 5 in 435 with 7 (the tens-place in 173), which equals 35. We add the carry-over 1 to get 36. We write down the 6 and carry over the 3 (or 30).
Finally, we multiply the 5 in 435 with 1 (the hundreds-place in 173). Then add the carried over 3, resulting in 8.
The process is repeated with the remaining numbers in 435.
So for the multiplication above, the regrouped amounts are 10 and 30, corresponding to option B: 20 and 3.
For more such question on multiplication operation visit:
https://brainly.com/question/550188
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Please help with math, The closest I got was 11/4 for the answer but its obviously not right, please get back as soon as you can!
Answer:
D
Step-by-step explanation:
1 1/4 + 3/4 + 2/4 + 1/4
1+1+ 3/4
2 3/4
Find an equation for the perpendicular bisector of the line segment whose endpoints are -7,-2 and 5,4
The equation of the perpendicular bisector of the line segment whose endpoints are (-7 , -2) and (5 , 4) is y = -2x - 1
Step-by-step explanation:
Let us revise some rules
The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]The formula of the slope of a line whose endpoints are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]The mid-point of a line whose endpoints are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]∵ A line has endpoints (-7 , -2) and (5 , 4)
∴ [tex]x_{1}[/tex] = -7 and [tex]x_{2}[/tex] = 5
∴ [tex]y_{1}[/tex] = -2 and [tex]y_{2}[/tex] = 4
- Use the formula of the slope up to find the slope of the line
∴ [tex]m=\frac{4-(-2)}{5-(-7)}=\frac{4+2}{5+7}=\frac{6}{12}=\frac{1}{2}[/tex]
To find the slope of the perpendicular line to the given line reciprocal it and change its sign
∵ The slope of the given line = [tex]\frac{1}{2}[/tex]
∴ The slope of the perpendicular line = -2
∵ The perpendicular line is a bisector of the given line
- That means the perpendicular line intersect the given line
at its midpoint
∵ The mid point of the given line = [tex](\frac{-7+5}{2},\frac{-2+4}{2})[/tex]
∴ The mid point of the given line = [tex](\frac{-2}{2},\frac{2}{2})[/tex]
∴ The mid point of the given line = (-1 , 1)
Now we wand to find the equation of the line whose slope is -2 and passes through point (-1 , 1)
∵ The form of the equation is y = mx + b, where m is the slope
and b is the y-intercept
∵ m = -2
- Substitute the value of m in the form of the equation
∴ y = -2x + b
- To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ Point (-1 , 1) lies on the line
∴ x = -1 and y = 1
∵ 1 = -2(-1) + b
∴ 1 = 2 + b
- Subtract 2 from both sides
∴ -1 = b
- Substitute the value of b in the equation
∴ y = -2x + (-1)
∴ y = -2x - 1
The equation of the perpendicular bisector of the line segment whose endpoints are (-7 , -2) and (5 , 4) is y = -2x - 1
Learn more:
You can learn more about the equations of the perpendicular lines in brainly.com/question/9527422
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Cami has correctly answered 70% of the first 20 questions on her final exam. At least how many of the remaining 12 questions must she get correct to get a final score that's greater than 80%?
Answer:
12
Step-by-step explanation:
Final answer:
Cami must answer all 12 of the remaining questions correctly to achieve a final score greater than 80% on her exam, having already secured 70% correct from the first 20 questions.
Explanation:
Cami has answered 70% of the first 20 questions correctly, which means she has 14 correct answers. As the final exam has 32 questions in total (20 + 12), to achieve a final score greater than 80%, she needs to get more than 80% of 32 total questions correct, which is more than 25.6 correct answers. Since she cannot get a fraction of a question correct, she needs at least 26 correct answers in total. Given she has already 14 correct, she needs at least 12 more correct answers out of the remaining 12 questions to achieve this score.
Sean read
1
-
5
of a book in
1
1
-
2
hours.
How long will it take Sean to read
1
-
2
of this book?
Enter your answer as a mixed number in simplest form in the box.
Answer:
[tex]3\frac{3}{4}[/tex] hours.
Step-by-step explanation:
Sean read [tex]\frac{1}{5}[/tex] of a book in [tex]1\frac{1}{2}[/tex] hours.
We are asked to determine the time that Sean requires to read [tex]\frac{1}{2}[/tex] of this book.
If the rate of reading the book is assumed to be constant, then we can use the unitary method to find the answer.
Now, Sean reads [tex]\frac{1}{5}[/tex] of a book in [tex]\frac{3}{2}[/tex] hours.
So, Sean reads the total of the book in [tex]\frac{3}{2} \div \frac{1}{5} = \frac{15}{2}[/tex] hours.
Hence, Sean reads [tex]\frac{1}{2}[/tex] of this book in [tex]\frac{15}{2} \times \frac{1}{2} = \frac{15}{4} = 3\frac{3}{4}[/tex] hours. (Answer)
Can someone help me with this T-T
Answer:
17 79 017.3.727m92Step-by-step explanation:
My frist store wen you I was a little kid and the most main street from this is
Answer:
Answers are in picture, if you want an explanation for anything, just ask.
Step-by-step explanation:
What is the GCF of 12 and 7
Answer:
The GCF of 7 and 12 is 1.
Answer:
Step-by-step explanation:
GCF of 12 and 7 = 1
If there is no common factor then , GCF will be 1
On two investments totaling $7,500, Lydia lost 2% on one and earned 5% on the other. If her net annual receipts were $158, how much was each investment
Lydia invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %
Solution:
Given that on two investment totaling $ 7500
Lydia lost 2% on one and earned 5% on the other
Her net annual receipts were $158
To find: amount invested in both investments
Let Lydia invest $ x in first investment where she lost 2 %
Let Lydia invest $ y in second investment where she earned 5 %
Total investment given = 7500
x + y = 7500 ---- eqn 1
Net annual receipt = 158
5 % y- 2 % x = 158
[tex]\frac{5}{100}y - \frac{2}{100}x = 158[/tex]
0.05y - 0.02x = 158 ------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 7500 - y
Substitute x = 7500 - y in eqn 2
0.05y - 0.02(7500-y) = 158
0.05y -150 + 0.02y = 158
0.07y = 158 + 150
0.07y = 308
y = 4400
Thus,
x = 7500 - y
x = 7500 - 4400
x = 3100
Thus she invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %
Final answer:
Lydia invested $3,100 at a 2% loss and $4,400 at a 5% gain. A system of equations is set up and solved using substitution to determine the amount invested in each scenario.
Explanation:
To solve Lydia's investment problem, we need to set up a system of equations based on the given information
Total investment is $7,500.
She lost 2% on one investment and earned 5% on the other.
Her net annual receipts were $158.
Let's define:
x = the amount of money invested at a 2% loss
y = the amount of money invested at a 5% gain
The system of equations can be written as:
x + y = 7500 (the total amount invested)
-0.02x + 0.05y = 158 (the net receipts from the investments)
Multiplying the second equation by 100 to simplify the decimals:
-2x + 5y = 15800
Now we can use the method of substitution or elimination to solve for x and y. For this example, we'll use the substitution method:
Solve for y in the first equation: y = 7500 - x
Substitute y into the second equation: -2x + 5(7500 - x) = 15800
Now solve for x: -2x + 37500 - 5x = 15800
Combine like terms: -7x = 15800 - 37500
-7x = -21700
Divide by -7: x = 3100
Substitute x into y = 7500 - x: y = 7500 - 3100 = 4400
So Lydia invested $3,100 at a 2% loss and $4,400 at a 5% gain.
A video game decreased in price from $50 to $45. What was the approximate percent decrease in the price? 0.1% 1% 5% 10%
Answer: 10%
50 is half of 100, so if it decreases 5 dollars from 50, then it has to be 10% of a decrease, or discount.
Hope this helps!
Answer:
10%
Step-by-step explanation:
50-45=5
5/50=1/10=10%
Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.
They equation needs to be in the form y=kx
K=
Equation:
Answer:
see explanation
Step-by-step explanation:
The equation of proportionality is
y = kx ← k is the constant of proportionality
k = y ÷ x, thus
k = 160 ÷ 25 = 320 ÷ 50 = 480 ÷ 75 = 640 ÷ 100 = 6.4
and
y = 6.4x ← equation of proportionality
An office building is 20 feet taller than twice the height of a bank building. If the office building is 320 feet tall, how tall is the bank building?
A. 150 feet
B. 160 feet
C. 180 feet
D. 300 feet
Plus explication thanks!
Answer: A the bank building is 150 feet tall.
Step-by-step explanation:
If you subtract 20 from 320 then you get 300 then divide that by 2 you get 150.
what is the answer for 100- the sum of 3+x
Answer:
97-x
Step-by-step explanation:
100-(3+x)
= 100-3-x (- sign is multiplied with the both 3 and x)
= 97-x
Answer:
Step-by-step explanation:
x + 3 = 100
x = 100 - 3
x = 97
Which property is illustrated by the statement?
(2 + 3.4) + 6 = 2 + (3.4 + 6) (1 point)
Associative Property of Addition
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
To which subset of real numbers does the number one-third belong? (1 point)
rational numbers
irrational numbers
whole numbers, integers, rational numbers
whole numbers, natural numbers, integers
What is the algebraic expression for the following word phrase: the product of 2 more than y and 7? (1 point)
7(y+2)
2(y+7)
7+(y+2)
7-(y+2)
Answer:
1. First option.
2. First option.
3. First option.
Step-by-step explanation:
1. You need to remember that the Associative Property of Addition states the following:
[tex](a+b)+c=a+(b+c)[/tex]
Notice that you can group the numbers "a", "b" and "c" in any combination.
In this case, given the statement provided in the exercise:
[tex](2 + 3.4) + 6 = 2 + (3.4 + 6)[/tex]
You can identify that it ilustrates the Associative Property of Addition.
2. Remember that:
- Natural numbers are known as "Counting numbers".
- Whole numbers include positive numbers and zero.
- Integers include the Whole numbers and the negative numbers.
- Rational numbers are those numbers that can be wriitten as a fraction:
[tex]\frac{a}{b}[/tex]
Where "a" is the numerator and "b" is the denominator.
- Integers are a subset of Rational Numbers.
- Irrational numbers cannot be written as a fraction.
Based on this, you can conclude that [tex]\frac{1}{3}[/tex] is a Rational number.
3. The product is the result of a multiplication.
In this case the word "more than" indicates Addition.
Then, the product of 2 more than "y" and 7 can be expressed as:
[tex]7(y+2)[/tex]
Freshly frozen yogurt is the popular place in town. Saturday is their busiest night. The ratio of number of cones to the number of cones to the number of cups sold is 6:5 however on Sunday night the ratio of the number of cones to the number of cups is 4:1 if freshly frozen yogurt sold 42 cones on Saturday night how many cups did it sell on Saturday night?
Answer:
On Saturday night it had sold 35 numbers of cups.
Step-by-step explanation:
On the Saturday night the ratio of the number of cones to the number of cups sold is 6 : 5 in Freshly frozen yogurt however on Sunday night the ratio of the number of cones to the number of cups is 4 : 1.
Now, if the Freshly frozen yogurt sold 42 cones on Saturday night then in the ratio of 6 : 5, it sold cups [tex]\frac{5}{6}[/tex] times the number of cones.
Therefore, on Saturday night it had sold [tex]42 \times \frac{5}{6} = 35[/tex] numbers of cups. (Answer)