Answer:
[tex]\boxed {\boxed {\sf 98 \ Small \ Cups}}\\\\\boxed {\boxed {\sf 57 \ Large \ Cups}}[/tex]
Step-by-step explanation:
Let's make a system of equations.
First, define the variables.
Let s= small cups and g= large cups
Next, make 2 equations. 1 for the money and 1 for the number of cups.
Money
A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265. 1.25s+2.50g=265Number
A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155. s+g=155Here is our system of equations:
[tex]1.25s+2.50g=265 \\s+g=155[/tex]
Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.
Subtract g from both sides of the equation. s+g=155 s+g-g=155-gs=155-gNow we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.
[tex]1.25s +2.50g=265[/tex]
[tex]1.25(155-g)+2.50g=265[/tex]
Distribute the 1.25
1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g[tex]193.75-1.25g+2.50g=265[/tex]
Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.
[tex]193.75-1.25g+2.50g=265-193.75[/tex] (Subtract 193.75)
[tex]-1.25g+2.50g=265-193.75[/tex]
[tex]1.25g=71.25[/tex] (Combine like terms).
1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25
[tex]1.25g/1.25=71.25/1.25\\g=71.25/1.25\\g=57[/tex]
Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.
[tex]s+g=155[/tex]
[tex]s+57=155[/tex]
Subtract 57 from both sides of the equation to isolate the variable, s.
[tex]s+57-57=155-57\\s=155-57\\s=98[/tex]
Ashley sold 57 large cups and 98 small cups.
small cup she sold = x = 98
large cup she sold = y =57
Carmen is playing draw & compare decimals with her partner. Carmen drew 4,7,6,0, and 2 and has to use three of the cards to make a decimal less then 1. If they are playing for "more" what decimal should Carmen make? If they are playing "less" what decimal should Carmen make?
Answer:
For more;
4.76
for less;
0.46
Step-by-step explanation:
Here, we intend getting the decimals that Carmen should make in her game given the numbers she drew
She has two types to make; a decimal less than 1 and a decimal more than 1
If the decimal should be less than 1, the number zero should lead;
And since she is using three of the numbers, we can have something like;
0.46
To make a decimal more than one, she could actually start with any of the numbers other than zero
we can have something like 4.76
What is the slope of a line with points -5,7 and 1,1
Answer
6/-11
Step-by-step explanation:
use the slope formula m= [tex]\frac{y 2-y 1}{x 2-x 1}[/tex]
then sub in numbers m=[tex]\frac{7-1}{-5-1}[/tex]
now subtract numerator and the denominator
[tex]7-1= 6[/tex] and
[tex]-5-6=-11[/tex] this now looks like [tex]\frac{6}{-11}[/tex]
y = 2x – 4
y = -x + 5
Answer:
(3, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x - 4
y = -x + 5
Step 2: Solve for x
Substitution
Substitute in y: 2x - 4 = -x + 5Add x to both sides: 3x - 4 = 5Add 4 to both sides: 3x = 9Isolate x: x = 3Step 3: Solve for y
Define equation: y = -x + 5Substitute in x: y = -3 + 5Add: y = 2The library at school is organized by fiction and non-fiction books. There are 3 non-fiction books for every 7 fiction books. How many total books are there if the library has 240 non-fiction books?
Answer:
Total = 800 books
Step-by-step explanation:
It is given that,
In a library, there are 3 non-fiction books for every 7 fiction books. It means that the ratio of non-fiction books to the fiction books is 3:7.
There if the library has 240 non-fiction books.
Let non fiction books are 3x and fiction books are 7x.
ATQ,
3x=240
x=80
Fiction books = 7x = 7(80) = 560
Total no of books = fiction books + non-fiction books
= 240 + 560
=800
Hence, the total no of books are 800.
what two numbers' sum=-4 and product=-2
Let a and b be the two numbers. Then
a + b = -4
a b = -2
Solve the second equation for b :
b = -2/a
Substitute this into the first equation:
a - 2/a = -4
Multiply both sides by a :
a² - 2 = -4a
Move 4a to the left side:
a² + 4a - 2 = 0
Use the quadratic formula to solve for a :
a = (-4 ± √(4² - 4(-2))) / 2
a = -2 ± √6
If a = -2 + √6, then
-2 + √6 + b = -4
b = -2 - √6
In the other case, we end up with the same numbers, but a and b are swapped.
James is earning money to buy a bicycle for $100. For each dollar James earns, his mother gives him $1. So far he has earned $14 mowing lawns and $7 wash cars. How much more must James earn in order to but the bike??
Answer:
James needs to earn 78 more dollars.
Step-by-step explanation:
If you add up all of the money James has earned, (1 + 7 + 14), it equals 22. If you subtract 22 from 100, it equals 78. Therefore James needs to earn 78 more dollars.
Answer:
$58
Step-by-step explanation:
$14*2=$28 as her mum gives another dollar for each dollar he earns
$7*2=$14 as her mum gives another dollar for each dollar he earns
then 28 + 14 = 42
100 - 42=$58
7 inches of snow in 7 hours rate and unit rate
Answer:
unit rate: (1,1)
Step-by-step explanation:
Work out (5X10^3) x (9X10^7) answer in standard form plz
Answer:
4.5×10¹¹
Answer:
[tex](5 \times 10 {}^{3} ) \times (9 \times 10 {}^{7} )[/tex]
i) use the commutative property to rearrange the terms: a+b = b+a
[tex](5 \times 9) \times (10 {}^{3} \times {10}^{7} )[/tex]
ii) multiply the number in the 1st bracket
[tex]45 \times ( {10}^{3} \times 10 {}^{7} )[/tex]
iii) multiply the 2nd bracket by adding their exponents
[tex]45 \times 10 {}^{3 + 7} [/tex]
[tex]45 \times 10 {}^{10} [/tex]
iv) write the answer in standard form
[tex]4.5 \times 10 {}^{10 + 1} [/tex]
[tex]4.5 \times {10}^{11} [/tex]
The given equation that should be in the standard form should be like a [tex]4.5\times 10^{11}[/tex].
Equation in standard form:Since
The equation is [tex](5\times 10^3) \times (9\times 10^7)[/tex]
Now here we use the commutative property
So,
[tex]45 \times (10^3 \times 10^7)\\\\45 \times 10^{10}\\\\4.5 \times 10^{11}[/tex]
Here, we multiply the number in the 1st bracket, then add, it and then finally in standard form.
Learn more about an equation here: https://brainly.com/question/24271130
Due tonight! PLEASE HELP The graph of a quadratic function has a domain of (-∞, ∞) and range of [4, ∞). In two or more complete sentences, explain how the given range of the function can help you to determine whether the graph opens up or down.
Answer:
Opens upStep-by-step explanation:
The range is:
[4, oo)It means the lowest point is 4 and all the other points are greater than 4
Point 4 is the y-coordinate of the vertex and the graph opens up.
the perimeter of a isosceles triangle is 5(2+root2) find the area
Answer:
12.5
Step-by-step explanation:
If an isosceles right triangle as the length of the equal sides is a , then the length of the hypotenuse will be a2–√ (using pythogoras theorem.
Hence the perimeter will be a+a+a2–√=a(2+2–√)
Hence the equal sides of the triangle in question has the length of a=5
Area of the triangle = 12∗Height∗Base
=12∗5∗5=12.5
JT has coordinates J (-2,-5) and T (2,3). The segment is rotated 180° about the origin to form J'T'. Then J'T' is translated 6 units to the right and 3 units down to form J''T''. What are the coordinates of J'T' and J''T''?
Answer:
(2,5)) ,(-2,-3),(8,2),(4,-6)
Step-by-step explanation:
it is rotated by 180 degree so evrything becomes positve beside the -6
Pls answer I need it
With work!!! Pls...
Answer:
5
Step-by-step explanation:
g(x) = 2 - 3x
g(-1) = 2 - 3(-1)
g(-1) = 2 + 3
g(-1) = 5
____ - 369 = 286?
help a sister out
Answer:
655
Step-by-step explanation:
655-369=286
I hope this is correct and have a great day
Determine if the triangles below are similar or not
Answer:
I dont see them
Step-by-step explanation:
A survey was conducted of students at a high school and at a college to determine students' favorite subjects. The results are shown in the table.
History Math Science Total
High School 80 50 70 200
College 70
60
70 200
Total 150 110 140 400
What percentage of the students are college students that prefer history?
O A. 17.5%
OB. 35%
OC. 37.5%
D. 46.7%
E 75%
Answer: 35%
Step-by-step explanation:
What is the solution set of the quadratic inequality x^2-5<_0
Answer:
b
Step-by-step explanation:
edg
Answer:
B
Step-by-step explanation:
right on edge 2021
How much will her mother donate
what is x? please help!
Answer:
x is 10x-33
Step-by-step explanation:
Long division 4/8,728
Answer:
0.0004582951
Step-by-step explanation:
I just put this equation into a calculator to solve.
Andrew ate 2/3 of the desert. cassandra ate 5/16 of the desert. what portion of the desert did andrew and cassandra eat altogether?
Answer:
Concept: Fractions
A ate 2/3 and C ate 5/16Let us find a common denominator Let 48 be our common DHence 32/48+ 15/48 = 47/48Answer:
The portions added together make 47/48 of the dessert.
Step-by-step explanation:
To find the total amount that Andrew and Cassandra ate of the dessert, we have to add the two fractions together:
[tex]\frac{2}{3} + \frac{5}{16}[/tex]
[tex]\frac{32}{48} + \frac{15}{48}[/tex]
[tex]\frac{47}{48}[/tex]
Hence, Andrew and Cassandra almost ate up all of the dessert, clocking in at 47/48 of the dessert.
Hope this helped!
The slope of the line below is 2. Which of the following is the point-slope form of the line?
The correct point-slope form of the line is A. y + 1 = 2(x - 1).
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Given that the slope of the line is 2 and the point on the line is (1, -1), we can substitute these values into the point-slope form to find the correct equation.
Using the point-slope form, we have:
y - (-1) = 2(x - 1)
Simplifying the equation, we get:
y + 1 = 2(x - 1)
Now we compare this equation to the answer choices:
A. y + 1 = 2(x - 1)
B. y - 1 = -2(x + 1)
C. y + 1 = -2(x - 1)
D. y - 1 = 2(x + 1)
Comparing the equation y + 1 = 2(x - 1) to the given point-slope form, we see that they match.
In this equation, the point (1, -1) lies on the line, and the slope of the line is 2. The equation represents a line with a slope of 2 that passes through the point (1, -1).
For more such questions on point-slope form
https://brainly.com/question/24907633
#SPJ8
1620, 540, 180, 60, 20,...
Find common ratio.
Answer:
multiplying by 3
Step-by-step explanation:
20x3=60 60x3=80. and the rest is the same.
A bee flies at 6 feet Per second directly to a flower bed from its hive. The bee stays at the flower bed for 19 minutes, and then flies directly back to the hive at 4 ft per second. Is away from the high for a total of 24 minutes. What equation can used to find the distance of the flower bed from the hive? How far is the flower bed from the hive?
Answer:
720 feet
Step-by-step explanation:
We can Find the travelling time. We know that the bee spends 19 minutes hunting down the nectar in the flowerbed. But was away from the hive for a total of 24 minutes, then the travelling time becomes(24min - 19min) = 5 min
Then let us Convert to seconds vfir consistency
1 minute = 60 seconds
5 minutes = (5×60 )= 300 seconds.
Then the travelling time becomes 300 seconds
We can Find the time each way, since we know that the total time is 300 seconds, though not evenly divided
Let us denote the time there = t
the time back = (300 - t)
But the distances are the same.
r = 6 m/s and r1 = 4 m/s
t1 = t and t2 = (300 - t)
Let dthere = dback
Where, d =( rate × time)
(6× t )= 4 (300 - t)
6t= 1200 - 4t
10t=1200
t=120 seconds
To Find the distance?
d =( rate × time)
d = ? r = 6 m/s and t = 120 second
d = r*t
d = 6 × 120
= 720 feet
Hence, instance of the flower bed from the hive is 720 feet while the equation is ( d = r*t)
Write two like terms using whatever variable(s) you'd like. Explain why these are like terms.
AQRS contains the points: Q (4,2) R (5.1) S (3.7). If the triangle is reflected across the y-axis, what will she?
Answer:
The answer is (-3, 7) hope this helps
Step-by-step explanation:
Answer:If it's reflected,then it should be (-3.7).
Step-by-step explanation:
Solve
Log(x-1)+log(2)=7
Answer:
x is 6 i believeee if you're solving for x!!
Step-by-step explanation:
Answer:
x = 1 + 0.5 * 10^7
Step-by-step explanation:
Use log(a) + log(b) = log(ab).
log(x-1) + log(2) = 7 <=> log(2(x-1)) = 7 <=> log(2x-2) = 7
Using log(a) = b <=> a = 10^b
log(2x-2) = 7 <=> 2x-2 = 10^7 <=> 2x = 2 + 10^7 <=> x = 1 + 0.5 * 10^7
can someone help me (3.7x10-8)(2.9x10⁶
I need help with my math homework. It would mean a lot to me if someone coupd explain it. Ill type the directions. It says: Using the graphs below, write the linear equation of the line in slope intercept form (use format: no spaces, y=mx+b) ansaers and earn pixels for correct answers. Answer all 18 problems correctly to reveal the pixel art image. Here are the graphs I need to do. Please help me out if you can. I will make another question on my account so I can add more pictures of the graphs because I can only do five on here.
11(4-6y)+5(13y+1)=9 help
Answer:
Y = 40
Step-by-step explanation:
44 - 66y + 65y + 5 = 9
49 - y = 9
-y = -40
y = 40
Answer:
y = 40
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
11(4 - 6y) + 5(13y + 1) = 9
Step 2: Solve for y
Distribute: 44 - 66y + 65y + 5 = 9Combine like terms: -y + 49 = 9Isolate y term: -y = -40Isolate y: y = 40Step 3: Check
Plug in y into the original equation to verify it's a solution.
Substitute in y: 11(4 - 6(40)) + 5(13(40) + 1) = 9Multiply: 11(4 - 240) + 5(520 + 1) = 9Subtract/Add: 11(-236) + 5(521) = 9Multiply: -2596 + 2605 = 9Add: 9 = 9Here we see that 9 does indeed equal 9.
∴ y = 40 is the solution to the equation.
Russia's currency is called the ruble, and is denoted with this symbol: Rub. An electrical contractor has Rub850,360 in his business's bank account.If at the end of the week he deposits Rub119,980 in payments made from clients and then pays out Rub79,205 in wages, how much money will he have left in his account?
Answer:
He will
have RUB 891,135 present to the same government
Step-by-step explanation:
Here, we want to calculate the amount of money that will be left in the account
To get this, we simply subtract the payments and add up the deposits to the initial
Thus, we have;
850,360 + 119,980 - 79,205 = 891,135