The total number of servings is given by the equation A = 60 servings
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of servings from 3 quarts be A
Now , the equation will be
The number of servings for 5 cups of milk = 25 servings
So , the number of servings for 1 cup = 25 / 5
The number of servings for 1 cup of milk = 5 servings
And , 1 quart = 2 pints
1 pint = 2 cups
So , 1 quart = 4 cups
And , 3 quarts = 12 cups
So , The number of servings for 3 quarts or 12 cups of milk = 12 x number of servings for 1 cup of milk
Substituting the values in the equation , we get
The number of servings for 3 quarts or 12 cups of milk A = 12 x 5
The number of servings for 3 quarts or 12 cups of milk A = 60 servings
Therefore , the value of A is 60 servings
Hence , the number of servings is 60
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Solve the equation by using the quadratic formula.
3x² - 1 = 7x
Answer:
Solutions: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]Step-by-step explanation:
We are given the following quadratic equation, 3x² - 1 = 7x, which requires us to find its possible solutions using the quadratic formula.
Definitions:In a quadratic equation, the leading term has a second-degree (or squared) variable. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers, and that a ≠ 0. Quadratic Formula:The quadratic formula is given by:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
We will use this formula to solve for the roots or the solution of the given quadratic equation.
Solution:Step 1: transform the given equaton into standard form.
First, we must subtract "7x" from both sides of the equation:
3x² - 7x - 1 = 7x - 7x
3x² - 7x - 1 = 0 ⇒ This is the standard form of the given quadratic equation where a = 3, b = -7, and c = - 1.
Step 2: Plug in the values for a, b, & c into the quadratic formula.
The derived values for a, b, & c from the previous step are: a = 3, b = -7, and c = - 1. Substitute these values into the following quadratic formula:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{(-7)^2-4(3)(-1)}}{2(3)}}[/tex]
Step 3: Following the PEMDAS Order of Operations, start by applying the Power rule of Exponents [tex]\displaystyle\mathsf{(a^m)^n = (a^{m*n})}[/tex] (under the radical) :
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{49-4(3)(-1)}}{2(3)}}[/tex]
Step 4: Next, multiply the integers under the radical, PEMDAS Order of Operations.
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{61}}{2(3)}}[/tex]
Step 5: Multiply the integers in the denominator, and apply the multiplication integer rule, -(-a) = a.
[tex]\displaystyle\mathsf{x\:=\:\frac{7\pm\sqrt{61}}{6}}[/tex]
Since [tex]\displaystyle\mathsf{\sqrt{61}}[/tex] is not a perfect square, it can remain the same.Step 6: Separate the solutions.
[tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , and [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]
Final Answer:Therefore, the solution to 3x² - 1 = 7x are: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex], [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex].
_____________________Keywords:Quadratic equation
Quadratic function
Standard form
Parabola
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An engineer wants to test the complex and dangerous process of filling and emptying a tank of liquid hydrogen. The tank has a volume of 400 cm3. The tank can be filled 50 cm3 per hour faster than it can be emptied.
Part A. Write an expression for the number of hours it takes to fill this tank, in terms of r
Part B. Wrote an expression for the number of hours it takes to empty this tank, in terms of r:
Part C. Wrote an equation for the total time in hours it takes to fill and empty this tank in terms of r. Simplify.
Part D. Find the rate that would allow you to fill and empty the tank in 100 hours. Check for extraneous solutions, and show your work. Round to the nearest tenth.
Answer:
the answer is 45%.
Step-by-step explanation:
if you add 5% divided by 3 = 15%.
So if you add all of those plus the 30% you will be getting 45%.
select all the expressions that are equivalent to 4 x 4 x 4 x 4 x 4
a. 4
b.5⁴
c.4² x 4³
d. 5² x 4(5)
e. 4¹ x 4(5)
Answer:
c
Step-by-step explanation:
4 x 4 x 4 x 4 x 4 = 1,024
-----
a. 4
b. 625
c. 1,024
d. 500
e. 80
Hey there!
4 × 4 × 4 × 4 × 4
= 16 × 16 × 4
= 256 × 4
= 256 + 256 + 256 + 256
= 512 + 512
= 1,024
Looking for something that’s equivalent to: 1,024
Option A. is INCORRECT because it is too small.
Option B. 5^4
5^4
= 5 × 5 × 5 × 5
= 25 × 25
= 625
Option B. is also INCORRECT because it is also too small.
Option C. 4^2 × 4^3
4^2 × 4^3
= 4^5
= 4 × 4 × 4 × 4 × 4
= 16 × 16 × 4
= 256 × 4
= 1,024
Option C. could possibly be one of the answers
Option D. 5^2 × 4(5)
5^2 × 4(5)
= 5 × 5 × 20
= 25 × 20
= 500
Option D. is also INCORRECT because it’s too small.
Option E. 4^1 × 4(5)
4^1 × 4(5)
= 4 × 4(5)
= 4 × 20
= 20 + 20 + 20 + 20
= 40 + 40
= 80
Option E. is last to be INCORRECT because it is also too small
MET the ANSWER:
Therefore, your answer is: Option C.
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Jo and Val are a couple. Jo's monthly net earnings are $4000, and Val's are $6000. Following the 80/20 rule, how much should the couple save every month?
Answer:
about 400
Step-by-step explanation:
Solve the inequality.
21 < 2x + 3
Answer:
x>9 I included a picture of the number line as well
Answer:
The answer is 9 > x
Step-by-step explanation:
Hope that helps!
can u answer with steps?
If the ratio a: b = 2 : 3, and b : c = 3 : 4. Find the ration a : c
ASAP
Answer:
if a:c=2:3 andb:c=3:4therefore a:c=2:4
Which statement does not describe a normal distribution?
A. The distribution can have two modes.
B. Most of the observations are near the mean.
C. The number of observations trails off as you move away from the
mean.
D. The median and mean are equal.
A .the distribution observation can have two modes
How many triangles can we make with two 7-centimeter sides. Explain why
Answer:
infinite number
Step-by-step explanation:
We can make infinite number of triangles with two 7-centimeter sides as long as the third side is less than 7 + 7 = 14 cm
Aiko works in the fish department of a pet store. She is asked to drain, clean, and refill two reef tanks.
The first tank holds 175 gallons of water and the second tank holds 200 gallons of water. The hoses that
she uses drain the tanks at a rate of 25 gallons of water per hour.
1. write an equation for each tank that represents the total amount of water in the gallons in the tank in terms of the number of hours that the tanks are draining
tank one equation ________
tank two equation ________
2. how much water is in each tank after 3 hours?
tank one ___
tank two___
The equation for the first tank will be 175 - 25h and the equation for the second tank is 200 - 25h.
How to solve the equation?From the information given, the first tank holds 175 gallons of water and the second tank holds 200 gallons of water while the hoses that she uses drain the tanks at a rate of 25 gallons of water per hour.
Therefore, the equation for the first tank will be:
= 175 - (25 × h)
= 175 - 25h
The equation for the second tank will be:
= 200 - (25 × h)
= 200 - 25h
The quantity in the first tank after three hours will be:
= 175 - 25h
= 175 - (25 × 3)
= 175 - 75
= 100 gallons.
The quantity in the second tank after three hours will be:
= 200 - 25h
= 200 - (25 × 3)
= 200 - 75
= 125 gallons.
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How do you write 48,600,000 in scientific notation?
Answer:4.8^10 power of 7
Step-by-step explanation:
Find the value of x, y, and z in the rhombus below
Answer:
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so [tex]6x+8=86 \longrightarrow x=13[/tex]
Also, adjacent angles of a rhombus are supplementary, so [tex]86+5z+4=86+7y+3=180 \longrightarrow y=13, z=18[/tex]
Find the range, median, upper extreme, lower extreme, and interquartile range of the following data: 85, 85, 2, 1, 204, 123, 24, 139, 20
in how many ways can 8 people line up for movie tickets
Answer:
40320 way
Step-by-step explanation:
Given:
In how many ways can 8 people line up for movie tickets?
You can do the following:
⇒ Tree diagram
⇒ List
⇒ Table
⇒ Multiply
Solve:
For me, I like to use Multiply for this question.
1 ×2×3×4×5×6×7×8
2 ×3×4×5×6×7×8
6×4×5×6×7×8
24×5×6×7×8
120 ×6×7×8
720×7×8
5040×8
40320
Hence, in 40320 ways can 8 people line up for movie tickets.
~Learn with Lenvy~
PLEASE HELP!!
WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!
Graph the line with slope 1/3 passing through the point (-4,-5).
Answer:
graphing done below.
Step-by-step explanation:
using the formula: y - y₁ = m(x - x₁)
equation:
[tex]\sf y - -5 = \frac{1}{3} (x - - 5)[/tex]
[tex]\sf y +5 = \frac{1}{3} x + \frac{5}{3}[/tex]
[tex]\sf y = \frac{1}{3} x + \frac{5}{3}-5[/tex]
[tex]\sf y = \frac{1}{3} x - \frac{10}{3}[/tex]
The colony of bacteria grows according to the law of inhibited growth of a function N(t)=100e^0.045t where N is measured in grams and t is measured in days. Determine the initial amount of bacteria.
4,000 i savings at end of 3 years earn 960 in simple interest how much in account
Answer:
She would have had $120 more should the rate were 1% greater.
Step-by-step explanation:
At the end of 3 years the amount in the account = Principal + Interest
Amount = 4000 + 960 = 4960
Amount at the end of 3 years = $4960
b) Formula for Rate , R = 100I/(PT)
Where I = Interest = 960, P = Principal = 4000, T= Time = 3 years
R = (100 × 960) / ( 4000 × 3)
R = 8
Rate, R = 8% per annum.
c) If the rate was 1% more, R = 8 + 1 = 9% per annum
Interest, I = PRT/100
Interest, I = 4000 × 9 × 3 /100 = 1080
Amount in her account would have been = $4000 + $1080 = $5080
Amount more = $5080 - $4960 = $120
Which function is the inverse of f(x) = (x − 3)3 + 2?
Answer: f = 3x -7 / x
Step-by-step explanation:
fx=(x−3)(3)+2
Step 1: Divide both sides by x.
fx/x = 3x -7 / x
f = 3x -7 / x
Answer: f = 3x -7 / x
Roger can type 1530 words in 1/2 hour. How many words can he type per
minute?
PLS HELP ME
Answer:
25.5
Step-by-step explanation:
1530 divided by 60 is 25.5 and 25.5 multiplied by 60 is 1530.
An ordinary (falr) dle is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a dle is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 8.
Event B: The sum is divisible by 5.
Write your answers as fractions.
(a) P(X) =
(b) P(B) =
By finding the number of outcomes that meet each criteria, we will see that the probabilities are:
A) P = 0.25B) P = 7/36 = 0.194How to find the probability?
We know that the fair die has 6 outcomes, so if we roll it twice, there are a total of:
6*6 = 36 outcomes.
To find the probability of getting a given event, we need to find the number of outcomes that make the event true.
A) The sum is greater than 8.
The outcomes that make this true are:
first roll second roll sum
4 5 9
4 6 10
5 5 10
5 6 11
6 3 9
6 4 10
6 5 11
6 6 12
3 6 9
So there are 9 outcomes whose sum is greater than 8, so the probability to getting this event is:
P = 9/36 = 0.25
B) The sum is divisible by 5.
The sum must be 5 or 10, the outcomes that give that are:
first roll second roll sum
1 4 5
2 3 5
3 2 5
1 4 5
4 6 10
5 5 10
6 4 10
There are 7 outcomes, so the probability is:
P = 7/36 = 0.194
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i once met six siblings whose ages are 6 consecutive whole numbers. i asked each of them the question how old is your oldest sibling. which of the following could not be the sum of their answers.
A. 95
B. 125
C. 167
D. 205
E. 233
The consecutive ages of the siblings mean that each sibling is a year older than the younger sibling
All the options cannot be the sum of their ages
How to determine the sum of their ages
Represent the age of the smallest sibling with x.
So, the sum of their ages is:
[tex]Sum =x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5[/tex]
Evaluate the like terms
[tex]Sum =6x + 15[/tex]
When the sum is 95 (from the options), we have:
[tex]6x + 15 = 95[/tex]
Subtract 15 from both sides
[tex]6x = 80[/tex]
Divide by 6
[tex]x = 13.3[/tex] -- this is not an integer
When the sum is 95 (from the options), we have:
[tex]6x + 15 = 125[/tex]
Subtract 15 from both sides
[tex]6x = 110[/tex]
Divide by 6
[tex]x = 6.875[/tex] -- this is not an integer
When the sum is 167 (from the options), we have:
[tex]6x + 15 = 167[/tex]
Subtract 15 from both sides
[tex]6x = 152[/tex]
Divide by 6
[tex]x = 25.33[/tex] -- this is not an integer
When the sum is 205 (from the options), we have:
[tex]6x + 15 = 205[/tex]
Subtract 15 from both sides
[tex]6x = 190[/tex]
Divide by 6
[tex]x = 31.67[/tex] -- this is not an integer
When the sum is 233 (from the options), we have:
[tex]6x + 15 = 233[/tex]
Subtract 15 from both sides
[tex]6x = 218[/tex]
Divide by 6
[tex]x = 36.33[/tex] -- this is not an integer
Hence, all the options cannot be the sum of their ages
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Answer:
Step-by-step explanation:
Bethany bought 42 liters of water for the running team. There are 16 members on the team. If each member gets an equal amount of water, how many liters does each memberget?
Write expression 4+ k as a verbal statement
Answer:
Four plus a number= a number
Step-by-step explanation:
I got this from my teacher
What is the current temperature in Fahrenheit on the thermometer below?
A.
B.
C.
D.
Answer:
the answer is D just did the quiz hope this helps!!!!!
Step-by-step explanation:
Which graph correctly represents the quadratic equation?
D (last slide) is the graph to the given equation.
As the equation is positive, the line of the graph will give smile shape.
Graph plotted below:
calculate the area of the rigt triangle
Answer:
Area = 1/2 × base × height
A = 1/2 × 5 × 3,3/5
= 9
find the slope of the line through the given points (-6,17),(-6,13)
Answer:
As Per Provided Information
Given points are (-6,17) & (-6,13).
here
x₁ = -6
x₂ = -6
y₁ = 17
y₂ = 13
We have been asked to find the slope of the line.
Using Formula
[tex] \bf \: m \: = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
m is the slope of line
Put the given value we get
[tex] \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 - ( - 6)}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 + 6}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \dfrac{0}{ - 4} \\ \\ \\ \qquad \sf \longrightarrow \: m = 0[/tex]
Therefore,
Slope of the line is 0 .pls help with this math homework.
Answer:
the first answer is 2/6 and 4/6 both (pick)
Step-by-step explanation:
second is 8/12
third is 9/15
fourth is 16/72
fifth is 2/5,
sixth is 4/10
seventh is 8/18
last one is 2/8
X3-Y3=28, X-Y=2, X2+XY+Y2=
it is = 14 but how?
Step-by-step explanation:
x³ - y³ = (x - y)³ + 3x²y - 3xy²
28 = (2)³ + 3xy(x - y)
28 = 8 + 3xy(2)
28 - 8 = 6xy
20 = 6xy → xy = 20/6 = 10/3
(x - y)² = 2²
x² - 2xy + y² = 4
x² - 2(10/3) + y² = 4
x² + y² = 4 + 20/3 = 32/3
x² + xy + y² = 32/3 + 10/3 = 42/3 = 14
First, create 3 equations of the form ax+by+cz=d , where a, b, c, and d are constants (integers between – 5 and 5). For example, x+2y-z=-1 . Perform row operations on your system to obtain a row-echelon form and the solution.
Go to the 3D calculator website GeoGebra: www.geogebra.org/3d?lang=pt and enter each of the equations.
After you have completed this first task, choose one of the following to complete your discussion post.
1. Reflect on what the graphs are suggesting for one equation, two equations, and three equations, and describe your observations. Think about the equation as a function f of x and y, for example, x+2y+1=z in the example above. Geogebra automatically interprets this way, that is, like z=f(x, y)=x+2y+1 , it isolates z in the equation.
Answer:
The solution is x=0, y=0, z=1
Step-by-step explanation:
Step1: -row2 + row1; -row2 + row3
x + 2y - z = -1
x + y + z = 1
x - y - z = -1
1 2 -1 -1
1 1 1 1
1 -1 -1 -1
0 1 -2 -2
1 1 1 1
0 -2 -2 -2
Step 2: row3/-2
0 1 -2 -2
1 1 1 1
0 1 1 1
step 3: -row3 + row1
0 0 -3 -3
1 1 1 1
0 1 1 1
step 4: row1/-3
0 0 1 1
1 1 1 1
0 1 1 1
step 4: -row1 + row3; -row1 + row2
0 0 1 1
1 1 0 0
0 1 0 0
step 5: -row3 + row2
0 0 1 1
1 0 0 0
0 1 0 0
The reduced row echelon form is:
1 0 0 0
0 1 0 0
0 0 1 1
what is the solution for 11 = y-6
Answer:
y = 17
Step-by-step explanation:
11 = y - 6
11 + 6 = y17 = yprove that the value of y is 17
11 = y - 6
11 = 17 - 611 = 11proven
Hello.
Let's solve this equation for y.
First, subtract 11 from both sides:
[tex]\mathrm{11-11=y-6-11}[/tex]
[tex]\mathrm{0=y-6-11}[/tex]
[tex]\mathrm{0=y-17}[/tex]
Subtract y from both sides:
[tex]\mathrm{-y=-17}[/tex]
[tex]\Large\boxed{\sf{y=17}}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]