The given function 3(t^4)-19 is thus written using the function rule in notations as: f(t) = 3(t^4)-19 for the input-output machine.
Explain about the function notation?Although equations are frequently used to represent functions, a sequence of equations all beginning with y = may make it difficult to distinguish between different functions.
So, giving functions names is a great touch. Functions and their variables are named in function notation.A function that involves the variables x and y can be expressed in the form y = "some expression involving x," or y = f(x) .By reading the last sentence as "y equals f of x," it is indicated because y is a function of x.A function called f is defined by the notation f(x).
This should be understood as "y is a function of x."The input value, called independent variable, is represented by the letter x.The output value, meaning dependent variable, is represented by f(x) in place of the letter y.The given function 3(t^4)-19 is thus written using the function rule in notations as:
f(t) = 3(t^4)-19.
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what even number is not a composite number 6,4,2,8
Answer: 2
Step-by-step explanation:
Answer and Explanation: The only even number that is not a composite number is 2. All even numbers are defined as numbers that are divisible by, or have a divisor of, 2.
Answer:
The answer to your question is, 2
Step-by-step explanation:
The reason why that is our answer is because, 2 can either be multiplied and divided but 2 NUMBERS.
Such as the following:
2 / 1 = 2.
1 x 2 = 2.
What is a composite number?
A composite number are numbers that have more than two factors like the number 2:
2 / 1 = 2.
1 x 2 = 2.
Thus the answer to your problem is, 2
Plot the points A(-6,-4), B(3, -8), C(7, 1) on the coordinate axes below. State the coordinates of point � D such that � A, � B, � C, and � D would form a rectangle.
The coordinates of point D are (-2,5) and the points given have been plotted. The solution has been obtained by using the distance formula.
What is distance formula?
The distance between two points can be calculated using the xy-plane distance formula.
We are given that ABCD should form a rectangle.
We know that opposite sides of a rectangle are equal.
So, AB = CD
Using the distance formula which is
d = √(x₂ - x₁)² + (y₂ - y₁)²
We get
⇒AB = √(3 - (-6))² + (-8 - (-4))²
⇒AB = √(3 + 6)² + (-8 + 4)²
⇒AB = √(9)² + (-4)²
⇒AB = √81 + 16
⇒AB = √97 ...(1)
Let the coordinates of Point D be (x, y)
So, similarly
⇒CD = √(x - 7)² + (y - 1)² ...(2)
On equating (1`) and (2), we get
⇒√97 = √(x - 7)² + (y - 1)²
On squaring both sides, we get
⇒97 = (x - 7)² + (y - 1)²
⇒97 = x² + 49 - 14x + y² + 1 - 2y
⇒97 = x² + 50 - 14x + y² - 2y
⇒47 = x² - 14x + y² - 2y ...(3)
Also, AC = BD as these are the opposite sides of the rectangle.
Using the distance formula, we get
⇒AC = √(7 - (-6))² + (1 - (-4))²
⇒AC = √(7 + 6)² + (1 + 4)²
⇒AC = √(13)² + (5)²
⇒AC = √169 + 25
⇒AC = √194 ...(4)
Similarly,
⇒BD = √(x - 3)² + (y - (-8))²
⇒BD = √(x - 3)² + (y + 8)² ...(5)
On equating (4`) and (5), we get
⇒√194 = √(x - 3)² + (y + 8)²
On squaring both sides, we get
⇒194 = (x - 3)² + (y + 8)²
⇒194 = x² + 9 - 6x + y² + 64 + 16y
⇒194 = x² + 73 - 6x + y² + 16y
⇒121 = x² - 6x + y² + 16y ...(6)
On subtracting (3) and (6), we get
8x + 18y = 74
On dividing by 2, we get
4x + 9y = 37
From this, we get
x = (37 - 9y) / 4
Substituting this in (3), we get
⇒47 = [(37 - 9y) / 4]² - [14 * [(37 - 9y) / 4]] + y² - 2y
On solving this, we get
y = 5
On substituting this in x, we get
x = (37 - 9(5)) / 4
x = (37 - 45) / 4
x = -8 / 4
x = -2
Hence, the coordinates of point D are (-2,5) and the points given have been plotted.
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consider the points P(0,0,1), Q(1,0,2), R(3,3,2) and let A be the area of triangle PQR. Select the correct interval for A.
a. A < 2
b. 2 <= A < 4
c. 4 <= A < 6
d. 6 <= A < 8
e. A >= 8
The correct interval for the area of triangle PQR is 2 <= A < 4.
To find the correct interval for the area of triangle PQR, we first need to calculate the area using the given points. We can do this by using the formula for the area of a triangle in three dimensions:
A = (1/2) * sqrt((x2*y3 - x3*y2)^2 + (x3*y1 - x1*y3)^2 + (x1*y2 - x2*y1)^2)
Plugging in the given points for P, Q, and R, we get:
A = (1/2) * sqrt((1*3 - 3*0)^2 + (3*0 - 0*1)^2 + (0*0 - 1*3)^2)
Simplifying, we get:
A = (1/2) * sqrt(9 + 9)
A = (1/2) * sqrt(18)
A = (1/2) * 3 * sqrt(2)
A = (3/2) * sqrt(2)
A = 2.12
Therefore, the correct interval for the area of triangle PQR is 2 <= A < 4. The correct answer is option b. 2 <= A < 4.
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Q1. Let \( A=\left[\begin{array}{lll}a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a\end{array}\right] \), where \( a \in \mathbb{F} \). Prove that \[ A^{n}=\left[\begin{array}{ccc} a^{n} & n a^{n-1} & \frac{n(n-
To prove that \[ A^{n}=\left[\begin{array}{ccc} a^{n} & n a^{n-1} & \frac{n(n-1)}{2}a^{n-2} \end{array}\right], we will use mathematical induction.
Base case: For \( n=1 \), \( A^{1}=A \). This is true since
\[ A=\left[\begin{array}{ccc} a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a \end{array}\right] \]
which matches the left side of our equation.
Inductive step: Assume that the statement is true for some \( n=k \), i.e.
\[ A^{k}=\left[\begin{array}{ccc} a^{k} & ka^{k-1} & \frac{k(k-1)}{2}a^{k-2} \end{array}\right] \]
We will now show that it is true for \( n=k+1 \).
\[ A^{k+1}=A^{k}\cdot A \]
We substitute the induction hypothesis into this equation and get:
\[ A^{k+1}=\left[\begin{array}{ccc} a^{k} & ka^{k-1} & \frac{k(k-1)}{2}a^{k-2} \end{array}\right]\cdot \left[\begin{array}{ccc} a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a \end{array}\right] \]
Calculating the matrix product yields:
\[ A^{k+1}=\left[\begin{array}{ccc} a^{k+1} & (k+1)a^{k} & \frac{(k+1)k}{2}a^{k-1} \end{array}\right] \]
which matches the left side of our equation, completing the proof.
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What is the least common denominator for his problem? A, b, c, or d
Answer:
the answer is "c"! :)
Step-by-step explanation:
2. Mrs. Roberts' dog, Rover, loves to eat peanuts. A large can of peanuts has a diameter of 4
inches and a height of 6 inches. The small can that she plans to purchase has the same diameter
but is 1/3 of the height of the large can. What is the approximate volume of the small can?
The volume of the small can is 25.12 inches cube.
How to find the volume of the small can?Mrs. Roberts' dog, Rover, loves to eat peanuts. A large can of peanuts has a diameter of 4 inches and a height of 6 inches. The small can that she plans to purchase has the same diameter but is 1/3 of the height of the large can.
Therefore, the approximate volume of the small can can be found as follows:
Hence,
volume of the small can = πr²h
where
r = radiush = heightTherefore,
r = 4 / 2 = 2 inches
h = 1 / 3 (6) = 2 inches
Hence,
volume of the small can = 3.14 × 2² × 2
volume of the small can = 3.14 × 4 × 2
volume of the small can = 3.14 × 8
volume of the small can = 25.12 inches cube
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Knowledge Check Add. (9)/(8)+(4)/(-3) Write your answer as a fraction in simplest form.
(9)/(8)+(4)/(-3) = (5)/(-24)
A. To add the fractions (9)/(8) and (4)/(-3), we need to find a common denominator. The common denominator of 8 and -3 is -24.
So, we will multiply the numerator and denominator of the first fraction by -3 and the numerator and denominator of the second fraction by 8. This will give us:
(-3)(9)/(-3)(8) + (8)(4)/(8)(-3)
B. Simplifying the numerators and denominators gives us:
(-27)/(-24) + (32)/(-24)
Now, we can add the numerators and keep the common denominator:
(-27 + 32)/(-24)
Simplifying the numerator gives us:
(5)/(-24)
Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 1:
(5/1)/(-24/1)
This gives us the final answer of:
(5)/(-24)
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A puppy weighed 28 ounces on Monday. It gained 7 ounces in one week. What is the percent increase of the puppy's weight rounded to the nearest percent?
The percent increase of the puppy's weight is 25%
How to calculate the percentage increase of the puppy's weight?A puppy weighed 28 ounces on Monday
It gained 7 ounces in one week
Total weight is = 28 + 7
= 35
The percent increase can be calculated as follows
= 35/28
= 1.25
= 1.25-1
= 0.25 × 100
= 25%
Hence the percent increase of the puppy's weight is 25%
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(a) Work out the value of x in each of the following.
[tex]16 ^{x} = 4[/tex]
The value of x from the exponential equation is x = 1/2
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
16ˣ = 4
On simplifying , we get
From the laws of exponents , we get mᵃ×mᵇ = mᵃ⁺ᵇ
So , 16ˣ = 4
when x = 1/2
16^(1/2) = 4
On further simplification , we get
√16 = 4
4 = 4
Therefore , the value of x is 1/2
Hence , the exponential equation is solved and the value of x = 1/2
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Knowledge Check Divide. (x+6)/(3x+9)-:(7)/(9x)+42 Simplify your answer as much as possible.
(3x²+18x)/(7x+21) is the simplified answer of (x+6)/(3x+9)-:(7)/(9x)+42.
To divide the given expressions, we need to first simplify the expressions as much as possible and then use the rule for dividing fractions. The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction.
Simplifying the expressions:
(x+6)/(3x+9) = (x+6)/(3(x+3)) = (x+6)/3(x+3)
(7)/(9x) = 7/9x
Now, using the rule for dividing fractions:
((x+6)/3(x+3)) ÷ (7/9x) = ((x+6)/3(x+3)) * (9x/7)
= (9x(x+6))/(3(x+3)*7)
= (3x(x+6))/(x+3)*7
= (3x²+18x)/(7x+21)
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What are the x-intercepts of the quadratic function?
f(x)=x^2+6x−27
enter your answer in the boxes
blank and blank
Step-by-step explanation:
To find the x-intercepts of the quadratic function f(x) = x^2 + 6x - 27, we need to set f(x) equal to zero and solve for x.
So we have:
f(x) = 0
x^2 + 6x - 27 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 6, and c = -27.
Substituting these values into the quadratic formula, we get:
x = (-6 ± sqrt(6^2 - 4(1)(-27))) / 2(1)
x = (-6 ± sqrt(180)) / 2
x = (-6 ± 6sqrt(5)) / 2
x = -3 ± 3sqrt(5)
So the x-intercepts of the quadratic function are approximately -10.16 and 4.16.
A $900 item is on sale for 20% off.
What is the final price with 7% sales tax?
Money off:
Amt, of tax:
Money paid:
Final price:
AW
IN. I need help I’m stuck
A $900 item on the sale of 20% discount the
Money off: $180
Amt. of tax: $50.40
Money paid: $770.40
Final price: $770.40
what is discount ?
A discount is a reduction in the price of an item or service, often offered as a promotion or incentive to encourage customers to make a purchase. The discount is usually expressed as a percentage of the original price and represents the amount of money that the customer can save on the purchase.
For example:
Percentage discount: a certain percentage of the original price is deducted from the selling price. For example, a 20% discount on a $100 item would reduce the price to $80.
According to the question:
To calculate the final price of the item with sales tax, we can follow these steps:
Calculate the amount of money off by multiplying the original price by the discount percentage:
Money off = 0.20 x $900 = $180.
Calculate the price after the discount by subtracting the money off from the original price:
Price after discount = $900 - $180 = $720.
Calculate the amount of sales tax by multiplying the price after discount by the tax rate:
Amount of tax = 0.07 x $720 = $50.40.
Calculate the money paid by adding the price after discount and the amount of tax:
Money paid = $720 + $50.40 = $770.40.
Therefore, the final price with 7% sales tax is $770.40.
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During a rugby contest 54342 people what's the first game or 49990 people what's the second game if 156330 people watched all three games how many what's the third game
The answer would be 51,998
The diagonals of a rhombus measure 8cm and 6cm .what is the length of a side of the rhombud
All sides of the given rhombus measure 5 cm respectively.
What is a rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry.
The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Quadrilaterals having four congruent sides are called squares.
Squares are rhombuses by definition since they are quadrilaterals with four congruent sides.
So, consider the following values: AC = 8 cm, BD = 6 cm, OD = OB = 3 cm, and OA = OC = 4 cm.
Now,
OB² + OC² = BC²
3²+ 4² = BC²
9 + 16 = BC²
25 = BC²
5 = BC
A rhombus has an equal number of sides.
Therefore, all sides of the given rhombus measure 5 cm respectively.
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Angle N = 40 degrees, side NP = 8, angle Q = 40 degrees, and side QS = 8. What additional information would you need to prove that ΔNOP ≅ ΔQRS by ASA?
a
Angle O is congruent to angle R.
b
Angle P is congruent to angle S.
c
Side NO is congruent to side QR.
d
Side OP is congruent to side RS.
Answer:
Option d: Side OP is congruent to side RS.
To prove that ΔNOP ≅ ΔQRS by ASA, we need to show that:
1. ∠N ≅ ∠Q (given)
2. Side NP ≅ Side QS (given)
3. Side OP ≅ Side RS (additional information needed)
Hence, option d is the correct answer.
336 fewer the the product of u and 258 is 168
Answer:
335.6511628
Step-by-step explanation:
Ux258-336=168
U-336=0.6511628
U=336.6511628
What is the Average salary of 125, 110, 95, 80, 70, 54
Answer: $89
Step-by-step explanation:
to find average add up all numbers and divide by how many there are
so, do
(125+110+95+80+70+54)/6
which equals 89
find the variation constant and an equation of variation where y
varies inversely as x and y = 11 when x = 2
the variation constant is...
The variation constant is 22 and the equation of variation where y varies inversely as x is y = 22/x.
When two variables, y and x, are inversely proportional, it means that as one variable increases, the other variable decreases proportionally, and vice versa. Mathematically, this can be expressed as:
y = k/x
where k is the variation constant. To find k, we can use the given information that "y = 11 when x = 2". Substituting these values into the inverse variation equation above, we get:
11 = k/2
Multiplying both sides by 2, we get:
k = 22
So, the variation constant is 22.
Now, we can write the equation of variation as:
y = 22/x
This means that as x increases, y decreases proportionally. For example, if x doubles to 4, y would be halved to 5.5, keeping the product (xy) constant.
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In triangle FGH shown below, what is the measure of ∠
F in degrees?
Record your answer on the keypad.
Answer:
∠F = 19.5
Step-by-step explanation:
180 - 127 - 33.5 = 19.5
Please Help! owo
1. Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $5. The price of each drink was $3. This can be represented by the equation 5x + 3y = 30
(a) Sketch the graph that represents the situation. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks
(b) Explain your graph and what the intercepts mean.
The coordinates (x,y) to sketch the graph is mentioned below. (b) The intercepts of the graph represent the situations where one of the items is not purchased.
Describe Graph?A graph is a visual representation of data that shows the relationship between variables. It consists of a set of points or vertices, connected by lines or curves called edges or arcs. Graphs are commonly used in mathematics, statistics, and other fields to display information in a way that is easy to understand and interpret.
a) To sketch the graph, we can create a table of values for the equation 5x + 3y = 30:
Bags of Popcorn (x) Drinks (y) Total Cost
0 10 30
1 8 30
2 6 30
3 4 30
4 2 30
6 0 30
Then we can plot the points from the table on a graph with the number of bags of popcorn on the x-axis and the number of drinks on the y-axis. Connecting the points gives us a line that represents all possible combinations of bags of popcorn and drinks that cost $30.
b) The intercepts of the graph represent the situations where one of the items is not purchased. The x-intercept (0,10) represents the situation where no bags of popcorn are purchased, so all $30 is spent on 10 drinks. The y-intercept (6,0) represents the situation where no drinks are purchased, so all $30 is spent on 6 bags of popcorn. The slope of the line represents the rate at which the cost of one item changes relative to the cost of the other item. In this case, the slope is -5/3, which means that for each bag of popcorn purchased, the cost of drinks decreases by $5/3.
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What is the answer for -3i²
Answer:
The answer is 3
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
The correct equation for the sentence is: 24 = 31.4n - 8.4.
Twenty-four is equal to 31.4 times a number plus a negative 8.4 multiplied by the proper equation, which is:
24 = 31.4n - 8.4
This formula can be rewritten as follows:
31.4n = 24 + 8.4
And after being distilled:
31.4n = 32.4
Finally, by multiplying both sides by 31.4, we can find the value of n:
n = 32.4/31.4
Thus, the following is the proper equation for the phrase:
24 = 31.4n - 8.4.
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can anyone please help me with this question -2u^5(-6u^3)
The simplified expression is [tex]12u^8[/tex].
What is simplification?
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.
Here the given expression is ,
=> [tex]-2u^5(-6u^3)[/tex]
Now simplifying the expression,
=> [tex]-2\times -6 \times u^5 \times u^3[/tex]
=> 12[tex]u^{5+3}[/tex]
=> [tex]12u^8[/tex]
Hence the simplified expression is [tex]12u^8[/tex].
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Please help me with this math question.
Answer:120
Step-by-step explanation:
Hey everyone and anyone of anybody could please help me with this math worksheet i would greatly appreciate it
The side x is 30 miles
The unknown side is 346 yards
What is the sine rule?The sine rule, also known as the law of sines, is a formula that relates the sides and angles of a non-right triangle (a triangle that does not have a 90-degree angle). The sine rule states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides of the triangle.
1) Using the sine rule;
x/sin 65 = 32/sin75
xsin75 = 32sin65
x = 32sin65/sin75
x = 30 miles
2) The angle = π/3 = 180/3 = 60 degrees
Using the cosine rule;
c^2 = (200)^2 + (400)^2 - (2 * 200 * 400) cos 60
c^2 = 200,000 - 80,000
c = 346 yards
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Houa is ordering a taxi from an online taxi service. The taxi charges $4 just for the pickup and then an additional $2 per mile driven. How much would a taxi ride cost if Houa is riding for 2 miles? How much would a taxi ride cost that is mm miles long?
Answer:
A) $8
B) 4+2x
Step-by-step explanation:
If it costs $2 for every mile driven, and Huoa rides for 2 miles, then you multiply 2×2=4. Then you add another $4 for the $4 the driver charges for just getting in, so 4+4=8
Another way to do that is to use the equation that's the answer for part B. As you don't know the number of miles, you substitute that unknown number for x.
4+2x
The x represents the number of miles
The 2 represents the amount charged for each mile
The 4 represents the flat fee for getting into the car
If you plug 2 (for the 2 miles driven) into the equation you get:
4+2(2)
4+4
8
Perform the addition or subtraction and simplify.
x
x2 + x − 2
−
9
x2 − 5x + 4
The final simplified expression turns out to be "-8x^2 + 6x - 6"
To perform the addition or subtraction and simplify the expression, we need to combine like terms and simplify the expression. First, we need to subtract the second expression from the first one:
x^2 + x − 2 - (9x^2 − 5x + 4)
Next, we need to distribute the negative sign to each term in the second expression:
x^2 + x − 2 - 9x^2 + 5x - 4
Now we can combine like terms:
-8x^2 + 6x - 6
This is the simplified expression. Therefore, the answer is:
-8x^2 + 6x - 6
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Aaron invested $7,500 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 8 years?
Answer:
The formula for calculating the amount of money in an account with continuous compounding is:
A = Pe^(rt)
Where:
A = the amount of money in the account after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time (in years)
Substituting the given values into the formula, we get:
A = 7500e^(0.0158)
A ≈ $9,071.21
Therefore, to the nearest hundred dollars, there would be $9,100 in the account after 8 years.
Step-by-step explanation:
PLEASE HELPP. jackie had 2 equal sized bottles. The first bottle contains 1 quart of water. the second bottle contains 5/9 quarts of water what amount of water must jackie pour from the first bottle into the second so that both bottles have tge samw amout of water. Express your answer as a fraction explain your answer using bar models
Jackie needs to pour 2/9of a quart of water from the first bottle to the second bottle to make them have the same amount of water.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us assume that we transfer an amount "x" from the first bottle to the second bottle.
This means that the first bottle will have 1-x quarts of water, while the second bottle will have 5/9 + x quarts of water.
Now, we want to find the value of "x" that makes both bottles have the same amount of water.
We can set up an equation:
1-x = 5/9 + x
We can then solve for "x" by adding "x" to both sides and subtracting 5/9 from both sides:
1 - 5/9 = 2x
4/9 = 2x
x = 2/9
Hence, Jackie needs to pour 2/9 of a quart of water from the first bottle to the second bottle to make them have the same amount of water.
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Can somebody PLEASE help me ASAP? I really need help. It’s due today!! Please show work!! I will give brainliest.
Answer:
1. c
2. b
3. a
Step-by-step explanation:
Surface Area of a cylinder = 2πrh + 2πr²
1. 2(3.14)(5)(11) + 2(3.14)(5)² = 502.4
2. 2(3.14)(6)(10) + 2(3.14)(6)² = 602.88
3. 2(3.14)(2)(12) + 2(3.14)(2)² = 175.84