Answer:
5 day book fee would be $1.25 and 5 day video is $2.25 + 1.25= $3.50
Step-by-step explanation:
Answer:
$10.00
Step-by-step explanation:
Fee for book: $0.25 * 5 = $1.25
Fee for day: $1.75 * 5 = $8.75
Total fee: $1.25 + $8.75 = $10.00
if two variables are correlated, a change in one must directly produce a change in the other. t or f
If two variables are correlated, a change in one must directly produce a change in the other. (False)
What is the Correlation?Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together. It is a value between -1 and 1 that represents the strength of the relationship between two variables.
False. If two variables are correlated, a change in one may or may not directly produce a change in the other. Correlation means that there is a relationship between two variables, but it does not necessarily mean that one causes the other. It's possible for two variables to be correlated without any causal relationship between them.
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slope of [3,5] and [0,11]
\\(\huge\text{Hey there!}\)
\(\huge\textbf{What is the formula for finding slope?}\)
\(\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}\)
\(\huge\textbf{Often people understand it better by:}\)
\(\mathbf{\dfrac{rise}{run} = slope}\)
\(\huge\textbf{Answering the given question:}\)
\(\mathbf{y_2 \rightarrow 11}\\\\\\\mathbf{y_1 \rightarrow 5}\\\\\\\mathbf{x_2 \rightarrow 0}\\\\\\\mathbf{x_1 \rightarrow 3}\)
\(\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}\)
\(\huge\textbf{Your equation should look like this:}\)
\(\mathbf{\dfrac{11 - 5}{0 - 3} = slope}\)
\(\huge\textbf{Solving for the answer:}\)
\(\mathbf{\dfrac{11 - 5}{0 - 3} = slope}\)
\(\mathbf{\rightarrow \dfrac{6}{-3} = slope}\)
\(\mathbf{\rightarrow 6 \div -3 = slope}\)
\(\mathbf{\rightarrow -2}\)
\(\huge\textbf{Therefore, your answer should be:}\)
\(\huge\boxed{\textsf{S}\frak{lope \rightarrow -2}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
please help in this one
Answer: \(49.79\ m\)
Step-by-step explanation:
Given
The volume of the spherical solid is \(V=123,456\ m^3\)
It is melted to form a solid cube
Suppose the edge length of the cube is \(a\)
The volume of the sphere is \(\frac{4}{3}\pi r^3\)
\(\Rightarrow 123,456=a^3\\\Rightarrow a^3=123,456\\\text{Factorising 123,456}\\\Rightarrow a^3=2^6\times 3\times 643\\\\\Rightarrow a=\sqrt[3]{2^6\times 3\times 643} \\\\\Rightarrow a=4\sqrt[3]{ 3\times 643}\\\\\Rightarrow a=49.79\ m\)
What is the LEAST number of apples that
can be shared equally among either 6,10 or 15 children?
A. 24
B. 30
C. 60
D. 90
Answer:
30 Ans
Step-by-step explanation:
6=2×3
10=5×2
therefore
lcm= 2*3*5=30 Ans
Answer:
I think B
Step-by-step explanation:
Well the first option A is out because it wouldn't be enough for the 10 or 15 kids equally.B seems right because every child would get some apples - equally.C is also equal but it's higher than 30.D is also equal but that would be the maximum number of apples.Shane, Cheryl, and Isaac went to the store to buy school supplies. Shane bought 4 pens, 3 folders, and 2 notebooks for a total of $12.25. Cheryl bought 4 folders and 6 notebooks for a total of $22. Isaiah bought 2 pens, 1 folder, and 3 notebooks for a total of $10.25. How much does each supply cost? Each pen costs $(1.25 0.50 0.75 1.75). Each folder costs $(2.75 1.75 2.50 1.25). Each notebook costs $(2.75 1.75 2.50 1.25).
The cost of each entity: each pen is $\(1.75\), each folder is $\(2.50\), and each notebook is $\(1.75\).
Let's assign variables to the costs of each supply:
Let the cost of each pen be P dollars.
Let the cost of each folder be F dollars.
Let the cost of each notebook be N dollars.
According to the given information, we can form the following equations:
For Shane:
\(4P + 3F + 2N = 12.25 (Equation \ 1)\)
For Cheryl:
\(4F + 6N = 22 (Equation \ 2)\)
For Isaiah:
\(2P + F + 3N = 10.25 (Equation \ 3)\)
To solve this system of equations, we can use substitution or elimination method.
Using the elimination method, let's multiply Equation 2 by 2 and Equation 3 by 4 to eliminate F:
\(8F + 12N = 44 (Equation \ 4)\\8P + 2F + 12N = 41 (Equation \ 5)\)
Now, subtract Equation 4 from Equation 5 to eliminate F:
\(8P + 2F + 12N - (8F + 12N) = 41 - 44\\8P - 6F = -3\)
Simplifying further, we have:
\(8P - 6F = -3 (Equation \ 6)\)
Now, let's multiply Equation 1 by 4 and Equation 3 by 3 to eliminate N:
\(16P + 12F + 8N = 49 (Equation \ 7)\\6P + 3F + 9N = 30 (Equation \ 8)\)
Now, subtract Equation 8 from Equation 7 to eliminate N:
\(16P + 12F + 8N - (6P + 3F + 9N) = 49 - 30\\10P + 9F - N = 19\)
Simplifying further, we have:
\(10P + 9F - N = 19 (Equation \ 9)\)
Now we have a system of equations consisting of Equation 6, Equation 9, and Equation 2:
\(8P - 6F = -3 (Equation \ 6)\\10P + 9F - N = 19 (Equation \ 9)\\4F + 6N = 22 (Equation \ 2)\)
To find the values of P, F, and N, we can solve this system of equations using any suitable method, such as substitution or elimination.
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r is inversely proportionate to a
when r = 12 a = 1.5
work out the value of r when a = 5
work out the value of a when r = 9
Answer:
r = 3.6 , a = 2
Step-by-step explanation:
given that r is inversely proportional to a then the equation relating them is
r = \(\frac{k}{a}\) ← k is the constant of proportion
to find k use the condition when r = 12 , a = 1.5
12 = \(\frac{k}{1.5}\) ( multiply both sides by 1.5 )
18 = k
r = \(\frac{18}{a}\) ← equation of proportion
when a = 5 , then
r = \(\frac{18}{5}\) = 3.6
when r = 9 , then
9 = \(\frac{18}{a}\) ( multiply both sides by a )
9a = 18 ( divide both sides by 9 )
a = 2
Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages
Answer:
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Step-by-step explanation:
Let the present age of Devi be x years.
Therefore, mother's present age = 3x
Five years ago:
Devi's age = (x - 5) years
Mother's age =( 3x - 5) years
According to the given condition:
Five years ago:
Devi's mother's age = 4 times Devi's age
3x - 5 = 4( x - 5)
3x - 5 = 4x - 20
20 - 5 = 4x - 3x
15 = x
x = 15 years
3x = 3* 15 = 45 years
Hence,
Devi's present age = 15 years
Devi's Mother's present age = 45 years
3
87. 8
98
-
8[?].
the question didn’t have enough letters for me to post so i’m using this to post it
Carlos invests £4500 for 3 years.
He receives compound interest of 1.5% per year.
Carlos thinks the total of the money he invests and the interest will be more than
£4750 at the end of the 3 years.
Is he correct?
Show why you think this.
Answer:
He is incorrect.
Step-by-step explanation:
4500 x ( 1 + 1.50%)^3
= 4500 x 1.045678
= 4705.551000
4705.551000 < 4750
Carlos is not correct, because the amount at the end of the 3 years of compounding is £4705.65 not more than £4750.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound \(A=P(1+\frac{r}{100})^{nt}\)
Given that, Carlos invests £4500 for 3 years.
He receives compound interest of 1.5% per year.
Here, amount =4500(1+1.5/100)³
= 4500(1+0.015)³
= 4500(1.015)³
= 4500×1.0457
= £4705.65
Carlos is not correct, because the amount at the end of the 3 years of compounding is £4705.65 not more than £4750.
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While solving an equation, if the variable term becomes zero, and the equation makes a true statement, then the solution is
The equation's remaining constant is the answer if the variable term eventually equals zero and the equation can be said to be true.
By isolating the variable on one side of the equation, we can arrive at a numerical value that satisfies the equation. However, in rare circumstances, the variable term may become zero while the equation is being simplified.
When a common factor is eliminated or an expression containing the variable is simplified, this can take place. The equation has a solution, and that solution is the constant value left over if, after removing the variable element, we arrive at a true assertion.
This is due to the equation's ability to be simplified to a declaration of equality between two constants if the variable term is zero. The constant value is the answer to the equation if the aforementioned assertion is accurate.
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Type the integer that makes the following addition sentence true:
-6 ??? = -8
Answer:
-2
Step-by-step explanation:
-6+x=-8
+6 +6
x=-2
DOUBLE CHECK
-6+(-2)=-8
-6-2=-8
True ✔
---
hope it helps
In the tournament described in Exercise 11 of Section 2.4, a top player is defined to be one who either beats every other player or beats someone who beats the other player. Use the WOP to show that in every such tournament with n players n∈ N, there is at least one top player.
Using the Well-Ordering Principle (WOP), it can be proven that in every tournament with n players (where n is a natural number), there is at least one top player, defined as someone who either beats every other player or beats someone who beats the other player.
We will prove this statement by contradiction. Assume that there exists a tournament with n players where there is no top player. This means that for each player, there exists either another player who beats them or a chain of players such that each player beats the next one. Now, consider the set S of all players in this tournament. Since S is a non-empty set of natural numbers, it has a least element, let's say k.
Now, player k either beats every other player in the tournament, making them a top player, or there exists a player, let's say player m, who beats player k. In the latter case, we have a chain of players: k, m, p_1, p_2, ..., p_t, where p_1 beats p_2, p_2 beats p_3, and so on until p_t.
However, this contradicts the assumption that there is no top player, as either player k beats every other player (if m does not exist), or player m beats someone who beats the other player (if m exists). Hence, by contradiction, we have shown that in every tournament with n players, there is at least one top player.
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A cubic die is biased, so that for each integer n,1≤n≤6 , the probability of the event {n} is p({n})=2p if n=3 or n=4 and p({n})=p , otherwise a) What is the expected number of times the die comes up 6 , when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?
Hence, the answers are a) 9.14 and b) 7.
a) What is the expected number of times the die comes up 6, when it is rolled 32 times?b) What is the expected number of times the die must be rolled until the first 6 comes up?Solutions:Part a) Let X be the number of times the die comes up 6 when it is rolled 32 times.To find the expected number of times the die comes up 6, we'll apply the formula E(X) = np, where n is the number of trials and p is the probability of success on any given trial.If we look at the bias in this particular cubic die, we see that when the event is {6}, then p({6}) = p = 2p/4. This implies that p = 2/7, therefore: E(X) = np = 32*2/7 = 9.14285714286 = 9.14Part b) Let Y be the number of times the die must be rolled until the first 6 comes up.Let's use the geometric distribution to calculate the expected number of rolls E(Y).Since the event "6" has a probability of 1/7, then p = 1/7. Thus, the expected number of times the die must be rolled until the first 6 comes up is given by E(Y) = 1/p, which is 7 rolls.Hence, the answers are a) 9.14 and b) 7.
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mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint?
If Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.
Number of cups of blue paint for each art station = 2 cups
Given that,
One cup = 8 ounce
1 gallon = 128 ounce
2 cups of blue paint = 2 × 8
= 16 ounce of blue paint
1 gallon of blue paint = 128 ounce of blue paint
Number of jars that he can fill with 1 gallon of blue paint = 1 gallon of blue paint / 2 cups of blue paint
Here we have to use division
= 128/16
= 8 jars
Hence, if Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.
The complete question is:
Mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint? One cup = 8 ounce and 1 gallon = 128 ounce
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mr patels home heating system uses oil at the beginning of december there was 500 litres of oil in his tank in anticipation of winter he bought enough oil to fill the tank completely the oil cost 60p per liter and he pain a total amount of 900 at the begining of feb had 300 leters oil left in his tank again he bought enough to fill it completly the cost of ail had incest by 5% work out te totle of the oil cost in feb
Answer:
£756
Step-by-step explanation:
To fill the tank completely, Mr. Patel needed:
500 liters initially + (total capacity of the tank - 500 liters) = 500 + (tank capacity - 500) = tank capacity
To find the tank capacity, we need to know how many liters of oil Mr. Patel bought initially:
Total cost of oil bought initially = 900
Cost per liter of oil = £0.60
Number of liters of oil bought initially = 900 / 0.60 = 1500
Therefore, the tank capacity is:
500 + (tank capacity - 500) = 1500
Tank capacity - 500 = 1000
Tank capacity = 1500 liters
At the beginning of February, Mr. Patel had 300 liters of oil left in his tank, so he needed to buy:
1500 - 300 = 1200 liters of oil
The cost of oil had increased by 5%, so the cost per liter was:
£0.60 + (£0.60 x 0.05) = £0.63
Therefore, the total cost of the oil in February was:
1200 x £0.63 = £756
Linda needs 6/9 cup of strawberries and 3/4 cup mashed peach for a recipe. She wants to find whether she needs more peaches or strawberries. How can you write 6/9 and 3/4 as a pair of fractions with a common denominator?
Answer: Smashed Peach i.e. \(\dfrac{27}{36}\)
Step-by-step explanation:
Given
Linda needs \(\frac{6}{9}\) cup of strawberries
and \(\frac{3}{4}\) cup of mashed peach for a recipe
For two fractions to have the same denominator, take L.C.M. of the denominator
\(\Rightarrow \text{L.C.M.(4,9)}=36\)
\(\therefore \dfrac{6}{9}=\dfrac{6\times 4}{36}=\dfrac{24}{36}\\\\\Rightarrow \dfrac{3}{4}=\dfrac{3\times 7}{36}=\dfrac{27}{36}\)
Therefore, she needs more mashed peach for the recipe.
Suppose that a researcher is interested in estimating the mean systolic blood pressure, , of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate . Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is mm Hg, what is the minimum sample size needed for the researcher to be confident that his estimate is within mm Hg of
The minimum sample size needed in the research of systolic blood pressure is 68.
Given standard deviation=25 mm Hg, confidence level=90%, Estimation =5 mm Hg.
We have to first find the level of alpha which is known as error.
α=(1-0.9)/2
=0.05
Now we have to find z in the z table as such z has a p value of 1-α,that is z with a p value of 1-0.05
=0.95 ,so Z=1.645.
now finding the margin of error, which is as under:
\(M=z st/\sqrt{n}\)
in which st is standard deviation and the n is sample size of population.
By assuming the standard deviation of 25 mm Hg we get values as under:
n is sample size.
\(M=z* st/\sqrt{n}\)
\(5=1.645*25/\sqrt{n}\)
\(5\sqrt{n}=1.645*25\\\)
dividing both sides by 5
\(\sqrt{n}=1.645*5\)
squaring both sides we get
n=67.65.
Hence the sample size needed by the researcher is 68.
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The given question is incomplete as it should includes :
standard deviation= 25mm Hg
Confidence level=90%
Estimation 5 mm Hg of u.
Determine if 27/44 is a rational number or not.
Answer:
rational
Step-by-step explanation:
A rational number can be expressed in the form
\(\frac{a}{b}\) ← where a and b are integers
Given
\(\frac{27}{44}\) ← where 27 and 44 are both integers, then it is a rational number
You have at most $20.75 to spend at a fair. Rides cost $0.50 each, and games cost $2 each. Let r be numbers of rides and g be numbers of games. Write an inequality that represents the numbers of rides and games you can afford.
Do not include the dollar sign ($) in your inequality.
An inequality is _.
Answer:
0.5r+2g>=20.75
Step-by-step explanation:
is Average velocity equation rearranged to find the area under the curve?
Yes, the equation of velocity is rearranged to find the area under the curve.
The equation of velocity in general is v = d/t
where v = velocity, d = distance, and t = time.
We rearrange this equation to create an equation for distance and the equation of distance determines the area under the curve.
Our motive is to isolate the variable whose equation we want to create. So, in this case, isolate 'd' and move all other variables to the other side.
1. Multiply both sides by t
v × t = d/t × t
2. Cancel the t where appropriate
v × t = d
3. We get the equation for d
d = v × t
Now, this equation is used to find the area under the curve.
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Triangle ABC has the following angle measures:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
What is m∠A?
pleaseee help
The measure of angle A in the triangle is 18°
How to determine the measure of angle A?The angles in the triangle are given as:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
The sum of angles in a triangle is 180
So, we have
m∠A + m∠B + m∠C = 180
Substitute the known values in the above equation
So, we have:
2x − 24 + x + 8 + 4x + 49 = 180
Evaluate the like terms
7x = 147
Divide both sides by 7
x = 21
Substitute x = 21 in m∠A = (2x − 24)°
m∠A = (2 * 21 − 24)°
Evaluate
m∠A = 18°
Hence, the measure of angle A in the triangle is 18°
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The _______ name of a number is how it sounds when we say its name the long way.
Answer:
Word. The word name
Step-by-step explanation:
I hope this helps you :)
PLEASE HELP!!! Using technology, graph these functions and find the solution to the system.
f(x) = x²+x-4
g(x) = -2x2-2x+14
(-2.5, 5) and (1.5, 5)
(-4, 14)
(-3, 2) and (2, 2)
No solution: They do not intersect.
The solution of the functions given will be (-3, 2) and (2, 2) as we can see in graph.
What is the definition of a function?
In mathematics, a function is a rule that associates each element in one set, called the domain, with a unique element in another set, called the range. In other words, a function is a relation between two sets such that each element in the domain is paired with exactly one element in the range.
A function can be represented by an equation, a graph, a table, or a verbal description. The notation f(x) is often used to represent a function, where f is the name of the function and x is the input (or independent variable). The output (or dependent variable) is then given by f(x).
Now,
For functions f(x) = x²+x-4
g(x) = -2x²-2x+14
the graph will be made as shown in image
and their intersection points will be the solution of the given functions
Hence,
The solution of the functions given will be (-3, 2) and (2, 2) as shown in graph.
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Solve these problems and give the answer with the correct number of significant figures: (4.307×10^4)×(6.2×10^−3)= 26.127+3.9+0.0324=
Let's solve the problems and provide the answers with the correct number of significant figures:
(4.307 × 10^4) × (6.2 × 10^-3)
Multiplying the numbers:
(4.307 × 6.2) × (10^4 × 10^-3) = 26.6974 × 10^1
Since the result is in scientific notation, we multiply the decimal part by the power of 10:
26.6974 × 10^1 = 266.974
To express the answer with the correct number of significant figures, we consider the least number of significant figures in the original values, which is three significant figures in this case.
Therefore, the answer is 267 with three significant figures.
26.127 + 3.9 + 0.0324
Adding the numbers:
26.127 + 3.9 + 0.0324 = 30.0594
To express the answer with the correct number of significant figures, we consider the least number of decimal places in the original values, which is one decimal place in this case.
Therefore, the answer is 30.1 with one decimal place.
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Determine whether y varies directly with x . If so, find the constant of variation.
y=6 x
The constant of variation in y = (6)x is (6)
y = kx (Where k is the constant)
Here,
⇒ y = (6)x
So, k = (6)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Write as a mathematical expression. The product of 5 and x.
O 5/x
O 5+x
O 5-x
O 5x
Answer:
5x
Step-by-step explanation:
The word "product" is used for multiplication.
Kim has a part-time job assembling bicycles for a local store. each day, she earns $20 plus $15 for each bike assembled. kim's boss daily goal is to assemble no more than 6 bicycles a day. if x represents the number of bikes assembled, the total amount she earns can be represented by . what is the range for the function for this situation?
The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.
The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).
The total amount she earns can be represented by
y = 15x + 20
where y is her daily earnings and x is the number of bikes she assembles
If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).
domain : {x| 0 ≤ x ≤ 6}
where x is a whole number
Substituting the minimum and maximum value of x in the function.
y = 15(0) + 20 when x = 0
y = 20
y = 15(6) + 20 when x = 6
y = 110
range : $20 ≤ y ≤ $110
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The midpoint of AB is M(0, – 7). If the coordinates of A are (-2,-6),
what are the coordinates of B?
Answer:
The answer is
( 2 , - 8)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
\(M = ( \frac{x_1 + x_2}{2} , \: \frac{y_1 + y_2}{2} ) \\ \)
where
(x1 , y1) and (x2 , y2) are the points
Let's represent the coordinates of B by
( x , y)
So we have
\((0 \: , \: - 7) = ( \frac{ - 2 + x}{2} \: , \: \frac{ - 6 + y}{2} )\)
To find the x and y - coordinates of B , we compare the the x and y coordinates of the left side to the ones on the right
So we have
For the x coordinate
\(0 = \frac{ - 2 + x}{2} \\ 0 = - 2 + x \\ \\ x = 2\)
For the y coordinate
\( - 7 = \frac{ - 6 + y}{2} \\ - 14 = - 6 + y \\ y = - 14 + 6 \\ \\ y = - 8\)
So the coordinates of B is
( 2 , - 8)Hope this helps you
Answer:
( 2 , - 8)
Step-by-step explanation:
Anna bought snacks for her team's practice. She bought a bag of oranges for $3.27 and a 4-pack of juice bottles. The total cost before tax was $5.03. How much was each bottle of juice?
Answer: $____
Answer:
0.44 cents per bottle
Step-by-step explanation:
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I need to simplify each side of the equation, THEN solve each equation.
Answer:
x=-8
Step-by-step explanation:
4x+8=16+5x
4x-5x=16-8
-x=8
x=-8