If the balance will be $1370.55 after 6 years, then The balance will be $1711.03 after approximately 14.3 years.
The formula for calculating the balance in a continuously compounded account is:
[tex]A = Pe^{rt}[/tex]
Where:
A = final balance
P = principal (initial deposit)
e = Euler's number (approximately 2.71828)
r = annual interest rate
t = time in years
We know that the initial deposit is $1000 and the balance after 6 years is $1370.55, so we can use these values to solve for the annual interest rate:
[tex]1370.55 = 1000*e^{6r}[/tex]
⇒ [tex]ln(\frac{1370.55}{1000}) = 6r[/tex]
⇒ [tex]r = \frac{ln(\frac{1370.55}{1000})}{6}[/tex]
⇒ [tex]r = 0.0345[/tex]
Now we can use the same formula to find out when the balance will be $1711.03:
[tex]1711.03 = 1000*e^{(0.0345*t)}[/tex]
⇒ [tex]ln(\frac{1711.03}{1000}) = 0.0345*t[/tex]
⇒ [tex]t = \frac{ln(\frac{1711.03}{1000})}{0.0345}[/tex]
⇒ t = 14.3 years.
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Which correlation coefficient reflects the strongest relationship?
a) +0.05
b) +0.25
c) +1.23
d) -0.33
The correlation coefficient that reflects the strongest relationship is +0.25, the correct option is b.
EXPLANATION:
The correlation coefficient ranges from -1 to +1.
The magnitude (absolute value) of the correlation coefficient indicates the strength of the relationship, with values closer to -1 or +1 indicating a stronger relationship.
Therefore, the correlation coefficient that reflects the strongest relationship is +1.23.
However, since this value is greater than +1, which is not possible, it seems to be an invalid value.
Among the given options,
The correlation coefficient that reflects the strongest relationship is b) +0.25.
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At a school of 550 children 80% walk to school
If at a school of 550 children 80% walk to school, the 110 children come to school by other means.
If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).
To find out how many children come to school by other means, we can use the following formula:
Number of children who come to school by other means = Total number of children x Percentage who don't walk to school
In this case, we have:
Number of children who come to school by other means = 550 x 20% = 110
Therefore, 110 children come to school by other means.
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The given question is incomplete, the complete question is:
At a school of 550 children 80% walk to school, how many comes in other way ?
Select the correct answer. Simon used these steps to solve an equation: Step 1: -6(x + 7) = 2(x − 11) Step 2: -6x − 42 = 2x − 22 Step 3: -8x − 42 = -22 Step 4: -8x = 20 Which property did he use to get from step 3 to step 4? A. addition property of equality B. distributive property C. subtraction property of equality D. transitive property
Answer: A - addition property of equality
Explanation: because -8x - 42 = -22
+42 +42
____________
-8x = 20
__ __
-8 -8
x = -2.5
(BRAINLIEST) A baker sells cupcakes and bases her prices on the number of cupcakes purchased.
The graph shows a piecewise function with one piece increasing from the point 0 comma 0 through the point 12 comma 18 to the endpoint 24 comma 36 and another piece going from the point 24 comma 36 through the point 48 comma 60 and increasing to the right.
Based on the graph, what is the pricing the baker uses for her sales?
The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 24 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
The first 36 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 36 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
Answer: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
Step-by-step explanation:
The graph shows two pieces of the function, with one increasing from the point (0, 0) through the point (12, 18) to the endpoint (24, 36) and the other increasing from the point (24, 36) through the point (48, 60) to the right.
This means that the first 24 cupcakes cost $1.50 each and all cupcakes after that cost $1 each, as shown by the first piece of the function. The second piece of the function shows that the price per cupcake does not increase after 36 cupcakes, so option 3 and option 4 can be eliminated.
Therefore, the correct answer is: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
Each yoga mat measures 2.2 ft by 6.3 ft. What is the area in square feet of each yoga mat?
The radius of the circular base of a cone measures 2.6 inches, and its slant height measures 1.5 inches.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest tenth in the box.
Answer:
11.6 sq. inches
Step-by-step explanation:
The lateral area of a cone can be found using the formula:
L = πrℓ
where r is the radius of the circular base and ℓ is the slant height.
Substituting in the given values, we have:
L = 3.14 x 2.6 x 1.5
L ≈ 11.6
Rounding to the nearest tenth, the approximate lateral area of the cone is 11.6 square inches.
Justin wants to buy a new football that costs 22.99. He has a discount coupon of 12% off. If Justin has exactly $20, does he have enough money to buy the football with the coupon? How much more money does he need OR how much money does he get in change?
He needs an additional $0.23 to buy the football with the coupon after the discount coupon.
What is Discount?A discount is a reduction in the price of a product or service. It is often used as a marketing tool to attract customers and increase sales. Discounts can be expressed as a percentage or a dollar amount.
What is discounted price?The discounted price is the price of a product or service after a discount has been applied. The discount is usually expressed as a percentage or a dollar amount and is subtracted from the original price.
In the given question,
The discount Justin can get is 12% of the original price, which is:
0.12 x 22.99 = 2.76
So the discounted price of the football is:
22.99 - 2.76 = 20.23
Since Justin has exactly $20, he doesn't have enough money to buy the football with the coupon. He needs:
20.23 - 20 = 0.23
So he needs an additional $0.23 to buy the football with the coupon.
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Which number is a perfect square
Responses
2
8
16
20
Answer:
16
Step-by-step explanation:
because it is a square number. The other numbers, if you square root them you won't get a whole number.
jamal throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. after how many seconds does the ball hit the ground? (1,16) (2,0) area amd projectile motion
Answer:
Step-by-step explanation:
Please help 20 points I’ve been struggling :(
5x + 4y = -16
Complete the steps to convert the equation in standard form to Slope intercept form
Answer: I'm pretty bad at math, but I made it more simple for you :)
Step-by-step explanation:
The answer is y = 4 + 5x/4
I hope it helped a bit sorryy
find the missing value to the nearest hundredth cos__=7/18
67.11
37.67
22.89
21.25
The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.
The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.
cos θ = 7/18
= arccos(7, 18, 7)
A 1.1181 radian angle
We can use the conversion factor /180 to convert radians to degrees.
θ = 1.1181 × 180/π
64.12 degrees.
As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.
Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.
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Tolosa sold 540 eggs if these are 35% of total eggs,then how many eggs are not sold?
The total number of eggs is 1542.
To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:
35/100 = 540/x
where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:
35x = 54000
x = 54000/35
x = 1542.86
Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.
To find the number of eggs that are not sold, we can subtract the number of eggs sold from the total number of eggs:
1542 - 540 = 1002
Find out more about The total number of eggs is 1542.
To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:
35/100 = 540/x
where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:
35x = 54000
x = 54000/35
x = 1542.86
Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.
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Please help I’ll give brainliest
The solutions to the equation [tex]15z^2 +6z -8 =4z[/tex] are z = 2/3 or z = -4/5.
To solve the quadratic equation [tex]15z^2 +6z -8 =4z[/tex], we first need to rearrange it into standard form:
[tex]15z^2 + 2z - 8 = 0[/tex]
Now we can apply the quadratic formula:
z = (-b ± √(b² - 4ac)) / 2a
where a = 15, b = 2, and c = -8.
Plugging in these values, we get:
z = (-2 ± √(2² - 4(15)(-8))) / (2(15))
z = (-2 ± √(4 + 480)) / 30
z = (-2 ± √484) / 30
z = (-2 ± 22) / 30
So z equals either (-2 + 22)/30 = 2/3 or (-2 - 22)/30 = -4/5.
Therefore, the solutions to the equation 15z² +6z -8 =4z are z = 2/3 or z = -4/5.
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Cullumber Beauty Corporation manufactures cosmetic products that are sold through a network of sales agents. The agents are paid a commission of 21% of sales. The income statement for the year ending December 31,2022 , is as follows. Under the current policy of using a network of sales agents, calculate the Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022. Break-even point
Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022 is $1,200,000.
What is the break-even point?
The break-even point is defined as the point at which a company's overall costs are equal to its total revenue. The company neither makes a profit nor incurs a loss at this point. The break-even point in dollar amount is calculated by dividing the fixed costs by the contribution margin ratio.The given information is:Net sales revenue = $3,500,000Commission expense = 21% of sales = 0.21 * $3,500,000 = $735,000Net sales revenue − Variable costs = Contribution marginContribution margin − Fixed costs = Operating incomeBreak-even point is the level of sales revenue required to cover all of a company's costs. At this point, the operating income is zero. The fixed expenses are divided by the contribution margin ratio to find the break-even point in dollars.
Fixed expenses = [tex]$900,000[/tex]Net sales revenue − Variable costs = Contribution marginContribution margin − Fixed expenses = Operating income0 = Net sales revenue − Variable costs − Fixed expenses0 = [tex]$3,500,000 − (0.75 × $3,500,000) − $900,0000.25 × $3,500,000 = $900,000$875,000 = $900,000[/tex] − Commission expense[tex]$3,500,000 − $875,000 = $2,625,000[/tex]
Break-even point = $900,000 ÷ (0.75 × $3,500,000)Break-even point = $900,000 ÷ $2,625,000Break-even point = 0.34 ≈ 34%Break-even point in sales dollars = 34% × $3,500,000Break-even point in sales dollars = $1,190,000 ≈ $1,200,000Therefore, Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022 is $1,200,000.
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A. 1/2 + 1/4
B. 5/6 + 5/12
C. 13/14 + 5/7
D. 3/4 + 5/24
Please
In Problem 3, determine the level of measurement of each variable. 1. Birth order among siblings in a family
2. Volume of water used by a household in a day
3. Highest degree conferred (high school, bachelor’s, and so on)
4. Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years
1) Birth order among siblings in a family: Nominal level of measurement
2) Volume of water used by a household in a day: Ratio level of measurement
3) Highest degree conferred (high school, bachelor's, and so on): Ordinal level of measurement
4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: Interval level of measurement
1) Birth order among siblings in a family: This variable is measured at the nominal level of measurement, as there is no inherent order or ranking to the categories
2) Volume of water used by a household in a day: This variable is measured at the ratio level of measurement, as it has a true zero point (i.e., no water usage) and the values can be compared in terms of ratios
3) Highest degree conferred (high school, bachelor's, and so on): This variable is measured at the ordinal level of measurement, as the categories have an inherent order or ranking (e.g., a bachelor's degree is higher than a high school diploma, but it does not necessarily indicate that someone with a bachelor's degree is "twice as educated" as someone with a high school diploma).
4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: This variable is measured at the interval level of measurement, as the values have a meaningful order and distance between them (i.e., the difference between 4 years and 5 years is the same as the difference between 7 years and 8 years). However, there is no true zero point, as "zero years old" is not a meaningful category in this context.
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When K is small, x is also small.The "x is small" approximation only works when: the initial concentration of the reactant is relatively large and the equilibrium constant is small.The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesnt' change that number by very much.The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is is less than 5% (or 0.05).The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small.
What does the "x is small" approximation mean? The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesn't change that number by very much. When does the "x is small" approximation work? The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small. What is the <5% rule? The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is less than 5% (or 0.05). What is the method of successive approximation? The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
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Please Help! I don't understand this question!
Answer:
all you gotta do is mirror that half u and make it a full u
and since the points it intersects at is (1,-1) plot the other half on (1,1)
please I really need help by tmr!!
How many intersections are there between the graphs of f(x) = 0.8x and g(x) = \lfloor x \rfloor?
The answer is one intersection.
What is a function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
The graph of the function f(x) = 0.8x is a straight line with slope 0.8 passing through the origin (0, 0). The graph of the function g(x) = ⌊x⌋ is the collection of all points (x, y) where y is the greatest integer less than or equal to x. This function is not continuous and has a discontinuity at each integer.
To find the intersections between the two graphs, we need to determine where the values of f(x) and g(x) are equal.
we need to find the integer values of x where 0.8x and x are equal.
0.8x = x
0.2x = 0
x = 0
Thus, the two graphs intersect at the point (0, 0). There are no other intersections between the two graphs, since they have different slopes and one is continuous while the other is not. Therefore, the answer is one intersection.
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Los números que hace verdadera a una ecuación se les denomina
pre-event tickets for a local theater fundraiser cost $35 and $40 for at-the-door tickets. organizers sell a total of 250 tickets and generate a total revenue of $9,375. how many pre-event and at-the-door tickets were sold?
This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
The local theater fundraiser sold 200 pre-event tickets at $35 each and 50 at-the-door tickets at $40 each to generate a total revenue of $9,375. This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
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Help please…… i need it
The sides of 15mm, 28mm and 11mm are the sides of a triangle.
What is the triangle inequality theorem?To determine if three given lengths can form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
If we add the two shorter sides together, we get [tex]15 + 11 = 26[/tex] . This sum is greater than the longest side, which is [tex]28[/tex] . Similarly, if we add the two smaller sides to the longest side, we get [tex]11 + 28 = 39[/tex] and [tex]15 + 28 = 43[/tex] , which are both greater than the remaining side.
Therefore, the three given lengths satisfy the Triangle Inequality Theorem and can form a triangle.
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solve for x, using a tangent and secant line
Check the picture below.
[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]
The value of x is 4.5 rounded to the nearest tenth.
What is Tangent and Secant of a Circle?Tangent of a circle is defined as the line which passes through exactly one point on the circle.
Secant of a circle is the line which passes through two points on the circle.
Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.
Using the theorem, we can say here that,
(8 + 2) 2 = x²
x² = 10 × 2
x² = 20
x = √20
x = 4.472 ≈ 4.5
Hence the value of x is 4.5.
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help pls
1. Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern.
2. Use a proof by mathematical induction to show that your equation from question 1 applies to the minimum number of moves required to defeat the Tower of Hanoi game, based on the number of disks you must move. Think about the process of the game; and describe how your equation applies to it.
The minimum number of moves required to complete the Tower of Hanoi game is related to the number of disks, and can be described by the equation m = [tex]2^n - 1[/tex].
Let n be the number of disks and m be the minimum number of moves required to complete the Tower of Hanoi game. Renae's observations suggest that the equation m = [tex]2^n - 1[/tex] describes this pattern.
When n=1, the minimum number of moves required to complete the game is m=1. Plugging this value into the equation m=[tex]2^n-1[/tex]gives m=[tex]2^1-1[/tex]=1. Therefore, the equation holds true for n=1.
Assume that the equation holds true for n=k. That is, m=[tex]2^k-1[/tex] is the minimum number of moves required to complete the game with k disks.
Now, consider the case where n=k+1. This requires a minimum of m=[tex]2^k-1[/tex] moves, according to the equation. Then, the largest disk can be moved to the ending peg in one move. Finally, the k disks that were moved to the spare peg must be moved to the ending peg, which requires another minimum of m=[tex]2^k-1[/tex] moves.
Thus, the total minimum number of moves required to complete the game with k+1 disks is:
m = [tex]2(2^k-1) + 1[/tex]
m = [tex]2^(k+1) - 2 + 1[/tex]
m = [tex]2^(k+1) - 1[/tex]
This is the same as the equation we started with, but with k+1 in place of n. Therefore, the equation holds true for all positive integers n by mathematical induction.
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Shaila is riding on a rollercoaster when her phone falls out of her pocket. The phone followed the equation y=−16t2+400
where y
gives the height of the phone after t
seconds. How long did it take her phone to hit the ground?
The phone hit the ground after seconds.
Answer:
5 seconds
Step-by-step explanation:
when the phone hits the ground then y = 0 , that is
- 16t² + 400 = 0 ( subtract 400 from both sides )
- 16t² = - 400 ( divide both sides by - 16 )
t² = 25 ( take square root of both sides )
t = [tex]\sqrt{25}[/tex] = 5
the phone hits the ground after 5 seconds
Answer:
5 seconds
Step-by-step explanation:
y = [tex]-16t^{2} + 400 \\[/tex]
Make t the subject:
[tex]16t^{2} = -400\\t^{2} = \frac{400}{16} = 25\\ t = \sqrt{25} = 5[/tex]
Therefore the answer is 5 seconds
candace is designing a card game with a standard deck of cards. each player gets points based on collecting groups of cards. which statements are true about certain groups of cards? select all of the true statements.
The true statements are:
a) P(3) = 4/52 or 1/13
b) P(black number cards) = 18/26 or 9/13
c) P(red ace) = 2/52 or 1/26
d) P(face card) = 12/52 or 3/13
Define the term Probability?Probability deals with the study of random events and their likelihood of occurrence. It is computed by dividing the proportion of positive results by the total number of possibilities that could occur.
As we know that the standard deck card has 52 cards, in which 26 red cards (13 are diamonds, 13 are hearts) 26 black cards (13 are clubs, 13 are spades). Where 12 cards are face cards, 36 cards are number cards.
a) P(3) = 4/52 or 1/13: This is true. There are four 3s in a standard deck of 52 cards, so the probability is 4/52 or 1/13.
b) P(black number cards) = 18/26 or 9/13: This is a true. There are 26 black cards, out of those there are 9+9=18 black number cards (2 through 10), so the probability of drawing a black number card is 18/26 or 9/13.
c) P(red ace) = 2/52 or 1/26: This is true. There are two red aces in a standard deck of 52 cards, so the probability of drawing a red ace is 2/52 or 1/26.
d) P(face card) = 12/52 or 3/13: This is a true. There are twelve face cards in a standard deck of 52 cards, so the probability of drawing a face card is 12/52 or 3/13.
e) P(even number card) < P(odd number card): This is a false. There are 5×4=20 even number cards (2, 4, 6, 8, and 10 of each suit) and 4×4=16 odd number cards (3, 5, 7, 9 of each suit) in a standard deck of 52 cards. Therefore, the probability of drawing an even number card, (20/52 or 5/13) is greater than the probability of drawing an odd number card, (16/52 or 4/13).
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Complete question-
Solve for x and y and how.
Answer:
The lines that go through all 3 sides of the triangle mean the angles are all equal. Since a triangle is 180 degrees, to find a single angle, we must divide by 3.
180 degrees / 3 = 60 degrees
Solve for X
60 = (2x + 10)
-10 from both sides:
50 = (2x)
x = 25
Solve for Y
60 = (3y + 3)
-3 from both sides:
57 = (3y)
y = 19
Hope that helps
(a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope.
(b) Write the equation using function notation where .
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
Slope intercept form:
The slope-intercept form of a line is given by
y = mx + c
Where 'm' is slope and c in y-intercept
Here we have
The coordinate of points (0, -8) and slope (m) = 3/2
As we know the formula for slope intercept form is y = mx + c
Where 'm' is the slope
=> y = (3/2)x + c
=> -8 = 3/2(0) + c
=> c = - 8
Hence, Equation of the line is y = 3/2(x) + (-8)
=> y = 3x/2 - 8
The equation can be rewritten using function notation as follows
=> f(x) = 3x/2 - 8
Therefore,
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
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Simplify: the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6
The simplified form of the expression the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6 is -0.3267
To simplify this expression, we'll work from the inside out, using the order of arithmetic operation
First, we'll evaluate the expression inside the parentheses:
(2 - 5 + 6) = 3
Next, we'll calculate the squared difference of 2 and 5:
(2 - 5)^2 = (-3)^2 = 9
Then, we'll subtract the result from step 2 from the result of step 1:
3 - 9 = -6
Next, we'll calculate the sum of 6.6 and 3.2:
6.6 + 3.2 = 9.8
Finally, we'll divide the result from step 4 by 5 times the result from step 3:
9.8 / (5 × -6) = 9.8 / -30
= -0.3267 (rounded to four decimal places)
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what is an equivalent expression to 4x(2x-3)-5(3x-4)
Answer:4x + 3x + 2x - 4 - 3
Step-by-step explanation:Hope this helps