To determine how long to leave $7500 in the bank at 6% interest compounded semi-annually to reach $16200, use the compound interest formula. Solving for t, time in years, yields approximately 11.9 years for the investment to grow to the desired amount.
Explanation:To calculate how long the person must leave their money in the bank for it to grow from $7500 to $16200 with an interest rate of 6% compounded semi-annually, we'll use the formula for compound interest:
A = P(1 + \frac{r}{n})^{nt}
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the number of years the money is invested for.We are given:
A = $16200P = $7500r = 0.06 (since 6% must be converted to a decimal)n = 2 (because the interest is compounded semi-annually)Our goal is to solve for t, the time in years. Plugging the known values into the formula:
$16200 = $7500(1 + \frac{0.06}{2})^{2t}
Divide both sides by $7500:
2.16 = (1 + \frac{0.06}{2})^{2t}
Now take the natural logarithm of both sides:
ln(2.16) = ln((1 + \frac{0.06}{2})^{2t})
Use properties of logarithms to bring down the exponent:
ln(2.16) = 2t \cdot ln(1 + \frac{0.06}{2})
Divide both sides by 2ln(1 + \frac{0.06}{2}) to solve for t:
t = \frac{ln(2.16)}{2 \cdot ln(1 + \frac{0.06}{2})}
t = \frac{ln(2.16)}{2 \cdot ln(1.03)}
Using a calculator, we find t ≈ 11.9 years. Therefore, the person must leave the money in the bank for approximately 11.9 years to reach $16200.
To the nearest tenth of a year, the person must leave the money in the bank for approximately 13 years.
To find the time required for the investment to reach $16200, we can use the formula for compound interest:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- ( A ) is the amount of money accumulated after ( t ) years.
- ( P ) is the principal amount (the initial investment).
- ( r ) is the annual interest rate (in decimal form).
- ( n ) is the number of times interest is compounded per year.
- ( t ) is the time the money is invested for (in years).
Given:
- ( P = 7500 )
- ( A = 16200 )
- ( r = 0.06 ) (6% interest, converted to decimal)
- Interest is compounded semi-annually, so ( n = 2 )
Step 1 :We need to solve for ( t ):
[tex]\[ 16200 = 7500 \left(1 + \frac{0.06}{2}\right)^{2t} \][/tex]
[tex]\[ \frac{16200}{7500} = \left(1 + 0.03\right)^{2t} \][/tex]
[tex]\[ 2.16 = \left(1.03\right)^{2t} \][/tex]
Take the natural logarithm of both sides:
[tex]\[ \ln(2.16) = \ln\left(\left(1.03\right)^{2t}\right) \][/tex]
[tex]\[ \ln(2.16) = 2t \cdot \ln(1.03) \][/tex]
Step 2 :Now, solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{\ln(2.16)}{2 \cdot \ln(1.03)} \][/tex]
[tex]\[ t \approx \frac{0.7693}{2 \cdot 0.0296} \][/tex]
[tex]\[ t \approx \frac{0.7693}{0.0592} \][/tex]
[tex]\[ t \approx 13 \][/tex]
So, to the nearest tenth of a year, the person must leave the money in the bank for approximately 13 years.
Simplify (2√6÷√2+√3)+(6√2÷√6+√3)-(8√3÷√6+√3)
The given expression simplifies to 0.
To simplify the expression (2√6÷√2+√3)+(6√2÷√6+√3)-(8√3÷√6+√3), we need to simplify each term and then combine like terms. Let's break it down step by step:
Simplify 2√6÷√2 by realizing that √6÷√2 is equivalent to √3. So, 2√3 remains.
In the second term, 6√2÷√6, √6÷√6 simplifies to 1, so we just have 6√2.
For the last term, 8√3÷√6, √3÷√6 simplifies to √(3÷6), which simplifies further to √(1÷2), or 8÷√2.
Combine like terms with the common denominator of √3, resulting in:
(2√3 + 6÷√3 - 8÷√3).
The terms with the square root denominators can be combined into (-2√3).
After combining, we have (2√3 - 2√3), which simplifies to 0. Therefore, the simplified expression is 0.
Solve the solution of equations.
3x + 4y = -23
X = 3y + 1
X =
Y =
Answer:
x = -5y = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+4y=-23&(1)\\x=3y+1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\3(3y+1)+4y=-23\qquad\text{use the distributive property}\\\\(3)(3y)+(3)(1)+4y=-23\\\\9y+3+4y=-23\qquad\text{subtract 3 from both sides}\\\\13y=-26\qquad\text{divide both sides by 13}\\\\\boxed{y=-2}\\\\\text{Put the value of }\ y\ \text{to (2)}:\\\\x=3(-2)+1\\\\x=-6+1\\\\\boxed{x=-5}[/tex]
Answer:
x = -5
y = -2
Step-by-step explanation:
Amal drives her car for work.
She claim 40p per mile from her employer.
Amal’s car travels 52 miles for each gallon of petrol.
She pays £5,36 per gallon for petrol.
On one journey Amal drives 260 miles.
For this journey, how much more does she claim than she pays for petrol?
Answer:
£7,878
Step-by-step explanation:
she gets:
40p× 260 miles = 10,400p
she pays:
52 : 5.36= £9.70 per mile
260 x 9.70 = £2,522
to find out what she claimes more than she pays: 10,400 - 2,522 = 7,878
Amal claims £77.2 more than what she spends on petrol for a 260 miles journey for work.
Explanation:To solve this problem, we need to calculate how much Amal earns for the journey and how much she pays for petrol.
First, let's calculate how much she earns: she claims 40p per mile and she drives 260 miles. So, her earnings would be 40p/mile * 260 miles = £104.Next, we determine how much she spends on petrol. Her car travels 52 miles per gallon, and she pays £5,36 per gallon. As the total distance driven is 260 miles, she will need 260 miles / 52 miles/gallon = 5 gallons. Total cost for petrol then is 5 gallons * £5.36/gallon = £26.8.Finally, to determine how much more Amal claims than she spends on petrol we subtract the petrol costs from what she earns: £104 - £26.8 = £77.2.Learn more about Cost Analysis here:https://brainly.com/question/34407434
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which equation represents the graph?
A) y=[x] + 2.5
B) y=[x] -2.5
C) y=[x -2.5]
D) y=[x + 2.5]
Answer:
y= |x|-2.5
Step-by-step explanation:
The attached picture is the graph for the function y=|x|
The picture you asked differs in the origin of the graph, which resides in the point (0, -2.5).
So our equation should look like the following
y=a|x|+b
From the first point you have (0, -2.5), This means 0=a*|0|+b, we have obtained that b=-2.5
Now 'a' is the slope, we need to find another point in the graph. that would be (2.5, 0) (obtained from the given graph)
the slope is obtained using the equation
[tex]a=\frac{x_{2}-x_{1} }{y_{2}-y_{1} }[/tex]
Where (x1, y1)= (0, -2.5), (x2,y2)=(2.5,0)
thus we have that a=1
So our equation is y=|x|-2.5
For every 2 pins that are sold the spirit club will make $4 how much money would the spirit club make if the club sold 12 and 14 pins
Answer:
52$
Step-by-step explanation:
ok so 2 pins cost 4$ so if you buy one pin its 2$ correct? take 12 and multiply it by 2 and take 14 and multiply by 2,
12×2=24$
14×2=28$
add those two together and you get 52$
A property agent charges a commission of 2.5% on the selling price of a house. If the agent sells a house $650000, find the amount of commission he receives
650000(0.025) = $16,250
Answer:
$16250 commission
($650,000 times .025 (2.5%) = $16250)
How can I send a pic of my work
You pess the thing that looks like a paperclip. Then you take a picture and crop it
Is 1/2 a solution to the equation 8-2x=10x+3 ?
8-2x = 10x+3 Subtract 3 from both sides
5-2x = 10x Add 2x to both sides
5 = 12x Divide 12 to both sides
Final answer X=5/12
The solution to the algebraic expression 8-2x=10x+3 is: x = 12/5
How to solve Algebra Expressions?An algebraic expression in mathematics is defined as an expression which is made up of variables and constants, along with algebraic operations
We are given the algebraic expression as:
8 - 2x = 10x + 3
Using addition property of equality, add 2x - 3 to both sides to get:
8 - 2x + 2x - 3 = 10x + 3 + 2x - 3
5 = 12x
x = 12/5
x = 2.4
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What is the interquartile range for the data set?
27, 4, 54, 78, 27, 48, 79, 64, 5, 6, 41, 71
Enter your answer in the box.
P.S: Not actually asking just for anyone with this question.
51 is the interquartile range for the set of data hope this helps;)
Answer:
Thank youuu
Step-by-step explanation:
if x=2 and t=4, what is the value of 1/8 (x^3-4)(t^2+8)
When substituting x=2 and t=4 into the expression 1/8 (x^3 - 4)(t^2 + 8), it simplifies to 12.
If x=2 and t=4, to find the value of 1/8 (x3 - 4)(t2 + 8), we must substitute the values of x and t into the expression and simplify.
Firstly, calculate x3:
x^3 = 23 = 8
Then, calculate t2:
t^2 = 42 = 16
Now we substitute x^3 and t^2 into the expression:
1/8 (8 - 4)(16 + 8) = 1/8 (4)(24) = 1/8 * 96 = 12
Hence, the value of the expression is 12 when x = 2 and t = 4.
The table below shows the heights of students in a group.
Student
Height
(in inches)
A
50
B
54
C
52
D
56
E
48
What is the mean height of the students in the group? (1 point)
48 inches
49 inches
51 inches
52 inches
Peter asked the students of his class their football scores and recorded the scores in the table shown below:
Football Scores
Score
Number of
Students
0
5
1
3
2
12
3
2
4
6
5
6
6
4
Based on the table, what is the mean football score? (1 point)
1.3
1.8
2.9
3.5
Answer:
1. 52
2. 2.9
Step-by-step explanation:
To find the mean, we take all the numbers, add them up then divide by the number of numbers.
1. mean height
mean = (50+54+52+56+48)/5
=260/5
=52
52 inches
2. mean score
There are 5+3+12+2+6+6+4 students = 38 students
Multiply the number of students times the score and add together
total points = (0*5+1*3+2*12+3*2+4*6+5*6+6*4)
= 111
The mean is the total points divided by the number of students
mean = 111/38
=2.92
Answer:
[tex]\bar x = 52inch\\\bar x_w = 2.92[/tex]
Step-by-step explanation:
According to the data recorded in the table, the average of the students' heights is calculated with the expression for the arithmetic mean:
[tex]\bar x =\frac{1}{n} \sum x_i[/tex]
[tex]\bar x = \frac{1}{5}(48 + 50 + 52 + 54 + 56) = \frac{260}{5} = 52[/tex]inch.
In the same way, the weighted average must be used to find the average football score:
[tex]\bar x_w = \frac{\sum x_i * w_i}{\sum w_i}[/tex], where wi are the frequencies of each response.
[tex]\bar x_w = (0 * 5 + 1 * 3 + 2 * 12 + 3 * 2 + 4 * 6 + 5 * 6 + 6 * 4) / (5 + 3 + 12 + 2 + 6 + 6 + 4) = \frac{111}{38} = 2.92[/tex]
Mika records the number of miles she walks each day.
How many days did she walk? What was her total distance
Answer: Mika walks 16 days and 26.5 total miles.
Step-by-step explanation: You count each x to figure out the days and and them all together like so: 1 1/2 x 5 = 7 1/2. 7 1/2 + 1 5/8 = 12.1875, and so forth and so on.
The 2006 value of a car was $18,000. In 2016, it was worth $4000. If the annual percent of decay has been constant, what is the annual percent of decay?
Answer:
[tex]13.96\%[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$18,000\\r=?\\x=10\ years\\V=\$4,000[/tex]
substitute in the formula
[tex]\$4,000=\$18,000(1-r)^{10}[/tex]
Simplify
[tex](2/9)=(1-r)^{10}[/tex]
[tex](2/9)^{1/10}=(1-r)[/tex]
[tex]r=1-(2/9)^{1/10}[/tex]
[tex]r=0.1396[/tex]
convert to percent
[tex]r=0.1396*100=13.96\%[/tex]
2 friends share 7 cookies equally how many cookies does each person get
3.5 cookies
Friend one: 3 Friend two: 3
One leftover cookie
Split in half give one to each and that makes 3.5
Each of the 2 friends gets 3.5 cookies when sharing 7 cookies equally.
When 2 friends share 7 cookies equally, you divide the total number of cookies by the number of friends. Here, you need to divide 7 cookies by 2 to find out how many cookies each person gets. The calculation would be:
Divide 7 by 2: 7 \/ 2 = 3.5
So, each friend gets 3.5 cookies. However, since you cannot share a cookie perfectly in half without changing its state, we assume this division is hypothetical. In a real-world scenario, they might have to decide how to divide the last cookie or simply share it equally, giving each friend half of the last cookie.
A $160 item is marked down 25%.what is the new cost of the item?
$160 marked down 25% would be 40
what measures of the three angles of a triangle are given by 4x,2x, and 6x. what is the measure of the smallest angle?
Answer:
2x=30 degrees
Step-by-step explanation:
Add up all of the angles and set them equal to 180 degrees, because triangles are always made up of angles with a sum of 180 degrees.
2x+4x+6x=180
12x=180
x=15
smallest angle is 2x
2(15)=30
A mechanic had a bolt with a diameter of 2/9 inch. Will the bolt fit into a hole with a diameter of 0.2 inch.
Answer:
No, the bolt won't fit into the hole
Step-by-step explanation:
We need to convert the diameter of the bolt into decimal by dividing:
2/9 = 0.222...
The hole has diameter of 0.2
Hence, 0.222 is larger than 0.2, so the bolt won't fit.
-4x + 5y=8 6x - y = 11
Final answer:
To solve the given system of linear equations, the elimination method is used, resulting in the solution x = 63/26 and y = -97/26.
Explanation:
The system of equations presented by the student:
-4x + 5y = 8
6x - y = 11
belongs to the topic of algebra, specifically to solving systems of linear equations. To find the values of x and y that satisfy both equations, we can use methods like substitution or elimination. Let's use elimination in this case:
Multiply the second equation by 5 so that the y terms will cancel out when we add the two equations together. The second equation becomes 30x - 5y = 55.
Add the modified second equation to the first equation:
-4x + 5y = 8
+ 30x - 5y = 55
____________________
26x = 63
Solving for x, we find that x = 63/26.
Substitute x into one of the original equations to find y.
Using 6x - y = 11:
6(63/26) - y = 11
378/26 - y = 11
y = 378/26 - 286/26
y = 92/26
Therefore, the solution to the system of equations is x = 63/26 and y = 92/26.
School A has 480 students and 16 classrooms. School B has 192 students and 12 classrooms.
How many Students would have to transfer from school Eddie to school be for the ratio of students to classrooms at both schools to be the same explain your reasoning
Answer:96
Step-by-step explanation:
A; 480/16 = 30 students per classroom
B: 192/12 =16 students per classroom
we need x such that [tex]\frac{480-x}{16} = \frac{192+x}{12}[/tex]
which means
(480-x )* 12 should be equal to (192+x) * 16
5,760 - 12x = 3,072+16x
5,760 - 3,072 = 12x + 16x
2,688 = 28x
x = 96
Adding -34 is the same as subtracting what number?
it is the same as subtraction 34
50+(-34)=50-34
Drag the tiles to the correct boxes to complete the pairs.
Match each polynomial function with one of its factors.
f(x) = x3 − 3x2 − 13x + 15
f(x) = x4 + 3x3 − 8x2 + 5x − 25
f(x) = x3 − 2x2 − x + 2
f(x) = -x3 + 13x − 12
x − 2
arrowRight
x + 3
arrowRight
x + 4
arrowRight
x + 5
arrowRight
Answer:
f(x) = x3 − 3x2 − 13x + 15 Factor: x+3
f(x) = x4 + 3x3 − 8x2 + 5x − 25 Factor: x+5
f(x) = x3 − 2x2 − x + 2 Factor: x-2
f(x) = -x3 + 13x − 12 Factor: x+4
Step-by-step explanation:
f(x) = x^3 − 3x^2 − 13x + 15
Solving:
We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1
x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15
Factor: x^2-2x-15 =(x+3)(x-5)
So, factors are: (x+1)(x+3)(x-5)
Factor: (x+5)
f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25
Solving:
We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)
x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5
So, factors are (x+5) (x^3-2x^2 +2x -5)
Factor: x+5
f(x) = x^3 − 2x^2 − x + 2
Solving:
x^2(x-2)-1(x-2)
(x-2)(x^2-1)
(x-2) (x-1) (x+1)
Factor: x-2
f(x) = -x^3 + 13x − 12
Solving:
-(x^3 + 13x -12)
We will use rational root theorem:
The 1 is a root of (x^3 + 13x -12) so, factor out x-1
Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)
So, roots are: - (x-1)(x-3)(x+4)
Factor (x+4)
Answer:
Polynomial 1 = x + 3
Polynomial 2 = x + 5
Polynomial 3 = x - 2
Polynomial 4 = x + 4
Step-by-step explanation:
We are given with Polynomials and and some factors.
We have to match the correct Pair.
We Map the polynomials on the graph then check which factors matches.
Polynomial 1).
x³ - 3x² - 13x + 15
factors are ( x + 3 ) , ( x - 1 ) , ( x - 5 )
Polynomial 2).
[tex]x^4+3x^3-8x^2+5x-25[/tex]
factors are ( x + 5 )
Polynomial 3).
[tex]x^3-2x^2-x+2[/tex]
factors are ( x + 1 ) ,( x - 1 ) , ( x - 2 )
Polynomial 4).
[tex]-x^3+13x-12[/tex]
factors are ( x + 4 ) ,( x - 1 ) , ( x - 3 )
Therefore,
Polynomial 1 = x + 3
Polynomial 2 = x + 5
Polynomial 3 = x - 2
Polynomial 4 = x + 4
Square KITE has vertices (-4, 0), (0, 4), (4, 0), and (0, -4), respectively. Name the square's diagonals and find their point of intersection.
Complete your work in the space provided or upload a file that can display math symbols if your work requires it.
hence the answer is 16units
hope helps you!!!!!!
The equation of diagonals of kite are x = 0 and y = 0 and their point of intersection is (0,0)
What is a straight line?A straight line is a one-dimensional figure that never ends and has no breadth.
Equation of line : y = mx + c
m - slope of the line
c - y intercept
Let the vertices of the Kite ABCD be A(-4 , 0), B(0 , 4), C(4 , 0), D(0 , -4)
The equation of Diagonal AC is y = 0
The equation of Diagonal BD is x = 0
The point of intersection of diagonals will be ( 0 , 0)
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Please help me, What is the 6th term of the geometric sequence 1024, 528, 256...?
A: 64
B: 32
C: 16
D: 8
The geometric sequence is B: 32
Final answer:
To find the 6th term in the given geometric sequence, the common ratio is calculated and the nth term formula is applied. However, the calculated value doesn't match any of the provided options, indicating a possible error in calculation or the sequence itself.
Explanation:
To find the 6th term of the geometric sequence 1024, 528, 256, we first need to determine the common ratio. We get this by dividing the second term by the first term:
Common ratio (r) = 528 / 1024 = 0.515625
Now, using the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and n is the term number:
a6 = 1024 × 0.515625(6-1) = 1024 × (0.515625)5
Calculating this, we get:
a6 = 1024 × 0.1184844970703125 = 121.234375
This value does not match any of the options provided (64, 32, 16, or 8), suggesting that there may have been a miscalculation or misunderstanding of the sequence. Please double-check the sequence or provide additional information.
Use the drawing tool(s) to form the correct answers on the provided graph.
Graph the system of equations given below on the provided graph.
2x– 3y = –18
3x + y = -5
Answer:
2x– 3y = –18
3x + y = -5
Converting the equation in slope-intercept form
2x-3y= -18
-3y= -2x-18
-3y= -(2x+18)
3y=2x+18
y=(2x+18)/3
And for equation 2
y= -5-3x
For plotting the graph, the online graphing calculator desmos.com can be used.
The points can be calculated by putting negative and positive values of x in both equations.
The graph is attached as a picture.
As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.
Answer:
[tex](-3,4)[/tex],
Step-by-step explanation:
The given system of equations is
[tex]\left \{ {{2x-3y=-18} \atop {3x+y=-5}} \right.[/tex]
To solve this system, we could multiply the second equation by 3, and solve for x:
[tex]\left \{ {{2x-3y=-18} \atop {9x+3y=-15}} \right.\\11x=-33\\x=\frac{-33}{11}=-3[/tex]
Now, we replace this value in a equation to find y-value:
[tex]3x + y = -5\\3(-3)+y=-5\\-9+y=-5\\y=-5+9\\y=4[/tex]
Therefore, the solution for the system is [tex](-3,4)[/tex], you can observe this in the graph attached.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A. g(-4) = -11
B. g(7) = -1
C. g(-13) = 20
D. g(0) = 2
Answer:
C.
Step-by-step explanation:
C is true because we already know g(0) is -2, and functions cannot repeat themselves with different numbers like that. A is not true because the range does not go that far down. B is not true because the domain does not go that far up.
Answer:
C is the answer
Step-by-step explanation:
C is the answer because
A 9-cm chord is 11 cm from the center of a circle.
What is the radius of the circle?
C. 13.0 cm
B. 11.9 cm
A. 9.0 cm
D. 14.2 cm
Answer: b 11.9
Step-by-step explanation:
the chord and the line to the center can be used to create a triangle
the radius is the hypotenuse of this triangle
4.5squared + 11 squared= 11.9
Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100. Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.
Answer:
Required inequality is [tex]4800+183x>8000[/tex].
Step-by-step explanation:
Given that Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100. Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.
Calculation is given by:
Salary per year = $4,800
Average price of a policy = $6,100.
commission on her sales = 3%
Then commission on $6,100 = 3% of $6,100 = 0.03 ($6,100) = $183
Let number of policies Mrs. Robinson must sell to make an annual income of at least $8,000 = x
then total commission on x policies = 183x
Total income using x policies = 4800+183x
Since she wants to make an annual income of at least $8,000. so we can write inequality as:
[tex]4800+183x>8000[/tex]
Hence required inequality is [tex]4800+183x>8000[/tex].
The price, p, for different size orders of printed programs for a musical production, n, is given in the tables. please help ill mark BRAINLYEST 15 points
For an equation to be linear, the slope has to be the same/constant.
To find the slope (m), you use the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] and substitute in 2 points
(1 , 60) [x₁ , y₁] and (5 , 70) [x₂ , y₂]
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{70-60}{5-1}[/tex]
[tex]m=\frac{10}{4} =\frac{5}{2}[/tex] or 2.5
Try a different point to see if the slope is the same:
(5, 70) and (20, 80)
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{80-70}{20-5}[/tex]
[tex]m=\frac{10}{15} =\frac{2}{3}[/tex] or 0.6666666
Since the slopes are different, a linear equation can not be used
Suppose you are working as a pastry chef. You have 12 cups of chocolate cream to fill eclairs. Each eclair requires 2.25 ounces of filling. If you use all of the chocolate cream, at most how many eclairs can you make? A) 32 B) 36 C) 42 D) 44
Answer:
C- 42
Step-by-step explanation:
there are 8 ounces in a cup so 12 x 8 = 96 oz
96/2.25 = 42.6666666667
Rounded back to 42
By using all the chocolate cream, at most the number of eclairs that can be made is:
C) 42
Step-by-step explanation:It is given that:
You have 12 cups of chocolate cream to fill eclairs.
Each eclair requires 2.25 ounces of filling.
We know that:
The universal conversion that is used is:
1 cups=8 ounces
and hence,
12 cups= 12×8=96 ounces.
Hence, the number of ounces of chocolate cream to fill eclairs= 96 ounces
Also,
amount of filling required by 1 eclair= 2.25 ounces.
Hence, Number of eclairs that can be made is:
[tex]Number\ of\ eclairs=\dfrac{96}{2.25}\\\\i.e.\\\\Number\ of\ eclairs=42.67[/tex]
This means that:
Atmost the number of eclairs than can be made= 42
Polygon DEFG is shown on the coordinate grid. Polygon DEFG is dilated with the origin as the center of dilation using the rule (x, y) → (2x, 2y) to create polygon D'E'F'G'.
Which statement is true?
A) Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.
B) Polygon D'E'F'G' is smaller than polygon DEFG, because the scale factor is less than 1.
C) Polygon D'E'F'G' is smaller than polygon DEFG, because the scale factor is greater than 1.
D) Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is less than 1.
Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Polygon DEFG is dilated with the origin as the center of dilation using the rule (x, y) → (2x, 2y) to create polygon D'E'F'G'. Therefore:
Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.
Find out more on equation at: https://brainly.com/question/2972832
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The dilation doubles the distances between corresponding vertices, indicating an enlargement.
Therefore, choice A is correct: Polygon D'E'F'G' is larger due to the scale factor exceeding 1.
To determine whether polygon D'E'F'G' is larger or smaller than polygon DEFG after dilation with the origin as the center and using the rule (x, y) → (2x, 2y), we need to understand the effect of the dilation on the coordinates of the vertices.
Let's assume the coordinates of the vertices of polygon DEFG are as follows:
D(x₁, y₁)
E(x₂, y₂)
F(x₃, y₃)
G(x₄, y₄)
Now, applying the dilation rule (x, y) → (2x, 2y) to each vertex, we get the coordinates of the corresponding vertices of polygon D'E'F'G':
D'(2x₁, 2y₁)
E'(2x₂, 2y₂)
F'(2x₃, 2y₃)
G'(2x₄, 2y₄)
Now, let's compare the distances between the vertices of the original and dilated polygons to determine if the dilation resulted in enlargement or reduction.
1. Distance between D and E:
Original: √((x₂ - x₁)² + (y₂ - y₁)²)
Dilated: √((2x₂ - 2x₁)² + (2y₂ - 2y₁)²) = √(4(x₂ - x₁)² + 4(y₂ - y₁)²)
The distance between D' and E' is twice the distance between D and E. So, the scale factor is indeed 2, indicating an enlargement.
2. Similarly, for the other sides (DE, EF, FG), we'll find the same result.
Since the scale factor is greater than 1, we can conclude that polygon D'E'F'G' is larger than polygon DEFG.
So, the correct answer is:
A) Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.