Answers
Answer:
1. (x, y) → (x + 3, y - 2)
Vertices of the image
a) (-2, - 3)
b) (-2, 3)
c) (2, 2)
2. (x, y) → (x - 3, y + 5)
Vertices of the image
a) (-3, 2)
b) (0, 2)
c) (0, 4)
d) (2, 4)
3. (x, y) → (x + 4, y)
Vertices of the image
a) (-1, -2)
b) (1, -2)
c) (3, -2)
4. (x, y) → (x + 6, y + 1)
Vertices of the image
a) (1, -1)
b) (1, -2)
c) (2, -2)
d) (2, -4)
e) (3, -1)
f) (3, -3)
g) (4, -3)
h) (1, -4)
5. (x, y) → (x, y - 4)
Vertices of the image
a) (0, -2)
b) (0, -3)
c) (2, -2)
d) (2, -4)
6. (x, y) → (x - 1, y + 4)
Vertices of the image
a) (-5, 3)
b) (-5, -1)
c) (-3, 0)
d) (-3, -1)
Explanation:
To identify each IMAGE you should perform the following steps:
List the vertex points of the preimage (the original figure) as ordered pairs.Apply the transformation rule to every point of the preimageList the image of each vertex after applying each transformation, also as ordered pairs.1. (x, y) → (x + 3, y - 2)
The rule means that every point of the preimage is translated three units to the right and 2 units down.
Vertices of the preimage Vertices of the image
a) (-5,2) (-5 + 3, -1 - 2) = (-2, - 3)
b) (-5, 5) (-5 + 3, 5 - 2) = (-2, 3)
c) (-1, 4) (-1 + 3, 4 - 2) = (2, 2)
2. (x,y) → (x - 3, y + 5)
The rule means that every point of the preimage is translated three units to the left and five units down.
Vertices of the preimage Vertices of the image
a) (0, -3) (0 - 3, -3 + 5) = (-3, 2)
b) (3, -3) (3 - 3, -3 + 5) = (0, 2)
c) (3, -1) (3 - 3, -1 + 5) = (0, 4)
d) (5, -1) (5 - 3, -1 + 5) = (2, 4)
3. (x, y) → (x + 4, y)
The rule represents a translation 4 units to the right.
Vertices of the preimage Vertices of the image
a) (-5, -2) (-5 + 4, -2) = (-1, -2)
b) (-3, -5) (-3 + 4, -2) = (1, -2)
c) (-1, -2) (-1 + 4, -2) = (3, -2)
4. (x, y) → (x + 6, y + 1)
Vertices of the preimage Vertices of the image
a) (-5, -2) (-5 + 6, -2 + 1) = (1, -1)
b) (-5, -3) (-5 + 6, -3 + 1) = (1, -2)
c) (-4, -3) (-4 + 6, -3 + 1) = (2, -2)
d) (-4, -5) (-4 + 6, -5 + 1) = (2, -4)
e) (-3, -2) (-3 + 6, -2 + 1) = (3, -1)
f) (-3, -4) (-3 + 6, -4 + 1) = (3, -3)
g) (-2, -4) (-2 + 6, -4 + 1) = (4, -3)
h) (-2, -5) (-2 + 3, -5 + 1) = (1, -4)
5. (x, y) → (x, y - 4)
This is a translation four units down
Vertices of the preimage Vertices of the image
a) (0, 2) (0, 2 - 4) = (0, -2)
b) (0,1) (0, 1 - 4) = (0, -3)
c) (2, 2) (2, 2 - 4) = (2, -2)
d) (2,0) (2, 0 - 4) = (2, -4)
6. (x, y) → (x - 1, y + 4)
This is a translation one unit to the left and four units up.
Vertices of the pre-image Vertices of the image
a) (-4, -1) (-4 - 1, -1 + 4) = (-5, 3)
b) (-4 - 5) (-4 - 1, -5 + 4) = (-5, -1)
c) (-2, -4) (- 2 - 1, -4 + 4) = (-3, 0)
d) (-2, -5) (-2 - 1, -5 + 4) = (-3, -1)
Related Questions
A circle with area 25pi has a sector with a central angle of 9/10pi radians. What is the area of a sector? Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal rounded to the nearest hundredth.
Answers
Answer:
11.25 pi
Step-by-step explanation:
Pi is 180 degrees, a circle is 360 degrees, 9/10's of 180 is 162, and divide that by the full 360 which is .45. Then, multiply that by 25 and you have 11.25 pi is the area of that sector.
What is the reciprocal of the number 2/7
Answers
Answer:
7/2
Step-by-step explanation:
4(x + 7) = 90(2+x)
4x + 28 = 180 + 90x
208 = 94x
What is the next step I have to do in solving this please help
Answers
Answer: 2.12
Step-by-step explanation: Divide by 94 on both sides to get X by itself
LeBron has 6 yards of cable.he needs 15 feet of cable to install a stereo.does he have enough cable to install the stereo?explain your answer
Answers
PLEASE MARK BRAINLIEST!
Answer:
Yes!Step-by-step explanation:
This is because 6 yards equals 18 feet. If there is 15 feet needed to install a stereo, and we have 18 feet of cable, we have MORE THAN ENOUGH cable to install the stereo. So yes, there is enough cable to install the stereo.
I hope this helps!
- sincerelynini
Answer:
Yes.
Step-by-step explanation:
There is 3 feet in every yard. So LeBron has 18ft of cable.
Mark wants to buy shoes that cost 200 dollars. They have him a dicount for 20 dollars and he used his 2 percent coupen. How much did mark pay for the shoes
Answers
Answer:
$176.40
Step-by-step explanation:
Lets assume the order of events to be:
20 dollars discount first,
2% coupon discount, next
So, original cost is 200
Discount of 20 dollars, means that it now costs:
200 - 20 = $180
Now, we have a 2% discount coupon on it. We have to find 2% of 180 and subtract that from 180.
Note: 2% is 2/100 = 0.02
So,
180 * 0.02 = 3.6
So, final price would be: 180 - 3.6 = $176.40
Mark paid $176.40 for the shoes
write an equation that represents (0,-1) and (3,-3
Answers
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{-3+1}{3}\implies -\cfrac{2}{3}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{0}) \\\\\\ y+1=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x-1[/tex]
An equation is shown below: 4(2x − 3) = 4 Part A: What is the solution to the equation above? Show your work using inverse operations. (5 points) Part B: Check using substitution to make sure your answer is correct. (5 points)
Answers
Answer:
see explanation
Step-by-step explanation:
(A) Given
4(2x - 3) = 4 ( divide both sides by 4 )
2x - 3 = 1 ( add 3 to both sides )
2x = 4 ( divide both sides by 2 )
x = 2
(B)
As a check substitute x = 2 into the left side of the equation and if equal to the right side then it is the solution.
4(2(2) - 3) = 4(4 - 3) = 4(1) = 4 = right side
Hence x = 2 is the solution
Answer:
The solution of the given equation is x = 2.
Step-by-step explanation:
The given linear equation is,
[tex]4(2x-3)=4[/tex]
At first, we will eliminate '4' from the LHS by dividing both sides i.e., LHS and RHS by 4 because '4' is present in multiplication with the term containing unknown in LHS.
So, dividing both sides by '4', we get
[tex]\frac{4(2x-3)}{4} = \frac{4}{4}[/tex]
[tex]\implies 2x - 3 = 1[/tex]
Our next step will be to eliminate '3' from the LHS that is being subtracted from the term containg unknown variable. For this, we will add '3' on both sides of the above obtained equation.
So, adding '3' on both sides, we get
[tex]2x - 3 + 3 = 1 + 3[/tex]
[tex]\implies 2x = 4[/tex]
Now, we will eliminate '2' from the LHS that is in multiplication with the unknown variable 'x'.
For this, we will divide both sides of the above obtained equation by '2'.
So, dividing both sides by '2', we get
[tex]\frac{2x}{2}=\frac{4}{2}[/tex]
[tex]\implies x = 2[/tex]
CHECKING :
For this, we will substitute x = 2 in the LHS of the given equation and then check whether it is equal to RHS or not.
LHS = 4(2x - 3)
= 4(2 × 2 - 3)
= 4(4 - 3)
= 4 × 1
= 4
= RHS
So, the solution of the given equation is x = 2.
Molly has 9 cups of flour. If this is -
of the number she needs to make bread, how many cups does she need?
struct the tape diagram by reading it backward. Draw a tape diagram and label the unknown.
Answers
Answer:
9 pounds of flour
Step-by-step explanation:
mix together
5 - 3 = 15 or 7 +5 = 20 true or false
Answers
Answer:
False
Step-by-step explanation:
The cost of a company picnic varies directly as the number of employees attending the picnic. If a company picnic costs $487.50 for 30 employees, how much does a company picnic cost for 80 employees? ANSWER ASAP PLEASEEE
Answers
The company picnic cost $ 1300 for 80 employees
Solution:
Given that cost of a company picnic varies directly as the number of employees attending the picnic
Let "c" be the company picnic cost
Let "n" be the number of employees attending the picnic
Therefore,
[tex]cost \propto \text{ number of employees attending picnic }[/tex]
[tex]c \propto n\\\\c = kn[/tex]
Where "k" is the constant of proportionality
c = kn ---------- eqn 1
Given that company picnic costs $487.50 for 30 employees
Therefore substitute c = 487.50 and n = 30
[tex]487.50 = k(30)\\\\k = \frac{487.50}{30} = 16.25[/tex]
How much does a company picnic cost for 80 employees?
Substitute n = 80 and k = 16.25 in eqn 1
[tex]c = 16.25(80) = 1300[/tex]
Thus $ 1300 is the cost for 80 employees
Answer:
$1,300.00
Step-by-step explanation:
I need help getting the answer to 1484 divided by 28
Answers
Answer:
53
Step-by-step explanation:
2. Choose all the expressions that are equal
to 2/3
1/6 + 1/2 yes or no
2/9 + 17/18 yes or no
5/12 + 1/4 yes or no
1 1/6-1/3 yes or no. 2 - 1 1/3 yes or no
Answers
Answer:
Yes, No, Yes, No, No
Step-by-step explanation:
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✉️ If any further questions, inbox me! ✉️
Just put it
What is
[tex] - |x + 2| + 1 = 4x - 6[/tex]
Answers
Answer:
x = 1
Step-by-step explanation:
Given
- | x + 2 | + 1 = 4x - 6 ( subtract 1 from both sides )
- | x + 2 | = 4x - 7 ( multiply both sides by - 1 )
| x + 2 | = - 4x + 7
The absolute value always returns a positive value, but the expression inside can be positive or negative, thus
x + 2 = - 4x + 7 ( add 4x to both sides )
5x + 2 = 7 ( subtract 2 from both sides )
5x = 5 ( divide both sides by 5 )
x = 1
OR
- (x + 2) = - 4x + 7, that is
- x - 2 = - 4x + 7 ( add 4x to both sides )
3x - 2 = 7 ( add 2 to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
As a check substitute these values into both sides of the equation and if both sides are equal then they are the solutions.
x = 1 : - |1 + 2| + 1 = - | 3 | + 1 = - 3 + 1 = - 2
right side = 4(1) - 6 = 4 - 6 = - 2 ← True
x = 3 : - |3 + 2| + 1 = - |5| + 1 = - 5 + 1 = - 4
right side = 4(3) - 6 = 12 - 6 = 6 ← False
Thus x = 3 is an extraneous solution and
x = 1 is the solution
Answer:
x = 1Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x+2|=\left\{\begin{array}{ccc}x+2&for&x+2\geq0\to x\geq-2\\-(x+2)&for&x<-2\end{array}\right[/tex]
[tex](1)\ x<-2\\\\-\bigg(-(x+2)\bigg)+1=4x-6\\\\+(x+2)+1=4x-6\qquad\text{combine like terms}\\\\x+(2+1)=4x-6\\\\x+3=4x-6\qquad\text{subtract 3 from both sides}\\\\x+3-3=4x-6-3\\\\x=4x-9\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\x-4x=4x-4x-9\\\\-3x=-9\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-9}{-3}\\\\x=3\notin(1)[/tex]
[tex](2)\ x\geq-2\\\\-(x+2)+1=4x-6\\\\-x-2+1=4x-6\\\\-x+(-2+1)=4x-6\\\\-x-1=4x-6\qquad\text{add 1 to both sides}\\\\-x-1+1=4x-6+1\\\\-x=4x-5\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x-4x=4x-4x-5\\\\-5x=-5\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-5}{-5}\\\\x=1\in(2)[/tex]
evaluate y=3^x for x=2
Answers
Answer:
y=9
Step-by-step explanation:
substitution x=2 in equation
y= 3^2
y=9
Final answer:
To evaluate y=3^x for x=2, substitute x=2 into the expression y=3^x to find that y=9.
Explanation:
The given expression is y = 3^x. To evaluate y for x = 2, substitute x = 2 into the expression:
y = 3^2
y = 9
Therefore, y = 9 when x = 2.
10. The measures of the bases of a
trapezoid are x2 – 19 and 10. The
measure of the midsegment is 8.
Find the value of x.
Answers
Answer:
The value of x is 2[tex]\sqrt{29}[/tex] .
Step-by-step explanation:
Given as :
The area of Trapezoid = x² unit²
The measure of base 1 = [tex]b_1[/tex] = - 19 unit
The measure of base 2 = [tex]b_2[/tex] = 10 unit
The height of the mid segment = 8 unit
Now, From the Area of Trapezoid
i.e Area = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height
Or, x² = [tex]\dfrac{1}{2}[/tex] × (19 + 10) × 8
Or, x² = [tex]\dfrac{8}{2}[/tex] × (29)
Or, x² = 4 × (29)
Or, x² = 116
∴ x = [tex]\sqrt{116}[/tex]
I.e x = 2[tex]\sqrt{29}[/tex]
Hence, The value of x is 2[tex]\sqrt{29}[/tex] . Answer
Final answer:
Using the properties of a trapezoid's midsegment being the average length of the bases, the equation (10 + (x² - 19))/2 = 8 was solved to find that x equals 5.
Explanation:
The question revolves around the properties of a trapezoid and its midsegment. In a trapezoid, the midsegment (also called the median) is the segment that joins the midpoints of the non-parallel sides and is parallel to both bases.
The length of the midsegment is the average of the length of the two bases, which can be expressed as (base1 + base2) / 2.
Given that the midsegment is 8 units long, and one base is given as 10 units, let the other base be expressed as x² − 19 units. The formula for the midsegment becomes:
(10 + (x² − 19))/2 = 8
Now we solve for x:
10 + x² − 19 = 16
x² − 9 = 16
x² = 25
x = ± 5
Since the measure of a base cannot be negative, the positive root is the realistic solution:
x = 5
identify the domain and range for (1,4) (2,5) (0,6) (1,7) (2,8)
Answers
The range are the y values: 4,5,6,7,8
Jacob has purchased a $129,000 home with a 30-year mortgage at 5.15%. He can make a monthly payment of $1000. If he were to make this
payment each month, how many months will it take him to pay off his mortgage? Round you answer to a whole number.
Answers
Answer: 188 months
Step-by-step explanation:
Principal = $129 000
Payment = $1000
Mortgage % = 5.15
Since,
Number of Months = log (1+[rate/(Payment/Principal)-rate] / log (1 + rate)
Also,
rate = 5.15/1,200 = 0.004292
Number of Months = log (1 + [0.004292/(1,000/129000) -0.004292] / log(1+0.004292)
Number of Months = log ( 1 + 0.004292/ ((0.007752 -0.004292) / log (1.004292)
Number of Months = log ( 1 + (0.004292/0.00346))/ log (1.004292)
Number of Months = log (1 + 1.240) / log (1.004292)
Number of Months = log (2.240) / log (1.004292)
Number of Months = 0.3502 / 0.001860
Number of Months = 188.28 months
Approximation to whole month,
Number of months = 188 Months.
if the measure of two exterior angles on the same side of the transversal are 3x and 7x+10, find the value of x
Answers
Answer:
The value of x is 17°.
Step-by-step explanation:
The two exterior angles on the same side of the transversal are always supplementary.
Therefore, if the measure of two exterior angles on the same side of the transversal are 3x and 7x+10, then we can write
3x + (7x + 10) = 180°
⇒ 10x = 180° - 10° = 170°
⇒ x = 17°
Therefore, the value of x is 17°. (Answer)
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located? (0, 1) (1, 3) (1, 7) (2, 1)
Answers
Answer:
Step-by-step explanation:
If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k). If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.
[tex]f(1)=-2(1)^2+4(1)+1[/tex]
so f(1) = 3. Your choice is (1, 3)
The solution is (1, 3) where the vertex of the function located.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have
given that,
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1.
now, we have to find the vertex of the function.
If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).
If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.
now, putting the value of x as 1 ,
so, we get,
f(1) = –2(1)^2 + 4*1+ 1
=-2 + 4 +1
=3
so f(1) = 3.
The solution is (1, 3).
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A new energy drink advertises 106 calories for 8oz. How many calories are in 12oz of the drink?
Answers
12oz of the drink contains 159oz of calories.
To Calculate How many calories are in 12oz of the drinkA new energy drink advertises 106 calories for 8oz.
Based on the given conditions, formulate: 12*(106/8)
=12*(13.25)=159
Calories are in 12oz of the drink is 159oz
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Express each of the following as the sum Of a whole number and a fraction 9/5
Answers
The fraction 9/5 can be expressed as the sum of 1 (whole number) and 4/5 (fraction).
Explanation:The fraction 9/5 can be expressed as a sum of a whole number and a fraction. First, divide 9 by 5 which will result in 1 with a remainder of 4. The 1 forms the whole number, and 4/5 forms the fraction. So, 9/5 is equivalent to 1 4/5, which means 1 (whole number) plus 4/5 (fraction) is equal to 9/5.
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Find the midpoint of the line segment (-5,-8), (-7,3)
Answers
Answer:
Step-by-step explanation:
(-5,-8), (-7,3)
midpoint = (x₁+x₂/2, y₁+y₂/2)
= ( -5+-7/2 , -8+3/2) = (-5-7/2,-8+3/2)
= (-12/2, -5/2) = (-6,-5/2)
Round 639.13787717 to 2 decimal places.
Answers
Answer: 639.14
Step-by-step explanation:
If Greg can build 1/7 of a brick wall in 1/12 of an hour whats his unit rate?
A: 1/84
B: 19/84
C: 1 5/7
D: 7
Answers
Final answer:
Greg's unit rate is [tex]1\frac{5}{7}[/tex] walls per hour, which is found by dividing 1/7 of a wall by 1/12 of an hour. The correct answer is option C: [tex]1\frac{5}{7}[/tex].
Explanation:
If Greg can build 1/7 of a brick wall in 1/12 of an hour, we want to find his unit rate, which is the amount of wall he can build per hour. To find Greg's unit rate, we divide the fraction of the wall built by the fraction of the hour spent building it. This calculation gives us:
Unit rate = (1/7) ÷ (1/12) = (1×12)/(7×1) = 12/7 = [tex]1\frac{5}{7}[/tex] walls per hour.
Therefore, the correct option is C: [tex]1\frac{5}{7}[/tex].
13x+2y=1
5x-2y=-19
Solve for x and y
Answers
Answer:
Step-by-step explanation:
13x+2y=1
+ 5x-2y=-19
-------------------
18x=18
x=1
5x1-2y=-19
5-2y=-19
-2y=-19-5
-2y=14
-y=7
y=-7
x=1
y=-7
To solve the system, eliminate variables, find [tex]\( x = -1 \)[/tex], then substitute into an equation to get [tex]\( y = 7 \)[/tex].
To solve the system of equations [tex]\(13x + 2y = 1\)[/tex] and [tex]\(5x - 2y = -19\)[/tex], you can use the method of elimination.
First, let's eliminate one of the variables. We can eliminate [tex]\(y\)[/tex] by adding the two equations together:
[tex]\[ (13x + 2y) + (5x - 2y) = 1 + (-19) \][/tex]
This simplifies to:
[tex]\[ 13x + 5x = -18 \][/tex]
[tex]\[ 18x = -18 \][/tex]
Now, divide both sides by 18:
[tex]\[ x = \frac{-18}{18} \][/tex]
[tex]\[ x = -1 \][/tex]
Now that we have found [tex]\(x\)[/tex], we can substitute it into one of the original equations to find [tex]\(y\)[/tex]. Let's use the first equation:
[tex]\[ 13(-1) + 2y = 1 \][/tex]
[tex]\[ -13 + 2y = 1 \][/tex]
Add 13 to both sides:
[tex]\[ 2y = 1 + 13 \][/tex]
[tex]\[ 2y = 14 \][/tex]
Divide both sides by 2:
[tex]\[ y = \frac{14}{2} \][/tex]
[tex]\[ y = 7 \][/tex]
So, the solution to the system of equations is [tex]\(x = -1\)[/tex] and [tex]\(y = 7\)[/tex].
an airplane travels at a rate of 250 miles/he with the wind and at a rate of 150 miles against the wind. what is the rate of the wind?
Answers
50 miles per hour is the rate (speed) of the wind.
Step-by-step explanation:
Let consider the variable ‘x’ for speed of wind.
Below we write two values of the speed of the airplane in the air in terms of ‘x’:
1. Subtract wind speed from airplane speed: 250 - x.
2. Add wind speed to the airplane speed against the wind: 150 + x.
And now, set these above two expressions equal to each other to find x (wind speed),
250 – x = 150 + x
2x = 100
x = 50 miles per hour
WORTH 15 POINTS PLEASE ANSWER ASAP!
"Jessica has 9/ 10 yard of fabric. She cut 5/ 12 of the length.
Jessica used this expression to find the amount of fabric she cut.
9/ 10×5/ 12
How much fabric did Jessica cut?"
Answers
Answer:
[tex]\frac{3}{8}[/tex] yards of fabric.
Step-by-step explanation:
Jessica has [tex]\frac{9}{10}[/tex] yards of fabric and she cut [tex]\frac{5}{12}[/tex] of the length.
Therefore, Jessica has cut fabric of the length [tex]\frac{9}{10} \times \frac{5}{12} = \frac{3}{8}[/tex] yards.
This is the answer as a fraction in simplest form.
Now, Jessica used the expression to find the amount of fabric she cut as [tex] \frac{9}{10} \times \frac{5}{12}[/tex] was correct. ( Answer )
14/1 ÷ 3/8 = please show work and answer fast
Answers
Answer: 37 1/3
Step-by-step explanation:
14/1÷3/8=?
Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
14/1 × 8/3=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
14×8/1×3 = 112/3
This fraction cannot be reduced.
The fraction
112/3
is the same as
112÷3
Convert to a mixed number using
long division so
112/3=37 1/3
Therefore:
14/1 ÷ 3/8=37 1/3
The amount of money in an account can be determined by the formula A re where is the
initial investment, r is the annual interest rate, and tis the number of years the money was
invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest
compounded continuously?
Answers
Answer: $10272.17
Step-by-step explanation: Please see attachment for explanation
Answer:
[tex]\$10272.17[/tex]
Step-by-step explanation:
Since it is compounded continuously, we will use:
[tex]A=A_0 \cdot e^{k t}[/tex]
[tex]A_0[/tex] is the amount invested.
[tex]k[/tex] is the rate.
[tex]t[/tex] is the number of years you let the money sit.
[tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.
(Note:
I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)
[tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]
[tex]A=5000 \cdot e^{0.72}[/tex]
[tex]A=5000 \cdot 2.0544332[/tex] (approximated)
[tex]A=10272.16605[/tex] (approximated)
To the nearest cent this is [tex]\$10272.17[/tex].
What is the volume of this solid? Recall the formula V=Bh.
A. 280 cubic inches
B. 385 cubic inches
C. 466 cubic inches
D. 560 cubic inches
Answers
Answer:
its A 280
Step-by-step explanation: