When the town of Bradyville first started its voluntary recycling program, 1500 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 15% each year.
Which explicit rule can be used to determine the number of people participating in the program in the fifth year?
an=1500(1.15)^n−1
an=1500(0.15)^n
an=1500(1.15)n
an=1500(0.15)^n−1
Answers
This is an example of an exponential equation.
These types of equations are in the form: y = ab^x
A is the starting amount, b is the rate and x is the number of years.
All you have to do is put the pieces in place. Since it is a 15% increase, we are using 1.15 for the rate. And the starting value (a) is 1500.
Answer:
Here you go. :)
Related Questions
How do u do question 27 and 29. Find the measure of angle x?
Answers
the arc has 88°, and therefore the central angle also has 88°.
notice the red tickmarks, since those two segments are radius, they are equal, that makes an isosceles triangle, with a "vertex" of 88°, and twin sides on the "bases".
so 180 - 88 is 92, and since "x" and the other angle are twins, 92/2 is "x".
for 29, check the right-side of the picture below.
"x" is sitting on a flat-line that runs through the center of the circle, and therefore that line is the diameter, now, a flat-line is always 180°.
we know the arc there is 130°, so, the arc of the area where "x" is at is 180° - 130°, now, that arc is the "intercepted arc" from an "inscribed angle".
by the "inscribed angle theorem" that you see there below, "x" is half that arc.
You are buying a $14.95 item that has 4.5% sales tax. You give the cashier a $20 bill. How much change do you get back?
Answers
Answer:
4.38 is the aount you get back
Step-by-step explanation:
14.95*.045=.67
14.95+.67=15.62
20-15.62=4.38
Brainleist plz
You give the cashier a $20 bill. $4.38 you get back.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
You are buying a $14.95 item that has 4.5% sales tax.
That means,
the total price = 14.95 + 4.5% of 14.95.
= 14.95 + 0.67
= 15.62
You give the cashier a $20 bill.
You get in return,
= 20 - 15.62
= $4.38
Therefore, you get back $4.38.
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54 points
BC is parallel to DE. What is the length of CE? A) 2 1/3 B) 2 2/3 C) 3 1/3 D) 3
Answers
We set up a proportion to solve this. We compare the segments from each side to each other:
2/3 = x/4
Cross multiply:
3*x = 2*4
3x=8
Divide both sides by 3:
3x/3 = 8/3
x = 2 2/3
Answer:
2 2/3
Step-by-step explanation:
AB
BD
=
AC
CE
3 /2 = 4 /CE → CE = 8 /3 = 2 2 /3
Which is a solution of x2 – x – = 0?
Answers
[tex]x^2-x=0\\\\x(x-1)=0\iff x=0\ \vee\ x-1=0\\\\\boxed{x=0\ \vee\ x=1}[/tex]
if dy/dx= sin x/ cos y and y(0) = 3pi/2, find an equation for y in terms of x
Answers
We rewrite the equation:
(cos (y) * dy) = (sin (x) * dx)
We integrate both sides of the equation:
sin (y) = - cos (x) + C
We use the initial condition to find the constant C:
sin (3pi / 2) = - cos (0) + C
-1 = -1 + C
C = -1 + 1
C = 0
The equation is then:
sin (y) = - cos (x)
Clearing y:
y = Arcosine (-cos (x))
Answer:
An equation for and in terms of x is:
y = Arcosine (-cos (x))
Final answer:
The problem requires finding an equation for y in terms of x given a differential equation and an initial condition. Solving for y, we get:[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Explanation:
To solve this ordinary differential equation (ODE), we can separate variables and then integrate both sides. Given:
[tex]\[\frac{dy}{dx} = \frac{\sin(x)}{\cos(y)}\][/tex]
We separate variables by multiplying both sides by \(dx\) and dividing by Cos(y) to isolate y terms:
[tex]\[\cos(y) \, dy = \sin(x) \, dx\][/tex]
Now, we integrate both sides. For the left side, we integrate with respect to y, and for the right side, we integrate with respect to x:
[tex]\[\int \cos(y) \, dy = \int \sin(x) \, dx\][/tex]
Integrating each side gives us:
[tex]\[ \sin(y) = -\cos(x) + C\][/tex]
Where C is the constant of integration.
Given the initial condition [tex]\(y(0) = \frac{3\pi}{2}\)[/tex], we can plug this into the equation to find [tex]\(C\):[/tex]
[tex]\[ \sin\left(\frac{3\pi}{2}\right) = -\cos(0) + C \][/tex]
[tex]\[ -1 = -1 + C \][/tex]
[tex]\[ C = 0 \][/tex]
So the equation becomes:
[tex]\[ \sin(y) = -\cos(x) \][/tex]
Therefore, solving for y, we get:
[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
A rental car costs a one time fee of $150 and then an additional $80 for each day it is rented. If the Nawa family's total bill was $470, how many days did they rent the car?
Answers
Nawa family rented the car for 2 days.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
A rental automobile costs $150 for the first day and an extra $80 for each consecutive day booked. If the entire bill for the Nawas family was $470.
The total cost of the rental car per day is :
⇒ one-time fee + additional fee
⇒ $150 + $80
Apply the addition operation,
⇒ $230 per day.
The Nawas paid $470 for the rental car, so they rented the car for $470 / $230 per day = 2 days.
Therefore, his family rented the car for 2 days.
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The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic function in this equation?
Answers
The larger integer is x + 1.
x(x + 1) = 420
x^2 + x = 420
x^2 + x - 420 = 0
The constant is -420.
The school store started selling music CDs five years ago. They sold $22,600 worth in the first year. But, since MP3 players became so popular, the total yearly sales of CDs have dropped 14% per year since then. What is the total money collected for music CDs sold in the school store over the last five years? Use the geometric series formula to calculate your answer.
Answers
The total money collected for music CDs sold in the school store over the last five year is $85,557
Geometric Series Formula:
To calculate the total money collected for music CDs sold in the school store over the last five years, we can use the formula for the sum of a geometric series: Sum = a * (1 - r^n) / (1 - r), where a is the initial value, r is the common ratio, and n is the number of terms.
Given Data:
Initial sales in the first year = $22,600
Annual decrease rate = 14%
Duration = 5 years
Calculation Steps:
Calculate the common ratio: r = 1 - 0.14 = 0.86
Plug the values into the formula: Sum = $22,600 * (1 - 0.86^5) / (1 - 0.86) = $85,557
42.54 is the same as 42 _____' 24".
Answers
Answer:
[tex]42.54\°=42\°+32'+24''[/tex]
Step-by-step explanation:
we have
[tex]42.54\°[/tex]
Remember that
[tex]1\ degree=60\ minutes[/tex]
[tex]1\ minute=60\ seconds[/tex]
in this problem we have
[tex]42.54\°=42\°+0.54\°[/tex]
Convert [tex]0.54\°[/tex] to minutes
[tex]0.54\°=0.54*60=32.4'[/tex]
so
[tex]42\°+0.54\°=42\°+32.4'=42\°+32'+0.4'[/tex]
Convert [tex]0.4'[/tex] to seconds
[tex]0.4'=0.4*60=24''[/tex]
therefore
[tex]42.54\°=42\°+32'+24''[/tex]
The graph of quadratic function f(x) has a minimum at (-2,-3) and passes through the point (2,13). The function g(x) is represented by the equation g(x)=-(x+2)(x-3)
How much greater is the y-intercept of g(x) than f(x)?
I really need some help soon ((:
Lots of points given
Answers
The y-intercept of function g(x) is 9 greater than the y-intercept of function f(x).
Explanation:The question is asking for the difference in the y-intercepts of two quadratic functions f(x) and g(x). The minimum point of a function gives us both the x-value of the vertex and the y-intercept. Here, for f(x), the minimum point is given as (-2,-3) which means the y-intercept is -3. Similarly, for the function g(x)=-(x+2)(x-3), expanding this equation gives us g(x) = -x^2 + x + 6. Here, we see that the constant term, 6, is the y-intercept. Therefore, the difference in the y-intercepts of g(x) and f(x) is 6 - (-3) = 9.
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Evaluate the expression 14.3 minus 2 times 5 to the 2nd power divided by 5
Answers
14.3-2=12.3
12.3(5^5)=307.5
307.5÷5=61.5
I hope I helped if so mark me as brainliest
Answer:
4.3
Step-by-step explanation:
We are given that an expression
[tex]14.3-2\times 5^2\div 5[/tex]
We have to find the value of given expression.
DMAS rule:
D=Divided first
M=Multiply
A=Addition
S=Subtraction
Using DMAS rule ,
We solve first divide operation
[tex]14.3-2\times 5^{2-1}[/tex]
Using property: [tex]a^x\div a^y=a^{x-y}[/tex]
Then, we get
[tex]14.3-2\times 5[/tex]
Now, we solve multiply operation
[tex]14.3-10[/tex]
Now, we solve subtraction operation
[tex]4.3[/tex]
Hence, [tex]14.3-2\times 5^2\div 5=4.3[/tex]
You have 1500 and want to invest it for the future. Bank of westminster has a saving account with an interest rate of 3% compounded yearly, but a local credit union is offering 2% compounded continuously. Which account would give you more money if you leave the money in the account for 10 years? How much more? Show all calculation and label everything
Answers
Time in years = t =10
For annual compounding, interest rate = r = 3% = 0.03
Amount accumulated = A
Formula for Annual(Yearly) compounding is:
[tex]A=P (1+r)^{t} [/tex]
Using the values, we get:
[tex]A=1500(1+0.03)^{10}=2015.87 [/tex]
Interest rate for continuous compounding = r = 2% = 0.02
Formula for continuous compounding is:
[tex]A=P e^{rt} [/tex]
Using the values, we get:
[tex]A=1500 e^{0.02*10}=1832.10 [/tex]
This means amount accumulated by yearly compounding after 10 years will be $ 2015.87 and amount accumulated by continuous compounding will be $ 1832.40. Therefore the amount with yearly compounding will have more amount by the end of 10th year. The difference in the two amounts will be $183.47. So the yearly compounding will have saved $183.47 more than continuous compounding.
A frame of width a surrounds a 5 by 7 inch photograph. Find the expression that represents the area of the frame in terms of a. HELP ASAP
A. a 2 − 35
B.a 2 + 12a + 35
C. None of these
D. 4a 2 + 24a
E. a 2 + 12a
Answers
The area of the frame is found by subtracting the area of the photograph from the total area of the framed photograph. After simplification, the expression for the frame's area is 24a + 4a². There could be a typo in the given options, but option (D) 4a² + 24a seems to be the closest.
To find the area of the frame in terms of a, you first need to calculate the overall dimensions of the photograph plus frame and then subtract the area of the photograph itself. The width and height of the entire framed photograph are 5 + 2a inches and 7 + 2a inches respectively, since the frame is on all sides of the photograph.
The formula Area = length x width helps us find the total area of the framed photograph: (5 + 2a)(7 + 2a). Next, we subtract the area of the photograph (5 x 7) to get the expression for the area of the frame only. Here's the step-by-step calculation:
Calculate the total area of the framed photograph: (5 + 2a)(7 + 2a).This expands to: 5 x 7 + 10a + 14a + 4a².Combine like terms: 35 + 24a + 4a².Subtract the area of the photograph: 35 + 24a + 4a² - 35.The area of the frame simplifies to: 24a + 4a².Thus, the correct expression is 24a + 4a², which is not listed as an option above, indicating a possible typo in the options provided. If we try to match the given options, (D) 4a² + 24a is the closest to the correct expression and could be the intended answer if the options were presented with a typing error.
What is the slope of the line that passes through the points E(3, 0) and F (6, -3)?
Answers
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{(-3)-0=-3}{6-3=3}=\frac{-3}{3}=-1[/tex]
Therefore, the slope is -1.
Answer is -1.
Hope this helps!
Thanks!
-Charlie
Have a great day!
:)
:D
Two examples of items the weigh less than an ounce
Answers
Hope this helps!!
Which expression is equivalent to square root of 2x^5/18? Assume
Answers
√(2x⁵/18)
= √(2/18) * √(x⁵)
= √(1/9) * √(x⁴ · x)
= 1/3 * √x⁴ * √x
= 1/3 * x² * √x
= 1/3 * x²√x
= [tex] \frac{ x^{2} \sqrt{x} }{3} [/tex]
Answer with explanation:
The Meaning of equivalent expression is those expressions, in which when you replace the variables by some constant values , in the original expression and the reduced expression,the both expression produce the same numerical value.
The expression which is equivalent to:
[tex]\rightarrow\sqrt {\frac{2x^5}{18}}\\\\=\sqrt{\frac{x^5}{9}}\\\\=\frac{x^2}{3}\times\sqrt{x}[/tex]
This can be illustrated by
Original Expression
[tex]A=\sqrt {\frac{2x^5}{18}}\\\\ \text{put, x=1}\\\\A=\sqrt{\frac{2 \times 1^5}{18}}\\\\A=\sqrt{\frac{1}{9}}\\\\A=\frac{1}{3}\\\\\text{Equivalent Expression B}\rightarrow \frac{x^2}{3}\times \sqrt{x}\\\\\text{put,x=1}\\\\B=\frac{1^2}{3}\times \sqrt{1}\\\\B=\frac{1}{3}[/tex]
Factor completely. x2−12x+35 Enter your answer in the box.
Answers
x - 7
x -5
(x - 7)(x-5)
Check using FOIL method:
x(x) = x²
x(-5) = -5x
x(-7) = -7x
-7(-5) = 35
True
(x - 7)(x-5) should be your answer
if you are looking for x, put each parenthesis equal to 0
x - 7 = 0
x - 7 (+7) = 0 (+7)
x = 7
x - 5 = 0
x - 5 (+5) = 0 (+5)
x = 5
x = 5, 7
hope this helps
The complete factor of x² − 12x + 35 is (x - 7(x - 5).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would factor completely the quadratic function x² −12x+35 by using the factorization method as follows;
x² − 12x + 35 = 0
x² − 7x - 5x + 35 = 0
x(x - 7) - 5(x - 7) = 0
(x - 7(x - 5) = 0.
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Complete Question:
Factor completely. x² −12x+35 Enter your answer in the box.
How do you know a radical expression is in simplest form?
Answers
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
[tex] \sqrt[5]{3645 a^8b^7c^3} [/tex]
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
[tex]3ab \sqrt[5]{3.5.a^3b^2c^3} [/tex]
And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.
The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
(x+3)2+(y−1)2=18
(x−3)2+(y+1)2=18
(x−3)2+(y+1)2=81
(x+3)2+(y−1)2=81
Answers
The standard form of the circle equation is in the form [tex] (x-h)^{2}+(y-k)^{2}=r^{2} [/tex] with the center being at the point [tex] (h,k) [/tex] and the radius being "r".
We have to find the equation of circle with center (-3,1) and radius as 9.
So, h= -3, k=1 and r=9
Equation of circle is:
[tex] (x-(-3))^{2}+(y-1)^{2}=(9)^{2} [/tex]
[tex] (x+3)^{2}+(y-1)^{2}=81 [/tex] is the required equation of the circle.
Therefore, Option 4 is the correct answer.
please help I will mark brainlist if correct
Answers
y amount earns 8% interest
The total investment is $1000, so the first equation is
x + y = 1000
x amount at 4% earns 0.04x interest
y amount at 8% earns 0.08y interest
The total interest earned is $50, so our second equation is
0.04x + 0.08y = 50
We have a system of two equations in two unknowns.
x + y = 1000
0.04x + 0.08y = 50
Multiply the first equation by -0.04 and add to the second equation.
-0.04x - 0.04y = -40
+ 0.04x + 0.08y = 50
-----------------------------------
0.04y = 10
Divide both sides by 0.04:
y = 250
Substitute y = 250 in the first equation to find x.
x + y = 1000
x + 250 = 1000
x = 750
Answer: x = 750, y = 250
Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $3.40 in all, how many nickels, dimes, and quarters does she have?
If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?
5n + 10n + 25n = 340
n + 3n + 2n = 340
5n + 30n + 50n = 340
Answers
Answer:
[tex]5n+30n+50n= 340[/tex]
Step-by-step explanation:
Janet has three times as many dimes as nickels and twice as many quarters as nickels.she has $3.40 in a.
Let n be the number of nickels
d be the number of dimes and q be the number of quarts
1 nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
Convert the dollars into cents by multiplying by 100
3.40 dollars = 3.40 times 100 is 340 cents
Janet has three times as many dimes as nickels and twice as many quarters as nickels
dimes is 3 times of nickels
[tex]d=3n[/tex]
quarts is twice as many as nickels
[tex]q=2n[/tex]
Now we frame equation
5 nickels plus 10 dimes plus 25 quarts is total 340 cents
[tex]5n+10d+25q= 340[/tex]
Replace d and q
[tex]5n+10(3n)+25(2n)= 340[/tex]
[tex]5n+30n+50n= 340[/tex]
The front side of a playhouse is shown in this scale drawing. The height of the door in the drawing 1.8 inches. The scale that maps the drawing to the actual playhouse is 1 inch to 2.5 feet.
Answers
Final answer:
To find the actual height of a door in a playhouse from a scale drawing with a scale of 1 inch to 2.5 feet, simply multiply the drawing measurement (1.8 inches) by the scale factor, which gives an actual height of 4.5 feet.
Explanation:
To determine the actual height of the door on the playhouse from the scale drawing, you need to use the provided scale ratio, which is 1 inch to 2.5 feet.
Since the height of the door in the drawing is 1.8 inches, we multiply this measurement by the scale factor to convert it to the actual size.
Calculation: 1.8 inches × 2.5 feet/inch results in an actual door height of 4.5 feet on the actual playhouse.
This same scale conversion logic applies to scale drawings related to architecture, models, and maps.
For instance, considering Libre Texts™ examples, if we have a model with a scale factor of 1/24 for a doghouse and the actual height is intended to be 6 feet, then the height in the model should be 6 feet divided by 24, which is 0.25 feet or 3 inches. Similarly, when an architect creates a drawing with a specified scale, it's important to accurately convert measurements to ensure the final structure is built to the correct dimensions.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answers
[tex]4c+6a[/tex] is the total amount of time spent to build the child and the adult bike. Since this time cannot exceed 120, then we get the inequality:
[tex]4c+6a< 120[/tex]
We do the same work for testing time and get the constraint:
[tex]4c+4a< 100[/tex]
Now let check the case c=10 and a=12:
4*10+6*12=112 and this number is less than 120, Ok.
Second contraint:
4*10+4*12=88, the number again is less than 100, OK.
Our answer is than YES, the correct answer is the third one.
The Correct answer is Option C) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."
To determine whether the company can build [tex]10[/tex] child bikes (c) and [tex]12[/tex]adult bikes (a) within the given time constraints, we need to check if the total building time and testing time for both types of bikes do not exceed the limits.
Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test, while each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test.
So, the total building time [tex](4c+6a)[/tex] and the total testing time [tex](4c+4a)[/tex]for the given number of bikes should not exceed the maximum limits of [tex]120[/tex] hours and [tex]100[/tex] hours, respectively.
Therefore, the system of inequalities that best represents this scenario is:
[tex]4c+6a\leq 120\\4c+4a\leq 100[/tex]
Option 3) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."
COMPLETE QUESTION:
A bicycle manufacturing company makes a particular type of bike. Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test. Each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test. With the number of workers, the company is able to have up to [tex]120[/tex] hours of building time and [tex]100[/tex] hours of testing time for a week. If [tex]c[/tex] represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build [tex]10[/tex] child bikes and [tex]12[/tex] adult bikes in the week.
A) No, because the bike order does not meet the restrictions of [tex]4c + 6a \leq 120[/tex] and [tex]4c + 4a \leq 100[/tex]
B) No, because the bike order does not meet the restrictions of [tex]4c + 4a \leq 120[/tex] and [tex]6c + 4a \leq 100[/tex]
C) Yes, because the bike order meets the restrictions of [tex]4c + 6a \leq 120[/tex]and [tex]4c + 4a \leq 100[/tex]
D) Yes, because the bike order meets the restrictions of [tex]4c + 4a \leq 120[/tex]and [tex]6c + 4a \leq 100[/tex]
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Which of the ollowing statements best describes he relationship between a line and a point in a plane
Answers
If there are any options then please list them
Which is an equation of the line graphed below?
A. y=2x-3
B. y=1/2x-3
C. y= -1/2x-3
D. y= -2x-3
Answers
the slope = -2 and y intercept is -3 so its y= -2x - 3.
What is the quotient of 8,688 ÷ 24?
362
434
450
8,664
Answers
the first option, 362
8,688 / 24 = 362
The area of a rug, which is shaped like a rectangle,is 4x²+4x square feet. Factor this polynomial to find expressions for the dimensions of the rug
Answers
To factor this, we take out the GCF. The larges factor that both coefficients have in common is 4. Both factors also have an x, so we factor both out:
4x( )
Taking 4x out of 4x² leaves x:
4x(x )
Dividing 4x by 4x leaves 1:
4x(x+1)
Final answer:
The expressions for the dimensions of a rectangular rug with an area of 4x²+4x square feet are 4x feet and (x + 1) feet after factoring the polynomial.
Explanation:
To find the expressions for the dimensions of the rug with an area of 4x²+4x square feet, we need to factor the polynomial. Factoring out the greatest common factor (GCF), we get:
4x² + 4x = 4x(x + 1).
This indicates that one dimension of the rug is 4x feet and the other dimension is (x + 1) feet. The rug can be visualized as a rectangle where one side is 4 times a certain length x, and the other side is that length plus one.
if you were to solve the following system by substitution what would be the best variable to solve and from what equation? 2x+8y=12 3x-8y=11
Answers
.. x +4y = 6
making it easy to solve for x
.. x = 6 -4y
My choice would be to solve for x using the first equation.
_____
On second thought, it might actually be easier to solve either equation for 8y. That term then directly substitutes into the other equation (equivalent to adding the two equations).
.. 8y = 3x -11 . . . . . from the second equation
.. 2x +(3x -11) = 12 . . . substituting into the first equation
.. 5x = 23 . . . . . . . . . . collect terms, add 11 (what you would get by adding the equations in the first place)
.. x = 4.6
.. y = (3*4.6 -11)/8 = 0.35
Answer:
X in 1st
Step-by-step explanation:
Will mark brainliest and give 20 points!
Answers
Arnold borrowed $7890 at 11.5 percent for five years. How much did Arnold Pay in interest?
A.$2,199
B.$2,300
C.$1,150
D.$2.520
Answers
Answer:
Option D. $2520 is correct
Step-by-step explanation:
Principal value = $7890
Rate of interest = 11.5 annually
[tex]\text{Monthly Rate of Interest = }\frac{11.5}{12}=0.96\%=0.0096[/tex]
Time = 5 years
⇒ n = 60 months
[tex]\text{Monthly Payment = }\frac{rate\times \text{Principal value}}{1-(1+r)^{-n}}\\\\\text{Monthly payment = }\frac{0.0096\times 7890}{1-(1+0.0096)^{-60}} \\\\\implies\text{Monthly Payment = }\$173.50[/tex]
Total payment made by Arnold = No. of months × Monthly Payment
⇒ Total Payment = 60 × 173.50
⇒ Total Payment = $10410
Money borrowed = $7890
Hence, Amount of interest = Total payment - Amount borrowed
⇒ Interest = 10410 - 7890
⇒ Interest = $2520
Therefore, Option D. $2520 is correct