Applying the area of square and triangle, the amount of paper needed is: 180 inches².
What is the Area of a Square Shape and Area of a Triangular Shape?The area of a square shape = (side length of the shape)².
The area of a triangular shape = 1/2(base)(height)
The diagram that illustrates the problem given is shown in the image attached below, where the triangular paper to cover the triangular plank and the square paper for the square plank are shown also with their dimensions.
Therefore, the amount of paper that would cover the piece of art = area of the square shape + area of the triangular shape.
Area of the square shape = 12² = 144 inches²
Area of the square shape = 144 inches²
Area of the triangular shape = 1/2(12)(6)
Area of the triangular shape = 36 inches²
Amount of paper needed = 36 + 144
Amount of paper needed = 180 inches²
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Complete Question:
Theresa created a piece of art by attaching a square plank to a triangular plank. The square plank has a perimeter of 48 inches. The triangular plank has a base length of 12 inches and a height of 6 inches. She wants to cover the piece of art with colored paper.
How many square inches of paper are needed to cover Theresa's art piece?
Write one quadratic equation that forms a graph through the points (−4,2) and (1,2) and has a
minimum value at the vertex.
Explain it in detail please
Quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.
Graph is attached.
As given in the question,
Quadratic equation passes through the points (-4,2) and (1,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (1,2)
(y-y₁)/ (x-x₁) = (y₂ -y₁)/(x₂ -x₁)
⇒(y-2)/(x +4) =(2-2)/)1+4)
⇒ (y-2)/(x+4) =0
⇒y -2 =0
⇒y =2
Quadratic equation formed from the given points (-4,2) and (1,2) is y =2.
which represents the horizontal line and does not have any vertex.
Graph of the quadratic equation y =2 is attached.
Therefore, quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.
Graph is attached.
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(Lesson 22)
P=L(+)
a. Find the monthly payment P on a $75,000 loan with an
annual interest rate of 4% (let r= .9967) and a term of
20 years (n = 240 months). Show your work below and
circle your final answer.
The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
Given that,
We have to calculate the monthly payment P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4% (let r=.9967).
We know that,
Formula for monthly payment is P(i(1+i)ⁿ/(1+i)ⁿ-1)
Here,
P is principal amount $75,000
n is number of months 240 months
i is interest rate 4% is 0.04
=P(i(1+i)ⁿ/(1+i)ⁿ-1)
=75,000(0.04(1+0.04)²⁴⁰/(1+0.04)²⁴⁰-1)
=75,000(0.04(1.04)²⁴⁰/(1.04)²⁴⁰-1)
=75,000(0.04(12246.20236)/(12245.20236)
=75,000(0.04×1.000081665)
=38455
Therefore, The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
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Please Help 2
find (f/g)(m)iff(m)=8m3+5m2-32m-20 and g(m)=8m+5
Diving the polynomial expression f(m) = 8m^3 + 5m^2 - 32m - 20 and g(m) = 8m + 5, as (f/g)(m) using long division gives m^2 - 4
What is long division ?Long division refers to a way of dividing large numbers including polynomials
performing the long division (f/g)(m) gives
divisor 8m + 5
dividend 8m^3 + 5m^2 - 32m - 20
quotient m^2
multiplication (quotient and divisor) = 8m^3 + 5m^2
subtraction (dividend - result of multiplication) = - 32m - 20 new dividend = - 32m - 20
divisor 8m + 5
dividend - 32m - 20
quotient -4
multiplication (quotient and divisor) = - 32m - 20
subtraction (dividend - result of multiplication) = 0
new dividend = 0
The quotient is then added as
m^2 - 4
The second option is the correct option
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1. Solve the equation (9-6p) =
-11 for p.
Answer:
p=p=10/3
Explanation:
9-6p =-11=p=10/3
What is the value of x?
Answer:
x = 62
Step-by-step explanation:
40 + (x + 16) + x = 180 (sum of angles in a triangle=180)
2x + 56 = 180
2x = 124
x = 62
Paula stands on the side of a river and sights the opposite bank at an angle of depression of 7 degrees. if Paula is 5.5 feet tall, approximately how wide is the river, to the nearest foot?
The width of the river to the nearest foot will be 45 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Paula remains on a waterway and sights the contrary bank at a point of the wretchedness of 7 degrees.
If Paula is 5.5 feet tall.
Let 'w' be the width of the river. Then the width of the river will be given as,
tan 7° = 5.5 / w
0.12278 = 5.5 / w
w = 44.79
w ≈ 45 feet
The width of the river to the nearest foot will be 45 feet.
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Lacey inherited some money from her grandfather and put it in a bank account that earns 4%
interest compounded monthly. After 2 years, Lacey had $700.00 in the bank account. How
much interest did she earn?
Round your answer to the nearest cent.
The interest eared from the given amount, rate of interest and time period is $426.883.
Given that, amount = $700, rate of interest = 4% and time period = 2 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]
Let the money deposited be x.
So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]
⇒ [tex]700=x(1+0.04)^{24}[/tex]
⇒ [tex]700=x(1.04)^{24}[/tex]
⇒ 700 = 2.563x
⇒ x=700/2.563
⇒ x=$273.117
So, interest = 700-273.117
= $426.883
Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.
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Adam has 6 cookies less than
Tony, there are a total of 15 cookies between both of them.
How many cookies does Tony
have?
Tony has 10.5 cookies.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
Given that, Adam has 6 cookies less than Tony, there are a total of 15 cookies between both of them.
Let the number of cookies Tony has be x,
x+x-6 = 15
2x - 6 = 15
2x = 21
x = 21/2 = 10.5
Hence, Tony has 10.5 cookies.
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
A) The data modelling is an exponential function.
B) The explicit funciton that will be used to represent the data is;
f(n) = 2(2)^(n - 1)
C) The average rate of change here is; 7
How to model a function?A) We are given the coordinates as;
(1, 2), (2, 4), (3, 8), (4, 16)
From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.
Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.
B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:
f(n) = ar^(n - 1)
Since first term ; a = 2
and common ratio r = 2, then we can say that;
f(n) = 2(2)^(n - 1)
C) The formula for average rate of change here is;
dy/dx = (y₂ - y₁)/(x₂ - x₁)
The coordinates of the 2nd and 4th day are;
(2, 4) and (4, 16)
Thus;
dy/dx = (16 - 4)/(4 - 2)
dy/dx = 14/2 = 7
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1. Assuming the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan. a. Calculate the total amount of loan, monthly rate, number of payment periods, monthly payment, total interest paid, and amount borrowed. b. With the aid of what PMT function in a one variable condition, calculate monthly payment, total amount payable, total interest payable for: 11 yrs, 14 yrs, 18 yrs ,20 yrs, 28 yrs, 31 yrs mortgage.
The total amount he will pay after 25 years is $18,97,500.
His monthly payment will be $6,325.
Given, the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan.
Now, the total amount of the loan be,
720000 - 60000 = 660,000
monthly rate = 7.5/12 = 0.625%
Number of payment periods = 25
Total amount he has to pay after 25 years,
660000 + (660000×7.5×25)/100
= $18,97,500
His monthly payment will be
1897500/25×12
= $6,325
Hence, the total amount he will pay after 25 years is $18,97,500
also, his monthly payment will be $6,325.
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Juan has a sandbox and wants to double the length, width and height. if the original box holds 1 cubic foot of sand, how many more cubic feet of sand must be added to fill the box
The box must be added with 7 cubic feet of sand
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also be defined as the capacity of an object.
It is measured in cubic units.
The volume of a box is length × width × height
represent the original length, width and height by x ,y ,z respectively
This shows that the volume of the original box= x× y× z = 1cubic foot
when the original length, width and height are doubled to give the new dimensions
Therefore the new length,width and height will be 2x, 2y and 2z
the volume of the new formed box = 2x×2y×2z
= 8xyz
XYZ= 1cubic foot
therefore 8xyz = 8cubic feet
since there is 1 cubic foot of sand in the box already,
then( 8-1)cubic feet = 7cubic feet will be added.
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3x ≥5 or -3/5x-3>7 solve the compound inequality
By using the concept of linear inequation, the required solution is
[tex]x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here the given linear inequation is
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7[/tex]
Now
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5} x > 7 + 3\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5}x > 10\\\\x > \frac{5}{3} \ or \ x < \frac{10 \times 5}{-3}\\\\x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
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Simplify completely. 3x+18 divided 18
solution
3x+18/18
ans4
Use the graph below to answer the following questions.
⦁ Estimate the available territory at 20 years
⦁ Estimate the available territory at 15 years
⦁ Does this graph represent exponential growth or decay?
⦁ As the time decreases the available territory _______________
Answer:
a) about 190 acres
b) around 240 acres
c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.
It takes a word processor 45 minutes to word process and spell check 12 pages. Find how long it takes her to word process and
spell check 40 pages.
It takes the word processor
minutes.
Answer: the correct answer is 150 minutes for 40 pages.
Step-by-step explanation:
It takes a word processor 45 minutes to word process and spell check 12 pages.
45 minutes / 12 pages = 3.75 minutes per page
3.75 min/page x 40 pages = 150 minutes
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Oliver saves 10% of his weekly earnings for living expenses. He usually makes $520 each week. This week he made 10% more. Oliver incorrectly claims that he has $520 left for spending money this week.
Answer:
10% of $520
=$52
Money made this week :
$520+$52=$572
Saving:
10% of $572
=$57.2
Money left:
$572-$57.2=$514.8
Please mark as brainliest
Answer: We have been given that,
Oliver's weekly earnings = $520
His earnings this week = 10% of $520 +$520
= $520+$52= $572
As he saves 10% of his weekly earnings so he would have been left with
= 10% of $572
= $57.2
So, he only has $52.7 left for spending money this week
Step-by-step explanation:
The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft. What is the mean height of the low tides? (I need to show work.)
The mean height of the low tides is 1.21 ft
The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft
The mean of a sample is given by the formula =
summation of all observation / number of observation
mean = (x₁ + x₂ + x₃ + x₄)/ 4
mean = -0.22 + 2.64 - 0.22 + 2.64 / 4
mean = 4.48 / 4 = 1.21
Therefore, the mean height of the low tides is 1.21 ft
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A local grocery store offers 3 brands of laundry detergent. Brand A costs $14.99 and contains 40 fluid ounces of detergent. Brand B costs $19.99 and contains 50 fluid ounces of detergent. Brand C costs $21.99 and contains a half-gallon of detergent. Which of the detergents has the best value?
Answer:
$ 52.63
Step-by-step explanation:
The brand C detergent has the best value.
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.
As per the given data in the question:
The information regarding the quantity and cost of 3 detergents is given in the question.
We have to find out which detergent is the most economical.
The detergent with the lowest cost/quantity will be the most economical.
For Brand A
Cost = $14.99
Quantity = 40 ounces
cost/quantity = 14.99/40 = 0.374 dollar/ounce
For Brand B
Cost = $19.99
Quantity = 50 ounces
cost/quantity = 19.99/50 = 0.399 dollar/ounce
For Brand C
Cost = $21.99
Quantity = 1/2 gallon = 64 ounces
cost/quantity = 21.99/64 = 0.343 dollar/ounce
The brand C detergent has the best value.
Hence, The brand C detergent has the best value.
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Find the measure of the exterior angle. (hint: find x first, then plug it in to the exterior angle)
Answer:
[tex]3x - 10 = 25 + x + 15[/tex]
according to theorem
[tex]3x - x = 40 + 10 \\ 2x = 50 \\ x = 25[/tex]
Hopefully this will help u
See question in screenshot below.
The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3
What is an exponential equation?An exponential equation is an equation that has exponents that consists of variables.
The given equation is y = 2ˣ
The equation for the transformation is; y = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the x and y-values to find the value A and k gives the following simultaneous equations;
When x = 0, y = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When x = 1, y = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
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The pH of solution measures its acidity and can be determined using the formula pH= -log(base of 10 )C, where is the concentration of hydronium ions in the solution. measured in moles per litre .A lower pH indicates a more acidic solution.
The concentration of Hydronium ions type of coffes is 1.3 x 10above-5 moles per liter .
Calculate the pH of the coffee.
The value of pH of the coffee is 4.89
How to determine the pH of the coffee?pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution
Given: The formula pH= -log₁₀ C,
where is the concentration of hydronium ions in the solution measured in moles per litre
The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter
To calculate the pH, we will substitute the value of the concentration (C) into the given formula:
pH= -log₁₀ C (C = 1.3 x 10⁻⁵ moles per liter)
pH = -log₁₀(1.3 x 10⁻⁵) = 4.89
Therefore, the pH of the coffee is 4.89
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helpppp!!
A certain number of quarters, five times as many pennies as quarters and 12 more
dimes than quarters are worth $8.00. How many of each coin are there?
Answer:
Step-by-step explanation:
i think the answer is 10 or 5
Exercises 12 -15, decide whether the statement is correct or incorrect. Explain your reasoning in words or by drawing pictures. 12. 1/3 equal to 4/12 13. 4/6 equal to 2/3 14. 2/5 equal to 1/3 15. 2/5 equal to 5/10.
The correct statement:
1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10
incorrect statement: 2/5 equal to 1/3
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
a) 4/12
Writing into Simplest form
4/12 = 1/3
b) 4/6
Writing into Simplest form
4/6 = 2/3
c) 2/5 cannot be simplified to 1/5
d) 5/10
Writing into Simplest form
5/10= 1/2
Hence, The correct statement: 1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement: 2/5 equal to 1/3.
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A person needs to borrow $10,000 for 240 days. A lender offers a 9% simple discount note/loan. Determine the amount of interest for the loan and the proceeds of the discounted note. Label each. (Use 365 days)
The simple interest on a $10000 loan offered at a rate of 9% over 240 days is $10591.78
Simple InterestSimple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
The formula is given as
S.I = p(1 + rt)
S.I = simple interestp = principalr = ratet = timeSubstituting the values into the equation,
S.I = 10000(1 + 0.09 * 240)
S.I = 10591.78
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Your friend uses the figure to say that all the exterior angles of any isosceles triangle are congruent. Is your friend correct? Explain your reasoning
Answer:
All the exterior angles of any isosceles triangle are congruent - FALSE statementStep-by-step explanation:
We know that the exterior angle of a triangle is the sum of remote interior angles.
If the triangle is equilateral then the sum of any two interior angles is same otherwise, with any isosceles triangle, we get different sums and therefore the friend is wrong.
Answer:
No.
Step-by-step explanation:
An isosceles triangle has two sides of equal length. Therefore, only two of its interior angles are congruent.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). Therefore, as not all of the three interior angles of an isosceles triangle are congruent, all the exterior angles will also not be congruent.
4. Which expression represents 7 more than the quotient of 12 and 4?
A. (12+4) + 7
B.7 x (12+4)
C.7+(12-4)
D. (7+12) + 4
Answer:
C
Step-by-step explanation:
Even though quotient means divide I instead used the minus symbol since they both mean something negative or taking away. Then, the 7 goes before everything adding onto what was left from the second part.
The operation * is defined as a*b=a+b-2ab
Evaluate 2* (3*5)
(2*3)*5
The value of 2*(3*5) = 68.
The value of (2*3)*5 = 68.
What is multiplication?
A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of 6 and 5 is 30.
Given: The operation * is defined as,
a*b = a + b - 2ab
We have to find the value of 2*(3*5) and (2*3)*5
First to find the value of 2*(3*5).
2*(3*5) = 2*(3 + 5 - 30) = 2*(-22) = 2 + (-22) - 2(-22)(2) = 68.
Now to find the value of (2*3)*5.
(2*3)*5 = (2 + 3 - 12)*5 = -7*5 = (-7) + 5 - 2(-7)(5) = -2 + 70 = 68.
Therefore, 2* (3*5) = 68 and (2*3)*5 = 68.
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Alan has 229 songs on a playlist. He's categorized them in the following manner: 11 rock, 21 Latin American, 46 gospel, 30 country, 39 rap, 25 classical, and 57 pop. If Alan begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song?
=================================================
Work Shown:
11 rock songs
229 total
11/229 is the probability of randomly selecting a rock song. The fraction doesn't reduce since 11 and 229 have no factors in common (other than 1).
If you wanted to convert to decimal form, then 11/229 = 0.04803 approximately. This converts to about 4.803%
QUEST
Find the median of the numbers in the following list.
Select the correct answer below:
O22
O 21
26
O24
O 14
26, 13, 39, 22, 42, 39, 18, 21, 32, 14
Step-by-step explanation:
first order them from least to greatest
13,14,18,21,22,26,32,39,39,42
then just look for the term in the middle
sunset there are 2 numbers in the middle you will add them both and subtract them by 2
42+39 then / 2 =40.5
Differentiate the function with respect to x.
On differentiating the given function with respect to x , we get f'(x) = 10x⁴ - 8x⁻⁵ .
In the question ,
it is given that
the function is f(x) = 2x⁵ + 3 + 2x⁻⁴
the derivative of x⁵ is [tex]=[/tex] 5x⁴ ,
the derivative of 3 is = 0
the derivative of x⁻⁴ = -4x⁻⁵ .
on differentiating the function f(x) = 2x⁵ + 3 + 2x⁻⁴ with respect to x is
f'(x) = 2*d/dx(x⁵) + d/dx(3) + d/dx(x⁻⁴)
Substituting the values of derivative ,
we get
f'(x) = 2*(5x⁴) + 0 + 2(-4x⁻⁵)
f'(x) = 10x⁴ - 8x⁻⁵
Therefore , On differentiating the given function with respect to x , we get f'(x) = 10x⁴ - 8x⁻⁵ .
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