The amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.
What is meant by compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given,
The principal amount P = $30,000
The time period t = 40 years
The rate of interest r = 10%
The number of times compounded in a year n = 1
The compound interest formula can be used to calculate the amount at the end of 40 years.
[tex]A = P(1 + \frac{r}{n})^{nt} = 30000(1 + \frac{0.1}{1})^{1*40}[/tex] = $1,357,777.67
Therefore the amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.
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Using the graph determine the coordinates of the zeros of the parabola
Answer:
-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,
find the measure of gpy
The value of ∠ GPY, given the angle measures on the figure, can be found to be 118 °
How to find the angle ?The angles ∠ GPY and ∠ KPR are congruent, which means that they are the same.
The angle ∠ GPY can therefore be found by equating both angles to themselves:
8 p + 94 = 5 p + 103
Collect like terms ;
8 p - 5 p = 103 - 94
3 p = 9
p = 9 / 3
p = 3
The value of ∠ GPY is therefore :
= 5 ( 3 ) + 103
= 15 + 103
= 118 °
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Your teacher has requested that two rows of strips be placed around the entire room what is the total length of strips that is required
The Length of wooden strip based on the information is 106 cm.
How to calculate the lengthThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
Length of wooden strip = Perimeter of a rectangular table.
= 2(Length+Breadth)
= 2(32+21)
= 2(53)
= 106 cm
Length of wooden strip is 106 cm.
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What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
Find the sum of the following arithmetic series:
Answer:
19107
Step-by-step explanation:
First, we need to find the common difference (d), which we can find by subtracting two consecutive terms. Thus, we can do d = 1 - (-3) = 4.
Now, we need to know how many terms are in the arithmetic series. We can find the number using nth term formula, which is
[tex]a_{n}=a_{1}+(n-1)*d[/tex], where a1 is the first term, n is the term position (e.g., 1st, 2nd).
Although we don't know the term position of 389, we can still plug it into the formula and solving for n will reveal it's term number and the total number of sums in the sequence:
[tex]389=-3+(n-1)*4\\392=(n-1)*4\\392=4n-4\\396=4n\\99=n[/tex]
Now, we can find the sum using the sum formula, which is
[tex]S_{n}=n/2*(a_{1}+a_{n})[/tex]
Sn can become S99 since there are 99 terms and we can let an = a99, which we know is 389.
Now, we must solve for S99:
[tex]S_{99}=\frac{99}{2}*(-3+389)\\ S_{99}=\frac{99}{2}*(386)\\ S_{99}=19107[/tex]
Triangle QRS has vertices Q(-2, 2), R(-3, -4), and S(1, - 2).
Write the coordinate notation for a clockwise rotation of 180° about the origin.
(x, y) →(
The coordinate notation for a clockwise rotation of 180° about the origin include the following: (x, y) → (-x, -y).
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Generally speaking, the mapping rule for the rotation of a geometric figure about the origin by 180° is given by this mathematical expression:
(x, y) → (-x, -y)
Where:
x represents the coordinates on the x-axis of a graph.y represents the coordinates on the y-axis of a graph.In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise direction.
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Suppose a company has fixed costs of $49,400 and variable cost per unit of
4
9
x + 222 dollars,
where x is the total number of units produced. Suppose further that the selling price of its product is
2148 −
5
9
x dollars per unit.
(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x =
(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$
(c) Form the profit function P(x) from the cost and revenue functions.
Find maximum profit.
$
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$
(a) The break-even points are approximately 1,581 and 2,809 units produced.
(b) The maximum revenue is approximately $2,088,931.47.
(c) P(x) = -5/9x² + 919x - 49,400
(d) The price that will maximize the profit is approximately $1,829.17 per unit.
What is the algebraic equations?An algebraic expression is when we use numbers and words in solving a particular mathematical question.
(a) To find the break-even points, we need to find the values of x at which the total revenue equals the total cost. The total revenue is the product of the selling price and the number of units sold, while the total cost is the sum of the fixed cost and the variable cost per unit multiplied by the number of units sold. Thus, we have:
Total revenue = Selling price × Number of units sold = (2148 - 5/9x)x
Total cost = Fixed cost + Variable cost per unit × Number of units sold = 49,400 + (49x/9 + 222)x
Setting the total revenue equal to the total cost, we get:
2148x - 5/9x² = 49,400 + (49x/9 + 222)x
Multiplying both sides by 9, we get:
19332x - 5x² = 445,110
Simplifying, we get:
5x²- 19332x + 445,110 = 0
Using the quadratic formula, we get:
x = (19332 ± sqrt(19332² - 4(5)(445,110))) / (2(5))
x ≈ 2808.6 or x ≈ 1581.4
Hence, the break-even points are approximately 1,581 and 2,809 units produced.
(b) The revenue function is given by:
R(x) = (2148 - 5/9x)x
To find the maximum revenue, we can take the derivative of the revenue function with respect to x, set it equal to zero, and solve for x:
R'(x) = 2148 - 10/9x = 0
x = 19332/10 ≈ 1933.2
Substituting this value of x into the revenue function, we get:
R(1933.2) ≈ $2,088,931.47
Hence, the maximum revenue is approximately $2,088,931.47.
(c) The profit function P(x) is given by:
P(x) = R(x) - C(x) = (2148 - 5/9x)x - (49,400 + (49x/9 + 222)x)
Simplifying, we get:
P(x) = -5/9x² + 919x - 49,400
(d) To find the maximum profit, we can take the derivative of the profit function with respect to x, set it equal to zero, and solve for x:
P'(x) = -10/9x + 919 = 0
x = 8265
Substituting this value of x into the profit function, we get:
P(8265) ≈ $1,077,927.78
Therefore, the maximum profit is approximately $1,077,927.78.
To find the price that will maximize the profit, we need to substitute the value of x into the selling price function:
Selling price = 2148 - 5/9x = 2148 - 5/9(8265) ≈ $1,829.17
Hence, the price that will maximize the profit is approximately $1,829.17 per unit.
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Can u do number 15 plsssssss
Answer:
y=x+5 x=3
Plug 3 into x
y=3+5
5+3=8
Step-by-step explanation:
The equation p=144b represents the number of pencils p in b boxes graph the relationship on the coordinate plane
Step-by-step explanation:
To graph the relationship between the number of pencils and the number of boxes, we can plot some points that satisfy the equation p = 144b.
We can choose any values of b and calculate the corresponding values of p using the equation. For example:
When b = 0, p = 144(0) = 0. So one point on the graph is (0, 0).
When b = 1, p = 144(1) = 144. So another point on the graph is (1, 144).
When b = 2, p = 144(2) = 288. So another point on the graph is (2, 288).
We can continue this process to find more points, or we can notice that the equation p = 144b represents a linear relationship between p and b with a slope of 144. This means that every time we increase b by 1, we increase p by 144.
We can use this information to graph the equation by starting at the y-intercept (0, 0) and then moving up 144 units for each unit we move to the right. This gives us a straight line with a slope of 144 passing through the origin.
The graph of the equation p = 144b looks like this:
|
| .
| .
| .
| .
| .
| .
| .
----------------------------------
0 1 2 3 4 b
The horizontal axis represents the number of boxes (b), and the vertical axis represents the number of pencils (p). Each dot on the graph represents a point that satisfies the equation p = 144b.
Jack has 7 yards of rope. He wants to cut it into pieces of different sizes. Jacks needs 84 inches of rope to tie some packages and 4 feet of rope for another project. Does Jack have enough rope? Explain.
Jack has enough rope for both projects.
What is multiplication?Multiplication is a type of mathematical operation. The repetition of the same expression types is another aspect of the practice.
For instance, the expression 2 x 3 indicates that 3 has been multiplied by two.
Given:
Jack has 7 yards of rope.
He wants to cut it into pieces of different sizes.
Jack needs 84 inches of rope to tie some packages and 4 feet of rope for another project.
First, we need to convert all the measurements to the same units.
Let's convert yards to inches and feet to inches:
7 yards = 21 feet = 252 inches
4 feet = 48 inches
Now, let's add up the lengths of rope that Jack needs:
84 inches + 48 inches = 132 inches
So Jack needs a total of 132 inches of rope.
Since 132 inches is less than the total length of rope that Jack has (252 inches).
Therefore, he does have enough rope for both projects.
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In cricket, one over consists of 6 balls being bowled. Determine the number of overs bowled if 120 balls are bowled. it form (2)
Based on the proportionate ratios of 1:6, the number of overs bowled if 120 balls are bowled is 20.
What is proportion?Proportion describes two ratios equated to each other.
Proportional values are like fractional values and can be depicted in percentages or fractions.
The ratio of one over and balls bowled = 1:6
This implies that for every 6 balls being bowled, one goes over.
Proportionately, for 120 balls bowled, the number of overs will be = 20 (120/6 x 1)
Thus, if one over consists of 6 balls being bowled, proportionately, the number of overs bowled if 120 balls are bowled is 20.
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The square below has 9X. Find the area of the square remaining after a circle of radius is 6X is removed from the square in other words find the area of the shaded region in factored form 
The area of the shaded region in factored form is 9x^2(9 - 4π)
How to find the area of the shaded region in factored formFrom the question, we have the following parameters that can be used in our computation:
Square length = 9x
Radius of circle = 6x
The area of the square is given by (side length)^2.
Since the square has 9x as a side length, its area is:
Area 1 = (9x)^2 = 81x^2
For the circle, we have
Area 2 = π(6x)^2
Area 2 = 36πx^2
The area of the shaded region is the area of the original square minus the area of the circle, which is:
Shaded = 81x^2 - 36πx^2
Factorize
Shaded = 9x^2(9 - 4π)
Hence, the area is 9x^2(9 - 4π)
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2+y2=(2x2+2y2−x)2,(0,1/2)
As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y² = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).
What is equatiοn?An equatiοn in mathematics is a claim that twο mathematical expressiοns are equivalent. An equatiοn has an equal sign, typically has οne οr mοre factοrs, and can be sοlved fοr by applying algebraic οr numerical techniques. Equatiοns are used tο represent real-wοrld phenοmena, resοlve issues, and make predictiοns in many branches οf mathematics, science, and engineering.
given:
We must first use implicit differentiatiοn tο determine the derivative οf the curve in οrder tο determine the equatiοn οf the tangent line tο the curve at the pοsitiοn (0,1/2).
By taking the derivative οf the equatiοn's twο sides with regard tο x, we arrive at:
dy/dx = 2x + 2y
(2x² + 2y²- x) * (4x - 1) (4x - 1)
When we sοlve fοr dy/dx and simplify this equatiοn, we get:
[(1 - 4x)(2x + 2y)] Equals dy/dx / [4(2x² + 2y² - x) - 2y(1 - 4x)]
The slοpe οf the tangent line at the pοint (0,1/2) can nοw be calculated by plugging in the numbers x = 0 and y = 1/2:
dy/dx = [(1 - 4(0))
(2(0) + 2(1/2))] / [4(2(0)² + 2(1/2)² - 0) - 2(1/2)(1 - 4(0))] = -1
Therefοre, the tangent line's slοpe at the pοsitiοn (0,1/2) is negative οne. We can use the pοint-slοpe fοrm οf a line tο determine the equatiοn οf the tangent line:
where (x1,y1) is the tangency pοint and m is the inclinatiοn οf the tangent line. When we enter the numbers we have, we οbtain:
y - 1/2 = -1(x - 0) (x - 0)
When we simplify this sοlutiοn, we οbtain:
y = -x + 1/2
As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y2 = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).
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"The graph of y=−3x+62
Answer:
-1/3x + 62/3
Step-by-step explanation:
Interchange the variables: y = -3x + 62
Swap the sides: -3y + 62
Move constant: -3y + 62 = x
Divide and simplify: -3y = x - 62
Answer: -1/3x + 62/3
Please help me with my answer. I'm stuck and really need help on it.
Answer:
-3 = slope, 62 = y intercept
Step-by-step explanation:
The length of a radius of a circle, measured in feet, is represented by the expression z + 3.6. The diameter of the circle is 11 4/5 ft.
What is the value of z?
Enter your answer as a decimal or mixed number in simplest form in the box.
Answer:
Step-by-step explanation:
The diameter of the circle is twice the length of the radius, so we can write:
2r = d
where r is the radius and d is the diameter.
Substituting the given diameter of 11 4/5 ft, we get:
2r = 11 4/5 ft
To find the length of the radius, we can divide both sides by 2:
r = (11 4/5) / 2
r = 5 9/10 ft
We also know that the length of the radius is z + 3.6, so we can set up the equation:
z + 3.6 = 5 9/10
Subtracting 3.6 from both sides, we get:
z = 5 9/10 - 3.6
z = 2 3/10
Therefore, the value of z is 2 3/10 or 2.3 as a decimal.
Answer: The correct answer is 2.3
Step-by-step explanation: Answer confirmed correct on test so no worries
1. Barbara has been keeping track of her long-
distance minutes. Her weekly totals for four weeks
are 48, 115, 62, and 35 minutes. What is Barbara's
weekly average, in minutes, over the four-week
period?
Barbara's weekly average for the four-week period is 65 minutes.
What is the average?
The average, also known as the arithmetic mean, is a measure of central tendency that represents the typical value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of numbers.
To find Barbara's weekly average for the four-week period, we need to add up her weekly totals and divide the sum by 4 (since there are four weeks in the period):
Average = (48 + 115 + 62 + 35) / 4
= 260 / 4
= 65
Therefore, Barbara's weekly average for the four-week period is 65 minutes.
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What is the total cost of a $713 tablet computer that is on sale at 11% off if the local sales tax rate is 7%?
The total cost of the tablet is S
(Round to two decimal places as needed.)
The total cost of the tablet is $684.48
How to calculate the total cost of the tablet?The first step is to write out the parameters given in the question
The cost of the tablet computer is $713
The tablet computer is on sale at 11%
Next is to multiply the total cost by the sales percent
11/100 × 713
= 0.11 × 713
= 78.43
= 713 - 78.43
= 634.57
The local sales tax rate is 7%
= 7/100 × 713
= 0.07 × 713
= 49.91
The total cost can be calculated as follows
= 49.91 + 634.57
= 684.48
Hence the total cost of the tablet is $684.48
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Emails arrive randomly on Oliver's computer at an average rate of 1.46 per hour. Stating a necessary assumption, find the probability that between 9.00am and 11.30am Oliver receives: (i) no emails
The probability that Oliver will receive no emails in between 9.00am and 11.30am is 2.599%.
What is Poisson Distribution?Poisson Distribution is defined as a discrete distribution which measures the likelihood of happening an event in a certain period of time.
The formula for Poisson distribution is,
P(x) = (e^(-λ) λˣ) / x!
Given that,
Average rate of arrival of emails in an hour = 1.46 per hour
Between 9.00 am and 11.30 am, there are 2.5 hours.
Average rate of arrival of emails in 2.5 hours = 2.5 × 1.46
= 3.65
So, λ = 3.65
x = 0 (since no emails.)
P(0) = (e^(-3.65) (3.65)⁰) / 0!
= e^(-3.65)
= 0.02599
= 2.599%
Hence the probability is 2.599%.
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST FOR ANSWERS
The explicit formula of the function s(n) is s(n) = 2n
The pattern of the infinite sequenceThe domain and the range of h(n)
Given that
h(n) is the number of houses
The possible values of n and h(n) are whole numbers
So, we have
Domain: All set of whole numbersRange: All set of whole numbersThe values of h(5) and h(11)
Based on the patterns in the sequence, we have
h(n) = n
So, we have
h(5) = 5
h(11) = 11
The explicit function of h(n)
In (b), we have
h(n) = n
The values of s(4) and s(7)
Given that
s(n) is the number of segments
Based on the patterns in the sequence, we have
s(n) = 2n
So, we have
s(4) = 8
s(7) = 14
The growth pattern of s(n)
Above, we have
s(n) = 2n
The above equation is a proportional equation
This means that
The growth pattern of s(n) is linear, with a constant rate of change
The explicit function of s(n)
Above, we have
s(n) = 2n
Hence, the explicit of s(n) is s(n) = 2n
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Suppose you take out a 45-year $150,000 mortgage with an APR of 6%. You make payments for 3 years (36 monthly payments) and then consider refinancing the original loan. The new loan would
have a term of 15 years, have an APR of 5.1%, and be in the amount of the unpaid balance on the original loan. (The amount you borrow on the new loan would be used to pay off the balance on the
original loan.) The administrative cost of taking out the second loan would be $1900. Use the information to complete parts (a) through (e) below.
a. What are the monthly payments on the original loan?
(Bound to the nearest cent as needed.)
The monthly payments on the original loan are $899.33.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the monthly payments on the original loan, we can use the formula for the monthly payment of an amortized loan:
M = P (r/12)(1 + r/12)ⁿ/ ((1 + r/12)ⁿ - 1)
where M is monthly payment, P is principal, r is monthly interest rate, n is total number of payments
For the original loan, P = $150,000, r = 0.06/12 = 0.005, and n = 45 years x 12 months/year = 540 months.
Substituting these values into the formula, we get:
M = 150,000(0.005)(1 + 0.005)⁵⁴⁰ / ((1 + 0.005)⁵⁴⁰- 1)
= 899.33
Therefore, the monthly payments on the original loan are $899.33.
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A survey of 520 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found:
172 watched TV
156 ate pizza
38 watched TV and ate pizza, but did not hang out with friends
36 watched TV and hung out with friends, but did not eat pizza
40 hung out with friends and ate pizza, but did not watch TV
38 watched TV, hung out with friends, and ate pizza
63 did not do any of these three activities
How may 18-24 year olds (of these three activities) only hung out with friends last Friday night?
Your Answer:
To find out how many 18-24 year olds only hung out with friends last Friday night, we need to subtract the number of people who engaged in other combinations of activities from the total number of people surveyed:
Total surveyed = 520
Watched TV only = 172 - 38 - 36 - 38 = 60
Ate pizza only = 156 - 38 - 36 - 40 = 42
Watched TV and ate pizza = 38
Did not do any of these three activities = 63
Therefore, the number of 18-24 year olds who only hung out with friends last Friday night can be calculated as follows:
Only hung out with friends = Total surveyed - (Watched TV only + Ate pizza only + Watched TV and ate pizza + Did not do any of these three activities)
Only hung out with friends = 520 - (60 + 42 + 38 + 63)
Only hung out with friends = 217
Therefore, 217 out of the 520 18-24 year olds surveyed only hung out with friends last Friday night.Bob's Gift Shop sold 550 cards for Mother's Day. One salesman, Arun, sold 2% of the cards sold for Mother's Day. How many cards did Arun sell?
Answer:
55 cards
Step-by-step explanation:
15 POINTS
Identify the zeros in the given graph
{-3,-1,4,1}
{-3,-1,1}
{-3,-4,1}
{-3,1}
Answer:
-3, 1
Step-by-step explanation:
these are points where the curve cuts the x-axis
at this point the value of y=0
Kabir has three fuel containers. One has a capacity of 7 litres,
one has a capacity of 4 litres and one has a capacity of 3 litres.
The 7 litre container is full, the other two containers are empty.
None of the containers has a measurement scale.
How can Kabir transfer the fuel so that two of the containers contain
a volume of 2 litres each, and the other contains a volume of 3 litres,
vithout having to estimate?
The solution is, the capacity of the largest container that can fill the tanks an exact number of times is, 44 litres.
What is CGF?In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.
here, we have,
We subtract the remainders from the amounts.
447 - 7 = 440
577 - 5 = 572
669 - 9 = 660
Now we need the GCF of 440, 572, 660
440 = 2³ × 5 × 11
572 = 2² × 11 × 13
660 = 2² × 3 × 5 × 11
GCF = 2² × 11 = 44
The greatest common factor is 44.
Answer: 44
Check:
447/44 = 10 reminder 7
577/44 = 13 remainder 5
669/44 = 15 remainder 9
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There are 5 positive integers with the mean +5, the median = 5, and the mode = 8. What is the range of this data?
In response to the query, we have that So, depending on the precise equation choice of five positive numbers, the data range might be 5, 6, or 7.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.
The five positive integers will be denoted as a, b, c, d, and e.
We know that c must equal 5, since the median is 5.
The three integers we now have add up to 15 (a + b + c = 15).
We may write the equation as follows since the mean is 5:
(a + b + c + d + e)/5 = 5
a + b + 18 = 25
a + b = 7
a = 1, b = 6, c = 5, d = 8, e = 8
a = 2, b = 5, c = 5, d = 8, e = 8
a = 3, b = 4, c = 5, d = 8, e = 8
Range = 8 - 1 = 7
Range = 8 - 2 = 6
Range = 8 - 3 = 5
So, depending on the precise choice of five positive numbers, the data range might be 5, 6, or 7.
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write the slope intercept form of the equation of the line described.
through: (5, 0) perp to y= -5/3x
The slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.
What is the slope-intercept form of a linear equation, and how can we determine the equation of a line perpendicular to another line?
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. This form is useful for graphing lines and solving problems involving linear relationships.
To determine the equation of a line perpendicular to another line, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
Calculate the slope-intercept form:
We are given that the line we are looking for passes through the point (5, 0) and is perpendicular to the line y = -5/3x. To find the equation of the line, we need to determine its slope and y-intercept.
The slope of the given line is -5/3, so the slope of the line perpendicular to it is:
-1/(-5/3) = 3/5
Therefore, the slope of the line we are looking for is 3/5.
Next, we can use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. We can substitute m = 3/5 and (x1, y1) = (5, 0) to get:
y - 0 = 3/5(x - 5)
Simplifying this equation, we get:
y = 3/5x - 3
which is the slope-intercept form of the equation of the line we were looking for.
Therefore, the slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.
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Which shows the function y=3x+12 in factored form and identifies the zero of the function?
The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.
What is a linear function?A linear function is a polynomial of degree 1, or a mathematical expression that describes a relation between two variables. It is often written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.
The factored form of a linear equation is the same as the standard form of the equation, with the exception that the coefficients of the variables are each expressed as a product of their prime factors. In the case of y=3x+12, the factored form is (3x+12). The zero of the function (also known as the root of the equation) is the value of the variable that will result in a value of 0 for the equation. To find the zero of the function, we need to set the equation equal to 0 and solve for the value of x. When we set y=0, we get 3x+12=0, which can be solved to get x=-4. Therefore, the zero of the function is -4.
The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.
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QUESTION 9
Consider the following argument: If Sarah-Beth applies a post-colonial reading to the required text, Sara-Beth impresses
her professor and earns an A for the class. Sarah-Beth impresses her professor and earns an A for the class. So, Sarah-
Beth applies a post-colonial reading to the required text. This argument is
a. valid
b. invalid
O c. true
d. false
O e. None of the above
What is the mathematical expression for twice a number by k?
Answer: less then
Step-by-step explanation: Less than means subtraction, whereas more than means addition. · Saying twice a number means that you are multiplying that number by 2.
HELP ASAP NO ROCKY
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NO LINKS
Answer:
A. the graph of the function does not form a straight line.
Step-by-step explanation:
MTH 115 Lesson 8 Practice Problems
Answer Key
1. A credit card charges 23% APR and a minimum of 2.5%. If you pay the minimum on a balance of $450 what would the decrease in your balance be? Round to the nearest cent $2.63.
2. A month has 30 days in it. You post a payment of $600 on the 15th of the month. The Balance was $2000 before the payment. What is the interest on the average daily balance if the APR is 23%? $32.58
3. The monthly payment on a house loan is $876. The purchase price of the house was $125,000. If you pay this for 30 years how much interest did you pay? $190,360
4. A house costs $275,000. The rate is 7.3% with monthly payments for 30 years. What is the payment? Round to the nearest dollar. $1885
1. The decrease in the balance would be $11.25 2. The interest on the average daily balance would be $28.77. 3. The total interest paid would be $214,960. 4. The payment would be $1,978.
Describe Interest?Interest refers to the amount of money that is charged or earned for the use of borrowed money. It is a fee paid by a borrower to a lender for the use of funds, or a payment received by a depositor from a bank for the use of their money.
Interest rates are typically expressed as a percentage of the principal amount and can be fixed or variable, depending on the terms of the loan or investment. The interest rate charged on a loan is determined by a number of factors, including the creditworthiness of the borrower, the length of the loan, and prevailing market conditions.
1. The decrease in the balance would be $11.25.
Calculation:
Minimum payment = 2.5% of $450 = $11.25
New balance after paying the minimum = $450 - $11.25 = $438.75
The decrease in the balance would be $450 - $438.75 = $11.25.
2. The interest on the average daily balance would be $28.77.
Calculation:
The balance for the first 14 days of the month = $2000
The balance for the last 16 days of the month = $1400
Average daily balance = (14 * 2000 + 16 * 1400) / 30 = $1666.67
Interest for the month = 0.23 / 12 * $1666.67 = $28.77
3. The total interest paid would be $214,960.
Calculation:
No. of payments = 30 * 12 = 360
Total amount paid = $876 * 360 = $315,360
Total interest paid = $315,360 - $125,000 = $190,360
4. The payment would be $1,978.
Calculation:
Monthly interest rate = 7.3% / 12 = 0.6083%
Number of payments = 30 * 12 = 360
Payment = $275,000 * 0.006083 / (1 - (1 + 0.006083)^-360) = $1,977.54 (rounded to nearest dollar: $1,978)
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