Therefore, for the first coordinate point (-x, y), the ultimate reflected points are (-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .
Describe coordinate plane.A coordinate system is a technique used to precisely find points or additional mathematical objects on a distance, such as Euclidean space, by using one or so more values or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations.
Here,
The x-coordinate remains constant and the y-coordinate is cancelled when a point on the coordinate plane is reflected over the x-axis (i.e. multiplied by -1). The y-coordinate remains constant and the x-coordinate is cancelled when a point is reflected over the y-axis.
Let's mirror the point (-2, 3) first over the x-axis and then over the y-axis as an illustration:
The x-coordinate remains constant while the y-coordinate is cancelled when reflecting over the x-axis. In light of this, the argument is (-2, -3).
The x-coordinate is cancelled while the y-coordinate remains constant when reflecting over the y-axis. In light of this, the argument is (2, -3).
We can reflect the coordinates (-x, y) and (x, -y) over the x-axis and then over the y-axis:
Therefore, for the first point (-x, y), the ultimate reflected points are
(-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .
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The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it
In the word problem, The account have left $67 in 13 weeks.
What is word problem?Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here the given expression represents the medical savings account.
=> y=-24x+379
Here y represent of money and x represent number of weeks.
Here Amount of money y = $67 then,
=> 67=- 24x+ 379
=> -24x = 67-379
=> -24x= -312
=> x = -312/-24
=> x = 13
Hence The account have left $67 in 13 weeks.
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i need help by tonight
7 x 4 = 28
than you need to do y + 5x
than you get you answer 6
sky can run 3 miles per hour faster than her sister rose can walk. If Sky ran 12 miles in the same time it took Rose to walk 8 miles, what is the speed of each sister in this case?
Sky can run 3 miles per hour faster than her sister rose can walk. If Sky ran 12 miles in the same time it took Rose to walk 8 miles, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.
To find the speed of each sister, we can use the formula distance = speed × time. We can set up a system of equations to solve for the speeds of Sky and Rose. Let s be the speed of Sky and r be the speed of Rose. Then we have:
12 = s × t (equation 1)
8 = r × t (equation 2)
We are also told that Sky can run 3 miles per hour faster than Rose, so we can write:
s = r + 3 (equation 3)
Now we can substitute equation 3 into equation 1 and solve for t:
12 = (r + 3) × t
t = 12 / (r + 3)
Next, we can substitute this value of t into equation 2 and solve for r:
8 = r × (12 / (r + 3))
8(r + 3) = 12r
8r + 24 = 12r
24 = 4r
r = 6
So the speed of Rose is 6 miles per hour. We can use equation 3 to find the speed of Sky:
s = 6 + 3
s = 9
So the speed of Sky is 9 miles per hour. Therefore, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.
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The speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.
Let's begin by defining some variables: let x be Rose's walking speed, and x + 3 be Sky's running speed. Since we know that Sky ran 12 miles and Rose walked 8 miles in the same amount of time, we can write an equation to represent this:
12 / (x + 3) = 8 / x
Cross-multiplying and simplifying gives us:
12x = 8x + 24
4x = 24
x = 6
So Rose's walking speed is 6 miles per hour, and Sky's running speed is 6 + 3 = 9 miles per hour.
Therefore, the speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.
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Blake has a 52% free throw success rate so his coach wants him to practice. What is the probability of him making more than 7 out of 25 shots in practice?
Therefore, the probability of Blake making more than 7 out of 25 shots in practice is 0.9984.
To determine the probability of Blake making more than 7 out of 25 shots in practice, we can use the binomial probability formula: P(X = x) = (n choose x) * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success.
In this case, n = 25, p = 0.52, and we want to find the probability of x > 7. We can calculate this by finding the probability of x ≤ 7 and subtracting it from 1.
P(X > 7) = 1 - P(X ≤ 7)
= 1 - [(25 choose 0) * (0.52)^0 * (0.48)^25 + (25 choose 1) * (0.52)^1 * (0.48)^24 + ... + (25 choose 7) * (0.52)^7 * (0.48)^18]
= 1 - 0.0016
= 0.9984
Therefore, the probability of Blake making more than 7 out of 25 shots in practice is 0.9984.
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Can you help me with these questions please
The solution is, the initial amount that you invested is $1200.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
Let the initial amount that you invested be $ x.
We are told that the new balance after investing $500 is $1760.
Thus, the balance you had before the deposit $500 us;
$1760 - $500 = $1260
So, when the amount invested was $x, the balance was $1260.
Since this money earned 5% interest on the amount you initially
Thus;
$1260 = initial deposit + (5% of inital deposit)
Thus;
x + (5% * x) = 1260
x + (0.05x) = 1260
1.05x = 1260
x = 1260/1.05
x = $1200
Hence, The solution is, the initial amount that you invested is $1200.
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The diameter of a circle is 13 m. Find its area to the nearest tenth.
Answer:
132.7cm²
Step-by-step explanation:
area of circle = πr²
6.5² * π
=132.7cm²
Consider the polynomial:
p(x) = x4+12x-5
A) Use the Rational Root Theorem to list the four possible rational zeros of p.
B) The complex number r= 1-2i is a zero of p. Give exact values for all four zeros.
A) The Rational Root Theorem states that the only rational zeros of p(x) = x4+12x-5 must be a factor of -5 divided by a factor of 1. Therefore, the four possible rational zeros are -5, -1, 1, and 5.
B) The other three zeros is 1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)
A) The Rational Root Theorem states that if a polynomial with integer coefficients has a rational root r = p/q (where p and q have no common factors), then p must divide the constant term of the polynomial and q must divide the leading coefficient.
The constant term of p(x) = x^4 + 12x - 5 is -5, which has the factors ±1 and ±5. The leading coefficient is 1, which has the factors ±1. Therefore, the possible rational roots are:
±1/1, ±5/1, ±1/5, ±5/5 (which simplifies to ±1)
B) If r = 1 - 2i is a zero of p(x), then its complex conjugate r* = 1 + 2i is also a zero of p(x), since p(x) has real coefficients. Therefore, we can factor p(x) as:
p(x) = (x - r)(x - r*)(x²+ bx + c)
where b and c are the coefficients of the quadratic factor. We can expand this and compare coefficients to get:
x⁴ + 12x - 5 = (x - 1 + 2i)(x - 1 - 2i)(x² + bx + c)
Expanding the first two factors gives:
(x - 1 + 2i)(x - 1 - 2i) = x² - 2x + 5
Therefore, we have:
x⁴ + 12x - 5 = (x² - 2x + 5)(x² + bx + c)
Expanding the right side and comparing coefficients, we get:
b = -2 and c = -6
So the quadratic factor is:
x² - 2x - 6
We can find its roots using the quadratic formula:
x = [2 ± √(4 + 4(6))] / 2
x = 1 ± √(7)
Therefore, the four zeros of p(x) are:
1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)
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Mail went to buy some veg he bought x kgs of tomato and y kgs of potato the total cost of veg comes out to be rs 200 now if the cost of 1 kg of tomato is rs50 and 1 kg of potato rs20 then ans the follow (1) liner equation to represent the total cost (2) if mail bought x kg of tomato and 2.5 kg of potato find the value of x (3) find the point at which the graph of 5x+2y=20 cuts x axis
Answer:
Linear equation to represent the total cost:
Let x be the number of kgs of tomatoes Mail bought, and y be the number of kgs of potatoes Mail bought. The cost of x kgs of tomato at Rs. 50 per kg is 50x, and the cost of y kgs of potato at Rs. 20 per kg is 20y. Therefore, the total cost of the vegetables is:
Total cost = 50x + 20y
Substituting the value of total cost as Rs. 200, we get:
50x + 20y = 200
This is the required linear equation to represent the total cost.
Finding the value of x:
Let's assume that Mail bought x kgs of tomato and 2.5 kgs of potato. Using the equation derived above:
50x + 20(2.5) = 200
Simplifying the equation:
50x + 50 = 200
50x = 150
x = 3
Therefore, Mail bought 3 kgs of tomato.
Finding the point at which the graph of 5x+2y=20 cuts x-axis:
To find the point at which the graph of 5x+2y=20 cuts the x-axis, we need to set y = 0 in the equation and solve for x:
5x + 2(0) = 20
5x = 20
x = 4
Therefore, the point where the graph of 5x+2y=20 cuts the x-axis is (4,0).
Which pair. of integers would be used to rewrite the middle term when factoring 6t^(2)+5t-4 by grouping?
The pair of integers to be used to rewrite the middle term when factoring 6t^(2)+5t-4 by grouping is (5t - 4) and (6t^2 + 5t). By factoring by grouping, we can factor the middle term out of the polynomial and then factor the remaining terms separately.
First, the middle term is factored out of the equation. This is done by multiplying the first and last terms together, which in this case is (6t^2)(-4). This results in the equation 6t^2 + 5t - 4 being rewritten as 6t^2 + (5t - 4)(-4).
Next, the remaining terms are factored separately. The first term, 6t^2, is a perfect square and can be factored as (3t)(2t). The second term, (5t - 4)(-4), can be factored by taking out a common factor from each term. In this case, the common factor is (-4). This results in the equation being rewritten as (3t)(2t) + (-4)(5t - 4).
The final step is to group the terms together and factor out the greatest common factor. In this equation, the greatest common factor is (3t)(-4). Thus, the equation 6t^2 + 5t - 4 can be rewritten as (3t)(-4)(2t + 5).
In conclusion, the pair of integers used to rewrite the middle term when factoring 6t^2 + 5t - 4 by grouping is (5t - 4) and (6t^2 + 5t).
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Teri has 12 paper weights in her collection. She has twice as many glass paperweights as metal, and three are wood. How many of each paper weight does she have?
Let's say that the number of metal paperweights is "x", then the number of glass paperweights is "2x" since she has twice as many glass paperweights as metal.
We know that she has a total of 12 paperweights, so we can set up an equation:
x + 2x + 3 = 12
Simplifying the equation, we get:
3x + 3 = 12
Subtracting 3 from both sides, we get:
3x = 9
Dividing both sides by 3, we get:-
x = 3
So Teri has 3 metal paperweights, and since she has twice as many glass paperweights as metal, she has:
2x = 2(3) = 6 glass paperweights.
Therefore, Teri has 3 metal paperweights, 6 glass paperweights, and 3 wood paperweights in her collection.
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Consider the following matrix \( A \) : \[ A=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \] For each of the following vectors, determine whether
To determine whether a given vector is a solution to the equation \(A\vec{x}=\vec{0}\), we need to multiply the matrix A with the vector \(\vec{x}\) and check if the resulting vector is equal to the zero vector \(\vec{0}\).
Let's consider the first vector \(\vec{x_1}=\left[\begin{array}{c} 2 \\ 1 \\ 1 \end{array}\right]\). Multiplying the matrix A with this vector, we get:
\[ A\vec{x_1}=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \left[\begin{array}{c} 2 \\ 1 \\ 1 \end{array}\right]=\left[\begin{array}{c} 12 \\ -4 \\ -3 \\ -3 \end{array}\right] \]
Since the resulting vector is not equal to the zero vector \(\vec{0}\), the vector \(\vec{x_1}\) is not a solution to the equation \(A\vec{x}=\vec{0}\).
Similarly, we can check for the other vectors:
For the vector \(\vec{x_2}=\left[\begin{array}{c} -1 \\ 2 \\ -1 \end{array}\right]\):
\[ A\vec{x_2}=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \left[\begin{array}{c} -1 \\ 2 \\ -1 \end{array}\right]=\left[\begin{array}{c} 6 \\ 1 \\ 1 \\ 1 \end{array}\right] \]
Again, the resulting vector is not equal to the zero vector \(\vec{0}\), so the vector \(\vec{x_2}\) is not a solution to the equation \(A\vec{x}=\vec{0}\).
For the vector \(\vec{x_3}=\left[\begin{array}{c} 1 \\ -1 \\ 1 \end{array}\right]\):
\[ A\vec{x_3}=\left[\begin{array}{ccc} 3 & 6 & -6 \\ -1 & -2 & 5 \\ -1 & -2 & 2 \\ -1 & -1 & 0 \end{array}\right] \left[\begin{array}{c} 1 \\ -1 \\ 1 \end{array}\right]=\left[\begin{array}{c} 0 \\ 0 \\ 0 \\ 0 \end{array}\right] \]
In this case, the resulting vector is equal to the zero vector \(\vec{0}\), so the vector \(\vec{x_3}\) is a solution to the equation \(A\vec{x}=\vec{0}\).
Therefore, only the vector \(\vec{x_3}=\left[\begin{array}{c} 1 \\ -1 \\ 1 \end{array}\right]\) is a solution to the equation \(A\vec{x}=\vec{0}\).
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1.) How can we get Equation B from Equation A?
A: Add/subtract the same quantity to/from both sides.
B: Add/subtract a quantity to/from only one side.
C: Multiply/divide both sides by the same non-zero constant.
D: Multiply/divide only one side by a non-zero constant.
2.) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
A: Yes
B: No
Multiply/divide both sides by the same non-zero constant (option C).
Both equations can be considered equivalent (yes).
How to solveTo solve the equation, we can start by simplifying equation A by opening the brackets:
3(x + 2) = 18
3x + 6 = 18
We can then solve for x by dividing both sides of the equation by a non-zero constant (3):
3x + 6 = 18
3x = 18 - 6
3x = 12
x = 4
From this solution, we can simplify equation A to obtain equation B:
x + 2 = 6
x = 6 - 2
x = 4
Hence, equation B can be obtained from equation A.
Part 2: Equivalent equations are algebraic equations that have the same solutions.
To determine if both equations are equivalent, we can solve them to their simplest form:
Equation A:
3(x + 2) = 18
3x + 6 = 18
3x = 18 - 6
3x = 12
x = 4
Equation B:
x + 2 = 6
x = 6 - 2
x = 4
Since both equations have the same solution, we can conclude that they are equivalent.
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What is the future value of $2000 earning 18% interest,
compounded monthly, for 4 years? (Round your answer to two decimal
places.)
The future value of $2000 earning 18% interest, compounded monthly, for 4 years is $6,116.23.
To calculate the future value, we use the formula:
[tex]FV = P(1 + r/n)^{nt}[/tex]
Where:
FV is the future value
P is the principal amount ($2000)
r is the annual interest rate (18%)
n is the number of times the interest is compounded per year (12 for monthly compounding)
t is the number of years (4)
Plugging in these values, we get:
[tex]FV = 2000(1 + 0.18/12)^{12*4}[/tex]
FV = 6116.23
Therefore, the future value of $2000 earning 18% interest compounded monthly for 4 years is approximately $6,116.23. This means that if you invest $2000 today and earn 18% interest compounded monthly for 4 years, your investment will grow to $6,116.23 at the end of the 4-year period. It's important to note that the actual value may vary depending on the exact compounding method used by the bank or financial institution.
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Simplify 7-5/6•7-7/6
To simplify 7-5/6•7-7/6, we need to follow the order of operations (PEMDAS) and perform the multiplication and division before addition and subtraction.
7-5/6•7-7/6
= 7 - (5/6) * 7 - (7/6) (Multiplication first)
= 7 - (35/6) - (7/6) (Simplify the multiplication)
= (42/6) - (35/6) - (7/6) (Convert 7 to a fraction with a common denominator)
= (42 - 35 - 7) / 6 (Subtract the numerators)
= 0 / 6
= 0
Therefore, 7-5/6•7-7/6 simplifies to 0.
Answer: 0
Step-by-step explanation:
7 - 5 / 6 • 7 - 7 / 6
7 - 35 / 6 - 7 / 6
7 - 42 / 6
7 - 7
0
Omar ordered a set of purple and red pins. He received 60 pins in all. 33 of the pins were purple. What percentage of the pins were purple?
55% of the pins were purple if Omar ordered a set of purple and red pins. He received 60 pins in all. 33 of the pins were purple.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To find the percentage of purple pins, we need to divide the number of purple pins by the total number of pins and multiply by 100.
Number of purple pins = 33
Total number of pins = 60
Percentage of purple pins = (Number of purple pins / Total number of pins) x 100
= (33 / 60) x 100
= 55%
Therefore, 55% of the pins were purple.
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Given the information, please find the simple multiplier in the economy:
AD: y = 710 -30p + 5g
AS: y = 10 + 5p - 2s
g is government purchases, and s is the world price of some commodity.
Please explain how to do this, I don’t need the answer unless I have the steps
Answer:
To calculate the simple multiplier in this economy, you need to subtract the autonomous spending (AS) from the aggregate demand (AD). This will give you the amount that changes in consumer spending influences all other economic variables. In this case, subtract 10 + 5p - 2s from 710 - 30p + 5g. The result is 700 - 35p + 3g, which shows how a change in consumer spending affects government purchases and the world price of some commodity.Manuel rewrote the expression 6x-x+5 as 6+5 are 6x-x+5 and 6+5 equivalent expression? Explain.
The expression 6x - x + 5 as 6 + 5 are not equivalent expression because one of the expression contain a variable while the other doesn't.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
Expression = 6x - x + 5
Expression = 5x + 5
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marys florist charges $3 per rose and plus $35 for a delivery. sam bought a bunch of roses and delivered to his mom. which value is the cost?
a) $69
b) $70
c) $71
d) $72
Question 5 of 5
The graph shows the number of weeks of practice (x) and the number of
shots missed in a free-throw drill (y). The equation of the trend line that best
fits the data is y = -x + 6. Predict the number of missed shots after 6
weeks of practice.
Number of shots missed
987654321
•
123456789
Weeks of practice
According to the information, it can be predicted that the number of missed shots after six weeks of practice is zero (0).
How to calculate the number of lost shots after six weeks of practice?To calculate the number of lost shots after six weeks of practice, we must take into account the function that relates the weeks of practice with lost shots. In this case we must replace the value of X that corresponds to the weeks of practice and we will obtain as a result the amount of lost shots as shown below:
y = -x + 6y = - 6 + 6y = 0According to this function, we can infer that after six weeks of practice there will be 0 missed shots.
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The length of a rectangular speaker is three times its width and the height is four more than the width. Write an expression for the volume V of the rectangular prism in terms of its width, w.
Formula: V = (length)(height)(width)
L=
W=
H=
PLEASE SHOW WORK
Answer:
Step-by-step explanation:
W = w
L = 3w
H = w+4
Now V = LHW
= (3w)(w+4)(w)
= (3w²+12w)(w)
= 3w³+12w²
Find the length of the third side.
Answer:
Your answer is 4
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex]
c = 2sqrt(5)
b = 2
a = length
[tex]a^2 = c^2 -b^2\\\\a =\sqrt{c^2-b^2} \\\\a=\sqrt{(2\sqrt{5} )^2-2^2}\\\\a=\sqrt{(2*2*5)-4}\\\\a=\sqrt{20-4}\\\\a=\sqrt{16}\\\\a=4[/tex]
In a right triangle, the length of the long leg is 2 inches more than the length of the short leg. The hypotenuse is 8 inches less than three times the length of the short leg. What is the length of each side of the triangle?
The length of the short leg is 2 inches, the length of the long leg is 8 inches, and the length of the hypotenuse is 10 inches.
In a right triangle, if the length of the long leg is 2 inches more than the length of the short leg and the hypotenuse is 8 inches less than three times the length of the short leg, then the length of the short leg is x and the length of the long leg is [tex]x+2[/tex] and the hypotenuse is [tex]3x-8[/tex].
We can use the Pythagorean theorem to solve for the lengths of each side. The Pythagorean theorem states that [tex]a^{2} = b^{2} + c^{2}[/tex], where a and b are the lengths of the legs and c is the length of the hypotenuse.
So, [tex]x^{2} + (x+2)^{2} = (3x-8)^{2}[/tex]
We can solve for x, which gives us x = 6. Therefore, the length of the short leg is 2 inches, the length of the long leg is 8 inches, and the length of the hypotenuse is 10 inches.
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I need quick help with this, please.
Answer:
c
Step-by-step explanation:
it makes sense
I really need some help please
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
multiply x by y multiply x by y multiply x by y 3 plus 5 minus 5 to the power of 2 then divide 3 plus 87 then you give your mom and dad a high five then go make out with a girl for an hour and then your answer is 72 to the power of x multiplyed by y.
Find an equation of the line that satisfies the given conditions. Through (1,6); parallel to the line y = 9x - 4
The equation of the line satisfying the given conditions. It passes through (1,6); parallel to the line y = 9x - 4 is y = 9x - 3.
To find an equation of the line that satisfies the given conditions, we need to use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Since the line we are looking for is parallel to the line y = 9x - 4, it will have the same slope, which is 9. Therefore, the equation of the line we are looking for will be y = 9x + b.
Now, we need to find the value of b. We can do this by plugging in the given point (1,6) into the equation and solving for b:
6 = 9(1) + b
6 = 9 + b
b = -3
So the equation of the line that satisfies the given conditions is y = 9x - 3.
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If 6 apples cost the same as 3 bananas, and 4 bananas
cost the same as 5 melons, how many melons can Jane buy for the
price of 32 apples?
Jane can buy 20 melons for the price of 32 apples.
To find out how many melons Jane can buy for the price of 32 apples, we need to use the given ratios to find the equivalent value of melons in terms of apples.
First, we know that 6 apples are equivalent to 3 bananas. So, we can simplify this ratio to 2 apples per 1 banana.
Next, we know that 4 bananas are equivalent to 5 melons. So, we can simplify this ratio to 4/5 of a banana per 1 melon.
Now, we can use these ratios to find the equivalent value of melons in terms of apples. If 2 apples are equivalent to 1 banana, and 4/5 of a banana is equivalent to 1 melon, then we can multiply these ratios together to find the equivalent value of melons in terms of apples:
2 apples/1 banana × 4/5 banana/1 melon = 8/5 apples/1 melon
This means that 1 melon is equivalent to 8/5 apples, or 1.6 apples.
Finally, we can use this ratio to find out how many melons Jane can buy for the price of 32 apples:
32 apples × 1 melon/1.6 apples = 20 melons
Therefore, Jane can buy 20 melons for the price of 32 apples.
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Convert 6 1/3 to an improper fraction.
Answer:
19/3
Step-by-step explanation:
Find m for the investment of $1000.00 for 2 years at 1.8% compounded semi-annually. A) 1
B) 0.9% C) 2 D) 4
(B) 0.9%. We can use the formula for compound interest to find the value of the investment after 2 years:
A = P(1 + r/n)^(nt)
where A is the amount of money after the time period, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Plugging in the given values, we get:
A = 1000(1 + 0.018/2)^(2*2)
= 1000(1 + 0.009)^4
= 1000(1.009)^4
≈ 1083.02
So the investment is worth approximately $1083.02 after 2 years.
To find the interest rate per year, we can use the formula:
r = n[(A/P)^(1/nt) - 1]
Plugging in the values we know, we get:
r = 2[(1083.02/1000)^(1/(2*2)) - 1]
= 2[(1.08302)^(1/4) - 1]
≈ 0.9%
Therefore, the answer is (B) 0.9%.
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Find the value of the variable.
Answer:
28
Step-by-step explanation:
So for this problem, you need to use the midsegment formula. The midsegment formula is [tex]SG = \frac{1}{2} (b_{1} + b_{2})[/tex]. In this case, [tex]b_{1}[/tex] is 21 and [tex]b_{2}[/tex] 35.
Adding these together get 56. The next part of the formula is dividing by two, so [tex]\frac{56}{2} = 28[/tex] so you answer is x=28
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The value of the function (f·g)(-9) is 186.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions f(x)=2x²-4x-15 and g(x)=x+12.
Here, (f·g)(x)=f(x)+g(x)
= 2x²-4x-15+x+12
= 2x²-3x-3
(f·g)(-9)=2(-9)²-3(-9)-3
= 2×81+27-3
= 162+27-3
= 162+24
= 186
Therefore, the value of (f·g)(-9) is 186.
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