An antique painting is purchased in 1980 for $995. The value increases by 3.1% every year, the increase in value of the painting in the 6th year after it was purchased is: $200.02
What is increase in value?Increased Value is the amount obtained after deducting the Base Value from the current assessed value.
Given that,
An antique painting is purchased in 1980 for $995 = P
The value increases by 3.1% every = r
r = 3.1%
r = 3.1/100
r = 0.031
As we know,
Value of painting after t years: [tex]P (1+r)^t[/tex]
So, after 6 years:
f(6) = [tex]995 (1+0.031)^6[/tex]
or, f(6) = [tex]995 (1.031)^6[/tex]
or, f(6) = 1195.0197
or, f(6) = 1195.02
Now, at t = 0, f(0) = 995
Thus, value increased by, f(6) - f(0)
= [1195.02 - 995]
= 200.02
Thus, increase in price since it purchased = $200.02
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multiplications of matrices
The product of A x B of matrix is
a) [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]
b) [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]
c) [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]
d) [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \left[\begin{array}{ccc}4\\5\\\end{array}\right][/tex]
The value of matrix B is
[tex]B = \left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]
Now , the dimensions of matrix A is 2 x 1 and of matrix B is 1 x 2
So , matrix multiplication is possible
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}4\\5\\\end{array}\right] *\left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]
So , the value of matrix C is calculated as
[tex]C = \left[\begin{array}{ccc}( 4 * 2 ) &( 4 * 3 )\\( 5 * 2 ) &(5 * 3 )\\\end{array}\right][/tex]
On simplifying the matrix , we get
[tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]
b)
C be the result of A x B
The value of matrix A
[tex]A = \left[\begin{array}{ccc}3\\4\\\end{array}\right][/tex]
The value of matrix B is
[tex]B = \left[\begin{array}{ccc}1&2\\\end{array}\right][/tex]
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}( 3 * 1 ) &( 3 * 2 )\\( 4 * 1 ) &(4 * 2 )\\\end{array}\right][/tex]
On simplifying the matrix , we get
[tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]
c)
C be the result of A x B
The value of matrix A
[tex]A = \left[\begin{array}{ccc}-1\\6\\\end{array}\right]\\[/tex]
The value of matrix B
[tex]B = \left[\begin{array}{ccc}7&2\\\end{array}\right][/tex]
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]
d)
C be the result of A x B
The value of matrix A
[tex]A = \left[\begin{array}{ccc}8\\5\\\end{array}\right]\\[/tex]
The value of matrix B
[tex]B = \left[\begin{array}{ccc}3&-12\\\end{array}\right][/tex]
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]
Hence , the matrix multiplication is done and the results are given
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- 4(3/2 * x - 1/2) = - 15
Answer:
2 5/6 OR 3
Step-by-step explanation:
1. Divide Both sides by four.
2. -15/-4 can be simplified to 15/4 by removing the negative sign from both the numerator and the denominator.
3. Add 1/2 to both sides
4. Least common multiple of 4 and 2 is 4. Convert 15/4 and 1/2 to fractions with the denominator 4.
5. Since 15/4 and 2/4 have the same denominator, add them by adding their numerators.
6. Add 15 and 2 to get 17.
7. Multiply each side by 2/3, the reciprocal of 3/2 (cancel out 3/2 and leave only X)
8. multiply 17/4 by 2/3 by multiplying numerator times numerator and denominator times denominator.
9. By doing the multiplications 17x2/4x3 you should get 34/12
10. Reduce the fraction 34/12 to lowest terms by extracting and cancelling out 2.
11. You should get 17/6.
Final Step: if you are asked for a mixed number, the answer is 2 5/6 OR if asked for a decimal, put 2.833333333 or 3 IF asked to round.
Evaluate (7.62 × 105) – (8.1 × 103). Express the result in scientific notation.
The value of the expression in the form of the scientific notation is 7.539 x 10⁵.
What is a scientific notation?Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may be called scientific form.
When a number is written using only the digits of the number, that is considered standard notation. Since words are not used in conventional number notation, this is the way that numbers are typically written.
The expression is (7.62 × 10⁵) – (8.1 × 10³). The expression will be solved as,
E = (7.62 × 10⁵) – (8.1 × 10³)
E = (7.62 × 10⁵) – (0.081 × 10⁵)
E = 7.539 x 10⁵
Therefore, the value of the expression in the form of the scientific notation is 7.539 x 10⁵.
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1. Write the equation of the parabola that contains these points (-2, -1), (-1, -6), (0, -7), (1, -4)
Answer:
(not a possible parabola)
Step-by-step explanation:
see the plot...
Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0.R′(x) = 0.06x^2 − 0.05x + 138
The demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.
Explain the term revenue function?The relationship between the demand function p(x) as well as the revenue function R(x) is given by the equation R(x)=xp(x), where x represents the quantity of units sold.In order to get the revenue function, we shall integrate the marginal revenue function R′(x).For the given question;
R′(x) = 0.06x² − 0.05x + 138
R(x) = ∫R′(x)dx
R(x) = ∫[0.06x² − 0.05x + 138] dx
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C
R(x) = 0.02x³ - 0.025x² + 138x + C
If R(0) = 0, revenue is 0.
Put x = 0.
0.02x³ - 0.025x² + 138x + C = 0
c = 0
Thus,
R(x) = 0.02x³ - 0.025x² + 138x
Factorizing the function,
R(x) = 0.02x³ - 0.025x² + 138x
R(x) = x(0.02x² - 0.025x + 138)
R(x) = xp(x) . Thus,
p(x) = 0.02x² - 0.025x + 138
Therefore, the demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.
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Consider these functions:
f(x)=-1/2x² + 5x
g(x)=x² + 2
What is the value of f(g(-2))?
O A. -28
OB.
O C. 12
O D.
-12
146
[tex]f(x)=-\cfrac{1}{2}x^2 + 5x\hspace{13em}g(x)=x^2+2 \\\\[-0.35em] ~\dotfill\\\\ g(-2)=(-2)^2+2\implies g(-2)=4+2\implies g(-2)=6 \\\\[-0.35em] ~\dotfill\\\\ f(~~g(-2)~~)\implies f(6)\implies f(6)=-\cfrac{1}{2}(6)^2+5(6) \\\\\\ f(6)=-\cfrac{36}{2}+30\implies f(6)=-18+30\implies \stackrel{f(~~g(-2)~~)}{f(6)}=12[/tex]
how do you use equilateral and isosceles triangles to compute values of the trig functions at multiples of 30 and 45 degrees
Drawing an altitude and computing the side lengths of the resulting half triangle for an equilateral and isosceles triangle, would give the trigonometric functions for multiples of 30 and 45 respectively.
What is the significance of 30°-60°-90° and 45°-45°-90° right triangles?In a 30°-60°-90° right triangle, the longer leg is [tex]\sqrt{3}[/tex] times longer than the shorter leg, and the hypotenuse is twice as long. In a 45°-45°-90° right triangle, sides opposite to the equal angles (45°) are equal and the hypotenuse is [tex]\sqrt{2}[/tex] times the other sides.
To find the trigonometric functions of multiples of 30°, first consider a equilateral triangle of, say, side-length 2. Draw an altitude for the triangle. Each of the half triangle are 30°-60°-90° right triangle. Clearly the base will be divided into 2 equal parts of length 1 each. Now using Pythagorean Theorem on one of the 30°-60°-90° right triangle, trigonometric functions for multiples of 30° could be obtained.
Draw x and y axis. Now take a length of , say , 2 in the x-axis and using a compass pointed at origin and mark the point on y axis with a length 2. Now join these points on x and y axis. A 45°-45°-90° isosceles right triangle with side-length 2 is obtained. Now using Pythagorean Theorem, trigonometric functions for multiples of 45° could be obtained.
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whats 1+1 im really confused about this one
can someone tell me.
Answer:
2
Step-by-step explanation:
take an example like
u have one apple then someone gives you another one apple
when you add them,
you get 2
An artist sold 128 pieces of jewelry. Of the pieces of jewelry sold, 32 were rings. What percent of the pieces of jewelry sold were rings?
Step-by-step explanation:
when you have a problem you can tell me please follow
Distribute -2 (6a-6)
Answer:
12 - 12 a
Step-by-step explanation:
Like ha blue and red ball. Every day he win 2 blue ball and loe 3 red. After 5 day he won the ame amount of blue ball a red. After 9 day he had twice a many blue ball a red. How many red ball he have at the beginning
He started out with 47 balls after winning 2 blue balls and losing 3 red balls.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party.
Here,
Let the number of blue balls be x and the number of red balls be y,
after 5 days ,
x + 10 = y - 15
after 9 days ,
x + 18 = 2 * ( y - 27 )
subtracting both,
8 = y - 39
y = 47
The number of red balls in beginning is 47.
He had 47 balls in the beginning as he win 2 blue ball and lose 3 red balls.
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You have 2 different aving account. For Account A, the imple interet earned after 15 month i $9. 25. For Account B, the imple interet earned after 18 month i $25. 20. If the interet rate i 3. 7% for Account A and 2. 4% for Account B, how much i the principal in each account? Which account earned you the mot interet the firt month? Explain your anwer
The principal amount for account A is $200 and for account B is $700.
Account B earns more simple interest than account B in first month.
Given,
Account A
Simple interest, SI = $9.25
Time period, T = 15 months = 1 1/4 = 5/4 years
Rate of interest, R = 3.7%
Account B
Simple interest, SI = $25.20
Time period, T = 18 months = 1 1/2 = 3/2 years
Rate of interest, R = 2.4%
We have to find the principal amount for each account and also the account which earned the more simple interest;
Here,
Simple interest, SI = PRT/100
P is the principal amount
Now,
Account A.
Principal amount,SI = PRT/100
9.25 = (P × 3.7 × 5/4) / 100
9.25 × 100 = P × 4.625
P = 925/4.625
P = $200
Simple interest for first month,SI = PRT/100
SI = (200 × 3.7 × 1/15) / 100
SI = 2 × 3.7 × 1/15
SI = $0.493
Next,
Account B
Principal amount,SI = PRT/100
25.20 = (P × 2.4 × 3/2) / 100
25.20 × 100 = P × 3.6
P = 2520/3.6
P = $700
Simple interest for first month,SI = PRT/100
SI = (700 × 2.4 × 1/18) / 100
SI = 7 × 2.4 × 1/18
SI = $0.933
Here,
The principal amount for account A is $200
The principal amount for account B is $700
Simple interest for first month;
Account A = $0.493
Account B = $0.933
Therefore,
In first month account B earns more simple interest than account A.
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The amount of money that mary earns varies directly with the number of hours worked. If mary earns $320 for working 40 hours, determine the constant of variation.
The constant of variation when the amount of money that Mary earns varies directly with the number of hours is 8.
According to the question,
We have the following information:
The amount of money that Mary earns varies directly with the number of hours worked. And Mary earns $320 for working 40 hours.
Now, following expression can be used to express this relationship where y is the amount of money and x is the number of hours.
y = kx
320 = 40k
Dividing by 40:
k = 320/40
k = 8
Hence, the constant of variation when the amount of money that Mary earns varies directly with the number of hours is 8.
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Milan runs7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes
Answer:
2.8 Miles in 24 minutes
Step-by-step explanation:
60 / 24 = 2.5
2.5 / 7 = 2.8
Answer:
17.5mi
Step-by-step explanation:
7mi = 17.5mi
60min = 24min
60/24=2.5
2.5*7=17.5
If 1.5 liters of washing up liquid is 2.70 find the cost of 1 liter
what is 7j + 5 - 8k when j = 0.5 and k = 0.25?
Answer: 6.5
Step-by-step explanation:
To perform this kind of exercise, it is necessary to replace the value indicated in each variable each time you find the variable in the equation.
Answer:
6.5
Step-by-step explanation:
Substitute the known variables into the equation
7(0.5) + 5 - 8(0.25)
Multiply: 3.5+5-2
Solve: 6.5
what is 1/12 simplified
Answer: it’s already in its simplest form
Step-by-step explanation:
Answer: The fraction [tex]\frac{1}{12}[/tex] is already at its simplest form.
Step-by-step explanation: Sorry if this isn't correct, hope this helps!
how do negative exponents represent reapeated division NEEED THIS DONE BEFORE MIDNIGHT 12/4/22
Billy went to the hardware store and bought 18 identical sections of pipe. The total length of the pipes was 45. 18 meters. How long was each pipe?.
The length of each identical section of pipe is 2.51 meters
Define Algebraic Expression
In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Given,
Billy bought 18 identical sections of pipe.
Total length of pipes = 45.18 meters
The length of each pipe is = 45.18 / 18
= 2.15 meters
Hence, the length of each identical section of pipe is 2.51 meters
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can some one help me with this please
Answer:
3⁰ = 1
x⁰ = 1
Step-by-step explanation:
You want powers of 3 filled in your table from an exponent of 4 down to an exponent of 0.
Powers of 33⁴ = 3·3·3·3 = 81 . . . . . . 3 is a factor 4 times
3³ = 3·3·3 = 27 . . . . . . . 3 is a factor 3 times
Each row of the table has 3 being a factor of 3^x one fewer times, so each value of 3^x is 1/3 of the previous value.
The last two rows of the table are ...
3¹ = 3
3⁰ = 1
See the attachment for the whole table.
In general, the meaning of x⁰ is ...
x⁰ = 1
__
Additional comment
In algebra, 0⁰ = 1 is the usual definition. In some contexts (mathematical analysis, calculus), it may be "undefined."
That means x⁰ = 1 for all real numbers x, including x = 0.
1 Select the statement that correctly describes the
solution to this system of equations.
18x-2y = -4
14x-y=-2
A.
There is exactly one solution at (2.0).
B. There is no solution.
C. There is exactly one solution at (0,-2).
D. There are infinitely many solutions.
The solution to the given system of equation has exactly one solution at (0,2).
Which property is used in elimination method?The addition property of equality is used in the elimination technique to solve systems of linear equations.
What is elimination formula?To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
So there is exactly one solution (0,2).
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The solution to the given system of equation has exactly one solution at (0,2).
Which property is used in elimination method?
The addition property of equality is used in the elimination technique to solve systems of linear equations.
What is elimination formula?
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
So there is exactly one solution (0,2).
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161% of 200 = what ?
Answer:332
Step-by-step explanation:Solution for 161 is what percent of 200:
161:200*100 =
(161*100):200 =
16100:200 = 80.5
Now we have: 161 is what percent of 200 = 80.5
Question: 161 is what percent of 200?
Percentage solution with steps:
Step 1: We make the assumption that 200 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $100\%=200$.
Step 4: In the same vein, $x\%=161$.
Step 5: This gives us a pair of simple equations:
$100\%=200(1)$.
$x\%=161(2)$.
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{200}{161}$
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{161}{200}$
$\Rightarrow x=80.5\%$
Therefore, $161$ is $80.5\%$ of $200$.
I really need to finish this
Answer:
A
Step-by-step explanation:
an open circle on a value means that x cannot equal that value
a closed circle on a value means that x can equal that value
from the number line
closed circle at - 3 means x can equal 3
open circle at 2 means that x cannot be equal to 2
all values between - 3 and 2 are solutions for x, then
x ≥ - 3 and x < 2 or - 3 ≤ x < 2
Question 1
Is this a function? Explain, why or why not!
X
-2
-4
-6
y
1
1
1
Edit View Insert Format Tools Table
2 pts
Rewrite the decimal fraction as a decimal number. 14 25 100
The decimal fraction as a decimal number.14,25
What is decimal?
The base-10 number system, arguably the most widely used number system, is referred to as decimal. The 10 single-digit digits of the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number following nine is 10. 19 is followed by 20, and so on.
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
14 25/100= 14*100+25/100=
1400+25/ 100
= 1425/100
= 14.25
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Find the value of a b c if 173a i diviible by 9, 173b i diviible by 11 and 173c i divible by 6
The value of a , b and c are 7, 11 and 1 respectively.
173a is divisible by 9.
Rule of divisible by 9 is:
The number itself is divisible by 9 if its digit sum is also divisible by 9.
digits sum = 1+7+3+a = 11+a.
11+a is divisible by 9. a can be 7 so that 11+7 = 18 is divisible by 9.
minimum positive value of a = 7.
173b is divisible by 11
Rule of divisible by 11 is:
A number is completely divisible by 11 if the difference between the sum of its alternative digits is divisible by 11.
sum of its alterative digits:
1+3 =4
7+b =7+b
difference of alternative digits sum = 7+b-4 = b+3 is divisible by 11 b = 8
so that 8+3 = 11 is divisible by 11.
minimum positive value of b = 11.
173c is divisible by 6.
Rule of divisible by 11 is:
Any number that can be divided by both 2 and 3 is also divisible by 6.
sum of digits of number = 1+7+3+c = 11 + c if divisible by 2 then it should be even if we put c = 1 , 11+1 = 12 which is divisible by both 2 and 3.
minimum positive value of c = 1.
So the value of a ,b and c are 7, 11 and 1 respectively.
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168 divided by 12 array
168 divided by 12 is 14.
Explanation:14 <-- quotient
---
168
12
--
48
48
--
<-- remainder
What is Long Division?The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions. When solving an issue involving long division, the dividend—a high number—is divided by the divisor, a smaller number. The excess amount that cannot be divided yields the quotient, which is known as the residual. Long Division Calculator Multiplication, which is the opposite of division, addition, and subtraction are the other fundamental arithmetic operations. You can uncover common factors and simplify fractions using the arithmetic skill of long division.To learn more about Long Division refer to:
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What is the unit rate per muffin if Anna chose to buy 15 for $6.15?
Answer:
2.44$ per muffin
Step-by-step explanation:
15/6.15
1 and (-1,-4) y-intercept
The graph's intersection with the x-axis is known as the x-intercept. The graph's intersection with the y-axis is known as the y-intercept.The y-intercept is (0,-4).
what is X-intercept and Y intercept?To find Y intercept substitute x=0;
here X interept is (1,-1)
Y intercept (0,-4)
The x- and y-intercept visual concept is quite straightforward. Where the graph crosses the x-axis is known as the x-intercept, and the y-intercept is where the graph crosses the y-axis. A line's X-intercept provides information about the point where the x-axis is crossed.In a similar manner, the line's y-intercept represents the location at which the y-axis is crossed. In a given equation, only one intercept can be determined at once.The point at which a line crosses the x axis is known as the line's x-intercept. (i.e., in the case where y = 0) X interept=(x,0)The point at which a line crosses the y axis is known as the line's y-intercept. (i.e. in the case where x = 0) Y interept =(0,y)To learn more about X-intercept and Y intercept refer to:
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The point (8, 36) is shown on the graph. Write an equation that represents this situation, where y
represents the amount of macaroni, in cups, and x represents the amount of cheese in cups.
The equation that represents this situation is y= 4x
How to determine the equation that represents this situation?From the question, we have the following parameters that can be used in our solution:
Point = (8, 36)
This point can be represented as
(x, y) = (8, 36)
From the above parameter, we can calculate the constant of variation
The constant of variation is calculated as
Constant of variation = y/x
Substitute the known values in the above equation
So, we have the following equation
Constant of variation = 36/8
Evaluate the quotient
Constant of variation = 4
Recall that:
Constant of variation = y/x
So, we have
y/x = 4
This gives
y = 4x
Hence, the equation is y = 4x
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