Ty bought a new computer for $499. This brand depreciates at a rate of 12% of the original price per year. The value y of Ty's computer, x years after he purchased it, is found using an equation in the form y = mx + b. What is the approximate value of m?
Answer:
the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.
Step-by-step explanation:
o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").
Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:
m = -12% / 100 = -0.12
Anna is 4 years older than her brother. Two years ago her brother was 3/4 her age. How old will her brother be in five years
Answer: he will be 14
Step-by-step explanation:
Anna is 14 and her brother is 10. Two years ago she was 12. 3/4 of 12 is 9. 9+5 more years is 14. :)))
Please look at the photo. Thank you.
The output value of (f∘g)(x) is: \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).
How to determine the corresponding output value for this function?In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;
\(f(x) = \frac{x-6}{x +3}\)
g(x) = 4x - 15
Next, we would write the numerators and denominators in factored form as follows;
(x - 6)(4x - 15)
4x² - 15x - 24x + 60
4x² - 29x + 60
Now, we can derive the corresponding composite function of f(x) and g(x);
\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x + 3 ≠ 0
x ≠ -3
Domain = (-∞, -3) U (-3, ∞).
Read more on domain here: brainly.com/question/17440903
#SPJ1
If y is inversely proportional to x and y=9 when x=3. Find x when y=12
Answer:
9/4
Variables in inverse proportion have a constant product.
\(xy=(9)(3)=27 \\ \\ xy=12x=27 \\ \\ x=\frac{9}{4}\)
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.
The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:
Define the formula p(x, y) as x = yo(x).
This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.
Define the set F as {(x, x) (x)}.
This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.
Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.
This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.
The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.
Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.
For more such questions on explicit
https://brainly.com/question/30394385
#SPJ8
The property tax on a house with an assessed value of $624,000 is $7280. Determine the property tax on a house with an assessed value of $762,000, assuming the same tax rate.
Using proportions, the property tax on a house with an assessed value of $762,000 is of $8,890.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The tax rate, as a proportion, is:
7280/624000 = 0.011667.
Hence, the property tax on a house with an assessed value of $762,000 is of:
0.011667 x 762,000 = $8,890.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
James T-shirt business uses the demand function P = -Q+31 and the supply function P = Q-17. According to these functions, what will the
equilibrium point (P.Q) be for James T-shirt business?
The equilibrium point for James T-shirt business is (P, Q) = (7, 24).
To find the equilibrium point (P, Q) for James T-shirt business
we need to set the demand function equal to the supply function and solve for the values of P and Q.
Demand function: P = -Q + 31
Supply function: P = Q - 17
Setting them equal:
-Q + 31 = Q - 17
Adding Q to both sides and subtracting 31 from both sides:
2Q = 48
Dividing both sides by 2:
Q = 24
Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.
P = Q - 17
P = 24 - 17
P = 7
Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ1
Share up 184 snail between a salamander how many snail does each salamander get
Answer:
How many salamanders are there
or does it say that there are "a salamanders"
If so, it's 184/a
10+(2x3)2 / 4 x (1/ 2)3
How to solve the inequality:
-6 > z/-2 +1
The solution to the inequality is z > 14
What is inequality?Mathematical expressions with inequalities include those in which the two sides are not equivalent. Contrary to equations, we assess and contrast two values in inequality. The inequality signs that are used in place of the equal signs are:
Less than (or less than or equal to), Larger than (or greater than or equal to), or Not equal to.Given:
-6 > z/-2 + 1
Rewrite so "z" is on the left side of the inequality.
z/-2 + 1 < -6
Move the negative in front of the fraction.
-z/2 + 1 < -6
Move all terms not containing z to the right side of the inequality.
-z/2 < - 6 - 1
-z/2 < - 7
Multiply both sides by 2
z < -14
Interchange the sign since z cannot be negative;
z > 14
Learn more about inequality here:
https://brainly.com/question/25275758
#SPJ1
State the domain and range of the relation given in the table below, and determine if it is a function,
х 16 -8 4 1 -8 7
y 8 -6 -14 -9 7 24
Domain: {
Range:{
Is the relation a function?
O No
OYes
Rational Equations
- It takes one worker 12 hours to complete a specific job. If two workers do the same job, it takes them 6 hours to finish the job. How long would it take 6 workers to do the same job?
It will take ____ hours.
Answer:
2 hours
Step-by-step explanation:
2,4,6,8,10,&12
1, 2,3, 4, 5, &6
Hope this helps :)
Find the principal needed now to get the given amount; that is, find the present value.
1
To get $1000 after 2 years at 4% compounded daily
2/7/27
The principal needed to get the given amount is $923.12.
How to find the principal needed to get the given amount?To determine the principal needed, we can use the compound interest formula:
\(A = P (1 + \frac{r}{n} )^{nt}\)
Where:
A = the final amount, $1000
P = the principal
r = the interest rate, 4% = 0.04
n = the number of times the interest is compounded per year, in this case daily (n = 365)
t = the time period in years, 2
Substituting the values :
\(1000 = P (1 + \frac{0.04}{365} )^{365 * 2}\)
1000 = P(1.00010959)⁷³⁰
1000 = 1.08328308P
P = 1000/1.08328308
P = $923.12
Learn more about compound interest on:
brainly.com/question/24274034
#SPJ1
What is the value of the rational expression below when xis equal to 4?
x-12/x-8
Answer:
= -7
Step-by-step explanation:
given x = 4
12/4 = 3
4 - 3 - 8 = -7
Subtract 89.768 from 201.316
show your work
Answer:
111.548
-------------------------------
Subtract 201 from 89.
\(201 - 89 = 112\)
we can estimate the answer will be close to 112
Next, work with the decimals. Note that the more you subtract, the bigger the decimal places get.
\(0.768 - 0.316 = 0.452\)
Round 0.452 up from the hundredths place to nearest tenths place.
\(0.452 = 0.5\)
Since the decimal place is bigger, estimate 0.55 instead.
Subtract 0.22
\(0.55 - 0.2 = 0.548\)
Add this number to 112
\(112 + 0.548 = 112.548\)
Subtract 1 because of the estimate.
\(112 - 1 = 111\)
Therefore, we have 111.548 based off of subtracting and estimating in a specific method.
The Frosty Ice-Cream Shop sells sundaes
for $2 and banana splits for $3. On a hot
summer day, the shop sold 8 more sundaes
than banana splits and made $156. Which
system of equations could be used to find the
number of sundaes, s, and banana splits, b,
that the shop sold that day?
Answer:b = # banana splits
s = # sundaes
s = b + 8
2s + 3b = 156
replace s with b+8
2(b+8) + 3b = 156
Solve this for b to find the number
of banana splits. Then add 8 to
that to find the number of sundaes.
Step-by-step explanation:
TWO DVDs and one videocassette tape cost $72. One DVD and two videocassette tapes
cost $57. What is the price of each item?
Answer:
dvd cost 36 dollars
casette costs 10.5 dollars
If the planes extend infinitely in all directions, where do plane ADB and line EC intersect?
Answer: In point C.
Step-by-step explanation:
Plane ADB is the plane that contains the points A, D and B.
If you look in the image, you can see that point C also does belong to this plane.
Line EC is the line that connects the points E and C.
Now, remember that Point C does belong to the plane ADB, then the point where the plane ADB and line EC intersect is in point C, because it is a common point to both elements.
A money box contains only 10-cent
and 20-cent coins. There are 28
coins with a total value of $3.80.
How many coins of each?
Answer:
Number of 10 cents = 18
Number of 20 cents = 10
Step-by-step explanation:
Let number of 10 cents be = x
Let number 20 cents be = y
Total number of coins = x + y = 28 -------- ( 1 )
Total amount in the box = 0.10 x + 0.20y = 3.80 ---------- ( 2 )
Solve the equations to find x and y
( 1 ) => x + y = 28
x = 28 - y
Substitute x in ( 2 )
( 2 ) => 0.10(28 - y) + 0.20y = 3.80
2.80 - 0.10y + 0.20y = 3.80
0.10 y = 3.80 - 2.80
0.10 y = 1.00
\(y = \frac{1}{0.10} = 10\)
y = 10
Substitute y in ( 1 ) => x + y = 28
x + 10 = 28
x = 28 - 10
x = 18
What is the value of x in the equation 3x – one-ninthy = 18, when y = 27? 5 7 45 63
Answer:
7
Step-by-step explanation:
3x – one-ninthy = 18, when y = 27?
one-ninthy 27 = 3
3x - 3 = 18
3 x 7 = 21
21 - 3 = 18
hope this helps
Answer:
7
Step-by-step explanation:
answered on edge
you are being watched type the secret code for your ticket
( each line below will pass through one point, graph each line to find your code word )
letter 1: y=1/2x-3
letter 2: y=-4x-2
letter 3: y=-1/3x+4
letter 4:y=1/4x+2
letter 5:y=-2x-1
Answer:
The answer is LSAGE
Step-by-step explanation:
Hope this helps lol
Answer:
SHINE
Step-by-step explanation:
remember : the slope (the factor of x in the equations) is the ratio "y coordinate change / x coordinate change".
and the constant at the end of the equations are the y-intercept (the y value for x = 0).
Marvin runs on a regular basis, but he knows he could get injured if he runs long distances too frequently. How far will he run if he wants to run 75% of his distance from last week, when he ran 20 total miles
find the general solution for: cos(x+30)=-1
The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.
To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.
In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:
x + 30 = (2n + 1)π
Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:
x = (2n + 1)π - 30
This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.
Learn more about trigonometric functions here:
https://brainly.com/question/25618616
#SPJ1
What is the solution of this system of linear equations?
3y = 3 y equals StartFraction 3 over 2 EndFraction x plus 6.x + 6
y – StartFraction one-half EndFraction y minus StartFraction 1 over 4 EndFraction x equals 3.x = 3
Answer:
\(x = 4\)
\(y = 4\)
Step-by-step explanation:
Given
\(3y = \frac{3}{2}x + 6\)
\(y-\frac{1}{4}x = 3\)
Required
The solution
Multiply the second equation by 3
\(3 * [y-\frac{1}{4}x = 3]\)
\(3y-\frac{3}{4}x = 9\)
Rewrite as:
\(3y =\frac{3}{4}x + 9\)
Subtract this from the first equation
\([3y = \frac{3}{2}x + 6]- [3y =\frac{3}{4}x + 9]\)
\(3y - 3y = \frac{3}{2}x - \frac{3}{4}x + 6 - 9\)
\(0 = \frac{3}{4}x -3\)
Rewrite as:
\(\frac{3}{4}x =3\)
Multiply both sides by 3/4
\(x =3*\frac{4}{3}\)
\(x = 4\)
Substitute \(x = 4\) in \(3y = \frac{3}{2}x + 6\)
\(3y = \frac{3}{2} * 4 + 6\)
\(3y = 6 + 6\)
\(3y = 12\)
Divide both sides by 3
\(y = 4\)
Answer:
C. no solution
Step-by-step explanation:
did it on edge2021
please help i dont know to do it please help
Given:
0.5
Let's write the decimal in form of a fraction a/b using integers.
To write the number in fractional form, we have:
\(0.5=5\times10^{-1}\)Since the exponent is the negative of 1, using the definition of negative exponent, we have:
\(5\times10^{-1}=\frac{5}{10^1}=\frac{5}{10}\)Therefore, the correct fraction is:
\(\frac{5}{10}\)ANSWER:
\(\frac{5}{10}\)Enter the exact values of the trigonometric ratios in the boxes.
sin 45°
cos 30
tan 60
=
The required value of trigonometric ratios is,
sin 45° = 1/\(\sqrt{2}\)
cos 30 = \(\sqrt{3}\)/2
tan 60 = 1/ √3
We know that,
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Therefore,
sin 45° = 1/\(\sqrt{2}\)
cos 30 = \(\sqrt{3}\)/2
tan 60 = 1/ √3
To learn more about triangles visit:
brainly.com/question/1058720
#SPJ1
3. What is the measure of angle F? A 120° D G B A. 60 degrees. B. 90 degrees. C. 120 degrees. D. 180 degrees.
Answer:
120°
Step-by-step explanation:
The angles that has 120° is the same as angle E.
Angle E = 120°
Angle D = 180° - 120° = 60°
60° + Angle F = 180°
Angle F = 180° - 60°
Angle F = 120°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Grapes are on sale for $0.98 per pound and Bart wants to purchase 4 pounds of grapes. How much will he spend?
$3.82
$3.91
$3.92
$3.93
Answer:
The answer is $3.91 hope it is help you
Solve for the exact solutions in the interval [0,2]
List your answers separated by a comma, if it has no real solutions, enter DNE.
The solutions to the trigonometric equation in this problem are given as follows:
θ = π/6.θ = 5π/6.θ = 7π/6.θ = 11π/6.What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
For complementary angles, we have that the sine of one of the angles is the cosine of the other angle, hence in this problem we have that 2θ and θ are complementary angles.
Then the value of θ is obtained as follows:
2θ + θ = 90
3θ = 90
θ = 30º.
θ = π/6.
The equivalent angles, which are also solutions to the equation, are given as follows:
θ = 5π/6. -> second quadrant.θ = 7π/6. -> third quadrant.θ = 11π/6. -> fourth quadrant.More can be learned about complementary angles at brainly.com/question/98924
#SPJ1
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ1