11. Jessica invested $18820 to buy a new car for her business. How many years would it take for
this car to depreciate to $4520? Assume declining-balance method of depreciation with a rate
of depreciation of 30%. (Answer to the nearest year.)
Answer :after four years the price of car depreciate
Final answer:
It will take approximately 4 years for the car to depreciate to $4520 using the declining-balance method of depreciation with a depreciation rate of 30%.
Explanation:
To calculate the number of years it would take for the car to depreciate to $4520, we can use the declining-balance method of depreciation. The declining-balance method is based on a fixed percentage of the remaining value of the asset. In this case, the rate of depreciation is 30%, so the car's value will decrease by 30% each year.
Let's start by finding the value of the car after one year. We can use the formula:
Value after one year = Initial value - (Rate of depreciation * Initial value)
Plugging in the values, we get:
Value after one year = $18820 - (0.3 * $18820) = $18820 - $5646 = $13174
Now, let's find the value after the second year:
Value after two years = $13174 - (0.3 * $13174) = $13174 - $3952.2 = $9221.8
We continue this process until we reach a value of $4520. By the time the car's value reaches $4520, it will have taken approximately 4 years.
What value of x will satisfy the equation:cos( x) = sin( 2x+ 57 )
Step-by-step explanation:
[tex]cos \: x = sin \: (2x + 57) \\ \\ \therefore \: sin(90 \degree - \: x) = sin \: (2x + 57) \\ \\ \therefore \:90 - \: x = 2x + 57 \\ \\ 90 + 57 \: = 2x + 3 \\ \\ \therefore \:3x = 147 \\ \\ \therefore \: x = \frac{147}{3} \\ \\ \huge \orange{ \boxed{\therefore \: x = 49 \degree}}[/tex]
Solve this. |-10 + 24z|
Answer:
5/12
Step-by-step explanation:
A cube has a volume of 1000 cubic feet. What is the length of an edge of the cube?
Answer:
The length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet
Step-by-step explanation:
i.) A cube has a volume of 1000 cubic feet.
ii) A cube has edges which are all the same length, let us say that the length of an edge of the cube = x feet.
iii) therefore the volume of the cube is = [tex]x^{3}[/tex] = 1000 cubic feet
iv) therefore the length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet
Final answer:
The length of an edge of a cube with a volume of 1000 cubic feet is 10 feet. If each smaller cube has linear dimensions one tenth those of the larger cube, then the volume of each smaller cube is 1 cubic foot.
Explanation:
The volume of a cube is calculated by raising the length of one of its edges to the power of three (cubing it). Since we know the volume of the cube is 1000 cubic feet, we can determine the length of an edge by finding the cube root of the volume. The cube root of 1000 cubic feet is 10 feet, so the length of an edge of the cube is 10 feet.
To find the volume of the smaller cubes mentioned, we note that if their dimensions are one tenth of the larger cube, then each side of a smaller cube will be 10 feet divided by 10, which is 1 foot. The volume of each small cube is then 1 foot cubed, which is 1 cubic foot.
For a visual reference, imagine a larger cube divided evenly into smaller cubes, where the length of each side of the big cube is ten times that of the smaller ones. The result is that each smaller cube's volume is the original volume divided by the cube of 10 (since there are 10 layers of small cubes along each dimension of the big cube).
1) Find the value of two numbers if their sum is 12 and their difference is 4.
Numbers are 4 and 8
Step-by-step explanation:
Step 1:
Let the numbers be x and y. Given that their sum is 12 and difference is 4. Form equations for this data.
⇒ x + y = 12 ------ (1)
⇒ x - y = 4 -------- (2)
Subtract eq (2) from (1)
⇒ 2x = 8
⇒ x = 4
Step 2:
Find y.
⇒ y = 12 - x = 12 - 4 = 8
gary kicks a field goal with an inital veritcal velocity of 38m/s how long will it take the football to hit the ground
The ball reaches the ground after 7.76 s
Step-by-step explanation:
The motion of the ball along the vertical direction is a free fall motion, which is affected by the force of gravity only; therefore it is a uniformly accelerated motion (=constant acceleration), so we can use the following suvat equation:
[tex]s=ut-\frac{1}{2}gt^2[/tex]
where
s is the displacement
u is the initial vertical velocity
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
t is the time
In this problem,
u = 38 m/s
Also, we want to find the time t at which the ball hits the ground again: so, when the displacement becomes zero again,
s = 0
Therefore the equation becomes:
[tex]0=38t-\frac{1}{2}9.8t^2\\0=38t-4.9t^2[/tex]
And solving for t,
[tex]t(38-4.9t)=0[/tex]
we have two solutions:
t = 0 (instant at which the ball is kicked)
[tex]38-4.9t=0\\t=\frac{38}{4.9}=7.76 s[/tex]
which is the solution to the problem.
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What is the range of the function y=square root x+5 ?
Answer:
all non-negative real numbers, [0, ∞)
Step-by-step explanation:
Replacing x in the parent function √x with (x+5) shifts the graph horizontally, but has no effect on the vertical extent of the graph. It still ranges from 0 to +∞.
The range of √(x+5) is [0, ∞).
Find the equation of the line that passes through (1,0) and is parallel to y=-3x-1
Show full working out ty
Answer:
y = -3x + 3
Step-by-step explanation:
Parallel lines have the same slope.
The given line has a slope of -3, its parallel line will also have a slope of -3... m = -3
y = -3x + c
When x = 1, y = 0
0 = -3(1) + c
c = 3
y = -3x + 3
If a player is 20 feet away from the basket and wants to shoot the basketball the ball should be at its maximum height at what distance
Answer:
The ball would be at its peak at 8 feet from the basket.
Step-by-step explanation:
The basketball should be at its maximum height when it is 10 feet away from the player.
We have,
In a standard basketball shot, the path of the ball follows a parabolic arc. The maximum height is reached at the peak of this arc, which occurs halfway between the player and the basket.
The distance at which the basketball should be at its maximum height is half the distance between the player and the basket.
Half of 20 feet is 10 feet.
Therefore,
The basketball should be at its maximum height when it is 10 feet away from the player.
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100 POINTS AND BRAINIEST TO THE BEST CORRCET ANSWER.
A scatter plot of data comparing the humber of years since Holbrook High School introduced a math club and the number of student participating contains the ordered pairs (3,19) and (8, 42). What is the slope-intercept form of an equation for the line of fit containg those two pairs?
A) y = 0.22x - 1.13
B) y = 4.6x + 5.2
C) y = 5.2x + 4.6
D) y = 3x + 1
Answer:
Option B, y = 4.6x + 5.2
Step-by-step explanation:
Slope-intercept form: y = mx + b
Step 1: Use those two points to get slope
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = [tex]\frac{42 - 19}{8 -3}[/tex]
m = [tex]\frac{23}{5}[/tex]
m = 4.6
Step 2: Find the y - intercept
Use point slope formula: (y - y1) = m(x - x1)
(y - 19) = 4.6(x - 3)
y - 19 + 19 = 4.6x - 13.8 + 19
y = 4.6x + 5.2
Answer: Option B, y = 4.6x + 5.2
Two cars at the same point on I-75. One heads north going 75mph and one heads south going 60mph. How long will it take for the cars to be at 420 miles apart?
It will take 3 hours 6 minutes 40 seconds for the cars to be 420 miles apart.
Step-by-step explanation:
Step 1; The cars are traveling in the opposite direction at different speeds. One is going north at a speed of 75 mph while the other is going 60 mph. So for every hour, the cars are traveling they increase the distance between in between themselves by 75 miles + 60 miles = 135 miles.
Step 2; Assume that in x hours the distance between them is 420 miles. To calculate x we divide the distance to be traveled by the distance being traveled every hour.
x = distance to be covered / distance being traveled every hour
= 420 / 135 = 3.11 hours
We multiply the 0.11 hours with 60 to convert it into minutes. 0.11 × 60 = 6.66 minutes and if we do the same for seconds, 0.66 minutes × 60 = 40 seconds.
a movie theater sold 4 adult tickets and 7 children’s tickets for $83 on friday the next day the theater sold 5 adult tickets and 6 children tickets for $90. what is the price for the adult ticket and the price for a child’s ticket
Answer:
Step-by-step explanation:
4 A + 7K= $83
5 A + 7 K= +7= $90
It means one adult ticket costs 7 more than a kid ticket. If I replace A with K+7 in equation one, it'll look like
4(K+7) + 7 K= $83
=> 4 K +28+ 7 K= $83
=> 11 K= 83-28= 55
K=5
A= 12
Please help! Solve for a: 1/8+6a/5=3/8+2a/5+7/8
Answer:
1 13/32
Step-by-step explanation:
Someone help.
What is 3y+39=16y
Answer:
y=3
Step-by-step explanation:
Step 1: Subtract from both sides
3y+39-16y=16y-16y
-13y+39=0
Step 2: Subtract 39 from both sides
-13y+39-39=0-39
-13y=-39
Step 3: Divide Both sides by -13
-13y/-13=-39/-13
y=3
What are the measurments of <BEC and <ABE
Check the picture below.
well, then we know that (3x-5) + (4x+10) = 180, so
[tex]\bf (3x-5)+(4x+10)=180\implies 7x+5=180\implies 7x=175 \\\\\\ x = \cfrac{175}{7}\implies x = 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \measuredangle BEC}{3x-5\implies 3(25)-5\implies 70} \\\\\\ \stackrel{~\hfill \measuredangle ABE}{180 - (x-5)\implies 180-(25-5)\implies 180-20\implies 160}[/tex]
What is the area of the triangle?
Answer:
14
Step-by-step explanation:
Answer: Area = 14 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula for calculating the area of Triangle is given by :
Area = [tex]\frac{1}{2}[/tex] x base x height
From the given triangle
base = 4
height = 7
substituting into the formula
Area = [tex]\frac{1}{2}[/tex] x 4 x 7
Area = [tex]\frac{1}{2}[/tex] x 28
Area = 14 [tex]units^{2}[/tex]
A number is chosen at random from 1 to 50. Find the probability of selecting either a multiple of 4 or a multiple of 5
The probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44
Solution:
Given that, A number is chosen at random from 1 to 50
selecting either a multiple of 4 or a multiple of 5
Sample space is given as:
{ 1, 2, 3, ................, 50 }
Muliples of 4 = 4, 8, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52
Favorable outcomes = 12
Muliples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Favorable outcomes = 10
The probability is given as:
[tex]Probability = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}[/tex]
[tex]probability = \frac{12}{50} + \frac{10}{50}\\\\probability = \frac{12+10}{50}\\\\probability = \frac{22}{50}\\\\probability = \frac{11}{25} \text{ or } 0.44[/tex]
Thus probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44
The probability of selecting either a multiple of 4 or a multiple of 5 is 11/25.
What is the probability of selecting either a multiple of 4 or a multiple of 5?A multiple of a number is the product of an integer and that number.
The first step is to determine the numbers that are a multiple of 4. They are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48. There are 12 numbers.
The second step is to determine the numbers that are a multiple of 5. They are : 5, 10 15, 20, 25, 30, 35, 40, 45, 50. There are 10 numbers.
Probability of picking a multiple of 4 or 5 = 12/50 + 10/50 = 22/50 = 11/25
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what is the difference between the product of 49 and 13 and the sum of 92 and 164
Answer:
391
Step-by-step explanation:
product of 49and 13= 49x13
sum of 92 and 164 =92+164
the difference of them =
49x13-(92+164)
=49x13-256
=637-256
=381
HELP!!!!!
What is the area of a circle with a radius of 1 foot?
One-fourth pi feet squared
One-half pi feet squared
Pi feet squared
2 pi feet squared
Answer
pi*R^2
Step-by-step explanation:
Answer:
Pi feet squared
Step-by-step explanation:
area of circle formula is pi radius squared substitute radius as 1²
Which graph shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes? On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 3) and ends at point (5.5, 24). On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). Solid circles are at points (0, 3), (1, 6), (2, 10), (3, 14), (4, 18), (5, 22). On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 4) and ends at point (6, 16). On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). Solid circles are at points (0, 4), (1, 6), (2, 8), (3, 10), (4, 12), (5, 14), (6, 16).
Answer:
The graph in option 3 will be the correct one.
Step-by-step explanation:
We have to choose the graph from the given options that shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes.
Now, the graph in option 3 will be the correct one.
On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 4) and ends at point (6, 16). (Answer)
Answer:
C
Step-by-step explanation:
Consider the figure below. Please help!!!!!
Answer:
B. T<-4, -2>, r(90°, O)
Step-by-step explanation:
Point A' is 4 units left and 2 units down from point A, so the translation is T<-4, -2>.
Segment C"D" is on the -x axis, 90° counterclockwise from segment C'D' on the +y axis. Since rotation angles are measured the same way other angles are measured (positive is CCW), the rotation is +90° about the origin.
The congruence transformation that maps the quadrilateral ABCD to A''B''C''D'' is [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex] which corresponds with the option B.
B. [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex]
What is a congruent transformation?A congruent transformation, which is also a rigid transformation is one in which the size and shape of the original figure is preserved.
The coordinates of the vertices of the quadrilaterals ABCD and A'B'C'D' indicates that the transformation from the quadrilateral ABCD to the quadrilateral A'B'C'D' is a translation of 4 units to the left and 2 units downwards, which can be expressed as T<-4, -2>
The side D'C' in the quadrilateral A'B'C'D' is vertical while the side D''C'' in the quadrilateral A''B''C''D'' is horizontal and due to the order of the letters D'' and C'' in D''C'' arranged from left to right suggesting a 90° counterclockwise rotation about the origin, which is a T90°, origin
The congruence transformation that maps ABCD to A''B''C''D'' therefore is the option B, [tex]T_{ < -4, \, -2 > }\circ T_{90^{\circ}}, origin > (ABCDE)[/tex]
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candace tells you that she bought new boots using a 20% coupon and saved $28.What was the original price of the boots?use a tape diagram.
Answer:
78
Step-by-step explanation:
40 x 76 is the equation by 4x4 of 86 and the 36
Answer:28×5=$140.00
Step-by-step explanation:
Which of the following inequalities is correct?
The correct inequality among the given options is -a > -c. Thus, option A is correct.
To determine the correct inequality among the given options, we need to compare the values of the variables a, b, and c in the number line.
Given: a = -4, b = 1, and c = 7
Let's evaluate each option:
A. -a > -c:
Substituting the values, we have -(-4) > -(7), which simplifies to 4 > -7.
This is true.
B. -a < -b:
Substituting the values, we have -(-4) < -(1), which simplifies to 4 < -1.
This is false.
C. a > 0:
Substituting the value, we have -4 > 0. This is false since -4 is not greater than 0.
Based on the comparisons, the correct inequality is A. -a > -c.
Therefore, the correct answer is A. -a > -c.
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What is 11.61 in simplest form?
Answer:
1161/100
Step-by-step explanation:
If you multiply the slopes of two perpendicular lines, the product is -1.
(As long as neither line is vertical.)
w
(0,4)
Use that fact and the graph to complete the statements below.
CLEAR
CHECK
The slope of line g is - 1/2.
= -1/2 • ____= - 1
So, the slope of line h is ___
The equation for line h is
y = ___x + _____ .
[tex]$-\frac{1}{2}\cdot2=-1[/tex]
Slope of the line h is 2.
The equation for line h is y = 2x + 4.
Solution:
General equation of a line is y = mx + c,
where m is the slope of the line and c is the y-intercept.
In the given image, line g and line h are intersecting lines and perpendicular to each other.
Equation of line g is [tex]y=-\frac{1}{2} x+2[/tex].
Slope of the line g ([tex]m_1[/tex]) = [tex]-\frac{1}{2}[/tex]
If two lines are perpendicular, then the product of the slopes is –1.
⇒ [tex]m_1 \cdot m_2=-1[/tex]
To find the slope of the line h:
[tex]$\Rightarrow-\frac{1}{2} \cdot m_2=-1[/tex]
[tex]$\Rightarrow m_2=-1 \times(-2)[/tex]
[tex]$\Rightarrow m_2=2[/tex]
Slope of the line h is 2.
To find the equation of a line h:
Line h passing through the point (0, 4) and slope 2.
Point-slope formula:
[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]
[tex]\left(y-4)=2\left(x-0\right)[/tex]
[tex]y-4=2x[/tex]
[tex]y=2x+4[/tex]
The equation for line h is y = 2x + 4.
A company produces fruity drinks that contain a percentage of real fruit juice. Drink
A contains 20% real fruit juice and Drink B contains 15% real fruit juice. The
company used 100.5 liters of real fruit juice to make 30 more liters of Drink A than
liters of Drink B. Write a system of equations that could be used to determine the
number of liters of Drink A made and the number of liters of Drink B made. Define
the variables that you use to write the system.
Let
System of Equations:
The system of equations representing the amounts of Drink A and B made by the company is 1) a = b + 30 and 2) 0.20a + 0.15b = 100.5, where a is the amount in liters of Drink A and b is the amount in liters of Drink B.
Explanation:Let's denote the number of liters of Drink A by the variable a and the number of liters of Drink B by the variable b. Based on the information given, we can establish a system of two equations in two variables that express the relationships between a and b. The first equation is a = b + 30, expressing the fact that the company makes 30 more liters of Drink A than Drink B.
The second equation is 0.20a + 0.15b = 100.5, which expresses the fact that the sum of 20% of a (the amount of real fruit juice in Drink A) and 15% of b (the amount of real fruit juice in Drink B) equals the total amount of real fruit juice used by the company, which is 100.5 liters.
So the system of equations is:
1) a = b + 30
2) 0.20a + 0.15b = 100.5
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To determine the number of liters of Drink A and Drink B made, we can set up a system of equations using the given information.
Explanation:To write a system of equations, we need to define the variables that represent the number of liters of Drink A and Drink B. Let's use:
A = number of liters of Drink A made
B = number of liters of Drink B made
From the given information, we can create the following equations:
A = B + 30 (since there are 30 more liters of Drink A than Drink B)
0.20A + 0.15B = 100.5 (since the company used 100.5 liters of real fruit juice)
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The solution to 2x-2+5=13 is
Answer:
x = 5
Step-by-step explanation:
Given
2x - 2 + 5 = 13, that is
2x + 3 = 13 ( subtract 3 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
How do you write y= 1/2 x+2 in standard form?
x - 2y = -4 is the standard form of equation
Solution:
Given equation is:
[tex]y = \frac{1}{2}x + 2[/tex]
We have to write the equation in standard form
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
From given,
[tex]y = \frac{1}{2}x + 2[/tex]
Simplify the above equation
[tex]y = \frac{x+4}{2}\\\\2y = x + 4[/tex]
Shift the variable terms to the left side of the equation and everything else to the right side
[tex]x - 2y = -4[/tex]
Thus the standard form of equation is found
Question 3: 12 points
3. The area of a rectangle is 45x8y9 square yards. If the length of the rectangle is 5x3y4 yards,
find expression represents the width of the rectangle in yards?
please help!! i will mark you brainiest
Answer:
[tex]9x^{5}y^{5}[/tex] yards.
Step-by-step explanation:
Given that the area of a rectangle (A) is [tex]45x^{8}y^{9}[/tex] square yards.
If the length of the rectangle (L) is given to be [tex]5x^{3}y^{4}[/tex] yards, then we have to find the width (W) of the rectangle in yards.
Now, A = L × W
⇒ [tex]W = \frac{A}{L} = \frac{45x^{8}y^{9}}{5x^{3}y^{4}} = (\frac{45}{5})\times (\frac{x^{8}}{x^{3}}) \times (\frac{y^{9}}{y^{4}}) = 9x^{8 - 3}y^{9 - 4} = 9x^{5}y^{5}[/tex] yards. (Answer)
Use the matrix tool to solve the system of equations. Enter the answer as an
ordered pair.
4x + y = 0
8x-y= 6
Answer:
(-1/2,2)
Step-by-step explanation:
2(4x+y=0)=8x+2y=0
8x+2y=0
-(8x-y=6)
3y=6
Divide both sides y=2
4x+2=0
4x=-2
divide both sides x=-1/2
To solve the system of equations, we can use the matrix tool. The solution to the system of equations is (1, 1.5) as an ordered pair.
To solve the system of equations using matrices, you can represent the coefficients and constants as matrices and then use matrix operations. The system of equations can be represented in matrix form as:
[A] [X] = [B],
Where:
[A] is the coefficient matrix,
[X] is the variable matrix (containing x and y),
[B] is the constant matrix.
For the given system of equations:
4x + y = 0
8x - y = 6
The coefficient matrix [A], variable matrix [X], and constant matrix [B] are:
[A] = [[4, 1],
[8, -1]]
[B] = [[0],
[6]]
Now, to solve for [X], you can use matrix multiplication:
[A] [X] = [B]
[X] = [A]⁻¹ [B]
First, calculate the inverse of [A]:
[A]⁻¹ = [[-1/12, -1/12],
[1/4, 1/4]]
Now, multiply [A]⁻¹ by [B]:
[X] = [[-1/12, -1/12],
[1/4, 1/4]] [0, 6]
[tex][X] = [(-1/12 \times 0 + -1/12 \times 6),[/tex]
[tex](1/4 \times 0 + 1/4 \times 6)][/tex]
Simplify:
[X] = [-(-1), 1.5)]
[X] = [1, 1.5]
So, the solution to the system of equations is (1, 1.5) as an ordered pair.
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