Using an exponential function, it is found that the equation that represents the value of the car after 5 years is:
[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the car is purchased for 21,800 dollars, and it's value deprecites 9.5% per year, hence the equation for it's value after t years is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 21800(1 - 0.095)^t[/tex]
[tex]A(t) = 21800(0.905)^t[/tex]
After 5 years, the value is given by:
[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]
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What is the smallest number greater than 1 that is both triangular and square
Answer:
36
Step-by-step explanation:
triangular numbers are
1, 3, 6, 10, 15, 21, 28, 36, .....
square numbers are
1, 4, 9, 16, 25, 36, ..........
the smallest number that is triangular and square is 36
Rewrite 4.86 x 10^12 in decimal notation.
help pleaseee
Answer:
second one down
4 860 000 000 000
Step-by-step explanation:
count out 12 zeros after the 4 and you will find the one in decimal notation
The decimal notation for the given scientific notation is 4860000000000. (option b)
What is decimal notation?The decimal notation is an alternate method to represent the fractional value. It means that it is the fractional representation using base 10. The fractions can be converted into decimals and vice versa.
Given is a scientific notation, 4.86 × 10¹², we need to convert it into a decimal notation,
4.86 × 10¹²
= 4.86 × 10,000,000,000,000
= 4.86 × 100 × 100000000000
= 486 × 100000000000
= 48600000000000
Hence, the decimal notation for the given scientific notation is 4860000000000. (option b)
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|x-b|=c, only one solution is -3
Answer:
x-b=-3
Step-by-step explanation:
1. Simplify
|x-b|=c
x-b=c
If c=-3 then,
Answer= x-b=-3
What are the solutions for the following system of equations?
y = 8x + 7
y = -x2 - 5x+7
(0,7) and (13, 97)
0 (0,7) and (-13, -97)
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
[tex](0,7),(-13,-97)[/tex]
Equation Form:
[tex]x=0,y=7\\x=-13,y=-97[/tex]
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(8*x+7)=0
Equation of a Straight Line
Solve y-8x-7 = 0
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.'
n this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-8x-7 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000
y-intercept = 7/1 = 7.00000
Calculate the X-Intercept :
When y = 0 the value of x is 7/-8 Our line therefore "cuts" the x axis at x=-0.87500
x-intercept = 7/-8 = -0.87500
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 23.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 23.000 - 7.000 = 16.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 16.000/2.000 = 8.000
Geometric figure: Straight Line
Slope = 16.000/2.000 = 8.000
x-intercept = 7/-8 = -0.87500
y-intercept = 7/1 = 7.00000
Pull out like factors :
-x2 - 5x - 7 = -1 • (x2 + 5x + 7)
Trying to factor by splitting the middle term
2.2 Factoring x2 + 5x + 7
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 1 • 7 = 7
Step-2 : Find two factors of 7 whose sum equals the coefficient of the middle term, which is 5 .
-7 + -1 = -8
-1 + -7 = -8
1 + 7 = 8
7 + 1 = 8
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Find the Vertex of y = -x2-5x-7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting "y" because the coefficient of the first term, -1 , is negative (smaller than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000
Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :
y = -1.0 * -2.50 * -2.50 - 5.0 * -2.50 - 7.0
or y = -0.750
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = -x2-5x-7
Axis of Symmetry (dashed) {x}={-2.50}
Vertex at {x,y} = {-2.50,-0.75}
Function has no real roots
Solve Quadratic Equation by Completing The Square
3.2 Solving -x2-5x-7 = 0 by Completing The Square .
Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:
x2+5x+7 = 0 Subtract 7 from both side of the equation :
x2+5x = -7
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
-7 + 25/4 or, (-7/1)+(25/4)
The common denominator of the two fractions is 4 Adding (-28/4)+(25/4) gives -3/4
So adding to both sides we finally get :
x2+5x+(25/4) = -3/4
Adding 25/4 has completed the left hand side into a perfect square :
x2+5x+(25/4) =
(x+(5/2)) • (x+(5/2)) =
(x+(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2+5x+(25/4) = -3/4 and
x2+5x+(25/4) = (x+(5/2))2
then, according to the law of transitivity,
(x+(5/2))2 = -3/4
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(5/2))2 is
(x+(5/2))2/2 =
(x+(5/2))1 =
x+(5/2)
please help pleaseeeeeeee
Answer:
9.5
Step-by-step explanation:
First order them:
5, 5, 8, 11, 12, 14
The go to the middle
2, 8, 11, 12
8, 11
8 + 11 = 19
19 / 2 = 9.5
Answer:
9.5 is your answer
WILL GIVE LOTS OF POINTS
Jenny has 9 cars available to rent. Let C be the number of cars she would have left after renting R of them. Write an equation relating C to R. Then graph your equation
9-R= C
hope this helps :)
4+6x=16 how to solve it
Answer:
Step-by-step explanation:
Remark
The first step is the key step. You have to get the xs on one side and the numbers on the other.
Solution
4 + 6x = 16 Subtract 4 from both sides
4-4+6x = 16 - 4 Combine
6x = 12 Divide both sides by 6. You want x by itself.
6x/6 = 12/6
Answer: x = 2
What is the value of z in the triangle ? Enter your answer in the box . Round your final answer to the nearest hundredth.
Answer:
32.97 inches
Step-by-step explanation:
Given
27 in. is the length one of the legsSolving
cosine function gives the ratio of the adjacent side of the angle and the hypotenuseTake cos35°cos35° = 0.819cos35° = 27/z⇒ 27/z = 0.819⇒ z = 27/0.819⇒ z = 32.97 inches1. Sixty-four unit cubes were glued together to make a 4 × 4 × 4 cube. How many 1 × 1 pairs
of faces were glued together to make the larger cube?
2. A cube is painted red and then cut into 64 identical smaller cubes. How many of these cubes
are painted red on at least one face?
3. A cube is painted red and then cut into 1000 identical smaller cubes. How many of these
cubes are painted red on at least two faces?
Answer:
The answer is 56 and that is no guess
A pick-up weighing 1.4 t is loaded with 40 bags of cement each weighing 50 kg. What in the total weight of the pick-up and its load.
Answer:
3.4 tonnes
Step-by-step explanation:
Kg --> tonnes = / 1000
50 x 40 / 1000 = 2. 2 + 1.4 = 3.4.
solve this system of equations using substitution, show your work (ANSWER QUICK PLEASE)
Answer: x=18/5 y=127/5
Step-by-step explanation:
For both equations
1. subtract from both sides
2. divide to find what the variable equals
How many ways can 10 students line up in a food counter?
Answer:
for the first student in the line there are 10 choices,then for the 9 choices left,for the third 8 choices left and so on...
so its 10x9x8x7x6x5x4x3x2x1=3628800
Step-by-step explanation:
sana makatulong
What is the partial fraction decomposition of StartFraction 6 x + 17 Over (x + 1) squared EndFraction?
Answer:
6/(x + 1) + 11/(x + 1)^2.
Step-by-step explanation:
6x + 17 / (x +1)^2 = A / (x + 1) + B /(x + 1)^2
Multiply through by (x + 1)^2:
6x + 17 = A(x + 1) + B
Let x = -1, then:
-6 + 17 = 0 + b
So B = 11.
Let x = 1:
6 + 17 = A(1+1) + 11
23 = 2A + 11
A = (23-11)/ 2
A = 6.
HELPPPPPPPPPPPPPPPPPPP
Answer:
i dont know use the internet
Step-by-step explanation:
this is the right way
The dot plot below shows the results of a recent patient survey at Brookwood Medical Center. Use
the data to answer the following questions. If necessary, round your answer to the nearest tenth.
Find the mean and median scores.
Answer:
the median is 3.5
Step-by-step explanation:
there are 27 dots 27/2=13.5 therefore the answer is the 13th dot and a half 3.5 :) (i dont know for sure but i think the mean is 3)
The mean is 3 and the median is 3 for this list of numbers.
From the dot pot,
Arrange the number in order:
1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5
Now,
Mean = Average of all the values.
Median = Midvalue of the number.
Now,
There are 30 numbers in the list, so the mean is:
Mean = 90/30 = 3
To find the median, we need to find the middle number.
Since there are an even number of numbers in the list, we take the average of the two middle numbers:
The middle two numbers are both 3, so the median is:
Median = (3 + 3)/2 = 3
Therefore,
The mean is 3 and the median is 3 for this list of numbers.
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A circle has a circumference of 6. It has an arc of length 1.
What is the central angle of the arc, in degrees?
The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:
6= πd and then divide both sides of the equation by π you get that d = 1.90
To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:
1 = 0.9549θ
Answer:
60
Step-by-step explanation:
1/6 x 360
Central angle is equal to measure of intercepted arc.
60 degrees
a random sample of 45 art students revealed that 20 prefer prefer painting over sculpture if there are 2k students in an art program how many would be expected to prefer painting over scultuprue
Using proportions, it is found that 889 students would be expected to prefer painting over scultuprue.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 20 out of 45 students prefer painting over sculpture. Out of 2000 students, how many students would be expected to prefer painting? The rule of three is given by:
20 - 45
n - 2000
Applying cross multiplication:
45n = 20 x 2000
n = (20 x 2000)/45
n = 889.
889 students would be expected to prefer painting over scultuprue.
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Zoe considers the lunch choices as she looks at the menu. What is the probability that she will choose cheese pizza, apple, milk?
Meal: Cheese Pizza, Cheeseburger, Hotdog, Salad
Side: Banana, Apple, Yogurt
Beverage: Milk, Water, Juice
Multiple choices:
1/10
1/21
1/12
1/36
Answer:
1/10
Step-by-step explanation:
There are ten options and Salad is one of them; therefore, the answer would be 1/10.
A bike shop has 35 bicycles and tricycles with a total of 81 wheels. How many bicycles and how many tricycles are in the shop?
Answer:
There are 24 bicycles and 11 tricycles in the shop
Step-by-step explanation:
We can make a system of equations to find the answer:
x for bicycles and y for tricycles:
x + y = 35
2x + 3y = 81
2x because bicycles have 2 wheels, 3y because tricycles have 3 wheels, and have set the total to 81 because 81 wheels in total.
Solving, we will find that there are 24 bicycles and 11 tricycles in the shop.
Noah finds some nickels and pennies in his change purse. How many coins does he
have if he has 100 nickels and 120 pennies? How many coins does he have if he has n
nickels and p pennies?
He has 100 + 120 = 220 coins in his purse.
He has n + p coins if he has n nickels and p pennies.
Naoki asked 200 students about their favorite movie genres. Of the 105 students who preferred comedy, 68 of them were girls. 94 of the students surveyed were boys. Construct a two-way table summarizing the data.
Here is the completed two-way frequency table:
Comedy Action Total
Boys 37 57 94
Girls 68 38 106
Total 105 95 200
How to complete the two-way table?Number of boys that prefer comedy = number of students that prefer comedy - Number of girls that prefer comedy
105 - 68 = 37
Number of boys that prefer action = total numer of boys - Number of boys that prefer comedy
94 - 37 = 57
Total number of students the prefer action = Total number of students - total number of students that prefer comedy
200 - 105 = 95
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Algebra
U perpendicure
All changes saved
4. Identify the equations as parallel lines, perpendicular lines, or neither.
Equation 1: -2x+5y=3
Equation 2: 2y=5x+1
perpendicular
Neither
parallel
Answer: Neither
Step-by-step explanation:
14. How much interest will you earn if depositing $25,000 to grow continuously at 9%
interest rate for 12 years?
Answer:
Step-by-step explanation:
i think this is the answer
When do you struggle finding the min and max in a binary search tree
One can struggle to find the min and max in a binary search tree when the search algorithm is error prone.
What is a binary search?It should be noted that a binary search simply means a searching algorithm for finding the elements position in an array.
In this case, one can struggle to find the min and max in a binary search tree when the search algorithm is error prone as this requires more stack space.
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One can struggle to find the min and max in a binary search tree when the search algorithm is error-prone as this requires more stack space.
What is the binary search tree?A binary Search Tree is a node-based binary tree data structure that has the following properties:
In Binary Search Tree, we can find the maximum by traversing the right pointers until we reach the rightmost node. But in Binary Tree, we must visit every node to figure out the maximum. So the idea is to traverse the given tree and for every node return a maximum of 3 values.
1) Node’s data.
2) Maximum in node’s left subtree.
3) Maximum in node’s right subtree.
Below is the implementation of the above approach.
The left subtree of a node contains only nodes with keys lesser than the node’s key. The right subtree of a node contains only nodes with keys greater than the node’s key. The left and right subtree each must also be a binary search tree.Hence, one can struggle to find the min and max in a binary search tree when the search algorithm is error-prone as this requires more stack space.
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You put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly. how much will you have after 23 years? round to the nearest cent. a. $46,683.28 b. $4,564,471.88 c. $2,949.39 d. $3,832.84
After 23 years $125.32 will be matured to $46,683.28.
What is the formula for recurring investment?The formula for Recurring maturity is given by:
[tex]A=Pn +\frac{ P*n*(n+1)}{24} *\frac{r}{100}[/tex]
Where A=matured amount
P =Principal value
n=Number of months
r=Interest rate(annual)
We have P= $125.32
n=23*12 = 276 months
r=2.5*12 =30%
Put these values in the above formula
we get A= $46,683.28
Therefore, After 23 years $125.32 will be matured to $46,683.28.
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What is the most specific name for the figure?
A(-4a, -2a)
B(-9a, -2a)
C(-5a, a)
D(0, a)
A. Trapezoid
B. Rectangle
C. Square
D. Rhombus
Answer: D
Step-by-step explanation:
The quadrilateral will be a rhombus. Then the correct option is D.
What is the quadrilateral?The definition of a quadrilateral is a planar form with four sides, four vertices, and four angles. Concave and convex are the two primary kinds.
Type of quadrilateral are:
Trapezoid.Rectangle.Parallelogram.Rhombus.Square.Kite.The length of the side CD is given as,
CD² = (0 + 5a)² + (a - a)²
CD = 5a units
The length of the side BC is given as,
BC² = (- 5a + 9a)² + (a + 2a)²
BC² = (4a)² + (3a)²
BC² = 25a²
BC = 5a units
The length of the adjacent sides is equal. Then the quadrilateral will be a rhombus.
Thus, the correct option is D.
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Which ratio is not equivalent to 3/5 ?
A. 15/20
B.6/8
C.30/50
D.12/20
Answer:
A & B
Step-by-step explanation:
15/20 is not equal
6/8 is not equal
30/50 is equal
12/20 is equal
Hey there!
3/5
= 3 ÷ 5
= 0.60
= 60%
• So, we’re looking for something that’s equivalent to 0.60 or 60%
Option A.
15/20
= 15 ÷ 20
= 15 ÷ 5 / 20 ÷ 5
= 3 / 5
= 3 ÷ 5
= 0.60
= 60%
So, Option A. could possibly be your equivalent to your fraction
Option B.
6/8
= 6 ÷ 8
= 6 ÷ 2 / 8 ÷ 2
= 3 / 4
= 3 ÷ 4
= 0.75
= 75%
So, Option B. isn’t equivalent because it’s too big and not what we’re looking for!
Option C.
30/50
= 30 ÷ 50
= 30 ÷ 5 / 50 ÷ 5
= 6 / 10
= 6 ÷ 2 / 10 ÷ 2
= 3 / 5
= 3 ÷ 5
= 0.60
= 60%
So, Option C. could possibly be your equivalent to your fraction.
Option D.
12/20
= 12 ÷ 20
= 12 ÷ 2 / 20 ÷ 2
= 6 / 10
= 6 ÷ 2 / 10 ÷ 2
= 3 / 5
= 3 ÷ 5
= 0.60
= 60%
So, Option D. could possibly be your equivalent to your fraction.
To sum it all up, your answer is:
Option B. 6/8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which of the following shows the true solution to the logarithmic equation solved below? log Subscript 2 Baseline (x) = log Subscript 2 Baseline (x 7) = 3. Log Subscript 2 Baseline left-bracket x (x 7) right-bracket = 3. X (x 7) = 2 cubed. X squared 7 x minus 8 = 0. (x 8) (x 1) = 0. X = negative 8, 1 x = negative 8 x = 1 x = 1 and x = negative 8 x = 1 and x = 8.
The value which shows the true solution to the given logarithmic equation is 1.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The given logarithmic equation is,
[tex]\rm log_{2} (x) + log_{2} (x +7) = 3.[/tex]
Use the addition property of log in the above expression.
[tex]\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0[/tex]
Solve the quadratic equation we get,
[tex](x+8)(x-1)=0[/tex]
x = -8, 1
Here, the logarithmic function is defined only for positive real numbers as its input.
Thus, the value which shows the true solution to the logarithmic equation solved above is 1.
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Answer:X=1
Step-by-step explanation:b on edge
A triangle has two side lengths: 18 in and 12 in. Which of the following could be the length of the third side?
Answer:
6<L<30
Step-by-step explanation:
because we know that the third side needs to be in between the sum of the other two it has to be less than 30 and then because it needs to apply to the other sides it is greater then 18-12 or 6.
1. (03.04)
What are the zeros of f(x) = (x - 5)(x – 4)(x - 2)? (2 points)
Answer:
for x=5, x=4 , x=2
Step-by-step explanation:
zero points, the x values that make this formula to be zero.
5-5=0
4-4=0
2-2=0
these values satisfied