The value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x
The value of a rare coin rises in accordance with the function f(x)
f(x) = 100(1.07)x
where x represents the number of years that the coin is owned and value is measured in US dollars
Now, Simplifying the given function, we have :
f(x) = 100(1.07)x
f(x) = 107x
Now, we need to find the value of the coin after five years, then
Putting x = 5 in the function,
f(x) = 107 * 5 = 535
Hence, the value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x
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Josie calculated 1/5+1/2 and said the answer was 2/7 is it wrong and why
Answer:
It's wrong because you don't add fractions the way you would add normal numbers.
Step-by-step explanation:
To add 1/5 to 1/2 you would need to write all numerators above the least common denominator which is 10. Then add the numerators, 5 + 2, which gives you 7/10.
Use the ray tool to graph f(x) = |-x – 5|.
First plot the endpoint of the ray, then any point on the ray.
The graph of the given absolute function is attached below and the end points (-5,0) (0, 5) of the rays are marked in it.
Absolute value function:
The function that contains an algebraic expression within absolute value symbols is called as absolute value function.
Given,
Here we have the absolute value function f(x) = |-x - 5|
Now, we have to plot the graph for this function and we have to mark the end point of the rays.
Here the given function is written as,
=> f(x) = | -x - 5|
In order to plot the graph for the function we need the table of values to point it on the graph,
For that we have to take following sample values,
When x = -5, then f(-5) = |-5 -5| = 0
When x = 0, then f(0) = |0 - 5| = 5
Therefore, the end points of the rays are (-5,0) and (0,5)
Now, we have to plot these values on the graph.
Then we get the graph like the following.
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Willis borrowed $1400 at 9% simple interest to be paid back in 2 years. How much interest will he pay?
If he borrowed $1400 at 9% simple interest to be paid back in 2 years. The interest he will pay is $1,663.34.
How to find the interest?Using this formula
Interest = Principal ( 1+ Interest rate)^ time
Where:
Interest =?
Principal = $1400
Interest rate = 9% or 0.09
Time = 2 years
Let plug in the formula
Interest = $1,400 ( 1+ 0.09) ^ 2
Interest = $1,400 ( 1.09) ^2
Interest = $1,400 ( 1.1881)
Interest = $1,663.34
Therefore he will pay the amount of $1,663.34 as interest.
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During a building project, a brick is
dropped from a height of 1,936 ft. If the
equation for height as a function of time is
h(t) = -16t2 initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the brick to
hit the ground?
Answer:
11 seconds
Step-by-step explanation:
[tex] - 16 {t}^{2} + 1936 = 0[/tex]
[tex] - 16 {t}^{2} = - 1936[/tex]
[tex] {t}^{2} = 121[/tex]
[tex]t = 11[/tex]
The cost in dollars of making x items is given by the function C(x)=10x+900 .
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
Fixed cost =$
b. What is the cost of making 25 items?
C(25)=$
c. Suppose the maximum cost allowed is $1900 . What are the domain and range of the cost function, C(x) ?
Domain:
Range:
Step-by-step explanation:
when we give a function an actual value as argument, we are using the variable(s) in the functional definition as intended : as placeholders for actual values.
so, we only need to replace any occurrence of the variable by the actual value and calculate.
a.
zero items are produced means x = 0.
C(0) = 10×0 + 900 = $900
fixed cost = $900
b.
making 25 items means x = 25.
C(25) = 10×25 + 900 = 250 + 900 = $1,150
c.
the domain is the interval or set of all valid values for x.
the range is the interval or set of all valid values for y (the functional result).
now, the maximum cost allowed is $1900.
how many items are that ?
1900 = 10x + 900
1000 = 10x
x = 100
so, the domain is
0 <= x <= 100
the range is
$900 <= y <= $1900
the sum of a number with the square of its following algebraic language
Answer:
a + (a+1)²
Step-by-step explanation:
The following of the number "a" is:
a+1
Then:
The sum of a number with the square of its following algebraic language is:
a + (a+1)²
The algebraic expression for the sum of a number with the square of its following number can be written as:
x + ( x + 1)²Where x is the given number and (x + 1 )² represents the square of the following number.
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Which of the following uses set builder notation to denote the set of all real numbers that are greater than or equal to 3 and less or equal to 9?
The given set written on set builder notation is:
{x| x ∈ R, 3 ≤ x ≤ 9}
How to write the set?We want to write the given set using set builder notation, the set is the set of all real numbers that are greater than or equal to 3 and less or equal to 9.
So the set can be written as an inequality as:
3 ≤ x ≤ 9
To define the set using the set builder notation, we also need to clarify that x belongs to the real number set, this is x ∈ R.
Then the set that we need to write is:
{x| x ∈ R, 3 ≤ x ≤ 9}
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x = 15.3568 - (1+x)^25
The value of x in the algebraic equation x = 15.3568 - 1(1+x)^25 is 0.115
Mathematical OperationArithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
In this case, we have to solve for x in the algebraic equation using mathematical operation.
x = 15.3568 - (1 + x)^25
Collect like terms
x + (1+x)^25 = 15.3568
Solving for x
x = 0.115
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The graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 6. Function 2 y = 2x + 7 How much more is the rate of change of function 2 than the rate of change of function 1? (4 points) a 1 b 2 c 3 d 4
The rate of change of function 2 is greater than the rate of change (slope) of function 1 by: B. 2.
How to determine the difference in the rate of change?Since the line on this graph is perpendicular to the y-axis (horizontal line), we can reasonably and logically deduce that its rate of change (slope) is equal to zero (0) because there is no change in the y-value on the y-axis.
This ultimately implies that, the rate of change (slope) of function 1 (y = 6) with an horizontal line is equal to zero (0).
Next, we would calculate the rate of change (slope) of function 2 i.e y = 2x + 7. Mathematically, the standard form of the equation of a straight line function is given by;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.By comparing the two (2) equations, we have the following:
y = mx + c ≡ y = 2x + 7
Therefore, the rate of change (slope) of function 2 is equal to 2.
Now, we can calculate the difference between the rate of change (slope) of function 2 and the rate of change (slope) of function 1 as follows:
Difference = 2 - 0
Difference = 2.
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Solve negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4 for y.
The solution to the equation as written is y = -96/161.
What is a linear equation?The term linear equation has to do with an equation in which the highest power of the variable is 1. In this case, we have been given a word problem and we would have to convert it to equation.
The equation is now to be written as;
5y + 7/3y = 5/8y - 4
Collect like terms and apply BODMAS;
5y + 7/3y - 5/8y = -4
22y/3 - 5/8y = -4
161y/24 = -4
24(-4) = 161y
y = 24(-4)/161
y = -96/161
Having solved the equation, the solution that is obtained for the linear system is y = -96/161
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15. Todd purchased two CDs and three cassette tapes for $75. Paulena went to the same
music store and purchased one CD and five cassette tapes for $76. If all CDs are the
same price and all the cassette tapes are the same price, find the cost of each CD and
each cassette tape.
The cost of each CD is $21 and the cost of each cassette tape is $11.
According to the question,
We have the following information:
Todd purchased two CDs and three cassette tapes for $75. Paulena went to the same music store and purchased one CD and five cassette tapes for $76.
Now, let's take the cost of each CD to be $x and the cost of each cassette tape to be $y.
So, we have the following expressions:
2x+3y = 75 ..(1)
x+5y = 76
x = 76-5y ..(2)
Putting the value of x in equation 1:
2(76-5y)+3y = 75
152-10y+3y = 75
152-7y = 75
Subtracting 152 from both sides:
-7y = 75-152
-7y = -77
y = 77/7
y = $11
Putting this value in equation 2:
x = 76-5y
x = 76-5*11
x = 76-55
x = $21
Hence, the cost of each CD is $21 and the cost of each cassette tape is $11.
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Unit form 3 tens 8 ones x 1000
The expression 3 tens 8 ones × 1000 can be evaluated and the value is; 38,000.
What is the value of the word phrase as given?It follows from the task content that the value of the expression represented by the word phrase as given is to be determined.
On this note, it follows that we have;
First, 3 tens and 8 ones can be written as;
(3 × 10) + (8 × 1)
= 30 + 8
= 38.
Therefore, the result of the evaluation is; 38 × 1000 = 38, 000.
Ultimately, the result of the expression is; 38,000.
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Is 11/16 greater than less than or equal to 3/8
Answer:
Greater than
Step-by-step explanation:
3/8 = 6/16
6<11
therefore, 11/16 is greater than 3/8
Given f(x)= x^2 +2x-8 and g(x)= x+2, find (fog)(x). Help is greatly appreciated. Thanks!
For given functions f(x)= x^2 +2x-8 and g(x)= x+2,
(fog)(x) = x^2 + 6x
For given functions f(x)= x^2 +2x-8 and g(x)= x+2,
we need to find (fog)(x).
We know that the composition of function f(x) and g(x) would be,
(fog)(x)
= f(g(x))
= f(x + 2)
= (x + 2)^2 + 2(x + 2) - 8
= x^2 + 4x + 4 + 2x + 4 - 8
= x^2 + 6x + 8 - 8
= x^2 + 6x
Therefore, for given functions f(x)= x^2 +2x-8 and g(x)= x+2,
(fog)(x) = x^2 + 6x
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Z
E
140⁰
180
D120°
40
mZAOC
60
135⁰
80
C
90°
80⁰
What is the measure for the following <?
m
40
60
80
Answer:
Question 1:
The angle m∠DOX is greater than 90 degrees, but less than 135 degrees.
Looking at the diagram we see that:
m∠DOX = 120 degrees.
Question 2:
The angle m∠COX is the sum of two angles that in total are 80 degrees.
Therefore, the equation is:
m∠COX = m∠AOX + m∠COA
Question 3:
The BOA angle measurement is given by:
BOA = 60 - 40
BOA = 20 degrees
Therefore, an angle that measures 20 degrees is:
BOA.
Question 4:
From the previous question we have:
m∠BOA = 60 - 40
m∠BOA = 20
The measure of m∠BOA is 20 degrees
Question 5:
The measure of the angle EOD is given by:
m∠EOD = 140 - 120
m∠EOD = 20 degrees
THANKS
50
4.8
(41 votes)
Step-by-step explanation:
Copy and complete the workings below to
calculate the value of c.
c² = 9² + 40²
C² =...
c=...
Answer:
41
Step-by-step explanation:
9² + 40² = 1681
the s.r of 1681 is 41
We s.r the answer because we need the singular of C, not C²
Hope this helps
Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = -2(x-3)
A florist makes centerpieces.
18 roses in each centerpiece.
best way to use compatible numbers to
estimate the number of roses the florist
needs for 24 centerpieces?
A 10 x 25 = 250
B 20 x 25 = 500
D
25 X 30 = 750
30 × 30 = 900
The best compatible number to use for 24 x 18 = 432.
24 can be written as 25
18 can be written as 20.
So,
20 x 25 = 500
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of roses in one centerpiece = 18 roses.
The number of roses in 24 centerpieces.
= 24 x 18
= 432
The best compatible number to use for 24 x 18 = 432.
24 can be written as 25
18 can be written as 20.
So,
20 x 25 = 500
Thus,
The best compatible number to use for 24 x 18 = 432.
24 can be written as 25
18 can be written as 20.
So,
20 x 25 = 500
Option B is the correct answer.
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Given the equation k over 12.6 equals 7.4, determine the value of k.
93.24
20.0
5.2
1.70
The value of k from the given equation as in the task content is; 93.24.
What is the value of k?It follows from the task content that the value of k for which the given equation is true is to be determined.
On this note, since the given equation is;
k / 12.6 = 7.4
Therefore, to isolate k, both sides of the equation must be multiplied by; 12.6 as follows;
k = 7.4 × 12.6
Ultimately, the value of k for which the given equation is true is; 93.24.
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 25 pounds each, and the small boxes weigh 50 pounds each. There are 105 boxes in all. If the truck is carrying a total of 3, 875 pounds in boxes, how many of each type of box is it carrying?
Choose one:
Number of large boxes: 5
Number of small boxes: 10
Number of large boxes: 50
Number of small boxes: 55
Number of large boxes: 38
Number of small boxes: 75
Number of large boxes: 55
Number of small boxes: 50
Answer:
There are 105 boxes in all. If the truck is carrying a total of 3, 875 pounds in boxes, how many of each type of box is it carrying?
50 large boxes
55 small boxes
Please help I was sick and missed out on class.Thank you
==========================================
Explanation:
Both points have the same x coordinate, which immediately tells us both points are on the same vertical line.
All vertical lines have an undefined slope. This is because when it comes to rise/run, the "run" is zero. Dividing by zero is not allowed.
Check out the steps below.
[tex](x_1,y_1) = (-10,9) \text{ and } (x_2,y_2) = (-10,18)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{18 - 9}{-10 - (-10)}\\\\m = \frac{18 - 9}{-10 + 10}\\\\m = \frac{9}{0}\\\\m = \text{UND}\\\\[/tex]
The "UND" is shorthand for "undefined". Some textbooks may use the notation "NaN" to refer to "not a number".
the third term of the sequence is 165 find the 1st term subtract 2 and multiply by 3
Answer:
Step-by-step explanation:
Formula for geometric sequence is:
[tex]a_{n} =a_{1} (r)^{n-1}[/tex]
Now we substitute the values in:
[tex]165=a_{1} (3)^{3-1}[/tex]
165=a1(-2x3)^2
165=a1x9
Answer is 23
2) The Peponi tuckshop sells + different kinds of muffin. Apple, blueberry, cherry and damson. A cherry muffin costs the same as two apple muffins. A blueberry muffin costs the same as two damson muffins. A Cherry muffin and two damson muffins costs the same as an apple and two blueberry muffins. All four types cost an integer multiple of 100 shillings. If Aanya buys one of each kind, which of these could be the amount she spends? 1,600, 1,800, 2000, 2200 or 2400 shillings.
Answer:
1800
Step-by-step explanation:
c = 2a;
b = 2d;
c + 2d = a + 2b
2a + b = a + 2b
a = b
a = b
c = 2a
d = b/2
Assume a = 100.
b = 100
c = 200
d = 50
This cannot be, but we can continue.
Add them: 100 + 100 + 200 + 50 = 450
The total must be an even multiple of 450.
The total can be 900, 1800, 2700, etc.
Answer: 1800
NO LINKS!! Please help me with the Angle Proofs Part 4
Answer:
1. Given.
2. Definition of a linear pair.
3. Given.
4. Congruent Supplements Theorem.
Step-by-step explanation:
Statement 1
∠JKM and ∠MKL form a linear pair.
Reason: Given
Statement 2
∠JKM and ∠MKL are supplementary
Reason: Definition of supplementary angles.
A linear pair is a pair of adjacent, supplementary angles.
If ∠JKM and ∠MKL form a linear pair then they are supplementary by definition.
Statement 3
∠JKM and ∠LKN are supplementary.
Reason: Given.
Statement 4
∠MKL ≅ ∠LKN
Reason: Congruent Supplements Theorem.
If two angles are supplements of the same angle, then the two angles are congruent.
As ∠MKL and ∠LKN are both supplementary to ∠JKM then ∠MKL and ∠LKN are congruent.
The Bloomington Times had 8,050 subscribers last year. This year, after the paper was bought out, it had 70% more. How many subscribers were there this year?
due tomorrow pleaseeeeeee help
Answer:
13685
Step-by-step explanation:
8050 x 0.70 = 5635
8050 + 5635 = 13685
The graph of a quadratic function with vertex (-3, 1)
Find the range and the domain.
Write the range and domain using Interval notation.
Answer:
Domain: (negative infinity, positive infinity)
Range: (negative infinity, 1]
Step-by-step explanation:
How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word "Honesty" ?
Answer:
The number of words with two vowels and 3 consonants from the letters of the word ‘HONESTY’ is 1200.
Step by step explanation:
Please help me giving 100 pts to whoever can help me the fastest!!!!!
Answer:
0.4294
Step-by-step explanation:
need help ASAP plspldplsplsplspls
1) The linear system has only one solution.
2) The linear system has infinite number of solutions.
3) The linear system has only one solution
4) The linear system has only one solution.
5) The linear system has only no solution.
What is meant by a linear equation?In the algebraic form y= mx+ b, where m denotes the slope and b the y-intercept, a linear equation is defined as a first-order (linear) term and a constant. The aforementioned is occasionally described as a linear equation with two variables, where x and y are the variables.
An equation is linear if the graph of the equation is a straight line. This will happen once x has the highest power of 1, which is. The equation is linear if it can be represented as a straight line.
1) x+y+7=0
x-y+1=0
By solving these two equations we get,
x=-4
y=-3
(x, y)=(-4,-3)
Consequently, there is only one solution to the linear system.
2) 3x+y-2=0
6x+2y-4=0
a₁/a₂=3/6
a₁/a₂=1/2
b₁/b₂=1/2
c₁/c₂=1/2
Therefore,
a₁/a₂=b₁/b₂=c₁/c₂
So, the linear system has infinite number of solutions.
3) x-y-5=0
x+5y+7=0
By solving these two equations we get,
y=-2 and x=3
(x, y)=(3, -2)
Consequently, there is only one solution to the linear system.
4) x+y-4=0
2x-3y-3=0
By solving these two equations we get,
x=3 and y=1
(x, y)=(3,1)
Consequently, there is only one solution to the linear system.
5) 5x-y-5=0
5x-y-15=0
a₁/a₂=1
b₁/b₂=1
c₁/c₂=1/3
∴ a₁/a₂=b₁/b₂≠c₁/c₂
Therefore, the linear system has no solution.
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Write an expression having only two terms that is equivalent to 2x – 3. Explain how you wrote the expression and how you can check that it is equivalent.
i will provide any pics, etc if neccesary
The equivalent two-term expression of 2x - 3 is 2(x - 1) - 1
What are Equivalent Algebraic expression?Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.
2x - 3 can be written by expressing -3 as a sum of two numbers in which one of the numbers is -2, those two numbers are -1 and -2
so that,
2x -2 -1
now we can factorize 2x -2, which is 2(x - 1)
Finally the expression becomes 2( x - 1) -1
To check that it is equivalent we substitute any number in to 2( x -1 ) -1 and 2x - 3, if it gives same answer, then they are equivalent.
using x = 1
2( 1 - 1) -1 = -1
2(1) -3 = -1
In conclusion, 2(x-1) -1 is the equivalent expression
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