Answer:
y = -2280x + 31,500
or
when x = 6
so 6 years
Step-by-step explanation:
y = -2280x + 31,500
y = -2280(6) + 31,500
y = -13,680 + 31,500
y = 17,820
Macy made an initial deposit of $250 into a bank account. assuming no interest, the function f(x)=80x+250 represents the total amount of money she will have in the account after x months. evaluate and interpret the function for f(9).
Answer:A
Step-by-step explanation:
Solve for x
2x^2=5x+3
Answer:
Step-by-step explanation:
ur mom
A bowl contains blueberries and strawberries. There are a total of 16 berries in the bowl. The ratio of blueberries to strawberries is 3 : 1. How many of each berry are in the bowl?
Answer:
12 Blueberries and 4 Strawberries
Step-by-step explanation:
12+4 = 16 and 12:4 = 3:1
A 5 kg bag of grass seed covers about 650 m². How many bags should Tshering buy to seed a 60 m-by-80 m football field?
Given: 5 kg bag of grass seed covers 650 m2
To find:
Bags to seed 60m-80m field
Solution:
Area of football field- 60x80=4800m²
Bags required-
Since 650 m² is covered by 5kg
So, 4800m² will be covered by-
=4800/650x5
= 36.9 bags
Therefore, 40 bags are required to seed a 60m-by-80m football field.
To know more about area problems, click on https://brainly.com/question/28280898
The table shows sets of ordered pairs that form a relation.
Does each set of ordered pairs represent a function?
Select Function or Not a Function for each set of ordered pairs.
The ordered pairs that are also functions are listed below.
1. {(2,4),(3,1),(0,5),(-1,-3)}
2. {(2,4),(-4,1),(0,4),(-3,-0)}
4.{(7,-3),(3,-7),(2,4),(4,2)}
The ordered pairs that are not functions are listed below.
3.{(-2,-3),(4,1),(4,4),(-3,2)}
A function is a relation between two sets of ordered pairs that describe that there should be only one output for each input, or that for every element in set A, there should be one and only one relation in set B.
A relation between two sets of ordered pairs can be considered a function when every X value is associated with only one Y value.
Here in the first, second, and fourth sets of ordered pairs
1. {(2,4),(3,1),(0,5),(-1,-3)}
2. {(2,4),(-4,1),(0,4),(-3,-0)}
4.{(7,-3),(3,-7),(2,4),(4,2)}
Hence, every value in X has only one single value in Y. Hence, all these relations can be considered functions.
In the third set, i.e.,
3.{(-2,-3),(4,1),(4,4),(-3,2)}
It can be seen that element 4 has two values as its output, which are 1 and 4 ((4,1),(4,4)). Hence, it cannot be considered a function.
Learn more about functions at
https://brainly.com/question/12979762?referrer=searchResults
#SPJ1
18-9.2x10 to the power of -4 subtract the following in.Write your answer in standard notation
The subtraction of the numbers, involving scientific notation, is given as follows:
18 - 9.2 x 10^(-4) = 17.99908.
What is scientific notation?A number in scientific notation is given according to the rule presented as follows:
[tex]a \times 10^b[/tex]
The base is [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.
In this problem, we are given the following subtraction:
18 - 9.2 x 10^(-4).
When two numbers are subtracted, they must have the same base, hence we are going to convert 9.2 x 10^(-4) to base 0.
This means that 4 has to be added to the exponent, meaning that the base has to be divided by 10000 to compensate, then:
9.2 x 10^(-4) = 0.00092.
Then the result of the subtraction is given as follows:
18 - 9.2 x 10^(-4) = 18 - 0.00092 = 17.99908.
A similar problem, also about scientific notation, is given at https://brainly.com/question/16394306
#SPJ1
The nth term of a sequence is given by 2n² + 1.
Write down the first three terms of this sequence.
Answer:
3, 9, 19
Step-by-step explanation:
substitute n = 1, 2, 3 into the nth term formula
n = 1 : 2(1)² + 1 = 2(1) + 1 = 2 + 1 = 3
n = 2 : 2(2)² + 1 = 2(4) + 1 = 8 + 1 = 9
n = 3 : 2(3)² + 1 = 2(9) + 1 = 18 + 1 = 19
the first 3 terms are 3, 9, 19
Work out the volume of this cylinder.
Give your answer rounded to 1 DP.
The diagram is not drawn to scale.
The volume of a cylinder is: V = π r² h then the volume of a cylinder is 5091.43 cm²
How to estimate the volume of the cylinder?The volume of a cylinder is:
V = π r² h
From the information provided it can be concluded that:
The height of the cylinder is, h = 20 cm
The radius of the base exists, r = 9 cm
Compute the volume of a cylinder as follows:
V = π r² h
substitute the values in the above equation, we get
= (22/7) × 9² × 20
simplifying the above equation, we get
= (22 × 81 × 20) / 7
= 5091.42857
≈ 5091.43
Therefore, the volume of a cylinder is 5091.43 cm².
The complete question is:
Calculate the volume of this cylinder, giving your answer to 1 decimal place.
20 cm
9 cm
To learn more about the volume of this cylinder refer to:
https://brainly.com/question/9554871
#SPJ9
Randy has $450 saved in the bank. He wants to purchase a bike for $700. He plans to save $25
per month until he has enough to buy the bike. Randy's savings plan is represented by the
equation s = 25m + 450, where (s) represents total saved and (m) represents total saved and (m) represents months.
Does the equation represent a proportional relationship? Explain.
Answer: Yes because an example of a proportional problem is 54x = 103
I am pretty sure that is the answer
can someone please help with this geometry
Answer:
∠ABD = 19.5°
∠ABE = 160.5°
Step-by-step explanation:
Given angle ABC = 39° and its bisector BD, you want the measures of angle ABD and ABE, its supplement.
Angle bisectorAn angle bisector divides an angle into two equal parts, each with half the measure of the whole.
∠ABD = 1/2∠ABC
∠ABD = 1/2(39°)
∠ABD = 19.5°
Linear pairThe angles of a linear pair are supplementary: they total 180°. Angles ABD and ABE form a linear pair.
∠ABE = 180° -∠ABD
∠ABE = 180° -19.5°
∠ABE = 160.5°
Determine the quotient of 5/6 and 2/3
Answer:
5/4
Step-by-step explanation:
There is a rule that dividing by a fraction is the same as multiplying by the reciprocal.
So:
[tex]\frac{5/6}{2/3} = \frac56 \cdot \frac32 = \frac{15}{12} = \frac54[/tex]
URGENT PLEASE
Zachary purchased a computer for $1600 on a payment plan. five months after he purchased the computer, his balance was $900. eight months after he purchased the computer, his balance was $480. What is an equation that models the balance y after x months
If Zachary purchased a computer for $1600 on a payment plan. five months after he purchased the computer, his balance was $900. eight months after his balance was $480. The equation that models the balance y after x months is: y = -140x + 1600.
EquationMonth Balance
0 1600
5 900
8 480
Slopes:
(1600 - 900) / 5 = 700 / 5 = 140
(1600 - 480) / 8 = 1120 / 8 = 140
(900 - 480 ) / - 3 = - 140
Hence,
y = -140x + 1600
Therefore the equation is y = -140x + 1600.
Learn more about equation here: https://brainly.com/question/6614160
#SPJ1
Write
–
1
.
5
y
=
4
.
5
x
–
9
in standard form.
juhfhfufyffuufzk Liznfndjdhs
3. A clothing store is having a sale with all clothes being 10% - 30% off the original retail price.
(CAREFUL)
What would be the possible prices for a shirt with an original price of $60?
Answer: between $42 and $54 including both endpoints.
In symbolic form we can say [tex]42 \le p \le 54[/tex] where p is the final price after the discount is applied.
===============================================
Explanation:
10% off means you save 10% but pay the remaining 90%
Then convert 90% to decimal form to get 0.90
If the original price is $60, then the final price is 0.90*60 = 54 dollars.
In other words,
10% of 60 = 0.10*60 = 6 dollars saved
60-6 = 54 is the final price
---------------------
If the discount is 30% then you pay the remaining 70%
0.70*60 = 42
Or you can think of it like this
30% of 60 = 0.30*60 = 18 dollars saved
60-18 = 42 dollars is the final price
---------------------
Let's summarize with this chart:
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}[/tex]
Therefore, the final price after the discount is between $42 and $54 including both endpoints.
Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.
The Reach French Club is raising money for a trip to Strasbourg. They have some money already, and will raise $700 per month for x months.
Their fundraising progress is modeled by the function $8000 = $1200 + $700x.
What is the meaning of 1200 in this equation?
A They started with $1200.They started with $1200.
B They will raise $1200 per month.They will raise $1200 per month.
C They will save money for 1200 months.They will save money for 1200 months.
D They have a goal of $1200 total.
Function : $8000 = $1200 + $700x
They will raise $700 per month for x months -> $700x is the amount of money they raise per month.
Since $8000 is the sum in the function, it is the goal.
Therefore, $1200 in this case means they started with $1200.
WILL GIVE BRAINLIST TO BEST ANSWER PLUS EXTRA POINTS
5. The cost of a ride in a taxi is $5.00 for the first half-mile plus a constant amount per half mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.
5.00, 5.75, 6.50, …
Part A: Write an Explicit Function that can be used to determine f(x), the cost in dollars, for a ride in the taxi of, x, half miles.
Part B: What is the cost, in dollars, for an 55-mile ride in the taxi? Provide mathematical justification for your answer.
The explicit function of the relation is Tn = 4.25 + 0.75n and the cost of a 55 miles ride is $45.5
How to determine the explicit function?The sequence of the relation is given as
5.00, 5.75, 6.50, …
In the above sequence, we can see that
The sequence have a common difference of 0.75
This means that the sequence is an arithmetic function
An arithmetic function is represented as
T(n) = a + (n - 1)d
Where
a = First term = 5.00d = common difference = 0.75n = Number of termsTn = Current termSubstitute the known values in the above equation
Tn = 5 + 0.75(n - 1)
Expand
Tn = 5 - 0.75 + 0.75n
Evaluate
Tn = 4.25 + 0.75n
The cost of a 55-mile rideThis means that
n = 55
Subsitute n = 55 in the equation Tn = 4.25 + 0.75n
So, we have
T55 = 4.25 + 0.75 * 55
Evaluate the product
T55 = 4.25 + 41.25
Evaluate the sum
T55 = 45.5
Hence, a 55-mile ride will cost $45.5
Read more about arithmetic sequence at
https://brainly.com/question/6561461
#SPJ1
4 = -(x + 3) implemented as a real life problem
Savannah is creating a stained glass windowpane that will be 5 inches by 5 inches. To make
the rectangular windowpane, Savannah fuses together two triangles of colored glass. What is
the perimeter of one triangle?
The dimensions of the windowpane = 5 inches x 5 inches
This means the windowpane is square in shape.
Now, for the triangle,
Sides of the triangle = 5 inches each
Diagonal of the Square = Hypotenuse of the Triangle
The diagonal of a square is given by = [tex]\sqrt{2}[/tex] x side of the square = 5[tex]\sqrt{2}[/tex] inches
So, the perimeter of the one triangle = 5 + 5 + 5[tex]\sqrt{2}[/tex] = 10 + 5[tex]\sqrt{2}[/tex]
= 5(2+[tex]\sqrt{2}[/tex]) Inches
= 5(2+1.414)
= 17.07 inches (Approx.)
What is Perimeter?A perimeter is a closed path that embraces, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's circumference is its furthest boundary.There are various useful situations where knowing the perimeter is useful. The length of fence needed to completely enclose a yard or garden is known as the calculated perimeter. A wheel's or circle's perimeter indicates how far it will travel in a single rotation. In a similar way, the circumference of a spool is connected to the length of string looped around it; if the string were exactly the same length, the two would be equal.In addition to being the basic shapes, polygons are essential for figuring out perimeters since many shapes' perimeters are determined by estimating them with series of polygons that tend to them. Archimedes, who calculated a circle's approximate perimeter by enclosing it in regular polygons, is the first mathematician documented to have applied this line of thought.To learn more about Perimeter, refer to:
https://brainly.com/question/6465134
#SPJ13
Use synthetic substitution to find f(−3) if f(x)=x^3+4x^2−5x+11 .
By using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35
The function is
f(x) = [tex]x^3+4x^2-5x+11[/tex]
The function is defined as the relationship between the one variable and another variable. If one variable is dependent variable and another variable will be independent variable
To find the value of f(-3), first we have to substitute the value x = -3 in the given function
The function is
f(x) = [tex]x^3+4x^2-5x+11[/tex]
Substitute the value of x = -3
f(-3) = [tex](-3)^3+4(-3)^2-5(-3)+11[/tex]
= -27 + 36 + 15 + 11
= 35
Hence, by using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35
Learn more about function here
brainly.com/question/27614472
#SPJ1
Calculate the volume for each right rectangular prism 5 3/4 in high 8 1/2 in long 2 1/4width
5 3/4 = 5.75
8 1/2 = 8.50
2 1/4 = 2.25
Volume = width × height × length
? = (5.75)(8.50)(2.25)
volume = 109.96875
in fraction form = 109 31/32
A used boat dealership buys a boat for $2800 and then sells it for $3800 what is the percent increase
Percent increase by 35.71%
What is Profit and Loss ?
Profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year.
Given,
cost price of a boat is = $2800
selling price of a boat is = $3800
There is profit since C.P is less than S.P.
so, Profit = S.P - C.P
= $3800 - $2800
= $1000
Now, find profit percent i.e, Profit% = (Profit / C.P) * 100
=> Profit % = (1000 / 2800)*100
= 35.71%
Therefore, Percent increase by 35.71%
To read more about Profit and Loss.
https://brainly.com/question/25896797
#SPJ9
Write each mixed number as an improper fraction 5 whole number and 1 3 fraction form. Can you show me how you did the problem.
Answer:
16/3.
Step-by-step explanation:
5 1/3
First multiply 5 by 3.
This gives 15.
Now add the numerator of the fraction (1) to 15
- to give 16.
The improper fraction is 16/3.
What is the prime factorization of 21?Enter your answer as a product of prime numbers, like 2 X 3, or asa single prime number. like 17.
Answer:
The prime factorization of 21 is;
[tex]21=3\times7[/tex]Explanation:
We want to find the prime factorization of 21;
The number 21 is a product of 3 and 7;
[tex]21=3\times7[/tex]since 3 and 7 are both prime number, then the prime factorization of 21 is;
[tex]21=3\times7[/tex]Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)
First, draw a diagram to visualize the situation:
As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.
Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(8--5)^2+(-3-4)^2} \\ \\ =\sqrt{(13)^2+(-7)^2} \\ \\ =\sqrt{169+49} \\ \\ =\sqrt{218} \\ \\ \approx14.7648... \end{gathered}[/tex]Therefore, the distance between the points (-5,4) and (8,-3) is: √218.
What is the inverse of the function
f
(
x
)
=
−
1
2
(
x
+
3
)
f(x)=−
2
1
(x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis?
The inverse function of the function f(x) = 12(x+3) is f(x) = -2x - 3
A function's inverse is a function that offers us the actual value for which the desired function produces a specific outcome.
The function given is:
To find the inverse, we must perform the following procedures.
y takes the place of f(x);
y = -(x+3)/2
Change the x and y variables.
x = -(y+3)/2
Calculate y
2x = - (y + 3)
2x = -y - 3
y = -2x - 3
We get the following in inverted notation:
f(x)⁻¹ = -2x - 3
Thus the obtained inverse function is f(X) = -2x - 3
Learn more about inverse of a function at
https://brainly.com/question/17129933
#SPJ1
72% of what weight is 50oz
Answer:
See below
Step-by-step explanation:
72 % is .72 in decimal
.72 x = 50 oz Divide both sides by .72
X = 50 / .72 = 69.44 oz ( or 69 4/9 oz )
having a half braincell moment again
attachment below
Using similarity of triangles, the length of side GH is given as follows:
GH = 18.
Similar trianglesSimilar triangles have congruent angle measures, thus the measures of the side lengths are proportional.
In this problem, triangles CAD and HGD are similar, and the equivalent sides are given as follows:
AC = GH. (the measures are AC = 12 and GH = x).CD = HD. (the measures are CD = 30 and HD = 45).Hence the following proportional relationship is established:
x/12 = 45/30
Applying cross multiplication, we can solve for x, which is the length of side GH, as follows:
30x = 45 x 12 (simplifying by 30)
x = 1.5 x 12 (multiply 1.5 and 12).
x = 18. (which is the length of side GH).
More can be learned about similar triangles at brainly.com/question/305520
#SPJ1
Graphing transformations of sine and cosine functions: Sketch function below given the domain x e [-360, 360] <-- both are in degrees
By following the steps below, we can plot the graph of →
y = 5 cos(2x + π/3) - 1
What are trigonometric functions?The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given is the following function -
y = 5 cos(2x + π/3) - 1
We have -
y = 5 cos(2x + π/3) - 1
We can sketch the function as follows -
Let y = cos(x)
The first step is Amplitude magnification -y = 5 cos(x)
The second step can be understand in an easy way as if we multiply [x] by 2, the frequency of the cosine wave increases i.e. the distance between consecutive crests decreases.y = 5 cos(2x)
Third step include shifting of graph along the [x] axis. This can be done by adding a phase value as -y = 5 cos(2x + π/3). This will shift the graph along the negative
[x] - axis by π/3.
Finally, we will shift the graph by 1 unit towards the negative [y] - axis.Therefore, by following the steps above, we can plot the graph of →
y = 5 cos(2x + π/3) - 1
To solve more questions on trigonometry, visit the link below-
https://brainly.com/question/27926943
#SPJ1
Repost, can someone help?
Answer:
x=65
y=32
Step-by-step explanation:
2x+x-15=180
combine like terms
3x-15=180
add 15 to both sides
3x=195
divide both sides by 3
x=65
now y's
4y+y+20=180
combine like terms
5y+20=180
subtract 20 from both sides
5y=160
divide both sides by 5
y=32
Answer:
x = 65
y = 32
Step-by-step explanation:
2x + (x - 15) = 180
2x + x - 15
3x - 15 = 180
+15 +15
-------------------
3x = 195
÷3 ÷3
----------------
x = 65
4y + (y + 20) = 180
4y + y + 20 =180
5y + 20 = 180
-20 -20
---------------------
5y = 160
÷5 ÷5
---------------
y = 32
2x + (x - 15) + 4y + (y + 20) = 360
2(65) + (65 - 15) + 4(32) + (32 + 20) = 360
130 + 50 + 128 + 52 = 360
180 + 180 = 360
360 = 360
I hope this helps!
pls help need to turn this in
Answer: y - 3 = -2(x + 2)
