Answer:
[tex]\boxed{1) V = 40 000(0.89)^{n}, \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_{n} = -2^{n}}[/tex]
Step-by-step explanation:
1) Depreciation
The formula for the value V of an asset after depreciation by an annual percentage rate is
V = P(1 - r)ⁿ
where
P = present value
r = annual percentage rate
n = number of years
Data:
V = 40 000
r = 11 % = 0.11
n = 8 yr
Calculations:
(a) Function model
V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ
The function model is [tex]\boxed{ V= 40 000(0.89)^{n} }[/tex]
(b) Future value
V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746
In eight years, the truck will be worth [tex]\boxed{ \text{\$15 476}}.[/tex]
2) Profit function
Income from 1 lawn = $15
Income from x lawns = 15x
Less gas and supplies = -50
Net income = 15x – 50
The function is [tex]\boxed{f(x) = 15x - 50}[/tex].
3) Geometric series
(a) Calculate the common ratio
a₁ = -2
a₂ = -4
a₃ = -8
a₄ = =16
The ratios of consecutive pairs are
a₄/a₃ = -16/(-8) = 2
a₃/a₂ = -8/(-4) = 2
a₂/a₁ = -4/(-2) = 2
All adjacent pairs have the same common ratio r = 2.
(b) Write the formula for the series
The formula for the nth term of a geometric series is
aₙ = a₁rⁿ⁻¹
If a₁ = -2, the formula for the series is
aₙ = -2(2)ⁿ⁻¹ = -2ⁿ
The formula for the series is [tex]\boxed{a_{n} = -2^{n}}[/tex].
The slope of the line passing through the points (-2, 6) and (4, 6) is
A) 0
B) no slope
C) 2
Your answer ish c. 2
A slope is also known as the gradient of a line. The correct option is B.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that is passing through (-2, 6) and (4, 6) can be calculated as,
Slope = (6-6)/(-2-4) = 0/(-6)
Hence, there exists no slope between the two of the given points.
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equation that represents each mixed number as a sum of a whole numbers and unit fractions 3 and 1/4 5 and 1/2 to 1 2/3 and 4 3/8 solve
Answer:
1) [tex]\frac{13}{4}[/tex]
2) [tex]\frac{11}{2}[/tex]
3) [tex]\frac{5}{3}[/tex]
4) [tex]\frac{35}{8}[/tex]
Step-by-step explanation:
we know that
A mixed number is the sum of a whole number and a fraction number
case 1) we have
[tex]3\frac{1}{4}[/tex]
so
[tex]3\frac{1}{4}=3+\frac{1}{4}=\frac{3*4+1}{4}=\frac{13}{4}[/tex]
case 2) we have
[tex]5\frac{1}{2}[/tex]
so
[tex]5\frac{1}{2}=5+\frac{1}{2}=\frac{5*2+1}{2}=\frac{11}{2}[/tex]
case 3) we have
[tex]1\frac{2}{3}[/tex]
so
[tex]1\frac{2}{3}=1+\frac{2}{3}=\frac{1*3+2}{3}=\frac{5}{3}[/tex]
case 4) we have
[tex]4\frac{3}{8}[/tex]
so
[tex]4\frac{3}{8}=4+\frac{3}{8}=\frac{4*8+3}{8}=\frac{35}{8}[/tex]
What is the area of this tile?
12 in. ²
a = bh
a = 2 x 6
a = 12 in. ²
Answer:
12 in. ^2
Step-by-step explanation:
The area of a rectangle can be found by using the formula legnth x width.
Here the legnth is 2 in. and the width is 6 in.
6 x 2 = 12
Whenever you find the area, unit of measurement is ^2, thus resulting in the answer 12 in. ^2
I hope this helps!
Shelby’s recipe says to add 3/4 cup of brown sugar and 1/8 cup of white sugar how much sugar recipe call for altogether
Answer:you need common denominatord 4*2=8 3*2=6 6/8+1/8=7/8 of sugar
Step-by-step explanation:
25 Points Attachment Below Thanks
Area of a circle = PI x r^2
r is 1/2 the diameter = 0.5 inches
Area = 3.14 x 0.5^2
Area = 0.79 in^2
It looks like it’s missing something...is it a part A ?
Find the point, M, that divides segment AB into a ratio of 2:3 if A is at (0, 15) and B is at (20, 0).
What is segment ab? is there a picture that is supposed to go with it?
Answer: The required co-ordinates of point M are (8, 9).
Step-by-step explanation: Given that the point M divides segment AB into a ratio of 2 : 3, where A is at (0, 15) and B is at (20, 0).
We are to find the co-ordinates of point M.
We know that
the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
For the given division, (a, b) = (0, 15), (c, d) = (20, 0) and m : n = 2 : 3.
Therefore, the co-ordinates of point M are given by
[tex]\left(\dfrac{2\times20+3\times0}{2+3},\dfrac{2\times0+3\times15}{2+3}\right)\\\\\\=\left(\dfrac{40}{5},\dfrac{45}{5}\right)\\\\\\=\left(8,9).[/tex]
Thus, the required co-ordinates of point M are (8, 9).
which is not a proportion???
The answer is C. C is not a proportion.
Hope this helps!
Answer:
C
Step-by-step explanation:
By definition a proportion should be equal to each other and can be multiplied by the same number on the numerator and the denominator to make the second fraction.
[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]
[tex]\frac{x_1}{y_1}*\frac{z}{z}=\frac{x_2}{y_2}[/tex]
A
[tex]\frac{3}{7}*\frac{3}{3}=\frac{9}{21}[/tex]
So it is a proportion.
B
[tex]\frac{24}{56}/\frac{8}{8}=\frac{3}{7}[/tex]
So it is a proportion.
C
[tex]\frac{3}{7}*\frac{3}{4}=\frac{9}{28}[/tex]
So it is not a proportion.
D
[tex]\frac{3}{7}*\frac{4}{4}=\frac{12}{28}[/tex]
31)
Note: Figure not drawn to scale.
The circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters, what is the measure of x?
A) 40°
B) 60°
C) 70°
D) 80°
If circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given,
Circle with centre O,
Radius of circle=18 centimeters
length of arc AB = 6π centimeters
We need to find the measure θ of x
We have a formula to find the length of arc.
Length of an Arc = θ × (π/180) × r
Apply the given values in formula
6π=θ × (π/180) × 18
π gets cancelled on both the sides
6=θ/10
θ=60°
Hence if circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°
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Using elimination, find the ordered pair.
6x + 15y = 15
-6x +7y = -37
Answer:
x = -1 and y = 7/5Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}6x+15y=15\\-6x+7y=-37\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad22x=-22\qquad\text{divide both sides by 22}\\.\qquad\qquad x=-1\\\\\text{Put the value of x to the first equation:}\\6(-1)+15y=15\\-6+15y=15\qquad\text{add 6 to both sides}\\15y=21\qquad\text{divide both sides by 15}\\y=\dfrac{21}{15}\to y=\dfrac{7}{5}[/tex]
A rectangular prism with a volume of 2 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4 unit cubes does it take to fill the prism?
Answer:
128
Step-by-step explanation:
Method A.
The volume of the prism is 2 cubic units.
Each cube has side length of 1/4 unit.
The volume of each cube is (1/4)^3 cubic unit.
The volume of each cube is 1/64 cubic unit.
To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.
(2 cubic units)/(1/64 cubic units) =
= 2/(1/64)
= 2 * 64
= 128
Method B.
Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128
He right answer is 128
What is the first step when solving present or loan amortizations using a formula?
Answer:
determine the periods in the problem, which is the number of periods per year
Step-by-step explanation:
Answer:
determine the periods, which is the number of periods per year
Step-by-step explanation:
n/a
Divide 15x15 by 3x3.
Answer:
25
Step-by-step explanation:
15 * 15 = 225
3 * 3 = 9
225 / 9 = 25
Answer:
the answer is 25
Step-by-step explanation:
So you multiple 15x15 which equals 225 then you multiply 3x3 which is 9
the you take 225 and divide it by 9 wich would then be 25................hope i helped
3w - 4z = 8 what is w
Final answer:
To find w from the equation 3w - 4z = 8, add 4z to both sides, and then divide by 3 to isolate w, giving w = (4z + 8) / 3.
Explanation:
The equation 3w - 4z = 8 is a linear equation in two variables (w and z). To find w in terms of z, you need to isolate w on one side of the equation. Here is the process step by step:
Add 4z to both sides of the equation: 3w - 4z + 4z = 8 + 4z.
Simplify the equation: 3w = 4z + 8.
Divide every term by 3 to solve for w: w = (4z + 8) / 3.
So, w is equal to (4z + 8) / 3 when isolated from the given equation.
The equation X squared plus Y squared minus 2X plus 7Y +1 equals zero can be written as which of the following equations
For this case we must write in algebraic symbology the expression described above:
We have an equation, then:
x squared plus y squared: [tex]x ^ 2 + y ^ 2[/tex]minus 2x plus 7y plus 1: [tex]-2x + 7y + 1[/tex]equals zero: [tex]= 0[/tex]We construct the equation:
[tex]x ^ 2 + y ^ 2-2x + 7y + 1 = 0[/tex]
Answer:
[tex]x ^ 2 + y ^ 2-2x + 7y + 1 = 0[/tex]
How many vertices does a square pyramid have
Answer:
5 vertices
Step-by-step explanation:
4 on the bottom and 1 on the top
Answer:
5
Step-by-step explanation:
What values of b satisfy 3(2b + 3)^2 = 36?
Answer:
3(2b+3)^2=36
(2b+3)^2=12
2b+3=+2 radical3
2b+3= 2 radical 3
b=- radical 3 -3 over 2
b= radical 3- 3 over 2
b=- radical 3 - 3 over 2
Answer:
The answer is A
Step-by-step explanation:
Which logarithmic graph can be used approximate the value of Y in the equation 2^y=5
Absolutely down graph is true!!
because, certainly 2<y<3
and we know 2^y=5 ==> log5 with base 2 =y
so it concludes we must have a node between 2<y<3 in x=5
HELP PLEASE HELP IF YOU CAN :)
Answer:
A
Step-by-step explanation:
If you plug them in you get 2≥-1
Which category do both shapes belong to?
A.square
B.parallelogram
C.rectangle
D.rhombus
B. Parallelogram
Explanation: both have parallel sides
The two of the given figures are parallelogram. The correct option is B.
What is parallelogram?In parallelogram the opposite sides are equals and it is not formed 90 degree angle between two sides.
In the two of the given figures, it can be observed that the two figures have opposite sides parallel and equal. Therefore, the two of the given figures are a parallelogram.
Hence, the two of the given figures are parallelogram.
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Plz help me with this
Answer options: No or yes
No and the graph has a greater minimum.
Answer: YES, Graph
Step-by-step explanation:
Graph: minima (lowest point) is (4, -4)
Equation f(x) = x² - 8x + 7
[tex]x=\dfrac{-b}{2a}=\dfrac{-(-8)}{2(1)}=\dfrac{8}{2}=4\\\\y=(4)^2-8(4)+7\\.\ =16-32+7\\.\ =-9\\[/tex]
minimima is (4, -9)
The x-values are the same
The y-value of the Graph is greater (higher)
can someone please help me with this!!! pleasee
Answer:
[tex]\large\boxed{Q6.\ \sin X\approx0.778}\\\boxed{Q7.\ x\approx5.9}[/tex]
Step-by-step explanation:
Q6.
[tex]\sin\theta=\dfrac{opposite}{hypotenuse}[/tex]
We have
[tex]opposite=14\\\\hypotenuse=18[/tex]
Substitute:
[tex]\sin X=\dfrac{14}{18}=\dfrac{14:2}{18:2}=\dfrac{7}{9}=0.777...\approx0.778[/tex]
Q7.
Use sine.
We have
[tex]opposite=x\\\\hypotenuse=8\\\\\alpha=48^o\\\\\sin48^o\approx0.7431[/tex]
Substitute:
[tex]\dfrac{x}{8}=0.7431[/tex] multiply both sides by 8
[tex]x=5.9448\to x\approx5.9[/tex]
Tina is attempting to factor the expression 10x^2-13-3. In her first step, she rewrites the expression as 10x^2-10x-3x-3. Which of the following statements in true about Tina's work?
ANSWER
B. The two middle coefficients add to the correct number but do not multiply to the correct number.
EXPLANATION
The given quadratic trinomial that Tina tries to factor is
[tex]10 {x}^{2} - 13x - 3[/tex]
Comparing to
[tex]a{x}^{2} + bx + c[/tex]
we have a=10, b=-13 and c=-3
ac=-3×10=-30
We split the middle term so that their sum is -13.
Tina use
-10,-3
to get
-10x-3x
The sum is -13x alright but the product is not -30.
B is correct.
evaluate c÷d÷[-1/6] if c=103
Answer:
-618/d
Step-by-step explanation:
103 divided by d is 103/d and that divided by -1/6 is -618/d
Jerry drove 10 miles in half the time it took Marcy to drive 10 miles. If jerry average speed was r miles per hour what was Marcy average speed in miles per hour
Answer:
0.5r
Step-by-step explanation:
If Jerry took half the time Macy did then that means Macy took twice as long as Jerry. If Jerry’s speed was r then Macy’s speed is 0.5r or half the speed of Jerry. This will mean Macy goes half as slow and takes twice as long to get there.
The average speed of Marcy in miles per hour is 0.5r.
If Jerry took half the time Marcy did then that means Marcy took twice as long as Jerry. If Jerry’s speed was r then Macy’s speed is 0.5r or half the speed of Jerry. This will mean Marcy goes half as slow and takes twice as long to get there.
Hence, The average speed of Marcy in miles per hour is 0.5r.
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A line passes through the point (-7,5) And has a slope of 1/2 which is another point that the line passes through
(9,13) would be another point that the line passes through.
Answer: 9/13 C
Step-by-step explanation:
(5,6), (9,1) slope intercept form
Answer:
y = (-5/4)x + 12.25
Step-by-step explanation:
Slope intercept form:
y = mx + b
Slope form:
m = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (9 , 1)
(x₂ , y₂) = (5 , 6)
Plug in the corresponding numbers to the corresponding variables.
m = (6 - 1)/(5 - 9)
Simplify.
m = (5)/(-4)
Your slope is -5/4
Plug in -5/4 for m in the slope-intercept form equation, and use a point to solve for b. For example, we will use (9, 1):
y = mx + b
y = (-5/4)x + b
(1) = (-5/4)(9) + b
Simplify.
1 = (-11.25) + b
Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Add 11.25 to both sides.
1 + (11.25) = -11.25 (+11.25) + b
1 + 11.25 = b
b = 12.25
your y-intercept is 12.25
Plug in the corresponding numbers to the corresponding variables.
y = mx + b
m = -5/4
b = 12.25
y = (-5/4)x + 12.25 is your answer.
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On Saturday,April 5th, Sena the baby giraffe was born at the Fresno Chaffee Zoo. At birth, she weighed 125 pounds. If she gained 96 ounces one week after her birth, how many pounds would she weigh all together at the end of her first week?
131 because u divide 96 and 16 and get 6 then add that to 125
An Isosceles triangle has single measures 55,55,and 70. The side across from the 70 angle is 10 inches long. How long are the other sides?
Answer:
8.717 both the sides
Step-by-step explanation:
Given:
Let ABC be the given triangle with
angle A= 55
angle B=55
angle C= 70
side across angle C, c= 10 inches
side across angle B, b =?
aide across angle A,a=?
Now using the law of sin to find a and b:
a/sinA=c/sinC
a= (c/sinC)(sinA)
Putting the values:
a= (10/sin70)(sin55)
a= 8.717
As the given triangle is isosceles so side a=b
hence a=b= 8.717 inches !
What is the cos of 2
Answer:
-0.41614683654
Step-by-step explanation:
Answer: The answer is -0.41614683654. hope I helped. :)
Carlos found that the length of the diagonal of his laptop monitor is squared root of 290. If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal? 12 17 97 245
Answer:
[tex]17\ in[/tex]
Step-by-step explanation:
Let
D -----> the diagonal of the laptop monitor
we have
[tex]D=\sqrt{290}\ in[/tex]
Using a calculator
[tex]D=\sqrt{290}=17.03\ in[/tex]
Round to the nearest whole number
[tex]17.03\ in=17\ in[/tex]
Answer:
17
Step-by-step explanation:
i jus did this on edg