The value of the car is January 2003 is $199,148.54.
What is the value of the car?Depreciation is the rate of decline in the value of an asset with the passage of time.
The exponential equation that can be used to determine the value of the car is:
Value of the car = purchase value(1 - rate of decline)^time
400,000 x (1 - 0.16)^(2003 - 1999)
400,000 x (0.84^4) = $199,148.54
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The length of a rectangular field is 4 meters less than 5 times the breadth of the hall. What is the length, if the breadth is b meters?
John bought 8 watches for $56 and his friend victor bought 7 watches for $63. whose watch is expensive ?
Mariana runs a farm stand that sells bananas and grapes. Each pound of bananas sells for $1 and each pound of grapes sells for $2.25. Mariana made $72 from selling a total of 52 pounds of bananas and grapes. Graphically solve a system of equations in order to determine the number of pounds of bananas sold, x, and the number of pounds of grapes sold, y.
Answer:
jackson sold 27 pounds of bananas and 12 pounds of grapes :D
Step-by-step explanation:
Taking into account the definition of a system of linear equations, the number of pounds of bananas and grapes sold are 36 and 16 respectively.
System of linear equationsA set of two or more first-degree equations with two or more connected unknowns is referred to as a system of linear equations.
Finding the value of each unknown in order to satisfy all of the system's equations constitutes the process of solving an system of equations. To put it another way, it is necessary to find the values of the unknowns, as they must be replaced with values that, when used to solve the equations, is the process of solving a system of equations
This caseIn this case, a system of linear equations must be proposed taking into account that:
"x" is the number of pounds of bananas sold."y" is the number of pounds of grapes sold.You know:
Each pound of bananas sells for $1 and each pound of grapes sells for $2.25. Mariana made $72 from selling a total of 52 pounds of bananas and grapes.The system of equations to be solved is
x +y= 52
x + 2.25y= 72
There are several methods to solve a system of equations, it is decided to solve it using the graphical method. The system's equations are graphically represented by graphs in the graphical method. The solution of the system is the point of intersection between the graphs, since the coordinates of said point satisfy both equations.
Graphically, it can be seen that the intersection point is (36; 16). That is, the value of x is 36 and the value of y is 16.
Finally, the number of pounds of bananas sold are 36 and the number of pounds of grapes sold are 16.
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its math can you help out
Answer:
81
Step-by-step explanation:
27 people will tell 3 people each. 3x27=81
Answer:
81
Step-by-step explanation:
Let g be the piecewise defined function shown.
g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5
Evaluate g at different values in its domain.
g(−4) =
g(−2) =
g(0) =
g(3) =
g(4) =
Answer:
g(4)= -2
g(-2)= 2
g(0)= 2
g(3)= -1
g(-4)= 0
Step-by-step explanation: See attachment, and don’t forget to check just in case ;)
Answer:
g(−4) = 0
g(−2) = 2
g(0) = 2
g(3) = -1
g(4) = -2
Step-by-step explanation:
Please Thank!
Figure B is a scaled copy of figure A.
What is the scale factor from figure A to figure B
Answer:
1/3
Step-by-step explanation:
We multiply 33(Figure A side) by 1 /3 to get 11(Figure B side).
If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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Find the equation of the line through point (4,−7) and parallel to =−2/3+3/2 Use a forward slash (i.e. "/") for fractions (e.g. 1/2
Answer:
y=-2/3x-13/3
Step-by-step explanation:
parralel line have the same gradient
y=mx+c is the general straight line equation
m represents the gradient
if the equation is y=-2/3x+3/2
m=-2/3
the coordinates (4,-7)
x=4
y=-7
substitute into equation
-7=-2/3×4+c
-7=-8/3+c
c=-7+8/3
c=-13/3
so the equation is :
y=-2/3x-13/3
Choose all of the following angles that cannot
be an interior angle in a regular polygon.
24° 72°
72°
135°
135° 164° 179⁰
In a regular polygon, all interior angles have equal measures because the polygon has congruent sides and angles. The sum of all interior angles in a polygon can be found using the formula:
(n-2) * 180°,
where n represents the number of sides of the polygon.
Based on this, we can determine which angles cannot be interior angles in a regular polygon.
24°: This angle can be an interior angle in a regular polygon because it is smaller than the interior angles of any polygon with more than 6 sides.
72°: This angle can be an interior angle in a regular pentagon (5 sides) or any polygon with more sides, as it satisfies the requirement for interior angles.
135°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 8 sides.
164°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 9 sides.
179°: This angle cannot be an interior angle in any regular polygon because it is larger than the maximum measure of interior angles in any polygon.
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If [tex]\rm \: x = log_{a}(bc)[/tex], [tex]\rm \: y = log_{b}(ca)[/tex], [tex]\rm \: z = log_{c}(ab)[/tex] , the xyz is equal to :
(a) x + y + z
(b) x + y + z + 1
(c) x + y + z + 2
(d) x + y + z + 3
Use the change-of-basis identity,
[tex]\log_x(y) = \dfrac{\ln(y)}{\ln(x)}[/tex]
to write
[tex]xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}[/tex]
Use the product-to-sum identity,
[tex]\log_x(yz) = \log_x(y) + \log_x(z)[/tex]
to write
[tex]xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}[/tex]
Redistribute the factors on the left side as
[tex]xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}[/tex]
and simplify to
[tex]xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)[/tex]
Now expand the right side:
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}[/tex]
Simplify and rewrite using the logarithm properties mentioned earlier.
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1[/tex]
[tex]xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}[/tex]
[tex]xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}[/tex]
[tex]xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)[/tex]
[tex]\implies \boxed{xyz = x + y + z + 2}[/tex]
(C)
What is the measure of x?
16
x=[?]
Give your answer in simplest form.
Answer: [tex]8\sqrt{5}[/tex]
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]
Thus, by the Pythagorean thoerem,
[tex]8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]
A flag pole is casting a 20ft. shadow. The flag pole measures 16 ft. Find the Angle of elevation of the sun.
Let's see
tanØ=16/20tanØ=4/5tanØ=0.8Ø=53°Answer:
53 the correct answer off your question.
x + 4 is prime x2 – 9 can be factored using the formula.
Answer:
difference-of-squares
Step-by-step explanation:
Ella has a collection of vintage action figures that is worth $430. If the collection
appreciates at a rate of 4% per year, which equation represents the value of the
collection after 7 years?
The equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
What is an Equation ?An equation is a mathematical statement , where the algebraic expression is equated to another algebraic expression.
It is given that
Ella has a collection of vintage action figures that is worth $430.
collection
appreciates at a rate of 4% per year
equation representing the value of the collection after 7 years is
value of collection = 430 + (0.04 * 430 )* t
value of collection = 430 + (0.04 * 430 )* 7
= $550.4
Therefore the equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
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a and b are positive integers and 7a+5b=49. Find the values of a and b.
a and b are positive integers and 23a+17b=320. Find the values of a and b.
please hel you can get 30 points
Solving a system of equations, it is found that the value of a is of -191.75 and the value of b is of 278.25.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
7a + 5b = 49.23a + 17b = 320.Multiplying the first equations by 17 and the second by -5, we have that the system is:
119a + 85b = 833.-115a - 85b = -1600.Then, adding them:
4a = -767
a = -767/4
a = -191.75
Then:
[tex]b = \frac{49 - 7a}{5} = \frac{49 - 7(-191.75)}{5} = 278.25[/tex]
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Can somebody help me, i would really appreciate it!!
It will take 5 seconds for the waste to hit the ground.
How many seconds will it take for the waste to hit the ground?We know that the bird releases the waste from a height of 400ft, so the height equation is:
[tex]h(t) = -16t^2 + 400[/tex]
The waste will hit the ground when its height is equal to zero, so we just need to solve the quadratic equation:
[tex]h(t) = 0 = -16t^2 + 400\\\\16t^2 = 400\\\\t^2 = 400/16 = 25\\\\[/tex]
Now we can apply the square root in both sides:
[tex]t = \sqrt{25} = 5[/tex]
It will take 5 seconds for the waste to hit the ground.
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Hi, so I know the answer to this problem (now that I got it wrong) but I'm not quite sure why I was wrong, help?
2x² + 2x + ? = x
⇒ ? = x - 2x² - 2x
⇒ ? = -2x² - x
Your answer is incorrect because 2x² - x² would mean x² is part of the answer, which is clearly incorrect.
Determine f(4) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than or equal to 4, and part 3 which is 5 times x plus 4, for x greater than 4..
23
24
41
64
Answer:
23
Step-by-step explanation:
seen it before
The distance between points (x₁, y₁) and (4, 8) is the square root of
(x₁ - 8)² + (₁-4)².
True or False?
The statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)². Hence, the given statement is false, it is √[(x₁-4)² + (y₁-8)²].
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
WE have been given two points.
So,
The distance between points (x₁, y₁) and (4, 8)
D = √[(x-p)² + (y-q)²]
D = √[(x₁-4)² + (y₁-8)²]
But the statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)².
Hence, the given statement is false, it is √[(x₁-4)² + (y₁-8)²].
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What is 0.000345 expressed in scientific notation?
3.45 × 102
3.45 × 104
3.45 × 10–2
3.45 × 10–4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
Expression in scientific notation :
[tex]\qquad \tt \rightarrow \:3.45 × {10}^{-4} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 0.000345[/tex]
[tex]\qquad \tt \rightarrow \: 0.000345 \times \cfrac{10000}{10000} [/tex]
[tex]\qquad \tt \rightarrow \: (0.000345 \times 10000) \times \cfrac{1}{10000} [/tex]
[tex]\qquad \tt \rightarrow \: 3.45 \times \cfrac{1}{10 {}^{4} } [/tex]
[tex]\qquad \tt \rightarrow \: 3.45 \times{10 {}^{ - 4} } [/tex]
[tex] \textsf{Correct option - D} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
3.45 x 10-4
Step-by-step explanation:
Show work, can someone help me out having trouble with this problem
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f = \cfrac{9}{a}+7[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \:a = \cfrac{9}{f - 7} [/tex]
[tex]\qquad \tt \rightarrow \:a(f - 7) = 9[/tex]
[tex]\qquad \tt \rightarrow \:(f - 7) = \cfrac{9}{a}[/tex]
[tex]\qquad \tt \rightarrow \:f = \cfrac{9}{a} + 7[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The sum of a number 8 and twice the number X is 28
ANSWERS ARE AT THE BOTTOM
To solve this question, we need to write the questions algebraically. Let's look at the problem first: The sum of a number 8, and twice the number x is equal to 28.
Algebraic form:
8 + 2x = 28
Lets solve this!
8 + 2x = 28 (Algebraic Form)
2x = 28 - 8 (Subtract 8 from both sides)
2x = 20 (Divide by 2)
x = 10 (Answer)
ANSWER:
x = 10
Just a question about the problem, dont need the answer if you dont want to solve it, but would 15 be negative? Thats all, Thanks!
[tex]f(x)=x^{2} +15x+3[/tex]
Answer:
[tex]x = -\frac{15}{2}[/tex]
Step-by-step explanation:
Hello!
The formula for the AOS is given to you, and you simply have to plug in the information given by the equation.
Equation of a Parabola (Standard): [tex]y = ax^2 + bx + c[/tex]
Comparing it to our equation:
a = 1b = 15c = 3Plug it in to the AOS formula:
[tex]x = \frac{-b}{2a}[/tex][tex]x = \frac{-15}{2(1)}[/tex][tex]x = -\frac{15}{2}[/tex]You only have to input 15 in to the correct box since the negative sign is already placed for you.
I need help with this math question (pic induced)
Answer:
A
Step-by-step explanation:
Set the equation equal to bx.
[tex](3x + 3)(ax - 2) - {x}^{2} + 6 = bx[/tex]
[tex]3a {x}^{2} - 6x + 3ax - 6 - {x}^{2} + 6 = bx[/tex]
Cancel out the constants
[tex]3 {ax}^{2} - 6x + 3ax - x {}^{2} = bx[/tex]
In order to cancel out the quadratics, we must solve for a.
[tex]3 {ax}^{2} - {x}^{2} = 0[/tex]
[tex]3 {ax}^{2} = {x}^{2} [/tex]
[tex]3a = 1[/tex]
[tex]a = \frac{1}{3} [/tex]
So plug in 1/3 for a.
[tex]3( \frac{1}{3} ) {x}^{2} - 6x + 3( \frac{1}{3} )x - {x}^{2} = bx[/tex]
[tex] - 6x + x = bx[/tex]
[tex] - 5x = bx[/tex]
[tex]b = - 5[/tex]
Pls help asap ily
one hour after junior space cadet had left his house, his sister gwen discovered that he had forgotten his head. if junior was driving at a speed of 50 mph, and gwen drove at a speed of 75 mph, how many hours did it take gwen to restore junior's head to his shoulders?
Answer:
2 hours
Step-by-step explanation:
you can write two linear equations and then set them equal to each other to see when they intersect. so for the first equation which will be representing the junior space cadets distance from his house. this can be written as
d = 50t + 50
where t represents time and d represents distance. there is 50 being added to the equation since he had already been traveling for an hour
the second equation which will represent his sister Gwen can be represented as
d = 75t
Now we set them equal to each other
50t + 50 = 75t
50 = 25t
2 = t
[tex]-2(bx - 5) = 16[/tex]
Answer:
bx=-3
Step-by-step explanation:
-2(bx-5)=16
Use distributive property.
-2bx+10=16
Now, subtract 10 from both sides.
-2bx=6
Divide -2 from both sides.
bx=-3
Hope this helps!
If not, I am sorry.
Which of the following is the graph of the piecewise function h of x is defined as negative x squared plus 2 for x is less than or equal to negative 2, or one half times x for negative 2 is less than x is less than 2, or x squared minus 2 for x greater than or equal to 2.?
The attached graph represents the piecewise function h(x)
Complete questionWhich of the following is the graph of the piecewise function
[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]
How to determine the graph of the function?The function is given as:
[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]
The above means that the piecewise function has 3 domains
2 of which are quadratic functionsThe last one is a linear functionNext, we plot the graph using a graphing tool
See attachment for the graph of the piecewise function h(x)
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what odd 3 digit number has digits that are all the same and that add up to 9?
Answer:
3
Step-by-step explanation:
3 is an odd number and obviously the only odd (same) three digit that add up to 9
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Given a=b+c2d solve for c
Step-by-step explanation:
rewrite the equation as follows
c2d = a - b
divide both sides by 2d
c = (a - b)/2d
In the diagram below, a sequence of rigid motions maps ABCD onto JKLM.
If m/ A = 76, m/ B = 110°, and m / L = 116, the m/ M ?
In the diagram, the value of the last angle will be 158°.
How to calculate the angle?It should be noted that the total angle is a quadrilateral is 360°.
In this case, the value of the last angle will be:
= 360° - (76° + 110° + 116°)
= 360° - 302°
= 158°
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