Answer:
let the original price be X
now new price = original price + increment
increment = 5 % of X = X/20
new price = 194.25
now, 194.25 = X + X / 20 = 21X / 20
X = 194.25 * 20 / 21
X = 185
original price = 185
The value of a car decreases as shown in the table below.
A 2-column table with 6 rows. The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5. The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.
Which statements are true? Check all that apply.
The statements which are true from the given table are:
The function that best represents the data is f(x) = 24,512(0.755)x.
The function decreases indefinitely.
It is reasonable to interpolate the value of the car at 4.5 years.
What is Depreciation?Depreciation refers to the accounting method where the value of a tangible asset reduces over a period of time.
The value of the car is shown with the purchase with entries that shows its value over time,
The function that best represents the data is f(x) = 24,512(0.755)x and that this function decreases indefinitely.
The statements which are true from the given table are:
The function that best represents the data is f(x) = 24,512(0.755)x.
The function decreases indefinitely.
It is reasonable to interpolate the value of the car at 4.5 years.
The complete question is
"The value of a car decreases as shown in the table below.
A 2-column table with 6 rows.
The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5.
The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.
Which statements are true? Check all that apply.
The function that best represents the data is f(x) = 24,512(0.755)x.
The function that best represents the data is f(x) = 554x2 – 5,439x + 24,600.
The function decreases indefinitely.
It is reasonable to interpolate to the value of the car at 4.5 years.
It is reasonable to extrapolate to 40 years"
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4sin2xcosx+sin3x=sin<3,14+x>
The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}
How to solve the equation?The equation is given as:
4sin2xcosx+sin3x=sin<3,14+x>
Rewrite properly as:
4sin(2x)cos(x)+sin(3x)=sin(3.14+x)
Next, we split the equation as follows:
y = 4sin(2x)cos(x)+sin(3x)
y = sin(3.14+x)
Next, we plot the graph of both equations (see attachment)
From the attached graph, we have:
x = nπ, where n = ±{0, 0.5, 1, 1.5....}
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Given the function f(x) = −5x2 − x + 20, find f(3).
Answer:
-28
Step-by-step explanation:
put 3 where is x
f(x) = −5(3)^2 − (3) + 20
exponents flrst
(−5*9) − (3) + 20
-45 -3 +20
-48 + 20
-28
Which pair of functions are inverses of each other?
f(x) = 10x -5 and g(x) = (x+5)/10 are inverses of each other , Option D is the correct answer.
What is a Function ?A function is a mathematical statement which relates two variables , a dependent and an independent variable.
The inverse of a function is found by replacing every y by x and vice versa , and then solve for y
The equation
f(x) = 4/x - 3
or
y= 4/x -3
Replacing y by x
x = 4/y -3
x +3 = 4/y
y = 4/(x+3)
Which do not correlate with the given inverse
f(x) = 10x -5
y = 10x -5
for finding inverse
10y -5 = x
10y = x+5
y = (x+5)/10
g(x) = (x+5)/10
Therefore , Option D is the correct answer.
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Make m the subject of the equation
(a) 5(m + y) = 4(m - 3y)
Answer:
m=(-5y-3y)
Step-by-step explanation:
5m+5y=4m-3y
5m-4m=-5y-3y
m(5-4)=-5y-3y
m=(-5y-3y)/1
Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms.
Answer:
y = -3x + 1
Step-by-step explanation:
The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.
You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.
DOWN3 and OVER1 is the slope -3/1, which is equal to -3.
Fill in -3 in place of the m in the equation.
y = -3x + 1
Done!
Answer:
y = -3x + 1
Step-by-step explanation:
The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)
The slope can be found by taking any two points on the line, (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)
If you look at the line 2 points on the line are P(2,-5) and (0,1)
Slope = (-5-1)/(2-0) = -3
The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1
Therefore equation is
y = -3x + 1
You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value
For example, in the graph we see that at x = 1, y = -2
Indeed -3(1) + 1 = -3 + 1 = -2 also
what equation describes a linear function
Answer: y = f(x) = a + bx y = f(x) = a + bx y = f(x) =
explanation: The following is the formula for a linear function. y = f(x) = a + bx y = f(x) = a + bx y = f(x) = One independent variable and one dependent variable make up a linear function.
Answer:
I don't knowwwwwwwwwwwwwwww
What subjects together do more than half of the class like?
Math 9 people
Science 3 people
Art 5 people
Writing 3 people
History 1 person
Math and Writing
Science and History
Art and Science
History and Math
Answer:
Math and Writing
Step-by-step explanation:
Well if we add up all the people we get (9 + 3 + 5 + 3 + 1) = 21. Half of that is 10.5 so the sum of the two subjects must be at least 11. The amount of people that like Math and Writing is 11 people so the two subjects that more than half the class like are Math and Writing.
Answer:
Math and Writing
Step-by-step explanation:
Number of students who like each subject:
Math = 9Science = 3Art = 5Writing = 3History = 1Total number of students = 9 + 3 + 5 + 3 + 1 = 21
Half of 21 = 21 ÷ 2 = 10.5
Therefore, more than half the class would be > 10.5 students
Total number of students who like:
Math and Writing = 9 + 3 = 12Science and History = 3 + 1 = 4Art and Science = 5 + 3 = 8History and Math = 1 + 9 = 10Therefore, the only combination of subjects that more than 10.5 students like is Math and Writing as 12 > 10.5
I think of a number and divide it by 3. The result is 2 less than the number I first thought of. Find the number I first thought of.
Answer:
Let the number be x
so, x/4 = x-3
x = 4(x-3)
x= 4x-12
x-4x = -12
-3x = -12
x= 12/3
x = 4
Step-by-step explanation:
Hope this helps! (:
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The graph represents a function.
2
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (2, -1) O (-5,2) O (2,-5) (-2,5)
(-5, 2) is the only point which we plot in given graph then it still represent a function.
What is Function?A function is a special type of relation in which each and every element of set A have a unique image in its codomain set B.
Here, Given points on graph
{(-4, 2), (-2, -3), (2, 3), (3, -1)}
2 and -2 are already available in given ordered pair.
so only (-5, 2) is the only option which satisfies the definition of function.
Thus, (-5, 2) is the only point which we plot in given graph then it still represent a function.
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please help me guys its math
Pls help ill give brainiest
I am lazy to type so here look at the picture and there is your answer
The sum of two consecutive even numbers is 38. What is the smaller number?
Even numbers = 2x +2
Consecutive even numbers = 2x+4
then
(2x+2) + (2x+4)= 38
2x + 2 + 2x + 4 = 38
2x + 2x + 2 + 4 = 38
4x + 6 = 38
4x = 38 - 6
x = 32 :4
x = 8
2x+ 2 = 2(8)+2 = 16 + 2 = 18
2x+4 = 2(8) +4 = 16 + 4 = 20
The smallest number is 18
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Answer:
18 is the smaller number
Step-by-step explanation:
Let us take X for the first even number (it will also be the smallest)
x, x+1, x+2, so on..
the consecutive even number of x+2 is the next even number after x.
so you now get this equation...
x+(x+2) = 38
2x + 2 = 38
2x = 36
x=18
Which table represents a linear function?
2
3
4
5
(J1
10
15
20
25
Answer:
I think it’s C
Step-by-step explanation:
I think
please help me
I'll mark you brainlist
Answer:
There are 16 notes of 20 paise's and 12 notes of 5 paise's.
Explanation:
The amount of notes for of 20 paise and 5 paise coins are not given.
So let there be x 20 paise's coins and y 5 paise's coins.
Equation buildup:
20x + 5y = 380 ___eq 1
20y + 5x = 380 - 60
20y + 5x= 320 ___ eq 2
Make x the subject for both:
1st
[tex]\rightarrow \sf 20x + 5y = 380[/tex]
[tex]\rightarrow \sf 20x = 380-5y[/tex]
[tex]\rightarrow \sf x = 19-0.25y[/tex]
2nd
[tex]\sf \rightarrow 20y + 5x = 320[/tex]
[tex]\sf \rightarrow 5x = 320-20y[/tex]
[tex]\sf \rightarrow x= 64-4y[/tex]
Solve them simultaneously:
[tex]\sf \rightarrow 64-4y =19 - 0.25y[/tex]
[tex]\sf \rightarrow -4y+0.25y =19 -64[/tex]
[tex]\sf \rightarrow -3.75y =-45[/tex]
[tex]\sf \rightarrow y =12[/tex]
Find x:
[tex]\sf \rightarrow x = 64-4y[/tex]
[tex]\sf \rightarrow x = 64-4(12)[/tex]
[tex]\sf \rightarrow x = 16[/tex]
Raphael graphed the system of equations shown.
y = – 3
y = x – 0.8
A coordinate grid with 2 lines. The first line passes through the points (0, negative 0.1) and (0.8, 0). The second line is horizontal passes through the point (0, negative 3). The lines intersect at a point with a coordinate of slightly to the left of negative 2 and negative 3.
What is the best approximation for the solution to this system of equations?
(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)
–3x + StartFraction one-half EndFractiony = –3
b =
2
4
6
8
Answer:
C. (-2.2, -3)
i need help asapppppp
Answer:
a
Step-by-step explanation:
2^3 = 8; 4^3 = 64; 8/64 = 1/8
(g^5)^3 = g^15
(h^2)^3 = h^6
g^15/8h^6
Two boats left a base camp at bearing of S60°E and S50°W at speeds of 50km/h and 70km/h respectively. Find the distance between the both boats after two hours.
Answer:
197.93 kmStep-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
AB = 50*2 = 100 kmAC = 70*2 = 140 kmThe angle between AB and AC is:
60 + 50 = 110 degrees (opposite directions from south)We are looking for the distance BC, which can be found by using the law of cosines:
BC² = AB² + AC² - 2AB*AC*cos ∠BACBC² = 100² + 140² - 2*100*140*cos 110°BC² = 39176.56 (rounded)BC = √39176.56 = 197.93 km (rounded)The distance between the boats is 197.93 km.
PLEASE PLEASE HELP WILL MARK BRAINLIEST!!
Which choice is equivalent to the product below when x > 0?
A. x/9
B. 1/3
C. x/3
D. 1/9
The equivalent expression to given expression is 1/3.
What is Equivalent Expression?Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression
[tex]\sqrt{2/x^2} X \sqrt{x^2/18}[/tex]
= [tex]\sqrt{2 X x^2/18x^2}[/tex]
= [tex]\sqrt{1/9}[/tex]
= 1/3
Thus, the equivalent expression to given expression is 1/3.
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can anybody help me?
f(-2) = 2(-2)² - 8(-2) + 6 = 30
f(-1) = 2(-1)² - 8(-1) + 6 = 16
f(0) = 2(0)² - 8(0) + 6 = 6
f(1) = 2(1)² - 8(1) + 6 = 0
f(2) = 2(2)² - 8(2) + 6 = -2
The vertex of this angle is:
R
T
S
The vertex of this angle is point S.
help please!!!!!!!!!
identify the coefficient of -24x7y3
Answer: -24
Step-by-step explanation:
See attached image.
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Select the correct answer.
Using synthetic division, find (2x + 4x³ + 2x² + 8x + 8) + (x + 2).
O A. 2x3 + 2x + 4
OB.
2x4 + 2x² + 4x
OC. 2x3 + 2x + 4 +
I
OD.
2x3 + 2x² + 4
1
+ 2
The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) = 2x³ + 2x + 4.
Division of the polynomialThe division of the polynomial is determined as follows;
(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)
2x³ + 2x + 4
-------------------------
x + 2 √(2x⁴ + 4x³ + 2x² + 8x + 8)
- (2x⁴ + 4x³)
-------------------------------------
2x² + 8x + 8
- (2x² + 4x)
------------------------
4x + 8
- (4x + 8)
-------------------
0
Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) = 2x³ + 2x + 4.
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The function h(x) is given below.
h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
Which of the following gives h–1(x)?
{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
{(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
{(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)}
The inverse function will be h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}. Then the correct option is B.
What is inverse of a function?Suppose that the given function is
f:X → Y
Then the inverse of the considered function will be
f⁻¹: Y → X
The function h(x) is given below.
h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
Then the coordinate of the inverse function gets swapped.
h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
Then the correct option is B.
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A rotation R takes A(1,-3) to A'(3,5) and B(0,0) to B'(4,-6). find the centre of rotation?
The center of rotation will be (0,4). The points are plotted and the center is found with the help of a graph.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
Given points;
A(1,-3)
A'(3,5)
B(0,0)
B'(4,-6)
C is the center point of rotation.
The given points are plotted on the graph and obtained as the center of rotation will be (0,4).
Hence the center of rotation will be (0,4).
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A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 millimeters and an upper specification limit of 23.1 millimeters. The standard deviation is 0.19 millimeters and the mean is 22.9 millimeters. What is the process capability index for the process? Note: Round your answer to 4 decimal places.
The process capability index for the process is 0.1754.
How to calculate the index?The first sided specification limit will be:
= (Upper specification limit - mean)/(3 × standard deviation)
= (23.1 - 22.9)/(3 × 0.19)
= 0.2/0.57
= 0.3508
The second sided specification limit will be:
= (22.9 - 22.8)/(3 × 0.19)
= 0.1/0.57
= 0.1754
The process capability index for the process is 0.1754 wine it's the lower value.
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sally sweeps 20 floors in 4 hours , at the same rate , how many floors can sally sweep in 6 hours ?
Answer:
35 Floors in 6 Hours
Step-by-step explanation:
20 / 4 = X Floors Per Hour
floors per hour = 5
6*5 = 35 Floors
Triangle 304 degrees and 115 degrees work out x
a straight line make an angle of 180° ,
so 115+y=180
y=65°
for the top part of the triangle it makes an angle of 360° , so 304+y=360
y=56
sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .
so
65+56+y= 180
121+y=180
y=59( the angle next to X)
X+59=180( together they make an angle of 180)
x=121°
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