Answers
The following are the answers:
23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;
The total cost of lessons is; f(x) = y = 10·x + 12 and one lesson costs $22
24. The equation of population of Laredo, Texas is :
p = 92500t/17 + 123000
25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).
26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Given:
23. Lydia wants to purchase guitar lessons.
7 lessons = $82
11 lessons = $122
we are asked to determine the linear equation which finds the total cost C for d lessons.
The general equation for the total cost of lessons is;
Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;
The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson
Therefore,
slope = b-a/11-7 = b-a/4
Expressing the equation in slope and intercept form, we get:
(y-a) = b-a/4 . (x-7)
y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4
y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b
where a=$82 and b=$122 we ahve:
y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12
The total cost of a lesson is:
y = 10×1+12
= 22
24. Given:
t = the number of years after 1990.
So, for 1990, t = 0. So the coordinate is (0, 123000).
For 2007, t = 17. So the coordinate is (17, 215500).
using point slope formula:
m = 215500-123000/17-0
m = 92500/17
⇒ p = 92500t/17 + 213000
25. The equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
We know the slope is (y₂ - y₁)/(x₂ - x₁).
∴ Here the temperature is y and the height is x.
And the points are (6000, 76) and (12000, 49)
So, slope =(12000 - 6000)/(49 - 76).
Slope = (6000/-27).
Slope = -(2000/9).
Now we have to determine the y-intercept by putting any of the points in y = mx + b.
So, 76 = -(2000/9)×6000 + b.
76 = -(12000/9) + b.
76 = -(4000/3) + b.
b = 4000/3 + 76.
b = 4228/3.
∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).
26. The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.
On first day, they collect = $60
On second day, they collect = $88
Now,
We have to find the equation as;
⇒ R = mc + b
We need to find the value of m and b.
Since, The first point = (15, 60)
The second point = (22, 88)
Hence, Slope (m) = (88 - 60) / (22 - 15)
m = 28 / 7
m = 4
And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,
⇒ R = mc + b
⇒ 60 = 4 x 15 + b
⇒ b = 0
Thus, Substitute m = 4 and b = 0 in equation (i) we get;
⇒ R = mc + b
⇒ R = 4c + 0
⇒ R = 4c
Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Hence we get the required answers.
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Related Questions
the international average salary income database provides a comparison of average salaries for various professions. the data are gathered from publications and reports obtained directly from government agencies (such as the u.s. bureau of labor statistics) or from the international labour organization. suppose you are told that a computer programmer in canada who makes $2,063.30 has a z-score of 0.50 relative to other computer programmers in canada and that the standard deviation of the salary of computer programmers in canada is $458.60. the average salary, then, for computer programmers in canada is . suppose you are also told that a computer programmer in portugal who makes $1,387.40 has a z-score of 2.00 relative to other computer programmers in portugal and that the mean of the salary of computer programmers in portugal is $925. the standard deviation of the salary, then, for computer programmers in portugal is
Answers
The instance has a mean of 1834 and a standard deviation of 231.2, respectively.
Given data;
A comparison of typical earnings for different professions can be found in the international average salary income database. The information is acquired from publications and reports that were obtained directly from governmental organizations, like the US Bureau of Labor Statistics or the ILO. Consider being informed that the standard deviation of the income of computer programmers in Canada is $458.60 and that a computer programmer in Canada making $2,063.30 has a z-score of 0.50 in comparison to other programmers in Canada. Consequently, the typical pay for computer programmers in Canada is. Assume you are also informed that the mean wage for computer programmers in Portugal is $1,387.40 and that a computer programmer in Portugal who earns $1,387.40 has a z-core of 2.00 in comparison to other computer programmers in Portugal is $925.
Since, the salaries are relative and we know that the z-score is given by;
z = X - μ / σ
0.50 = 2063.30 - μ / 458.60
μ = 2063.30 - 229.3
μ = 1834
As, the salaries are relevant so;
2 = 1387.40 - 925 / σ
σ = 462.4/2
σ = 231.2
Hence, the mean and standard deviation of the case is 1834 and 231.2 respectively.
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A store is having a sale on televisions. All televisions are on sale for 15% off. A customer buys a television for $750.99. What was the original price for the television? WILL MARK BRAINLIEST
Answers
The original price for the television is $883.51
What is discount?A store will discount an item by a percent of the original price.
Given that, a store is having a sale on televisions, all televisions are on sale for 15% off, a customer buys a television for $750.99.
Let the original price be x
x*(100-15)% = 750.99
x = 750.99*100/85
x = 883.51
Hence, the original price for the television is $883.51
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solve x-6y=9 to find x coordinates
Answers
_ _ _ _ _ _ _ _ _ _ _ _ _
| | | _ _ _ | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | _ _ _ _ _ _ | | _ _ _| | | | _ _ _ _ _ _
| _ _ _ _ _ _ _ _| | _ _ _ _ _ _| | _ _ _ _ _ _ _ _|
The slope is 1/6x
You have to re-arranged the problem
x - 6y = 9 --> 6y = x - 9
6y = x - 9
__ ____ ----> y = 1/6x - 3/2
6 6
931.9572 Find the digits in the hundreds place, in the hundredths place, and in the ten thousandths place for the following number.
Answers
5 in the hundredths place
2 in the ten hundredths thousands
A wooden door costs AED 600 plus a 12% tax. What is the price of the door including the tax?
Answers
Answer:
672
Step-by-step explanation:
600+ .12(600)
600 + 72 = 672
A sweater priced at 34.99 is on sale for 25% off, find the cost with 7.5% sales tax.
Answers
Answer:
$24.27
Step-by-step explanation:
Original price: $
34.99
Discount percentage:
25
%
Results
Discount:
$8.75
Final Price:
$26.24
Details
Discount = Original Price x Discount %/100
Discount = 34.99 × 25/100
Discount = 34.99 x 0.25
You save = $8.75
Final Price = Original Price - Discount
Final Price = 34.99 - 8.7475
Final Price = $26.24
- 7.5% = $24.27
The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A sweater priced at 34.99 is on sale for 25% off. Then the cost after the discount is calculated as,
⇒ (1 - 0.25) x 34.99
⇒ 26.24
If the sales tax is 7.5%. Then the cost after the sales tax is given as,
⇒ (1 + 0.075) x 26.2425
⇒ 28.21
The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.
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1. Find x.
Q
S
16
U
C
2x
V
R
5x-9
16
I will mark brainly for this who show me how to solve it not just give me the answer
Answers
Step-by-step explanation:
because
ST = QR = 16
that means that also the distance from the center point is the same.
in other words :
UC = VC
therefore,
2x = 5x - 9
0 = 3x - 9
9 = 3x
x = 3
PLS HELP ,,,
which function increases faster?
function g
function f
they both increase at the same rate
Answers
The function, g(x), has a constant rate of change and will increase at a faster rate than the function f(x) for all the values of x.
Given:
g(x) = 5/2 x -3 ..... (1)
f(x) = - 3.5 at x = 0
So, putting the value of x=0 in equation (1) for comparison. We get,
g(x) at x = 0
=> g(x) = 5/2 x (0) - 3
=> g(x) = -3
In this value of x function g(x) is faster than function f(x) having a value equal to -3.5.
Similarly, put x = 1 in equation (1) for comparison. We get,
=> g(x) = 5/2 x (1) - 3
=> g(x) = (5-6)/2
=> g(x) = -1/2
In this value of x function g(x) is faster than function f(x) having a value equal to -1.
Similarly, put x = 2 in equation (1) for comparison. We get,
=> g(x) = 5/2 x (2) - 3
=> g(x) = (5-3)
=> g(x) = 2
In this value of x function g(x) is faster than function f(x) having a value equal to 1.5.
Similarly, put x = 3 in equation (1) for comparison. We get,
=> g(x) = 5/2 x (3) - 3
=> g(x) = (15/2 - 3)
=> g(x) = 7.5 - 3
=> g(x) = 4.5
In this value of x function g(x) is faster than function f(x) having a value equal to 4.
Therefore, for all values of x function g(x) is faster than function f(x).
function f(x).
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41.98 km = blank cm this is for a math assignment i need help me please
Answers
The conversion of 41.98km to centimeters is gotten as; 4198000 cm
How to carry out units conversion?We are dealing with units conversion here and in this concept it involves converting from unit to the other using a standard conversion ratio.
Now, we are given the value as 41.98 km. However, we want to convert this value from kilometers to centimeters. The conversion ratio is;
1 kilometer = 100000 centimeters
Thus, using the conversion ratio above, we can say that;
41.98 km = (41.98 * 100000)/1
= 4198000 cm
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what is the value of expression 8(-9)-6(-3)
Answers
hope this helps
Answer:
-54
Step-by-step explanation:
8(-9)=-72
6(-3)=-18
-72+(-18)=-54
-Hope this helped
What is the solution of the system? Solve using matrices. ( -3x + 2y = 10 -4x + 3y = 2 (-26 -34) (-34 -26) (26 34) O( no solution)
x + 2y = -1,, x-3y=-2
(-7 ,3)(3,-7) (7,-3)(no solution)
Inverse Matrices and Systems
Answers
Answer:
(a) (-26, -34)
Step-by-step explanation:
You want the solution to the system of equations ...
-3x +2y = 10-4x +3y = 2apparently using inverse matrices.
Matrix equationThe system can be represented by the matrix equation ...
AX = B
where A is the 2×2 matrix of coefficients, X is the 2×1 variable vector, and B is the 2×1 matrix of constants.
The solution to this system is found by multiplying on the left by the inverse of A:
A⁻¹·AX = A⁻¹·B
X = A⁻¹·B
The attachment shows the result of making this calculation:
[tex]\boxed{X=\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}-26\\-34\end{array}\right]}[/tex]
A rental car company charges $56. 37 per day to rent a car and $0. 09 for every mile driven. Hawa wants to rent a car, knowing that: she plans to drive 500 miles. She has at most $440 to spend. Which inequality can be used to determine xx, the maximum number of days hawa can afford to rent for while staying within her budget?.
Answers
Using the inequality concept, the expression which models the maximum
number of days in which she can rent the car is 56. 37x + 45 ≤ 440.
Maximum amount allowed to spend
= $440
Rental car company fixed charge per day to rent a car = $56.37
Hawa drives a car to 500 miles.
Rate per mile drive = $0.09
let x days be maximum number of days hawa afford rent with budget.
the inequality equation exists here is
(days × charge of rent per day) + (rate per mile x number of miles) ≤ 440
=> 56.37x + 0.09 × 500 ≤ 440
=> 56.37x + 45 ≤ 440
Therefore, the required inequality is 56.37x + 45 ≤ 440
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Find the angle between the following two vectors.
< 8, 3 > and < 4, −3 >
Answers
The angle between the two vectors < 8, 3 > and < 4, −3 > is 57.43°
How to determine the angle between the following two vectors?Given: vectors < 8, 3 > and < 4, −3 >
To find the angle between two vectors, we can use the dot product method:
First, you will compute the dot product and magnitudes of both vectors. Thus,
Let a = < 8, 3 > and b = < 4, −3 >
a · b = <8, 3> ·<4, -3> = 8(4) + (3)(-3) = 32-9 = 23
|a| = √(8² + 3²) = √(64+9) = √73
|b| = √(4² + (-3)²) = √(16 + 9) = √25 = 5
By using the angle between two vectors formula using dot product,
θ = cos⁻¹ [ (a · b) / (|a| |b|) ]
θ = cos⁻¹ (23 / √73 · 5)
θ = cos⁻¹ (23/42.72) = 57.43°
Therefore, the angle between the following two vectors is 57.43°
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On Mars, the temperature can get cold really quickly. Yesterday, the temperature
dropped 528 degrees in 8 hours straight. What integer represents the average temperature per hour change during the 8 hours
Answers
4224 hours integer represents the average temperature per hour change during the 8 hours.
What is the short definition of temperature?
Temperature is a unit of measurement that can be expressed on a variety of scales, including Fahrenheit and Celsius. Temperature shows the direction of the spontaneous flow of heat energy, i.e., from a hotter body (one with a higher temperature) to a colder body.the temperature dropped = 528 degrees
total time = 8 hours
the average temperature per hour change during the 8 hours = 528 * 8
= 4224 hours
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7 Résoudre les équations d'inconnue x suivantes:
a.-2x + 7 = -x +9
c.4x +15=2x+6
b. 8x+26=5x+14
d. 7x+31= 16x +17
Answers
Answer:
A)
[tex]\sf -2x+7=-x+9[/tex]
[tex]\sf -2x+7-7=-x+9-7[/tex]
[tex]\sf -2x=-x+2[/tex]
[tex]\sf -2x+x=-x+2+x[/tex]
[tex]\sf -x=2[/tex]
[tex]\sf \cfrac{-x}{-1}=\cfrac{2}{-1}[/tex]
[tex]\boxed{\sf x=-2}[/tex]
____________________
B)
[tex]\sf 4x +15=2x+6[/tex]
[tex]\sf 4x+15-15=2x+6-15[/tex]
[tex]\sf 4x=2x-9[/tex]
[tex]\sf 4x-2x=2x-9-2x[/tex]
[tex]\sf 2x=-9[/tex]
[tex]\sf \cfrac{2x}{2}=\cfrac{-9}{2}[/tex]
[tex]\boxed{\sf x=-\cfrac{9}{2}}[/tex]
____________________
C)
[tex]\sf 8x+26=5x+14[/tex]
[tex]\sf 8x+26-26=5x+14-26[/tex]
[tex]\sf 8x=5x-12[/tex]
[tex]\sf 8x-5x=5x-12-5x[/tex]
[tex]\sf 3x=-12[/tex]
[tex]\sf \cfrac{3x}{3}=\cfrac{-12}{3}[/tex]
[tex]\boxed{\sf x=-4}[/tex]
____________________
D)
[tex]\sf 7x+31=16x+17[/tex]
[tex]\sf 7x+31-31=16x+17-31[/tex]
[tex]\sf 7x=16x-14[/tex]
[tex]\sf 7x-16x=16x-14-16x[/tex]
[tex]\sf -9x=-14[/tex]
[tex]\sf \cfrac{-9x}{-9}=\cfrac{-14}{-9}[/tex]
[tex]\boxed{\sf x=\cfrac{14}{9}}[/tex]
A line connects the midpoint of BC (point E), with point D in the square ABCD shown below. Calculate the area of the acquired trapezoid shape of the square has a side of 4 m.
Answers
The area of the trapezoid formed is equal to 12 square meters.
The area of the trapezium is calculated by using the formula.
A =(a + b) × h / 2
In the given trapezium the length of the parallel sides are:
2 m and 4 meters.
The distance between the parallel sides is 4 m
Area of the trapezium = (2+4) × 4÷2 = 12 square meters
A trapezoid is a quadrilateral that has at least one pair of parallel sides.
A trapezoid is a convex quadrilateral by definition in Euclidean geometry. The parallel sides serve as the trapezoid's bases. The remaining two sides are referred to as the lateral sides or the legs if they are parallel; otherwise, the trapezoid appears to be a parallelogram, with two pairs of bases.
Therefore the area of the trapezium is 12 square meters .
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i need help fast please !
Answers
5) Move the decimal to the right three times to get a value that can be put into scientific notation. 1.5 x 10^3
The population of Monterrey, Mexico, i 4×106 people, and the population of Shanghai, China, i 2×107 people. How many time larger i the population of Shanghai compared to Monterrey? Repone 2 time larger 2 time larger 5 time larger 5 time larger 20 time larger 20 time larger 50 time larger 50 time larger
Answers
The population of Shanghai is 5 times larger than population of Monterrey.
What is population?
Typically, the term "population" refers to the total number of people living in a particular area, be it a city or town, region, country, continent, or the entire world.
Main body:
The population of Monterrey, Mexico is people = [tex]4*10^6[/tex]
The population of Shanghai, China is people = [tex]2*10^7[/tex]
To find how many times the population of Shanghai is lager than Monterrey.
In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and Monterrey.
Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.
Thus, we have:
[tex]\frac{2*10^7}{4*10^6}[/tex]
Simplifying by using properties of exponents.
⇒ [tex]\frac{2*10^7}{4*10^6}[/tex] , USING [tex]a^{x} -a^{y} =a^{(x-y)}[/tex]
⇒ [tex]\frac{2*10}{4}[/tex]
⇒ 20/4
⇒ 5
Therefore, we can say that the population of Shanghai is 5 times larger than population of Monterrey.
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3x-2y>2 graphs and solution
Answers
The graph of the inequality 3x - 2y > 2 is attached below.
We are given an inequality. The inequality is given below.
3x - 2y > 2
First of all, we will simplify the inequality. We need to keep the variable "y" on one side of the inequality. The inequality is modified as given below.
3x - 2y > 2
3x > 2 + 2y
3x - 2 > 2y
2y < 3x - 2
y < (3x - 2)/2
Now, to draw the graph of the inequality. We will first find the equation of the straight line corresponding to the given inequality.
y = (3x - 2)/2
We will draw a dotted line according to the above equation. Now, we will shade the area that satisfies the inequality. Hence, the graph is obtained.
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Given f(x)=2x-5, what would be the expression for f(t-1)?
A f(t-1)=2t-3.
B f(t-1)=21-5
C
f(t-1)=2t-7
Answers
C. f(t-1)=2t-7
Step-by-step solution
To find f(t-1) given f(x)=2x-5, we sub (t-1) in for x:
f(x) = 2x-5
f(t-1) = 2(t-1)-5
= 2t-2-5
= 2t-7
Two parts: Make sure to answer EACH part:
1. What is the rate of change for each shop shown below?
2. Which shop has the GREATEST rate of change?
Answers
Answer: Carol's Thrift shop rate of change = $4.99/item
Wilma's Child Care rate of change is $7.50/hr
Step-by-step explanation:
Carol's Shop: equation of the line is in y=mx + b form, where m = slope = rate of change = $4.99/item
Wilma's slope = (y2 - y1) / (x2 - x1) = (15-0)/ (2-0) = $7.5/hr
Wilma's has the greater rate of change
A line passes through the points (0, 0) and (–17, –11). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form
Answers
A line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that, the line passes through the points (0, 0) and (–17, –11).
The slope of the line is,
m = (5+4)/(5-0)
m= 9/5
The equation of the line passes through the point as,
(y-y₁)=m(x-x₁)
(y-0)=9/5(x-0)
5(y-0)=9(x-0)
5y=9x+0
y=9/5x+0
Thus, a line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0
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What is the constant of proportionality of 9/6 and 19/13
Answers
The relationship has a constant of proportionality of 38/39
How to determine the constant of proportionality?From the question, the given parameters are
Variable 1 = 9/6
Variable 2 = 19/13
The above parameters can be represented as the following points
(x, y) = (9/6, 19/13)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have the following equation
k = (19/13)/(9/6)
Evaluate the quotient
So, we have
k = 38/39
Hence, the constant of proportionality is 38/39
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Which statements about this situation are true?
Answers
Answer:
D) Alan was farther away from Madison when he started driving
F) Alan and Andrew started the same distance from Madison
Step-by-step explanation:
Hopefully I got them all!!!
developing proof: what’s wrong with the triangles? explain.
Answers
For the given triangles , developing proof is not possible due to following reasons:
First triangle : 21 + 25 < 48 not true.
Second triangle : Interior angle 130° > Exterior angle 125°
As given in the question,
For the given triangles developing proof is not possible due to following reasons:
First triangle:
Measure of three sides are given as 21, 25 , and 48.
As per the property to form a triangle : Sum of two sides is always greater than the third side.
Here, 21 + 25 < 48 .
Above mention property does not satisfied by given triangle.
Second triangle:
In a triangle, measure of exterior angle is always greater the opposite interior angles.
Here, measure of interior angle 130° > measure of exterior angle 125°
Does not satisfy the relation of exterior angles with interior angle.
Therefore, for the given triangles , developing proof is not possible due to following reasons:
First triangle : 21 + 25 < 48 not true.
Second triangle : Interior angle 130° > Exterior angle 125°.
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What is the equation of the line that passes through the point (5, 5) and has a slope
of -3/5
Answers
Answer:
y = - [tex]\frac{3}{5}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{3}{5}[/tex] , then
y = - [tex]\frac{3}{5}[/tex] x + c ← is the partial equation
to find c substitute (5, 5 ) into the partial equation
5 = - 3 + c ⇒ c = 5 + 3 = 8
y = - [tex]\frac{3}{5}[/tex] x + 8 ← equation of line
for two positive integers a and b, we know g c d (a comma b )equals 15 comma space l c m (a comma b )equals 90, what is a b?
Answers
Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.
Suppose we have 2 positive integers, a and b, then:
gcd (a, b) = the greatest common divisor = common prime factors of a and b
lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b
In the given problem:
gcd (a, b) = 15
prime factorization of 15:
15 = 3 x 5
Hence,
a = 3 x 5 x ....
b = 3 x 5 x ....
lcm (a, b) = 90
prime factorization of 90:
90 = 3 x 5 x 2 x 3
Therefore the possible pairs of a and b are:
Combination 1:
a = 3 x 5 = 15
b = 3 x 5 x 2 x 3 = 90
Combination 2:
a = 3 x 5 x 2 = 30
b = 3 x 5 x 3 = 35
We can conclude the two integers are 15 and 90 or 30 and 45.
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Four boxes are sliding with constant speed before each box experiences an unbalanced force of 8 n. Which box would experience the greatest acceleration when the unbalanced force is applied?.
Answers
The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)
Acceleration: it is defined as rate of change of velocity with respect to time.
Unbalanced Force: it means that the force applied in one direction is greatest than the force applied in the opposite direction.
Given that, F = 8n.
let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.
According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.
F = m × a
⇒ a = F/ m
where, F is Force, m is mass and a is acceleration.
Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²
acceleration of the box of 4kg = 8÷ 4 = 2 m/m²
acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²
acceleration of the box of 8kg = 8÷ 8 = 1 m/s²
∴ the box with mass of 2kg experience the greatest acceleration.
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Given the function f(x) = 0.5|x - 4|-3, for what values of x is f(x) = 7?
Ox= -24, x = 16
Ox= -16, x = 24
Ox= -1, x = 9
O x = 1, x = -9
Answers
The value of x is when the value of the function f(x) = 7 is x= -24 and x = 16
Function:
A correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to output is known as the function of the relation.
Given,
Here we have the function f(x) = 0.5|x - 4| - 3.
Now, we have to find the value of x when the value of f(x) = 7.
In order to find the value of x as have to equate the give function with the value of f(x), that is 7,
So, when we apply these on the function then we get,
=> 7 = 0.5|x - 4|-3
Now, we have to move all the numbers instead of x, then we get,
=> 7 + 3 = 0.5|x - 4|
=> 10 = 0.5 |x - 4|
=> 10/0.5 = |x - 4|
=> 20 = |x - 4|
So in this place we can get the following forms,
=> x - 4 = 20 and
=> x - 4 = - 20
Because we get two values being an absolute value function.
Now, we have to add 4 on both sides
Then we get
=> x - 4 + 4 = 20 + 4 and
=> x - 4 + 4 = - 20 + 4
So, the value of x is
=> x = 24 and x = - 16
Therefore, for the given function the values of x are 24 and - 16.
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Twice a number subtracted from 10 is 14
Answers
Let the number be x
10 - 2x = 14
2x = -4
x = -2