What are the magnitude and direction of w = ❬–5, –14❭? Round your answer to the thousandths place.
Answers
To solve the question, we will have to determine the quadrant within which the point falls
Since both values are negative
[tex](x,y)=(-5,-14)[/tex]So the values are in the third quadrant
So we will have to get the magnitude first
[tex]\begin{gathered} \text{Magnitude}=\sqrt[]{x^2+y^2} \\ \text{Magnitude}=\sqrt[]{(-5)^2+(-14)^2} \\ \text{Magnitude}=\sqrt[]{25+196} \\ \text{Magnitude}=221 \\ \text{Magnitude}=14.866 \end{gathered}[/tex]Next, we will have to get the direction
[tex]\begin{gathered} \text{direction}=\tan ^{-1}(\frac{y}{x}) \\ \text{direction}=\tan ^{-1}(\frac{-14}{-5}) \\ \text{direction}=\tan ^{-1}(2.8) \\ \text{direction}=70.346^0 \end{gathered}[/tex]So, since we know that the point is on the third quadrant, then
We will add 180 degrees (90 degrees from first and 90 degrees from the second quadrant)
So we will have
[tex]180^0+70.346^0=250.346^0[/tex]Thus the answer is
[tex]\mleft\Vert w\mleft\Vert=\mright?\mright?14.866,\theta=250.346^0[/tex]
Related Questions
Solve the equation. 42 = d2 - 22 d = and d =
Answers
we have
[tex]42=d^2-22[/tex]solve for d
[tex]\begin{gathered} d^2=42+22 \\ d^2=64 \\ \text{square root both sides} \\ d=\pm\sqrt[]{64} \\ d=\pm8 \end{gathered}[/tex]therefore
d=+8 and d=-8Which player is more likely to score more than 18 points in a game?Who is more likely to have a very bad game and score less than 3 points?(sorry for all the equations next to the whisker plots)
Answers
The boxplot that shows points that Dwight scored in each game has a minimum value of 1 point and a maximum value of 20 points.
The box plot that shows the points that Ron scored in each game, has a minimum value of 4, and a maximum value of 18 points.
The values below the minimum point and above the maximum point of the data set can be considered "outliers", i.e. atypical observations, and the probability if them being observed is very low.
Ron's box plot goes from 4 to 18 points, it is very unlikely for him to score less than 3 points or above 18, both scores would be considered "outliers" for him.
But, Dwigth's box plot goes from 1 to 20, which means that "scoring less than 3 on a game" or "scoring more than 18 on a game" are more possible situations for him.
So Dwight is more likely to score more than 18 points on a game and he is also more likely to have a very bad game and score less than 3 points.
What happens to the graph of y=2x^3+x^2−7x−6 as x heads toward ∞ and −∞?A. as x→∞, y→∞ as x→−∞, y→−∞B. as x→∞, y→∞ as x→−∞, y→∞C. as x→∞, y→−∞ as x→−∞, y→−∞D. as x→∞, y→−∞ as x→−∞, y→∞
Answers
Answer:
A. as x→∞, y→∞ as x→−∞, y→−∞
Explanation:
Given the function:
[tex]y=2x^3+x^2−7x−6[/tex]In order to determine the end behavior of f(x), we use the leading coefficient test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd and the leading coefficient is positive,, the graph falls to the left and rises to the right.
,• When the ,degree is odd and the leading coefficient is negative,, the graph rises to the left and falls to the right.
,• When the ,degree is even and the leading coefficient is positive,, the graph rises to the left and right.
,• When the ,degree is even and the leading coefficient is negative,, the graph falls to the left and right.
From the function, f(x):
• The degree of the polynomial = 3 (Odd)
,• The leading coefficient is 2 (Positive)
Thus, using the 1st rule of the 4 given above, we have that as x→∞, y→∞ as x→−∞, y→−∞.
The correct option is A.
Make a question similar (but not the same!) to those in #2 Post your question and full solution
Answers
Write a function with vertical asymptote x=4, horizontal asymptote y=1, y intercept at (0,2).
A possible function can be express as:
[tex]f(x)=\frac{x-8}{x-4}[/tex]Let's prove that this function fulfils our conditions. Let's start with the y-intercept, we know that this happens when x=0, then we have:
[tex]f(0)=\frac{0-8}{0-4}=2[/tex]Hence the y-intercept is at (0,2).
Now, we know that a rational function has horizontal asymptote y=b if:
[tex]\begin{gathered} \lim_{x\to\infty}f(x)=b \\ \text{ or } \\ \lim_{x\to-\infty}f(x)=b \end{gathered}[/tex]Let's find these limits:
[tex]\begin{gathered} \lim_{x\to\infty}\frac{x-8}{x-4}=\lim_{x\to\infty}\frac{\frac{x}{x}-\frac{8}{x}}{\frac{x}{x}-\frac{4}{x}} \\ =\lim_{x\to\infty}\frac{1-\frac{8}{x}}{1-\frac{4}{x}} \\ =\frac{1-0}{1-0} \\ =1 \end{gathered}[/tex]and:
[tex]\begin{gathered} \lim_{x\to-\infty}\frac{x-8}{x-4}=\lim_{x\to-\infty}\frac{\frac{x}{x}-\frac{8}{x}}{\frac{x}{x}-\frac{4}{x}} \\ =\lim_{x\to-\infty}\frac{1-\frac{8}{x}}{1-\frac{4}{x}} \\ =\frac{1-0}{1-0} \\ =1 \end{gathered}[/tex]This means that we have a horizontal asymptote y=1 as we wanted.
Now, a rational function has vertical asymptote at x=a if:
[tex]\begin{gathered} \lim_{x\to a^-}f(x)=\pm\infty \\ \text{ or } \\ \lim_{x\to a^+}f(x)=\pm\infty \end{gathered}[/tex]to determine the value of a we need to look where the function is not defined, that is, the values which make the denominator zero, in this case we have:
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]Then we need to find the limits:
[tex]\begin{gathered} \lim_{x\to4^-}\frac{x-8}{x-4} \\ \text{ and } \\ \lim_{x\to4^+}\frac{x-8}{x-4} \end{gathered}[/tex]Now, if we approach the value x=4 from the left we notice that as x gets closer to 4 the function gets bigger and bigger, for example:
[tex]f(3.9999)=\frac{3.9999-8}{3.9999-4}=400001[/tex]if we follow this procedure, we conclude that:
[tex]\lim_{x\to4^-}\frac{x-8}{x-4}=\infty[/tex]Similarly, if we approach x=4 from the right the function gets smaller and smaller, for example:
[tex]f(4.0001)=\frac{4.0001-8}{4.0001-4}=-39999[/tex]Then we can conclude that:
[tex]\lim_{x\to4^+}\frac{x-8}{x-4}=-\infty[/tex]Hence, we conclude that the function we proposed has a vertical asymptote x=4 like we wanted.
the properties we gave can be seen in the following graph:
Question 9 of 22Which number produces a rational number when added to5?O A. 5.38516480...B. 10C.O D. 0.22SUBMIT
Answers
A rational number can be said to be a number that is expressed as a quotient of s fraction. The denominator of a rational number must be a non-zero number.
You can simply say a rational number is any number that can be written as a fraction.
To find the number when added to 5 produces a rational number, we have:
A. 5.38516480...
This number has infinite decimal so it is an irrational number
B. 10
10 + 5 = 15
This is not a rational number
C. 0
0 + 5 = 5
This is not a rational number
D. 0.22
0.22 + 5 = 5.22
This is a rational number because it can be written as a fraction
[tex]5.22=\frac{522}{100}[/tex]Therefore, the number that produces a rational number when added to 5 is 0.22
ANSWER:
D. 0.22
Given the function k(n) = -3n + 2, and its domain is described by the set {6,-8, 4, 2}, what is therange?
Answers
The domain of a function is the set of values where the function is defined (values of x where y is defined).
The range of a function are the values of the function where is defined (values of y).
For the given function:
[tex]k(n)=-3n+2[/tex]Domain: values of n {6,-8, 4, 2}
Range: values of k(n)
n= 6
[tex]\begin{gathered} k(6)=-3(6)+2 \\ =-18+2 \\ =-16 \end{gathered}[/tex]n=-8
[tex]\begin{gathered} k(-8)=-3(-8)+2 \\ =24+2 \\ =26 \end{gathered}[/tex]n=4
[tex]\begin{gathered} k(4)=-3(4)+2 \\ =-12+2 \\ =-10 \end{gathered}[/tex]n=2
[tex]\begin{gathered} k(2)=-3(2)+2 \\ =-6+2 \\ =-4 \end{gathered}[/tex]Then, the range is: {-16, 26, -10, -4}
Write the slope-intercept form of the equation of each line.3) 10 = -2y-x
Answers
Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.
To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.
Let's add x on both sides, we get
[tex]-2y=10+x[/tex]Now, lets divide by -2 on both sides, we get
[tex]y=\frac{10}{-2}+\frac{x}{-2}=-\frac{1}{2}\cdot x-5[/tex]we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5
Zach bought a pair of jeans for $54.The next week he noticed that the price for the same pair of jeans was now $74. Find the percent of change.
Answers
Let's begin by listing out the information given to us:
Old Price = $54
New Price = $74
The percentage change is given by:
[tex]\begin{gathered} \text{\%}\Delta=\frac{|OldPrice-NewPrice|}{OldPrice}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|54-74|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|-20|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{20}{54}\cdot100\text{\%} \\ \text{\%}\Delta=37.04\text{\%} \\ \text{\%}\Delta\approx37\text{\%} \end{gathered}[/tex]1 1/6cdx (-6/7c raised to the 9 power d raised to the 7 power.I'll upload a picture
Answers
ANSWER:
[tex]-c^{10}d^8[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]1\frac{1}{6}cd\cdot\mleft(-\frac{6}{7}c^9d^7\mright)[/tex]We simplify as follows:
[tex]\begin{gathered} 1\frac{1}{6}=\frac{6+1}{6}=\frac{7}{6} \\ \frac{7}{6}cd\cdot(-\frac{6}{7}c^9d^7) \\ \frac{7}{6}\cdot-\frac{6}{7}\cdot cd\cdot(c^9d^7)=-1\cdot c^{10}d^8=-c^{10}d^8 \end{gathered}[/tex]Sketch the graphs for each of the following equations. 7 a. y = 5-X+7 b.y=9 c. y= 3x + 6
Answers
a)
Given:
The equation is,
[tex]y=-\frac{7}{5}x+7[/tex]The objective is to sketch the graph of the equation.
Since, the highest degree of the equation is 1, it could be a straight line. The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the equation and c represents the y intercept. Then comparing the both equations,
[tex]\begin{gathered} \text{slope, m=-}\frac{\text{7}}{5} \\ y\text{ intercept, c=7} \end{gathered}[/tex]Substitute, y = 0 in the given equation.
[tex]\begin{gathered} 0=-\frac{7}{5}x+7 \\ \frac{7}{5}x=7 \\ x=7\cdot\frac{5}{7} \\ x=5 \end{gathered}[/tex]Thus, at y = 0, the value of x = 5.
Using the coordinates (5,0) and y intercept c = 7, the graph will be,
Hence, the required graph is obtained,
The water temperature of the Pacific Ocean vanes inversely as the water's depth. At a depth of 1000 meters, the water temperature is 4.4 degrees Celsius. What is the water temperature at a depth of 5000 meters?
Answers
If 6 garbage trucks can collect the trash of 36 homes in a day. How many trucks are needed to collect in 180 houses?
Answers
In the question, we are given that 6 garbage trucks can collect the trash of 36 homes in a day. We can find how many trucks are needed to collect in 180 houses below.
Explanation
[tex]\begin{gathered} \text{If 6 trucks collect for 36 houses} \\ x\text{ truck will collect for }180\text{ houses} \\ \text{Therefore using direct proportion} \\ \frac{6}{x}=\frac{36}{180} \\ \frac{6}{x}=\frac{1}{5} \\ \text{cross multiply} \\ x=30 \end{gathered}[/tex]Answer: 30 trucks
Identify the mistake
Answers
There is no mistake in Chase solving steps.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a equation :
(1/3)(g - 3) = 3
We can write -
(1/3)(g - 3) = 3
We can write -
g - 3 = 3 x 3
g - 3 = 9
g = 12
Therefore, there is no mistake in Chase solving steps.
To solve more questions on equation solving, visit the link below-
brainly.com/question/18067015
#SPJ1
3x squared negative 4x squared plus 7x 4x squared negative 4x
Answers
ANSWER
[tex]12x^5-28x^4+44x^3-28x^2[/tex]EXPLANATION
First we have to find the partial products by multiplying each term of the first polynomial by each term of the second polynomial:
Now the second term of the second polynomial:
And now we just have to add these partial products:
A student
answered 72
questions
correctly and
scored a 90%. How
many questions
were on the test?
Answers
Answer: 80
Step-by-step explanation:
= 72/90
= 72/0.9
= 80
6. Find all the solutions of the recurrence relation an = 2an-1 + an-2 + 2n + 1 with initial conditions a1 =7 and a2 = 19
Answers
aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
What is Recurrence relation?Recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms
aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
Homogenous case,
aₙ -2aₙ₋₁ + aₙ₋₂ with characteristic t²-2t-1=0
t=1
aₙ=C₁.(1-√2)ⁿ+C₂.(1+√2)ⁿ
Special case, Since non homogenous part is 2n+1
Let aₙ=pn+q, then
aₙ -aₙ₋₁ + aₙ₋₂=2n+1
pn+q-2(p(n-1)+q)-p(n-2)-q=2n+1
-2pn+qp-2q=2n+1
p=-1 and q=4p-1/2=-5/2
Combine both cases, aₙ = C₁(1-√2)ⁿ+C₂((1+√2)ⁿ-n-5/2
Substitute a₁=7 and a₂=19
a₁ = C₁(1-√2)+C₂((1+√2)-1-5/2
a₁ = C₁(1-√2)+C₂((1+√2)-7/2=7
(C₁+C₂)+(C₂-C₁)√2)=21/2..(1)
a₂ = C₁(1-√2)²+C₂((1+√2)²-2-5/2
= C₁(1-√2)²+C₂((1+√2)²-9/2=19
3(C₁+C₂)+2(C₂-C₁)√2)=97/2..(2)
By solving 1 and 2 we get
C₁=1/2(5/2-4√2)
C2=1/2(5/2+4√2)
aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2
Hence, aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
To learn more on recurrence relation click:
https://brainly.com/question/9521757
#SPJ1
A six-sided number cube is rolled. Event A consists of rolling an even number. Event B consists of rolling a number greater than four. Match the correct sample space to each event.
Answers
EXPLANATION :
From the problem, we have two events :
Event A : rolling an even number {2, 4, 6}
Event B : rolling a number greater than four {5, 6}
1. Union of A and B is the combination of Event A and B
Since there's a common element, 6, we will take this as one only.
That will be {2, 4, 5, 6}
2. Intersection of A and B is the common element between the two events.
So that is {6}
3. Complement of A is the set of elements that is NOT present in Event A.
Since a cube has 6 sides, the elements are {1, 2, 3, 4, 5, 6}
The complement of A will be {1, 3, 5}
4. Event B, from the data we have from above, B will have {5, 6}
The sum of 4 consecutive integers is 254. What is the value of the greatest integer?
Answers
The sum of 4 consecutive integers is 254. What is the value of the greatest integer?
Let
x -----> the first integeer
x+1 ----> second integer
x+2----> third integer
x+3 ----> fourth integer
we have that
x+(x+1)+(x+2)+(x+3)=254
solve for x
4x+6=254
4x=254-6
4x=248
x=62
therefore
the greatest integer is x+3
so
62+3=65
answer is 65Is this the correct solution for this question? I need help please
Answers
Given equation:
[tex]9x^2\text{ - 12x + 4 = 0}[/tex]Let's solve the question to identify the type of solution.
Using factorization method:
[tex]\begin{gathered} 9x^2\text{ - 12x + 4 =0} \\ 9x^2-6x\text{ -6x + 4 = 0} \\ 3x(3x-2)\text{ -2(3x-2)= 0} \\ (3x-2)(3x-2)\text{ =0} \end{gathered}[/tex]The solution is thus
[tex]\begin{gathered} 3x\text{ -2 = 0} \\ 3x\text{ = 2} \\ x\text{ = }\frac{2}{3} \end{gathered}[/tex]Hence, there is one solution and it is real.
Answer: 1 real (Option B)
WILL GIVE BRANLIEST Use the graph to write a linear function that relates y to x (for both please)
Answers
Question:
Use the graph to write a linear function that relates y to x
Solution:
To find the linear function that relates y and x in the above graph, we have to know that a linear function is given by the following formula:
[tex]y\text{ = mx+b}[/tex]where m is the slope of the line and b is the y-coordinate of the y-intercept (when x = 0). Now, notice that in this case, when x = 0 then y= 2, thus we can conclude that b = 2 and:
[tex]y\text{ = mx+}2[/tex]On the other hand, by definition, the slope of the line is given by:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2, Y2) are any two points on the line. Take for example:
(X1,Y1) = (0,2)
(X2,Y2) = (6,10)
then, replacing this data in the equation of the slope, we obtain:
[tex]m\text{ = }\frac{10-2}{6-0}=\text{ }\frac{8}{6}[/tex]then, using the slope obtained above, we can conclude that the equation of the linear function is:
[tex]y\text{ = }\frac{8}{6}x\text{ + 2}[/tex]if G(t)=(3t-5)^2 + 4t - 1 find each of the following g of a and g of a plus 2
Answers
For point A, you just have to replace t by a in the given function, like this
[tex]\begin{gathered} G\mleft(t\mright)=\mleft(3t-5\mright)^2+4t-1 \\ \text{ Replacing} \\ G\mleft(a\mright)=\mleft(3a-5\mright)^2+4a-1 \\ \text{ Solving you have} \\ G(a)=(3a-5)(3a-5)+4a-1 \\ G(a)=9a^2-30a+25+4a-1 \\ \text{ Add similar terms} \\ G(a)=9a^2-26a+24 \end{gathered}[/tex]For point B, you just have to replace t by a+2 in the given function, like this
[tex]\begin{gathered} G(t)=(3t-5)^2+4t-1 \\ \text{ Replacing} \\ G(a+2)=(3(a+2)-5)^2+4(a+2)-1 \\ \text{ Solving you have} \\ G(a+2)=(3a+6-5)^2+4(a+2)-1 \\ G(a+2)=(3a+1)^2+4a+8-1 \\ G(a+2)=(3a+1)(3a+1)+4a+8-1 \\ G(a+2)=9a^2+6a+1+4a+8-1 \\ \text{ Add similar terms} \\ G(a+2)=9a^2+10a+8 \end{gathered}[/tex]a system of equations is graphed on the set of axes below
Answers
You have to determine the solution of the equation system by looking at the graph.
For any equation system there are three possible scenarions, that the system has "no solution", that the system has "infinite solutions" and that the system has "one solution"
Looking at the graph you can determine which situation if:
- both lines are parallel, they never meet, which indicates that the system has no solution.
- both lines are superimposed, i.e. they seem as if there is only one line, the system has infinite solutions.
- both lines cross at one point, this indicates that the system has only one solution and the solution will be the point where the lines intersect.
In the given graph, the lines cross at one point, which means that the system has one solution. To determine said solution you have to read the x and y coordinates of the point in the grid.
The lines meet at x=4 and y=2, which means that the solution of this system is a
8. * The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically. 9. ** f(x) = 5x – 2 and g(x) = 2x + 4. Are f(x) and g(x) parallel, perpendicular or neither parallel nor perpendicular to each other. Justify.
Answers
Entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. How much would it cost for a car with 4 people in the vehicle to enter the park?
Answers
From the information given, the entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. Given that 4 people entered the one vehicle, the amount that would be paid for the vehicle is $5. Sinec it is $2 per person, the amount for 4 persons would be 2 * 4 = 8
Thus, the total cost would be
5 + 8 = $13
What is 5x2 (This is a joke)
Answers
Answer:
10 (duh)
Step-by-step explanation:
Can someone help me out with this because i looked at all the videos that my teacher gave us and none of them explained it.
Answers
The meaning of;
[tex]\frac{x}{4}[/tex]In algebra, when there is an unknown number it is generally represented by a letter (such as x,y,z etc.)
The letters x in x/4 represents an unkown number.
So, x/4 represent the unknown number x divided by 4.
For example; if x=20, then;
[tex]\frac{x}{4}=\frac{20}{4}=5[/tex]Find thr value of x for which 1 II m.
Answers
The value of x is 50 for which line l is parallel to line m and the angles are equal by the properties of parallel lines that is vertically opposite angles are equal.
What is parallel lines?Two lines (in the same plane) are said to be parallel if they never collide, regardless matter how far they are extended on either side. Parallel lines travel parallel to each other, like train tracks. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.
Here,
Since l ⇵ m,
Vertically opposite angles are equal by the properties of parallel lines.
2x-5=95
2x=100
x=50
The value of x is 50, which means that line l is parallel to line m and the angles are equal according to the property of parallel lines, which states that vertically opposing angles are equal.
To know more about parallel lines,
https://brainly.com/question/28766787?referrer=searchResults
#SPJ1
Use the function y = 200tan x on the interval 0 deg <= x <= 141 deg Complete the ordered pair (x, 0). Round your answer to the nearest whole number.
Answers
The value of x for the ordered pair (x,0) is 0. B is the correct option.
What is ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Given function is
y = 200 tan x.
Given ordered pair is (x,0).
The value of y for the given ordered pair is 0.
The value of tangent function is increasing with increase the value of degree.
The value of tangent at 0 degree is 0 that is tan 0 = 0.
If we multiply a number with zero it returns 0.
The possible value of x is 0.
Hence option B is the correct option.
To learn more about ordered pair, you visit below link:
https://brainly.com/question/28737707
#SPJ1
Solve each inequality. Then graph the solution.1. -6t-3-2t - 192. - 3(m - 4) <63. 4(1 - x) < 164. 2y <-35. 3(v - 4) 5V - 246. -X – 1 > 3x + 1Solve each inequality.7. 2(k + 4) – 3k < 148. 3(4c – 5) – 2c> 09. 15(j – 3) + 3j < 4510. 22 > 5(2y + 3) – 3y11. -53 > -3(3z + 3) + 3z12. 20(d – 4) + 4d < 813. -2(6 + s)< -16 + 2s14. 9 - 2x < 7 + 2(x – 3)Solve each inequality.If all real-number values of x are solutions of the inequality, write TRUE.If no real-number values of x are solutions of the inequality, write FALSE.15. 2(n − 3) < -13 + 2n16. -3(w + 3) < 9 - 3w17. The unit cost for a piece of fabric is $4.99 per yard including tax. You havto spend on material. How many whole feet of material can you buy?
Answers
7. The unit cost for a piece of fabric is $4.99 per yard including tax. You have $30 to spend on material. How many whole feet of material can you buy?
we know that
1 yard --------> cost $4.99
so
x yards ------> $30
Applying proportion or rule of three
x=30/4,99
x=6.01 yd
answer 6 yards
6 The length of a city block running north to south in New York City is about 5 X 10-2 miles The distance from New York City to Mumbai, India, is about 7.5 X 103 miles. The distance from New York City to Mumbai is about how many times the length of a New York City north-south block? Show your work.