Answer and Step-by-step explanation: To find the B-coordinate vector of x:
[tex]b_{1} = \left[\begin{array}{ccc}1\\2\\-3\end{array}\right][/tex] , [tex]b_{2} = \left[\begin{array}{ccc}-4\\-7\\11\end{array}\right][/tex], x = [tex]\left[\begin{array}{ccc}-10\\-17\\27\end{array}\right][/tex]
The augmented matrix will be:
[tex]\left[\begin{array}{ccc}1&-4&-10\\2&-7&-17\\-3&11&27\end{array}\right][/tex]
Transforming into reduced row-echelon form:
= [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&-1&-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&0&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\0&0&0\end{array}\right][/tex]
The values for the vector will be:
x = 2
y = 3
The B-coordinate vector is of the form:
V = [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]
The B-coordinate vector of x is V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]
Kimberly wants to paint all the surfaces of the table shown below.
Which measure BEST helps her determine how much paint she needs?
А
the volume of 1 rectangular prism and 4 cylinders
B
the surface area of 1 rectangular prism and 4 cylinders
С
the surface area of 5 rectangular prisms
D
the volume of 5 rectangular prisms
Answer:
C. surface area of 5 rectangular prisms.
Step-by-step explanation:
The table in the given figure as shown above has a rectangular flat top that has a solid shape of rectangular prism.
It also has 4 legs that are also rectangular in shape. The legs are rectangular prisms.
To determine the quantity of paint Kimberly would need, she needs to make use of the surface area of the table.
The surface area of the table = surface area of the top + surface area of the 4 legs = surface area of 5 rectangular prisms.
Answer:
C
Step-by-step explanation:
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes. This system of equations models the situation. x + y =125 5x + 8y = 775
Step-by-step explanation:
5q+8p=775
q + p = 125
5q + 8q = 775
-5q -5q = -625
3q = 150
q = 50 premium
q + 50 = 125
q = 75 quick
Correct answer is
A: 5x+8y=775 and x+y =125
Next Answer is
50 premium car washes
75 Quick Car Washes
can someone answer this
Hey there! :)
Answer:
(-6, -7)
Step-by-step explanation:
Given the equations:
y = -1/6x - 8
y = 2x + 5
When graphed, we get a solution, or point of intersection, at (-6, -7). This is the point at which the two equations are equal to each other. This can even be proven:
-7 = -1/6(-6) - 8
-7 = 1 - 8
-7 = -7
----------------------
-7 = 2(-6) + 5
-7 = -12 + 5
-7 = -7
Thus, proving graphically and algebraically, the solution is at (-6, -7).
Calculate the length of the unknown side of this right angled triangle
Answer:
12.04
Step-by-step explanation:
Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,
[tex]a^2 + b^2 = c^2[/tex]
We already have a and b which are 8 and 9 so we plug them in.
[tex](8)^2 + (9)^2 = c^2[/tex]
64 + 81 = c^2
145 = c^2
c = 12.04 rounded to the nearest hundredth.
Thus,
the unknown side is about 12.04.
Hope this helps :)
4+9(3x-7)=-42x-13+23(3x-2)
Answer:
x = 0
Step-by-step explanation:
[tex]4+9(3x-7)=-42x-13+23(3x-2)\\4+27x-63=-42x-13+69x-46\\27x+4-63=-42x+69x-13-46\\27x-59=25x-59\\2x-59=-59\\2x=0\\x=0[/tex]
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2
Answer:
The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
Step-by-step explanation:
GIven that :
[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]
This implies that the distance between the x-axis and the axis of the rotation = 2 units
The distance between the x-axis and the inner ring is r = (2+sec x) -2
Let R be the outer radius and r be the inner radius
By integration; the volume of the of the solid can be calculated as follows:
[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]
[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]
[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
Sven starts walking due south at 7 feet per second from a point 190 feet north of an intersection. At the same time Rudyard starts walking due east at 4 feet per second from a point 130 feet west of the intersection.
A. Write an expression for the distance d between Sven and Rudyard t seconds after they start walking.
B. What is the minimum distance between them?
C. When are Sven and Rudyard closest?
Answer: A. [tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]
B. Minimum distance between them = 18.61 feet.
C. After 28.76 seconds Sven and Rudyard are closest.
Step-by-step explanation:
A) Let (0,0) be the intersection point.
Then, Initial Location of Sven (0,190).
Speed of Sven = 7 feet per second
Then, position of Sven after t seconds = (0,190-7t) [speed = distance x time]
Similarly, Initial position of Rudyard= (130,0)
Speed of Rudyard = 4 feet per second
Position after t seconds = (130-4t,0)
Distance d between Sven and Rudyard t seconds after they start walking:
[tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]
B) Let [tex]d(t)=\sqrt{(190-7t)^2+(130-4t)^2}\\[/tex]
[tex]d'(t)=2(190-7t)(-7)+(2)(130-4t)(-4)\\\\=130t-3700[/tex]
Put d'(t)=0
[tex]130t-3700=0\\\\\Rightarrow\ t=\dfrac{3700}{130}\approx28.46\ sec[/tex]
Minimum distance :
[tex]d(28.46)=\sqrt{(190-7(28.46))^2+(130-4(28.46))^2}\\\\=\sqrt{346.154}\approx18.61\ feet[/tex]
Hence, the minimum distance between them = 18.61 feet.
c) After 28.76 seconds Sven and Rudyard are closest.
An amount of $49,000 is borrowed for 15 years at 3.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be
paid back?
round your answer to the nearest dollar.
Answer:
[tex]\boxed{\sf \ \ \ $82,092 \ \ \ }[/tex][tex]\large\boxed{\sf \ \ \ \$82,092 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
At the beginning we have $49,000
After the first year we get 49,000*(1+3.5%)=49,000*1.035
After n years we get
[tex]49,000\cdot1.035^n[/tex]
So in 15 years it comes
[tex]49,000\cdot1.035^{15}=82,092.09...[/tex]
rounded to the nearest dollar is $ 82,092
Hope this helps
A concert starts at 7:45pm and ends at 1:35 am. How long was the concert?
Answer:
The concert starts at 7:45 pm and ended at 1:35 am which mean the concert going on 5 hours and 50 minutes.
Colossus Added to six flags st. Louis in 1986, the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet above the ground. Determine an equation that relates a rider's height the ride at the bottom of the wheel.
Given:
D=165 feet and the frequency of the motion is 1.6 revolutions per minute.
Solution:
The radius is half of the diameter.
The radius of the wheel is 82.5 feet.
[tex]T=\frac{1}{1.6} \text{ minutes}[/tex]
As we know: [tex]\omega=\frac{2\pi}{T}[/tex]
Substitute the value of T in the above formula.
[tex]\omega=\frac{2\pi}{\frac{1}{1.6}}\\\omega=3.2\pi[/tex]
If the center of the wheel is at the origin then for [tex]t=0[/tex] the rest position is [tex]-a[/tex].
This can be written as:
[tex]h(t)=-a\cos(\omega t)\\h(t)=-82.5cos(32.\pi t)[/tex]
The actual height of the rider from the ground is:
[tex]h(t)=\text{ Initial height from bottom}+\text{ radius}-82.5\cos(3.2\pi t)\\h(t)=15+82.5-82.5\cos(3.2\pi t)\\h(t)=97.5-82.5\cos(3.2\pi t)[/tex]
The required equation is [tex]h(t)=97.5-82.5\cos(3.2\pi t)[/tex].
Simplify the expression:
1 – 5b + – b + – 8b – 2b
Answer:
The answer is 1 - 16b.
Step-by-step explanation:
You have to collect like-terms :
[tex]1 - 5b - b - 8b - 2b[/tex]
[tex] = 1 + b( - 5 - 1 - 8 - 2)[/tex]
[tex] = 1 + b( - 16)[/tex]
[tex] = 1 - 16b[/tex]
Answer:
The answer is
1 - 16bStep-by-step explanation:
1 – 5b + – b + – 8b – 2b can be written as
1 - 5b - b- 8b - 2b
Subtract the like terms
That's
We have the final answer as
1 - 16b
Hope this helps you
i have to write equations in standard form using integer coefficients for A,B, and, C Example: y= -8/15x + 1/20
Answer:
c
Step-by-step explanation:
Which graph shows all the values that satisfy Two-ninths x + 3 greater-than 4 and five-ninths
Answer:
It is the first graph
Step-by-step explanation:
Just got it right on the test review :)
Inequalities help us to compare two unequal expressions. The graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be solved as,
[tex]\dfrac29(x+3) > 4(\dfrac59)\\\\\dfrac{2x+6}{9} > \dfrac{20}{9}\\\\2x + 6 > 20\\\\2x > 20 - 6\\\\x > \dfrac{14}{2}\\\\x > 7[/tex]
Hence, the graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.
Learn more about Inequality:
https://brainly.com/question/19491153
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The average American consumes 8.8 liters of alcohol per year. Does the average college student consume less alcohol per year? State your null and alternative hypothesis
Answer:
Null hypothesis: u = 8.8 liters
Alternative hypothesis: u < 8.8 liters
Step-by-step explanation:
The null hypothesis is always opposite to Tue alternative hypothesis and is the default hypothesis.
In this case study, the null hypothesis is that the average American consumes 8.8 liters of alcohol per year: u = 8.8
The alternative hypothesis is that does the average American consumes less than 8.8 liters of alcohol per year: u < 8.8 liters
Which of the following points are on the line given by the equation y= 1/2x ?
Check all that apply.
D A. (-2,-1)
DB. (-2,1)
| C. (3,6)
D. (3, 15)
D E. (2.1)
D F. (4,2)
Answer:
(-2,-1), (2,1), (4,2)
Step-by-step explanation:
This is how I did it: (took me like a minute)
Draw a graph or get graph paper. You could also probably find a graph online that you can write on. (remember to label)
Now mark two points of the line. So for this question you could use (0,0) and (2,1).
Now draw a line connecting both points.
Finally you can check whether the points are on the line or are not.
Hope this helps!
Which statement best describes the end behavior of the following function?
F(x) = -x3 - 2x2 +7x-10
A. The graph of the function is high on the extreme left side, and low on the extreme right side.
The graph has no "start" or "end". It's defined for all 'x' between negative and positive infinity. So no matter how far left or right you go, there's always a 'y' for whatever 'x' you're at.
But it's guaranteed that once you get far enough left (negative x), the first term -x³ will definitely be positive, and will become more and more positive as you go farther left.
And similarly, once you get far enough right (positive x), the first term, -x³ will definitely be negative, and it'll become more and more negative as you go farther right.
So, except for some wiggling within a short distance either side of the origin, if you look at this graph from 10 miles away, f(x) comes out of the sky on the left side, and it heads down into the salt mine on the right side.
Answer:
guys omg the answer is A its not a scam guys
Step-by-step explanation:
[PLEASE HELP] in the function above, the slope of it will be multiplied by 1/2 and it’s y value of its y intercept will be increased by 3 units, which of the graphs below best shows the new function???
Answer:
The graph at the bottom left in your group of possible answers.
Step-by-step explanation:
Notice that the original given graph corresponds to the equation:
[tex]y=2x+1[/tex]
since the line's slope is 2/1 = 2 and the y-intercept is at the point (0, 1).
So if one modifies the equation multiplying the current slope by 1/2, and the y intercept increased by 3 units, Then the new function would be:
[tex]y=x+4[/tex]
A line of slope 1 and y-intercept at (0, 4)
Notice that the graph at the bottom left in your possible answers is representing such function.
Answer:
Answer Y: or Bottom Left of Given Answers
Step-by-step explanation:
The length of a rectangle is six times its width. The area of the
rectangle is 294 square centimeters. Find the dimensions of the
rectangle.
Answer:
length= 42
width = 7
Step-by-step explanation:
Given: AB=BC,AM=MC BM ⊥AC , EF⊥BC Prove: EC/AB = FC/MA
Answer:
90 degree EFC. and. BMC
across fc/ma
across ec/ab
hellllllllppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
see below.
Step-by-step explanation:
1st row has four small boxes
2nd row has three big boxes
big box 1 has no items ragged in it.
big box 2 has small box 1 and also small box 1 dragged into it.
big box 3 has small box 3 and small box 4 dragged into it.
2x - y = 6
4
x-y
13
anch
Answer:
x=-7, y= -20
Step-by-step explanation:
2x - y =6
x - y = 13
when I subract (x-y =13 ) from (2x-y =6)
2x -y =6
-x +y=-13
______________
x = -7
substitute x=-7 in the second equation
-7 - y =13
-y = 13 +7
-Y = 20
Y=-20
x=-7, y= -20
Answer:
x= -7/6
y= -25/3
Step-by-step explanation:
2x-y =6
4 x-y =13
Firstly, 4x-y=13(-) =>> - 4x+y=-13
Then we make the sum and result 6x= -7. Result x= -7/6.
We need to find y. So:
-y= 6-2x =>> y= -6 +2x =>> y= -6 +2*(-7/6) =>> y= -6-7/3 =>> y=(-18-7)/3 =>>y= -25/3
Find the circumference of a circular field with a diameter of 16 yards.
(Let it = 3.14)
Answer:
Hey there!
The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.
The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.
The circumference of the circle is 50.24 yards.
Hope this helps :)
Which of the following
examples have a constant rate of change?
A : You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles.
B : The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year.
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
D : The amount bacteria double every hour.
Answer:
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
Step-by-step explanation:
If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Let's check all the options, then we have
A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.
B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.
C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.
D: The number of bacteria doubles every hour. It is an example of the exponential function.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
More about the average rate change link is given below.
https://brainly.com/question/28744270
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surface area of a equilateral by hand
surface area of a equilateral by hand a 140.4 cm and 9cm
The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test
Answer:
The number expected to pass that test is [tex]k = 14 \ employees[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.91
The sample size is n = 15
The number of employee that will pass the test is mathematically represented as
[tex]k = n * p[/tex]
substituting values
[tex]k = 15 * 0.91[/tex]
[tex]k = 14 \ employees[/tex]
The doubling time of a cityʹs population is 8 years. How long does it take for the population to quadruple.
Answer:
16 Years
Step-by-step explanation:
In parallelogram ABCD, the coordinates of A are (4,3) and the coordinates of the midpoint of diagonal AC
are (2,5). What are the coordinates of C?
Answer:
D. (0, 7).
Step-by-step explanation:
Moving from (4,3) to (2, 5) we move 2 to the left; 2 - 4 = 2 then 2 up 3 + 5 = +2.
So the point C is 2-2, 5+2 = (0, 7).
Find the area of the shaded triangle, if the side of each square is 1 unit long.
Answer:
10 units²
Step-by-step explanation:
The shape is a triangle.
The area can be found by multiplying the base (in units) with height (in units) divided by 2.
base = 4 units
height = 5 units
[tex]\frac{4 \times 5}{2}[/tex]
[tex]\frac{20}{2} =10[/tex]
Please explain what this means! (no math needs to be done as I got the answers but I don't understand the explanation...)
you can imagine this as a venn diagram. the "or" event would consist of everything in both sides and the middle of the venn diagram because you can choose form either event x or event y.
the "and" event would consist of everything in the middle of the venn diagram because you choice must be a part of both event x and event y.
the complement of an event is just everything that is not included in the event. for example, in a coin flip, the complement of heads is tails. in a dice roll, the complement of {1,2} is {3,4,5,6}
so if you come across these just think "either or" or "both and." and remember that the complement is everything excluding what is listed.
i apologize if this does not help, im not that great at explaining things
Which of the following is false? Correlation measures the strength of linear association between two numerical variables. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.