The closest answer choice is (c) -577-617, with a 30-word summary: The expression 2ū - 6v - 67, with ū = <-97, 8> and v = <77, 57>, simplifies to -723i - 393j, matching option (c).
To find 2ū - 6v in terms of unit vectors, we first need to compute 2ū and 6v, and then subtract 6v from 2ū.
Given vectors ū = <-97, 8> and v = <77, 57>, we can find 2ū and 6v as follows:
1. 2ū = 2<-97, 8> = <-194, 16>
2. 6v = 6<77, 57> = <462, 342>
Now, subtracting 6v from 2ū:
2ū - 6v = <-194, 16> - <462, 342> = <-194 - 462, 16 - 342> = <-656, -326>
Now, we need to express this result in terms of unit vectors. The unit vectors in the x and y directions are <1, 0> and <0, 1> respectively.
The final expression is then -656<1, 0> - 326<0, 1>, which simplifies to -656i - 326j, where i and j are the unit vectors in the x and y directions, respectively.
In summary, 2ū - 6v in terms of unit vectors is -656i - 326j.
Now, if we subtract 67 from each component, we get -656 - 67 in the x-direction and -326 - 67 in the y-direction:
-656 - 67 = -723
-326 - 67 = -393
So, the final result is -723i - 393j.
The closest answer choice is (c) -577-617, with a 30-word summary: The expression 2ū - 6v - 67, with ū = <-97, 8> and v = <77, 57>, simplifies to -723i - 393j, matching option (c).
2u - 6v in terms of unit vectors i and j is equal to -24i - 14j.
To find 2u - 6v in terms of unit vectors i and j using the given vectors ū = 9i + 8j and v = 7i + 5j, we perform the following calculations:
1. Multiply vector u by 2:
2u = 2(9i + 8j) = 18i + 16j
2. Multiply vector v by 6:
6v = 6(7i + 5j) = 42i + 30j
3. Subtract 6v from 2u:
2u - 6v = (18i + 16j) - (42i + 30j)
= 18i + 16j - 42i - 30j
= (18i - 42i) + (16j - 30j)
= -24i - 14j
Therefore, 2u - 6v in terms of unit vectors i and j is equal to -24i - 14j.
The probable question maybe:
Given vectors ū = 9i + 8j and v = 7i +5j. find 2u - 6v in terms of unit vectors i and j.
11) Solve the system by the elimination method. Check the solution.
x + 5y = 25
3x + 4y = 20
Step-by-step explanation:
I hope this is what you need
PLEASE MAKE ME BRAINLIEST
The mean of 4 data values is calculated. One of the data values is 3 above
the mean. Another value is 4 above the mean. A third value is 1 above the
mean. What is true about the fourth data value? olla
A It is 8 below the mean.
B It is 6 below the mean.
C It is equal to the mean.
D It is 2 above the mean.
Answer:
It is 2 above the mean
9514 1404 393
Answer:
A. It is 8 below the mean
Step-by-step explanation:
The sum of differences from the mean is always zero. If x is the difference from the mean that the fourth data value has, then we must have ...
3 + 4 + 1 + x = 0
x = -8 . . . . . . . . . subtract 8
The fourth data value must be 8 below the mean.
_____
Additional comment
I find this property of the mean to be very useful in solving any number of problems related to differences from an actual or a desired mean.
Asking easy questions so people can get points (answer must be right)
756 divided by 18 (show work)
Evaluate the expression when c=3 and x=-5.
c-7x
Steps to solve:
c - 7x; c = 3, x = -5
~Substitute
3 - 7(-5)
~Multiply
3 - (-35)
~Simplify
3 + 35
~Add
38
Best of Luck!
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Hope it will help u....
X^2+(y+)4^2=64 khan academy
Answer: The center is 0,4
Step-by-step explanation:
Use this form to determine the center and radius of the circle:
(
x-h)^2+(y-k)^2=r^2
Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin:
r=8
h=0
k=4
The center of the cirle is found at (h,k): (0,4)
The radius is 8
One cup is equal to 14.4375 in^3. If a 1-cup measuring cylinder has a radius of 3 in., what is its height? If
the radius is 1 in., what is its height? Round to the nearest tenth.
If the measuring cup has a radius of 3 in. then its height is
height is _____ in., and it it has a radius of 1 in. then it’s height is _____ in.
Answer:
The height of the cup is 0.51 in.
The height of the cup is 4.59 in.
Step-by-step explanation:
The volume of the cylinder is [tex]\pi r^2 h[/tex]
Given that,
The volume of the cup is 14.4375 in³.
If the measuring cup has a radius of 3 in.
Then,
[tex]\pi r^2h=14.4375[/tex]
Plug r= 3 in.
[tex]\pi (3)^2h=14.4375[/tex]
[tex]\Rightarrow h=\frac{14.475}{9\pi }[/tex]
⇒h=0.51 in.
The height of the cup is 0.51 in.
If it has radius of 1 in.
Then,
[tex]\pi r^2h=14.4375[/tex]
Plug r= 1 in.
[tex]\pi (1)^2h=14.4375[/tex]
[tex]\Rightarrow h=\frac{14.475}{1\pi }[/tex]
⇒h=4.59 in.
The height of the cup is 4.59 in.
What expression represents the volume of the prism, in cubic units?
One-halfx3 + x2
One-halfx3 + Three-halves x2
x3 + x2
x3 + 3x2
Answer:
V = [tex]1/2 x^{3}[/tex] + [tex]x^{2}[/tex]
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
The oblique prism below has an isosceles right triangle base. An oblique right triangular prism is shown. The triangular bases have 2 sides with a length of x. The length of they hypotenuse is unknown. The distance from the 2 triangular bases is (x + 3). The vertical height of the prism is (x + 2). What expression represents the volume of the prism, in cubic units?
One-halfx3 + x2
One-halfx3 + Three-halves x2
x3 + x2
x3 + 3x2
My answer:
Given that:
The oblique prism below has an isosceles right triangle base and the length of the base is x
=> the area of the base: 1/2 *x*x = 1/2[tex]x^{2}[/tex]
The vertical height of the prism is (x + 2)
=> The volume of the oblique prism is:
V = the base area * the vertical height
<=> V = 1/2[tex]x^{2}[/tex] (x + 2)
<=> V = [tex]1/2 x^{3}[/tex] + [tex]x^{2}[/tex]
We choose A
Answer:
A
Step-by-step explanation:
When calculating total gross pay, you should ___
A) use only your hourly wage
B)use your hourly wage and tips
C) use only your tips
D) use your hourly wage and tips minus any deductions
Final answer:
To calculate total gross pay, sum the hourly wage and tips earned. This sum represents the entire earnings before any deductions such as tax or social security are taken into account. Thus, option b is correct.
Explanation:
When calculating total gross pay, you should use your hourly wage and tips. The gross pay represents the total amount earned before any deductions, such as taxes or social security, are subtracted. To find the total gross pay, simply add the total amount of earned hourly wage to the amount received from tips.
For instance, if an employee receives $15 per hour and works for 8 hours and also earns $40 in tips, their gross pay for that day would be:
Hourly wage: $15/hour x 8 hours = $120
Tips: $40
So, the total gross pay would be $120 + $40 = $160 for that day.
So, option b is correct.
7. Given f(x) = x 3 (x +
5)2( 2 x-7)
a) What is the degree of this polynomial?
b) List the real zero's of f. Give the multiplicity of each zero.
c) Does the graph off touch or cross the x-axis at each zero?
d) Determine the 'end behavior' of this function. Find the monomial power function that the graph off
resembles for very large positive or negative values of x.
Answer:
a) 6.
b) 0 (multiplicity 3), -5 (multiplicity 2) and 7/2.
c) and (d) - See below.
Step-by-step explanation:
(a) f(x) = x^3(x + 5)^2 (2x - 7)
The highest degree of x (= x^3*x^2*x) = 3+2+1 = 6.
(b) The zeros are 0 ( from the x^3 = 0) multiplicity 3, from x + 5 = 0 we have -5 (multiplicity 2) and from 2x - 7 =0, 7/2.
(C) The graph just touches the x axis at (-5, 0) and pass through at (0,0) and (7/2, 0).
(d) The graph rises to the left for very large negative values of x and falls to the right at very large values of x.
At the extreme ends this graph resembles the graph of -x^3.
solve the inequality
|0.2x+6| <0.15
Answer:
- 30.75 < x < - 29.25
Step-by-step explanation:
Inequalities of the type | x | < a , always have solutions of the form
- a < x < a
Given
| 0.2x + 6 | < 0.15, then
- 0.15 < 0.2x + 6 < 0.15 ( subtract 6 from all 3 intervals )
- 6.15 < 0.2x < - 5.85 ( divide all intervals by 0.2 )
- 30.75 < x < - 29.25
To solve the inequality |0.2x+6| < 0.15, we split it into two separate inequalities and find that the solution for x is -30.75 < x < -29.25.
Explanation:To solve the inequality |0.2x+6| < 0.15, we first consider the absolute value function. This means we are looking for values of x that make 0.2x + 6 less than 0.15 and greater than -0.15. We split this into two separate inequalities:
0.2x + 6 < 0.150.2x + 6 > -0.15Solving the first inequality for x:
0.2x < 0.15 - 6
0.2x < -5.85
x < -5.85 / 0.2
x < -29.25
Solving the second inequality for x:
0.2x > -0.15 - 6
0.2x > -6.15
x > -6.15 / 0.2
x > -30.75
Therefore, combining the two inequalities, we find the solution for x is:
-30.75 < x < -29.25.
I NEED HELP, I NEED TO SHOW WORK
Answer: 9 over 12 is = 15 over x
Step-by-step explanation:
a town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number
Answer: P(t) = 5000(1.02)^5
Step-by-step explanation:
Determine the slope
Y=7/1x+10
Step-by-step explanation:
Which is larger, 3.2 x 10⁴ or 3.2 x 10⁵?
A. 3.2 x 104
B. 3.2 x 105
Answer:
3.2 x 10^5
Step-by-step explanation:
Scientific Notation
3.2 x 10^4 = 32000
3.2 x 10^5 = 320000
Final answer:
The number 3.2 x 10⁵ is larger than 3.2 x 10⁴ because it represents 320,000, compared to 32,000 which is represented by 3.2 x 10⁴. The exponent indicates the number of zeroes to follow the digit.
Explanation:
To determine which number is larger between 3.2 x 10⁴ and 3.2 x 10⁵, we need to understand the notation being used. In scientific notation, the number 10 raised to an exponent indicates how many places to move the decimal point. The larger the exponent, the larger the value.
For 3.2 x 10⁴, it means we have a 3.2 followed by 4 zeros, which is equal to 32,000. In contrast, 3.2 x 10⁵ means we have a 3.2 followed by 5 zeros, which is equal to 320,000. Clearly, 320,000 is larger than 32,000.
Thus, 3.2 x 10⁵ is larger than 3.2 x 10⁴.
5 seconds is what fraction of a minute?
Answer:
5 seconds is 1/12 of a minute
Step-by-step explanation:
60 seconds per minute so 5/60
5/60=1/12
5 seconds is 1/12 fraction of a minute.
Fraction is used to show the quantity of a part that makes up the whole number.
One minute is = 60seconds
Therefore 5 seconds= 5/60
= 1/12
This means that 1/12 of one minute is = 5 seconds.
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If a line is 10 feet long but needs to be enlarged 150%, how long will the new line be?
Answer:
23
Step-by-step explanation:
find 10 percent and times the rest
Mark has three 4 1/2 oz cans and five 8 1/4 oz cans. How many ounces of tomatoes does Mark need?
Answer:
54.74 ounces of tomatoes mark need.
Step-by-step explanation:
Given : Mark has three [tex]4\frac{1}{2}[/tex] oz cans and five [tex]8\frac{1}{4}[/tex] oz cans.
To find : How many ounces of tomatoes does Mark need?
Solution :
Mark has three [tex]4\frac{1}{2}[/tex] oz cans.
i.e. [tex]3\times 4\frac{1}{2}=3\times \frac{9}{2}=\frac{27}{2}[/tex]
Mark has five [tex]8\frac{1}{4}[/tex] oz cans.
i.e. [tex]5\times 8\frac{1}{4}=5\times \frac{33}{4}=\frac{165}{4}[/tex]
Total ounces of tomatoes does Mark need is
[tex]T=\frac{27}{2}+\frac{165}{4}[/tex]
[tex]T=\frac{54+165}{4}[/tex]
[tex]T=\frac{219}{4}[/tex]
[tex]T=54.75[/tex]
Therefore, 54.74 ounces of tomatoes mark need.
Which is an exponential decay function?
f(x) = 3/4(7/4)
f1x) = 2/3(4/5)*
f(x)= 3/3(8/7)
f(x) = 1/3(-9/2)
Answer: f(x) = 3/2 (8/7)-x
Step-by-step explanation:
What is the circumference of the base?
A)37.23
B)40.80
C)43.96
D)52.34
Answer:
43.96 or c
Step-by-step explanation: formula is d times pi and that gives you c hope this helps god bless
Side A B is parallel to Side D E in the map below.
Which proportion solves for the distance between D and E?
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction
StartFraction 6 Over x EndFraction = StartFraction 15 Over 9 EndFraction
StartFraction 9 Over 6 EndFraction = StartFraction 15 Over x EndFraction
StartFraction 6 Over 15 EndFraction = StartFraction 9 Over x EndFraction
Given:
Given that the side AB is parallel to side DE.
The length of AB is 15 feet.
The length of BC is 9 feet.
The length of CD is 6 feet.
The length of DE is x feet.
We need to determine the proportion that solves the distance between D and E.
Proportion:
The proportion that solves the distance between D and E can be determined by the similar triangle property.
Thus, we have;
[tex]\frac{BC}{CD}=\frac{AB}{DE}[/tex]
Substituting the values, we have;
[tex]\frac{9}{6}=\frac{15}{x}[/tex]
Thus, the proportion that solves the distance between D and E is [tex]\frac{9}{6}=\frac{15}{x}[/tex]
Answer:the answer is c
Step-by-step explanation:
Where did Cailou come from?
Answer:
its canadian
Step-by-step explanation:
do all quadratic equations have an axis of symmetry?
Answer:
Yes,Axis of Symmetry of a Parabola.The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a.
Step-by-step explanation:
Answer:yes
Step-by-step explanation:
When do you use the 1+ and 1-? in Exponential Functions
A.When there is a percent
B. All of the time
C. Never
Answer:
B. All of the time
at a currency exchange,11 U.S. dollars can be exchanged for 10Euros. How many Euros will you receive for 1 U.S. dollars?
Answer:
.92 euros
Step-by-step explanation:
Answer:
$0.90
Step-by-step explanation:
10:11 = 1:1.1
?:1
Euros = U.S Dollars - 0.10
0.90:1
the diameter of a circle is 12 in. Find the circumference to the nearest tenth
please helppp
Answer:
37.68in
Step-by-step explanation:
circumference = 2πr
r= radius = diameter/2 = 12/2 =6 in
C= 2πr = 2 x 3.14 x 6= 37.68in
Which equations have the same value of x as 5/6x+2/3=-9? Select three options.
Answer:
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
Step-by-step explanation:
Answer:
a b c
Step-by-step explanation:
Which model shows
64
−
−
√
3
=4
643=4
?
In the equation √64 - 3 = 4, we first take the square root of 64 to get 8, then subtract 3 to get 5, NOT 4. Thus, the given equation is not accurate.
Explanation:The model to represent the mathematical expression √64 - 3 = 4 is firstly taking the square root of 64 which gives 8, and then subtracting 3 from it to get 4. The complete equation is as follows:
Take square root of 64 which is 8.Then subtract 3 from 8, which equals 5 NOT 4, meaning the given equation is incorrect.
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Which expression is the as 400.902
Answer:
4*100+.9*0.1+.002*.001
Step-by-step explanation:
The student's question is unclear and lacks clarity. It is recommended that they provide more information or context so that an accurate explanation can be given.
Explanation:The question seems to be unclear. As a tutor, I would ask the student to clarify their question more specifically. The number '400.902' is indeed an expression, however, it's not clear what it's supposed to be equivalent to. Understanding the context can help provide a more accurate answer, as '400.902' could represent a multitude of things, such as a decimal, a fraction, a percentage or even part of a scientific notation. Without this information, I can't provide a reliable explanation or comparison.
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0.4(5x – 12) + 0.5x = 15.2
Look at the attached picture ⤴
Hope it will help u..
0.4(5x-12)+0.5x=15.2
We move all terms to the left:
0.4(5x-12)+0.5x-(15.2)=0
We add all the numbers together, and all the variables
0.5x+0.4(5x-12)-15.2=0
We multiply parentheses
0.5x+2x-4.8-15.2=0
We add all the numbers together, and all the variables
2.5x-20=0
We move all terms containing x to the left, all other terms to the right
2.5x=20
x=20/2.5
x=8
solve for x.
3x − 2(x + 3) = 5 − 2x
Answer:
3 2/3
Step-by-step explanation: