A vector is a quantity in physics that has both magnitude and direction. The component form of Vector CD minus vector EF is <5, 8, -4>.
What is a vector?A vector is a quantity in physics that has both magnitude and direction. It is often represented by an arrow whose length is proportionate to the magnitude of the quantity and whose direction is the same as that of the quantity.
The value of the Vector CD can be written as,
[tex]|\vec{CD}| = (0+7)\hat i+(7-2)\hat j+(3-8)\hat k = 7\hat i+5\hat j-5\hat k[/tex]
The value of the Vector EF can be written as,
[tex]|\vec{EF}| = (6-4)\hat i+(-2-(-1))\hat j+(-3-(-2))\hat k = 2\hat i-3\hat j-5\hat k[/tex]
Now, the component form of Vector CD minus vector EF can be written as,
[tex]\vec{CD} - \vec{EF} = < (7-2) , (5-(-3)) , (-5-(-1)) > = < 5,8,-4 >[/tex]
Hence, the component form of Vector CD minus vector EF is <5, 8, -4>.
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pls help i give 38 points
I NEED HELP SOON! THESE ARE DUE SOON!
Answer:
Q2: J. all real numbers.
Q4: [tex]f(3)=-20[/tex]
Q15: [tex]y=-3x+5[/tex]
Step-by-step explanation:
Q2: J. All real numbers.
Range: It can be [tex]y\geq 1[/tex].
It can't be [tex]y\geq 2[/tex].
Domain: It can't be [tex]x\geq 1[/tex] because it is going from (-∞,+∞)
Q4:
[tex]f(x)=-2x^2+x-5,f(3)=?[/tex]
Plugin x with 3 into the equation.
[tex]f(3)=-2(3)^2+(3)-5\\f(3)=-2*9+3-5\\f(3)=-18+3-5=-20\\f(3)=-20[/tex]
Q15: point-slope form.
[tex]y-(y_1)=m(x-x_0)[/tex], plugin [tex](2,-1)=(x_0,y_0)[/tex] and m=-3
[tex]y-(-1)=-3(x-(2))\\y+1=-3(x-2)\\y+1=-3x+6\\y=-3x+5[/tex]
The number of children's movie tickets sold over a period of a week is
shown below.
18, 23, 9, 16, 30, 16, 7
What is the mean number of movie tickets sold during the week?
A. 17
B. 21
C. 18
D. 16
Answer:
A. 17
Step-by-step explanation:
The "mean" is the same as an average.
To find the mean, add all the numbers.
Then divide that sum by the total numbers you added.
18+23+9+16+30+16+7=119.
119/7= 17. (We divided by 7 because we added 7 numbers)
Hope this helps!
What is the volume of this figure?
6) Find the approximate perimeter of the following shape. Use 3.14 for pi
Answer:
where is the shape ???????
Which linear inequality represents the solution set graphed?
Answer:
Your Answer is D.
Step-by-step explanation:
There isn't much to explain but look at the graph.
The slope of m = rise/run.
m = 1/2
b = -3/2
y = mx + b
Miquel runs 5 days a week. He runs 2 7/10 miles each day that he runs. What is the total number of miles Miguel runs each week?
Answer:
13.5
Step-by-step explanation:
If he runs five times a week and his route is 2 7/10 then you do 5x2 7/10
A rental car company charges $72.37 per day to rent a car and $0.06 for every mile
driven. Colton wants to rent a car, knowing that:
• He plans to drive 275 miles.
• He has at most $450 to spend.
Answer:
5.99 days.
Step-by-step explanation:
If you are asking how many days he can rent the car then this is the correct answer.
So first multiply 275 x .06 to get how much money he will spent on the mileage. Which is $16.50. Then subtract that from $450 which is $433.50 and divided by $72.37.
Find the area of the shaded regions
your answer would be 254 I just did it and I got it right ✨
What is the value of x in |-6|=x
The amount of time a certain brand of light bulb lasts is normally distributed with a
mean of 1400 hours and a standard deviation of 50 hours. Using the empirical rule,
determine what interval of hours represents the lifespan of the middle 68% of light
bulbs.
The interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.
What is empirical rule?According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
Here, we had where mean of distribution of X is \mu and standard deviation from mean of distribution of X is \sigma
The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 50 hours. Thus,
[tex]\mu=1300\\\sigma=90[/tex]
Using the empirical rule, the interval of hours represents the lifespan of the middle 68% of light bulbs is,
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(1300- 90 < X < 1300+ 90) = 68\%\\P(1210 < X < 1390) = 68\%[/tex]
Thus, the interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.
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Find the perimeter of the figure. Round to the nearest hundredth and show work.
Answer:
38 cm
Step-by-step explanation:
The perimeter of the figure is the sum of the lengths of all its sides.
We have two unknown length, so let's find their lengths first.
x= 10 -6= 4 cm
y= 9 -2= 7cm
Let's add all the lengths together to find the perimeter:
Perimeter
= 9 +10 +2 +6 +7 +4
= 38 cm
How many kilograms in 1 1/2 pounds?
Answer:
67.5 kgs.
Step-by-step explanation:
1 pound = 0.45 kg
1 1/2 pounds = 0.45 + 1/2 * 45
= 67.5 kgs.
A box contains 3 orange pencils, 9 yellow pencils, and 5 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.
The probability that the first pencil is green and the second pencil is yellow is 0.16.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the first pencil is green and the second pencil is yellow = (number of green pencils / total number of pencils) x (number of yellow pencils / total number of pencils)
5/17 x 9/17 = 0.16
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which angle is conterminal with a 645 degree angle
a. an angle measuring 75 degrees
b. an angle measuring 265 degrees
c. an angle measuring 345 degrees
d. an angle measuring 285 degrees
Answer:
D. An angle measuring 285 degrees
Step-by-step explanation:
An angle that is coterminal is congruent to the other angle whether negative or positive or more than 360.
An angle that is 645 degrees can be broken down into 360 + 285.
Since 360 is one revolution the angle would finish with 285 degrees.
Therefore the coterminal angle to 645 is 285.
Based on the graph below, how would you describe the curve?
A. The curve is a linear function
B. The curve is a "many-to-one" function.
C. The curve is a "one-to-one" function.
D. The curve is not a function.
Based on the curve ; The graph is:
B. The curve is a many-to-one function.
Step-by-step explanation:Function--
A function is a relation in which each element is mapped to a single element i.e. no element is mapped to two different elements.
Also, the graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to the y-axis should intersect the graph exactly once.
and one-to-one function--
A one-to-one function is such that no two elements have the same image i.e. any line passing through the co-domain and parallel to the x-axis should intersect the graph at most once.
The graph passes the vertical line test and hence is a function.Also, the graph of a linear function is a straight line.Hence, by looking at the graph we see that the graph is not a straight line.
Hence, it is not a linear function.
Also, it does not passes the horizontal line test (since somewhere in the interval (2,3) the same value is obtained many times )and hence it is not a one-to-one functionHence, the correct answer is:
Option: B
Based on the graph how many distinct real number solutions does the equation x^3-3x^2+4=0 have
Answer:
2 solutions
Step-by-step explanation:
In order to answer a question "based on the graph," we need to have a graph of the equation. A graph provided by a graphing calculator is attached.
The cubic intersects the x-axis at two distinct points.
There are two (2) distinct real solution to the equation. (x = -1, x = 2).
enter a negative number that has an absolute value greater than 10
Answer:
-11
Step-by-step explanation:
Joe wants to lay tile for his bathroom floor. His bathroom is 10 1/2 feet by 8 1/4 feet. What is the area of the floor?
Answer:
86 5/8 square feet
Step-by-step explanation:
[tex]10 \frac{1}{2} \times 8\frac{1}{4} = \frac{21}{2} \times \frac{33}{4} = \frac{693}{8} = 86 \frac{5}{8} [/tex]
Match the median to the data set.
101, 108, 98, 105, 94. 106
median = 103
98, 100, 103,107, 108, 112
-a
median 105
93, 96, 98, 101, 104
-0
median = 98
Answer:
First one: median= 98
Second one: median= 105
Thrid one: median= 103
Step-by-step explanation:
The median is the middle number.
PLEASE HELP ME! If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁? (I need the steps too please).
Answer:
[tex]\displaystyle a_1 = 44[/tex]
Step-by-step explanation:
Recall the direct formula for an arithmetic sequence:
[tex]\displaystyle a_n = a_1 + d(n-1)[/tex]
Where d is the common difference.
Therefore, we can write the following two equations:
[tex]\displaystyle \left \{ {a_4 = 107 = a_1 + d(4-1)\atop {a_8 = 191 = a_1 + d(8-1)}} \right.[/tex]
Solve the system. Simplifying yields:
[tex]\displaystyle 107 = a_1 + 3d\text{ and } 191 = a_1 + 7d[/tex]
Subtracting the two equations into each other yields:
[tex]\displaystyle \begin{aligned} (191) - (107) & = (a_1 + 7d) - (a_1 + 3d) \\ \\ 84 & = 4d \\ \\ d & = 21 \end{aligned}[/tex]
Using either equation, solve for the initial term:
[tex]\displaystyle \begin{aligned} 107 & = a_1 + 3(21) \\ \\ a_1 & = 107-63 \\ \\ & = 44\end{aligned}[/tex]
In conclusion, the initial term is 44.
Answer:
[tex]\huge\boxed{\bf\:a_{1} = 44}[/tex]
Step-by-step explanation:
In the given arithmetic series,
[tex]a_{4} = 107[/tex][tex]a_{8} = 191[/tex][tex]a_{1} = ?[/tex]We know that,
[tex]\boxed{a_{n} = a + (n - 1)d}[/tex]
Therefore,
[tex]a_{4} = a + 3d = 107 -----(1)\\a_{8} = a + 7d = 191 -----(2)[/tex]
By solving the two equations (1) & (2)....
[tex]\:\:\:\:a + 7d = 191 \\-\underline{a + 3d = 107 }\\ \underline{\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:4d = 84\:\:\:\:\:\:\:\:}}\\\\\\\\4d = 84\\d = 84 \div 4\\\boxed{d = 21}[/tex]
Now, we have the value of the common difference (d). To find [tex]a_{1}[/tex] or a, let's substitute the value of 'd' in (1).
[tex]a + 3d =107\\a + 3(21)=107\\a + 63 = 107\\a = 107 - 63\\\boxed{\bf\:a_{1} = 44}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
17) Find sine and cot
Answer:
79/156
Step-by-step explanation:
we know that cosx is the adjacent side over the hypotenuse.
hence, we can find the opposite side using the pythagorean theorem.
sqrt(13^2 - 5^2)
therefore, the opposite side is 12
opposite: 12
adjacent: 5
hypotenuse: 13
not that cot is adjacent over opposite while sin is opposite over hypotenuse.
So,
12/13 - 5/12
the answer is 79/156
Pleas I need help now
Answer:
addition, subtraction, multiplication
Step-by-step explanation:
If you add two polynomials, the result is a polynomial. If you subtract two polynomials, the result is a polynomial. If you multiply two polynomials, the result is a polynomial.
The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acre = 43,560 ft?)
у
5001
E
F
F
х
lo
-500
500
G
-500
H
The farmer needs approximately
corn plants.
Since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
How to determine the area of a trapezium?The trapezium is a 2 -dimensional shape consisting of a triangle and a square.
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Area = 0.5(500 + 900) * 800
Area = 700 * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Required acre = 560000/43560
Required acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
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The graph shown here is the graph of which of the following rational
functions?
Answer:
b
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
Step-by-step explanation:
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Answer:
So this is what hello means :):):):):):):)
Step-by-step explanation:
Assume that the weights of ripe watermelons grown at a particular farm are normally distributed with a mean of 30 pounds and a standard deviation of 1.9 pounds. If the farm produces 400 watermelons, how many will weigh less than 27.87 pounds?
We know that,
[tex] \rightarrow \: z = \frac{x - \mu}{\sigma} \\ [/tex]
z = standard scorex = measuring valueμ = meanσ =standard derivationinserting the given values in the formula
[tex]\rightarrow \: z = \frac{27.87 - 30}{1.9} \\\rightarrow \: z = - 1.121[/tex]
Area that's left to z = -1.121
Area that's left to -1.121 = 0.1311
= 13.11%
Hence ,
13.11% of the watermelons weigh less than 27.87 pounds
To find the number of watermelons,
We'll find 13.11% of 400
= 13.11% x 400
= 13.11/100 x 400
= 52.44
hence , approx 52 watermelons would be lesser than 27.87 pounds
Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line?
A) y - F = -2(x - G)y
B) y + F = 2(x + G)
C) y - G = -1/2(x - F)
D) y - G = -1/2(x + F)
The equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex]. Option C is the correct answer.
The equation of the line is [tex]y-y_1=m(x-x_1)[/tex] where, [tex]m[/tex] is the slope of the line and [tex](x_1,y_1)[/tex] is the point through which it is passing.
How to determine the equation of a line?
A line is drawn perpendicular to the line shown in the image. The perpendicular line passes through the coordinate point [tex](F,G)[/tex].
The slope of the line from the graph is-
[tex]m=\dfrac{y-intercept}{x-intercept}\\=2[/tex]
Therefore, the slope of the perpendicular line is [tex]\dfrac{-1}{2}[/tex].
Also, it is being given that Leo's line is passing through the coordinate point [tex](F,G)[/tex].
So, the equation of the Leo's line is-
[tex]y-G=\dfrac{-1}{2}(x-F)[/tex]
Thus, the equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex].
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describe a set of transformatios that would map red triangle to the blue triangle
The set of transformations that would map the red triangle to the blue triangle are translation by 2 units up and 4 units left
How to determine the set of transformations?From the graph, we have the following highlights:
The red triangle is at the top of the blue triangle by 2 unitsThe red triangle is at the left of the blue triangle by 4 unitsThis means that the transformation is 2 units up and 4 units left
Hence, the set of transformations that would map the red triangle to the blue triangle are translation by 2 units up and 4 units left
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