Answers
We know that two vectors are ortogonal if and only if:
[tex]\vec{v}\cdot\vec{w}=0[/tex]where
[tex]\vec{v}\cdot\vec{w}=v_1w_1+v_2w_2[/tex]is the dot product between the vectors.
In this case we have the vectors:
[tex]\begin{gathered} \vec{a}=\langle-4,-3\rangle \\ \vec{b}=\langle-1,k\rangle \end{gathered}[/tex]the dot product between them is:
[tex]\begin{gathered} \vec{a}\cdot\vec{b}=(-4)(-1)+(-3)(k) \\ =4-3k \end{gathered}[/tex]and we want them to be ortogonal, so we equate the dot product to zero and solve the equation for k:
[tex]\begin{gathered} 4-3k=0 \\ 4=3k \\ k=\frac{4}{3} \end{gathered}[/tex]Therefore, for the two vector to be ortogonal k has to be 4/3.
Related Questions
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x.
(x ^4 - 3x^3 + 3x^2 - 3x + 6) / (x - 2)
Answers
SOLUTION
We want to perform the following division using synthetic division
[tex]\frac{x^4-3x^3+3x^2-3x+6}{x-2}[/tex]This becomes
First we write the problem in a division format as shown below
Next take the following step to perform the division
Now, we have completed the table and we obtained the following coefficients, 1, -1, 1, -1, 4
Note that the first four ( 1, -1, 1, -1) are coefficients of the quotient, while the last one (4) is the coefficient of the remainder.
Hence the quotient is
[tex]x^3-x^2+x-1[/tex]And the remainder is 4.
Hence
[tex]\frac{x^4-3x^3+3x^2-3x+6}{x-2}=x^3-x^2+x-1+\frac{4}{x-2}[/tex]Question 3 4.5 pts At the honor roll party, students had the choice of cheese or pepperoni pizza and coke or sprite. Of the 125 students that made the honor roll 64% had cheese pizza. There were 48 students that had cheese pizza and a coke. 5 more students chose to have a Coke rather than Sprite. Complete the table below.
Answers
The table would look like this;
We are told that Of the 125 students that made the honor roll 64% had cheese pizza.
64% of 125 is 80 students, therefore, 80 students in total had cheese pizza.
Let's fill that in.
We now know that those who had pepperoni pizza are 125 - 80 = 45 in number.
There were 48 students that had cheese pizza and a coke, let's fill that in too, we have.
This means that the number of students that had a cheese and sprite is 80 - 48 = 32 students.
We are also told that 5 more students chose to have a coke than a sprite.
Let the total number that chose coke be x.
Then the total who chose sprite would be x - 5.
But these total must add up to 125.
So;
[tex]\begin{gathered} x+x-5=125 \\ 2x-5=125 \\ 2x=130 \\ x=\frac{130}{2}=65 \\ x-5\text{ = 60} \end{gathered}[/tex]Therefore, 65 students took coke in total and 60 took sprite, let's fill that in too.
We can now fill in the pepperoni column.
For pepperoni and coke, we subtract 48 from 65 to obtain 17
For pepperoni and sprite, we subtract 32 from 60 to obtain 28
ii. The joint relative frequency of the students who had a sprite and pepperoni pizza.
From the table, the joint relative frequency of those who had a sprite and a pepperoni pizza is
[tex]\begin{gathered} \frac{28}{45} \\ \end{gathered}[/tex]i.e 28/45 or 0.6 of those who had pepperoni pizza, took sprite.
Find the volume of the figure round to the nearest 10th if needed
Answers
Given: A triangular prism with base 6ft,height of triangle is 8 ft and height of prism is 12ft
Find : the volume of the prism.
Explanation: the volume of the triangular prism is equal to area of the base triangle times height of the prism.
[tex]\begin{gathered} =\frac{(8\times6)\times12}{2} \\ =288\text{ ft}^3 \end{gathered}[/tex]final answer: the volume of the rectangular prism is
[tex]288ft^3[/tex]What’s the correct answer answer asap for brainlist
Answers
Answer:
your answer is B
Step-by-step explanation:
Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire
which ordered pair is a solution of the equation 7x−5=4y−6?PLEASE HURRY THIS IS DUE NOW A. only (2,4)B. only (3,6)C. both A and BD. neither A or B
Answers
To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:
1. Case: Ordered pair (2, 4):
[tex]7\cdot(2)-5=4\cdot(4)-6\Rightarrow14-5=16-6\Rightarrow9\ne10[/tex]This ordered pair is NOT a solution.
2. Case: Ordered pair (3, 6):
[tex]7\cdot(3)-5=4\cdot(6)-6\Rightarrow21-5=24-6\Rightarrow16\ne18[/tex]This ordered pair is NOT a solution.
Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).
is y=10 a solution to the inequality y + 6 < 14
Answers
The inequality given is
[tex]y+6<14[/tex]Collecting like terms we will have
[tex]\begin{gathered} y+6<14 \\ y<14-6 \\ y<8 \end{gathered}[/tex]With the above solution, we can conclude that y=10 is not a solution to the inequality because the values of y are less than 8
Hence, The answer is NO
David is laying tiles on his kitchen floor. His kitchen measures 16 feet by 20 feet Each tile is a square that measures 2 feet by 2 feet (a) What is the area of his kitchen floor? (b) How many tiles will David need to purchase to cover the floor? One Tile 2 ft 2 ft
Answers
(a) To find the area of the kitchen floor, we just have to multiply
[tex]A=16ft\times20ft=320ft^2[/tex](b) To find the number of tiles needed, we have to find the area of each tile, which is
[tex]A_{\text{tile}}=2ft^{}\times2ft^{}=4ft^2[/tex]Then, we divide the total area of the kitchen floor by the area of each tile.
[tex]n=\frac{320ft^2}{4ft^2}=80[/tex]Hence, David will need 80 tiles to cover the floor.
A. Side a is 24 inches longand side bis 21 inches longB. Side a is 63 inches long and side bis 54 inches long.C. Side a is 18 inches long and side bis 15 inches long.D. Side a is 7 inches long and side bis 6 inches long.
Answers
Since both drawings are similar and have a scale factor, we can say that all sides keep the same scamle factor, if the scale drawing is in a proportion of 3:1 means that all of its sides is 3 times the real objects sides.
write this as equations
[tex]\begin{gathered} 3\cdot a=21in \\ 3\cdot b=18in \end{gathered}[/tex]to find the respetive values for a and b we divide the sides by 3
[tex]\begin{gathered} a=\frac{21in}{3}=7in \\ b=\frac{18in}{3}=6in \end{gathered}[/tex]The correct answer is D.
Gabrielle is 8 years older than Mikhail. The sum of their ages is 104. What is Mikhail's age?
Answers
Let x represent Mikhail's age.
Since Gabrielle is 8 years older than Mikhail, it means that Gabrielle's age is
x + 8
If the sum of their ages is 104, it means that
x + x + 8 = 104
2x = 104 - 8
2x = 96
x = 96/2
x = 48
Mikhail's age is 48
If tan A = ã and tan B=16calculate and simplify the following:?tan(A - B) = +
Answers
SOLUTION
[tex]\begin{gathered} In\text{ Trigonometry} \\ \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\text{ tan B}}_{} \end{gathered}[/tex]Given:
[tex]\begin{gathered} \tan \text{ A= }\frac{5}{6} \\ \tan \text{ B= }\frac{1}{6} \end{gathered}[/tex]Now substitute these given into the expression above:
[tex]\tan (A-B)=\frac{\frac{5}{6}-\frac{1}{6}}{1+(\frac{5}{6}\times\frac{1}{6})}[/tex]Simplifying further:
[tex]=\frac{\frac{2}{3}}{1+\frac{5}{36}}[/tex][tex]\begin{gathered} =\frac{\frac{2}{3}}{\frac{41}{36}} \\ =\frac{2}{3}\times\frac{36}{41} \\ =\frac{72}{123} \\ =\frac{24}{41} \end{gathered}[/tex]The answer therefore is:
[tex]\frac{24}{41}[/tex]Need help asap !! Thank you
Answers
The coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.
What is a linear equation?A connection between a set of variables results in a linear system when presented on a graph. The variable will have a degree of only one.
The linear equation is given below
- 2x - 3y = 6
For the x-intercept, the value of the y will the zero. Then we have
- 2x - 3(0) = 6
-2x = 6
x = -3
The x-intercept is at (-3, 0).
For the y-intercept, the value of the x will the zero. Then we have
- 2(0) - 3y = 6
-3y = 6
x = -2
The y-intercept is at (0, -2).
Thus, the coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.
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14|x + 14| + 13 =-69
Solve for x
Answers
Answer: No real solutions
Step-by-step explanation:
[tex]14|x+14|+13=-69\\\\14|x+14|=-82\\\\|x+14|=-82/14[/tex]
Since absolute value is always non-negative, there are no real solutions.
Hallum hardware created flyers to advertise a carpet sale . A portion of the flyer is shown below. Based on the chart, which statement describes the relationship between area and the cost of carpet?
Answers
The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.
Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.
Ratio = cost / area
750 / 500 = 1.50
1500 / 1000 = 1.50
2,250 / 1500 = 1.50
3000 / 2000 = 1.50
Since the ratios are constant, the relationship is proportional.
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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.
What is the volume of this cone round to the nearest hundreth
Answers
We have to calculate the volume of the cone.
The volume of the cone is 1/3 of the area of the base times the height.
As the base has diameter D = 16 yd, we can calculate the area of the base as:
[tex]\begin{gathered} A_b=\frac{\pi D^2}{4} \\ A_b\approx\frac{3.14*16^2}{4} \\ A_b\approx\frac{3.14*256}{4} \\ A_b\approx200.96 \end{gathered}[/tex]Knowing the height is h = 14 yd, we then can calculate the volume as:
[tex]\begin{gathered} V=\frac{1}{3}A_bh \\ V=\frac{1}{3}*200.96*14 \\ V\approx937.81 \end{gathered}[/tex]Answer: the volume is 937.81 cubic yards.
The coordinates of point F are (8,4) and the coordinates of point G are (-4,9). What is the slope of the line that is perpendicular to line FG. Enter the answer as a simplified fraction.
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial values of y
x2 and x1 are the final and initial values of x
From the given points ,
x1 = 8, y1 = 4
x2 = - 4, y2 = 9
m = (9 - 4)/(- 4 - 8) = 5/- 12 = - 5/12
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. The negative reciprocal of - 5/12 is 12/5
Thus, the slope of the perpendicular to line FG is 12/5
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
[tex]x^2+y^2=400[/tex]
a) find dy/dt given x=16, y=12 and dy/dt=7
b) find dx/dt given x=16, y=12, and dy/dt =-3
Answers
For the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.
What are differentiable functions?
If the derivative f '(a) exists at each point in its domain, then f(x) is said to be differentiable at the point x = a. Given two functions g and h, where y = g(u) and u = h(x). A function is referred to as a composite function if its definition is y = g [h (x)] or goh(x). Therefore, fog is also differentiable and (fog)'(x) = f'(g(x) if g (x) and h (x) are two differentiable functions. g’(x).
Given, the equation for x and y is: x² + y² = 400
Differentiating the equation above with respect to t using chain rule, we have: (2x)(dx/dt) + (2y)(dy/dt) = 0 -(i)
Rearranging (i) for dy/dt, we have: dy/dt = (-x/y)(dx/dt) - (ii)
Again, rearranging (i) for dx/dt, we have: dx/dt = (-y/x)(dy/dt) - (iii)
For (a), x = 16, y = 12 and dx/dt = 7, thus dy/dt using (ii) can be written as:
dy/dt = (-x/y)(dx/dt) = (-16/12)*7 = (-4/3)*7 = (-28)/3
For (b), x = 16, y = 12 and dy/dt = -3, thus dx/dt using (iii) can be written as:
dx/dt = (-y/x)(dy/dt) = (-12/16)*(-3) = (4/(-3))*(-3) = 4
Therefore, for the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.
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Ninety percent of a large field is cleared for planting. Of the cleared land, 50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?*
Answers
For the given question, let the size of the original field = x
Ninety percent of a large field is cleared for planting
So, the size of the cleared land = 90% of x = 0.9x
50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants.
So, the size of the land planted with blueberry plants and strawberry plants =
[tex]0.5\cdot0.9x+0.4\cdot0.9x=0.45x+0.36x=0.81x[/tex]The remaining will be = 0.9x - 0.81x = 0.09x
Given: the remaining 360 acres of cleared land is planted with gooseberry plants
so,
[tex]0.09x=360[/tex]divide both sides by (0.09) to find x:
[tex]x=\frac{360}{0.09}=4,000[/tex]So, the answer will be:
The size of the original field = 4,000 acres
Which of these describes the transformation of triangle ABC shown below?A) reflection across the x-axisB) reflection across the y-axisC) reflection across the line y=xD) translation
Answers
From the figure, we have the coordinates of the vertices:
ABC ==> A(2, 1), B(5, 1), C(1, 5)
A'B'C' ==> A'(-2, 1), B'(-5, 1), C(-1, 5)
Let's determine the type of transformation that occured here.
Apply the rules of rotation.
For a rotation acorss the y-axis, only the x-coordinates of the points will change to the opposite. i.e from negative to positive or from positive to negative.
For a rotation across the y-axis, we have:
(x, y) ==> (-x, y)
From the given graph, we can see that the only the x-coordinates changed from positive to negative.
Therefore, the transformation that occured here is the reflection across the y-axis.
ANSWER:
B) Reflection across the y-axis.
In a cricket match, you have a squad of 15 players and you need to select 11 for a game. The two opening batsmans are fixed and the rest of the players are flexible. How many batting orders are possible for the game?
Answers
The number of batting orders that are possible for the game is 1365 orders.
What are combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
This will be:
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
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Math help!!! Only a tutor that can give me answers to 9 and 10!!
Answers
9.
Alternative interior angles are congruent
Therefore;
5x + 42 = 18x -12
collect like term
5x - 18x = -12 - 42
-13 x = -54
Divide both-side of the equation by -13
x=4.15
distance of (-5,-3) and (-9,4)
Answers
Answer:11
Step-by-step explanation:
A bank features a savings account that has an annual percentage rate of 4.8 % with interest compounded monthly. Umbrosia deposits $6,500 into the account.
How much money will Umbrosia have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?
Answers
S(8)=3500(1+(.047/4))^32
S(8)=$5086.40 in the account after 8 years.
a)The relative growth rate is .25, or 25%
b)at t=0, the population is 955e^.25(0)=955
c)at t=5; the population is 955*e^.25(5)=955*3.49=3333.28 bacterium.
Which expression allows us to find the discount amount of ANY price thatis discounted 25%?*
Answers
the expression of the discount amount is
[tex]discountamount=x\times\frac{25}{100}[/tex]here x is the price
and the discount is 25%
What is the probability that a student does not play on a sports team?
Answers
Answer:
P = 0.5
Explanation:
The probability can be calculated as the division of the number of students that does not play on sports team by the total number of students.
Taking into account the table, there is a total of 20 students and from those 10 does not play on a sports team. Therefore, the probability is:
P = 10/20 = 0.5
create a model for (x + 7)(2x - 6). What is the product
Answers
The oil tank in your car is leaking at a rate of 1.2 oz per mile driven you drove 15 miles how many cups of oil did your car leak
Answers
we know that
The unit rate is equal to
1.2 oz per mile
so
To obtain the number of ounces
multiply the unit rate by the number of miles driven
1.2*(15)=18 oz
step 2
Convert ounces to cups
Remember that
1 oz=0.125 cups
so
18 oz=18*0.125=2.25 cups
therefo
Cisco Enterprises in Ontario purchased the following in a single month all-inclusive of taxes:
16,000 units of network routers at $79.25 each
Answers
Answer:
1268000
Step-by-step explanation:
16000x79.25=1268000
Write expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
Answers
Solution
Note: Laws Of Logarithm To Use
[tex]\begin{gathered} (1).\text{ }log_a(M)-log_a(N)=log_a(\frac{M}{N}) \\ \\ (2).\text{ }log_a(b^n)=nlog_a(b) \end{gathered}[/tex]From the question, we have
[tex]\begin{gathered} log_3(18)-log_3(2) \\ \\ log_3(\frac{18}{2}) \\ \\ log_3(9)\text{ } \\ \\ The\text{ above expression is single logarithm} \end{gathered}[/tex]To evaluate, we have
[tex]\begin{gathered} log_3(9)=log_3(3^2) \\ \\ log_3(9)=2log_3(3) \\ \\ log_3(9)=2(1) \\ \\ log_3(9)=2 \end{gathered}[/tex]The answer is
[tex]2[/tex]The perimeter of a rectangle is 48 centimeters. The relationship between the length, the width, and the perimeter of the rectangle can be described with the equation 2⋅length+2⋅width=48. Find the length, in centimeters, if the width is w centimeters
Answers
Using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.
Recall:
Perimeter of a rectangle (P) = 2(L + W) (relationship between the width, length and perimeter)
Given:
Width (W) = 3.6 cm
Perimeter (P) = 48 cm
Length (L) = ?
Using the relationship between the dimension of a rectangle and its perimeter, the following equation would be derived:
48 = 2(L + 3.6)
Solve for the value of L
48 = 2L + 7.2
Subtract 7.2 from each side
48 - 7.2 = 2L
40.8 = 2L
Divide both sides by 2
20.4 = L
L = 20.4 cm
Therefore, using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.
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Find the perimeter of the following quadrilateral.The bottom side measures 2 ft.
Answers
The perimeter of a quadrilateral is given by the sum of all the sides.
In order to add mixed numbers, let's rewrite them as a sum of the integer part and the fraction part.
So we have:
[tex]\begin{gathered} P=1\frac{5}{12}+3\frac{3}{4}+2\frac{1}{6}+2 \\ P=1+\frac{5}{12}+3+\frac{3}{4}+2+\frac{1}{6}+2 \\ P=(1+3+2+2)+(\frac{5}{12}+\frac{9}{12}+\frac{2}{12}) \\ P=8+\frac{16}{12} \\ P=8+1+\frac{4}{12} \\ P=9+\frac{1}{3} \\ P=9\frac{1}{3}\text{ ft} \end{gathered}[/tex]Therefore the perimeter is 9 1/3 ft.