1) (-5, 5), 2) (7, -5), 3) (- 3, 28), 4) (- 12, 0), 5) 10, 6) 14, 7) (- 9, 9), 8) [tex]\sqrt{26}[/tex], 9) - 2, 10) 10, 11) [tex]\left(\frac{\sqrt{26}}{26}, \frac{5\sqrt{26}}{26}\right)[/tex], 12) [tex]\left(\frac{21\sqrt{10}}{10}, -\frac{7\sqrt{10}}{10} \right)[/tex], 13) (0, 7), 14) [tex](- 3\sqrt{3}, - 3)[/tex], 15) The vectors [tex]\vec a[/tex] and [tex]\vec b[/tex] are orthogonal, 16) [tex]7\sqrt{2}[/tex], [tex]135^{\circ}[/tex], 17) [tex]17[/tex], [tex]137^{\circ}[/tex], 18) [tex]12[/tex], [tex]240^{\circ}[/tex], 19) [tex](19.700, 15.392)[/tex]
How to analyze vectors
Vectors are elements that are charaterized for having a magnitude and a direction, whereas scalar are only characterized by magnitude. In this question we must apply different vector properties to obtain the corresponding results.
The first two exercises consist in calculating each vector based on its initial and terminal points, whose results are obtained below by sum of vectors with initial points at origin:
1) (-1, 3) - (4, -2) = (-5, 5)
2) (2, -6) - (- 5, -1) = (7, -5)
The following eight exercises are resolved by applying the operations of addition of vectors and multiplication of a vector by a scalar, and the definition of norm and dot product as well:
3) 3 · (3, 4) + 2 · (- 6, 8) = (9, 12) + (- 12, 16) = (- 3, 28)
4) (- 6, 8) - 2 · (3, 4) = (- 12, 0)
5) [tex]\| \vec v\| = \sqrt{(-6)^{2}+8^{2}}[/tex] = 10
6) [tex]\vec u \,\bullet \,\vec v =[/tex] 3 · (- 6) + 4 · 8 = 14
7) 3 · [(0, 2) - (3, -1)] = 3 · (- 3, 3) = (- 9, 9)
8) [tex]\|\vec v\| = \sqrt{1^{2}+5^{2}} = \sqrt{26}[/tex]
9) [tex]\vec u \,\bullet \,\vec v =[/tex] 3 · 1 + (- 1) · 5 = - 2
10) [tex]\vec w \,\bullet \, \vec v =[/tex] 0 · 1 + 5 · 2 = 10
11) The unit vector is obtained by dividing the vector by its magnitude:
[tex]\vec u_{v} = \frac{1}{\sqrt{26}}\cdot \left(1, 5\right) = \left(\frac{1}{\sqrt{26}}, \frac{5}{\sqrt{26}} \right) = \left(\frac{\sqrt{26}}{26}, \frac{5\sqrt{26}}{26}\right)[/tex]
12) The vector is equal to the product of the magnitude and its unit vector:
[tex]\vec r = 7 \cdot \frac{\vec u}{\|\vec u\|}[/tex]
[tex]\vec r = \frac{7}{\sqrt{10}}\cdot (3, -1) = \left(\frac{21}{\sqrt{10}}, -\frac{7}{\sqrt{10}} \right) = \left(\frac{21\sqrt{10}}{10}, -\frac{7\sqrt{10}}{10} \right)[/tex]
13) and 14) The vector is the product of the magnitude and the directional vector:
13) [tex]\vec r = 7 \cdot (\cos 90^{\circ}, \sin 90^{\circ}) = (0, 7)[/tex]
14) [tex]\vec r = 6\cdot (\cos 210^{\circ}, \sin 210^{\circ}) = (- 3\sqrt{3}, - 3)[/tex]
15) Two vectors are orthogonal if and only if their dot product is zero:
[tex](3.2, 4.8) \,\bullet\,(-3, 2) =[/tex] 3.2 · (- 3) + 4.8 · 2 = 0
The vectors [tex]\vec a[/tex] and [tex]\vec b[/tex] are orthogonal.
The next three exercises are resolved by definitions of norm and direction:
16) [tex]\|\vec v\| = \sqrt{(-7)^{2}+7^{2}} = 7\sqrt{2}[/tex], [tex]\theta = 135^{\circ}[/tex]
17) [tex]\|\vec v\| = 17[/tex], [tex]\theta = 137^{\circ}[/tex]
18) [tex]\|\vec q\| = 12[/tex], [tex]\theta = 240^{\circ}[/tex]
The last exercise consist in defining the vector as a product of magnitude and direction vector:
19) [tex]\vec v = 25\cdot (\cos 38^{\circ}, \sin 38^{\circ}) = (19.700, 15.392)[/tex]
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Write the equation of a line in point-slope form that passes through the point (4, -2) and has a slope of 5.
classify 8x³-9x the polynominal by its degree and number of term
Answer:
Degree: cubic
Number of terms: binomial
Step-by-step explanation:
Look at the exponents to find the degree. Biggest exponent is 3, third power, that's a cubic, like a cube.. 3D.
There's a plus separating the two terms...Two terms-that's the "bi-" in binomial, like a bicycle or bifocals or binational. The prefix "bi-" means two.
If x= m + 2, find the value of m from the 3m-4/2 - 4x-3/6 equation = 3.
Answer:
Step-by-step explanation:
3m-4/2-4 (m+2 )-3/6=3
3m-4/2-4m-8-3/6=3
-m-3/2-8=3
-m-11=3
-m=3+11
-m=14
m=-14
Matt is putting a border around a right triangle and needs to figure out the triangle's height. If the triangle has a base length of 12 cm and a total area of 24 cm², what is the height?
Answer:
4 cm
Step-by-step explanation:
area of a triangle = 1/2 * base * height
24 = 1/2 12 * height
height = 4 cm
1)
What is the volume of this rectangular prism? Type your answer in the box.
Use unit cubes to solve. Click the Unit Cube button below.
= 1 cubic unit
3 units
2 units
8 units
Answer: 48 units³
Step-by-step explanation:
Volume can be solved with V = L * W * H
V = L * W * H
V = 8 units * 2 units * 3 units
V = 48 units³
need help asap !!!!!
Answer:
The answer is in Step.
Step-by-step explanation:
Very simple.
B(4,8)
Scalar Factor of 2: 2*B(4,8) -> B'(8,16)Scalar Factor of 1/2: 1/2*B(4,8) -> B'(2,4)Scalar Factor of 2: 4*B(4,8) -> B'(16,32)Scalar Factor of 2: 1/4*B(4,8) -> B'(1,2)Lara surveyed all of the 11th grade students at her school about the number of languages they speak and whether or not they have allergies. Here are her results:
Answer:
57.6% have allergies
42.4% have no allergies
Step-by-step explanation:
We only need to consider the students who speak two languages according to the question.
To find the percent with allergies, divide the number of students with allergies by the total number of students (that speak two languages).
19/33 = 0.5757 = 57.6%
To find the percent without allergies, divide the number of students without allergies by the total number of students (that speak two languages).
14/33 = 0.4242 = 42.4%
Check your work by adding the percentages to make sure they equal 100%
57.6 + 42.4 = 100
Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection. y + 5 = 2 x y = 7 − 2 x
Answer:
The point of intersection is (3,1)
Step-by-step explanation:
Manipulate these equations to achieve the form of y = mx + c
1) y + 5 = 2x
Y = 2x - 5
2) y = 7 - 2x
Y = -2x + 7
Point of intersection is (3,1) on the graph attached
To check algebraically:
2x - 5 = -2x + 7
4x = 12
X = 3
Substitute to get y
Y = 2x - 5
Y = 2 x 3 - 5
Y = 1
Therefore (3,1)
90 divded by 18
what is the answer
Answer:
Answer to your question is 5
Step-by-step explanation:
hope it helps(^-^)
Thom needs 3/4 yard of brown fabric, 2/4 yard of blue fabric, and 3/4 yard of green fabric to make some costumes for a play.
Answer:
Step-by-step explanation:
Hey there!
I think that some of the content in your question is missing so I will be solving for how much yards of fabric is needed in total
Since all of the fractions have common denominators, we can comfortably add them together
3/4+3/4+2/4 is 8/4
8/4 can be simplied to 2
So the total amount of yards of fabric Thom needs in total is 2 yards
Solve the system of equations:
y= 2x - 2
y= x2 - x-6
O A. (-1,-5) and (4,2)
O B. (0, -2) and (2, 2)
O C. (-1,-4) and (4, 6)
D. (-2,0) and (3,0)
Answer:
C) (-1, -4) and (4, 6)
Step-by-step explanation:
[tex]\textsf{Equation 1}:y=2x-2[/tex]
[tex]\textsf{Equation 2}:y=x^2-x-6[/tex]
Substitute Equation 1 into Equation 2 and solve for x:
[tex]\implies 2x-2=x^2-x-6[/tex]
[tex]\implies x^2-3x-4=0[/tex]
Find two numbers that multiply to -4 and sum to -3: -4 and 1
Rewrite the middle term as the sum of these two numbers:
[tex]\implies x^2-4x+x-4=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x-4)+1(x-4)=0[/tex]
Factor out the common term [tex](x-4)[/tex]:
[tex]\implies (x+1)(x-4)=0[/tex]
[tex]\implies (x+1)=0 \implies x=-1[/tex]
[tex]\implies (x-4)=0 \implies x=4[/tex]
Substitute the found values of x into Equation 1 and solve for y:
[tex]x=-1 \implies y=2(-1)-2=-4[/tex]
[tex]x=4 \implies y=2(4)-2=6[/tex]
Therefore, the solution to the system of equations is:
(-1, -4) and (4, 6)
The circle graph shows the rooms in a house and their percentages of the house's total area.
Rooms in a House
Bathrooms
5%
Living Room
20%
Bedrooms
30%
Kitchen
15%
Family
Room
30%
The area of the kitchen is 300 square feet. How many square feet is the entire house? Record your answer in the box.
Answer:
2,000 square feet
Explanation:
If the kitchen is 300 square feet, we can divide that by the percentage(15%). We get the answer 20, which will be our conversion factor!
Now, we multiply this conversion factor by all the other percentages(without decimals)
5 x 20 = 100
20 x 20 = 400
30 x 20 = 600
15 x 20 = 300
30 x 20 = 600
Now we add up all of these factors and get the answer :D
100 + 400 + 600 + 300 + 600 = 2,000 square feet
A car travels xkm in 3 hours. How far will it travel in 9 hours?
Answer: 9X/3 km or divide it further
Step-by-step explanation:
Distance traveled = X
TIME = 3hours
Speed = X/3 km/hr
Distance in 9hours = X/3 × 9/1
help please
simplify (5x-3)^2
Answer:
[tex]\Longrightarrow: \boxed{\sf{25x^2-30x+9}}[/tex]
Step-by-step explanation:
Isolate the term of x from one side of the equation.
Use the perfect square formula.
[tex]\underline{\text{PERFECT SQUARE FORMULA:}}[/tex]
[tex]\Longrightarrow: \sf{(A-B)^2=A^2-2AB+B^2}[/tex]
(5x-3)²
(5x-3)²= (5x)²-2*5x*3+3²
Solve.
[tex]\sf{(5x)^2-2*5x*3+3^2=\boxed{\sf{25x^2-30x+9}}}[/tex]
Therefore, the final answer is 25x²-30x+9.Answer:
25x² - 30x + 9Step-by-step explanation:
The identity
(a - b)² = a² - 2ab + b²In this case, a = 5x and b = 3, so substituting the values :
(5x - 3)²(5x)² - 2(5x)(3) + (3)²25x² - 30x + 9formula for area of triangle
Answer:
[tex]area \: of \: triangle \: = \frac{1}{2} b \times h[/tex]
The area of a triangle formula is A = 1/2 × b × h, where b is base and h is height.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
Here,
The area of a triangle formula is 1/2× b × h, where b=base and h=height.
Example: Find the area of a triangle with base 12 units and height 3 units.
Now, area of a triangle = 1/2× 12 × 3
= 6 × 3
= 18 square units
Therefore, area of a triangle formula is A = 1/2 × b × h.
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"Your question is incomplete, probably the complete question/missing part is:"
What is formula for area of a triangle?
Which statement is not true about the data shown by the box plot below?
5 number summary: 23, 40, 55, 65, 79
A. The median of the data is 55.
B. The interquartile range is 55.
C. Three fourths of the data is less than 65.
D. The median of the upper half of the data is 65.
Reset Selection
Answer:
B. The interquartile range is 55
Step-by-step explanation:
the interquartile range is Q3 minus Q1, you would get 15 ,not 55. So B is the answer to your question
Answer:
B. The interquartile range is 55.
Step-by-step explanation:
In this problem, I refer to the right part of the box as the median of the upper half and the left part of the box as the median of the lower half.
The median of the data is going to be the middle line of the box and whisker plot. The middle line lies on 55, so the median is 55.
Choice A is true
The interquartile range is the right end of the box subtracted from the left end of the box. The right end of the box is 65. The left end of the box is 40. Subtracting the left end from the right end, we get 25.
Choice B is false
3/4 of the data will be where we see the right end of the box. The right end of the box is at 65. So, 3/4 of the data is less than 65.
Note: 1/4 of the data is less than the left side of the box at 40. 1/2 of the data is less than the median of the box which is at 55.
Choice C is true
The median of the upper half is the right end which is 65.
Note: The median of the lower half is 40.
Choice D is true
You buy a car for $48,000. For each year, t, the value, V, of the car decreases by 14%.
Write a model to represent this scenario?
Answer:48.014
Step-by-step explanation:you got to say 48,000 plus 0.014 and you hit the equal button and see what u get and i hit the equal button and i got this answer 48.014 is my answer for this question
Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 i) (21 5i)?
Answer:
C i think
Step-by-step explanation:
find the circumference of a circle 18.8yd
Answer:
59.062yd
Step-by-step explanation:
C=πd
π*18.8yd
=18.8π≈59.0619189=59.062yd
What’s 1+2842-40+7263-1000
Answer:
9,066 is your answer
Ria has to pay 20% tax on any income above £11,000 per year.
Ria's salary before tax is £3,000 per month.
Calculate the amount of money she receives after tax each year.
Answer:
£28,800
Step-by-step explanation:
Given:
Ria has to pay 20% tax on any income above £11,000 per year. Her salary before tax is £3,000 per month.To find:
Amount of money she receives after tax each year.Solution:
Ria's salary before tax is £3,000 per month.
(i.e) £12 * 3,000/year = £36,000.
Now she has to pay 20% tax.
(i.e) 80/100 * 36,000 = £28,800
Hence, Ria receives £28,800 each year after tax.
This soup can has deiameter of 7 centimeters and a height of 10 centimeters the total surface is what
Answer:
Step-by-step explanation:
Formula
SA = 2*pi r^2 + 2*pi * r * h
Givens
pi = 3.14
r = d/2 radius = diameter /2
r = 7/2 = 3.5
h = 10 cm
Solution
SA = 2*3.14 *3.5^2 + 2*3.14 * 3.5 * 10
SA = 76.93 + 219.8
SA = 296.73 cm^2
Answer
Surface Area = 296.73 cm^2
what is 15 divided by 2590 I will give you 55 you will get it
The requried division of 15 by 2590 gives the decimal value of approximately 172.6667.
To calculate the division of 15 by 2590, we perform the following steps:
When we divide 15 by 2590, we can express it as 15 ÷ 2590.
Dividing 15 by 2590 yields a decimal value of approximately 172.6667. This means that 15 is approximately 172.67 times the value of 2590.
In simpler terms, if you divide 15 by 2590, the quotient or result is 172.6667 (rounded to four decimal places).
Therefore, the division of 15 by 2590 is approximately 172.6667.
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If you buy something for $3.84 how much change will you get back from $5.00?
Answer:
1.16
Step-by-step explanation:
Answer: you’d get $1.16
Step-by-step explanation: Simple. Do $5 and subtract 3.84 and you’d get $1.16 hope this helps. :)
When x = 5, the value of the expression
.-2(x - 10) is
O -21
O-9
O 9
O 19
[tex]{\boxed{\mathfrak\pink{\fcolorbox{pink}{pink}{Answer:-}}}}[/tex]
★ Points to be noted 1st:-
★ Given equation=
-2(x-10)nd
x= 5[tex] \underline{\rule{60mm}{2.9pt}} [/tex]
★ Let's substitute x = 5 in given equation to the value of expression
[tex]\sf\:↬-2((5)-10)\\ \sf \:↬Distribution \: of \: -2 \:with \: "5" \: nd \: "-10" \: \\↬ - 10 + 20 \\↬10[/tex]
soo when x = 5 the value of expression is 10
[tex] \underline{ \underline {\rule{70mm}{2.9pt}}}[/tex]
Answer:
10
Step-by-step explanation:
Given
x = 5To solve
-2(x - 10)To find the value of the expression, substitute x = 5 in the equation.
-2(5 - 10)-2(-5)1030 POINTS!
Find x if ∠m1 = 2x + 10 and m∠2 = 3x - 6
Answer choices:
42, 24, 4, 16
Answer: 16
Step-by-step explanation:
which expression is equivalent to c-10c +3c
Answer:
[tex]c-10c+3c=4c-10c=-6c[/tex]
Step-by-step explanation:
The expression which is equal to the given expression c - 10c + 3c will be -6c.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given expression,
c - 10c + 3c = c + 3c - 10c
= 4c - 10c
= -6c
Hence "The expression which is equal to the given expression c - 10c + 3c will be -6c".
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What is the value of x in the equation 3x + 2 = 5x - 8?
Answer:5
Step-by-step explanation:
3(5)+2=17
5(5)-8=17
X=5
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What will the equation be if f(x)= x^2 is translated 6 units left and 3 units up?
Answer:
f(x) = (x+6)^2 +3
Step-by-step explanation: