Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
The base and height of a triangle are in the ratio 4: 5. If the area is 640 sq. cm, find the base and height.
Answer:
base = 32 cm , height = 40 cm
Step-by-step explanation:
ratio of base : height = 4 : 5 = 4x : 5x ( x is a multiplier )
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ) , then
A = [tex]\frac{1}{2}[/tex] × 4x × 5x = 2x × 5x = 10x²
given A = 640 , then
10x² = 640 ( divide both sides by 10 )
x² = 64 ( take square root of both sides )
x = [tex]\sqrt{64}[/tex] = 8
Then
base = 4x = 4 × 8 = 32 cm
height = 5x = 5 × 8 = 40 cm
pls help-
5(u+1)-u=3(u-1)+7
No solution?
[tex]5(u + 1) - u = 3(u - 1) + 7 \\ 5u + 5 - u = 3u - 3 + 7 \\ 5u - u + 5 = 3u - 4 \\ 4u + 5 = 3u - 4 \\ 4u - 3u = - 4 - 5 \\ u = - 9[/tex]
sorry if this is not correct
I can’t figure out how to solve this problem someone please help me
Answer:
x=30
Step-by-step explanation:
i actually dont know but thnks for the points BTW
Answer:
x = 4
Step-by-step explanation:
In this geometry, all of the right triangles are similar. That means the ratio of short side to long side is the same for all of the right triangles:
x/10 = 10/25
x = 100/25 = 4 . . . . . multiply by 10
_____
Additional comment
You may notice that the two segments of the hypotenuse, x and 25, have a product that is the square of the altitude. Another way to say this is that the altitude is the geometric mean of the segments x and 25.
There are two other geometric mean relations in this geometry:
the short side at the right is the geometric mean of x and (x+25).
the long side at the bottom is the geometric mean of 25 and (25+x).
That is, the segments that intersect the hypotenuse are the geometric mean of the two segments of the hypotenuse that they meet.
geometric mean of A and B is √(AB)
two consecutive odd numbers between 60 and 80 which are both prime?
Answer:
Hello I'll help you :))!
So there are 21 numbers from 60 to 80 both terms inclusive.
We ignore all even numbers in this range as even numbers can not be prime.
The odd numbers are 61,63,65,67,69,71.73,75,77,79.
So remaining numbers are prime. They are 61,67,71,73,79.
So there are 5 prime numbers in this range.
Write a sequence of transformations that maps circle B onto circle A.
A translation 4 units right and 2 units up is done followed by a dilation of 3/2.
TransformationTransformation is the movement of point from its initial location to a new location. Types are rotation, translation, reflection and dilation
Translation is the movement of point up, down, left or right. Dilation is the increase or decrease in the size.
To map circle B onto circle A, first a translation 4 units right and 2 units up is done followed by a dilation of 3/2.
Find out more on Transformation at: https://brainly.com/question/1462871
Answer: All 3 Parts
Part A :
Part B : A translation 4 units right and 2 units up is done followed by a dilation of 3/2
Part C : the two circles are equation congruent
Step-by-step explanation:
For what value of x the rational expression 1/3x-6 is undefined?
Answer:
2
Step-by-step explanation:
A fraction is undefined when the denominator is 0 because division by 0 is undefined.
When x=2, we have 3x-6=0 and the denominator is undefined.
If 7x – 24 = 8x – 39, then x = ?
Answer:
15
Step-by-step explanation:
-x=-15
x=15
105 -24 = 120 - 39
81 = 81
Answer:
X= 15
Step-by-step explanation:
7x – 24 = 8x – 39
39 - 24 = 8x - 7x
15 = 1x
x=15
Three trigonometric functions for a given angle are shown below. Sine theta = Negative StartFraction 77 Over 85 EndFraction, cosine theta = StartFraction 36 Over 85 EndFraction, tangent theta = Negative StartFraction 77 Over 36 EndFraction What are the coordinates of point (x, y) on the terminal ray of angle mc020-2. Jpg, assuming that the values above were not simplified? (–77, –36) (–77, 36) (–36, 77) (36, –77).
Trigonometric functions are the ratio of the different sides of a right-angled triangle. We can say that the coordinates of the point are (-77, 36).
What are trigonometric functions?
Trigonometric functions are the ratio of the different sides of a right-angled triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
Given to us
[tex]Sin(\theta) = \dfrac{-77}{85}[/tex]
[tex]Cos(\theta) = \dfrac{36}{85}[/tex]
[tex]Tan(\theta) = \dfrac{-77}{36}[/tex]
As we know that the Tangent(Tan) is the ratio of perpendicular and base. therefore, we can write the function as,
[tex]\rm Tan(\theta) = \dfrac{Perpendicular}{Base} = \dfrac{-77}{36}[/tex]
therefore, the length of the perpendicular is 77, while the length of the base is 36.
As given to us that the value of sin is negative, therefore, the perpendicular will be on the negative side of the y-axis. While the value of cos is positive, therefore, the base will be on the positive side of the x-axis.
Thus, we can say that the coordinates of the point are (-77, 36).
Learn more about Trigonometric functions:
https://brainly.com/question/6904750
Answer:
B
Step-by-step explanation: just did it gang 100%
Sandra went for pizza with friends. She ordered a slice of pizza with a side salad for $9. 50. The tax was 6. 2%. What was the total amount Sandra paid for her meal? Enter your answer in the box.
Percentage represents a part of a whole. The total amount that Sandra needs to pay for a slice of pizza and salad is $10.09.
What is the percentage?The percentage is a way to represent a part of a whole. for example, one-fourth of an area A can be written like 25% of A(0.25 A).
Give to us
Sandra ordered a slice of pizza with a side salad for $9.50.
The tax was 6. 2%.
The amount of tax that Sandra needs to pay,
[tex]6.2\%\ of\ \$9.50\\\\=0.062 \times 9.50\\\\= \$0.589[/tex]
As we know that tax is the extra cost that we need to pay, therefore, the total amount Sandra needs to pay,
Total Amount = Cost + tax
= $9.50 + $0.589
= $10.089 ≈ $10.09
Hence, the total amount that Sandra needs to pay for a slice of pizza and salad is $10.09.
Learn more about Percentage:
https://brainly.com/question/6972121
12 1/3 - ( 2x + 3 2/3)
Answer:
hello there the correct answer is 16−2x
Step-by-step explanation:
Please try and help me answer this question. Thank you for any responses!
The location of XY is shown on the coordinate plan.
Please help
Answer:
,,,
Step-by-step explanation:
how do you convert 1.5cm2 into mm2
Answer: 150mm squared
Step-by-step explanation:
Multiply by 100
Answer:
150mm²
Step-by-step explanation:
[tex]here,\\ (1.5*100)mm^{2} =150mm^{2}[/tex]
Tell whether the angles are adjacent or vertical. Then find the value of x.
The angles are
Question 2
x = ?
Answer:
x=20
Step-by-step explanation:
These these angles are adjacent
because they share a vertex and side. They also form a linear pair meaning they add up to 180 degrees...
x+20+7x=180
Combine like terms
8x+20=180
Subtract 20 from both sides
8x=160
Divide both sides by 8
x=20
what is 30 + 12 = e - 42
Answer:
e = 84
Step-by-step explanation:
30 + 12 = e - 42
e = 42 +42
e = 84
Using postulates and/or Theorems learned in unit 1, determine weather ABC ~ AXY. show all your work and explain why the triangles are similar and why they are not.
https://brainly.com/question/26558770
Answer:
AX / AB = 6/18 = 1/3
AY / AC = 10/25 = 2/5
They are not similar because the two ratios is not the same.
Step-by-step explanation:
Find the nth term rule for 18,15,12,9
Answer:
an = a+(n-1) d
this is the rule
Answer:
nth term = 21 - 3n
Step-by-step explanation:
18,15,12,9....
This is an arithmetic sequence.
a= first term = 18
Common difference = d = second term - first term
d = 15 - 18
d = -3
nth term = a + (n-1)d
= 18 + (n-1)*(-3)
= 18 + n*(-3) - 1*(-3)
= 18 - 3n + 3
= 21 - 3n
Please help asap
I cant figure out the answer
Answer:
3
Step-by-step explanation:
[tex]x=\sqrt{2x+3}[/tex]
square both sides: [tex]x^2=2x+3[/tex]
subtract [tex]2x + 3[/tex] from both sides: [tex]x^2-2x-3=0[/tex]
factorize: [tex](x-3)(x+1)[/tex]
Therefore, [tex]x=3 \ and \ -1[/tex]
Substitute found values of [tex]x[/tex] back into original equation:
[tex]3=\sqrt{2\times3+3}=3 \ \ \checkmark[/tex]
[tex]-1=\sqrt{2\times-1+3}=1[/tex] incorrect!
So answer is [tex]x = 3[/tex] only
Please help me with this
Answer:
42.9
Step-by-step explanation:
Something tells me that you want it as fast as possible, but if you need an explanation just ask!
Good luck!
[:
Answer:
58.57 approximately 58.6
Step-by-step explanation:
we've been given the value for line MN as 67.2m and also line AN as 32m so we look for line MA by saying 67.2 minus 32m to give 35.2m
considering the big triangle we have line MN and we have line MP but we don't have line NP to get line NP we use pythagoras theorem
hypotenuse Square = opposite Square + adjacent Square
81.9*2= 67.2*2 + x*2
therefore x is 46.8m
note that line NP is equal to line AB therefore line AB is also 46.8m
so we now look at the smaller triangle to find x
that's also pythagoras theorem
hypotenuse Square = opposite Square + adjacent Square
x^2 = 38.5^2 + 46.8^2
therefore our value for x is 58.6
Find the probability of getting a prime number from 1 to 10
Step-by-step explanation:
For example, to find the probability that a prime is selected from 1 to 10 requires us to divide the number of primes from 1 to 10 by 10. The numbers 2, 3, 5, 7 are prime,
hope this helps you
please mark me brainliest
Twice a day Cameron's cat eats 4 ounces of dry cat food and 2 ounces of wet cat food dry food comes in 5 pound bags and wet food comes in 6 ounce cans
A how many cans of wet food should he buy to feed his cat for a week?
B How many ounces of wet cat food will be left over at the end of the week
C How many days can he feed his cat from a 5 pound bag of dry food
Which expression means five times the sum of b and two?
A. 5 (b+2)
B. 5b+2
C. (b+2) over 5
D. b over (5+2)
Answer:
A
Step-by-step explanation:
Brackets are used to show multiplication.
For A if we multiple out the brackets we get: 5b+10 which means 5 times the sum if b and 2
1 - 2 + 5 - 2 + 5 x 2
Answer: 12
Step-by-step explanation:
Following PEMDAS, I’ll solve the multiplication first and then add or subtract the values from left to right.
1-2+5-2+5x2
1-2+5-2+10
-1+5-2+10
4-2+10
2+10
12
Answer:
12
Step-by-step explanation:
You need to use the order of operations, PEMDAS. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
First, multiplication on 5x2 so now it is 1-2+5-2+10.
Next, is addition and subtraction. When it says left to right you are starting with the part of the equation closest to the left, so 1-2=-1. Then add five to get 4. Subtract 2 to get 2. Finally, add 10 to get 12.
Hope you get an A! <3
ginger still has 40% of her book to read. if she has read 180 pages, how many pages does she still have to read?
Answer:
Ginger still has 40 percent of her book to read. If she has read 180 pages, the number of pages she still have to read:
N = 180 x (100 - 40)/40 = 270 pages
60%
Step-by-step explanation:
Which is the smallest ratio?
3 to 4 , 23 , 10:12 , 2 to 1
Answer: 2/3 is the smallest ratio.
Step-by-step explanation:
3,328 divided by 8 show your thinking
Answer:
416
Step-by-step explanation:
Well I know 8 x 100=800 so I did 8 x 400=3,200
Then I added 8 x 10=80 which is 3,280
and from there I did 8 x 6=48
And then what's 3,280+48=3,328 because 3,280+40=3,320 and then add 8=3,328
Hope it helps
Answer:
If we break apart 3,328 and first divide 3,000 by 8 we get 375, and then divide 328 by 8 we get 41, this helps us understand that if we divided 3,328 by 8 we would get 416
g(x) =2x + 4; Find g(-3)
Answer:
[tex]g(-3)=-2[/tex]
Step-by-step explanation:
Substitute g(-3) into the function:
[tex]g(-3)=2(-3)+4[/tex]
Multiply:
[tex]g(-3)=-6+4[/tex]
Add:
[tex]g(-3)=-2[/tex]
Answer: -2
Step-by-step explanation:
plug g(x) with -3 so it would be 2(-3) + 4 and then simply and add so 2(-3) equals -6 + 4 is -2
What is 2 cups of flour to 3 cups of sugar
Answer:
2:3 or 2/3
this is a ratio problem
Answer:
2:3?
Step-by-step explanation:
I'm kinda guessing from the question u gave cuz it doesn't really have a lot of information
Tameka’s plant measured 3 inches at the beginning of the week and 5 inches at the end of the week. What was the approximate percent increase in the height of Tameka’s plant?
40%
25%
60%
67%
Answer:
25%
Step-by-step explanation:
Multiply:
3 × 5 = 25%
Hope this helps!! <3
Jack went to a local restaurant and ordered the following:
Soda - $2.75
Hamburger - $5.75
French Fries - $2.00
Chocolate Chip Cookie - $0.75
a) What was his subtotal?
Answer: I think it is 8.55
Step-by-step explanation:
have a nice day♥️