Triangles RST and MNP are congruent. Name the congruent sides and the congruent angles.

(a) Both conditions are satisfied with x = (1, 0) for [tex]\mathbb R^2[/tex] and x = (1, 0, 0) for [tex]\mathbb R^3[/tex]:

||(1, 0)|| = √(1² + 0²) = 1

max{1, 0} = 1

||(1, 0, 0)|| = √(1² + 0² + 0²) = 1

max{1, 0, 0} = 1

(b) This is the well-known triangle inequality. Equality holds if one of x or y is the zero vector, or if x = y. For example, in [tex]\mathbb R^2[/tex], take x = (0, 0) and y = (1, 1). Then

||x + y|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(0, 0)|| + ||(1, 1)|| = √(0² + 0²) + √(1² + 1²) = √2

The left side is strictly smaller if both vectors are non-zero and not equal. For example, if x = (1, 0) and y = (0, 1), then

||x + y|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2

and of course √2 < 2.

Similarly, in [tex]\mathbb R^3[/tex] you can use x = (0, 0, 0) and y = (1, 1, 1) for the equality, and x = (1, 0, 0) and y = (0, 1, 0) for the inequality.

(c) Recall the dot product identity,

x • y = ||x|| ||y|| cos(θ),

where θ is the angle between the vectors x and y. Both sides are scalar, so taking the norm gives

||x • y|| = ||(||x|| ||y|| cos(θ)|| = ||x|| ||y|| |cos(θ)|

Suppose x = (0, 0) and y = (1, 1). Then

||x • y|| = |(0, 0) • (1, 1)| = 0

||x|| • ||y|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0

For the inequality, recall that cos(θ) is bounded between -1 and 1, so 0 ≤ |cos(θ)| ≤ 1, with |cos(θ)| = 0 if x and y are perpendicular to one another, and |cos(θ)| = 1 if x and y are (anti-)parallel. You get everything in between for any acute angle θ. So take x = (1, 0) and y = (1, 1). Then

||x • y|| = |(1, 0) • (1, 1)| = |1| = 1

||x|| • ||y|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2

In [tex]\mathbb R^3[/tex], you can use the vectors x = (1, 0, 0) and y = (1, 1, 1).

Answer:

Step-by-step explanation:

you can see this is a geometric progression which a ratio of [tex]{2\over{5}}[/tex]. the sum of the firs n term is:

[tex]S=a_1\frac{(1-r^n)}{(1-r)}=175\frac{1-(\frac{2}{5})^{10}}{1-\frac{2}{5}}=291.6360832[/tex]

the nearest integer would be:

292

The sum of the first 10 terms of the series 175, 70, 28, ...   is  291.636

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number. This fixed number is called common ratio.. This progression is also known as a geometric sequence of numbers that follow a pattern.

Common ratio = (Any term) / (Preceding term)

It means the sum of all the first "n" numbers in the series. The formula for first "n" natural numbers is

Sn = a + a r + ar2 + ar3 +…+ arn-1

or

Sₙ = a[(rⁿ – 1)/(r – 1)]

where "r" is called common ratio

"a" is called the first term in the series

From the given question the given series is  175, 70, 28, ...

70/175 = 0.4 (or) 28?70 = 0.4

As each succeeding term is produced by multiplying each preceding term by 0.4 .Here the common ratio (r) is 0.4

let first term "a" be 175

then Sₙ = 175[(0.4¹⁰-1)/(0.4 - 1)

      Sₙ= 291.636

Thus the sum of the first 10 terms of the series 175, 70, 28, ...   is  291.636

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Answer:

3x - 7y = 14

Step-by-step explanation:

standard form is: ax + by = c

first, add 2 to each side of the equation to get:

2 + y = 3/7x

now multiply each term by 7 to eliminate fraction:

14 + 7y = 3x

now subtract 7y from each side to get:

3x - 7y = 14

===========================================================

Explanation:

Start at the origin (0,0). Move 2 units up (rise) and move to the right 3 units (run) to arrive at the point (3,2).

This shows that the slope is rise/run = 2/3.

---------------------

You could also use the slope formula, which is,

m = (y2-y1)/(x2-x1)

You can use any two points from the orange line.

Answer:

The answer would be 3.33.

Step-by-step explanation:

Simplifying 12x + 5 = 3x + 35

Reorder the terms: 5 + 12x = 3x + 35

Reorder the terms: 5 + 12x = 35 + 3x

Solving 5 + 12x = 35 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation. 5 + 12x + -3x = 35 + 3x + -3x

Combine like terms: 12x + -3x = 9x 5 + 9x = 35 + 3x + -3x

Combine like terms: 3x + -3x = 0 5 + 9x = 35 + 0 5 + 9x = 35

Add '-5' to each side of the equation. 5 + -5 + 9x = 35 + -5

Combine like terms: 5 + -5 = 0 0 + 9x = 35 + -5 9x = 35 + -5

Combine like terms: 35 + -5 = 30 9x = 30

Divide each side by '9'. x = 3.333333333

Simplifying x = 3.333333333

Answer:

I don't no answer sorry

Step-by-step explanation:

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Answer:

(x, y) = (-1, 1)

Step-by-step explanation:

8x + y = −7

for y = 1

8x + 1 = -7

subtract 1 from boh sides

8x = -8

divide bot sides by 8

x = -1

(x, y) = (-1, 1)

Answer:

4.196.754

Step-by-step explanation:

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Answer:

25x - 45

Step-by-step explanation:

5(5x - 9)

Distribute

5*5x - 5* (9)

25x - 45

Answer:

➛ 25 x - 45

Step-by-step explanation:

➛ 5 ( 5 x - 9 )

Using distributive property multiply both by 5

➛ 5 × 5 x - 5 × -9

➛ 25 x - 45

Answer:

The volume of the prism is 243 ft^3.

Step-by-step explanation:

The equation you have to use is A=Bh

Answer: 121.5 ft3

Step-by-step explanation:

Use this formula for volume of triangulsr prism:

1/2 • length • width • height

That will be 1/2 • 4.5 • 9 x 6 = 121.5

Unit of measurement is ft3 (also same as cubic feet)

Welcomeee!

Answer:

10.787

Step-by-step explanation:

Given :

23.3×0.463

After multiplying this equation ,

10.787

Therefore, answer will be 10.787

Answer:

314 m²

Step-by-step explanation:

the formula for the surface area of a sphere (As) is

As = 4×pi×r²

the radius r (half of the diameter) is clearly indicated as 5m.

so, As = 4×3.14×5² = 4×3.14×25

I don't even need a calculator for this, as 4×25 = 100

so, As = 100×3.14 = 314

(you know, when multiplying by 10, the decimal point moves right one position. multiply by 100 it moves 2 positions, and so on).

Answer:

2.13%

Step-by-step explanation:

assume that the distribution is approximately normal

[tex]\frac{6700-5000}{850} =2[/tex]

the value is 2 s.d. more than the mean

according to normal distribution, approximately 2.13% of the data is 2 s.d. more than the mean.

Answer:

172.8 m^3

Step-by-step explanation:

Volume for triangualr prism formula:

1/2 • length • width • height

Use formula with given dimensions:

1/2 • 7.2 m • 10 m • 4.8 m = 172.8

Volume is measured in cubic meters

(meters in this situation)

FINAL ANSWER:

172.8 cubic meters

Hope this helps!

The volume of the given prism is 172.8 cubic centimeters.

The given prism is a triangular prism with base length of 7.2m.

Height of 4.8m

Length of 10m.

The formula for volume of prism is V=1/2 bhl

Plug in the values of length , breadth and height:

V=(1/2) × 10 × 4.8 × 7.2

V=5×4.8×7.2

V=172.8 cubic centimeters.

Hence, the volume of the given prism is 172.8 cubic centimeters.

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Answer:

BCDE

Step-by-step explanation:

You can see it in the image. Parallel = if the line keeps going and will never touch each other.

Answer:

The appropriate solution is Option D (22 m/sec).

Step-by-step explanation:

The given equation is:

[tex]s(t)= -(t-15)^2 + 225[/tex]

Now,  

The instantaneous velocity at t = 4 will be:

= [tex][-2(t-15)(1)+0][/tex]

= [tex]-2(4-15)[/tex]

= [tex]-2\times (-11)[/tex]

= [tex]22 \ m/sec[/tex]

Thus, the above is the correct option.

Answer:

4a

Step-by-step explanation:

4ax^2 + 4ax + 4a

here in every term there is 4 and a so take 4 and a common

4a(x^2 + x + a)

Answer:

.43 · 80 = 34.4

Step-by-step explanation:

percentages into decimals = move decimal place to left two places

'of' means multiply in math

equations have equal (=) signs

The diagonals of a rectangle are equal and bisect each other.

NQ= 2×5 =10

Using Pythagoras theoram,

PQ²+NP²=NQ²

4²+ NP²= 10²

NP²= 100-16

NP²= 84

NP =√84

Answer:

the answer is 220

Step-by-step explanation:

the formula for surface area of a rectangular prism is A=2(wl+hl+hw)

w = width

h= height

l = length

and when you have those lengths, you have to substitute.

Answer:

30

Step-by-step explanation:

that is the procedure above

Answer:

-2

Step-by-step explanation:

f(x) = 3x^2 + 5x - 14

substitute -3 inplace of x

f(-3) = 3*(-3)^2 + 5*(-3) - 14

=3*9 - 15 - 14

=27 - 15 - 14

= -2

Answer:

976 ÷ 8 =

8 groups of n = 976

n groups of 8 = 976

122

____

8 | 976

- 8

____

176

- 16

_____

160

- 160

______

0

Answer:

504/8=63/6=10.5

10 rooms per floor with 3 leftover

Answer:

Answer: (C)A picnic table is on sale for 60 percent off.

Step-by-step explanation:

well someone copied me but okay :[

9514 1404 393

Answer:

  8

Step-by-step explanation:

The notation n=1 .. 8 means that n takes on all integer values from 1 to 8. Each value of n gives one term that is added to the series.

  The number of terms is 8.

Answer:

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