What Number is 16/ of 44

How to write a paragraph proof? Given: ∠T and ∠V are right angles TW║VU. Prove: ΔTUW≅ΔVWU

mafiozo [28]

Note: The missing diagram is attached below for a reference.

Answer:

Δ $TUW$ ≅ Δ $VWU$ by $AAS$ case.

Step-by-step explanation:

Given:

∠T and ∠V are right angles.

$TW$ ║ $VU$

To Prove:

Δ $TUW$ ≅ Δ $VWU$

As

∠ $T$ ≅ ∠ $V$ ≅ $90^{0}$ (Given)

Side $UW$ ≅

$TW$ ║ $UV$

and $UW$ is a transverse

So,

∠ $TWU$ ≅ ∠ $WUV$ $\left[alternate\:\:interior\:\:angles\right]$

$As\:Angle\:=\:Angle\:=\:side\:are\:equal$

Thus,

Δ $TUW$ ≅ Δ $VWU$

Keywords: proof, paragraph, logic, reason

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4 0

4 years ago

How do you solve 4x - 18 < -x -3

GaryK [48]

Answer:

x<3

Step-by-step explanation:

--add 18--

$4x-18+18$

--simpifly--

$4x$

--add x--

$4x+x$

--simpifly--

$5x$

--divide both side by 15--

x<3

sorry for late

<3

Red

6 0

3 years ago

A painting in an art gallery is valued at $10,000. The gallery owner estimates that its value will increase by 6% every year.

zvonat [6]

Every year the value will go up about 600 added to the original price

6 0

3 years ago

Read 2 more answers

On a unit test in a statistics class, the teacher determines that the mean test grade was 77.5 with a standard deviation of 5.2.

katovenus [111]

Answer: B. This student's test grade was 2.4 standard deviations above the mean test grade.

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

Explanation:

The z score tells us how far away the raw score is from the mean. This distance is in terms of standard deviations.

z = 1 means we're 1 standard deviation above the mean
z = 2 means we're 2 standard deviations above the mean

and so on.

Negative z scores indicate the raw score is below the mean.

z = -1 means we're 1 standard deviation below the mean
z = -2 means we're 2 standard deviations below the mean

and so on. So that's why z = 2.4 indicates the students test grade was 2.4 standard deviations above the mean.

5 0

3 years ago

12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

never [62]

Answer:

Part a) Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Domain of f+g = {-1, 0, 1, 2, 3}

Part d) Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

Part a) Determining the domain of f

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Determining the domain of g

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Determining the domain of f+g

When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.

As,

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

Domain of g : {-1, 0, 1, 2, 3, 4}

As when there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains

So, the domain of f+g = {-1, 0, 1, 2, 3}

Part d) List the ordered pairs of f-g

As

f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1) = 14 - 4 = 10

(f - g)(x) = f(0) - g(0) = 7 - 5 = 2

(f - g)(x) = f(1) - g(1) = 4 - 6 = -2

(f - g)(x) = f(2) - g(2) = 5 - 1 = 4

(f - g)(x) = f(3) - g(3) = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords: domain, function, f+g, f-g

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7 0

4 years ago