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3 years ago

Is this angle side angle, angle angle side, or not congruent.

Mathematics

1 answer:

KatRina [158]3 years ago

3 0

<h3>Answer: C) Not congruent</h3>

We have 2 pairs of congruent angles, so we can prove the triangles are similar triangles (using the AA similarity theorem). But we don't have enough information to prove them to be congruent. We would need at least one pair of sides to be congruent so we could use either AAS or ASA.

For instance, if we knew that AT = AP, then we would use AAS. If we knew that HT = MP, then we would use ASA instead. However, we don't have either bit of information like this. The triangles may or may not be congruent. We simply don't have enough information to say either way. We can't definitively say they are congruent, so we just lean toward "not congruent".

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I NEED HELP FAST! Find the measure of the missing angles.

loris [4]

Angle G = 130 degrees

Angle H = 50 degrees

Angle K = 74 degrees

Angle M = 106 degrees

<u>Angle G would be 130 degrees</u> because it's a vertical angle, and vertical angles are always alike.

<u>Angle H would be 50 degrees</u> because it's an adjacent angle, and we also know that one side of the line is always 180 degrees so we have an equation that looks like this 180 - 130 = 50 degrees

<u>Angle K would be 74 degrees</u> because it's a vertical angle.

<u>Angle M would be 106 degrees</u> because it's an adjacent angle.

7 0

3 years ago

Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2

LUCKY_DIMON [66]

Make a change of coordinates:

$u(x,y)=xy$
$v(x,y)=\dfrac xy$

The Jacobian for this transformation is

$\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}$

and has a determinant of

$\det\mathbf J=-\dfrac{2x}y$

Note that we need to use the Jacobian in the other direction; that is, we've computed

$\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}$

but we need the Jacobian determinant for the reverse transformation (from $(x,y)$ to $(u,v)$ . To do this, notice that

$\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}$

we need to take the reciprocal of the Jacobian above.

The integral then changes to

$\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv$
$=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2$

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4 years ago

State the coordinates of the reflection of the isosceles trapezoid across the line of reflection y = –x.

Oxana [17]

Based on the given image, the coordinates of the pre image are:
A (-3,4)
B (-1,4)
C (1,1)
D (-5,1)

When you do a reflection in the line y = -x ; (x,y) coordinate becomes (-y,-x)

A (-3,4) → (-(4),-(-3)) → A' (-4,3)
B (-1,4) → (-(4),-(-1)) → B' (-4,1)
C (1,1) → (-(1),-(1)) → C' (-1,-1)
D (-5,1) → (-(1),-(-5)) → D' (-1,5)

I attached what the reflection will look like over line y = -x

5 0

4 years ago

a garden is 15 m × 10 m . It has a 2.6. m wide flower bed all around outside it. There is also a 2.5 m wide grassy path all arou

erastova [34]

Answer:

flower bed = 157.04 $m^{2}$

grassy path = 202 $m^{2}$

Step-by-step explanation:

If you draw this out, it's basically a rectangle inside a rectangle inside a rectangle. I'm going to call those rectangles A, B, and C. with A being the smallest and C being the biggest.

first we need to find the area of A, B, and C.

A will be easy because we're already given that its 15x10

Area A = 150 $m^{2}$

To find area B, we need to add the 2.6 pathway to all the sides, so it'll be:

length: 15+2.6(2) = 20.2 m

width: 10+2.6(2) = 15.2 m

Area B = 307.04 $m^{2}$

Then we do the same for area C but with 2.5 m.

length: 20.2+2.5(2) = 25.2 m

width: 15.2+2.5(2) = 20.2 m

Area C = 509.04 $m^{2}$

To find the area of just the flower bed, we need to subtract area A from area B, then to find grassy path we need to subtract area B from area C.

flower bed: 307.04-150 = 157.04 $m^{2}$

grassy path: 509.04-307.04 = 202 $m^{2}$

6 0

3 years ago

Tamara wants to rent a jet-ski. Tamara's deal is to pay $60 to rent the jet-ski, plus $12.50 per hour. If

Pani-rosa [81]

Answer:

6 hours.

Step-by-step explanation:

deal: 135-(60+12.5h)=y

let h= # of hrs

135-60=75.

75/12.5=6 hours.

6 0

3 years ago

Is this angle side angle, angle angle side, or not congruent.​

Is this angle side angle, angle angle side, or not congruent.