The perimeter of a rectangle garden is 54 feet. The width is 5 more feet than the length. What is the length of the garden

List the 6 congruency statements given ABC = DEF

galina1969 [7]

Answer:

∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF

Step-by-step explanation:

Given that triangles ABC and DEF are congruent. Now we need to choose correct congruency statements from the given choices.

We know that corresponding angles of congruent triangles are equal so we can write:

∠A ≅ ∠D

∠B ≅ ∠E

∠c ≅ ∠F

We know that corresponding sides of congruent triangles are equal so we can write:

AB = DE

BC = EF

AC = DF

comparing these with given choices we see that, First choice is correct.

5 0

3 years ago

Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

3 years ago

What is the degree measure of x in this triangle?

Crank

So this is trig, and when it comes to right (90°) triangles, it's imperative that you know:
SOH-CAH-TOA

Sine (x) = Opposite/Hypotenuse
Cosine (x) = Adjacent/Hypotenuse
Tangent (x) = Opposite/Adjacent

*hypotenuse is always the largest side, and the one opposite the 90° angle in right triangles

therefore we'll use SOH, because the opposite of x (O) and the hypotenuse (H) are given:

Sine (x) = Opposite/Hypotenuse
Sine (x) = 32/58 = 16/29 = 0.552
Sine (x) = 0.552
now we use something called arc-sine, or
${(sin)}^{ - 1}$
it's basically a fancy function of most advanced calculators, so we'll plug it in as:
$x = {(sin)}^{ - 1} (0.552)$
x = 33.49° --> answer B) is correct

4 0

3 years ago

Please answer asap Please Please

nordsb [41]

Answer:

hmm sorry

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Isabel put $4,000 into a saving account that pays interest monthly at a simple-interest rate of 2.5% per year. If she takes the

never [62]

9514 1404 393

Answer:

$49.98

Step-by-step explanation:

The interest credited to Isabel's account each month is ...

I = Prt

I = $4000·(0.025)(1/12) = $8.33

If she withdraws that amount each month, the original balance is restored, and she will earn the same amount the next month.

Isabel's total earnings in 6 months will be ...

$8.33 · 6 = $49.98

4 0

3 years ago