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snow_tiger [21]

3 years ago

13

The perimeter of a rectangle is 80 feet. Find the dimensions if the length 5 feet longer than four times the width. Then find th

e area of the rectangle.

1 answer:

nydimaria [60]3 years ago

3 0

Answer:

l=33 feet

w=7 feet

Area= 231 feet

Step-by-step explanation:

Solution in Picture is attached

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Solve the SYSTEM: <br> 2x - 3y = 12<br> 3x - 2y = 13

dangina [55]

Answer:

x =69 y= 420

Step-by-step explanation:

69⁹99999999999999999999999999999999999

6 0

2 years ago

In circle O, BC=14 and DC=25. What is the length of diameter BA? -58.6 -12.2 -44.6 -30.6

Savatey [412]

The picture in the attached figure

we know that
If a tangent segment and a secant segment are drawn to a <span>circle </span><span>from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
</span>so
DC²=BC*CA-----> CA=DC²/BC
DC=25
BC=14
CA=25²/14-----> CA=44.64
CA=BC+BA----> BA=CA-BC----> BA=44.64-14----> BA=30.64

BA is the diameter
hence
<span>the length of diameter BA is 30.64----> round to the nearest tenth---> 30.6
</span>
the answer is
<span>the length of diameter BA is 30.6</span>

7 0

3 years ago

Can u plz help me i don't get it

marishachu [46]

Answer:

w=9x+4

Step-by-step explanation:

2(3x-3+w)=12x+2

6x-6+2w=12x+2

subtract 6x for both sides

-6+2w=18x+2

add 6 for both sides

2w=18x+8

Divide by 2 to find w

w=9x+4

3 0

2 years ago

The interior angles of a triangle have measures k°, 27°, and 10°. What is the value of k? Enter your answer in the box.

Triss [41]

To find the measure of the third angle you should keep in mind the following:
The sum of the three interior angles of a triangle is 180 °.
We have then
k + 27 + 10 = 180
Clearing k:
k = 180-27-10 = 143
K = 143 °
Answer:
the value of k is 143 °

3 0

2 years ago

Read 2 more answers

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

<u>The volume of the tetrahedon is 1087.5 cubic units.</u>

3 0

2 years ago