There are a total of 71 students in the cafeteria.

The perimeter of △CDE is 55 cm. A rhombus DMFN is inscribed in this triangle so that vertices M, F, and N lie on the sides CD ,

tamaranim1 [39]

Answer:

CD=20 cm and DE=15 cm. CD=20 cm and DE=15 cm.

Step-by-step explanation:

A rhombus DMFN is inscribed in such a way that it is inscribed in triangle CDE with the vertices M, F, and N l on the sides CD , CE , and DE respectively.

Now, in rhombus, the parallel sides are always parallel, therefore

MF║DE, thus, $\frac{CM}{MD}=\frac{CF}{EF}$ by the basic proportionality condition.

It is given that CF=8 cm and EF=12 cm, therefore, $\frac{CM}{MD}=\frac{8}{12}$ .

That is CM=8 cm and MD=12 cm. Therefore, CD=CM+MD=8+12=20.

According to question, Perimeter of △CDE =55 cm

⇒CD+DE+CE=55

⇒20+DE+20=55

⇒DE=15 cm

Hence, CD=20 cm and DE=15 cm.

8 0

3 years ago

Read 2 more answers

. Shanice is making a garden. The area of the garden is 24 ft2. Use the following shape and information to find the base (6−4) a

crimeas [40]

Answer:

The base and height of the garden are 4.60 ft and 5.60 ft.

Step-by-step explanation:

The area of the garden is, A = 24 ft².

The base height of the garden are:

base (b) = 6x - 4

height (h) = x + 3

Compute the value of x as follows:

$A=\frac{1}{2}\times b \times h\\\\24=\frac{1}{2}\times (6x-4) \times (x+3)\\\\48=6x^{2}+18x-4x-12\\\\6x^{2}+14x-60=0\\\\3x^{2}+7x-30=0\\$

The last equation is a quadratic equation.

Compute the roots of the quadratic equation as follows:

$x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\\x = \frac{ -14 \pm \sqrt{14^2 - 4(3)(-30)}}{ 2(3) }\\x = \frac{ -14 \pm \sqrt{556}}{ 6 }\\x = \frac{ -14 }{ 6 } \pm \frac{2\sqrt{139}\, }{ 6 }\\x = -\frac{ 7}{ 3 } \pm \frac{ \sqrt{139}\, }{ 3 }\\x = 1.59661\\x\approx 1.60$

The value of base and height are:

$\text{base}=6x-4=(6\times 1.60)-4=5.60\ \text{ft}\\\\\text{height}=x+3=1.60+3=4.60\ \text{ft}$

Thus, the base and height of the garden are 4.60 ft and 5.60 ft.

3 0

3 years ago

You and your friend are in a canoe race. Your friend is a half mile in front of you and paddling 3 miles per hour. You are paddl

julsineya [31]

Let the time that you caught up with your friend be t, then
8.5 - 3.4t = 8 - 3t
3.4t - 3t = 8.5 - 8
0.4t = 0.5
t = 0.5/0.4 = 1.25
therefore, you will catch up with your friend after 1.25 hours.

b.) time it will take you to cross the finnish line = 8.5/3.4 = 2.5 hours
After 2.5 hours, distance covered by your friend = 3 x 2.5 = 7.5 miles
Therefore, when you cross the finish line, you are 8 - 7.5 = 0.5 miles ahead of your friend.

7 0

3 years ago

Read 2 more answers

2. Solve the following system. Show all your work. {3x - 2y + 2z = 30 {-x + 3y - 4z = -33 {2x - 4y + 3z = 42

Semmy [17]

From the system of equations, we have 3 unknowns and 3 equations. Therefore, it can be solved.

3x - 2y + 2z = 30 (1)
-x + 3y - 4z = -33 (2)
2x - 4y + 3z = 42 (3)

We can write equation 2 x as a function of y and z and substitute the new equation to the other equations.
x =3y - 4z + 33 (2)

3 (3y - 4z + 3) - 2y + 2z = 30 (1)
2 (3y - 4z + 3) - 4y + 3z = 42 (3)

We simplify and solve the equations and we get values,

x = 4
y = -7
z = 2

6 0

3 years ago

Help this is due tomorrow please! Carter has 88 feet of fencing to enclose a dog pen in his yard. He is trying to decide whether

svet-max [94.6K]

<h3>Answer:</h3>

The circle makes the larger area

The difference in the two areas is roughly 132.2479 square feet.

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Explanation:

If Carter decides to go for a circle, then 88 is the circumference, which is the distance around the circle (aka perimeter of the circle).

Use this to find the radius needed

C = 2*pi*r

r = C/(2pi)

r = 88/(2pi)

r = 44/pi

I'll leave it in exact form rather than approximate it.

Once we know the radius, we can find the area of the circle.

A = pi*r^2

A = pi(44/pi)^2

A = pi*(1936/(pi^2))

A = 1936/pi

A = 616.247939651819 approximately

I used my calculator's stored version of pi to compute the area in the final step.

We'll be comparing this number later, so hold onto it for now.

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If Carter instead decides for a square, then 88 is the perimeter since it's the amount of fencing he has to work with.

Divide it into 4 pieces to find the length of each side of the square (all sides are equal in a square)

88/4 = 22

Each side is 22 feet

The area of this square is (22)^2 = 22*22 = 484 square feet

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Summary:

If Carter goes for a circular enclosure, then he gets roughly 616.2479 square feet.
The square enclosure only gets him exactly 484 square feet.

The circle wins in terms of larger area.

The difference being roughly 616.2479 - 484 = 132.2479 square feet.

3 0

2 years ago