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3 years ago

7

Hoover Dam, in the United States, is 223 meters high. Ertan Dam, in China, is 240 meters high. Write and evaluate a numerical ex

pression to find the difference between the highest of the two dams.

1 answer:

Black_prince [1.1K]3 years ago

5 0

Your expression would be: 240-233

The correct answer is: The Ertan Dam is 7 meters higher than the Hoover Dam.

I hope this helps!
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Given: KLMN is a trapezoid m∠N = m∠KML

horrorfan [7]

Answer:

The length of sides KM, LM and KN are $\sqrt{109}, \frac{48}{5}$ and 16 respectively. The area of KLMN is $\frac{192\sqrt{5}}{5}$ square unit.

Step-by-step explanation:

According to given information: KLMN is a trapezoid, ∠N= ∠KML, $\frac{LM}{KN}=\frac{3}{5}$ , ME ⊥ KN, KE=8 $ME=3\sqrt{5}$ .

Use pythagoras theorem is triangle EKM

$Hypotenuse^2=base^2+perpendicular^2$

$(KM)^2=(KE)^2+(ME)^2$

$(KM)^2=(8)^2+(3\sqrt{5})^2$

$KM^2=64+9(5)$

$KM=\sqrt{109}$

Let angle N and angle KML be θ.

Since angle KML and angle MKE are alternate interior angles, therefore angle MKE is θ.

In triangle KME,

$\tan\theta=\frac{3\sqrt{5} }{8}$ .... (1)

In triangle KNE,

$\tan\theta=\frac{3\sqrt{5} }{EN}$ .... (2)

Equate (1) and (2),

$\frac{3\sqrt{5} }{8}=\frac{3\sqrt{5} }{EN}$

$EN=8$

The length of side KN is

$KN=KE+EN=8+8=16$

Sides LM:KN are in the ratio 3:5. Let the side lengths are 3x and 5x respectively.

$5x=16$

$x=\frac{16}{5}$

$3x=3\times \frac{16}{5}=\frac{48}{5}$

The area of KLMN is

$Area=\frac{1}{2}(b_1+b_2)h$

$A=\frac{1}{2}\times (LM+KN)\times ME$

$A=\frac{1}{2}\times (\frac{48}{5}+16)\times 3\sqrt{5}$

$A=\frac{192\sqrt{5}}{5}$

Therefore length of sides KM, LM and KN are $\sqrt{109}, \frac{48}{5}$ and 16 respectively. The area of KLMN is $\frac{192\sqrt{5}}{5}$ square unit.

6 0

4 years ago

How can you find a unit rate when given a rate?

myrzilka [38]

Answer:

hopefully this

Step-by-step explanation:

divide the numerator and denominator of the given rate by the denominator of the given rate.

example you have 30 kids in a class but five pizzas how many slices can each kid get?

givens :30 kids, 5 pizzas, x slices

30 divided by 5 is 6 slices

7 0

3 years ago

Feeling dumb for posting this

Tamiku [17]

Answer:

P = 3 or P = 5/3

Step-by-step explanation:

3p^2 -14p + 15 ➡ (3p - 5) • (p - 3)

7 0

4 years ago

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A (5,3) and B(3,-2) are two fixed points. Find the equation of the locus of P, so that the

andre [41]

Answer:

$37=5x-2y,\,1=5x-2y$

Step-by-step explanation:

If $(x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)$ are coordinates of a triangle then area of a triangle is equal to $\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Let point P be $(x,y)$

Put $(x_1,y_1)=(5,3),\,(x_2,y_2)=(3,-2),\,(x_3,y_3)=(x,y)$

Area of a triangle = $\frac{1}{2}|5(-2-y)+3(y-3)+x(3+2)|$

$=\frac{1}{2}|-10-5y+3y-9+5x|\\\\=\frac{1}{2}|-19+5x-2y|$

Also,

Area of a triangle = 9 square units

$9=\frac{1}{2}|-19+5x-2y|\\\\18=|-19+5x-2y|$

±18 = -19 + 5x - 2y

$18=-19+5x-2y,\,-18=-19+5x-2y\\\\37=5x-2y,\,1=5x-2y$

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3 years ago

Mrs. JOHNSON paid $40.68 for 3kg of shrimp. What’s the cost of 1 kilogram of shrimp?

Goshia [24]

Answer:

It is 13.56

Step-by-step explanation:

You would have to divide 40.68 by 3. 3 goes 1 time into 4 so it is 10.

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3 years ago

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