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3 years ago

Help me, select all that apply

Mathematics

1 answer:

Burka [1]3 years ago

4 0

Answer:

1.5ft, 2ft, 2.5ft

12ft, 35ft, 37ft

Step-by-step explanation:

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Given: ABCD trapezoid BC=1.2m, AD=1.8m AB=1.5m, CD=1.2m AB∩CD=K Find: BK and CK

stepladder [879]

Answer:

The value of BK is 3m and the value of CK is 2.4m.

Step-by-step explanation:

Given information: ABCD trapezoid

, BC=1.2m, AD=1.8m

, AB=1.5m, CD=1.2m

, AB∩CD=K.

Using the given information draw a figure.

Two sides of a trapezoid are parallel.

Since AB∩CD=K, therefore AB and CD are not parallel, because parallel line never intersect.

$AD\parallelBC$

$\angle KBC=\angle KAD$ (Corresponding angles)

$\angle KCB=\angle KDA$ (Corresponding angles)

By AA rule of similarity

$\triangle KBC\sim \triangle KAD$

Corresponding sides of similar triangles are proportional.

$\frac{KB}{KA}=\frac{KC}{KD}=\frac{BC}{AD}$

$\frac{x}{x+1.5}=\frac{y}{y+1.2}=\frac{1.2}{1.8}$

$\frac{x}{x+1.5}=\frac{1.2}{1.8}$

$\frac{x}{x+1.5}=\frac{2}{3}$

$3x=2x+3$

$x=3$

The length of BK is 3 m.

$\frac{y}{y+1.2}=\frac{1.2}{1.8}$

$\frac{y}{y+1.2}=\frac{2}{3}$

$3y=2y+2.4$

$y=2.4$

The length of CK is 2.4 m.

5 0

3 years ago

Read 2 more answers

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96m long and 74m wide.

Oduvanchick [21]

Answer:

$11402.66 m^{2}$

Step-by-step explanation:

The width of rectangle is the diameter of the semi-circle part

Area of one semicircle is given by $\frac {0.5\pi d^{2}}{4}$

Total area of semi circle will be $2\times\frac {0.5\pi d^{2}}{4}$

Substituting 74 m for d and $\pi$ as 3.14 we obtain

Total area semi-circle= $2\times\frac {0.5*3.14\times 74^{2}}{4}=4298.66 m^{2}$

Area of rectangle is given by the product of length and width

Rectangular area= $96 m*74 m=7104 m^{2}$

Total area of rectangular and semi-circles will be

$4298.66 m^{2}+7104 m^{2}=11402.66 m^{2}$

Therefore, area of training field is $11402.66 m^{2}$

6 0

3 years ago

¿Cuál es la suma de los ángulos 1 al 6 en este paralelogramo?

Sveta_85 [38]

Answer:

Un paralelogramo es una forma plana con lados opuestos paralelos y de igual longitud.

Step-by-step explanation:

Los ángulos "a" y "b" suman 180 °, por lo que son ángulos suplementarios. NOTA: ¡Los cuadrados, rectángulos y rombos son todos paralelogramos

Espero que esto te ayude :)

4 0

3 years ago

How do i solve this?

vovikov84 [41]

Answer:

x = 4

y = 9

Step-by-step explanation:

It is given that figure (NPQR) is a square. One property of a square is that all sides of a square are congruent. This property also applies to the given square, thus one can make the following statement;

PQ = NR

Substitute,

10y - 29 = 5y + 16

Inverse operations,

10y - 29 = 5y + 16

-5y -5y

5y - 29 = 16

+29 +29

5y = 45

/5 /5

y = 9

Another property of a square is that all of the interior angles of a square have a measure of (90) degrees. Moreover, the diagonals (segment connect non-adjacent vertices) bisect these angles. Thus, twice the measure of an angle formed between a side and a diagonal forms a (90) degree angle. Therefore, one can draw the following conclusion;

2(m<QPR) = 90

Substitute,

2(6x + 21) = 90

Simplify,

12x + 42 = 90

Inverse operations,

12x + 42 = 90

-42 -42

12x = 48

/12 /12

x = 4

4 0

3 years ago

Evaluate the expression when a = -4 and c=5. 6c-a

igomit [66]

=26
Explanation: 6 x 5 (c) = 30 30 - 4 (a) =26
Hope that helps :)

8 0

3 years ago

Read 2 more answers