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1 year ago

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Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two si

des measure 13 cm each. One diagonal, EG, measures 24 cm.
Kite E F G D with diagonals is shown. The lengths of sides E F and F G are 20 centimeters. The lengths of sides E D and D G are 13 centimeters.

What is the length of the other diagonal, DF?

5 cm
16 cm
21 cm
32 cm

2 answers:

pshichka [43]1 year ago

7 0

Answer:

21

Step-by-step explanation:

kogti [31]1 year ago

5 0

Answer: 21

Sofia cuts a piece in the shape of a kite for an art project

top two sides measure 20 cm each

bottom two sides measure 13 cm each.

One diagonal, EG, measures 24 cm

Find out the length of the other diagonal, DF.

explanation-

DE = EF = 20cm

DG = GF = 13cm

EG = 24cm

DF = ?

In kite shape

One diagonal is the perpendicular bisector of the other diagonal.

i.e EG is the perpendicular bisector of DF

i.e EG is divided into two equal parts

thus EA = AG = 12cm

in Δ EAF

By applying the pythagorus theorem

we have

EF² = FA²+ EA²

20² = 12² + FA²

400 -144 = FA²

256 =FA²

16cm = FA

Now in Δ DAG

DG² = AG² + DA²

13² = 12 ²+ DA²

169 -144 = DA²

25 = DA²

5cm = DA

Step-by-step explanation:

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The height of two similar pails are 12cm and 8cm.The larger pail can hold 2litres. What is the capacity of the smaller pail?

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Answer:

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Step-by-step explanation:

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1 year ago

Drag each expression to show whether it is equivalent to (5⋅9x)+(5⋅1), 45x+15, or 15(3x−1).

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Part A: Option e: $5(9 x+1)$

Option f: $45 x+5$

Part B: Option c: $15(3 x+1)$

Option d: $(5 \cdot 9 x)+(5 \cdot 3)$

Part C: Option a: $(5 \cdot 9 x)-(5 \cdot 3)$

Option b: $45 x-15$

Explanation:

Part A: The equation is $(5 \cdot 9 x)+(5 \cdot 1)$

Simplifying, we have,

$45x+5$

Taking the term 5 common out, we have,

$5(9 x+1)$

Thus, the above two expressions are equivalent to the equation $(5 \cdot 9 x)+(5 \cdot 1)$ .

Hence, Option e and Option f are the correct answers.

Part B: The equation is $45 x+15$

Taking the term 15 common out, we have,

$15(3 x+1)$

Also, the equation can be rewritten as,

$(5 \cdot 9 x)+(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $45 x+15$

Hence, Option c and Option d are the correct answers.

Part C: The equation is $15(3 x-1)$

Multiplying, we have,

$45 x-15$

The above expression can be rewritten as,

$(5 \cdot 9 x)-(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $15(3 x-1)$

Hence, Option a and Option b are the correct answers.

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1 year ago

What are the coordinates of R' for the dilation D(0.5. p)(PQRS)?

RideAnS [48]

Answer:

Step-by-step explanation:

Three step process.

Step 1, convert Q, R, P, and S to coordinates measured from point P rather than from the origin by subtracting P from each point:

Q' = Q-P = (-3-(-3),2-(-3)) = (0,5)

R' = R-P = (1-(-3),2-(-3)) =(4,5)

P' = P-P = (-3-(-3),-3-(-3)) =(0,0)

S' = S-P = (1-(-3),-3-(-3)) = (4,0)

Step 2, Apply the dilation factor (0.5):

Q'' = (0.5)Q' = (0.5*0, 0.5*5) = (0,2.5)

R'' = (0.5)R' = _____

P''= (0.5)P' = _____

S''= (0.5)S' = _____

Step 3, Convert coordinates back to the origin (vice point P) by adding P to each point. These are the dilated points.

Q''' = Q'' + P = (0+(-3),2.5+(-3)) = (-3, -0.5)

R''' = R'' + P = _____

P''' = P'' + P = _____

S''' = S'' + P = _____

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