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3 years ago

9

Danny had 20 minutes to do a three-problem quiz. He spent 9 1/4 minutes on question A and 5 4/5 minutes on question B. How much

time did he have left for question C?

1 answer:

Travka [436]3 years ago

6 0

Answer:

4 19/20

Step-by-step explanation:

9 1/4 + 5 4/5 = 15 1/20

20- 15 1/20 = 4 19/20

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Answer:

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Read 2 more answers

Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of K, where k

STALIN [3.7K]

$\bold{\huge{\underline{\pink{ Solution }}}}$

<h3><u>Given </u><u>:</u><u>-</u><u> </u></h3>

<u>Rectangle </u><u>1</u><u> </u><u> </u><u>has </u><u>length </u><u>x</u><u> </u><u>and </u><u>width </u><u>y</u>
<u>Rectangle</u><u> </u><u>2</u><u> </u><u>is </u><u>made </u><u>by </u><u>multiplying </u><u>each </u><u>dimensions </u><u>of </u><u>rectangle </u><u>1</u><u> </u><u>by </u><u>a </u><u>factor </u><u>of </u><u>k </u>
<u>Where</u><u>, </u><u>k </u><u>></u><u> </u><u>0</u><u> </u><u> </u>

<h3><u>Answer </u><u>1</u><u> </u><u>:</u><u>-</u></h3>

Yes, The rectangle 1 and rectangle 2 are similar .

<h3><u>According </u><u>to </u><u>the </u><u>similarity </u><u>theorem </u><u>:</u><u>-</u></h3>

If the ratio of length and breath of both the triangles are same then the given triangles are similar.

<u>Let's </u><u>Understand </u><u>the </u><u>above </u><u>theorem </u><u>:</u><u>-</u>

The dimensions of rectangle 1 are x and y

<u>Now</u><u>, </u>

Rectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k .

Let assume the value of K be 5

<u>Therefore</u><u>, </u>

The dimensions of rectangle 2 are

$\sf{ 5x \:and \:5y }$

<u>Now</u><u>, </u><u> </u><u>The </u><u>ratios </u><u>of </u><u>dimensions </u><u>of </u><u>both </u><u>the </u><u>rectangle </u><u>:</u><u>-</u>

$\bold{Rectangle 1 = Rectangle 2}$

$\bold{\dfrac{ x }{y}}{\bold{ = }}{\bold{\dfrac{5x}{5y}}}$

$\bold{\blue{\dfrac{ x }{y}}}{\bold{\blue{ = }}}{\bold{\blue{\dfrac{x}{y}}}}$

<u>From </u><u>above</u><u>, </u>

We can conclude that the ratios of both the rectangles are same

Hence , Both the rectangles are similar

<h3><u>Answer </u><u>2</u><u> </u><u>:</u><u>-</u><u> </u></h3>

<u>Here</u><u>, </u>

We have to proof that, the

Perimeter of rectangle 2 = k(perimeter of rectangle 1 )

In the previous questions, we have assume the value of k = 5

<h3><u>Therefore</u><u>, </u></h3>

<u>According </u><u>to </u><u>the </u><u>question</u><u>, </u>

Perimeter of rectangle 1

$\sf{ = 2( length + Breath) }$

$\bold{\pink{= 2( x + y ) }}$

Thus, The perimeter of rectangle 1

Perimeter of rectangle 2

$\sf{ = 2( length + Breath) }$

$\sf{ = 2(5x + 5y) }$

$\sf{ = 2 × 5( x + y) }$

$\bold{\pink{= 10(x + y) }}$

Thus, The perimeter of rectangle 2

<u>According </u><u>to </u><u>the </u><u>given </u><u>condition </u><u>:</u><u>-</u>

Perimeter of rectangle 2 = k( perimeter of rectangle 1 )

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>

$\sf{ 2(x + y) = 10(x + y)}$

$\bold{\pink{2x + 2y = 5(2x + 2y) }}$

<u>From </u><u>Above</u><u>, </u>

We can conclude that the, Perimeter of rectangle 2 is 5 times of perimeter of rectangle 1 and we assume the value of k = 5.

Hence, The perimeter of rectangle 2 is k times of rectangle 1

<h3><u>Answer 3 :</u></h3>

<u>Here</u><u>, </u>

We have to proof that ,

<u>The </u><u>area </u><u>of </u><u>rectangle </u><u>2</u><u> </u><u>is </u><u>k²</u><u> </u><u>times </u><u>of </u><u>the </u><u>area </u><u>of </u><u>rectangle </u><u>1</u><u>.</u>

<u>That </u><u>is</u><u>, </u>

Area of rectangle 1 = k²( Area of rectangle)

<h3><u>Therefore</u><u>, </u></h3>

<u>According </u><u>to </u><u>the </u><u>question</u><u>, </u>

<u>Area </u><u>of </u><u>rectangle </u><u>1</u>

$\sf{ = Length × Breath }$

$\sf{ = x × y }$

$\bold{\red{= xy }}$

<u>Area </u><u>of </u><u>rectangle </u><u>2</u>

$\sf{ = Length × Breath }$

$\sf{ = 5x × 5y }$

$\bold{\red{ = 25xy }}$

<u>According </u><u>to </u><u>the </u><u>given </u><u>condition </u><u>:</u><u>-</u>

Area of rectangle 1 = k²( Area of rectangle)

$\sf{ xy = 25xy }$

$\bold{\red{xy = (5)²xy }}$

<u>From </u><u>Above</u><u>, </u>

We can conclude that the, Area of rectangle 2 is (5)² times of area of rectangle 1 and we have assumed the value of k = 5

Hence, The Area of rectangle 2 is k times of rectangle 1 .

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2 years ago

Classity 2 and 1 using all relationships that apply.

goldfiish [28.3K]

Answer:

Vertical Angles

Step-by-step explanation:

Vertical Angles are the angles opposite each other when two lines cross.

4 0

3 years ago