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3 years ago

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The length of an object in feet is equal to three times its length in yards. The length of a water slide is 48 feet. Write and s

olve a multiplication equation to find the length of the water slide in yards

1 answer:

wariber [46]3 years ago

5 0

Yards=x
ft=3x
48=3x
x=16
the length if the water slide in yards is 3. 3 yards

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find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - <u>A </u><u>trapezium</u><u> </u><u>ABCD </u><u>with </u><u>non </u><u>parallel </u><u>sides </u><u>of </u><u>measure </u><u>1</u><u>5</u><u> </u><u>cm </u><u>each </u><u>!</u><u> </u><u>along </u><u>,</u><u> </u><u>the </u><u>parallel </u><u>sides </u><u>are </u><u>of </u><u>measure </u><u>1</u><u>3</u><u> </u><u>cm </u><u>and </u><u>2</u><u>5</u><u> </u><u>cm</u>

To find - <u>Area </u><u>of </u><u>trapezium</u>

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

<u>Construction</u><u> </u><u>-</u>

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

<u>Since </u><u>we've </u><u>obtained </u><u>the </u><u>height </u><u>now </u><u>,</u><u> </u><u>we </u><u>can </u><u>easily </u><u>find </u><u>out </u><u>the </u><u>area </u><u>of </u><u>trapezium </u><u>!</u>

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

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Kim and Jose shared one whole pizza. Kim ate 4/6 of the pizza, and Jose ate 3/12 of the pizza. How much of the pizza was eaten?

adelina 88 [10]

Answer: 11/12

Step-by-step explanation: You need to make 4/6 by multiplying it by 2. 4/6 would become 8/12. You would then add it by 3/12 getting 11/12.

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3 years ago

Lisa has a rope that measures 9 1 4 feet in length. She will cut the rope into pieces that are each 3 4 foot long. How many full

Harman [31]

Answer:

Lisa can cut the rope into 12 pieces with 1/4 foot remaining.

I found the answer on USATestprep.

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3 years ago

Read 2 more answers

Can someone answer this question please?

Slav-nsk [51]

Answer:

Therefore,

(x , y) YES / NO

(-4, -5) Yes, It is a Solution.

(1 , - 3) No, not a Solution.

(9 , 6) No, not a Solution.

(-6 , 2) No, not a Solution.

Step-by-step explanation:

Given:

$4x-7y=19$

To Determine:

Given ordered pair is a solution or not ?

Solution:

For (-4,-5)

Substitute x = -4 and y = -5 in above equation

Left Hand Side = 4 × (-4) - 7 × (-5)

= -16+35

= 19

Right Hand Side = 19

Left Hand Side = Right Hand Side

Satisfied

Hence (-4, -5) is the SOLUTION to 4x - 7y =19 (YES)

For (1, -3)

Substitute x = 1 and y = -3 in above equation

Left Hand Side = 4 × (1) - 7 × (-3)

= 25

Right Hand Side = 19

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (1, -3) is NOT the Solution to 4x - 7y =19 (NO)

For (9, 6)

Substitute x = 9 and y = 6 in above equation

Left Hand Side = 4 × (9) - 7 × (6)

= -6

Right Hand Side = 19

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (9, 6) is NOT the Solution to 4x - 7y =19 (NO)

For (-6, 2)

Substitute x = -6 and y = 2 in above equation

Left Hand Side = 4 × (-6) - 7 × (2)

= -38

Right Hand Side = 19

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-6, 2) is NOT the Solution to 4x - 7y =19 (NO)

Therefore,

(x , y) YES / NO

(-4, -5) Yes, It is a Solution.

(1 , - 3) No, not a Solution.

(9 , 6) No, not a Solution.

(-6 , 2) No, not a Solution.

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3 years ago