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mezya [45]
3 years ago
13

A parallelogram has sides 10m and 12m and an angle of 45°. Find the distance between the 12m-sides.

Mathematics
1 answer:
stich3 [128]3 years ago
4 0

Answer:

The distance between 12m-sides is 5\sqrt{2}m.

Step-by-step explanation:

It is given that the parallelogram has sides 10m and 12m and an angle of 45°.

Draw an altitude from one 12m side to another 12 m side as shown in below figure.

The opposite angles of parallelogram are same. Two angles are obtuse angles and two are acute angle.

Since angle C is acute angle therefore it must be 45 degree.

\sin\theta=\frac{perpendicular}{hypotenuse}

\sin C=\frac{BE}{BC}

\sin(45^{\circ})=\frac{d}{10}

\frac{1}{\sqrt{2}}=\frac{d}{10}

\frac{10}{\sqrt{2}}=d

\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=d

\frac{10\sqrt{2}}{2}=d

5\sqrt{2}=d

Therefore the distance between 12m-sides is 5\sqrt{2}m.

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Jada makes sparkling juice by mixing 2 cups of sparkling water with every 3 cups of apple juice. How much sparkling water does J
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Answer:

Step-by-step explanation:

2 cups of sparkling water with every 3 cups of apple juice = sparkling juice

Sparkling water : apple juice

2 : 3

How much sparkling water does Jada need if she uses 8 cups of apple juice.

Sparkling water : apple juice

x : 8

Equate both ratios

2 : 3 = x : 8

2/3 = x / 8

2*8 = 3*x

16 = 3x

x = 16 / 3

= 5.33 cups

Sparkling water = 5.33 cups

How much apple juice does Jada need if she uses 8 cups of sparkling water

Sparkling water : apple juice

8 : y

Equate both ratios

2 : 3 = 8 : y

2/3 = 8 / y

Cross product

2 * y = 3 * 8

2y = 24

y = 24 / 2

= 12

y = 12

Apple juice = 12 cups

NOTE: There is an error in your question, you wrote "How much sparkling water does Jada need if she uses 8 coups of sparkling water." but I solved for both sparkling water and apple juice using 8 cups since your question was not clear enough.

8 0
2 years ago
Playland Park charges $25 admission plus $2 per ride. Funland Park charges $35 admission plus $1 per ride. For what number of ri
Ket [755]

Answer:

10 rides

Step-by-step explanation:

Make an equation.

25 + 2x = 35 + 1x

Subract 1x from the 2x to get 1.

New Equation: 25 + 1x = 35

Subtract 25 from 35 to get 10.

New Equation: 1x = 10

Divide 1 from both sides.

Answer: 10 rides

8 0
3 years ago
Teresa bought 16 roses for $20.64. How much did she pay for each rose
jeka94
Roses: 16
Total Cost: $20.64

Divide:
$20.64 ÷ 16
=  $1.29

Each Rose cost $1.29

Hope This Helped! :3
6 0
3 years ago
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The equation of a circle centered at the origin is x^2+y^2=16. what is the radius of the circle?
vekshin1

Answer:

The center is (0,0) and the radius is 4

Step-by-step explanation:

x^2+y^2=16.

The equation of a circle can be written in the form

(x-h)^2+(y-k)^2=r^2  where ( h,k) is the center and r is the radius

(x-0)^2+(y-0)^2=4^2

The center is (0,0) and the radius is 4

4 0
3 years ago
Does this graph represent a function? Why or why not?
DedPeter [7]

Answer: C

Step-by-step explanation: For a function, each x-coordinate corresponds to exactly one y-coordinate.

To determine whether the graph shown here

is a function, we can use the vertical line test.

The vertical line test tells us that if each x-coordinate on the graph corresponds to exactly one y-coordinate, then any vertical line that we draw on the graph should hit the graph at only one point.

For the graph show here, any vertical line that you draw with hit the graph at only one point which means it does pass the vertical line test.

So this graph is a <em>function</em>.

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