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dangina [55]
3 years ago
7

The Smiths spend 11% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year

they plan to spend $4,950 on entertainment. What was their total budget last year?
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
3 0
Hi,
11%= $4950
1%= $4950/ 11
     = $450
100%= $450 x 100 
         = $45 000 (this year)
Last year= $45 000- $2000
               = $43 000
Hope this helps:))

~Top
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Answer:

The ratio of the songs is 5:3

Step-by-step explanation:

This means that for every 5 songs Adam has, his mother has 3. We can do that in intervals of 5:3, with 10:6, 15:9, 20:12, and etc.

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In a quadrilateral ABCD, angle A + angle D = 90°. Prove that AC^2 + BD^2 = BC^2 + AD^2​
olga2289 [7]

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AD^{2}+BC^{2}=AE^{2}+ED^{2}+BE^{2}+EC^{2}

AC^{2}+BD^{2}=AE^{2}+EC^{2}+BE^{2}+ED^{2}

Hence prove.

AC^{2}+BD^{2}=BC^{2}+AD^{2}

Step-by-step explanation:

Given:

∠A + ∠D = 90°

We are prove to that

AC^{2}+BD^{2}=BC^{2}+AD^{2}

Solution:

See required figure in attached file.

We know sum of the all angles of a triangle is 180°.

So, in triangle AED.

∠A + ∠E + ∠D = 180°

∠E + (∠A + ∠D) = 180°

Now, we substitute ∠A + ∠D = 90° in above equation.

∠E + 90° = 180°

∠E = 180° - 90°

∠E = 90°

Using Pythagoras Theorem for triangle ADE and triangle BEC.

AD^{2}=AE^{2}+ED^{2}

BC^{2}=BE^{2}+EC^{2}

Now, we add both above equations.

AD^{2}+BC^{2}=AE^{2}+ED^{2}+BE^{2}+EC^{2}--------(1)

Similarly, Using Pythagoras Theorem for triangle AEC and triangle BED.

AC^{2}=AE^{2}+EC^{2}

BD^{2}=BE^{2}+ED^{2}

Now, we add both above equations.

AC^{2}+BD^{2}=AE^{2}+EC^{2}+BE^{2}+ED^{2}--------(2)

We get From equation 1 and equation 2.

AC^{2}+BD^{2}=BC^{2}+AD^{2}

Hence prove,

AC^{2}+BD^{2}=BC^{2}+AD^{2}

4 0
3 years ago
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