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3 years ago

ABCD is a rectangle.Work out the angle 'a' in each diagram.Help please!!

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

6 0

Top one: Since corners of rectangles are 90 degrees, angle ABD would be 28 degrees, and angle CBE would be 41 degrees. Subtract 90 by both numbers, and the answer is 21.

Bottom one: With the same logic, angle ADE would be 38 degrees, and angle CDB would be 35. Because of that, angle a is 55 degrees (90-35=55)

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A restaurant has 1,996 forks 1,745 knives and 2,116 spoons. The owner wants to have 2,000 of each utensil. How many additional f

a_sh-v [17]

2000-1996=4 forks

2000-1745=255 knives

since there are extra spoons it is reversed-->2116-2000=116 spoons

the owner needs 4 forks,255 knives and there are 116 extra spoons

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3 years ago

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The answer is A the line isn't sloping they are on the same y axis

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3 years ago

Combine like terms to write an equivalent expression. Then use y = 5 to prove the expressions are equivalent. 1 + y + y + y + 1

NeX [460]

Answer:

The equivalent expression is

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Step-by-step explanation:

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3 years ago

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A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the

Kay [80]

Answer: The required number of quarters in the collection is 11.

Step-by-step explanation: Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05, 1 dime = $ 0.10 and 1 quarter = $0.25.

Then, according to the given information, we have

$x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

$(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

and

$y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Comparing the values of y from equations (iv) and (v), we get

$47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.$

Thus, the required number of quarters in the collection is 11.

7 0

3 years ago

Jill jumped 6

MatroZZZ [7]

Answer:

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Step-by-step explanation:

You would subtract 657 - 613

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4 years ago