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3 years ago

A rectangle has dimensions 10 cm by 6 cm. determine the measures of the angles at the point of where the diagonals intersect

Mathematics

1 answer:

Sophie [7]3 years ago

3 0

See the attached figure to better understand the problem

we know that

in the triangle ABC
tan(alfa/2)=AC/BC----> 5/3
so
(alfa/2)=arctan (5/3)---------> 59.0362°
alfa=2*59.0362--------> alfa=118.07°
alfa+beta=180°----------> because are supplementary angles
beta=180-118.07-------> beta=61.93°

the answer is
the angles are
alfa=118.07°
beta=61.93°

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A basket full of 10 apples costs 23$, another basket full of 15 apples costs 33$. The prices of the baskets are the same. How mu

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Answer:

Equations:

y + 10x = 23

y + 15x = 33

cost of basket with 25 apples = $53

Step-by-step explanation:

A basket with 10 apples cost $23 and a basket with 15 apples cost $33. Note that these costs also include the cost of the basket, which is same in both case. Let the cost of empty basket with "y" and cost of each apple be "x"

Cost of basket and 10 apples is $23. We can transform this statement into an equation as:

y + 10x = 23 Equation 1

Similarly,

Cost of basket and 15 apples is $33. This gives us another equation:

y + 15x = 33 Equation 2

Subtracting Equation 1 from Equation 2 , we get:

y + 15x - (y +10x) = 33 - 23

5x = 10

x = 2

Using the value of x in equation 1, we get:

y + 10(2)= 23

y = 23 - 20

y = 3

This means, cost of basket is $3 and cost of each apple is $2.

Now we can calculate the cost of basket with 25 apples, which will be:

Cost of basket + Cost of 25 apples = Total Cost

3 + 25(2) = 3 + 50 = $53

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Answer:

The answer would be 7 and 13/16

Step-by-step explanation:

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