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2 years ago

Help me answer this question about congruent triangles. 50 points available.

Mathematics

1 answer:

Anuta_ua [19.1K]2 years ago

3 0

Answer:

Step-by-step explanation:

No these triangles are not congruent.

Left triangle

Shortest side = 6 cm

Longest side = 13 cm

3rd side = unknown but < 13

Right triangle

Shortest side = 6 cm

Longest side = unknown but > 13

3rd side = 13 cm

Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.

We do not know if any of the angles are congruent. If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.

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Step-by-step explanation:

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By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ .

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Differential equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a differential equation, that is, substituting the variables and see if the equivalence is conserved.

If we know that $z = \cos (2\cdot x + 3\cdot y)$ and $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ , then we conclude that:

$\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)$

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3 years ago

Bill and Mary Ann went to the Viola bakery. Bill bought 3 danishes and 8 filled donuts for $14.67. Mary Ann bought 7 of each fo

harina [27]

Answer:

donuts cost $1.5

danishes cost $1.57

Step-by-step explanation:

This is a typical 2-equation syestem with 2 unknown variables problem. Lets find out which are our equations and unknowns.

Bill ought 3 danishes and 8 filled donuts for $14.67. Lets call d the price of donuts and c the price of danishes. We can then write Bill expenditures as an equation (I will omit $ symbol for simplicity):

3 c + 8 d = 14.67 [eq 1]

Now we can do the same for Mary's expenditures, as she bought 7 of each for $16.73:

7 c + 7 d = 16.73 [eq. 2]

Now, lets take eq. 1 and try to get the value of one of the variables, for example c, as function of the other -in this case, d. Notice you could also do this with eq. 2.

So:

3 c + 8 d = 14.67

Subtract 8d in both sides:

3c = 14.67 - 8d

Now, divide both sides by 3:

c = (14.67 - 8d)/3

So, we have c in function of d. Now, replace this value in eq 2:

7*(14.67 - 8d)/3 + 7 d = 16.73

(7/3)*(14.67 - 8d) + 7d = 16.73

Applying distributive:

(7/3)*14.67 - (7/3)*8d + 7d = 16.73

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34.23 - 11.67d = 16.73

Now, subtract 34.23 in both sides:

-11.67 d = -17.5

Dividing both sides by -11.67

d = 1.50

So, every donuts costs $1.5. If we replace this value in any of the equations of the system we get c. Lets replace in eq. 1:

3 c + 8 d = 14.67

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Subtract 12 in both sides:

3c = 4.67

Divide by 3 in both sides:

c = 1.57

Important: notice that the results may variate in some decimals or less depending on how many numbers after the coma you use. For example, d is really 1.49957155098543 but I used 1.50, if you are more precise and use 1.49957 you results may variate a little but not significantly.

So, c=1.57 and d=1.50 is the solution. A donuts cost $1.5 and a danish $1.57.

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