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AnnZ [28]
4 years ago
10

Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is

45°. How many parallelograms can you construct given these conditions? What are the lengths of the sides and the measurements of the angles for the parallelogram(s)? Using the given information, can you determine the lengths of all the sides of the parallelogram? If so, what are the side lengths?
Mathematics
1 answer:
Musya8 [376]4 years ago
8 0

9514 1404 393

Answer:

  (a) one parallelogram

  (b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°

  (c) yes, all side lengths can be determined, see (b)

Step-by-step explanation:

Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.

The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.

Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)

You might be interested in
A. Is the sum of two polynomials always a polynomial? Explain
IgorLugansk [536]

Answer:  The answers for both (a) and (b) is YES.


Step-by-step explanation: A polynomial is an algebraic expression containing   two or more algebraic terms, i.e., the sum of several terms that contain different powers of the same variable or variables with real coefficients.

For example, p(x) = 4x²+x+2 is a polynomial in variable 'x'.

(a) Yes, the sum of two polynomials is again a polynomial. For example,

if p(x) = ax² + bx + c  and  q(x) = dx² + ex + f, where, a, b, c, d, e and f are real numbers, then their sum will be

p(x) + q(x) = (a+d)x²+(b+e)x+(c+f), which is again a polynomial in 'x' with real coefficients.

(b) Yes, the difference of two polynomials is again a polynomial. For example,

p(x) - q(x) = (a-d)x²+(b-e)x+(c-f), which is again a polynomial in 'x' with real coefficients.

Thus, the answer is YES.

6 0
3 years ago
In ΔSTU, m∠S=(11x+3)∘,∠T=(2x+16)∘, and m∠U=(x+7)∘. Find .
frozen [14]

Answer:

x = 11

Step-by-step explanation:

In ΔSTU ,

m∠S = (11x+3)° ; m∠T = (2x+16)° ; m∠U = (x+7)°

According to angle sum property of a triangle , sum of all the interior angles of the triangle is 180°.

So,

11x + 3 + 2x + 16 + x + 7 = 180

=  > 14x + 26 = 180

=  > 14x = 180 - 26 = 154

=  > x =  \frac{154}{14}  = 11

6 0
3 years ago
A space is totally disconnected if its connected spaces are one-point-sets.Show that a finite Hausdorff space is totally disconn
marysya [2.9K]

Step-by-step explanation:

If X is a finite Hausdorff space then every two points of X can be separated by open neighborhoods. Say the points of X are x_1, x_2, ..., x_n. So there are disjoint open neighborhoods U_{12} and U_2, of x_1 and x_2 respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods U_{13} and U_3 of x_1 and x_3 respectively, and disjoint open neighborhoods U_{14} and U_4 of x_1 and x_4, and so on, all the way to disjoint open neighborhoods U_{1n}, and U_n of x_1 and x_n respectively. So U=U_2 \cup U_3 \cup ... \cup U_n has every element of X in it, except for x_1. Since U is union of open sets, it is open, and so U^c, which is the singleton \{ x_1\}, is closed. Therefore every singleton is closed.

Now, remember finite union of closed sets is closed, so \{ x_2\} \cup \{ x_3\} \cup ... \cup \{ x_n\} is closed, and so its complemented, which is \{ x_1\} is open. Therefore every singleton is also open.

That means any two points of X belong to different connected components (since we can express X as the union of the open sets \{ x_1\} \cup \{ x_2,...,x_n\}, so that x_1 is in a different connected component than x_2,...,x_n, and same could be done with any x_i), and so each point is in its own connected component. And so the space is totally disconnected.

4 0
4 years ago
A recipe for pizza crust call for 3 cups of flour for every 1 cup of water.How many cups of water are needed for 21 cups of flou
Zina [86]
The answer is 7 cups of water are needed for 21 cups of flour.

Shown work:
1 cup of water=3 cups of flours
? Cup of water=21 cups of flours

21 divided 3=7
1 multiply by 7= 7 cups of water needed
4 0
3 years ago
Help please guys thankyouu
ZanzabumX [31]

You have the right idea so far, but you forgot to finish it up.

Point slope form is

y - y1 = m(x - x1)

where m is the slope, and (x1,y1) is the point the line goes through. As you can see, we have infinitely many choices for (x1,y1). If you use the y intercept point (0,5), then

y - y1 = m(x - x1)

y - 5 = -1(x - 0) ..... this is one of infinitely many possible answers

OR

If you use the point (2,3), then we'd say

y - y1 = m(x - x1)

y - 3 = -1(x - 2) ..... which is another possible answer

There are infinitely many other choices, but I'm only picking the points in which your teacher has shown as big dots.

By the way, nice work on getting the correct answer for the slope-intercept form.

8 0
3 years ago
Read 2 more answers
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