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3 years ago

Jeremiah is working on a model bridge. He needs to create triangular components, and he

Mathematics

2 answers:

Darina [25.2K]3 years ago

6 0

Answer:

The answer is No, according to the Triangle Theorem.

Step-by-step explanation:

When you have the sides of the triangle, you must be able to add up 2 sides and have a larger number than the other side.

4+5 = 9 which is greater than 1

5+1 = 6 which is greater than 4

4+1=5 which is equal but not greater than 5

tekilochka [14]3 years ago

3 0

Answer:

No, he would not be able to create a triangle without modifying the lengths of the toothpick

Step-by-step explanation:

In order to determine if the toothpicks can be used to create the triangle, make use of the Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c = hypotenuse

the square of the longest side of the triangle should be equal to the sum of the square of the two shortest sides

4² + 1²

16 + 1 = 15

5² = 25

15 is not equal to 25

So the lengths cannot be used

the 1 in length would need to be extended by 2 inches to be used

To confirm

3² + 5²

16 + 9 = 25

This is correct

In conclusion, in order to determine if the lengths can be used, check with Pythagoras theorem. If the lengths can be used, the square of the longest side of the triangle should be equal to the sum of the square of the two shortest sides

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What is 28 = 7y in multiplication

Agata [3.3K]

Y= 4 because when a number is put next to a letter is usally means times/multiply so 7x4= 28

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4 years ago

Read 2 more answers

Solve the equation using the substitution u = y/x. When u = y/x is substituted into the equation, the equation becomes separable

bekas [8.4K]

Answer:

$\frac{u^2+3}{-u^3+u^2-2u}u'=\frac{1}{x}$

Step-by-step explanation:

First step: I'm going to solve our substitution for y:

$u=\frac{y}{x}$

Multiply both sides by x:

$ux=y$

Second step: Differentiate the substitution:

$u'x+u=y'$

Third step: Plug in first and second step into the given equation dy/dx=f(x,y):

$u'x+u=\frac{x(ux)+(ux)^2}{3x^2+(ux)^2}$

$u'x+u=\frac{ux^2+u^2x^2}{3x^2+u^2x^2}$

We are going to simplify what we can.

Every term in the fraction on the right hand side of equation contains a factor of $x^2$ so I'm going to divide top and bottom by $x^2$ :

$u'x+u=\frac{u+u^2}{3+u^2}$

Now I have no idea what your left hand side is suppose to look like but I'm going to keep going here:

Subtract u on both sides:

$u'x=\frac{u+u^2}{3+u^2}-u$

Find a common denominator: Multiply second term on right hand side by $\frac{3+u^2}{3+u^2}$ :

$u'x=\frac{u+u^2}{3+u^2}-\frac{u(3+u^2)}{3+u^2}$

Combine fractions while also distributing u to terms in ( ):

$u'x=\frac{u+u^2-3u-u^3}{3+u^2}$

$u'x=\frac{-u^3+u^2-2u}{3+u^2}$

Third step: I'm going to separate the variables:

Multiply both sides by the reciprocal of the right hand side fraction.

$u' \frac{3+u^2}{-u^3+u^2-2u}x=1$

Divide both sides by x:

$\frac{3+u^2}{-u^3+u^2-2u}u'=\frac{1}{x}$

Reorder the top a little of left hand side using the commutative property for addition:

$\frac{u^2+3}{-u^3+u^2-2u}u'=\frac{1}{x}$

The expression on left hand side almost matches your expression but not quite so something seems a little off.

5 0

3 years ago

Which of the following statements are true?

lana [24]

Answer:

B, C, E, & F

Step-by-step explanation:

Option A is incorrect because the equation Ax = b is referred to as a matrix equation, not a vector equation.

Option B is correct. If Ax = b has a solution, vector b will a linear combination of columns of matrix A.

Option C is correct. In a matrix equation, product Ax when defined, is a sum of products.

Option D is incorrect. If an augmented matrix [Ab] had a pivot position in every row, there could be a pivot in the last column which would make it inconsistent.

Option E is correct. If the columns of an m×n matrix A span $R^m$ , then the equation Ax=b is consistent for each b in