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3 years ago

What is the length of XZ

Mathematics

1 answer:

Artemon [7]3 years ago

6 0

Answer:

$XZ=13\ units$

Step-by-step explanation:

we know that

In the right triangle of the figure XYZ

Applying the Pythagorean Theorem

$XZ^2=XY^2+YZ^2$

substitute the given values

$XZ^2=12^2+5^2$

$XZ^2=144+25$

$XZ^2=169$

square root both sides

$XZ=13\ units$

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What is the variable in the expression 2X - 25

SpyIntel [72]

The variable is x.

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8 0

2 years ago

The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the

yuradex [85]

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

$y=x\,(10-x)=10x-x^2$

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

$y=ax^2+bx+c$

is given by the formula:

$x_{vertex}=-\frac{b}{2\,a}$

which in our case gives:

$x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5$

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

$y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25$

8 0

3 years ago

Marco is making three tiles pictures. he uses 310 green tiles to make each picture. he uses 50 fewer red tiles than green tiles

Anettt [7]

Hi there!

To solve this problem, we need to first find the amount of red tiles he used by subtracting 50 from 310, and then finding the sum of the two numbers.

310 - 50 = 260

Now, we know that there are 260 red tiles.

3 * 310 = 930
3 * 260 = 780

930 + 780 = 1710

So, the answer is 1710 tiles total.

Hope this helps!

7 0

3 years ago

In △ABC, a=31, b=22, and c=18. Identify m∠A rounded to the nearest degree. HELP ME PLEASE!!

4vir4ik [10]

Answer:

The measure of angle A is $101\°$