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3 years ago

How can I solve proportions for missing sides in geometry?

Mathematics

1 answer:

Nadya [2.5K]3 years ago

3 0

Try either the Law of Sines or the Law if Cosines to use interior angles to create a ratio to the side proportions.

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To find 61 × 1,000, annex ______ zeros to _____ to form the product _______

NARA [144]

The answer is 61,000

8 0

3 years ago

(X^4)-(45x^2)+324 what are the zeroes? And how many turning points?

dmitriy555 [2]

Zeroes:

We must solve

$x^4-45x^2+324=0$

To do so, we define the auxiliary variable $t=x^2$ . The equation becomes

$t^2-45t+324=0$

The quadratic formula yields the solutions

$t=9,\quad t=36$

Substituting back $t=x^2$ gives

$x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6$

So, the zeroes are -6, -3, 3, 6.

Turning points:

Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.

We have

$f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x$

If we set the derivative to be zero, we have

$4x^3-90x=0 \iff x(4x^2-90)=0$

So, the derivative is zero if x=0 or

$4x^2=90 \iff 2x^2=45 \iff x^2=\dfrac{45}{2}\iff x=\pm\sqrt{\dfrac{45}{2}}$

6 0

3 years ago

What is the value of the expression below

natulia [17]

Answer:

a=2,b=4. (3a+b)=3*2+4=10.

5 0

2 years ago

My answer is 8, but I'm not completely sure, if I'm wrong could someone please explain how to find the length.

Verdich [7]

By knowing that S is bisected by the line shown, we will conclude that PD = 8

So here we know that PC = 8, we also can see that:

PCS is a right triangle
PDS is a right triangle.

Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.

Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.

And notice that both of these triangles share one side, then:

Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.

This implies that the triangles are congruent, thus, the <u>measures of the corresponding sides must be the same.</u>

<u />

Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.

So you are correct.

If you want to learn more about congruent triangles, you can read:

brainly.com/question/12077512

8 0

2 years ago

Assume the bear can walk in any direction at a rate of 2 miles per hour. Suppose the bear was last seen 4 hours ago.how large an

Arisa [49]

The bear can walk at a rate of 2 mph, which means after 4 hours it could have traveled 8 miles. That is our radius. To calculate the area of a circle, remember the formula
A = $\pi$ r^2

3.14 * 8^2 = A
3.14 * 64 = A
200.96 = A

An area of 200.96 square miles must be searched.

8 0

3 years ago