Help solving this math problem

Mathematics

1 answer:

daser333 [38]3 years ago

5 0

Diagram of two triangles

The two triangles are similar because they are both right triangles, meaning that one angle is 90° and the other two are acute (less than 90°).

The diagram on the left is missing its hypotenuse - the variable c. The hypotenuse is opposite of the right angle. The diagram on the right side is missing one of its legs.

Note: The hypotenuse is the longest side of a right triangle.

Word Problen

The legs are 21 blocks and 20 blocks because they are by the right angle. Use the Pythagorean theorem to find the diagonal path's length, which is the hypotenuse.

${a}^{2} + {b}^{2} = {c}^{2}$

Standard form of Pythagorean theorem.

${21}^{2} + {20}^{2} = {c}^{2}$

Equation with the legs substituted and the missing hypotenuse value - c.

$841 = {c}^{2}$

Square the legs and add.

$\sqrt{841} = c$

$29 = c$

Take the square root and simplify. The square root of 841 is 29 and -29, but distance is positive.

Thus the diagonal distance is 29 blocks.

Check by substituting.

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Which fraction is less than 1 chose all of the correct answer, and explain why you chose and write it down and explain your answ

EleoNora [17]

Answer:

$(3/4)$ and $(2/3)$ .

Step-by-step explanation:

For a fraction of the form $(p / q)$ , the number in front of the division ( $p$ ) is the numerator. The number after the division ( $q$ ) is the denominator.

$\begin{aligned} \frac{p}{q} \quad \genfrac{}{}{0}{}{(\text{numerator})}{(\text{denominator})}\end{aligned}$ .

A positive fraction $(p/q)$ ( $p,\, q > 0$ ) is less than $1$ as long as the numerator $p$ is smaller than the denominator $q$ (that is, $p < q$ .) The reason is that as long as $p,\, q > 0$ :

$\begin{aligned} & \frac{p}{q} < 1 \\ \iff & (q)\, \left(\frac{p}{q}\right) < (q)\, (1) && (\text{given that $q > 0$}) \\ \iff & p < q\end{aligned}$ .

For example, in the fraction $(2/3)$ , $2$ is the numerator while $3$ is the denominator. Both the numerator and the denominator are positive, while the numerator $2\!$ is smaller than the denominator $3\!$ . Therefore, $(2/3)$ would be less than $1$ .