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3 years ago

in a 30-60-90 triangle, the hyptenuse has a length of 10. how long is the shorter leg (across from the 30 degree angle)?

Mathematics

1 answer:

larisa [96]3 years ago

6 0

Answer:

5 units

Step-by-step explanation:

in a 30-60-90 triangle, the hypotenuse is 2 times the value of the shorter leg. So, if the hypotenuse is 10, then the shorter leg will be 5 units because 10 ÷ 2 is 5.

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The price of a pair of shoes increases from $62 to $81. What is the percent increase to the nearest percent?

maksim [4K]

The answer is 30%

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2 years ago

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Suppose that the functions s and t are defined for all real numbers x as follows.

jeka94

Answer:

$(s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39$

Step-by-step explanation:

Given functions are:

$s(x)= x+6\\t(x)= 4x^2$

We have to find:

(s.t)(x) => this means we have to multiply the two functions to get the result.

So,

$(s.t)(x) = s(x)*t(x)\\= (x+6)(4x^2)\\=4x^2.x+4x^2.6\\=4x^3+24x^2$

Also we have to find

(s-t)(x) => we have to subtract function t from function s

$(s-t)(x) = s(x) - t(x)\\= (x+6) - (4x^2)\\=x+6-4x^2$

Also we have to find,

(s+t)(-3) => first we have to find sum of both functions and then put -3 in place of x

$(s+t)(x) = s(x)+t(x)\\= x+6+4x^2$

Putting x = -3

$= -3+6+4(-3)^2\\=-3+6+4(9)\\=3+36\\=39$

Hence,

$(s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39$

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2 years ago

The wait time to ride the thunder boats is 30 minutes when 180 people are in line. Write and solve a proportion to find the wait

mars1129 [50]

SO EASY 60 people = 10 minutes in line 240 people = 40 minutes in line

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3 years ago

According to the rational root theorem, which of the following are possible

White raven [17]

Given:

The polynomial function is

$F(x)=4x^3-6x^2+9x+10$

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of $\dfrac{p}{q}$ , where, p is a factor of constant and q is the factor of leading coefficient.

We have,

$F(x)=4x^3-6x^2+9x+10$

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

$x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}$

Therefore, the correct options are A, C, D, F.

7 0

3 years ago