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3 years ago

There are 600 performers in a dance recital. The ratio of men to women is 4:6. How many men performers were in the dance recital

Mathematics

1 answer:

posledela3 years ago

5 0

Answer: 240 men

Step-by-step explanation:

From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.

Fraction of men at the recital = 4/10

Fraction of women at the recital = 6/10

The number of men performers that were in the dance recital will be:

= 4/10 × 600

= 240 men

There were 240 men at the recital.

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∠G and ∠H are supplementary; m∠G = (x + 4)° and m∠H = (4x + 11)°. What is the measure of ∠G? What is the measure of ∠H?

iogann1982 [59]

Answer:

∠G = 37°

∠H = 143°

Step-by-step explanation:

As we know ,

Sum of supplementary angles is 180 degrees.

Hence sum of ∠G and ∠H is also 180 degrees

∠G + ∠H = 180

Substituting the given values in above equation, we get -

$(X+4) + (4X +11) = 180\\5X + 15 = 180\\5X = 165\\X = 33$

∠G = (x + 4)° = (33 + 4)° = 37°

∠H = (4x + 11)° = (33*4 + 11)° = 143°

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2 years ago

Without using a calculator, determine the number of real zeros of the function

kumpel [21]

The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

<h3>How to determine the number of real zeros?</h3>

The equation of the function is given as:

$f(x) = x^3 + 4x^2 + x - 6$

Expand the function

$f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6$

Reorder the terms

$f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6$

Factor the expression

$f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)$

Factor out x -1

$f(x) = (x^2 + 5x + 6)(x -1)$

Expand

$f(x) = (x^2 + 3x + 2x + 6)(x -1)$

Factorize

$f(x) = [x(x + 3) + 2(x + 3)](x - 1)$

Factor out x + 2

$f(x) = (x + 3)(x + 2)(x- 1)$

The function has been completely factored and it has 3 linear factors

Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3