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3 years ago

Solve for x - Pre algebra

Mathematics

2 answers:

aniked [119]3 years ago

7 0

In this case you would set it up as
$6x + 4x + 130 = 180$
(180 represents the degree of the triangle)

Add up like terms
$10x + 130 = 180$
Subtract 130 to the other side (180-130)

$10x = 50$
Divide 10 to the other side ( 50/10)
.
$x = 5$
Hope this was clear :)

Montano1993 [528]3 years ago

7 0

The sum of the measures of the interior angles of a triangle is 180 degrees.

Make the three angles add up to 180 in an equation.

6x + 130 + 4x = 180

Combine like terms.

10x + 130 = 180

Subtract 130 from both sides.

10x = 50

Divide both sides by 10.

x = 5 is your answer.

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A park ranger observed the number and ages of children who visited the park on a Friday morning. The results of his observations

aleksandr82 [10.1K]

ANSWER

The number of children between the ages of 9 and 15 who visited the park is
$20$

EXPLANATION

The number of children between the ages of 9 and 15 who visited the park are those within the age group 9 to 12 and 12 to 15.

We can from the graph that, the height of the bar that corresponds to the age group 9 to 12

$= 14$
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$= 6$

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8 0

3 years ago

Given cosα = −3/5, 180 < α < 270, and sinβ = 12/13, 90 < β < 180

torisob [31]

I got

$- \frac{6 3}{65}$

What we know

cos a=-3/5.

sin b=12/13

Angle A interval are between 180 and 270 or third quadrant

Angle B quadrant is between 90 and 180 or second quadrant.

What we need to find

Cos(b)

Cos(a)

What we are going to apply

Sum and Difference Formulas

Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

$\cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b)$

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

${12}^{2} + {y}^{2} = {13}^{2}$

$144 + {y}^{2} = 169$

$25 = {y}^{2}$

$y = 5$

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

$( - 3) {}^{2} + {x}^{2} = {5}^{2}$