What is the measure of the angle labeled (5x+42)° ?

Mathematics

2 answers:

kakasveta [241]2 years ago

5 0

These angles are known as alternate interior angles. A fact about them is that they are always congruent. Since they are congruent, we can set them equal to each other:

$8x-3=5x+42$

Let's find the value of x so that we can find what (5x + 42) is:

$8x-3=5x+42$

$8x=5x+45$

$3x = 45$

$x = 15$

x = 15 so we can plug that in to find the angle:

$5(15)+42 = 75+42 = 117$

Thus, that angle is equal to 117°.

barxatty [35]2 years ago

4 0

We see two parallel lines crossed by a transversal.

The two labelled angles are alternate interior angles, hence they are equal.

The equality allows us to equate the two expressions and hence solve for x.

8x-3=5x+42

transpose terms

8x-5x=42+3

solve for x

3x=45

so x=45/3=15.

This means 5x+42=5*15+42=75+42=117 degrees.

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one tamk of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of

Zarrin [17]

Answer:

20 gallons were used from the tank with the octane rating of 80.

Step-by-step explanation:

Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.

To find : How many gallons should be used from the tank with the octane rating of 80?

Solution : Let x be the volume of gas whose octane rating is 140 and

y be the volume of gas whose octane rating is 80.

Then, we form the equation as:

(1) $x\times140 + y\times80 = 60\times120$