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3 years ago

What is the Value of x?

Mathematics

2 answers:

satela [25.4K]3 years ago

8 0

$\text{It's an isosceles triangle. Therefore}\ m\angle C=m\angle A:\\\\9y-3=69\qquad\text{add 3 to both sides}\\\\9y=72\qquad\text{divide both sides by 9}\\\\\boxed{y=8}\\\\\text{We know: The sum of the measures of the angles of a triangle is 180}^o.\\\\\text{Therefore we have the equation:}\\\\m\angle A+m\angle B+m\angle C=180^o\\\\\text{Substitute}\ m\angle A=m\angle C=69^o:\\\\69+(5x+2)+69=180\\\\138+5x+2=180\\\\140+5x=180\qquad\text{subtract 140 from both sides}\\\\5x=40\qquad\text{divide both sides by 5}\\\\\boxed{x=8}$

$Answer:\ \boxed{\boxed{x=8}}$

Ronch [10]3 years ago

7 0

Answer:

x=8

Step-by-step explanation:

Since this is an isosceles triangle <A is equal to <C

<A = <C = 69

<A+ <B +<C = 180 because the 3 angles of a triangle add to 180 degrees.

69 + 5x+2 + 69 = 180

Combine like terms

140+ 5x = 180

Subtract 140 from each side

140-140 +5x =180-140

5x = 40

Divide by 5

5x/5 =40/5

x=8

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2 years ago

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The function y = x 2 - 10x + 31 has a ____

katrin [286]

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

$f(x) = x^2-10x+31$

Taking first derivative

$f'(x) = 2x-10$

Now the first derivative has to be put equal to zero to find the critical value

$2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5$

The function has only one critical value which is 5.

Taking 2nd derivative

$f''(x) =2$

$f''(5) = 2$

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

$f(5) = (5)^2-10(5)+31\\=25-50+31\\=6$

Hence,

The function y = x 2 - 10x + 31 has a minimum value of 6

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

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2 years ago

Solve for X. Please solve all four. First person to do so will get brainliest.

natali 33 [55]

Answer:

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Step-by-step explanation:

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3 years ago

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Ok need help this is the question :Use the Pythagorean theorem to write an equation for the distance Jane's trainer bikes.

IRINA_888 [86]

Answer:

Jane traveled 8 miles farther then her trainer

Step-by-step explanation:

The Pythagora's Theorem

In any right triangle, the square of the measure of the hypotenuse is the sum of the squares of the legs. This can be expressed with the formula:

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

Where

c = Hypotenuse or largest side

a,b = Legs or shorter sides

Jane's path from the Health Club to the end of her route describes two sides of a right triangle of lengths a=16 miles and b=12 miles.

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Her trainer goes directly from the Health Club to meet her through the hypotenuse of the triangle formed in the path.

We can calculate the length of his route as:

$c=\sqrt{16^2+12^2}$

$c=\sqrt{256+144}=\sqrt{400}=20$

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The difference between their traveled lengths is 28 - 20 = 8 miles

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2 years ago