Is the triangle obtuse, acute, equilateral or right?

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Answer:

  obtuse

Step-by-step explanation:

The law of cosines tells you ...

  b² = a² +c² -2ac·cos(B)

Substituting for a²+c² using the given equation, we have ...

  b² = b²·cos(B)² -2ac·cos(B)

We can subtract b² to get a quadratic in standard form for cos(B).

  b²·cos(B)² -2ac·cos(B) -b² = 0

Solving this using the quadratic formula gives ...

  [tex]\cos(B)=\dfrac{-(-2ac)\pm\sqrt{(-2ac)^2-4(b^2)(-b^2)}}{2b^2}\\\\\cos(B)=\dfrac{ac}{b^2}\pm\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}[/tex]

The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...

  [tex]\cos(B)=\dfrac{ac}{b^2}-\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}[/tex]

The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.

Sylvain spent a total of 18 hours on English and math homework over the last 3 weeks. He spent twice as much time on English than on math. Let x represent the number of hours spent on English and y represent the number of hours spent on math.

x + y = 18. x = 2 y.

What is the solution of the system of equations?
(12, 6)
(6, 12)
(9, 9)
(15, 3)

Identify the initial value and rate of change for the graph shown

A coordinate plane graph is shown. A line passes through the y-intercept at 1 and through the point 5 comma 4.

Initial value: 1, rate of change 3 over 5.
Initial value: 3 over 5., rate of change: 0
Initial value: 1, rate of change 5 over 3.
Initial value: 5 over 3., rate of change: 0

In which line is an error first made when solving the equation below? -18 = 19z -9
Line One = z -9
Line Two = 11 = z
Line Three = z = 11
* Choose one of the following, A, B, C, D.*
A) no mistake was made
B) line 3
C) line 2
D) line 1

How would you do this?

find the value of a and be when x is 12 a= 5x^2/2 b= 2x^2(x-5)/10x

HELP PLEASE!!! i will give brainly! +10 points

Suppose each cube in this right rectangular prism is a -inch unit cube.



What are the dimensions of the prism?
What is the volume of the prism?

lets evaluate 81^-3/4.

The blue shape is a dilation of the black shape. What is the scale factor of the dilation? Simplify your answer and write it as a fraction or whole number.

Which of the equations is graphed below?

Which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4.? (5 points)

x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 7 multiplied by y to the power of negative 1.
x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of 12 multiplied by y to the power of negative 12.
x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3.
x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 3 multiplied by y to the power of 3.

simplify

(x^a.x^b)^a-b*(x^b.x^c)^b-c*(x^c.x^a)^c-a

step by step..

From an 18-pound cut of meat, Mr. Rand cuts off steaks weighting 1 pound 15 ounces, 3 1/8 pounds, and 4 1/2 pounds. He divides up the rest into 9-ounces patties and sells them at 3 for $3.12. How much money does he receive for the patties?

In the figure shown, line AB is parallel to line CD.

Part A: What is the measure of angle x? Show your work. (5 points)

Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)

Pls help
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Give a good explanation

Please help! I’m confused.

Leon used the number line below to show -5 + 4. explain what is wrong with his model.

Marly gets 5 gems every 5 minutes. If Marely has 180 gems, how many minutes have passed?

15 POINTS!!!
Identify the initial value and rate of change for the graph shown

A coordinate plane graph is shown. A line passes through the y-intercept at 1 and through the point 5 comma 4.

Initial value: 1, rate of change 3 over 5.
Initial value: 3 over 5., rate of change: 0
Initial value: 1, rate of change 5 over 3.
Initial value: 5 over 3., rate of change: 0

Eight hundred tickets are sold for a play. Thirty-five percent of those tickets were sold in advance. Which equation can be used to find the number of tickets sold in advance? StartFraction 800 divided by 8 Over 35 divided by 8 EndFraction = StartFraction 100 Over 4.375 EndFraction StartFraction 100 divided by 8 Over 800 divided by 8 EndFraction = StartFraction 12.5 Over 100 EndFraction StartFraction 35 times 8 Over 800 times 8 EndFraction = StartFraction 280 Over 6400 EndFraction StartFraction 35 times 8 Over 100 times 8 EndFraction = StartFraction 280 Over 800 EndFraction

Rewrite 24.5 as a mixed number in lowest terms.



Rewrite 0.85 as a fraction in lowest terms.

What are some transformations that would map DFE to ABC on this coordinate plane? Other than a unit movement

pls help find the angle

does this make sence to anyone

Help me please! It’s due in like 10 minutes and I’m barely on the 8th question !!!