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nydimaria [60]
2 years ago
15

Anyone know this please???

Mathematics
1 answer:
Kazeer [188]2 years ago
6 0

Answer: Choice A

The triangles are congruent because both the corresponding sides of the triangles and the corresponding angles of the triangles are congruent.

==============================================

Explanation:

Congruent triangles are identical copies of one another. This means the corresponding pieces must be the same.

It's like saying two houses are identical, so that means the all the various parts (eg: front door, windows, etc) must be identical. If let's say the two front doors were different, then the houses wouldn't be completely identical.

Going back to the triangles, we know that the sides are congruent by the tickmarks

  • side MN = side RS (single tickmark)
  • side NP = side ST (double tickmarks)
  • side MP = side RT (triple tickmarks)

That takes care of the first part of choice A.

And similarly, the angle markers tell us which angles are congruent

  • angle M = angle R  (single arc)
  • angle N = angle S (90 degree angle marker)
  • angle P = angle T (double arc)

That concludes the second part of choice A.

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What is the solution of the following quadratic inequality? x4 – 18x2 ≥ –64
Alexus [3.1K]

Answer:

x<=-4 or -2<=x<=2 or x>=4

Step-by-step explanation:

First, you have to get the formula in its standard form,

x^4 - 18x^2 + 64 >= 0

Next, you factorise the expression as you would any trinomial. The fact that the degree of the inequality is 4 instead of 2 just adds an extra step,

(x^2 - 16)(x^2 - 4) >= 0

Get the zeroes/critical values of the equation by equating either bracket to zero.

x^2 - 16 = 0  and  x^2 - 4 = 0

x^2 = 16                x^2 = 4

Since both values are positive, both answers are valid as squares of x. The aforementioned extra step is just square rooting these values. Remember: This means that both a positive and negative answer will arise from both equations.

x = 4 or x = -4 or x = 2 or x = -2

Now you have to show these values on a number line.

 -4     -2       2       4

_|____|____|____|_

These are the critical values of the inequality, i.e. those values that make it equal zero (zeroes). Now to solve the inequality you need to substitute a value larger than 4 (called x big positive) and then a value between 2 and 4, between -2 and 2... until you sub a value less than -4 into the factorised expression. The point of this is to get the SIGN of the answer. As a rule, since no factors repeat themselves, after calculating x big positive you can simply alternate the signs going left. Try it out yourself!

+ -4 -  -2  +   2   -   4  +

_|____|____|____|_

Since we're looking for values greater than or equal to zero, all critical values as well as "plus signs" will form part of the answer, namely:

x<=-4 or -2<=x<=2 or x>=4

P.S. If you prefer, you could also factorise each bracket further as both of them were DOTS brackets and you would have ended up with the same critical values.

4 0
2 years ago
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