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4 years ago

jay thinks that the inequality k< 3 implies the inequality k squared < 9 but val thinks otherwise. Who is right and why

Mathematics

1 answer:

telo118 [61]4 years ago

7 0

Answer:

Val is right

Step-by-step explanation:

One of the solutions to k < 3 is k = -4. When you square that, you get ...

k² = (-4)² = 16

which is not less than 9.

_____

k < 3 and k² < 9 will have the same solution set for |k| < 3, but their solution sets will differ for k ≤ -3.

When performing operations on inequalities, one needs to be aware of the order preserving/changing effects of the operation. Whether squaring a value preserves order or not depends on the relative magnitudes:

2 > 1; 2² > 1²
-1 < 1; (-1)² = 1²
-2 < 1; (-2)² > 1²
-2 < -1; (-2)² > (-1)²

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3 years ago

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3 years ago

the lengths of the side of a rectangular window have the ratio 1.7 to 1 the area of the window is 2,720 sqaure inches what are d

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Answer:

$Lenght: 68\ in\\\\Width: 40\ in$

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

$A=lw$

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You know that the ratio of the sides of the rectangular window is:

$1.7:1$

Then, let be $x$ the width (in inches) of the rectangular window and $1.7x$ the lenght (in inches) of the rectangular window.

Knowing that the area of the window is 2,720 square inches, you can know that:

$(1.7x)(x)=2,720$

Now you must solve for "x" in order to find the width:

$(1.7x)(x)=2,720\\\\1.7x^2=\\\\x=\sqrt{\frac{2,720}{1.7} }\\\\x=40$

Finally, the lenght is:

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4 years ago

What is the measure of angle "A"?

Zolol [24]

Answer:

Step-by-step explanation:

The given figure is an isosceles trapezoid, this means that the two non-parallel sides in the trapezoid are congruent. One of the properties of an isosceles triangle is that opposite angles are supplementary. This means that the sum of angles opposite each other in an isosceles trapezoid is (180) degrees. One can apply this here by stating the following,

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3 years ago

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3 years ago