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3 years ago

Which is a counterexample that shows the statement is false? If you square a number, then the answer is greater than the number.

Mathematics

1 answer:

Iteru [2.4K]3 years ago

7 0

Answer:

A. ( $\frac{1}{2}$ )² = $\frac{1}{2}$ × $\frac{1}{2}$ = $\frac{1}{4}$

Step-by-step explanation:

Answer choice (A) is the counterexample because squaring number $\frac{1}{2}$ results into number $\frac{1}{4}$ which is less than $\frac{1}{2}$ .

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The height, h, in feet of a rock above the ground is given by the equation h = -16t^2 + 24t + 16, where t is the time in seconds

boyakko [2]

The rock will hit the ground at 2 seconds.

Explanation:

Given that the height, h, in feet of a rock above the ground is given by the equation $h=-16t^2+24t+16$ , where t is the time in seconds after the rock is thrown.

We need to determine the time at which the rock will hit the ground.

To determine the time, let us equate the height h = 0 in the equation $h=-16t^2+24t+16$ , we get,

$0=-16t^2+24t+16$

Switch sides, we have,

$-16 t^{2}+24 t+16=0$

Let us solve the equation using the quadratic formula.

Thus, we have,

$t=\frac{-24 \pm \sqrt{24^{2}-4(-16) 16}}{2(-16)}$

Simplifying, we get,

$t=\frac{-24 \pm \sqrt{576+1024}}{-32}$

$t=\frac{-24 \pm \sqrt{1600}}{-32}$

$t=\frac{-24 \pm 40}{-32}$

Hence, the two values of t are

$t=\frac{-24 + 40}{-32}$ and $t=\frac{-24 -40}{-32}$

Simplifying the values, we get,

$t=\frac{16}{-32}$ and $t=\frac{-64}{-32}$

Dividing, we get,

$t=-\frac{1}{2}$ and $t=2$

Since, t cannot negative values, we have,

$t=2$

Thus, the rock will hit the ground at 2 seconds.

8 0

3 years ago

What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?

vivado [14]

Answer:

hello there,

the answer for this equation is:

The value of Start Fraction 6 Over x End Fraction + 2x2, when x = 3 is 20.

Step-by-step explanation:

: $\frac{6}{x} + 2x^{2} \\ \\\\ \frac{6}{3} + 2(3)^{2}\\\\\\2+2*9 =\\\\\\\\2+18=20$

5 0

3 years ago

Read 2 more answers

In the diagram below, AB and TC are tangent to 0. Which equation could be solved to find x, the measure of AC?

LekaFEV [45]

The equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

<h3>Circle theorem</h3>

The given diagram shows two intersecting lines tangential to a circle at points A and C.

Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.

Mathematically;

<B = 1/2(arcADC - arcAC)

58 = 1/2(238 -x)

Hence the equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

Learn more on circle theorem here: brainly.com/question/26594685

#SPJ1

4 0

2 years ago

What is the algebraic rule for this statement: "Translate the point right 6

ivann1987 [24]

I think it’s D. (x+6, y-4)
because you go right on the x and down on the y

8 0