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2 years ago

Which equation represents the data in the table?

Mathematics

1 answer:

gavmur [86]2 years ago

8 0

Answer:

Step-by-step explanation:

It all adds up. Ex; 2*2=4 4-3=1

and continues through the rest of the table

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A book weighs 6 pounds.How many ounces is the book?

BigorU [14]

The book weighs 96 ounces.

One pound is 16 ounces, and 16 x 6 is 96.

6 0

3 years ago

Read 2 more answers

Which rational exponent represents a square root?<br> A. 1 / 2<br> B. 3/2<br> C. 1/3<br> D. 1/4

Fofino [41]

Answer:

1/2 rational exponent represents a square root.

Therefore, option A is correct.

Step-by-step explanation:

As we know that raising to the one-half power i.e. $\frac{1}{2}$ is the same

as taking the square root.

so $x^{\frac{1}{2}}$ is the same as the square root of $x$ .

For example, taking the square root of 4 will determine:

$4^{\frac{1}{2}}$

$\mathrm{Factor\:the\:number:\:}\:4=2^2$

$4^{\frac{1}{2}}=\left(2^2\right)^{\frac{1}{2}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0$

$\left(2^2\right)^{\frac{1}{2}}=2^{2\cdot \frac{1}{2}}$

so the expression becomes

$4^{\frac{1}{2}}=2^{2\cdot \:\frac{1}{2}}$

$=2^1$

$=2$ ∵ $\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a$

so, 1/2 rational exponent represents a square root.

Therefore, option A is correct.

5 0

2 years ago

Read 2 more answers

Which pair of angles are same side exterior angles?

In-s [12.5K]

Answer:

Exterior angles are the ones on the outside and same side means they sit on the same side of the bisector so your answer is 1 and 8

Step-by-step explanation:

6 0

3 years ago

Find the length of the leg a of a right triangle with leg length b = 21.5 inches and the hypotenuse c = 31.9 inches. Use a calcu

mylen [45]

The length of the leg a of the right triangle is obtained by applying the Pythagorean theorem which is given as:

$\text{opposite}^2+adjacent^2=hypothenus^2$

Thus, we have that:

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

Given that b = 21.5 inches and c = 31.9 inches, we now have:

$a^2+(21.5)^2=(31.9^2)$ $a^2+462.25=1017.61$ $a^2=1017.61-462.25$ $a^2=555.36$ $\begin{gathered} a=\sqrt[]{555.36}=23.57 \\ \Rightarrow a=23.6\text{ inches (to one decimal place)} \end{gathered}$

Therefore, the length of the leg a of the right triangle is 23.6 inches

4 0

1 year ago

A boat on the ocean is 2 mi from the nearest point on a straight? shoreline; that point is 15 mi from a restaurant on the shore.

Sladkaya [172]

Answer:

a) x = 0,70 miles

T = 1/2* (√4 + x²) +( 15 - x )/3 Objective Function to minimize

b) V(min) = 2.59 m/hr

Step-by-step explanation:

Let assume the boat is in Point A, she lands in point B, and R is the restaurant

Let call x distance between the point O in which perpendicular line from the boat get to shoreline, and the point were she land.

We know distance is

d = v*t ⇒ t = d/v

She rows at 2 miles/hr and walk at 3 miles /hr

According to that she takes

c (hypotenuse) of right triangle AOB/ 2 rowing

and 15 - x /3 walking

Total time is:

T = c/2 + ( 15-x )/3 c =√(2)² + x² ⇒ T = [√(2)² + x² ] /2 + ( 15-x )/3

T = 1/2* (√4 + x²) +( 15 - x )/3 (1)

And that is the Objective function to minimize

a) Taking derivatives on both sides of the equation we get

T´(t) = x /( √4 + x²) - 1/3 ⇒ T´(t) = 0 x /( √4 + x²) - 1/3 = 0

3*x - √( √4 + x²) = 0 ⇒ 3*x = √( √4 + x²)

Squaring both sides

9x² = 4 + x² ⇒ 8x² = 4 x² = 1/2 x = 0,70 miles

If we plug this value in the Objective function we will get the minimum time

1/2* (√4 + x²) +( 15 - x )/3 ⇒ [√ 4 + 0,5] /2 + 14,3/3 = T (min)

T(min) = 1.06 + 4.77 = 5.83 hr

Distance L (hypotenuse of right triangle AOR)

L = √(2)² + (15)² L = 15,13 miles

And that distance have to be traveled at least in 5.83 hr rowing

Then as v = d/t V(min) = 15.13/ 5.83 ⇒ V(min) = 2.59 m/hr

6 0

3 years ago