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Alex777 [14]
2 years ago
15

Which equation represents the data in the table?

Mathematics
1 answer:
gavmur [86]2 years ago
8 0

Answer:

c

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=1017.61a^2=1017.61-462.25a^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
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