Which of the following units are most commonly used in the United States?

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

$648=2 \cdot 324$

324 divides by 2,

$648=2 \cdot 2 \cdot 162$

162 divides by 2,

$648=2 \cdot 2 \cdot 2 \cdot 81$

81 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27$

27 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9$

9 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Thus, we have,

$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

Therefore, equating the powers of 2 and 3, we get,

$a=3, b=4$

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

4 0

3 years ago

Read 2 more answers

A restaurant offers a special pizza with any 4 toppings. If the restaurant has 15 topping from which to choose, how many differe

OlgaM077 [116]

Answer: 1,365 possible special pizzas

Step-by-step explanation:

For the first topping, there are 15 possibilities, for the second topping, there are 14 possibilities, for the third topping, there are 13 possibilities, and for the fourth topping, there are 12 possibilities. This is how you find the number of possible ways.

15 * 14 * 13 * 12 = 32,760

Now, you need to divide that by the number of toppings you are allowed to add each time you add a topping.

4 * 3 * 2 * 1 = 24

32,760 / 24 = 1,365

There are 1,365 possible special pizzas

8 0

3 years ago

A patio 44, feet wide is being constructed next to a house. To drain water off the patio and away from the house, a slope of 1/2

navik [9.2K]

Answer:

the total difference in height will be 22 inches

Step-by-step explanation:

since the slope is 0.5 inch per foot, and the patio is 44 feet wide, the end of the patio will be 0.5 x 44 = 22 inches lower

the slope measures how much the height (Y axis) will change as the length (X axis) increases by 1 unit. In this case, since the height decreases as the length increases the slope is negative.

3 0

3 years ago

Determine the value of $a$. [asy] pair w=(0,4); pair x=(0,0); pair y=(4,0); pair z=y+7/sqrt(2)*(1,1); dot(w); dot(x); dot(y); do

grandymaker [24]

Answer:

a=7

Step-by-step explanation:

The image is rendered and attached below.

Triangle WXY is an Isosceles right triangle, since WX=XY.

First, we determine the length of WY using Pythagoras Theorem.

$WY=\sqrt{4^2+4^2}\\WY=\sqrt{32}$

Since triangle WXY is Isosceles, $\angle XYW=45^\circ$

$\angle XYZ=\angle XYW+\angle WYZ\\135^\circ=45^\circ+\angle WYZ\\\angle WYZ=135^\circ-45^\circ=90^\circ$

Therefore:

Triangle WYZ is a right triangle with WZ as the hypothenuse.

Applying Pythagoras Theorem

$WZ^2=WY^2+YZ^2\\9^2=(\sqrt{32})^2+a^2\\a^2=81-32\\a^2=49\\a^2=7^2\\$Therefore: a=7$

3 0

3 years ago

In a multi-digit number, the number place that a digit is in determines it's?

slavikrds [6]

Answer:

PLACE VALUE

Step-by-step explanation:

To Find:in a multi-digit number, the number place that a digit is in determines it's?

Solution :

The number place that a digit is in determines it's PLACE VALUE

Definition of place value : Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Thus in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.

Eg . 389

Since the digit 8 is on tens place

So, it makes us to determine its place value

Place value of 8 is 80

Hence in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.

8 0

2 years ago