Solve: √x=25. Explain how you found your answer. Explain how to check your work.

A rectangle has length 4 yards more than its width. The area of the rectangle is 96 square yards. Find the

stepladder [879]

Answer:

Length = 12

Width = 8

Step-by-step explanation:

Area of a Rectangle = l x w

12 x 8 = 96

7 0

3 years ago

Jon's closet has 3 black shirts, 8 blue shirts, 6 black pants and 7 blue pants. He wants to determine the probability of selecti

algol [13]

Answer:

Jon did determine the probability correctly.

Step-by-step explanation:

In Jon's closet, there are a total of 24 clothes. Among those pieces of clothing, there are a total of 9 out of 24 clothes that are black. There are also 11 shirts out of 24 clothes.

When a probability has OR in it, it means to add.

11/24 plus 9/24 gives you 20/24.

Therefore, Jon is correct.

3 0

3 years ago

Match the numerical expressions to their simplest forms.

Aloiza [94]

Answer:

$(a^6b^1^2)^\frac{1}{3}$ = $a^2b^4$

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$ = $a^3b^2$

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$ = $a^2b$

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$ = $ab^3$

Step-by-step explanation:

Simplify each of the expressions:

1

$(a^6b^1^2)^\frac{1}{3}$

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

$(a^6b^1^2)^\frac{1}{3}$

$a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}$

Simplify,

$a^2b^4$

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$

Rewrite as square roots:

$\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}$

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

$\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}$

Simplify,

$\sqrt{a^5b^3}*\sqrt{ab}$

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

$\sqrt{a^5b^3*ab}$

Simplify,

$\sqrt{a^6b^4}$

Since this operation is taking the square root, divide the exponents in half to do this operation:

$a^3b^2$

3

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

$(\frac{a^8}{b^-^4})^\frac{1}{4}$

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

$(a^8b^4)^\frac{1}{4}$

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

$\sqrt[4]{a^8b^4}$

SImplify, divide the exponents by (4) to simulate taking the quartic root,

$a^2b$

4

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

$(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}$

$(a^2b^6)^\frac{1}{2}$

Rewrite to the half-power as a square root,

$\sqrt{a^2b^6}$

Simplify, divide all of the exponents by (2),

$ab^3$

7 0

3 years ago

Which of the following terms are like terms 17j3, 92m, 32j2, 12j, 10m2, 42j, 18j3, and 6m4? Choose all answers that are correct.

zhenek [66]

A. 12j and 42j
C. 17j³ + 18j³
This is because the variables and their powers are the same in these terms

4 0

3 years ago

Read 2 more answers

What are the x- and y-intercepts of the line tangent to the circle (x – 2)2 + (y – 2)2 = 52 at the point (5, 6)?

Mrrafil [7]

1 ) They are perpendicular.
2 ) m · (-1) / m = -1.
The product of the slopes is -1.
3 ) The center of the circle is ( 2, 2 ).
4 ) m = (6-2 ) / 5 -2 = 4/3
5 ) Slope of the tangent: m = - 3/4.
6 ) m = -3/4, passes through the point: ( 5. 6 ):
6 = - 15/4 + b
b = 24/4 + 15/4
b = 39/4
The slope-intercept equation is:
y = -3/4 x + 39/4
7) We will put : x = 0 in the linear equation.
8 ) We will put y = 0 in the linear equation.
9 ) y-intercept : y = 9.75
Zero: x = 13.

3 0

3 years ago