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2 years ago

Identify the values of a, b, and c that make the statement below true. log2 64 = 6 if and only if ab =

2 answers:

7 0

Given that $\log_264=6$ if and only if $a^b=c$ .

The relationship between logarithm and indices is given by

$x^y=m\Leftrightarrow\log_xm=y$

Combaring with the original relation, we have that a = 2, b = 6 and c = 64.

tia_tia [17]2 years ago

5 0

Answer:

The answer to the first part is:

a = 2

b = 6

c = 64

The answer to the second question is:

A: log232 = 5

Step-by-step explanation:

on edg.. good luck!!

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Raymond just got done jumping at Super Bounce Trampoline Center. The total cost of his session was \$43.25$43.25dollar sign, 43,

Elodia [21]

Answer:

29 minutes

Step-by-step explanation:

Given

$Total = \$43.25$

$Entrance\ Fee = \$7$

$Per\ Minute = \$1.25$

Required

Determine the number of minutes (t) that he was on the trampoline.

This can be expressed as:

$Total\ Payment = Entrance\ Fee + Amount\ per\ minute * t$

Where t represents the number of minutes

Substitute values for Total, Entrance Fee and Amount per minute

$43.25 = 7 + 1.25 * t$

$43.25 = 7 + 1.25t$

Solving further to get the value of t, we have:

$1.25t = 43.25 - 7$

$1.25t = 36.25$

$t = 36.25/1.25$

$t = 29$

3 0

2 years ago

Read 2 more answers

A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Ex

MissTica

Answer:

Part A) The slope is undefined

Part B) The equation of the line is $x=p$

Part C) None y-intercept

Part D) The slope of a line perpendicular to the given line is equal to zero

Step-by-step explanation:

we have that

Describe

A) slope of the line

B) equation of the line

C) y-intercept

D) slope of a line perpendicular to the given line

Part A) slope of the line

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$(p,a)\ (p,-a)$

Substitute the values

$m=\frac{-a-a}{p-p}$

$m=\frac{-2a}{0}$ -----> the slope is undefined

Its a vertical line (parallel to the y-axis)

Part B) Equation of the line

we know that

The equation of a vertical line is equal to the x-coordinate of the points through which the line passes.

$x=p$

Part C) The y-intercept

The y-intercept is the value of y when the value of x is equal to zero

The vertical line not intercept the y-axis

None y-intercept

Part D) slope of a line perpendicular to the given line

A line perpendicular to the given line is a horizontal line (parallel to the x-axis)

therefore

The slope is equal to zero

6 0

2 years ago

In circle M shown, chords GH and EF intersect at K such that EK  5 and FK  6 . If GK  3 , then which of the following is the

myrzilka [38]

The length of the GH segment is 13

Step-by-step explanation:

For solving this problem we need to remember some of the circle corollaries-

When two-chord intersects each other, the product of the chord segments are equal

The above corollary can be easily understood by looking at a diagram attached below-

In the figure, EF and GH are two chords intersecting at K

Thus, EK*KF= GK*KH

Values of the EK, KF, GK are given as 5, 6 and 3 respectively

Substituting the values we get

5*6=3*KH

KH= 10

We know that GH= GK+KH

Thus GH= 3+10= 13

6 0

2 years ago

Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

2 years ago

A machine takes 5.4 hours to make 9 parts. At that rate how many parts can the machine make in 25.8 hours

Sliva [168]

$\frac{5.4}{9} = \frac{25.8}{x}$ Cross multiply.

5.4x=9*25.8

5.4x=232.2 Divide both sides by 5.4

x=43

4 0

2 years ago

Read 2 more answers