Select true and false for each question.

a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2

Answers

Answer 1

Select true and false for each question.

a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2 = True

Related Questions

A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?

Answers

[tex]\bf 1\frac{1}{3}\div 8\implies \cfrac{1\frac{1}{3}}{8}\implies \cfrac{\frac{1\cdot 3+1}{3}}{\frac{8}{1}}\implies \cfrac{\frac{4}{3}}{\frac{8}{1}}\implies \cfrac{4}{3}\cdot \cfrac{1}{8}\implies \cfrac{4}{24}\implies \cfrac{1}{6}[/tex]

What are the counting numbers in base 6

Answers

In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1 one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we would need:

Base 6 Base 10

1 1

2 2

3 3

4 4

5 5

10 (1 six plus 0 ones) 6

11 (1 six plus 1 one) 7

12 (1 six plus 2 ones) 8

13 9

14 10

15 11

20 (2 sixes plus 0 ones) 12

21 (2 sixes plus 1 one) 13

22 14

23 15

Final answer:

The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.

Explanation:

The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.

The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.

Write the quadratic function in the form g(x)= a (x-h)^2 +k . Then, give the vertex of its graph. g(x)=3x^2+30x+72
Writing in the form specified: g(x)= ___
Vertex:___

Answers

so hmmm as you may know by now... [tex]\bf \begin{array}{cccccllllll} {{ a}}^2& + &2{{ a}}{{ b}}&+&{{ b}}^2\\ \downarrow && &&\downarrow \\ {{ a}}&& &&{{ b}}\\ &\to &({{ a}} + {{ b}})^2&\leftarrow \end{array}\qquad % perfect square trinomial, negative middle term \begin{array}{cccccllllll} {{ a}}^2& - &2{{ a}}{{ b}}&+&{{ b}}^2\\ \downarrow && &&\downarrow \\ {{ a}}&& &&{{ b}}\\ &\to &({{ a}} - {{ b}})^2&\leftarrow \end{array}[/tex]

is a perfect square trinomial

now, let's take a closer look at the middle guy
is just 2 * guy on the left * guy on the right
so the middle term is just the product of the two terms of the binomial, without the exponent, or square rooted, and 2

alrite... that said.... now let's do some grouping

[tex]\bf g(x)=3x^2+30x+72\implies g(x)=(3x^2+30x)+72 \\\\\\ g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x+\boxed{?}^2)+72[/tex]

so hmm we're missing the guy on the right there... who may that be?

well, we know the middle term is 10x, wait a minute, 10x is just 2 * 5 * x

so, if the guy on the left is "x", the other guy must be "5", 2*5*x = 10x

now, what we do is, we add 5²

however, bear in mind that, all we're doing is, borrowing from our very good friend Mr Zero, 0

so, if we add 5², we also have to subtract 5², so +5² - 5²

let's do so

[tex]\bf g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x\boxed{+5^2-5^2})+72 \\\\\\ \textit{let's take out the negative from the group} \\\\\\ g(x)=3(x^2+10x+5^2)+\boxed{3(-5^2)}+72 \\\\\\ g(x)=3(x^2+10x+5^2)-75+72\implies g(x)=3(x+5)^2-3 \\\\\\ g(x)=3[x-(-5)]^2-3[/tex]

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} y=a(x-{{ h}})^2+{{ k}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ \begin{array}{lcclll} g(x)=3[x-&(-5)]^2&-3\\ &\uparrow &\uparrow \\ &h&k \end{array}[/tex]

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=52t-16t^2 . What is the maximum height that the ball will reach? Do not round your answer.
Height: ________Feet

Answers

A quick way to do this problem is to use the vertex formula as if you were trying to graph the parabolic function.
We know that in this case the vertex is at a maximum height because the leading coefficient is negative. If it were positive, then the vertex would be at the lowest point, in other words, they would ask you to solve for the lowest point. In this case we are solving for the highest point.
Primarily, we can use the axis of symmetry formula to solve for the x-coordinate of the vertex which demonstrates the time the object takes to reach its apex. Once we find the t or the x-coordinate, we can plug it back into the equation to solve for the h or height.
Axis of symmetry formula: -b/ 2a

(b) is 52 in this case. (a) is -16 in this case. Just plug the numbers in but be mindful of the signs included in the formula.
-(52)/ 2(-16) = -52/-32
The quotient would be a terminating decimal: 1.625

Therefore, the time it takes for the ball to reach its highest point would be 1.625 seconds. Now you can plug this number back in as a substitution for the variable t and you can solve for h.

h = -16(1.625)^2 + 52(1.625)
h = -16(2.640625) + 84.5
h= -42.25 + 84.5
h = 42.25
Therefore, the maximum height that the ball will reach in 1.625 seconds is 42.25 feet.

The maximum height would be 42.25 feet that the ball will reach.

What is the velocity?

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²

Here h(t) = 52t - 16t²

Differentiate with respect to t to get maximum height

h'(t) = 52 - 2 × 16t

h'(t) = 52 - 32t

In this position, the acceleration would be zero,

So 0 = 52 - 32t

32t = 52

t = 52/ 32

t = 1.625

Substitute the value of t = 1.625 in the given function,

⇒ h = 52(1.625) - 16(1.625)²

⇒ h = 84.5 - 42.25

⇒ h = 42.25

Therefore, the maximum height would be 42.25 feet that the ball will reach.

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What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?

Answers

Final answer:

The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).

Explanation:

In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:

First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).

Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.

So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).

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Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?

Answers

Yes, because by the triangle inequality, a triangle can be formed from three segments of which the sum of the lengths of the two shorter ones exceed the longest segment.

Here we have 36+48=84 > 60, so the three segments form a triangle.

Since the ratio of the sides are 36 : 48 : 60 form the ratio of 3:4:5, which is exactly the ratio of a right triangle, we conclude that the triangle is a right triangle.

Final answer:

Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.

Explanation:

The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.

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Peter decides to mix grades of gasoline in his truck. He puts in 11 gallons of regular and 7 gallons of premium for a total cost of $76.99. If premium gasoline costs $0.25 more per gallon than regular, what was the price of each grade of gasoline?

Answers

11r + 7p = 76.99
p = r + 0.25

11r + 7(r + 0.25) = 76.99
11r + 7r + 1.75 = 76.99
18r = 76.99 - 1.75
18r = 75.24
r = 75.24/18
r = 4.18 <=== regular : $ 4.18 per gallon

p = r + 0.25
p = 4.18 + 0.25
p = 4.43 <=== premium : $ 4.43 per gallon

Final answer:

Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.

Explanation:

We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.

Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:

11r + 7(r + $0.25) = $76.99r = regualar gasoline price per gallon

Simplifying the first equation:

11r + 7r + $1.75 = $76.99

18r + $1.75 = $76.99

18r = $76.99 - $1.75

18r = $75.24

r = $75.24 / 18

r = $4.18

So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.

this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box

Answers

Since each cube has a volume of 1 cubic meter and the box and fit 48 unit cubes the volume of the box is 48 cubic meters.

Answer:

48 cubic meters.

Step-by-step explanation:

48x1

unit meter is cubic meters

The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 25 feet. Round your answer to the nearest tenth.

Answers

I assume you are looking for the formula, and the velocity.

The formula:
v1^2-v0^2=2aS

where
v0=initial velocity (0 if object falls from rest), ft/s
v1=velocity reached after falling a distance S, ft/s
S=distance from initial position, positive downwards (for falling objects), ft
a=acceleration due to gravity, 32.2 ft/s^2 in imperial units

So substituting numbers, assuming initial velocity is zero (from rest), then
S=25 ft
v1^2-0^2=2*32.2*25
v1^2=1610
v1=sqrt(1610)
=40.1 ft/s

a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, how many miles from earth is the star?

Answers

You just multiply these two.

3.4 * 5.87х10^12 miles

In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]

How can the number of miles be calculated?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that star=3.4 light years from earth

1 light years= [tex]5.87*10x^{12} miles[/tex]

The number of miles from earth is

[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]

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how do write an equation to represent a real world situation?

Answers

You can write about cars. Like for example, Cydney wants to buy a car but doesnt know which one to buy. One of them costs ... and the other costs... or you can write about houses. You can write about anything if you think about, you just need to make sure it looks and sounds real.

Write 337,060 in expanded form using exponents

Answers

3x10^5 \\ +3x10^4 \\ +7x10^3 \\ + 0x10^2 \\ +6x10^1 \\ +0x10^0

“the sum of eight and twice w”

Answers

8+2w
Sum is +
twice w=2w
Sum of 8 and 2w
8+2w
hope this helps:)
please mark thanks and brainliest:)

Answer:

the expression is [tex]8+2w[/tex]

Step-by-step explanation:

WE need to write the expression for the given statement

“the sum of eight and twice w”

Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'

Difference represents the subtraction operation.

Sum represents the addition operation.

twice 'w' means 2 times w that is 2w

the sum of 8 and 2w

For sum we use '+'

so ,the expression becomes [tex]8+2w[/tex]

What is a ratio equivalent to 8/10 with lower terms

Answers

You divide both the top and bottom by the GCF (Greatest common factor)

In this case the gcf is 2 so you divide both 8 and 10 by 2, and you get 4/5.

In a circle of radius 25 inches, a central angle of 35 degrees will intersect the circle forming an arc of length ____

Answers

arc length = (central angle/360) x 2 x PI x r

= (35/360) x 2 x 3.14 x 25

=15.2638

round answer as needed, you don't say how to round it.

Which if the following is the smallest value 0.79, 2.40, 3.00007, 0.424, or 100?

Answers

0.424 is the smallest value
hope this helps

Hi there!

The smallest value is 0.424

-----------------------------------------------------------------------------

You might think that 0.79 is the smallest one but it also has 0 which is not written. 0.790 is bigger than 0.424

I hope that helps!

Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?

Answers

First find the volume of the box: 8•4•4.5=144 cubic inches.
8 of the 1/8 inch=1 of the 1 cubic inch
He could do 144 and 0
143 and 8
142 or 16
Or just keep following the pattern... Hope that helped

If using spss, what is the exact likelihood of obtaining a t-test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true

Answers

Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.

To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.

ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?

Answers

41*41 = 1681
40*40 = 1600
9* 9 = 81
so a^2 = b^2 + c^2
1681 = 1600 + 81
1681 = 1681 ...it's right triangle

CA = 41 = Hypo.
cosC = Adj / Hypo
cosC = BC / CA = 40/41

answer
cosC = 40/41

Answer:

The correct answer is

C 40/41

Step-by-step explanation:

Based on the historical record what is the empirical probability that the city will be hit by a tornado

Answers

25.875% Chance of the city being hit by a tornado.

What is the area of a parallelogram with a base of 20 inches and an altitude of 8 inches?

Answers

140 i think think think or 160

The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.

What is a parallelogram in math?

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.

Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.

A = base * altitude

A = 20 * 8

A = 160 inches square.

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Write 935.97 in expanded form

Answers

935.97 = 900 + 30 + 5 + 0.9 + 0.07

hope it helps

A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.

Answers

t=d/v

540/(230+w)=380/(230-w)

540(230-w)=380(230+w)

124200-540w=87400+380w

124200-920w=87400

-920w=-36800

w=40

So the wind speed is 40 miles per hour.

Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7

Answers

[tex]2x^2 + 6x - 9 = 3x^2 - 11x - 7\\ x^2-17x+2=0\\ a=1\\ b=-17\\ c=2[/tex]

2x^2 + 6x - 9 = 3x^2 - 11x - 7

Subtract 2x^2 from both sides
6x - 9 = x^2 - 11x - 7

Substract 6x from both sides
-9 = x^2 - 17x - 7

Add 9 to both sides
0 = x^2 - 17x + 2

a = 1
b = -17
c = 2

2^-1 ∙ 2^-4 is what?

Answers

1/2 . 1/16 = 1/32

When the power is minus just flip the number and make it denominator and make the power positive

The rule for multiplying similar bases with exponents...

(a^b)(a^c)=a^(b+c)

In this case:

(2^-1)(2^-4)

2^(-1-4)

2^-5 which is equal to:

1/(2^5)

1/32

Which of the following is a polynomial with roots negative square root of 5, square root of 5, and −3?
x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15

Answers

If the roots are -sqrt(5), sqrt(5), and -3, then the three factors of the polynomial are: (x + sqrt(5)), (x - sqrt(5)), and (x+3) Let's multiply the first two factors together. (x + sqrt(5)) * (x - sqrt(5)) = x^2 - 5 Let's multiply this by the third factor (x+3). (x^2 - 5) * (x+3) = x^3 + 3x^2 -5x - 15 The correct answer is the last polynomial in the list of choices above.

What is the next number of 2 7 8 3 12 9

Answers

6 would be the next number in pattern

Answer with Step-by-step explanation:

We are given a pattern

2 7 8 3 12 9

and we are asked to find the next term of this pattern

2+1=3

7+5=12

and 8+1=9

We can view this pattern in the set of three numbers and then, the next three are formed by adding one, five & one, respectively.

See these COLUMNS of groups of three:

2 3 4

7 12 17

8 9 10

Hence, next number in the pattern is:

How do I answer this question?

Answers

see attached picture for steps and answer

what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4

Answers

x^2 - 16 x^3 - 2x^2+x
------------- * ---------------------
2x+8 x^2 + 3x -4

(x+4)(x-4) x (x - 1)(x - 1)
= ----------------- * ----------------------
2(x+4) (x + 4)(x - 1)

x(x- 4) (x - 1)
= -----------------
2 (x + 4)

Answer:

A on Edge 2021

[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]

In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide

Answers

First the glide, and second a reflection

Final answer:

In a glide reflection, the reflection comes first and the glide comes second.

Explanation:

In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.

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Select true and false for each question. a.) LN(x^a) = a + LN x b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y) c.) (ln a)^3b = 3b ln a d.) log_a b^2 = (log_a b)^2

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Select true and false for each question.

a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2