Which expression has a greater value: log3 1/3 or logb 1/b? Explain how you know.​

The ball hits the ground after x = 6 seconds.

Two or more expressions with an equal sign are defined as an equation.

The given equation is h(x) = -2x² + 8x + 24.

(a) when the ball is thrown, the time is t = 0 sec.

Therefore, the height of the ball when it is thrown is,

h(0) = -2(0)² +8(0) +24

h(0) = 24

(b) The derivative of the function is,

h'(x) = -4x + 8

Substitute h'(x) = 0 into the above equation,

0 = -4x +8

4x = 8

x = 2

The second derivative of the function is,

h''(x) = -4

Since the second derivative of the function is negative, the function is maximum at x = 2.

(c) The maximum height of the ball is,

h(2) = -2(2)² + 8(2) +24

h(2) = -8 +16 +24

h(2) = 32

(d) The ball hits the ground when h(x)= 0, therefore,

0 = -2x² +8x +24

0 = -2x² +12x - 4x + 24

0 = -2x(x - 6) - 4(x - 6)

0 = (x - 6)(-2x - 4)

(x - 6) = 0 or (-2x-4) = 0

x = 6 or x = -2

Since time cannot be negative, it follows, x = 6 seconds.

Hence, the ball hits the ground after x = 6 seconds.

Learn more about equations here:

https://brainly.com/question/10413253

#SPJ1

Answer:

Step-by-step explanation:

so,  I was just commenting about word problems to another person and here is a great example of a word problem that is too complex.  They are using the term  "function rule"  that is too broad.  They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about.  We need to understand what "function rule"  really means.   They have also used the varible "s"  which is mostly reserved for  Laplace /  Fourier  transformations.  This is just a really badly written question.   Don't feel bad if  you don't get what it's asking.  it's messy at best.   t(s) is then name of our function,  it's rule ( the function rule)  is 40/s  it's constant of proportionality is 40  ,  This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH  , which is obviously not correct.   There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH,  this function rule is probably not accurate after some time.  the speed probably starts out fast,   slows down till the close to the very end of the race... they jumps up dramatically to the finish.   Watch the Tour de France writer of this question.  :D   The riders slow down as the race progress according to this function rule.  But I don't think that's at all accurate for a real bike race.   they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH  :0

The interest rate that would be required for Emma to end up with $2440 in her bank account is 6.8%

Given,

P = $720

A = $2440

t = 18 years.

r = n[(A/P)^1/nt - 1]

r = 12 × [(2440/720)¹/⁽¹²⁾¹⁸ - 1]

r = 0.06799764

Then convert r to R as a percentage.

R = r × 100

R = 0.06799764 × 100

R = 6.8%/year

Hence the rate of interest is 6.8%

Learn more about Compound Interest here:

brainly.com/question/24924853

#SPJ1

a. The discount amount of the exercise machine is $3.39.

b. The exercise machine's sale price will be $561.61

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since the exercise machine with an original price of $565 is on sale at 6% off. The discount will be:

= Discount percentage × Price

= 6% × $565

= $3.39

The exercise machine's sale price will be:

= Original price - Discount

= $565 - $3.39

= $561.61

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

The corresponding standard deviation percentage area for -2 to -1,  0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85%

To find the Standard Deviation Percentage Area, you have to consider the lower and upper points:

-2 to -1

The gap between -2 and -1 is 1 step, you will subtract -1 from -2:

-2 to -1 =>  0.4772 - 0.3413 = 0.1359 = 13.59%

Note: the values for -2 and +2 are the same. The same also applies to -1 and +1 and others

0 to +1

Check the value under 1. That is 0.3413 = 34.13%

0 to +2

Check the value under 2. That is 0.4772 = 47.72%

+1 to +3

The gap between +1 and +3 is 2 steps, you will subtract  1 from 3:

+1 to +3 =>  0.4987-0.3413 = 0.1574 = 15.74%

-1 to +2

-1 to +2 is the same as moving -1 to 0 and then moving from 0 to +2, you will add the values for -1 and +2:

-1 to +2 => 0.3413 + 0.4772 = 0.8185 = 81.85%

Therefore, the Standard Deviation Percentage Area for -2 to -1,  0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85% respectively

Learn more about Standard Deviation Percentage Area on:

https://brainly.com/question/10416371

#SPJ1

The value of the inequality X + 3 < 6 is x < 3.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information given, the inequality will be illustrated thus:

x + 3 < 6

Collect like terms

x < 6 - 3

x < 3

The value is x < 3.

Learn more about inequalities on:

brainly.com/question/25275758

#SPJ1

Harold's solution for the given division problem is not valid because it is not accurate.

We are given two numbers. The numbers are given in scientific notation. The first number is 8.4×10^(-7). The second number is 3.6×10^(-2). We need to find the result of the division of the first number by the second number. Let the result of division be denoted by the variable "Q".

Q = [8.4×10^(-7)] ÷ [3.6×10^(-2)]

Q = [(8.4/3.6)×10^(-7 - (-2))]

Q = [(8.4/3.6)×10^(-7 + 2)]

Q = 2.33×10^(-5)

Harold solved this division problem by first rounding the numbers. His result is 2×10^(-5).

Harold's result differs a lot from the actual result. So, his result is not accurate. Hence, his solution is not valid.

To learn more about division, visit :

https://brainly.com/question/13263114

#SPJ1

Protein intake, if he consumes 9 egg whites a day is 32.4 grams.

Given:

Candice eats six egg whites a day with a protein content of 21.6 grams.

6 egg white = 21.6 grams.

1 egg white = 21.6/6

= 216/10/6

= 216/10*6

= 216/60

= 3.6 grams.

9 eggs white = 9 * 3.6

= 9 * 36/10

= 324/10

= 32.4 grams.

Therefore protein intake, if he consumes 9 egg whites a day is 32.4 grams.

Learn more about the egg consumes here:

https://brainly.com/question/14504168

#SPJ1

Answer:

(x - 3)

Step-by-step explanation:

4x² - 12x ← factor out 4x from each term

= 4x(x - 3)

the factors are 4x and (x - 3)

Answer:

12a + 13b

Step-by-step explanation:

3(5a + 4b) - 3a + b

multiply 3 by 5a and 4b

15a + 12b - 3a + b

Now add the a terms together and b terms together

15a - 3a + 12b + b

12a + 13b

Answer:

12a + 13b

Step-by-step explanation:

3(5a+4b)-3a+b

To simplify the expression, we need to distribute the 3 to all terms inside the parentheses

3*5a+3*4b-3a+b

15a+12b-3a+b

Combine like terms

12a + 13b

The volume of the cylindrical jar be 1130.97 in³.

Also, 56 whole marbles can fit in the jar.

Given, a cylindrical jar has a radius of 6 inches and a height of 10 inches.

The jar is filled with marbles that have a volume of 20 in³.

(a) The volume of the cylindrical jar be,

Volume = πr²h

Volume = (3.14)(6)²(10)

Volume = 1130.97 in³

(b) Now, if each marble has the volume of 20 in³

then, the number of marbles that can be fit in the jar be,

The number of marbles = 1130.97/20

The number of marbles = 56.

Hence, the volume of the cylindrical jar be 1130.97 in³.

Also, 56 whole marbles can fit in the jar.

Learn more about Volumes here https://brainly.com/question/463363

#SPJ1

Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

Since we're subtracting the entire quadratic, we can place the second equation in parentheses and distribute the subtraction sign.

[tex]2x^2-9x+8-(6x^2-5x-12)\\2x^2-9x+8-6x^2+5x+12\\2x^2-6x^2-9x+5x+8+12\\-4x^2-4x+20[/tex]

Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

To find the difference of the two quadratic expressions, subtract the second expression from the first expression:

[tex]\implies (2x^2-9x+8)-(6x^2-5x-12)[/tex]

Remove the parentheses and apply the distributive law
[tex]-\left(a-b\right)=-a+b[/tex]

[tex]\implies 2x^2-9x+8-6x^2+5x+12[/tex]

Collect like terms:

[tex]\implies 2x^2-6x^2+5x-9x+8+12[/tex]

Combine like terms:

[tex]\implies -4x^2-4x+20[/tex]

Therefore, the difference of the two quadratic expressions is:

[tex]\large \boxed{-4x^2-4x+20}[/tex]

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Answer:

x = 6

Step-by-step explanation:

2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )

x = - 3 × - 2 = 6

x = 6

Jamal need to invest $35838.77 in an account.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

As given Jamal wants to save $54,000 for a down payment on a home with 8.2% APR, compounding daily for 5 years.

The compound interest formula is,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here, A = $54000, r = 8.2% = 0.082, t = 5, n = 365

Plug the values in the above formula,

[tex]54000 = P(1+\frac{0.082}{365} )^(^3^6^5^)^(^5^)\\54000 = P(1.0002246575)^1^8^2^5\\54000= P(1.5067483068)\\P = \frac{54000}{1.5067483068} \\P = 35,838.766\\P = 35838.77[/tex]

Hence, Jamal need to invest $35838.77 in an account.

To know more about the compound interest, click on the link

https://brainly.com/question/24274034

#SPJ4

Answer:

-1.1

Step-by-step explanation:

:)

Answer:

the exact form is 419/104

decimal for:4.02884615...

mixed number form: 4 3/104

Step-by-step explanation:

calculator

The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

Learn more about Equations here

https://brainly.com/question/17612414

#SPJ4

Answer:

[tex]y=3x-13[/tex]

Step-by-step explanation:

Parallel lines have the same slope. So, the equation is:

[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]

Answer:

Assuming w=2 and r=3, we plug in these values

2+5*3 = 2+15 = 17

Step-by-step explanation:

Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.

As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.

When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.

Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ1

Answer:

a

Step-by-step explanation:edge

Answer:

A

Step-by-step explanation:

36x = 535 - 31

36x = 504

36/36 x = 504/36

x = 14

[tex]{ \green{ \boxed{ \red{ \sf{x = 14}}}}}[/tex]

Step-by-step explanation:

[tex]{ \purple{ \tt{36x + 31 = 535}}}[/tex]

[tex]{ \purple{ \tt36x = 535 - 31}}[/tex]

[tex]{ \purple{ \tt{36x = 504}}}[/tex]

Divide both the sides by 36 then,

[tex]{ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = 14}}}}}[/tex]

Answer:

y = 8/5

Step-by-step explanation:

Formula we use,

→ y = kx

Then the value of y will be,

→ y = kx

→ y = (-2/5) × (-4)

→ y = (-2 × -4)/5

→ [ y = 8/5 ]

Hence, the value of y is 8/5.

The number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80 from the algebraic equation is; 12 pounds

Let x represent the number of pounds of Chamomile tea needed.

We are told to find the number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80.

Therefore,

9x + 6(8) = 7.8(8 + x)

9x + 48 = 62.4 + 7.8x

9x - 7.8x = 62.4 - 48

1.2x = 14.4

x = 14.4/1.2

x = 12

Read more about Algebraic Equations at; https://brainly.com/question/4344214

#SPJ1

The equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.

Given: A line is perpendicular to line y = 4x – 7  and passes through point A (8, 2).

We know that,

Slope of line perpendicular to another line is negative reciprocal of its slope.

So, m(slope) = -1/4

Equation of line is given as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 8)

y + (1/4)x = 4

Therefore, the equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

Learn more about point-slope form here:

https://brainly.com/question/22250570

#SPJ1

A linear graph with a negative slope indicates that as the independent variable decreases, the dependent variable increases.The line with a negative slope is sloping down to the right.

This relationship is represented by a line sloping down to the right. A line with a negative slope indicates that there is a negative correlation between the two variables. This means that as one variable decreases, the other variable increases.

This is because the line is going down from left to right, which means that the y-value is increasing as the x-value decreases. This relationship is known as a negative correlation.It is also known as an inverse relationship. In an inverse relationship, the two variables move in opposite directions. As one variable decreases, the other variable increases.

Learn more about variable at : https://brainly.com/question/15078630

#SPJ4

Proved that the length of AB ≅ the length of CD

The conditions are given that

The line BC and the line AD are parallel lines

The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other

Similarly

The measure of angle BAD is equal to the measure of angle DCB

If angle BAD = angle DCB, then we can say that the given shape is a parallelogram

In the parallelogram the opposite sides will be equal

Then the length of the length of AB equal to the length of CD

Hence, proved that the length of AB ≅ the length of CD

Learn more about parallelogram here

brainly.com/question/16578666

#SPJ1

The dimensions that will minimize the cost is

h= 2.82876 and r = 1.06078

Given That, C₁ = $10 and C₂= $10 and C₃ = $15

lets multiply the top and bottom, we get,

C₁ × C₂ = $10 ×$ 20 = $ 30

The total cost is,

C = (2πr²) C₁ + (2πrh)C₂

Here,  r is base radius and h is the side length.

The volume is given by and the volume to 20 m³

∴ V = πrh² ⇒ πr²h = 20

So, h = 20/πr²

Now, the problem can be  stated as

minimum h, r C(h, r) restricted to V(h, r) = V₀

Using language multiplier it reads,

L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]

Solving for h, r, λ, we get,

h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)

λ = -2 ∛2πC₁C₂² /V₀

or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214

We know that is a minimum because,

(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r

d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³

and for the found solution has the value

d²/dr² (C₀V) (r) = 240 π > 0

Learn more about multiplier:

https://brainly.com/question/23536361

#SPJ4