Which exponential equation is equivalent to the logarithmic equation below? c = ln 2

Answer:

[tex]x_1 = -8[/tex]

[tex]x_2 = -3[/tex]

Step-by-step explanation:

Given the equation:

[tex]x^2+24 = -11x[/tex]

Add 11x to both sides we have;

[tex]x^2+11x+24 = 0[/tex]

Split the middle terms we have;

⇒[tex]x^2+8x+3x+24 = 0[/tex]

⇒[tex]x(x+8)+3(x+8)= 0[/tex]

⇒[tex](x+8)(x+3)= 0[/tex]

By zero product property we have;

x+8 = 0 and x+3= 0

⇒x = -8 and x = -3

Therefore, the roots of the given equations are:

[tex]x_1 = -8[/tex]

[tex]x_2 = -3[/tex]

Answer: 5 units

Step-by-step explanation:

We know that the general equation of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given : The equation of a circle : [tex]3x^2 + 3y^2 = 75[/tex]

Taking 3 as common from the left side of the given equation , we get

[tex]3(x^2 + y^2) = 75[/tex]

Divide 3 on both the sides , we get

[tex]x^2 + y^2 = 25[/tex]

Comparing to the general equation of circle , we get

[tex]r^2 = 25\\\\\Rightarrow\ r=5[/tex]

Hence, the radius of the circle = 5 units

Answer:

[tex]x=7.39[/tex]

Step-by-step explanation:

we are given equation as

[tex]6+ln(x)=8[/tex]

Since, we have to solve for x

so, we will isolate x on anyone side

Firstly, we will subtract both sides by 6

[tex]6+ln(x)-6=8-6[/tex]

[tex]ln(x)=2[/tex]

now, we can take exponent of e on both sides

[tex]e^{ln(x)}=e^2[/tex]

now, we can use property of log

and we get

[tex]e^{ln(a)}=a[/tex]

we can use it

[tex]x=e^2[/tex]

So, solution is

[tex]x=7.39[/tex]

Answer:

352,716 juries of 10 people can be formed from 21 possible candidates

Step-by-step explanation:

I am supposing that there are no roles in the jury, which means that the order in which the people are chosen is not important. So i calculate the number of possible juries using the combinations formula.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

10 people from a set of 21

[tex]C_{21,10} = \frac{21!}{10!(21-10)!} = 352,716[/tex]

352,716 10 person juries can be formed from 21 possible candidates

Answer:  The required number of subsets is 63.

Step-by-step explanation:  We are given to find the number of  subsets of at least one element that a set of six elements have.

We know that

the number of subsets of a set having n elements is given by

[tex]N=2^n.[/tex]

So, the number of subsets of the set having six elements will be

[tex]N=2^6=64.[/tex]

Since there is only one subset of every set that contains less than one element (that is the empty set), so

the number of subsets of the set with at least one element is given by

[tex]N-1=64-1=63.[/tex]

Thus, the required number of subsets is 63.

Yes, they reach the goal and increased their score by 9%.

% Increase = Increase / Original Number × 100. This gives you the total percentage change, or increase.

Given:

Last week game score=66

Next week game score= 72

Change in score= 72-66=6

So,

% increase= Change in score/original score *100

                   =6/66*100

                  =9.09 %

Hence, the score increase by 9.09%.

Learn more about percentage increase here:

https://brainly.com/question/20818421

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Answer:

Option C is a cubic function

Step-by-step explanation:

Given the options we have to choose the cubic function

Cubic function is the function with degree 3 i.e the highest power of variable is 3.

Option a: [tex]f(x)=3x+1[/tex]

The above polynomial has highest power 1 i.e of degree 1

∴ not a cubic function

Option b: [tex]f(x)=3x^2+x+2[/tex]

The above polynomial has highest power 2 i.e of degree 2

∴ not a cubic function

Option c: [tex]f(x)=5x^3+2x+1[/tex]

The above polynomial has highest power 3 i.e of degree 3

∴ above is a cubic function

Option d: [tex]f(x)=x^3+x^4+5[/tex]

The above polynomial has highest power 4 i.e of degree 4

∴ not a cubic function

we are given

m∠3 = 120° and m∠12 = 80°

we will check all

Calculation of m∠1:

we can see that angles 1 and 3 are linear

so, their sum must be 180

m∠1+m∠3 = 180°

now, we can plug values

m∠1+ 120°= 180°

m∠1=60°

Calculation of m∠13:

we know that

angles 12 and 13 are alternate angles

so, they must be equal

m∠13=m∠12 = 80°

m∠13= 80°

Calculation of m∠6:

we know that

angles 3 and 6 are alternate angles

so, they must be equal

m∠3=m∠6 = 120°

m∠6= 120°

Calculation of m∠5:

we know that

angles 1 and 5 are corresponding angles

so, they must be equal

m∠1=m∠5 = 60°

m∠5= 60°

Calculation of m∠10:

we can see that angles 10 and 12 are linear

so, their sum must be 180

m∠10+m∠12 = 180°

now, we can plug values

m∠10+ 80°= 180°

m∠10=100°

Calculation of m∠14:

we know that

angles 10 and 14 are corresponding angles

so, they must be equal

m∠10=m∠14 = 100°

m∠14= 100°

Answer:

A, B, D, F

Step-by-step explanation:

Well to summarize what the previous person mentioned:

1 = 60

13 = 80

6 = 120

5 = 60

10 = 100

14 = 100

So given that information the correct answers are:

A, B, D, F

the piano lesson ends at 5:15

Final answer:

Cecil should pay $14.29 for his golf hats.

Explanation:

To determine what Cecil should pay for his golf hats, we need to calculate the cost price and apply the 40% markup. Let's assume the cost price is 'x'. Since Cecil needs a 40% markup on cost, the selling price will be 140% of the cost.

To find the selling price, we can use the equation: 140% of 'x' = $20. Solving this equation, we get: x = $20 / 1.4 = $14.29.

Therefore, Cecil should pay $14.29 for his golf hats.