Solve the logarthmic equation. Round answers to the nearest hundredth.
6+In x=8

Answer:

7

Step-by-step explanation:

Using the trigonometric identity

• 1 + cot²x = cosec²x, then

2(cosec²Θ + cosec²Θ - 1 )

= 2(2cosec²Θ - 1)

= 4cosec²Θ - 2

= 4 × ([tex]\frac{3}{2}[/tex] )² - 2

= 4 × [tex]\frac{9}{4}[/tex] - 2

= 9 - 2

= 7

321

Look for a pattern: The term is 11 more than the number before. this means 11 is added each time.

Since you start with 2 and the number goes up by 11 per term, the equation you would use to find the nth term would be 11n+2

To find the 29th term, simply plug in 29

11n+2

11(29)+2

321 

The 29th term is 321.

First you have to find the rate of change. It would be 11 because 35 - 24 = 11, 24 - 13 = 11 and 13 - 2 = 11.

These are the first 4 terms so just keep adding on 11 until you get 29 terms.

2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178, 189

1    2   3    4    5    6    7    8    9    10    11    12  13    14     15    16   17      18

200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310

   19   20   21     22    23    24    25    26    27    28    29

Your final answer would be 310.

Check the picture below.

Answer:

Step-by-step explanation:

[tex]\dfrac{1}{2}x+3<2x-6\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+2\cdot3<2\cdot2x-2\cdot6\\\\x+6<4x-12\qquad\text{subtract 6 from both sides}\\\\x<4x-18\qquad\text{subtract 4x from both sides}\\\\-3x<-18\qquad\text{change the signs}\\\\3x>18\qquad\text{divide both sides by 3}\\\\x>6[/tex]

Answer: A?

Step-by-step explanation:

Answer:

-5x

Step-by-step explanation:

you multiply them together

(-5)(x)= -5x

Answer:

-5x

Step-by-step explanation:

-5 * X =

Answer:

4/21

Step-by-step explanation:

⇒This question is on probability

⇒Number of boys=3

⇒Number of girls=4

⇒P(S)= 4+3=7

Probability for a girl to win is= 4/7

We have 3 awards a free movie ticket, a collectible poster, or a free popcorn

P(S)= 3

Probability of being awarded a free popcorn = 1/3

The probability that a girl will win free popcorn =

[tex]\frac{4}{7} * \frac{1}{3} = \frac{4}{21}[/tex]

Answer:

4/21

Step-by-step explanation:

The correct answer is 6

Answer:

Option B is the correct answer

Step-by-step explanation:

Both collections follow arithmetic progression.

Back then, they had the same number of rare coins, which means their first term of AP is same. Let it be a.

Miguel's AP have a common difference 5 and Grace's AP have a common difference 3.

Let the number of weeks completed be n.

We have

           a + ( n-1 )x 5 = 38  -------- eqn 1

           a + ( n-1 )x 3 = 24  -------- eqn 2

eqn 1 - eqn 2

          a + ( n-1 )x 5 - (a + ( n-1 )x 3) = 38 - 24

          ( n-1 )x 2 = 14

          n-1 = 7

          n = 8

Substituting in eqn 1

           a + ( 8-1 )x 5 = 38

                     a = 38 - 35 =3

So at starting they both have 3 rare coins.

Total rare coins = 3 + 3 = 6

Option B is the correct answer

Answer:

C) The discriminant is 0.

Step-by-step explanation:

Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.

If a quadratic equation has only one real root, then the discriminant is 0

Answer:

B. 7

Step-by-step explanation:

When you solve the series for each term, you get 4 + 2 + 1 = 7

Answer:

A

Step-by-step explanation:

Answer: his shoe size was 11

Step-by-step explanation:

Answer:

I hope this helps

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

f(x) × g(x)

= (4x - 2)(5x - 6) ← expand factors

= 20x² - 24x - 10x + 12 ← collect like terms

= 20x² - 34x + 12

This is a polynomial of degree 2 and is defined for all real values of x

domain : x ∈ R

3 kids and $24 will give each 24/3=$8 each

$8 for 4days is 8/4=$2 a day they spent

ANSWER

P'(6,-1)

EXPLANATION

The mapping for a reflection in the line y=x is

The line y=x is the mirror line for a function and it's inverse.

[tex](x,y)\to (y,x)[/tex]

The x and y coordinates swap position.

The reflection of point P(−1, 6) across the line y = x is

P'(6,-1)

Answer:

The solution is the point (3,5)

The graph in the attached figure

Step-by-step explanation:

step 1

Line A ----> (2,6),(6,2)

Find the equation of the line A

Find the slope

m=(2-6)/(6-2)

m=-1

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-1

point (2,6)

substitute

y-6=-1(x-2)

y=-x+2+6

y=-x+8 ------> equation of the line A

step 2

Line B ----> (0,3),(4.5,6)

Find the equation of the line B

Find the slope

m=(6-3)/(4.5-0)

m=(2/3)

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=(2/3)

point (0,3)

substitute

y-3=(2/3)(x-0)

y=(2/3)x+3 ------> equation of the line B

step 3

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both lines

The solution is the point (3,5)

see the attached figure

Its DE and ik its too late but the points is good. oof

Answer:

475

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

Answer:

x=28 (Yup you're correct)

Step-by-step explanation:

As this problem is involving the Opposite angle and the Hypotenuse, we can use the sin function in order to solve this. The setup is as follows

[tex]sin(30)=\frac{14}{x}[/tex]

Now we can solve for x

[tex]sin(30)=\frac{14}{x}\\\\x=\frac{14}{sin(30)}[/tex]

Now we can plug it into a calculator to get

[tex]x=28[/tex]

Answer:

Step-by-step explanation:

(Look at the picture)

We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

We have a = 14. Therefore x = 2a ⇒ x = 2(14) = 28

Answer:

94%

Step-by-step explanation:

Since there are 100 questions, it's like 1% for each question. If she answers 94 questions right, then it is 94%.

-3+m/9=10

Add 3 to both sides:

m/9 = 13

Multiply both sides by 9:

m = 13 * 9

m = 117

Answer:

The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation  

. Write the equation in standard form with a constant of proportionality greater than 1.

Step-by-step explanation:

ANSWER

The y-intercept is (0,-11)

The x-intercepts are:

(-1,0) and (11,0)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 10x - 11[/tex]

To find the y-intercept, we put x=0 into the function.

[tex]f(0) = {0}^{2} - 10(0) - 11[/tex]

[tex]f(0) = - 11[/tex]

The y-intercept is (0,-11)

To find the x-intercepts, we put f(x)=0.

[tex]{x}^{2} - 10x - 11 = 0[/tex]

[tex](x + 1)(x - 11) = 0[/tex]

This implies that,

[tex]x = - 1 \: or \: x = 11[/tex]

The x-intercepts are:

(-1,0) and (11,0)

For Future Reference____

-1 & 11 are the X Intercepts

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3[/tex]

Answer:

x⁸y³

Step-by-step explanation:

x⁵ ÷ y² × x³ × y⁵

It will be easier to solve this problem if you first rearrange the expression to associate like terms.

(x⁵ × x³) × (y⁵ ÷ y²)

Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.

x⁵ × x³ = x⁵⁺³ = x⁸  

y⁵ ÷ y² = y⁵⁻² = y³

Thus,

(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³

Answer:

All answers in the pic attached

Answer:

-8

Step-by-step explanation:

-4a + 8z

= -4(8)+8(3)

= -32+24

= -8

use the substitution method

-4a+8z

-4(8)+8(3)

-32+24 Negative number times (*) and positive number=negative number

=-8

Answer is -8

Answer:

- 160 I think

Step-by-step explanation

I think i'm right but there are

200 blocks and there are 40 left out so then i did 40 - 200 = -160

Answer:

A.22

Step-by-step explanation:

Answer:

d. 19

Step-by-step explanation:

A matrix is an array of rectangular shape which consists of numbers, symbols, or expressions, arranged in rows and columns.

[tex]\begin{bmatrix}28&21&19\\17&24&15\\22&29&17\end{bmatrix}[/tex]

[tex]w_{1,3}[/tex] means element in first row third column. First row means Frank and third column means August.

So, the number of lawns mowed by Frank in August is

[tex]w_{1,3}=19[/tex]

Answer:

See picture below.

Answer:

Graph??

Step-by-step explanation:

I can't really graph, but the answer to this is...

[tex]3x+2y=12\\\\2y=3x+12\\\\y=\frac{3}{2} x+6[/tex]

I divided all by 2 to get y

[tex]y=\frac{3}{2} +6\\\\(2,9) -- (x,y)[/tex]

Answer: [tex]g(x)=(3)^{-x}[/tex]

Step-by-step explanation:

We know that if a figure is reflected across y axis then its y coordinate remains same but the x coordinate changes its polarity.

i.e. the function [tex]f(x)[/tex] will become [tex]f(-x)[/tex] .

Now, the given function :[tex]f(x)=(3)^x[/tex]

Then , after reflection across y axis the new function will become:

[tex]g(x)=f(-x)=(3)^{-x}[/tex]

This statement is true.

When you buy a share in a company, you are investing your money, and you may earn more money if the share’s value rises, or you may lose money if the share’s value falls.

Investing in a company by buying shares makes you a shareholder, with potential income from dividends and stock appreciation. However, it carries risk as there is no guarantee for profits. Diversification is a key strategy when investing in stocks to mitigate risks.

Buying shares in a company is a common method of investment, wherein you become a shareholder and own a part of the company's equity. As a shareholder, you have a claim to the company's assets and profits proportional to the amount of stock you own. There are two primary ways that shareholders can earn money from their investments. One way is through dividends, which are payments distributed from the company's profit to shareholders. The other way is through appreciation in the stock's value, as the company grows and becomes more profitable; this increases the stock's market price, and you can sell your shares for a profit. It's important to understand that purchasing stock does involve risk, as there is no guarantee of dividends or stock appreciation. However, for many, owning stock is preferred over other investments like bonds because of the potential for higher returns. Lastly, when buying stock, especially that of your employer, it's advisable to follow general rules of portfolio investing, such as diversification, not to expose yourself to undue risk.

Answer:

$482.11 in interest

Step-by-step explanation:

Use the compound amount formula.  Calculate the compound amount and then subtract the principle to find the amount of interest earned.

A = P(1 + r)^t, where r is the interest rate as a decimal fraction

This becomes:

A = $575(1 + 0.07)^9, or A = $1057.11.

Subtracting the principal:  A - P:  $1057.11 - $575 = $402.11

The total interest earned is $482 on a principal of $575 invested at an interest rate of 7% compounded annually for nine years

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given, P = $575, n = 9 and r = 7%.

∴ A = 575(1 + 7/100)⁹.

A = 575(1.07)⁹.

A = 575(1.84).

A = 1057.

So, Interest earned is (A - P) = (1057 - 575) = $482.

learn more about compound interest here :

https://brainly.com/question/14295570

#SPJ2

Answer:

392 ft²

Step-by-step explanation:

Break this area into two parts, that is, into two trapezoids.  The first trapezoid, on the left, has length 8 ft and average length (30 ft + 27 ft)/2, so its area is (8 ft)(28.5 ft) = 228 ft ².

The second trapezoid has width 8 ft and average length (19 + 22)/2 ft, or 8 ft by 20.5 ft).  The area of this part is 164 ft².

Thus, the total area is 164 ft² + 228 ft², or 392 ft²