Use a half-angle identity to find the exact value of sin 90°

The logarithm statement log_b x / log_b y = log_b x/y is a false statement as log_b x / log_b y = log_b x - log_b y.

We are given the logarithm as:

log_b x / log_b y = log_b x/y

We need to tell if it is true of not.

We get that, it is false statement.

We know that log a / log b = log a - log b

So, log_b x / log_b y = log_b x - log_b y

So, it is not equal to log_b x / y

Therefore, we get that, the logarithm statement log_b x / log_b y = log_b x/y is a false statement as log_b x / log_b y = log_b x - log_b y.

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The factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4 and the value of the maximum profit is 680

The given parameters are

f(x) = x^3 + 5x^2 - 16x - 80

x = -4 is a root

To set up the synthetic division, we start by writing out the coefficient of each term

So, we have

-4 |  1    5    -16    -80

Bring down the first coefficient

-4 |  1    5    -16    -80

      1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)

      1

Add

-4 |  1    5    -16    -80

           (-4)

      1     1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1

Add

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1     -20

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20

Add

So, we have

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20    0

This means that,

Quotient = x^2 + x - 20

Remainder = 0

Expand x^2 + x - 20

x^2 + x - 20 =x^2 + 5x - 4x - 20

Factorize

x^2 + x - 20 = (x + 5)(x - 4)

Recall that the initial root is

x = -4

Rewrite as

x + 4 = 0

So, we have the complete factor to be

f(x) = (x + 4)(x + 5)(x - 4)

Set to 0

(x + 4)(x + 5)(x - 4) = 0

Solve for x

x = -4,  = -5 and x = 4

Hence, the factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

The equation of the profit function is given as

P(x) = 230 + 30x - 0.5x^2

Differentiate the function

So, we have

P'(x) = 0 + 30 - x

Evaluate the like terms in the function

So, we have

P'(x) = 30 - x

Set the function to 0

So, we have

30 - x = 0

Evaluate

x = 30

Substitute x = 30 in the equation P(x) = 230 + 30x - 0.5x^2

So, we have

P(30) = 230 + 30 x 30 - 0.5 x 30^2

Evaluate

P(30) = 680

Rewrite as

Pmax = 680

Hence, the value of the maximum profit is 680

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It will take 5.689 yrs . for the account to contain $2500 .

Simple Interest = ( P * R * T ) / 100

P ( principal amount ) = 2000

R ( rate of interest ) = 4

T ( no . of yrs . for which amount is deposited ) = unknown

According to question

Account Balance = $ 2500 = A( t ) = a [tex]( 1 + r ) ^{t}[/tex]

2500 = 2000 [tex]( 1 + 0.04 )^{t}[/tex]

1.25 =  [tex]( 1 + 0.04 )^{t}[/tex]

t = [log ( 1.25 ) ] / [ log ( 1.04 ) ]

t = 5.689

Hence , it will take 5.689 yrs . for the account to contain $2500 .

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Answer:

Here's b > 4 on the number line. When greater than, the arrow always starts with an open circle. If less than, then it will start with a closed circle.

The result of simplifying the number 4¹/₂ . 4¹/₂  using the properties of exponents is 4

To solve this exercise we have to resolve algebraic operations following the exponent properties.

4¹/₂ . 4¹/₂

Base= 4

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

(4) ⁽¹/₂ ⁺ ¹/₂⁾

(4) ⁽¹⁺¹⁾/₂

(4) ⁽²/₂⁾

(4)⁽¹⁾

4

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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The total amount that Amy will spend is $17.98

Amy goes out to eat at El Parral. She orders a Burritos Deluxe dinner for $8.75, fried ice cream for $4, and a Coke for $2.

Amy's gross total is $8.75 + $4 + $ 2  = $14.75

Now, sales tax of 6 percent

Her net bill is $14.75 + 6% of $14.75

$ 14.75 + 0.885

= $15.635

Here, Amy also gives a tip of 15 percent

Her total spending becomes

$15.635 + 15% of $ 15.635

$15.635+ 2.345

$17.980

or $ 17.98

Hence, the total amount that Amy will spend is $17.98

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Answer:

-8

Step-by-step explanation:

[tex]-2\left(-4\right)\left(-1\right)\\\left(-4\right)\left(-1\right)\\\left(-a\right) \times \left(-b\right)=(+c)\\= 4\\=-2 \times 4\\(-a) \times (+b) = -c\\=-8[/tex]

The equation is,

→ -2 (-4) (-1)

Let's solve the problem,

→ -2 (-4) (-1)

→ (-2 × -4) × (-1)

→ 8 × -1 = -8

Thus, the answer is -8.

Answer:

5000

Step-by-step explanation:

5x1000=5000

Answer:

(-4, 0) U (1, ∞)

Step-by-step explanation:

Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).

x = 0           x-1 = 0             x + 4 = 0

                  x = 1                x = -4

Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.

far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0   →  (-)(-)(-) > 0  →   negative > 0  FALSE

- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0   →  (-)(-)(+) > 0  →   positive > 0  TRUE

0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0   →  (+)(-)(+) > 0  →   negative > 0  FALSE

far right (I choose 2): 2(2 - 1)(2 + 4) > 0   →  (+)(+)(+) > 0  →   positive > 0  TRUE

The radical expression 3√0.008 y^3 x^6 can be simplified into 0.2 y x^2.

Radical expression is an expression containing a √ symbol. It shows the nth root of a number or variable. This number or variable inside a radical expression is the nth power of another number. Radical expression can also be expressed in exponent notation such that the nth root of x is equal to x raised to 1 over n.

n √x = x^1/n

Expressing 3√0.008 y^3 x^6 into exponent notation:

3√0.008 y^3 x^6 = (0.008 y^3 x^6)^1/3

Applying the distributive property of exponents,

(0.008 y^3 x^6)^1/3 = 0.008^1/3 (y^3)^1/3 (x^6)^1/3

Using the Power Rule for Exponents which states that to raise a number with an exponent to a power, multiply the exponent times the power:

(a^m)^n = a^(m*n).

0.008^1/3 (y^3)^1/3 (x^6)^1/3 = 0.008^1/3 y x^2

Simplifying the constant,

0.008^1/3 y x^2 = 0.2 y x^2

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Answer:

2 and - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

f(x) = 2x - 1 ← is in slope- intercept form

with gradient m = 2

• Parallel lines have equal gradients , then

the gradient of a parallel line is also 2

given a line with gradient m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

Answer:

12

Step-by-step explanation:

In this problem, we need to arrange 150 chairs in rows for a school play. You want each row to have the same number of chairs.

We can find the prime factorization of 150 as follows :

150 = 2, 3, 5, 5

150 is not a perfect square. 144 is a perfect square and 12² = 144. So, there are 12 possible arrangements.

The correct answer is ( -2.2, -3).

We occasionally discover the value of an unknown variable while solving the system of equations. We can display the graph using the equation, but if the graph and the equation are parallel, we will not be able to solve the system of equations.

We have a condition that, if applied, allows us to determine how many solutions this equation has: if it has one solution, no solutions, or infinitely many solutions.

y = -3 _____(1)

y = x-0.8 _____(2)

to substitute the value of y in the equation in 2

-3 = x - 0.8

-3 + 0.8 =x

-2.2 = x

Thus the correct answer is  ( -2.2, -3).

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Answer:

$3.42 spent on folders, She will receive $6.58 back in change

Step-by-step explanation:

$0.57 times 6 = $3.42 spent on the folders. $10-$3.42=$6.58 she will receive back.

Part 1: She spent $3.42 on the folders.

This is calculated by multiplying 6 folders by $0.57 for each folder

($0.57 x 6 = $3.42).

Part 2: She will receive $6.58 in change. This is calculated by subtracting the amount spent on the folders from the amount of money Gi Gi had to begin with ($10 - $3.42 = $6.58).

Answer: 0.004 = 4.0 x [tex]10^{-3}[/tex]

Step-by-step explanation:

Rules guiding exponential notation :

Writing numbers in exponential notations have some guiding rules. These include:

The base is always 10

The exponent cannot be zero and must be an integer. It can be positive or negative.

The coefficient can take any form - negative or positive, integer or decimal. All significant digits must be included after the decimal.

Following these rules :

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Answer:

.9

85%

5/6

4/5

Step-by-step explanation:

In percentages .9 is 90%

which is larger than 85%

5/6 as a percentage is 83.33r%

4/5 as a percentage is 80%

After solving the given equation 25²x=144, the value of x = 144/625.

So,

Then,

Therefore, after solving the given equation 25²x=144, the value of x = 144/625.

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Answer:

QR = 3

Step-by-step explanation:

given Q is the midpoint of PR , then

PQ = QR , that is

3x = x + 2 ( subtract x from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Then

QR = x + 2 = 1 + 2 = 3

Answer:

QR = 3

Step-by-step explanation:

since Q is the midpoint, then PQ is the same as QR. so we equate the two as follows:

3x = x+2

then find x as shown below.

3x-x = 2 ( I grouped the like terms)

2x = 2. now divide by 2 to find x

x= 1,

since QR is x+2, now substitute x for 1

1+2 =QR

3 is the answer.

.thanks

[tex]f(x) = \alpha (x - 4) {}^{2} (x - 2) {}^{2} \\ f(x) = \alpha (x {}^{2} - 8x +16 )(x - 4x - 4) \\ f(x) = \alpha (x {}^{4} - 12x {}^{3} + 52x {}^{2} - 96 x + 64) \\ where \: \alpha ∈ \: \real[/tex]

14x+70+20x+8=180

34x+78=180

34x=102

x=3

XBC= 20(3) +8

60+8

68

XBA= 14(3)+70

42+70

112

Angle XBC= 68 degrees

Angle XBA= 112 degrees

According to the question, to express the rational function for the vertical asymptote whose equation is [tex]x=8[/tex] and horizontal asymptote whose equation is at [tex]y=0.[/tex]

As per the question, the function 'f(x)' is vertical at [tex]x=8[/tex]. Therefore, the denominator be [tex](x-8)[/tex]

[tex]f(x)=\frac{g(x)}{(x-8)}[/tex]

The function 'g(x)' should have same degree as the denominator function has and it is defined as[tex]y=0[/tex]

The rational function can be written as:

Rational function = [tex]\frac{y}{(X-8)}[/tex]

What is rational function?

Rational function is a function whose numerator and denominator terms are in polynomials. Basically, it is a ratio of polynomials. The important condition for these type of function is that denominator should be of degree one.

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Answer: 2.2

Step-by-step explanation: twenty percent of 11 is 2.2

Answer:

154

Step-by-step explanation:

Use the correct order of operations.

(120 - 14) + 4² × 3 =

First, do the parentheses and the exponent.

= 106 + 16 × 3

Now do the multiplication.

= 106 + 48

Finally, add.

= 154

Answer: -13

Step-by-step explanation: so order of operations is also PEMDAS.

and u go from left to right so using this you would multiply 8 x 5 and then you get 35. after this subtract 23-36 and u get -13.

The constant of variation is 1/4 .

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means if one value increases than another one will automatically decrease and vice versa.

Let say if x and y are two values and k is a constant value, then

According to inverse variation,

k = xy or y = k/x

In the given question,

Take the order pair  [tex](\frac{3}{8} ,\frac{2}{3} )[/tex]

As it is an inverse variation, we can substitute it

y=k/x  or k = xy

put the values from order pair

k = [tex]\frac{3}{8}[/tex] × [tex]\frac{2}{3}[/tex]

k = [tex]\frac{1}{4}[/tex]

Therefore, the constant of variation for order pair  [tex](\frac{3}{8} ,\frac{2}{3} )[/tex] is 1/4 .

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Answer:

1920 rings

Step-by-step explanation:

Our equation: 16 x 10 x 12

16 x 10= 160

160 x 12= 1920

Answer:

83°

Step-by-step explanation:

Supplementary angles are angles that add up to 180°.
Za + Zy = 180
Za + 97 = 180
Za + 97 - 97 = 180 - 97
Za = 83

The equation that shows proportionality is in the form y = kx; Where k is the constant of proportionality.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two variables are said to be proportional if an increase or decrease in one variable leads to a corresponding increase or decrease in the other variable.

The equation that shows proportionality is in the form:

y = kx

Where k is the constant of proportionality.

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