Solve the following logarithmic equation. Express all solutions in exact form.√log x-3 =log x-3

A rectangular box has six faces. The surface area is given by the sum of the area of those faces. Parallel faces have the same area, therefore, we just need to calculate the area of three of them and multiply by 2. The surface area of our gift box is:

The surface area of the box is 5400 cm².

We have that 1 cubic meter is equivalent to 1.308 cubic yards. Then, we can use a rule of three to find the value in yards of 1.37 cubic meters:

therefore, 1.37m³ is equivalent to 1.792yd³

We can solve the expression as:

The answer is 1. 17x-4.

Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].

What is the rectangle?

A rectangle is a two-dimensional flat shape. In an [tex]XY[/tex]  plane, we can easily represent a rectangle, where the arms of x-axis and y-axis show the length and width of the rectangle, respectively.

Area of rectangle = Length × Width

Here given that,

[tex]L=\frac{7}{8}m[/tex]

[tex]W=\frac{3}{4}m[/tex]

So,

Area of rectangle = [tex](\frac{7}{8}m)*(\frac{3}{4}m)\\[/tex]

[tex]=\frac{21}{32}m^2[/tex]

Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].

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1.

Let:

Using the point-slope equation:

2.

If two lines are perpendicular, then:

Let:

Using the point slope equation:

The US consume 5.25 million metric tons of banana per year.

This is equivalent to 5.25 million x 1000kg = 5250 000 000 kg

US population = 317 million = 317 000 000

The number of kilogram of bananas consumed per person per year

= 5250 000 000 kg / 317 000 000

=16.6 kg

Therefore, the number of kilogram of bananas that are consumed per person per year is 16.6kg

Step 1

Given;

Step 2

The probability of an event is given as;

Thus,

Answer;

Given the function:

It is a quadratic function where:

a=1

b= -2

c= -8

The x-coordinate of the vertex is given by:

Substitute a and b:

Substituting in the original equation to obtain the y-coordinate, we obtain:

So, the vertex is (0, -9)

c. For the intercept at x we make y = 0:

And solve for x by factorization:

So, the x-intercepts are:

(-2, 0) and (4,0)

Answer: (-2,0), (4,0)

d. For the intercept at y we make x = 0:

So the y-intercept is (0, -8)

Answer: (0, -8)

e. Graphing the function:

Answer:

Explanation:

The formula for calculating the effective interest rate is expressed as

R = (1 + i/n)^n - 1

where

R is the effective interest rate

i is the nominal rate

n is the number of compounding periods in a year

From the information given,

n = 12 because it was compounded monthly

i = 3.2% = 3.2/100 = 0.032

Thus,

R = (1 + 0.032/12)^12 - 1

R = 0.03247

Multiplying by 100, it becomes 0.03247 x 100

Effective interest rate = 3.25%

We would apply the formula for calculating compound interest which is expressed as

A = a(1 + r/n)^nt

where

a is the principal or initial amount

t is the number of years

A is the final amount after t years

From the information given,

A = 1000

a = 600

n = 12

We want to find t

By substituting these values into the formula, we have

1000 = 600(1 + 0.032/12)^12t

1000/600 = (1.00267)^12t

Taking natural log of both sides, we have

ln (1000/600) = ln (1.00267)^12t = 12tln(1.00267)

12t = [ln (1000/600)]/ln (1.00267) = 191.5758

t = 191.5758/12

t = 16

It takes 16 years for the amount to reach $1000

She bought the bike by 3,000 six years ago, we are assuming the value of her mountain bike depreciated 20% each year

1 year

3,000*20% = 600

2year

3,000-600 = 2,400*20% = 480

3year

2,400-480 = 1920*20% = 384

4 year

1920-384= 1,536*20% = 307.2

5 year

1,536-307.2= 1,228.8*20% = 245.76

6year

1,228.8 - 245.76 = 1,043.04*20% = 208.608

1,043.04 - 208.608 =834.432

Rounded to the nearest dollar

= 834

To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.

Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.

Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.

To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.

Step 1:

6x - 3 = 5

step 2:

6x = 8

Step 3:

x = 4/3

An equation is a mathematical expression that contains an equal sign. The objective of an equation is usually to determine the value of an unkown variable, commonly referred to x or y. In order to do that, however, we need to isolate the variable on the left side and this has to be done in a way that mantains the balance in the equation. This means that whatever operation we do on one side we have to perform the same exact operation on the other side. Let's take a look at an example.

For this equation we have the unknown variable x, which is the value we want to find. Our goal is to isolate the variable on the left side, however we can see that there is one x on the right side, the first step will be to move this to the left side, this is what means to move the lowest variablem term first, because if we were to move "3x", which is the highest variable term, we would have to perform more steps to solve the equation.

To move the term "x" from the right to the left we need to subtract both sides by "x", this is because when we subtract "x-x" on the right side, the result will be 0 and we will be left with unkown variables only on the left. Let's check this out:

As we can see by doing so we eliminated the variable on the right side. Now we want to remove the 9 from the left side, we will have to perform a similar operation by subtracting 9 from both sides.

Now we have only a variable term on the left side, but it still being multiplied by 2 and we don't want that, so we have to divide both sides by 2.

With this we achieved the goal of the equation, which was to find the value of x. In short we always want to isolate the variable on the left side and to do that we will have to perform the inverse operation of the other terms in both sides of the equation, if a term is adding we need to subtract on both sides, if it is multiplying we need to divide on both sides and so on. We have to do that first with the term that contains the letter of lowest value, like we did with this one.

Given: A square pyramid with a base length of 5 inches and a height of 9 inches.

Required: To find the volume of the given square pyramid.

Explanation: The volume of the square pyramid is given by the formula

Where a is the base length, and h is the height of the square pyramid.

Hence,

Final Answer: The volume of the square pyramid is 75 cubic inches.

Check below, please.

1) In this question, we're going to remember two concepts: The perimeter is the sum of the lengths of each segment of each letter.

2) So let's start counting each tiny square so that we can get to know the length.

The letter "L" is actually, with this typography, two rectangles:

So, the perimeter (2P) is equal to:

2P =15 +15 +7+3+3+10+3

2P= 56 units

As for the area:

Using the Rectangle formula, then we can write down the area as:

Area:

3) In this letter "O" we can divide it into two trapezoids, and two parallel rectangles:

Note that we need to find the length of those corners shaped like triangles, we can use the Pythagorean Theorem, considering the "rise over run" and write:

So the Perimeter can be written:

And for the area, we can find the area of those two trapezoids and two rectangles writing this:

4) And now, finally the letter "u":

For the corners let's assume they are triangles, and then we can write the following since those corners are like hypotenuses:

And for the inclined lower part of the letter "u", we can write:

Therefore, we can write the Perimeter as:

And for the area, we can see from bottom to top: One trapezoid, a par of parallelograms, and two rectangles. Hence, we can write:

5) So, each letter by area and perimeter:

Solution

For this case we can do the following:

m < PQR = 7x -19

m < OPQ= 2x-3

m < QOP= x+16

We need to satisfy that:

(180- m Replacing we got:

(180- 7x +19) + 2x -3 + x+16= 180

-7x +2x +x = -19+3 -16

-4x = -32

x= 8

Then m

Given:

12 3/8 x 6 7/8

We can round 12 3/8 down to 12 because converting 12 3/8 to decimal will give 12.375.

We can round up 6 7/8 which is equivalent to 6.875 to 7

Hence, the estimate is 12 x 7 = 84

Question:

Solution:

Let us denote by x the blank space in the given equation. Then, we get:

this is equivalent to:

this is equivalent to:

that is:

solving for x, we obtain:

that is:

so that, the blank space would be:

and the complete expression would be:

ok

Total money = $300

money spend = $15

300 ---------------------- 100

15 ---------------------- x

x = (15 x 100)/300

x = 1500/300

x = 5

Jennie spent 5% of her money

To solve it, use a rule of three. $300 is 100%, so we need to calculate which percent is $15 of the total amount.

In a rule of three, it's necessary to use cross multiplication and then division.

That's why I multiplied 15 by 100 and then I divided by 300.

15 is 5% of $300

Explanation

Given

We will have;

Answer: Option D

The simplified value of the given expression in the form of a fraction is  [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .

The given expression is:  [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

we will use the properties of exponents to simplify the expression.

Taking the powers of the like terms and combining we get :

[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]

[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]

Therefore we get the simplified equation for the expression.

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.

A variable is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.

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Answer:

$2875

Explanation

Given

Principal P = $2,500

Rate R = 15%

Time T = 1year

Get the interest on $2500

Simple Interest = PRT/100

Simple Interest = 2500 * 15 * 1/100

Simple Interest = 25*15

Simple Interest = $375

Amount owed altogether = Pricipal + Interest

Amount owed altogether = $2500 + $375

Amount owed altogether = $2875

Let's remember that the equation of a line always has the form:

where "m" and "b" are constant numbers that we must find. Now, let's find "m" first. "m" is called the slope of the line, and it represents the relationship between the changes in y (second component) and the changes in x (first component). So it isn't surprising that we can compute it by:

Having calculated "m", we know that, (for the point (42.3,82) must lie in the line)

Then,

This implies that the equation of our line is

Here is a graph of the line:

Comment: Our line is represented with a red color.

Answer:

Explanation:

Here, we want to get the gradient of the line L3

The equation of a straight line can be expressed as:

where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)

Now,let us write the equation of the first line in the slope-intercept form

Mathematically, we have this as:

The gradient of the first line is 3

Now,let us get the gradient of the second line L3

Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1

Thus, we have it that:

Given that,

The length of baby's hair at first time = 6cm

After a month, the length was 2 cm longer = 6 + 2 = 8 cm

As mentioned in the question, the hair continues to grow at this rate. Therefore, after two months, the length would be = 8 + 2 = 10 cm

It results in a sequence with a common difference of 2,

6, 8, 10, 12, ............

If a sequence has a common difference, it is called an arithmetic sequence. In such sequences, the nth term is calculated as:

an = a1 + (n-1)*d

Here,

a1 = first term = 6

d = common difference = 2. (8-6 or 10 - 8 = 2)

Now, put all the values in the equation,

an = a1 + (n-1)*d

an = 6 + (n-1)*2

an = 6 + 2n - 2

an = 2n + 4

an = 2(n+2)

Hence, the function that represents growth is an = 2(n+2).

By varying the value of 'n', you can get the values of 'an'. Both will generate ordered pairs that will help you in plotting. For example:

n = 1

an = 2(n+2) = 2(1+2) = 2 (3) = 6

=> ordered pair (1, 6)

n = 2

an = 2(n+2) = 2(2+2) = 2 (4) = 8

=> ordered pair (2, 8)

n = 3

an = 2(n+2) = 2(3+2) = 2 (5) = 10

=> ordered pair (3, 10)

n = 4

an = 2(n+2) = 2(4+2) = 2 (6) = 12

=> ordered pair (4, 12)

With the ordered pairs, you can plot the graph.

Coordinate of the Hospital = (-6, -4)

Coordinate of City Hall = (0,0)

The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. The

water output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a

total water output of 1025 L. How long was each sprinkler used?

Let

x ------> the number of hours of Hill family's sprinkler

y ------> the number of hours of Stewart family sprinkler

so

we have that

x+y=55 -------> x=55-y ------> equation 1

15x+25y=1025 ------> equation 2

Solve the system

Substitute equation 1 in equation 2

15(55-y)+25y=1025

solve for y

825-15y+25y=1025

10y=1025-825

10y=200

y=20

Find the value of x

x=55-20) -----> x=35

therefore

If we know the roots (solutions) we can find the equation of the second-degree function using the formula above:

In this case, a = -1, x1 = 2 and x2 = 4. Therefore the equation will be:

The vertex is maximum (see that the function has a clear max value).

The solutions to the function are the roots (place in the x-axis where the function cross). They are 2 and 4.

The y-intercept is the point with the format (0,y). Thus to find this point we can substitute 0 into the function:

The y-intercept will be y = -8.

Given:

y = -2(x - 1) + 4

The effect the number 4 has on the graph of the function is that there will be a vertical shift of 4 units up.

+4 here indicates a vertical shift of 4 upwards

ANSWER:

C) It shifts the graph up 4 units

The distributive property states:

so: