The Davenports just got plans approved to install a Rectangular patio in their backyard a scale drawing of the paddle using a scale of 3in.: 10ft on the scale drawing, the patio measures 6 in. by 12 in. How many square feet will their patio cover?

Using the change of base formula log base b of y equals log y over log b x = 4.69743.

To solve 3x + 1 = 15 for x, we can use the change of base formula, which states that log base b of y equals log y over log b. In this case, we can use log base 3 on both sides of the equation to solve for x.

First, we take the log base 3 of both sides of the equation:

log base 3 (15) = log base 3 (3x + 1)

Next, we can use the property of logarithms, which states that log base b (xy) = log base b (x) + log base b (y):

log base 3 (15) = log base 3 (3) + log base 3 (x + 1/3)

We can solve for x by subtracting log base 3 (3) from both sides of the equation:

log base 3 (15) - log base 3 (3) = log base 3 (x + 1/3)

We can then use the change of base formula to solve for x:

log 15/3 = log x + 1/3 over log 3

We can then solve for x by taking the antilog of both sides of the equation:

15/3 = x + 1/3

We can then solve for x by subtracting 1/3 from both sides of the equation:

15/3 - 1/3 = x

Finally, we can solve for x by dividing both sides of the equation by 3:

x = (15/3 - 1/3) / 3

Therefore, x = 4.69743.

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Answer:

No, z =9 isn't a solution to 3z+8=25

Step-by-step explanation:

Let's see if it is...

[tex]\sf 3z+8=25[/tex]

Subtract 8 from both sides:-

[tex]\sf 3z+8-8=25-8[/tex]

[tex]\sf 3z=17[/tex]

Divide both sides by 3:-

[tex]\sf \cfrac{3z}{3}=\cfrac{17}{3}[/tex]

[tex]\sf z=\cfrac{17}{3}\;\; or \;\; z=5.6666....[/tex]

Therefore, no z = 9 isn't a solution to 3z+8=25.

____________________

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The ratio of the area of two circles can be found by dividing the area of one circle by the area of the other.

The formula for the area of a circle is A = πr^2, where r is the radius of the circle. To calculate the ratio of the areas of two circles, take the area of one circle and divide it by the area of the other:

Ratio of area of two circles = A1/A2 = (πr1^2)/(πr2^2)

For example, if the radius of one circle is 3 and the radius of the other is 5, then the area of the first circle is 28.27 and the area of the second circle is 78.54. The ratio of the areas of these two circles is then 28.27/78.54, which is 0.36.

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The absolute value of the complex number z = 2∠45° is therefore equal to 2.

Value can be defined as the worth of something, which may be monetary, social, or personal. It is an intangible concept that is based on individual beliefs and opinions. Value can be determined by considering the utility, quality, scarcity, desirability, and other factors associated with an item. Values can be measured in terms of tangible goods, such as money, or in terms of intangible goods, such as love or honor.

The absolute value of a complex number in polar form is the magnitude of the complex number. It is also referred to as the modulus of the complex number. To find the absolute value of a complex number in polar form, we need to use the following equation:

Absolute Value = r = |z| = √(a² + b²)

Where 'r' is the absolute value of the complex number, 'z' is the complex number, and 'a' and 'b' are the real and imaginary parts of the complex number respectively.

For example, if we have a complex number in polar form, such as z = 2∠45°, then the absolute value of the complex number is calculated by taking the square root of the sum of the squares of the real and imaginary parts:

Absolute Value = r = |2∠45°| = √(2² + 0²) = 2

The absolute value of the complex number z = 2∠45° is therefore equal to 2.

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Answer:

$9

Step-by-step explanation:

because we would take the total which is $39 so we divide 39/ 4 1/3 = to 9 so for one crate it is going to be $9 a crate

hope this helps

Answer:

0.29 miles per minute.

Step-by-step explanation:

Please let me know if this helped!!!

Logarithm is a mathematical operation that is the inverse of exponentiation. It is denoted by log b (x), which means the logarithm of x to base b.

For example, log2 8 = 3, since 23 = 8. Logarithm is useful in solving equations that involve exponential terms.

The properties of logarithm are:

1. log b 1 = 0: This property states that the logarithm of 1 is zero for any base b.

2. log b b = 1: This property states that the logarithm of any base b is 1.

3. log b (xy) = log b (x) + log b (y): This property states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. For example, log2 (8x32) = log2 8 + log2 32 = 3 + 5 = 8.

4. log b (x/y) = log b (x) - log b (y): This property states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the two numbers. For example, log2 (8/32) = log2 8 - log2 32 = 3 - 5 = -2.

5. log b c = clog b (c): This property states that the logarithm of a number c to the base b is equal to c times the logarithm of b. For example, log2 32 = 32log2 2 = 5.

These properties of logarithm are very useful in solving mathematical problems involving exponential terms.

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The average depth of the Atlantic Ocean is given by the equation

A = 12,880 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the average depth of the Atlantic ocean be A

From the graph the sum of the Atlantic Ocean’s average depth (in feet) and its greatest depth is 43,126 feet

The greatest depth of the Atlantic ocean is D = 30,246 feet

So , the equation will be

A + D = 43,126 feet   be equation (1)

Substituting the values in the equation , we get

A + 30,246 = 43,126

On simplifying the equation , we get

Subtracting 30,246 on both sides of the equation , we get

A = 43,126 - 30,246

A = 12,880 feet

Therefore , the value of A is 12,880 feet

Hence , the average depth is 12,880 feet

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Answer:

x ≈ 50.06°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{23}{30}[/tex] , then

x = [tex]sin^{-1}[/tex] ( [tex]\frac{23}{30}[/tex] ) ≈ 50.06° ( to 2 decimal places )

Answer:

x = 3

Step-by-step explanation:

6x = 18

Divided both sides by 6

x = 3

Let's check

6(3) = 18

18 = 18

So, x = 3 is the correct answer.

Answer:

x = 3

Step-by-step explanation:

1) 6x = 18

2) Divide by 6.

6x = 18

6 6

x = 3

The value of f(1) is equal to 7

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=8x-2/2x putting x=1 we get

f(1)= 8-2/2

     = 7

Hence f(1) is equal to 7

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While reflecting about the line y=x, option (c) [tex]r_{y=x}(x,y) = (y,x)[/tex] is correct and while reflecting about the line y= -x, option (b) [tex]r_{y=-x}(x,y) = (-y,-x)[/tex] is correct.

The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The line y = x is the point of reflection of the point (x,y) across (y, x).

Firstly, the rule for reflecting a point about the line y=x is:

[tex]r_{y=x}(x,y) = (y,x)[/tex]

While reflecting about the line y=x, we get the reflected points by swapping the coordinates.

So, Option 3 is correct.

Now, the rule for reflecting a point about the line y= -x is:

[tex]r_{y=-x}(x,y) = (-y,-x)[/tex]

While reflecting about the line y= -x, we get the reflected points by multiplying '-1'  with the swapped coordinates.

So, Option 2 is correct.

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Answer:

15

Step-by-step explanation:

Since the sum of all angles in a triangle is 180, we can make an equation

111 + 44 + 2x - 5 = 180

2x - 5 = 25

2x = 30

x = 15

Answer:

X = 45, Y = 14√2

Step-by-step explanation:

We are given that the diagram is a square, and is cut in half using the length that is 28. Therefore x = 45

Now for y, we know that we have a 45 45 90 triangle with hypotenuse of 28, and the formula for that is the legs have length of x, and hypotenuse of x√2

y = x

=> 28 = x√2

x = 14√2

=> y = 14√2

The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Therefore, the graph is a number line with closed point at 10 with arrow pointing left

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Answer:

0.0081

Step-by-step explanation:

n^4

n = 0.3

We just need to put 0.3 in for n and solve

(0.3)^4 = 0.3 x 0.3 x 0.3 x 0.3 =  0.0081

The solution of the expression for x is y+ 5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is y = x - 5. The solution of the expression for x will be,

y = x - 5

x = y + 5

Therefore, the solution of the expression for the value of x will be x = y + 5.

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assuming they are the same unit, -1.2 is colder

when a number is negative, the further the number is from zero the less (colder) it is

On solving the provided question we cans say that the inequality is 16x+5y320

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

Firm the question, the amount she spends on food every month is 16x and the amount he spends on travel every month is 5y.

Therefore, the total amount she spends every month is 16x+5y.

Since she can't spend more than $320 each month, the inequality is

16x+5y320.

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It is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 1.5 and 2

1.5 + 2 > 2.5

3.5 > 2.5

Now we add 2.5 and 2

2.5 + 2 > 1.5

4.5 > 1.5

Now we add 1.5 and 2.5

1.5 + 2.5 > 2

4 > 2

It is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm because the sum of two sides are greater than third sides.

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Answer: Katie is 9 years old now. ✅

Step-by-step explanation:

By using the second equation, we can find that k = e+4,

then we can substitute k = e+4 into the first equation

k-9 = 2(e-9)

e+4-9 = 2(e-9)

e-5 = 2e-18

5 = e

so k = e + 4 = 5 + 4 = 9

Therefore, Katie is 9 years old now.

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Answer:

y = 9

Step-by-step explanation:

[tex]\frac{2}{6}[/tex] = [tex]\frac{y}{27}[/tex] ( cross- multiply )

6y = 2 × 27 = 54 ( divide both sides by 6 )

y = 9

Answer:

Step-by-step explanation: From the question 2/6 = y/ 27

Cross multiply

It becomes 2 * 27 = 6 * y

54 = 6y

Make y the subject

y = 54/ 6

y = 9

Answer:

JM is the answer

Step-by-step explanation:

i was going to explain but my brain is in shambles right now

The given statement "The notation "f(x)" (f of x) is another way of representing y-values in a function" is true because it represents the range or output values.

In Mathematics, a function is a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically indicates the relationship between input values (domain or x-values) and output values (range or y-values) of a data set, including the ways in which the elements in a table are uniquely mapped (paired).

In conclusion, we can reasonably infer and logically deduce that the output values (range or y-values) of a function are plotted on the y-coordinate of a graph and they are primarily denoted by either the notation f(x) or y.

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Answer:

x<-13 or x>-3

Step-by-step explanation:

solve 9 abs(x + 8)>45 = x<-13 or x>-3

Answer:1.75

Step-by-step explanation:

Therefore , the solution of the given problem of surface area comes out to be 46.80909  inch square.

The amount of space it occupies on the surface is a decent indication of its overall size. The complete surroundings is taken into account when calculating the area of a tri shape. Something's total size is determined by its surface area. The volume of water inside a cuboid is equal to the total of the volumes on each and every six of its rectangular sides. To calculate the box's measurements, use the formula below: In 2lh, 2lw, and 2hw, the region is identical (SA). The surface area of the multipurpose shape represents the region.

Here,

Given :

Length = 5 inches

Width = 3 inches

and

height = 2.5 inche

To find the total surface area for triangular prism

=>A=ah+bh+ch+1/2 √﹣a⁴ +2(ab)² +2(ac)²﹣b⁴+2(bc)² c⁴

=> 5·2.5+3·2.5+5·2.5+1/2√﹣5⁴+2·(5·3)²+2·(5·5)²﹣34+2·(3·5)²54

=> 46.80909 inch square

Therefore , the solution of the given problem of surface area comes out to be 46.80909  inch square.

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