Bradley rents a fishing boat for the day. The total cost for gasoline is
represented by the expression 3.25m + 15. What is the constant in the
expression?

a. Value of f(-2) is -15. b. Value of g(2) is 4. c. Value of x when f(x)=0 is 3.

The above values are obtained using substitution.

When in place of a variable, we substitute a value in the function, it is known as substitution.

a. We are given f(x)= 3x-9

So, for finding f(-2), we need to put x=-2

Thus, we get,

f(-2)= 3(-2)-9

f(-2)= -6-9

f(-2)= -15

b. We are given g(x)= x^2

So, for finding g(2), we need to put x=2

Thus, we get,

g(2)= 2^2

g(2)=4

c. Now, we are given that f(x)=0.

In order to find the value of x, we need to put f(x)=0

Thus, we get,

3x-9=0

3x=9

x=3

Hence the values of f(-2), g(2) and x when f(x)=0 are -15, 4 and 3 respectively.

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1. An equation that can be used to calculate the length and width of the garden,  l = 2w + 5 and 2l + 2w = 61

2. Length = 22

    Width =  51/6

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Given that,

The perimeter of the garden = 61 feet

The length is 5 more than the twice of width

Suppose,

length = l

width  = w

According to given condition,

l = 2w + 5

Perimeter = l + w + l + w

                 =  61

2l + 2w = 61       _______(i)

By putting value of l in the equation (i)

⇒ 2( 2w + 5 ) + 2w = 61

⇒ 4w + 10 + 2w = 61

⇒  6w + 10 = 61

⇒  w = 51/6

By putting value w in the equation (i)

2l + 2×51/6 = 61  

2l   = 61 - 17

l = 22

Hence, the length and width of the garden are respectively, 22 & 51/6

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The whole number 5 can be written as an equivalent fraction with a denominator of 2 is 10/2

An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). For example, 7/3 is an improper fraction because 7 is greater than 3.

The whole number 5 can be written as an equivalent fraction with a denominator of 2 by looking for a number which when divided by 2 will give 5. That is:

10/2 = 5

Notice that 10/2 is an improper fraction

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The solution set to the inequality is x >= -5/6.

Inequality is a relationship between two expressions or values that are not equal to each other. It is used most often to compare two numbers on the number line by their size.

To solve this inequality, we can start by expanding both sides of the inequality:

-1.5(4x + 1) <= 4.5 - 2.5(x + 1)

-6x - 1.5 <= 4.5 - 2.5x - 2.5

-6x - 1.5 <= 2 - 2.5x

Next, we'll isolate the x terms on one side of the inequality and the constant terms on the other side:

-6x <= 3.5 + 1.5x

-6x <= 5

-6x/6 <= 5/6

And finally, we'll divide both sides of the inequality by -6 to find the solution set:

x >= -5/6

Therefore, The solution set to the inequality is x >= -5/6.

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The first 10 terms sum in the geometric series is 5115.

The first term of geometric series = 5

Common ratio = 2

First, let us discuss how to calculate the sum of n terms of GP. Assume the sum of the first n terms of a GP with first term a and common ratio r. Then the first 'n' terms of GP are of form a, ar, ar², ... ar^(n-1). Let S be the sum of the GP of n terms. Then:

Sₙ = a + ar + ar² + ... + ar^(n-1) ... (1)

Multiply both sides by r:

rSₙ = ar + ar² + ... + arⁿ ... (2)

Subtracting equation (1) from equation (2):

rSₙ - Sₙ = (ar + ar² + ... + arⁿ) - [a + ar + ar² + ... + ar^(n-1)]

Sₙ (r - 1) = arⁿ - a

Sₙ (r - 1) = a(rⁿ - 1)

Sₙ = a(rⁿ - 1)/(r - 1)

Note that, here, r ≠ 1.

Sₙ = -a(1 - rⁿ)/(-(1 - r)) = a(1 - rⁿ)/(1 - r).

Sₙ = a[1-rⁿ]/[1-r]

S₁₀ = 5[1-2¹⁰]/[1-2]

S₁₀ = 5[1023]

S₁₀ = 5,115

--The given question is incorrect, the correct question is

"The first term in a geometric series is 5 and the common ratio is 2. Find the sum of the first 10 terms in the series."--

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The place value of zero in any numeral is always zero. Zero May have any place in a number, but its value will remain to be zero. In numbers having zeros such as 105, 350, 42017, and 90218, the place value of 0 in each number is 0.

(0)zero is a number, and the numerical digit is utilised to represent the number in any numerals. It meets a major function in mathematics such as it plays the role of the additive identity of real numbers, integers, and many other algebraic systems. As a number, 0 is used as a placeholder in place value systems.

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The value of [tex]\alpha ^0 = (5\alpha ^0) =1[/tex], as anything raised to the power of 0 is equal to 1. Hence, the answer to the equation [tex]5\alpha ^0 + (5\alpha ^0)[/tex] is 6.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The value of [tex]\alpha ^0 = (5\alpha ^0) =1[/tex], as anything raised to the power of 0 is equal to 1.

Substituting the value of [tex]\alpha ^0 =(5\alpha ^0) = 1[/tex] in the given equation we have:

5(1) + 1 = 6

Hence, the answer to the equation [tex]5\alpha ^0 + (5\alpha ^0)[/tex] is 6.

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To find the domain and range of a log graph, identify the x- and y-intercepts, determine the asymptotes, if any, and identify the intervals between the asymptotes and intercepts. The domain and range of the graph are the union of all of these intervals.

To find the domain and range of a log graph, identify the x- and y-intercepts, determine the asymptotes, if any, and identify the intervals between the asymptotes and intercepts. The domain and range of the graph are the union of all of these intervals.The domain of a log graph is the set of all possible x-values and the range is the set of all possible y-values. To find the domain and range of a log graph, first identify the x- and y-intercepts. Then, determine the asymptotes of the graph, if any. Finally, determine the intervals of the graph, which are the areas of the graph between the asymptotes and the intercepts. The domain and range of the graph are then the union of all of these intervals.

To find the domain and range of a log graph, identify the x- and y-intercepts, determine the asymptotes, if any, and identify the intervals between the asymptotes and intercepts. The domain and range of the graph are the union of all of these intervals.

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Answer: $20.25

Step-by-step explanation:

1. First you need to find the discount

  -multiply .55 (55%) by 45 to get 24.75

2. Then subtract the discount from the actual price

  - 45-24.75=20.25.

                             So then you get the answer, $20.25

Answer:

Step-by-step explanation:

24

Answer:

x = 5.132 cm

Step-by-step explanation:

We are given a right triangle and are asked to find a missing side length, x.

To find a missing side length in a right triangle, we often use the Pythagoras theorem.

However, we need at least two known side lengths to use the Pythagoras theorem.

So, what do we do?

We use trigonometric functions.

⭐What are trigonometric functions?

⭐The trigonometric functions

To find out which trigonometric function we use, we have to look at the types of side lengths we are given (opposite, hypotenuse, or adjacent).

We are given a side length with a measure of 6.8 cm, which is the hypotenuse of the triangle.

We are also given a side length with a measure of x cm (we want to solve for x), which is adjacent to the 41 degrees.

Thus, we will use cos(θ).

First, substitute the side lengths and angle measures we are given/want to solve for.

cos(θ) = adjacent/hypotenuse

cos(41) = x/6.8

Next, multiply both sides of the equation by 6.8 to isolate x, as we want to solve for x.

6.8cos(41) = x

Finally, compute using a scientific calculator.

6.8cos(41) = 5.132025146 cm

Make sure to round to 3 significant figures.

∴ 6.8cos(41) = 5.132 cm

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An equation's solution is a value for a variable that, when added to the equation, produces a true statement.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. A mathematical sentence with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

A value for a variable that, when added to the equation, results in a true statement is the solution of an equation.

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The distance between point M and point N is 13 units.

What is the distance formula?

Using their coordinates, an algebraic expression provides the distances between two places (see coordinate system). The distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.

Here, we have

Given: M is located at (-6,5) and point N is located at (7,5).

If we know that M(x,y) = (-6,5)  and N(x,y) = (7,5), then the distance between point M and point N is:

MN = [tex]\sqrt{(7-(-6))^2+(5-5)^2}[/tex]

MN = 13

Hence,  the distance between point M and point N is 13 units.

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There are 7 ounces of applesauce in each container

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let x represent the quantity of Newton applesauce

Descartes makes 72.5 ounces of applesauce, which is 2.5 times of Newtons, hence:

2.5x = 72.5

x = 29 ounce

Newton eats 8 ounces, hence:

Remaining = 29 - 8 = 21 ounces

The remaining is placed into 3 containers. If y represent the amount per container:

3y = 21

y = 7 ounces

There are 7 ounces in each container

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Therefore , the solution of the given problem of slope intercept comes out to be  y = 2x + 10

In mathematics, the inflection point is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The equations for the long line is given as Y = mx+c, wherein m denotes the inclination and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercepting form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to appear to be gradient intercepts.

Here,

To obtain the line orthogonal to y=2x3,

determine the negative inverse of slope of the original version and

employ the point-slope formula: y-y1=m(x-x1).

So,

Point(-5,3)

Thus, Putting value in the given formula:

=> y -3 = 2(x-(-5)) -3

=> y- 3 = 2x +10 -3

=> y = 2x + 10

Therefore , the solution of the given problem of slope intercept comes out to be  y = 2x + 10

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The total number of peaches is given by the equation A = 25 peaches

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 total number of peaches be represented as A

Now , the equation will be

The percentage of peaches that equals 7 peaches = 28 %

Substituting the values in the equation , we get

28 % of A = 7   be equation (1)

On simplifying the equation , we get

( 28 / 100 ) x A = 7

Multiply by 100 on both sides of the equation , we get

28A = 700

Divide by 28 on both sides of the equation , we get

A = 700/28

A = 25 peaches

Therefore , the value of A is 25 peaches

Hence , the number of peaches is 25 peaches

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The length of the hypotenuse is 17 cm.

Pythagoras' Theorem is the way in which you can find the missing length of a right-angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), the Opposite (which doesn't touch the hypotenuse), and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

However, it can also be written in the form of c²=a²+b²

In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.

As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.

3²=9 and 4²=16.

As you're looking for C, you've got to add these together

9+16=25

As a²+b²=c², this means that the answer for C is the square root of 25.

√25= 5

We are given that a = 8 cm and b = 15 cm.

Using Pythagoras' theorem,

c² = a² + b²

Substitute the values,

⇒ c² = 8² + 15²

⇒ c² = 64 + 225

⇒ c² =289

∴ c = 17

Thus, the length of the hypotenuse is 17 cm.

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Therefore , the solution of the given problem of function comes out to be g(x) = -3|x-1| - 4.

Mathematics is a science that investigates numbers, their variations, mathematics and the local tissues, shapes, and the both their actual and potential placements. Function describes the connection between a collection of inputs, each of which has an associated output. A function is an association of inputs that results in a single, distinctive output for each input. Each function is given a city or municipality or a scope, often known as a realm. Functions are typically denoted by the letter f. (x). An x can be found in the input. The four primary categories of procedures—on features, each process, a range few additional attributes, within procedures, and on functions—are already present.

Here,

Given :

g(x) = -f(x) to reflect it over the x-axis.

So , In order to find the g(x) of the given f(x) is

=> -f(x) = -3|x-1|-4,

so

=> g(x) = -3|x-1| - 4

Therefore , the solution of the given problem of function comes out to be

g(x) = -3|x-1| - 4.

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Answer:

V=-3

W=4

Step-by-step explanation:

-v + w = 7

v + w = 1

[tex]\space \space [/tex]2w=8

[tex]\space \space [/tex]w=8/2

[tex]\space \space [/tex]w=4

[tex]\space \space [/tex]

-v+w=7

-v+4=7

-v=7-4

-v=3

(-1)-v=(-1)3

V=-3

[tex]\space [/tex]

.....

Answer:

Hundreds place!

Step-by-step explanation:

Hope it helps! =D

Shortest length of ramp that can be built to reach a ledge .83 meters from the ground is 8.333 meters, according to the ADA standards.

What is Shortest length?

Shortest length is the shortest distance measured from one end to the other.

According to the ADA standard, the maximum slope for a wheelchair-accessible ramp is one unit vertically for every twelve horizontal units. To find the length of the ramp needed to reach a height of .83 meters, we can use the formula:

rise / slope = run

Where:

rise = the vertical distance to be covered (in this case, .83 meters)

slope = the maximum allowed slope (1:12, or 1/12)

So we can plug in the values we know:

.83 meters / (1/12) = run

To find the length of the ramp, we need to multiply the run by the slope:

run * slope = ramp length

Therefore, the length of the ramp is:

run * (1/12) = (run/12) meters = (10/12) = 8.333 meters.

So, the shortest length of ramp that can be built to reach a ledge .83 meters from the ground is 8.333 meters, according to the ADA standards.

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Step-by-step explanation:

All the explanation in the photo

The exact value of tangent of theta in simplest radical form is -4/3

The coordinates (3, -4) represent a point on the Cartesian plane, and if the terminal side of the angle θ passes through this point, then we can use the coordinates to find the exact value of tangent of theta.

To find the tangent of theta, we can use the formula:

tangent of theta = y/x = -4/3

The tangent of theta is -4/3, but it is not in the simplest radical form.

To simplify it, we can divide both numerator and denominator by their greatest common factor which is 1, so the simplified form will be -4/3

Therefore, the exact value of tangent of theta in simplest radical form is -4/3

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The population for which it is appropriate for Emma to generalize the results from her sample is the population of one-bedroom apartment rental prices in the large city where Emma is moving.

This population includes all the prices of one-bedroom apartments that are available for rent in that city, not just the ones that are listed on the website where Emma obtained her sample. Emma is most likely to be utilizing the information from her sample to make inferences about the population as a whole, such as the typical monthly rental prices, the range of prices, and the distribution of prices.

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Robbie Knievel, a daredevil stuntman, passed away on Friday morning, 13 january 2023 at the age of 60.

He was battling pancreatic cancer, which, according to the American Cancer Society, accounts for around 3% of all cancers but about 7% of all cancer fatalities in the U.S. He was in a hospice in Reno, Nevada. Because the pancreas is hidden deep inside your abdomen, where it cannot be seen in selfies, the diagnosis of pancreatic cancer is frequently delayed. Therefore, the tragic news of Knievel's departure presents a chance to spread greater awareness of this terrible sickness, which will likely claim the lives of over 50,000 individuals once more in 2023.

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We see here that the set of survey results is most likely to show biased results for people who buy food at the mall is: D. Lewie's because he surveyed people who may or may not have bought food.

Surveying is the process of collecting data or information from a sample of individuals or a population. Surveys can be conducted in various ways, such as through in-person interviews, telephone calls, online forms, or mail-in questionnaires.

The goal of surveying is to gather information about the characteristics, attitudes, opinions, or behaviors of the people being surveyed in order to make inferences about the larger population from which the sample was drawn. Surveying is widely used in research, marketing, and various other fields for data collection.

Surveying people at the mall's main entrance does not guarantee that they have bought food, and therefore the results may not accurately represent the average number of people who buy food at the mall.

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Answer:

A. Kelvin’s because he surveyed people leaving an area where food is sold

Step-by-step explanation:

The highest common factor (HCF) of 12, 18 and 42 is 6, which is the greatest number that can divide each of these numbers evenly with no remainder.

1. List out the prime factors of 12, 18 and 42:

12 = 2 x 2 x 3

18 = 2 x 3 x 3

42 = 2 x 3 x 7

2. Find the highest common factors for each pair of numbers:

12 and 18 = 2 x 3

12 and 42 = 2 x 3

18 and 42 = 2 x 3

3. Find the common factor that appears in all three numbers:

2 x 3 = 6

4. Therefore, the HCF of 12, 18 and 42 is 6.

The HCF of 12, 18 and 42 is 6. This is because 6 is the highest number that can evenly divide each of these numbers without any remainder. To find the HCF, the prime factors for each number must be listed out, and the highest common factor for each pair of numbers must be identified. The common factor that appears in all three numbers is then the HCF. In this case, the common factor is 2 x 3, which is equal to 6. Therefore, the HCF of 12, 18 and 42 is 6.

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After solving, the value of [tex]log_{7}[/tex](49) is 2.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

The value of [tex]log_{7}[/tex](49) is 2.

[tex]log_{7}[/tex](49)=x

To find the value of the expression the formula is:

1) log([tex]a^n[/tex])=nlog(a)

2) [tex]log_{a}[/tex](a)=1

Step1:Rewrite in exponential form first.

[tex]log_{7}[/tex](49)=[tex]log_{7}(7^2)[/tex]Use the log rule log [tex]a^x[/tex] = x log a

[tex]log_{7}[/tex](49)=2[tex]log_{7}[/tex](7)

Using [tex]log_{a}[/tex](a) = 1

[tex]log_{7}[/tex](49)=2*1

[tex]log_{7}[/tex](49)=2

The value of [tex]log_{7}[/tex](49) is 2.

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