What are the 3 steps in solving linear equations in two variables?

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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The length of the adult crocodile more than the young crocodile is 5.0 feet.

A young crocodile is 0.4 feet long. An adult crocodile is 13.5 times as long. The length the adult crocodile is more than the young crocodile can be calculated as follows:

Hence,

length of the adult crocodile = 13.5(0.4)

length of the adult crocodile = 13.5 × 0.4

length of the adult crocodile = 5.4 feet

Therefore,

the length of the adult crocodile more than the young crocodile = 5.4 - 0.4 = 5.0 feet

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No, the quadratic form is not the same as the factored form of a quadratic equation.

A quadratic function can usually be represented by many equivalent expressions. For example, a quadratic function might be defined by f(x) = x² + 3x + 2. The quadratic expression f(x) = x² + 3x + 2 is called the standard form, the sum of a multiple x² of and a linear expression (3x + 2 in this case).

In general, the standard form is  ax² bx + c

We refer to 'a' as the coefficient of the squared term 'x²', 'b' as the coefficient of the linear term 'x', and 'c' as the constant term.

The function 'f' can also be defined by the equivalent expression (x +2)(x + 1). When the quadratic expression is a multiplication of two factors where each one is a linear expression, this is called the factored form.

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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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The length of the diagonal is 17.

Given that, In quadrilateral ABCD, sides AB and BC both have a length of 10, and sides CD and DA both have a length of 17.

The measure of ∠ADC = 60°

AD = CD ( according to the question)

So, Δ ABC is an isosceles triangle with ∠DAC = ∠DCA.

According to the image,

Angles in a triangle add up to 180°, and since ∠ADC = 60°, the other two angles are also 60°.

And Δ ADC is an equilateral triangle.

Therefore,  AC = DA = 17

S0, the diagonal of quadrilateral ABCD is 17.

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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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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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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:

Step-by-step explanation:

24

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 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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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

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 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 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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The solution to the formula using f as the subject is given by f = 9/(a + 7)

a = 9/f - 7

Add 7 to both sides

a + 7 = 9/f

cross product

f(a + 7) = 9

divide both sides by a + 7

f = 9/(a + 7)

Hence, the formula a = 9/f - 7 can be written as f = 9/(a + 7) using f as the subject.

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To determine how many solutions an equation has, you must first solve the equation. If the equation has an exact solution, then it has exactly one solution.

To determine how many solutions an equation has, you must solve the equation. If you can solve the equation exactly, then it has one solution. However, if the equation has two different solutions, then it has two solutions. This means that the equation has two different values that can make the equation true. On the other hand, if the equation does not have any solutions, then it has no solutions. This means that the equation does not have any values that can make it true. Therefore, to determine how many solutions an equation has, you must solve the equation and check if it has one, two, or no solutions.

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If there are 1410 students and teachers together, then there are 60 teachers present.

Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle provide an example.

given

total=1410

students=45x

teachers=2x

2x + 45x = 1410

47x = 1410

x = 3

students=45x

=45×30

=1350

teachers=2x

=2×30

=60

If there are 1410 students and teachers together, then there are 60 teachers present.

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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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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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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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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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Answer:

when doing my math the answer I got was 1/2 hope it helps

Answer:

The car can travel 30 miles per 1 gallon.

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:

A qualifying child or dependent is typically required to be eligible for head of household filing status.

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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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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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