what information does the standard form of a linear equation reveal about a line

The graph of the simultaneous linear equation

[tex]y = \frac{1}{3}x + 12\\[/tex]

y = 3x + 4

is the graph given in the third option.

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

The simultaneous linear equation are

[tex]y = \frac{1}{3}x + 12\\[/tex]

y = 3x + 4

Now,

[tex]y = \frac{1}{3}x + 12\\[/tex]

At x = 0, y = 12

The graph passes through (0, 12)

First option is wrong

y = 3x + 4

At x = 0, y = 4

The graph passes through (0, 4)

Second option is wrong

So the third option is correct.

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It is possible to compare the square roots of one hundred seventy and one hundred six eighths using the formulas sqrt(170) sqrt(106/8), and sqrt(170) = sqrt(106/8).

A number's square root is a value that yields the original number when multiplied by itself. The other way to square an integer is to find its square root. Squares and square roots are hence linked ideas.

Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.

For comparing them, we should always keep in mind that if square or cube roots of two numbers ('a' and 'b') are to be compared, such that 'a' is greater than 'b', then a2 will be greater than b2 and a3 will be greater than b3 and so on, i.e., nth

The square root of 170 is approximately 13.038404810405015, while the square root of 106/8 is approximately 3.2403703492039303. Therefore, the square root of 170 is greater than the square root of 106/8. This can be written as:

sqrt(170) > sqrt(106/8)

Alternatively, you can compare the two numbers using the less than (<) or equal to (=) symbols as follows:

sqrt(170) < sqrt(106/8)

sqrt(170) = sqrt(106/8)

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The square root of an integer is a quantity that, when multiplied by itself, equals the original value. Finding an integer's square root is another technique to square it. Thus, squares and square roots are related concepts.

The equation would be expressed as x=y or as x2 = y if x were the square root of y. In this case, the radical symbol for the number's root is "". By multiplying the positive integer by itself, the square of the number is represented. By taking the square root of the square of a positive number, the original number can be found.

The square root of 170 is approximately 13.038404810405015, while the square root of 106/8 is approximately 3.2403703492039303. Therefore, the square root of 170 is greater than the square root of 106/8. This can be written as:

sqrt(170) > sqrt(106/8)

Alternatively, you can compare the two numbers using the less than (<) or equal to (=) symbols as follows:

sqrt(170) < sqrt(106/8)

sqrt(170) = sqrt(106/8)

Answer:

X=3

Step-by-step explanation:

7x-1=5x+5

do the same on both sides of the =

+1 to each side to get rid of the negative number

7x=5x+6

-5x from both sides

2x=6

divide by 2

x=3

Answer:

  1/2

Step-by-step explanation:

Given right triangle ABC with right angle A and tan(B) = 1, you want the value of the expression tan(C) -sin(B)cos(C).

Angle A is given as 90°.

Angle B is found from ...

  tan(B) = 1   ⇒   B = arctan(1) = 45°

Angle C is its complement:

  C = 90° -B = 45°

The relevant trig functions are ...

  tan(C) = tan(45°) = 1

  sin(B) = sin(45°) = 1/√2

  cos(C) = cos(45°) = 1/√2

Then the value of the expression is ...

  tan(C) -sin(B)cos(C)

  = 1 -(1/√2)(1/√2) = 1 -1/2

  = 1/2

Answer: 52 computers

Step-by-step explanation:

First, take 96 divided by 24 = 4

Then take 13 times 4 = 52 computers

Answer: 52 computers

Step-by-step explanation: 96 is four times 24, meaning the expected amount of computers can be identified by multiplying the numerator by 4:

13 × 4 = 52

24 × 4 = 96

Our fraction is 52/96, which can be reduced to 13/24.

On a street with 96 people, 52 computers are expected throughout all 96 houses.

Yes, a discontinuous function is a function that is not continuous.

A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.

A continuous function in mathematics is a function without discontinuities, or any sudden changes in value. If we can guarantee arbitrarily small changes in the input of a function by limiting small enough changes, then the function is continuous.

A function is continuous if its graph can be drawn without lifting the pencil from the paper, or if the function's values remain "close" to one another as the input values change. A discontinuous function, on the other hand, has "breaks" or "jumps" in its graph, indicating that the function's values become "far" from one another as the input values change. An example of a discontinuous function is the absolute value function.

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If the graph of a function can be traced without removing the pencil from the paper or if the function's values stay "near" to one another while the input values change, the function is continuous. Contrarily, a discontinuous function's graph shows "breaks" or "jumps," suggesting that the function's values move "far" apart as the input values alter. The absolute value function is an illustration of a discontinuous function.

The average rate of change in concentration of b from t=0 s to t=222 s as calculated from the data given is 0.00916M/s.

The changes happening in A  can be found as ,

= 0.140 - 0.650

= -0.510 M

Time  = 222 s - 0 s

= 222 s

Therefore the average rate of change of A is

= -0.510 M / 222 s = -0.00229 M/s

Since the value obtained is negative we can conclude that the rate is decreasing.

Using stoichiometry equation we can find the value of B as ,

The average rate of change of B

= 2 x 0.00229

= +0.00458 M/s

-∆[A]/∆t = +1/2∆[B]/∆t

-0.00458 = +∆B/2

∆B = 2x 0.00458 = 0.00916M/s

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William Samuel Johnson felt that ,when men were born, they were equal.

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From the given expression , following represents the binomial :

Option d.  6 (a² + b).

As given in the question,

Given expressions  represents the different types of polynomial are explain as follow:

Simplify all the given options to get the binomial we have:

a. 7 × a + a

= 7a + a

= 8a it represents the monomial with single term.

b.  6a² + 7b + 2c

We cannot add these terms as all are having three different variables.

It represents the trinomial.

c. 4a × 3b × 2c

= 24abc it represents the monomial.

d.  6 (a² + b)

= 6a² + 6b represents the two terms, it is binomial.

Therefore, from the given set of expressions the option d.  6 (a² + b) represents the binomial.

The above question is incomplete , the complete question is :

Which of the following is a binomial?

(a) 7 × a + a

(b) 6a² + 7b + 2c

(c) 4a × 3b × 2c

(d) 6 (a² + b)

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The mean of the numbers  2 4 6 8 10 12 is 7

In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.

mean is calculated getting the summation of all the numbers and dividing by the number of times or occurrences of the number are

In this problem the numbers are 6 and the sum is calculated as follows

= 2 + 4 + 6 + 8 + 10 + 12

= 42

the mean is calculated by dividing the summation by number of occurrence

= 42 / 6

= 7

the mean is 7

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The value of the expression a^4 depends on "a". It is different for every "a" which can be any numerical value.

A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.

Dependent, independent and controlled are three types of variable.

The given expression a^4 can be written as:

a^4= a*a*a*a

And the value of this expression depends on "a". It is different for every "a" which can be any numerical value.

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Answer:

456748

Step-by-step explanation:

you 463uy2iuswhk then 13456

The standard error of the sample mean is approximately 8.9 pounds.

What is standard error of the sample mean?

Simple division of the standard deviation by the square root of the sample size yields the SEM. By evaluating the sample-to-sample variability of the sample means, standard error determines the accuracy of a sample mean.

To find the standard error of the sample mean, we need to first find the sample mean weight of the students. To do this, we add up the weights of all the students and divide by the number of students:

(128 + 193 + 166 + 147 + 202 + 183 + 181 + 158) / 8 = 171.5

Next, we need to find the variance of the sample. The variance is a measure of the spread of the data around the mean, and is calculated as follows:

       [tex]variance = ((weight - mean)^2) / (n-1)[/tex]

where weight is the weight of each student, mean is the sample mean weight, and n is the number of students.

Plugging in the values from our data, we get:

variance = (128 - 171.5)^2 + (193 - 171.5)^2 + (166 - 171.5)^2 + (147 - 171.5)^2 + (202 - 171.5)^2 + (183 - 171.5)^2 + (181 - 171.5)^2 + (158 - 171.5)^2 / 7

= 1096.5

Finally, we can find the standard error of the sample mean by taking the square root of the variance and dividing by the square root of the number of students:

                [tex]standard\ error = \sqrt{(variance / n)} \\\\= \sqrt{1096.5 / 8 )\\\\=8.9[/tex]

So, The standard error of the sample mean is approximately 8.9 pounds.

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A linear function can be represented by an equation of the form y = mx + b, where m is the slope of the function and b is the y-intercept. The x-intercept is the point where the graph of the function intersects the x-axis, and the y-intercept is the point where the graph intersects the y-axis.

Given that the x-intercept of the linear function is −8 and the y-intercept is 4, an equation of the function can be written as:

y = mx + b

Substituting the values of the x-intercept and the y-intercept into this equation, we get:

y = m(-8) + 4

Since the y-intercept is 4, this equation can be rewritten as:

y = 4 + mx

This equation represents a linear function with a y-intercept of 4 and a slope of m.

Therefore, an equation of the linear function with an x-intercept of −8 and a y-intercept of 4 is y = 4 + mx.

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Given that the x-intercept of the linear function is −8 and the y-intercept is 4, an equation of the function can be written as:

y = mx + b

Substituting the values of the x-intercept and the y-intercept into this equation, we get:

y = m(-8) + 4

Since the y-intercept is 4, this equation can be rewritten as:

y = 4 + mx

This equation represents a linear function with a y-intercept of 4 and a slope of m.

Therefore, an equation of the linear function with an x-intercept of −8 and a y-intercept of 4 is y = 4 + mx.

Answer:

  ... centroid, or center of gravity.

Step-by-step explanation:

The point of concurrency of the medians of a triangle is always inside the triangle and is called the ______.

A median joins a vertex of a triangle with the midpoint of the opposite segment. It is a line segment that lies entirely within the triangle. Hence any two medians will meet at a point that is within the triangle.

The point of concurrency of medians is called the "centroid." If the triangle has uniform areal density, the centroid will be the center of gravity, the point at which the triangle could be balanced.

The centroid divides each median into parts in the ratio 1:2, where the longer part is the segment to the vertex, and the shorter is the segment to the midpoint of the side.

Answer:

2 + (S ÷ 180)

Step-by-step explanation:

S is the sum of the measure of the interior angle measures for a polygon, while n is the number of sides.

We are given the equation S = 180(n - 2). In order to solve for n in terms of S, we must isolate the n on one side.

S = 180(n - 2) ⇒ divide both sides by 180

S ÷ 180 = n - 2 ⇒ add 2 to both sides

2 + (S ÷ 180) = n

Therefore, n = 2 + (S ÷ 180)

The rule is that words, not numerals, should be used to represent numbers and ordered events that are less than 10 in total.

An arithmetic value known as a number is used to calculate and represent a quantity. Numerical writings, such as the letter "3," are used to represent numbers. A number system is a way of writing numbers that uses logical symbols or digits to represent them.

here

There are occasional exceptions, but generally speaking, numbers and ordered events that are less than 10 in total should be expressed as words.

Except for when they are the first digit of a phrase, numbers with two or more digits should be written as numerals.

The rule is that words, not numerals, should be used to represent numbers and ordered events that are less than 10 in total.

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The pictogram shows information about the houses in a street. the number of bedrooms each house have is 82 bedrooms

Using the pictogram the number of houses are listed

3-bedroom houses = 9 houses

4-bedroom houses = 10 houses

5-bedroom houses = 3 houses

Multiplying out to get the number of bedroom per house

9 * 3= 27 bedrooms

10 * 4= 40 bedrooms

3 * 5 = 15 bedrooms

Adding the bedrooms together

27 + 40 + 15

= 82 bedrooms

the house has 82 bedrooms

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Two triangle is called SAS to each other when they have two similar side lengths along with identical angles between these two sides. SSS is called when both triangles have three similar side lengths.

Two triangles satisfy congruence theorem when they have equal corresponding side lengths and equal corresponding angles.

Triangles needed to satisfy at least one of 4 criteria. If two triangles have two similar side lengths having equal angles between these two sides. if two triangles have two equal angles along with one similar corresponding side length. If two triangles have identical 3 side lengths or two triangles which are right-angled having equal hypotenuse and an equal corresponding side.

hence, SAS and SSS are the indicator of congruent triangle.

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The simple interest earned on investing $880 at 5.25% for 2 years is $92.4

Simple interest is calculated using the formula;

SI = P × R × T

Where,

So,

SI = P × R × T

= 880 × 0.0525 × 2

= $92.4

Consequently, $92.4 is the simple interest earned on $880 at 5.25% for 2 years

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The graph of the function y = x is shown and the data of the function is tabulated below.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
Let's assume the function,
f(x) = x or y = x
Now,
the graph of the function is shown,
and data is given as,
put x = 1,
so
y = 1
Similarly,

Other values can be obtained as y = 2, 3 , 4 for x = 2, 3, 4
Now the table is given as
x     y
1      1
2      2
3     3
4     4

Thus, the graph of the function y = x is shown and the data of the function is tabulated above.

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Answer:

Step-by-step explanation:

This scatter plot has a moderate negative correlation.

If the age requirements for academic progressions set by a school is satisfied, than yes it is possible for a 13 year old to be in 7th grade.

The age at which a child is ready to start schooling can vary depending on a number of factors, including the child's physical, social, and emotional development. In general, children who are at least 5 years old and are able to meet certain developmental milestones are typically ready to start school.

Because academic skills are directly tied to a pupil's capacity for academic success, they are sometimes seen as being more significant than age when deciding whether a student is prepared to proceed to a higher grade level. Age is not always a reliable indicator of a student's intellectual aptitude or preparation for a higher grade level. Even if they are younger than their peers, some children may be farther along in their studies and possess the abilities and knowledge required to succeed in a higher grade. Even if they are older than their friends, some kids may be falling behind in their academics and not yet ready to advance to a higher grade.

Depending on the school's age requirements and the student's academic standing, a 13-year-old may be in the 7th grade. A kid who is 13 years old might be in seventh grade since in many educational systems, pupils in this grade are between the ages of 12 and 13. It is usually recommended to verify with the school to clarify their age requirements because they might differ from one school system to another. The intellectual ability of a student may also play a role in establishing what grade they are in addition to their age.

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The two main CPUs in laptops are called i3 and i5, and their names vary according to their level of efficiency.

In general, Core i5 CPUs perform better than Core i3 CPUs in terms of CPU performance. The Core i3 processors are all dual-core, in contrast to the dual-core and quad-core i5 CPUs. Along with cores and threads, you must also consider the processor generation.

In terms of CPU performance, Core i5 components often exceed Core i3 components. Dual-core and quad-core Core i5 CPUs are both available. When it comes to multimedia applications like video transcoding and photo editing, a true quad-core CPU will often beat a dual-core CPU.

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By assuming that both tests measure the same kind of ability, Bob did better in terms of the standardized Z-score.

We have provide a data about two major math's tests.

First Major test : SAT math score normally distributed with

Mean , μ = 516 and

Standard deviations, σ = 115

Second Major test: ACT math score normally distributed with

Mean, μ = 22

Standard deviations, σ = 5

Anna scores in SAT test 650

i.e x = 650

Using Z-Score formula,

Z = (x - μ)/σ

Z = (650 - 516)/115 = 154/115 = 1.17

Also, Bob score on ACT math test is 29 i.e x = 29

Z-Score = (x - μ)/σ

=> Z = (29 - 22)/5 = 7/5

=> Z = 1.4

Since, Z-Score for Bob's ACT math test is high as compared to Anna's SAT math test.

So, Bob did better in terms of the standardized z-score.

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Yes, we can take the square root of 0, the value of square root 0 is equal to 0.

A number's square root is the amount that, when multiplied by itself, equals the original value.

The square root of 0 is x multiplied by itself to give the number to give 0.

Which means x*x=0.

To get the product of numbers as 0, at least one number should be 0.

Therefore here x=0.

0 × 0 = 0

0² = 0

0 = √0

Hence we can take the square root for 0 and yes, it is defined.

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The real-life measurement, if the scale factor is 2, is 4, 4, 1, 18 for the second table.

A scale factor, also known as a conversion factor, is a number that is used to increase or decrease the size of a figure without changing its shape. It is used to modify an object's size.

Given:

Scale factor = 2

Calculate the actual measurements as shown below,

[tex]Actual \ measure = Scale \ factor \times Scale \ measurement\ on\ paper[/tex]

Actual measurement = 2 × 2 = 4

Actual measurement = 2 × 2 = 4

Actual measurement = 2 × 0.5 = 1

Actual measurement = 2 × 9 = 18

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The median for the next batch of observations is 5.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=3,4,5,8,9

n=5

median=(5+1)/2

=3rd term

=5

The median for following set of observation is 5.

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Answer:

(gf)(a)

=[g{f(a)}]

=g(3a-5)

=-4(3a-5)+5

=-12a+20+5

=-12a+25 is the right answer I think

but according to your options,

(gf)(a)

=g(a)×f(a)

=(-4a+5)(3a-5)

=-12a²+20a+15a-25

=-12a²+35a-25 which is option d.but I don't think it is the right process

Answer:

Step-by-step explanation:

The correct answer is option (D).

Given , g(a) = -4a + 5

f(a) = 3a-5

Here we have to find (gf)(a)

So,  we will replace  (gf)(a) with g(a).f(a)

= g(a).f(a) =( -4a+5 ).(3a-5)

= -4a*3a -4a*(-5)+ 3a*5+5*(-5)

= -12a2 + 20a + 15a - 25

Answer = -12a2 + 35a -25

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