What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2-28=12x

The two triangles called congruent if two sides the associated angle in one triangle is congruent with two sides and the contained angle in the other triangle.

According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides as well as the angle of another triangle.

Thus, two triangles are termed to be comparable if their two sides are in the same ratio as the two sides of some other triangle and their two sides' angles inscribed in both triangles are equal.

To know more about the Side-Angle-Side (SAS), here

https://brainly.com/question/22472034

#SPJ4

The option B is true which is m2=m1+3, s2=s1

From the given information,

The required correct answers are,

m2= m1 + 3

s2= s1

Hence,

Option b. is correct.

A standard deviation (or σ) is a proportion of how distributed the information is comparable to the mean. A low standard deviation implies information is grouped around the mean, and an elevated requirement deviation demonstrates information is more fanned out.

The standard deviation of a population or sample and the standard error of measurement (e.g., of the example mean) is very unique however related. The example implies the standard error is the standard deviation of the arrangement of implies that would be found by drawing an endless number of samples from the population and registering a mean for each sample. The mean standard error ends up equaling the population standard deviation partitioned by the square base of the example size and is assessed by utilizing the example standard deviation separated by the square foundation of the sample size.

To learn more about standard deviation, mean, median, and mode,

https://brainly.com/question/14747159

#SPJ4

a) The distance travelled on the cycle in the first 14 seconds is; 96 m

b) The acceleration in the first 4 seconds is; 2 m/s²

The velocity time graph for a cycle is as attached.

The distance covered will be the area under the curve.

Formula for area of trapezium is;

A = (1/2)(sum of parallel sides) * height

Area for 0 to 14 sec is a trapezium formed with parallel sides as 14 and  10 while distance between them is 8 is solved as;

Area = (1/2)(14 + 10) * 8  

Area = 24 * 4  = 96  

Thus;

Distance covered = 96 m

Distance travelled on the cycle in the first 14 seconds is 96 m.

Therefore, the acceleration in first 4 seconds = (8 - 0)/(4 - 0)

= 8/4 = 2 m/s²

Read more about Velocity Time Graph at; https://brainly.com/question/10824584

#SPJ1

They are congruent by SAS as follows if I understand you correctly:

Since x is shared by both NR and AG, it must be at their intersection.

Because it lies in the middle of both, NX = XR and AX = XG.

We join point A to point N and point R to point G to complete the triangles (any 2 points define a line).

Due to the fact that there are two triangles on either side of the point X, angle AXN is perpendicular to angle RXG. Angle AXN is equal to angle RXG because the vertical (opposite) angles formed by two intersecting lines are equal.

The following is how the SAS evidence of congruency is established:

Angle RXG in triangle RXG and angle AXN in triangle AXN are congruent (vertical angles)

Triangles AX in AXN and XG in RXG are congruent (midpoint X of line AG created these).

Triangle RXG and triangle AXN's NX and XR are congruent.

By SAS, triangles are congruent. this means they have two corresponding sides that are congruent and the angle between those 2 corresponding sides is congruent also.

To know more about congruency, visit;

https://brainly.com/question/7888063

#SJP9

The multiplied form of the Algebraic expression is 10x -0.8[tex]x^{2}[/tex]

An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators.

These expressions may be linear, quadratic or polynomials and the numbers in front of each term is called coefficient while the symbols or letters are called variable

2x( 5 - 0.4x)

we multiply each term in the bracket by 2x

2x  x 5  - 2x x 0.4x = 10x - 0.8[tex]x^{2}[/tex]

In conclusion, 2x(5 - 0.4x) reduces to 10x - 0.8[tex]x^{2}[/tex]

Learn more about Algebraic expression: https;//brainly.com/question/2164351

#SPJ1

The solution set of 6 ㏑ e = e ^ ㏑ 2x is 3

What is relation between Exponents and logarithms ?

Exponents and logarithms are inverse functions, you can use exponents to "undo" logarithms and use logarithms to "undo" logarithms. Exponents specify the number of times you must multiply a value, while logarithms specify which exponent to apply to obtain a certain value.

The given expression is,

6 ㏑ e = e ^ ㏑ 2x

we know, ㏑ (e) = 1 and e ^ ㏑(x)  = x

Put these values,

6 * 1 = 2x

Now, find x

6 = 2x

x = 3

Hence, the solution set of 6 ㏑ (e) = e ^ ㏑ (2x)  is 3

To read more about Exponents and logarithms.

https://brainly.com/question/28596269

#SPJ9

The value of f(-1) when f(x) is defined as given in the question is 0.

What is the substitution method?

One method for solving simultaneously linear equations using algebra is the substitution method. It involves changing the value of any one of the variables in one equation & applying it to another one.

Given, f(x) = 2x + 2  ......... (i)

Now, we need to find the value of f(-1), by substituting the value of x = -1 in above equation (i), then

f(-1) = 2*(-1) + 2 = -2+2 = 0

Hence, the required answer of f(-1) is 0.

To learn more about the substitution method

https://brainly.com/question/22340165

#SPJ1

Answer:

double whatever you got

100 percent increase of 2 is 4

Step-by-step explanation:

hopes this helps please mark brainliest

Answer:

It means that whatever you have just doubled.

Step-by-step explanation:

If I have a total of 100 widgets, that is 100%.  If I have a 100% increase of that value, that means I now have 200 widgets.

The solution of equation written by M. Carey is -6.

We will use PEMDAS rule to solve the equation. So, firstly solving the bracket by multiplying it with 2/3.

3x - 7 - 6x + 12/3 = 15

Simplifying this equation

3x - 7 - 6x + 4 = 15

Rewriting the equation with identical variables on each side

3x - 6x = 15 + 7 - 4

Solving the part of equation on Right Hand Side

3x - 6x = 18

Performing subtraction on Left Hand Side of the equation

-3x = 18

Shifting 3 to Right Hand Side of the equation

x = 18/-3

Performing division on Right Hand Side of the equation

x = -6

Thus, the solution of equation is -6.

Learn more about evaluation of equation -

https://brainly.com/question/4344214

#SPJ4

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since the aspect ratio of 4:6 is closer to that of an 11-inch by 14-inch frame (which is approximately 1:1.5) than the aspect ratio of 3.5:5 (which is approximately 7:10).

By minimizing the difference in aspect ratio between the photo and the frame, you will minimize the loss of the edges of the picture when trying to fit it into the frame.

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize the loss of the edges of the picture when trying to fit it into an 11-inch by 14-inch frame.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ2

Answer:

  m∠6 = 61°

Step-by-step explanation:

Given a transversal crossing parallel lines AB and CD, you want the measure of angle 6 given that angle 2 is 61°.

Where a transversal crosses parallel lines, corresponding angles and vertical angles are congruent. This has the effect of making all acute angles congruent, and all obtuse angles congruent.

Acute angle 6 is congruent to acute angle 2, which measures 61°. (They are "corresponding" angles.)

  m∠6 = 61°

The answer to the question is 5.

The calculation can be calculated as follows :

3√125

= 3√(5 x 5 x 5)

= 5

We can write 125 as 5 x 5 x 5.

Or 5 power 3.

The value of the cube root of 125 is 5.

It is the real solution of the equation x3 = 125.

The number 125 is called a perfect cube number since its cube root value is a whole number.

Read more about cube root here

https://brainly.com/question/12726345

#SPJ1

Answer:

$37,500

Step-by-step explanation:

There are 10 lots of 100g in 1kg

so $150 * 10 = $1,500 per kg

$1,500 * 25 = $37,500

The sampling distribution of the sample mean will always have the same Mean as the original distribution.

Sampling distribution:

Sampling distribution means a probability distribution of a statistic that is obtained through repeated sampling of a specific population.

Given,

Here we have the statement "The sampling distribution of the sample mean will always have the same _________ as the original distribution."

Now, we have to find the missing word in the statement.

We know that, the mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. Simply said that the sample mean is equal to the population mean.

To know more about Sampling Distribution here.

https://brainly.com/question/13501743

#SPJ1

The solution set for both inequalities overlap and are same.

The general equation of a straight line inequality is -

[y] < [m]x + [c]

[y] > [m]x + [c]

[y]  [m]x + [c]

[y] < [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following inequalities -

-0.3n ≤ 5.4

n ≥ -18

Plot the graph of both inequalities. The common region would be the solution set. Refer to the graph below. The solution region of both inequalities overlap with each other. Hence, the solution set for both inequalities is same.

Therefore, the solution set for both inequalities overlap and are same.

To solve more questions on LINEAR INEQUALITIES, visit the link below-

https://brainly.com/question/11897796

#SPJ1

The Domain is R i.e all real numbers and the range is [-16,∞).

What is the domain and range of function?

A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.

f(x)=x²-4x-12  

For Domain it can take all the real numbers as there is no term in the denominator. so Domain is "R"

Range will be f(x) is minimum at x = 2 i.e. f(x=2) = -16

f(x) maximum value is +infinity.

So Range [-16,∞)

Hence the Domain is R and Range is [-16,∞).

Learn more about Domain and Range, by the following link.

https://brainly.com/question/1942755

#SPJ4

Answer:

Step-by-step explanation:

You want to know the number of adult ticket sold if there were 61 fewer student tickets sold and the total number sold was 689.

Let a = the number of adult tickets sold. Then a-61 is the number of student tickets sold, and the total is ...

  a + (a -61) = 689

Simplifying, we get

  2a -61 = 689

  2a = 750 . . . . . . add 61

  a = 375 . . . . . . . divide by 2

The number of adult tickets sold was 375.

__

Additional comment

The number of student tickets is 375-61 = 314.

Four fifth times and eight ninth times would be simplified as 32/45.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

To simplify four-fifth times and eight-ninth times, we have to use the fractions,

Simplifying, we get

                           [tex]=\frac{4}{5}* \frac{8}{9}\\\\=\frac{4*8}{5*9}\\\\\=\frac{32}{45}[/tex]

Hene, four fifth times and eight ninth times would be simplified as 32/45.

To learn more about fractions visit:

https://brainly.com/question/78672

#SPJ9

As we can conclude from the graphical method that this system has no common intersection point they have no solution.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given system of equations are x + 2y = 4, 3x + 6y = 6, 3x - y = 5 and

6x - 2y = 10.

The graphical representation of these equations are attached in the image below.

As we can observe , 3x - y = 5(green line)  and 6x - 2y = 10(purple line) are coinciding with each other so they have infinite no. of solutions.

x + 2y = 4(red) and 3x + 6y = 6(blue) are parallel to each other and hence have no solution.

And in together all these 4 lines have no common intersection point so they have no solution.

learn more abut the system of equations here :

https://brainly.com/question/24065247

#SPJ5

Answer:

46 more people can go on the field trip

Answer:

∴ m∠6 = 60°

Step-by-step explanation:

Since AB is parallel to CD,

m∠2 = m∠6 = 60°

Answer:

Step-by-step explanation:

width:length =1:3

width:15=1:3

width =5

The width of the actual car is 45 feet.

Given that,

A automobile model is 3 feet long and 1 foot wide. Considering that the automobile is 15 feet long

To find : The width of the actual car

Model Car's Width (W) = 1 foot

Model Car's Length (L) = 3 feet

Actual Car's Length (l) = 15 feet

Actual Car's Width (w) = x feet

To solve,

We know that,

Product of Means = Product of Extremes which means ,

1 : 3 :: 15 : x

1 * x = 15 *3

x = 45.

Therefore, the Actual Car's Width (w) is 45 feet.

Learn more about Extremes :

brainly.com/question/9258688

#SPJ4

To write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1.

A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So if we have a slope of 1 or 1/1. our perpendicular line needs a slope of -1.

y - y1 = m(x - x1)

slope(m) = -1

(1,-5)...x1 = 1 and y1 = -5

now we sub...pay close attention to your signs

y - (-5) = -1(x - 1)....not done yet

y + 5 = -1(x - 1)...or it can also be written as : y + 5 = - (x - 1)

To learn more about parallel lines click here https://brainly.com/question/24607467

#SPJ4

Answer:

-11

Step-by-step explanation:

3(-2)-5

-6-5

-11

h=-11

Answer:

3:10 ratio of mangos to rest of the fruits or 15:50 unsimplified

Step-by-step explanation:

There are 50 fruits in total with 15 of them being mangos. Simplify this (divide by both numbers by 5) to get 3:10

Based on the line on the graph, the price per gallon at Miguel's Gasoline Station is equal to: B. $2.50

In order to calculate the price per gallon at Miguel's Gasoline Station, we would have to determine the slope of the line representing the number of gallons bought and the total cost of their purchases are plotted on the graph below (see attachment).

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:

Substituting the given parameters into the formula, we have;

Slope, m = (20 - 10)/(8 - 4)

Slope, m = 10/4

Slope, m = 2.5

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer:

y = x-5

Step-by-step explanation:

-x + y = - 5

y = - 5 + x

y = x - 5

Answer:

4 pounds

Step-by-step explanation:

12/3=4 remember it says about!

Answer:

m = - 3

Step-by-step explanation:

since the line passes through (1, 3 ) then the coordinates of the point make the equation true.

substitute x = 1, y = 3 into the equation and solve for m

3 = m + 6 ( subtract 6 from both sides )

- 3 = m