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The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64

Given,

The equation  x² - 28 = 12x

We need to find the intermediate step in the form (x + a)² =b as a result of completing the square for the given equation

Equation; x² - 28 = 12x

Arrange the equation;

x² - 12x = 28

Take the coefficient of x

k = -12

Divide it by 2

k/2 = -6

Square both sides

(k/2)² = 36

Add 36 to both sides of x² - 12x = 28

x² - 12x + 36 = 28 + 36

(x - 6)² = 64

Therefore,

The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64

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Left Blue Dot (5,9)

Right Blue Dot (7,0)

m = (y2 - y1)/(x2-x1)

= (9-0)/(5-7)

=9/-2

m = -9/2

Don't know the y-intercept so use the formula below to calculate equation of line

y-b = m(x-a)

y-9 = -9/2(x-5)

y-9 = -9x/2 + 45/2

y = = -9x/2 + 45/2 + 18/2

y = -9x/2 + 63/2

By Pythagoras theorem, The given triangle with sides 37 mm, 39 mm, 56 mm is not a right triangle as the theorem is false in this case.

The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Pythagorean Theorem demonstrates how the side lengths of a right triangle can be calculated from the sum of the areas of three intersecting squares. This theorem is a very helpful tool that serves as the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite.

Here,

We can prove this by Pythagoras theorem,

b²+p²=h²

b=39 mm

p=37 mm

h=56 mm

=39²+37²

=2,890

56²=3,136

As 2890≠3136,

The triangle is not a right triangle. The triangle with sides of 37, 39, and 56 millimeters is not a right triangle according to Pythagoras' theorem because the theorem is incorrect in this case.

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Answer:

6√5 - 4√15

Step-by-step explanation:

√5(6 - 4√3) =

Distribute √5

= 6√5 - 4√3√5

= 6√5 - 4√15

Price of Tv at Store A = $ 94.5

Price of Tv at Store B = $ 95

Given that

Price of tv player = $ 100

Sales Tax = 5%

The price of tv at store A after 10% discount = 100 - 10% of 100

The price of tv at store A after 10% discount:

= 100 - 0.1x100

= 100 - 10 = $90

Price of tv at store A after sales tax = 90 + 5% of 90

= 90 + 0.05x90

= 90 + 4.5

= $94.5

Now, lets calculate price of of tv at store B.

The price of tv at store B= 100

Price of tv at store B after sales tax:

= 100 + 5% of 100

Price of tv at store B after sales tax = 100 + 0.05x100

= 100 + 5

= $105

Price of tv at store B $10 rebate

= 105 - 10

= $95

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Complete questions

John wants to buy a tv. The price is $100, and the sales tax is 5 percent. Store A is offering a 10 percent discount and Store B is offering a $10 rebate. What would John's total cost be at the two stores? Total cost at Store A = Total cost at Store B =

Answer:

241.9026

Step-by-step explanation:

2*pi*r

Answer:

241.9 cm

Step-by-step explanation:

circumference= [tex]\pi[/tex]d

circumference= [tex]\pi[/tex](77)

circumference= 241.9 cm

Answer:

x = 7

Step-by-step explanation:

2 (-4x + 2) + 5x - 2 = -19       Distribute 2 to -4x and 2

-8x + 4 + 5x - 2 = -19            Combine like terms

-3x + 2 = -19                          Subtract 2 from both sides

-3x = -21                                To get x by itself, divide -3 on both sides

x = 7

The exponential decay of the function shows it will take approximately 81 years for the population to decrease to 200

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. This could also be an exponential growth or exponential decay which depends on the situation.

The exponential function is an important mathematical function which is of the form f(x) = ax

The details given in this question are;

The exponential function to represent this will be given as

200 = 525(1 + 0.012)⁻ˣ

x = number of years

This can be simplified as

200 = 525(1.012)⁻ˣ

x = 80.9 years

It will take approximately 81 years

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Answer:

A

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - 2x - 1 ← equation of line b

Answer:

-9/4  Negative As a Fraction

How I got the answer:

2 (x+3) = (1/8) (x+2)

x+ 3 = -3 (x+ 2)

x = -9/4

I helped you so mark me BRAINLIEST

Answer:

YesTheorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent.

A and B are complementary, and C and B are complementary.

The 95% confidence interval estimate of the population mean is between $50,555.51 and $51.444.49.

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x (SD / √n)

where CI = confidence interval

μ = sample mean

z = found by using a z-score table

SD = sample standard deviation

n = sample size

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.95, z = 1.96

Plug in the values and solve for the confidence interval.

CI = μ ± z x (SD / √n)

CI = $51,000 ± 1.96 x ($1,200 / √28)

CI = $51,000 ± $444.49

CI = [$50,555.51, $51.444.49]

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The list of minerals that is grouped based on color is B. chalcopyrite, pyrrhotite, and pyrite.

Chalcopyrite is a mineral that has a high concentration of copper ore. As a result, it has a golden yellow color due to the copper in it. It also has crystals of a tetragonal form.

Pyrrhotite is a mineral with iron in it. It has the color of bronze yellow which means that it is similar in color to Chalcopyrite. We also have Pyrite which is brass yellow in color and looks golden. This puts it in the same color group as Chalcopyrite.

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The measure of m∠5 is 31 degrees.

What are alternate angles?

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal

Given that,

The AB is perpendicular to CD.

And, the m∠2=31°.

Based on the above information, the following information should be considered:

The alternate angles should be equal i.e. ∠2 = ∠5 and ∠1 and ∠6.

So, ∠5 = ∠2 = 31 degrees.

Therefore we can conclude that the measure of m∠5 is 31 degrees.

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13 cm  long is PQ in  parallelogram .

What does parallelogram mean in a nutshell?

Perimeter of ∥gm = - 40 cm

 2(PQ+ PS) = - 40

  2 ( PQ + 7 ) = 40

        PQ + 7 = 20

           PQ = 20 - 7

           PQ = 13 cm

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Answer: y = 2x - 13

Step-by-step explanation:

y=mx + b

[tex]m= \frac{-7-(-1)}{3-6}[/tex]

   [tex]= \frac{-6}{-3}[/tex]

[tex]m = 2[/tex]

y = 2x + b

(6, -1) <-- use to find "b" by substituting either one of the coordinates

-1 = 2(6) + b

-1 = 12 + b

-13 = b

y = 2x - 13

The absolute value of +4 will be 4 units as it is the distance from (0,0) to (4,0) in coordinate plane.

Without taking into account direction, absolute value defines how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A number's absolute value is determined by how far it is from zero on the number line. For instance, the absolute value of -7 would be 7, as it is 7 units away from zero. Additionally, since 0 is 7 units distant, the value of 7 would likewise be 7.

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Answer:

If two triangles are congruent, then by the definition of congruent triangles, 3 pairs of sides are congruent and 3 pairs of angles are congruent. In all, this is 6 statements of congruence.

There are ways of proving triangles congruent that require only 3 statements of congruence of corresponding parts, such as ASA, SAS, AAS, etc.

Sometimes in order to prove two segments or two angles congruent, since these segment and angles are parts of triangles, you prove the triangles congruent using some other statements of congruence, not involving these parts, and then you get 6 statements of congruence that includes the parts you wanted to prove congruent. That is where you use "corresponding parts of congruent triangles are congruent", or CPCTC for short.

Answer:

1

Step-by-step explanation:

(y2-y1)/(x2-x1) is the formula for slope (aka m)

6-(-2)/1-(-3) = 8/4 = 2

In the expression 1.5x + 18 = 36.5 - 8 x is 7, hence 4x is 28.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An expression 18 + 1.5x is 8 less than 36.5.

∴ 1.5x + 18 = 36.5 - 8.

1.5x = 36.5 - 8 - 18.

1.5x = 10.5.

x = 10.5/1.5.

x = 7.

Therefore 4x is equal to 4(7) = 28.

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The value of x + y is -12i.

What are complex numbers?

Real numbers and imaginary numbers combine to form complex numbers, which have two components. Complex numbers serve as the foundation for more complex math, including algebra. They have numerous practical applications, particularly in the fields of electronics and electromagnetism.

Here, we have

Given x = 4 - 5i and

y = -4 - 7i

Now we have to find the value of x+y.

We will add both complex numbers and we get

x + y = 4 - 5i + (-4 -7i)

x + y = - 12i

Hence, the value of x + y is 12i.

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Answer:

[tex]\frac{7}{b+4}[/tex]

Step-by-step explanation:

[tex]\frac{7}{b^2+5b+4}[/tex] × [tex]\frac{b^2+8b+7}{b+7}[/tex] ← factor quadratics on numerator/ denominator

= [tex]\frac{7}{(b+1)(b+4)}[/tex] × [tex]\frac{(b+1)(b+7)}{b+7}[/tex]

cancel factors (b+ 1) and (b + 7) on numerator/ denominator

= [tex]\frac{7}{b+4}[/tex] × 1

= [tex]\frac{7}{b+4}[/tex]

Answer:

The intercept would be -6/5

Step-by-step explanation:

Answer:

y=-3 x=-3

Step-by-step explanation:

The amount owed is $10865, based on the given parameters

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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After 8 years the balance of the account would be $9600.

What is simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Simple Interest =(P×r×t)/100

where:

P =Principal

r = interest rate

t = time

​

​Given:

Principal, P = $8400

Rate of  interest, r = 1.8%

Final amount, A = $9600

Simple  interest, S.I = Final amount - Principal = 9600 - 8400 = $ 1200

Now, 1.8% of 8400 = (1.8/100) × 8400 = 151.2

⇒ Interest of 1 year = $151.2

Interest after x years = $1200

x = 1200/151.2 = 7.94 ≈ 8 years

Therefore, after 8 years the balance of the account would be $9600.

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The graph of the linear function f(x) = 2 - 3x is a straight line attached below

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

The function given y = 2 - 3x can be plotted on a graph using function table

When x = -3

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

f(-3) = 11

when x = -2

f(-2) = 8

when x = - 1

f(-1) = 1

when x = 0

f(0) = 2

when x = 1

f(1) = -1

when x = 2

f(2) = -4

when x = 3

f(3) = - 7

We can use this data and plot a graph.

Kindly find the attached graph of the function below

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The total number of small boxes is 1.72 and the large boxes is 5.1.

Given;

To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 100 nails in each small box and 450 in each large box. The contractor purchased 3 more tiny boxes—totaling 2500 nails—than large boxes.

To calculate the proportion of small and large boxes that were bought,

Let's assume the small boxes as 's' and the big boxes as '3s'.

∴ s(100) + 3s(450) = 2500

   100s + 1350s = 2500

   1450s = 2500

   s = 2500/1450

   s = 1.72

∴ 3s = 1.72 * 3

       = 5.1

Hence, the total number of small boxes is 1.72 and the number of large boxes is 5.1.

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The number of small boxes purchased is 7 and the number of large boxes purchased is 4 by the contractor.

Let the number of large boxes purchased = x

then the number of small boxes purchased = x + 3

It is also given that,

small box contains = 100 nails

large box contains = 450 nails

According to the question:

450x + 100(x + 3) = 2500

450x + 100x + 300 = 2500

550x = 2500 - 300 = 2200

x = 2200/550

x = 4

and x + 3 = 4 + 3 = 7.

Thus, Let the number of small boxes purchased = 4 and the number of small boxes purchased = 7.

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Answer:

x = 7/2

Step-by-step explanation:

-28/5 x -2/5 = -2x -4x + 1

-28/5 x -2/5 = -6x + 1

-28 x -2 = -30x + 5

30 x -28 x = 5 + 2

2x = 7

2/2 x = 7/2

x = 7/2

Answer:

(7/2)

Step-by-step explanation:

I'll rewrite "4/5(-7x-1/2)=-2x-(4x-1)" to (4/5)(-7x-1/2)=-2x-(4x-1) to clarify the fraction (I am not interpreting it as 4/(5(-7x-12))).  [The five is not part of the denominator in my rewrite]

(4/5)(-7x-1/2)=-2x-(4x-1)

(-28x-2)= 5*((-6x+1)) [multiply the numerator by 4 on the left side, and multiply both sides by 5]

-28x-2= -30x + 5   [Combine like terms]

2x   = 7          [Put like terms together by adding 30x and +2 to both sides]

x = (7/2)  This satidfies the equation.

Answer:

3x + 5 =3x + 8

Step-by-step explanation:

3x - 3x = 8-5

x = 3

Step-by-step explanation:

we have to soft the ones that have no solutions.

3x + 5 = 3x + 8

5 = 8

that is never true, and therefore there is no solution.

3(x + 5) = 3x + 15

3x + 15 = 3x + 15

that is always true, and it has therefore infinitely many solutions.

2(x + 1) = 2x + 1

2x + 2 = 2x + 1

2 = 1

this is never true, so, there is no solution.

2x + 1 = 2x + 1

this is always true, so this has infinitely many solutions.

The answer is 47.

Step-by-step explanation:

To find the median, you need to write the numbers in order from least to greatest. However, that is already done.

Then, you need to count the numbers from the ends to the middle.

For example, if the numbers were 2, 4, 8, 9, and 10, you would do it like this (see the example below)

So, you would go from 32 to 45 and 72 to 63, and from 45 to 47 and 63 to 47.

This means that the median is 47.