The equation y = m x b is the slope-intercept form of the equation of a line. what is the equation solved for b?

Answer:hello again

Step-by-step explanation:

In the given homogeneous system in parametric vector form, where the solution set is x = x₁ x₂ x₃, x = x₃. where the value of x₁ = 5k, x₂ = 5k and x₃ = 10k.

The system is

x₁ + x₂ - 15x₃ = 0 .......(1)

2x₁ + x₂ - 15x₃ = 0 .......(2)

-x₁ + x₂ = 0

We write the system in the matrix form or AX = 0

Where A = ( 1   2   -15)                 and X = ( x₁)

                 ( 2   1    -15)                               (x₂)

                 ( -1   1      0)                               (x₃)

Now, | A | = [15] -2 [-15] -15 [2+1]

= 15 + 30 - 45

= 0

∴ Since, | A | = 0, ∴ Given system has non-trivial solution.

Let x₃ = k

∴ From equation (1), x₁ + x₂ = 15k

from equation (2), 2x₁ + x₂ = 15k × 2

4x₁ + 2x₃ = 30k - x₁  + 2x₂ = 15k

= 3x₁ = 15k

∴ x₁ = 5k

and x₂ = 15k - 2x₁ = 15k - 10k

∴ x₂ = 5k.

To find x₃ = x₁ + x₂

x₃ = 5k + 5k

∴ x₃ = 10k.

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The minimum value of the bacterial population on the interval [2, 6] is 4, and the maximum value is 64.

To find the minimum and maximum values of the bacterial population along the interval [2, 6], we need to evaluate the function b(t) at t = 2 and t = 6, respectively, and then compare the results.

at t = 2

b(2) = 2^2 = 4, which means that after 2 days, the sample has 4 bacteria.

at t = 6

b(6) = 2^6 = 64, which means that after 6 days, the sample has 64 bacteria.

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The converted value of Celsius to degrees Fahrenheit using the standard formula is 48 degrees Celsius equals to 118.4 degree Fahrenheit.

Scale factor using which we relate the two units of the temperature Celsius and Fahrenheit is equal to :

(°C × 9/5) + 32 =°F

Now , to get the value of 48 degree Celsius and converted value into Fahrenheit by applying the above formula we have,

(48°Celsius × 9/5) + 32

= ( 432 / 5 ) + 32

= ( 86.4 ) + 32

= 118.4°Fahrenheit

Therefore, the converted value from degrees Celsius to Fahrenheit for the given temperature 48 degrees Celsius is equivalent to  118.4 Fahrenheit.

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The volume of an aquarium is 2071.875 cubic inches. Below, you will learn how to solve the problem.

The volume of an aquarium can be calculated by multiplying its length, width, and height. In this case, the length is 19 1/2 inches, the width is 8 1/2 inches, and the height is 12 1/2 inches.

To calculate the volume, we need to multiply these three measurements together:

Volume = Length × Width × Height
Volume = (19 1/2) × (8 1/2) × (12 1/2)
Volume = 2071.875 cubic inches

So the volume of the aquarium is 2071.875 cubic inches.

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The area for the given geometric shape will be 166.5 inch² i.e. B.

What are geometric shapes, exactly?

Geometric forms are mathematical representations that represent the shape of everyday items. Geometric forms with boundary lines, angles, and surfaces are known as shapes. There are several 2d and 3d forms.

Shapes can also be classed based on their regularity or homogeneity. A symmetrical regular form, such as a square or circle, is common. Asymmetry can take on irregular shapes. They're also referred to as organic forms or freeform shapes. A tree, for example, has an irregular or organic shape.

In plane geometry, two-dimensional forms are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, and so on. In solid geometry, the three-dimensional shapes are the cube, cuboid, and sphere.

Now,

Area of the shape will be = Area of rectangle + Area of triangle

For rectangle, length=16 inch, Breadth=9 inch

For triangle, base=6 inch, height=7.5 inch

then area of shape=l*b+1/2*b*h

=16*9+1/2*6*7.5

=144+22.5

=166.5 inch²

hence,

             The area for the given geometric shape will be 166.5 inch².

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Answer:

May you please give me the brainliest answer:

To find the value of x, we can set the two given equations equal to each other, since they both represent the same value of y:

2/3x + 8 = 1/2x + 10

We can simplify this equation by first getting rid of the fractions. To do this, we can multiply both sides of the equation by the least common multiple of the denominators, which is 6:

6(2/3x + 8) = 6(1/2x + 10)

4x + 48 = 3x + 60

Next, we can isolate the x term on one side of the equation by subtracting 3x from both sides:

4x - 3x + 48 = 60

Simplifying this gives:

x + 48 = 60

Finally, we can isolate x by subtracting 48 from both sides:

x = 60 - 48 = 12

Therefore, x = 12.

The 55-gallon drum size is a popular choice for storing and transporting materials because it is convenient, cost-effective, and safe.

The size of the 55-gallon drum is not arbitrary. It is a standard size that has been adopted by industry and regulatory agencies for many practical reasons.

Firstly, the 55-gallon drum is a convenient size for handling and transport. It is large enough to hold a significant amount of material but still small enough to be moved around with relative ease. Its cylindrical shape makes it easy to roll and stack, which saves space and simplifies handling.

Secondly, the 55-gallon drum is a cost-effective option for storage and transport. Its size allows for efficient use of space and materials, which translates into lower costs for manufacturers and shippers.

Thirdly, the 55-gallon drum size is closely linked to regulatory standards. Many regulations and guidelines in the industry specify the use of 55-gallon drums for storing and transporting hazardous materials. This is because the size is considered to be a safe and manageable option for handling such materials.

Its dimensions have been standardized by industry and regulatory agencies, making it a common sight in many settings.

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The probability that the sample average exceeded 5100 is given as follows:

0%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 250, \sigma = 5000, n = 64, s = \frac{5000}{\sqrt{64}} = 625[/tex]

The probability that a sample average exceeds $5,100 is one subtracted by the p-value of Z when X = 5100, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (5100 - 250)/625

Z = 7.76

Z = 7.76 has a p-value of 1.

1 - 1 = 0.

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The total number of pages in Rhett's book is 183 pages.

A solution to an equation is a number that can be substituted for the variable to provide a piece of true number information.

To determine the total number of pages in Rhett's book, we need to solve for p in the equation:

p + 31 = 214

First, we can separate p on one side of the equation by subtracting 31 from both sides:

p + 31 - 31 = 214 - 31

Simplifying:

p = 183

Therefore, the total number of pages in Rhett's book is 183 pages.

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Answer: 90.718 kilograms

Step-by-step explanation:

The length of each side of the square by factoring the area expression are  (4x+3).

A square's area is equal to the square of each side since all of its sides are the same length.

The following is the formula for determining a square's area:

A = L²

where L is the length of each side of square.

Given the area of a square expressed as 16x² + 24x + 9

Factorize 16x² + 24x + 9

16x² + 24x + 9

=  16x² + 12x + 12x + 9

= 4x(4x+3) + 3(4x+3)

= (4x+3)²

Hence the length of each side of the square is (4x+3).

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the type of slope of the line is positive, as the coefficient of x (which is the slope) is positive. The y-intercept is -0.9, which means that the line intersects the y-axis at the point (0, -0.9).

The equation of the line y = 1.4x - 0.9 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Comparing the given equation with the slope-intercept form, we can see that the slope is 1.4 and the y-intercept is -0.9. Therefore, the type of slope of the line is positive, as the coefficient of x (which is the slope) is positive. The y-intercept is -0.9, which means that the line intersects the y-axis at the point (0, -0.9). The y-intercept, on the other hand, is the point where the line intersects the y-axis. In the equation y = mx + b, b is the y-intercept. In the case of the given equation, we can see that the y-intercept is -0.9. This means that the line intersects the y-axis at the point (0, -0.9). The slope and y-intercept are important characteristics of a line because they can be used to graph the line and to write its equation in slope-intercept form. In addition, they can be used to calculate the x-intercept, which is the point where the line intersects the x-axis, and to determine the equation of a parallel or perpendicular line.

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Answer:

GJ=6.5, JH=9.2

Step-by-step explanation:

The measures of the angles of the triangle are:

Angle 1: −3 degrees
Angle 2: 10 degrees
Angle 3: −14 degrees

To solve for g and find the measures of the angles of the triangle, we need to use the fact that the sum of the angles in a triangle is 180 degrees. This means that:

−3 + (2+8) + (3−17) = 180

Simplifying the equation, we get:

−3 + 10 + (−14) = 180

−7 = 180

To solve for g, we need to isolate it on one side of the equation. To do this, we can add 7 to both sides of the equation:

g = 180 + 7

g = 187

Now, we can plug g back into the original equation to find the measures of the angles:

−3 + (2+8) + (3−17) = 187

−3 + 10 + (−14) = 187

−7 = 187

Therefore, the measures of the angles of the triangle are:

Angle 1: −3 degrees
Angle 2: 10 degrees
Angle 3: −14 degrees

I hope this helps! Let me know if you have any further questions.

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The price of the TV, including tax, is $161.17 rounded to the nearest cent. To find the price of the TV including tax, we need to calculate the sale price of the TV after the 15% discount, add the sales tax, and then round to the nearest cent.

Here are the steps:

Calculate the sale price after the 15% discount:

Sale price = Original price - Discount amount

Sale price = $177.21 - (15% * $177.21)

Sale price = $150.63

Calculate the sales tax on the sale price:

Sales tax = 7% * $150.63

Sales tax = $10.54

Add the sales tax to the sale price:

Price including tax = Sale price + Sales tax

Price including tax = $150.63 + $10.54

Price including tax = $161.17

Therefore, the price of the TV, including tax, is $161.17 rounded to the nearest cent.

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Answer:

pair c has the inverse functions

A subset is when all elements of any set A are present in another set B. Its working has been explained below.

Let us take two sets on random i.e., set A and set B. If we find that all elements of set A can be found in set B as well, we deem it to be a subset of set B. If we were to explain in simpler terms, we can say that set A is a part of set B.

Let us further assume that set A has the elements {1,2,3} and set {1,2,3,4,5,6}. From what we can see is that all elements in set A are also present in set B. This means that set A is a subset of set B.

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Answer:

6

Step-by-step explanation:

∆ABC is congruent with ∆BDE

so BD/BA = DE/AC

=> 8/(8 + 16) = x/18

8/24 = x/18

24x = 8(18)

24x = 144

x = 144/24 = 6

Answer: X =  6

Step-by-step explanation:

Since the triangles are congruent (similar), then

8/24   =   X/18

Cross Multiply

X x 24  =  8 x 18

24X =  144

X =  144/24

X =  6

A graph of the function,

f(x) = log₃(x - 1) + 2 is given in the image below.

The inverse of exponentiation is the logarithm. 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.

Given:

A function,

f(x) = log₃(x - 1) + 2.

let y = f(x) = log₃(x - 1) + 2.

To find the y-intercept:

y = log₃(-1) + 2

y = 1.111

Therefore, the graph of the function is given in the attached image.

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From the decimal theory 10 has no decimal places, as it is a whole number.

As per the data given in the above question are as bellow,

The provided details are as bellow,

We have given the number as 10.

we have to find the decimal in the given number.

Thus we have to know about decimal value.

The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal. Up until there are no more digits, the remaining ones keep the place values filled in.

Here don't have any decimal value in the given number 10.

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The solutions to the equation k³ + 6k² + 9k = 0 are given as follows:

k = 0 and k = -3.

The equation for this problem is defined as follows:

k³ + 6k² + 9k = 0.

Simplifying the common factor k, we have that:

k(k² + 6k + 9) = 0.

The first solution is of:

k = 0.

The second solution is obtained as follows:

k² + 6k + 9 = 0

Applying the perfect square trinomial:

(k + 3)² = 0

k + 3 = 0

k = -3.

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The converted values of the volume fluid ounce to gallons is given by :

128 oz  = 1 gallons.

Relation to convert fluid ounce to gallons in standard form is given by :

1 fluid ounce = 0.0078125 gallons

Now multiply both the side by 128 to get the required relation ,

⇒ ( 128 × 1 ) fluid ounce = ( 128 × 0.0078125 ) gallons

⇒ 128 fluid ounce = 1 gallons

Therefore, using the standard relation of fluid ounce to gallons the value of 128 oz is equal to 1 gallons .

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The postulate that can be used to prove that triangles ABC and DEF are similar triangles is A. AA Similarity Postulate.

According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell. As just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.

We have, triangles ABC and DEF with:

two pairs of congruent angles - ∠B ≅ ∠E and ∠C ≅ ∠F.

Therefore, the postulate that has been used to prove that the triangles ABC and DEF are similar triangles is AA Similarity Postulate.

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The complete question is:

Which theorem or postulate proves that â–³ABC and â–³DEF are similar?Select from the drop-down menu to correctly complete the statement. The two triangles are similar by the ________. A. AA Similarity Postulate B. SSS Similarity Theorem C. SAS Similarity Theorem

Answer: 69, 420

Step-by-step explanation:

grrrr

The solution is, Alice makes 3 bunches with 2 red balloons and 5 blue balloons.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

We are given that Alice is making balloon bunches from 6 red balloons and 15 blue balloons.

She wants the same number of red balloons and the same number of blue balloons in each bunch.

We have to find the greatest number of balloon bunches that Alice can making from  all the balloons.

We will find the HCF of 6 and 15

6 = 2×3

15 = 3×5

Common factor of 6 and 15 is 3.

Hence, HCF of 6 and 15=3

Therefore, Alice makes 3 bunches with 2 red balloons and 5 blue balloons.

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The solution to the differential equation is:

[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]

What is a differential equation?

Any equation involving the derivatives of one dependent variable with respect to another independent variable is referred to as a differential equation. Differential equations are widely used in mathematics, but they also play an important role in the sciences of medicine, chemistry, physics, and engineering.

To solve this differential equation, we need to find a function y(x) that satisfies the equation. Here's how to do it:

First, we can divide both sides of the equation by D³ + 1 to get:

y = (eˣ+1)² / (D³+1)

Next, we can take the derivative of both sides with respect to x:

dy/dx = d/dx[(eˣ+1)² / (D³+1)]

Using the quotient rule of differentiation, we get:

dy/dx = [(D³+1)(2eˣ)(eˣ+1) - (eˣ+1)²(3D²)] / (D³+1)²

Simplifying the numerator, we get:

[tex]dy/dx = [2e^{(2x)} + 2e^x - 3D^{2}(e^x+1)^2] / (D^3+1)^2[/tex]

Therefore, the solution to the differential equation is:

[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]

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Answer:

400 m

Step-by-step explanation:

According to Pythagorean theorem, c^2 = a^2 + b^2

c^2 = 600^2 + 800^2 = 360000 + 640000 = 1000000

c = √1000000 = 1000 mm

(600 + 800) - 1000 = 1400 - 1000 = 400

Answer:

Step-by-step explanation: