Please explain the process!
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The missing side length BE can be found by using the proportion of corresponding side lengths in similar triangles. We can set up the proportion AB/AD = BE/DF and solve for BE.

To find the missing side length in similar triangles, we can use the fact that corresponding side lengths are proportional. In other words, if two triangles are similar, then the ratio of any corresponding side lengths will be the same.

This allows us to set up a proportion with the known side lengths and the missing side length, and solve for the missing side.

For example, in the given problem, we have two similar triangles ABC and ADEF, with corresponding side lengths AB and AD, BC and DE, and AC and DF. We are given the values of AB, BC, AD, and DF, but we need to find the value of BE. We can set up the proportion AB/AD = BE/DF, which tells us that the ratio of AB to AD is equal to the ratio of BE to DF. We can then cross-multiply to get AB x DF = BE x AD, and solve for BE by dividing both sides by AD.

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Answer:

25000(1-.14)^t

Step-by-step explanation:

it's just a simple decreasing equation it's your start number 1 minus your percentage because we're decreasing and to the power of t which equals time

When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

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

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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Answer:

hope this helps you out :)

Answer:

-1 - ( -2 ) = 1

Step-by-step explanation:

Answer:

12 or 24 apples.

Step-by-step explanation:

If you can divide the apples evenly among 4 children, then you can automatically divide them among 2 children (since 4 is a multiple of 2). Therefore, the possible number of apples that the box could contain are given by:

\(n_1 = 3*4 = 12\ apples\\n_2 = 3*4*2 = 24\ apples\)

The box could contain 12 or 24 apples.

Answer:

12 or 24 because they are divisable by 2 3 and 4

Step-by-step explanation:

Answer:$387.27

Step-by-step explanation:

Hope this helps.

Answer:

9 / 4

Step-by-step explanation:

The slope of line V can be found using the formula for slope: (y2 - y1) / (x2 - x1).

(y2 - y1) / (x2 - x1)

(13 - 9)  / (1 - 10)

(4) / (-9)

Two slopes are perpendicular when the values are reciprocals. The slope of line V is 4 / (-9). The reciprocal of this is: 9 / 4.

The solution of the given differential equation is \(y=2e^x-1\).

A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.

We have the differential equation -

\(\frac{dy}{dx}-y=1\\\\\frac{dy}{1+y}=dx\\\\log(1+y)=x+c\\1) y(0)=1\\log2=c\\\\1+y=e^{x+c}\\y=2e^x-1\)

2)

y(1)=0

log(1+0)=1+c

c=-1

\(y=e^{x-1}\\\)

3)

y(0)=6

log7=c

\(y=e^{x+log7}-1\\y=7e^x-1\)

4)

c=log5

\(y=5e^x-1\)

The complete question is-

The given differential equation is \(\frac{dy}{dx}-y=1\),

find the particular solution on ivp y(0)=1,y(1)=0 ,y(0)=6 and y(0)=5

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The solution of x^2 + 10x+ 25 = 8 is x = ± 2√2 - 5.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

the given equation is,

x^2 + 10x+ 25 = 8

⇒ x^2+ 2.x.5 + 5^2 = 8

⇒ (x+5)^2 = 8   [ by taking square root both side]

⇒ x+5 =± 2√2

⇒ x = ± 2√2 - 5

Hence, The solution of x^2 + 10x+ 25 = 8 is x = ± 2√2 - 5.

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The answer is B. the y-intercept is where the line intercepts the y axis. x will always be zero.

The y-intercept is -3

Answer:

A

Step-by-step explanation:

from a to b to c it makes the angle 75 degrees im 90 percent sure

Answer:

Step-by-step explanation:

ABC = (1/2)(75 +45)

ABC = 60º

Answer:

the 4th and 6th one

Step-by-step explanation:

A function is when there are x- and y-values but each x value has only 1      y-value

Simple: If the x-value is repeated its not a function

Answer:

Step-by-step explanation:

1,2,3

Answer:720 inches cubed

Step-by-step explanation: volume=lengthxwidthxheight

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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Answer:

No.

Step-by-step explanation:

We can set this proportion up as:

\(\frac{4.2}{1.5}=\frac{12}{5}\)

For this to be true, cross-products need to be equal:

\(4.2(5)=12(1.5)\),

However, we can see that this is not the case:

\(4.2\cdot 5 \neq 12 \cdot 1.5\)

Therefore, these ratios are not proportional.

Answer:

With the formula of lwh/3 the answer is 305.37

Step-by-step explanation:

l×w×h /3 =305.37

Answer:

916.11 ft³

Step-by-step explanation:

(9×6)×7.83/2×13/3

= 211.41×13/3

= 916.11 ft³

Answered by GAUTHMATH

(a) The two vectors and the path on a quadrant I plot: Given vectors: S = 2m  i  + 10m  j ;E = 8m  i  + 4m  j .Plotting the given vectors on the Cartesian plane, we get, Graphical representation of the given vectors
(b) A point on the path is a fraction f of the way between the start and the end. Write this as a vector equation involving f.If a point on the path is a fraction f of the way between the start and end points, then the position vector of this point can be given as:
P(f) = fE + (1 - f)S
= f(8m  i  + 4m  j ) + (1 - f)(2m  i  + 10m  j )
= (8f + 2 - 6f) m i  + (4f + 10 - 6f) m j
= (6f + 2) m i  + (6 - 2f) m j
So, the required vector equation is P(f) = (6f + 2) m i  + (6 - 2f) m j .
(c) Evaluate your expression from part (b) for f=0, P(0), and f=1, P(1).

Explain whether these results confirm if your expression in part (b) is reasonable or not.
For f = 0, P(0) = (6 × 0 + 2) m i  + (6 - 2 × 0) m j  = 2 m i  + 6 m j
For f = 1, P(1) = (6 × 1 + 2) m i  + (6 - 2 × 1) m j  = 8 m i  + 4 m j
These results are reasonable since P(0) is the starting vector S and P(1) is the ending vector E, which is as expected.

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Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

The equation, 3y = 9x -12, written in standard form is 9x - 3y =12

From the question, we are to write the given equation is standard form.

The given equation is

3y = 9x - 12.

The standard form of a linear equation is

Ax + By = C

Where A, B, and C are constants

x and y are variables

Now, we will write the given equation is the standard form of a linear equation.

3y = 9x - 12

Substract 3y from both sides

3y - 3y = 9x - 3y - 12

0 = 9x - 3y - 12

Therefore

9x - 3y - 12 = 0

Add 12 to both sides of the equation

9x - 3y -12 + 12 = 0 + 12

9x - 3y = 12

Hence, the standard form is 9x - 3y = 12

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The solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.

The given system of equations is given as,z + 5x = 243x + 2z + 3y = 7-x + 2y = -9

To solve the given system of equations by using the Cramer's rule, we have to first represent the given system in matrix format.

             Matrix format: ⎡1 0 5⎤ ⎡x⎤ ⎡24⎤ ⎢0 3 2⎥ ⎢y⎥=⎢7⎥ ⎣-1 2 0⎦ ⎣z⎦ ⎣-9⎦

Using the formula for Cramer's rule, we know that,

                       x = Dx / D, y = Dy / D, z = Dz / D, whereD is the determinant of the coefficient matrix, Dx is the determinant of the matrix obtained by replacing the x column with the constant matrix, Dy is the determinant of the matrix obtained by replacing the y column with the constant matrix, and Dz is the determinant of the matrix obtained by replacing the z column with the constant matrix.

       Calculation of D: D = | A | = ⎡1 0 5⎤ ⎡0 3 2⎥ ⎣-1 2 0⎦

Applying the Laplace expansion along the first column, D = 1 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦| D = 6 Calculation of Dx: Dx = ⎡24 0 5⎤ ⎡3 2⎤ ⎢7 3 2⎥ ⎢-1 2⎥ ⎣-9 2 0⎦ ⎣2 0⎦

Applying the Laplace expansion along the first column, Dx = 24 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-9 2⎤| |⎣3 2⎦| |⎣3 2⎦| |⎣3 2⎦|

                          Dx = -18

Calculation of Dy: Dy = ⎡1 24 5⎤ ⎡0 2 2⎤ ⎢0 7 2⎥ ⎢-1 -1 0⎥ ⎣-1 -9 0⎦ ⎣2 0 0⎦

Applying the Laplace expansion along the second column, Dy = 0 |⎡1 5⎤| - 24 |⎡0 2⎤| + 5 |⎡0 2⎤| |⎣-1 0⎦| |⎣-1 0⎦| |⎣-1 0⎦|

                            Dy = 10

Calculation of Dz: Dz = ⎡1 0 24⎤ ⎡0 3 2⎥ ⎢0 3 7⎥ ⎢-1 2 -1⎥ ⎣-1 2 -9⎦ ⎣3 2 0⎦

Applying the Laplace expansion along the third column,

                              Dz = 24 |⎡3 2⎤| - 10 |⎡-1 2⎤| + 0 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦|

                         Dz = -24

Now we have the values of D, Dx, Dy and Dz.

Therefore, x = Dx / D, y = Dy / D, z = Dz / D,x = -18/6 = -3 y = 10/6 = 5/3 z = -24/6 = -4

Hence, the value of x, y, and z is (-3, 5/3, -4) respectively.

Therefore, the solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.

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Answer:

x < 2

Step-by-step explanation:

Given

5(x - 2) < - 3x + 6 ← distribute parenthesis on left side

5x - 10 < - 3x + 6 ( add 3x to both sides )

8x - 10 < 6 ( add 10 to both sides )

8x < 16 ( divide both sides by 8 )

x < 2

Hey there!☺

\(Answer:\boxed{x<2}\)

\(Explanation:\)

Let's start by simplifying both sides of the inequality:

\(5x-10<-3x+6\)

Now add 3x to both sides:

\(5x-10+3x<-3x+6+3x\\8x-10<6\)

In our third step, we will add 10 to both sides:

\(8x-10+10<6+10\\8x<16\)

In our last step, we will divide both sides by 8:

\(\frac{8x}{8}=\frac{16}{8}\)

Simplify 16/8:

\(\frac{16}{8}=2\\ x<2\)

x<2 is your answer.

Hope this helps!☺

\(\text{-TestedHyperr}\)

False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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The variance of a sample or a population cannot be negative. This means that option c, negative, is the correct answer.

Variance is a statistical measure that quantifies the dispersion or spread of data points around the mean. It tells us how much the individual data points deviate from the average. The variance is always a non-negative value because it is calculated by summing the squared differences between each data point and the mean, divided by the total number of data points.
If the variance were negative, it would imply that the sum of the squared differences between each data point and the mean is less than zero. However, this is not possible because squared differences are always positive or zero.
On the other hand, options a, zero, and d, less than 1, are incorrect. The variance can be zero if all the data points in the sample or population are the same, indicating no dispersion. Additionally, the variance can be any positive value, including values less than 1.
To summarize, the variance of a sample or a population cannot be negative, making option c, negative, the correct answer.

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\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{r}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-1)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -3 }\implies \cfrac{r-9}{4+1}=-3\implies \cfrac{r-9}{5}=-3 \\\\\\ r-9=-15\implies \boxed{r=-6}\)

Answer:

gradient = \(\frac{1}{2}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Given

2y - x = 10 ( add x to both sides )

2y = x + 10 ( divide through by 2 )

y = \(\frac{1}{2}\) x + 5 ← in slope- intercept form

with gradient = \(\frac{1}{2}\)

Answer:

k(3)=37

Step-by-step explanation:

This questions asks us to find k(3).

We want to find what k(t), or y is, when t, or x is equal to 3.

k(t)=13t -2

Therefore, we can substitute 3 in for t.

k(3)= 13(3)-2

Solve according to PEMDAS ( Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

First, multiply 13 and 3

k(3)=39-2

Subtract 2 from 39

k(3)=37

Answer:

37

Step-by-step explanation:

Answer: aaaaaaaaaaaaaaaa

Step-by-step explanation: what is this first grade