Solve for and the indicated angles.
G
90°
F
(4x + 13)
(5x + 14)
D
E

Answer:

Step-by-step explanation:

5*10*2=100

8*10/2=40

12*4*2=96

12*5=60

4*5*2=40

100+40+40+96+60=336cm²

The surface area for the given composite figure is 442 cm²

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is a composite figure, composed of a triangular prism and rectangular prism, attached to each other.

We will find the surface area of the composite figure by adding surface areas of both the solids and subtracting the common base area from it.

We know that, surface area of a triangular prism and rectangular prism, are S = bh+(b1+b2+b3)l and 2(lh+wh+lw) respectively.

Therefore, SA = 12(8)+(12+10+8)5 +2(12×5+4×5+12×4) - lw

= 96+150+2(60+20+48) - 12×5

= 246+256-60

= 442

Hence, The surface area for the given composite figure is 442 cm²

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Considerando la expresión de una ecuación lineal, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.

Una ecuación lineal o línea se puede expresar en la forma y = mx + b

donde

La ecuación lineal se puede expresar también mediante la ecuación punto-pendiente de la recta, que se plantea si se conoce la pendiente de la recta y cualquiera de sus puntos. Con ello queda determinada la recta, conociendo la pendiente  “m” y un punto  (x1, y1) dado:

y - y1= m(x -x1)

En este caso, la recta que pasa por el punto (5, –8) con pendiente 5.

Reemplazando en la ecuación punto-pendiente de la recta:

y - (-8)= 5(x -5)

Resolviendo:

y + 8= 5(x -5)

Aplicando propiedad distributiva:

y + 8= 5x - 5×5

y + 8= 5x - 25

Aislando la variable "y":

y= 5x - 25 - 8

y= 5x - 33

Finalmente, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.

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South Florida Water Management

The South Florida Water Management District is a regional governmental agency that manages the water resources in the southern half of the state, covering 16 counties from Orlando to the Florida Keys and serving a population of 9 million residents.

Water management is the control and movement of water resources to minimize damage to life and property and to maximize efficient beneficial use. Good water management of dams and levees reduces the risk of harm due to flooding.

Water management is the activity of planning, developing, distributing and optimum use of water resources under defined water polices and regulations.

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The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.

The real rate of return exists at 2.926%.

The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.

The formula for the real rate of return:

R = (1+N)/(1+i) - 1

Where, N exists the nominal rate and i exists the inflation rate, as decimals.

A certificate of deposit offers a nominal interest rate of 5.5 percent annually.

This means that N = 0.055

Inflation exists 2.5 percent

i = 0.025

Substitute the values in the above equation, we get

[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]

= [1.055/1.025] - 1

= 1.02926 - 1

= 0.02926

0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%

The real rate of return exists at 2.926%.

Therefore, the correct answer is option D. 3%.

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Answer:

A translation 8 units right and 2 units down

Given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.

The ratio of the shares of business partners Mr. Jake to Mr. Sebastian given to us is 3:2.

So we assume Mr. Jake's share of profit to be 3x, and Mr. Sebastian's share of profit to be 2x.

Thus, the total profit between them is 3x + 2x = 5x.

The total profit given is 24,000.

Thus, we get an equation:

5x = 24000,

or, x = 24000/5 = 4800.

Thus, the share of profit Mr. Jake receives is 3x = 3*4800 = 14400.

Thus, given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.

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Answer:

see explanation

Step-by-step explanation:

(a)

play ends at 9 : 55 pm

15 minutes to get to bus stop , then time is

9 : 55 + 15 min = 10 : 10 pm = 22 : 10

the earliest bus she can catch is 22 : 25

(b)

time to wait 22 : 10 → 22 : 25 = 15 minutes

The exponential equation for the number of Bacterian Camels in Mongolia is:

[tex]P(t) = 600(0.982)^t[/tex]

The parameters can be described as follows:

A decaying exponential function is modeled by:

[tex]P(t) = A(1 - r)^t[/tex]

In which:

For this problem, the values of the parameters are given as follows:

A = 600, r = 0.018.

Then the equation is:

[tex]P(t) = A(1 - r)^t[/tex]

[tex]P(t) = 600(0.982)^t[/tex]

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Based on the triangle inequality theorem, the statement that the given segments will form a triangle is TRUE.

If a, b, and c are lengths of a triangle, then,

a + b > c

a + c > b

b + c > a

Given the segments:

AC = 6

CB = 5

BA = 8

6 + 5 > 8 [true]

6 + 8 > 5 [true]

5 + 8 > 6 [true]

Therefore, it is true that the segments given could form a triangle.

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The value of sin(∝) is -√56/15

The given parameter is:

cos(∝) = -13/15

To determine the sine, we use the following identity

sin^2(∝) = 1 - cos^2(∝)

So, we have:

sin^2(∝) = 1 - (-13/15)^2

This gives

sin^2(∝) = 1 - 169/225

Evaluate the difference

sin^2(∝) = 56/225

Take the square root of both sides

sin(∝) = ±√56/15

sin(∝) is negative in quadrant III.

So, we have:

sin(∝) = -√56/15

Hence, the value of sin(∝) is -√56/15

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By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.

Herein we must apply the definition of absolute value prior to evaluating the quadratic equation defined in the statement. From algebra we know that absolute values are defined as:

|x| = x, when x ≥ 0 or - x, when x < 0. (1)

Then, we apply (1) on the quadratic equation:

F(|x|) = |x|² - 2 · |x| + 4

As x < 0, by absolute value properties:

F(|x|) = x² + 2 · x + 4

F(|- 4|) = (- 4)² + 2 · (- 4) + 4

F(|- 4|) = 16 - 8 + 4

F(|- 4|) = 12

By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.

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You can approximate e by substituting large values for (1 + 1/n)^n into the expression.

It should be noted that an expression can simply be used to illustrate the information given in a data.

In this case, you can approximate e by substituting large values for (1 + 1/n)^n into the expression.

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Answer:

7.5 m           457.5[tex]\pi[/tex] [tex]m^{2}[/tex]

Step-by-step explanation:

First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.

The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = [tex]\frac{1}{3} \pi r^{2}h[/tex].

Original Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *7.5^{2}*50[/tex] = 937.5[tex]\pi[/tex]

Smaller Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] =  [tex]\frac{1}{3} \pi *6^{2}*40[/tex] = 480[tex]\pi[/tex]

Frustum = 937.5[tex]\pi[/tex] - 480[tex]\pi[/tex] = 457.5[tex]\pi[/tex]

The maximum number of relative extrema of the given polynomial is; 3

When trying to find the maximum number of relative extrema of a polynomial, we usually use the formula;

Maximum number of relative extrema contained in a polynomial = degree of this polynomial - 1.

We are given the Polynomial as;

f(x) = 3x⁴ - x² + 4x - 2

Now, the degree of the Polynomial would be 4. Thus;

Maximum number of relative extrema = 4 - 1

Maximum number of relative extrema = 3

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Answer:

Step-by-step explanation:

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -2

                     C   =  -10

 B2  -  4AC   =

       4 - (-120) =

             =  124

Applying the quadratic formula :

              2 ± √ 124

  x  =    —————

                   6

 √ 124 simplified

 The prime factorization of  124   is

  2•2•31

To be able to remove something from under the radical, there have to be  2  instances of it

√ 124   =  √ 2•2•31   =

               ±  2 • √ 31

 √ 31, rounded to 4 decimal digits, is   5.5678

So now we are looking at:

          x  =  ( 2 ± 2 •  5.568 ) / 6

Two real solutions:

x =(2+√124)/6=(1+√ 31 )/3= 2.189

or:

x =(2-√124)/6=(1-√ 31 )/3= -1.523

Answer:

Step-by-step explanation:

3x^2-2x-10=0

This is a quadratic equation that can be solved using the quadratic formula where

a = 3, b = -2, and c = -10

x=−b±(b^2−4ac)^(1/2)/2a

x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))

x=2±(124)^(1/2)/6

Simplify the Radical:

x=((2/6) ±2(31)^(1/2))/6

x=26±231−−√6

Simplify fractions and/or signs:

x=1/3±√31/3

which becomes

x=2.18925

See the attached image for a more clear display of solving using the quadratic equation.

x=−1.52259

The reason the graph given is misleading is that there is an Inconsistent scale on the y-axis.

The y-axis is inconsistent because it went from 0 to 200 and instead of continuing to increase by 200, it begins to increase by 10.

This is misleading because the scale used has to be uniform or else it would be hard to read the data.

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Answer:

first option

Step-by-step explanation:

Always remember to graph a diagram :)

Finding a sunken submarine in the middle of the ocean using Bayes' theorem to  the search for  USS Scorpion.

The ocean using Bayes' theorem: the search for the Scorpion.

What is Bayes' theorem?

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Answer:

Below in bold.

Step-by-step explanation:

P = 1.50(1.065)^t        where P = population in millions and t = no. of years.

So we have

2.31 = 1.50(1.065)^t

(1.065)^t = 2.31/1.50

Taking logs:

t log 1.065 = log (2.31/1/50)

t  =   log (2.31/1/50) / log 1.065

  =  6.856 years.

The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.

The distance between two points on a graph can be determined using the equation;

D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]

Given that;

We substitute our values into the equation above.

D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]

D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]

D = √[ ( -19 )² + ( 42 )² ]

D = √[ 361 + 1764 ]

D = √[ 2125 ]

D = 46.10

Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.

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I think for the first part 505 m and 53.1 degrees (Like they wrote, you need to repeat it) and same goes for the drcond part. In the last part, I think you need to add the directions. HOPE IT HELPS

*TIP: you can delete the answer the second person gave you to be able to recive more answers :)

Using a system of equations, it is found that 10,000 children attended the park that day.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The attendance at the amusement park is 30,000 attendees, hence:

c + a = 30,000, which is the first equation in matrix form.

Then:

a = 30,000 - c

The cost of attending an amusement park is $10 for children and $20 for adults. The total money earned by the park is $500,000, hence:

10c + 20a = 500,000, which is the second equation in matrix form.

Since a = 30,000 - c, we replace:

10c + 20a = 500,000

10c + 20(30000 - c) = 500,000

10c = 100,000

c = 10,000.

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Answer:

Step-by-step explanation:

43.55 + 18.62 = 62.17

The slope in question seven is 1. Below are the solutions to the remaining questions

Transformation of an object can occur in different ways. Such as translation, rotation, enlargement of different scale factors, reflection and dilation.

Given that Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.

1. The transformations to use on the blue segment CD to get it to match with the red segment C2D2 is ROTATION of 180° Clockwise

2.The transformations to use on the blue triangle to get it to match with the red triangle is ROTATION of 360° Clockwise Explain your movement using the coordinates of the vertices.

3.The line segments on the boat that is parallel is line B2 to A2 because it is parallel to line D2 to C2

4.The line segments on the boat is perpendicular is line BCA because they are perpendicular to line CFD and AB.

5.The line segments on the boat have a slope of 0 is line BCA because change in y axis is 0

6.The line segments on the boat have an undefined slope is line DFC because change in x axis is 0. When denominator is zero, the fraction is undefined.

7.Given that E is at (−11,4) and D is at (−10,5), the slope of ED will be  

Slope = Δy ÷ Δx

Slope = (5 - 4) ÷ (-10 + 11)

Slope = 1 ÷ 1

Slope = 1

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Answer:

[tex]-\frac{61}{14}[/tex]

Step-by-step explanation:

Question: 5 - 7(z+1) = 7(-9-3z)

We multiply the number in front of the bracket first, since that is multiplication.

--> 5 -7z -7 = -63 - 21z

--> -7z -2 = -63 - 21z

Now, we move all the z and all the numbers to each side.

--> -7z +21z = -63 +2

--> 14z = -61

--> z = -61/14

This cannot be simplified further, so z is -61/14.

Answer: x = 3

Step-by-step explanation:

The equation of the line perpendicular to a horizontal line is a vertical line, which has an equation of the form x=c.

In the context of data models, relationships among records in a hierarchical model are called Branches. This is further explained below.

Generally, The act of generating a visual representation of either a whole information system or portions of it in order to express the linkages between different data points and structures is known as data modeling.

In conclusion, When discussing data models, the connections between different records in a hierarchical structure are referred to as "Branches."

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Answer:

Slope: 2; Y-Intercept: (0,3)

Step-by-step explanation:

As you can see from the graph, it rises 4 and runs 2. So, the slope is 2. It intersects the y axis at (0,3)

Answer:

Slope: 3/2

Y-intercept: 3

Step-by-step explanation:

The line passes the y-axis at 3, and to find the slope you use rise over run. Our rise (which is going up) is 3, and our run (which is going across) is 2 (and since it moves from left to right, it is positive). The slope would be 3/2.

I hope it helps! Have a great day!  

bren~

Answer:

Step-by-step explanation:

You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?