What is the perimeter of quadrilateral EFGH?

Step-by-step explanation:

good job then !

the first thing I see in the graphic is that

BG is half of BD (as a major definition of diagonals in a parallelogram).

BD on the other hand is the Hypotenuse (the side opposite of the 90° angle at A) of the triangle ABD.

to be able to use Pythagoras to get BD, I need to find the length of AB.

this I get from the triangle ABE. this is also a right-angled triangle. AE = 4cm. the angle B1 = 50°. the angle A = 90°.

so, the angle E1 = 180 - 90 - 50 = 40° (remember, the sum of all angles in a triangle is always 180°).

now we use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles.

so, we have here

AE / sin(50) = AB / sin(40)

4 / sin(50) = AB / sin(40)

AB = 4×sin(40) / sin(50) = 3.356398525... cm

so (Pythagoras),

BD² = AB² + AD² = 3.356398525...² + 9² =

= 11.26541106... + 81 = 92.26541106...

BD = 9.60548859... cm

BG = BD/2 = 4.802744295... cm

and now look at that.

because of the fact that I did not have to go through the other points, I chose the first approach that went through my mind.

and it showed that your teacher created an impossible (contradicting) scenario :

the angle of B1 does not fit to the ratios of the various line segments.

as you correctly calculated CD as 3 cm, that must mean that AB is also 3 cm.

that makes

BD² = 9² + 3² = 81 + 9 = 90

BD = 9.486832981... cm

BG = BD/2 = 4.74341649... cm

PLEASE, USE THIS VALUE.

there is a difference to my previous calculation. and the reason for this is : the 50° for B1 are not correct.

with AE = 4, AB = 3 and then BE = 5, we get

AE / sin(B1) = BE / sin(A)

4 / sin(B1) = 5 / sin(90) = 5

sin(B1) = 4/5 = 0.8

B1 = 53.13010235...°

and not 50° !!!!

Answer:

The last digit you multiplied by.

Step-by-step explanation:

It's not that hard, but here you go  :)

If you multiplied 12 by 11 you would get 2 as your last digit, because 2 is the last digit of 12. (12x11=132)

So for 123 by 11, following this pattern, 3  is the last digit of 123 so the answer must end in 3. (123x11=1353)

If you still don't get the pattern I'll give you a few more examples here:

If you multiply 1234 by 11 you would get a number ending in 4 because the last digit of 1234 is 4! (1234x11=13574)

So what would be the last digit of 12345?

Hope this was helpful!

(The answer was 5 btw)

Answer:

0.01

Step-by-step explanation:

Nearest hundredth is the second digit after the decimal point.

If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit.

Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:

1.) 3.075 gallons.

To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.

We have that:

Hence the remaining amount is:

15 - 11.925 = 3.075 gallons.

Which means that option 1 is correct.

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Answer: 3.075 gallons

Step-by-step explanation:

Answer:

{(5,1),(5,0),(1,0),(0,-3),(-3,0),(-4,-3),(2,5)}

Step-by-step explanation:

This is all I could get from the cropped out picture of the graph

This problem is related to the formation of a function. We need to know how an function is formed. Here it is given that there is a function which is affected by the value of t. Which means the value of t in  the function decides the value of that function.

Similarly we have to write the function as the variable r so that the value of function is related to the value of r.

h(r)=6-18r ; where 6 is the constant and 18r is the variable in the function.

Hence, the required function is  h(r)=6-18r.

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(A∩B)∪(A∩C) using roster method is as follows:

(A∩B)∪(A∩C)  = {a, e, f}

Sets are an organized collection of objects that can be represented in set-builder form or roster form.

Therefore,

The universal sets is as follows:

U = {a, b, c, d, e, f, g, h}

The subsets are as follows:

A = {c, e, f}

B = {a, e, f}

C = {a, b, d, g, h}

Therefore, let's find (A∩B)∪(A∩C) using roster method.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Hence,

(A∩B) = {e, f}

(A∩C) = {a}

Finally,

(A∩B)∪(A∩C) = {a, e, f}

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Given the length and width, the expression for the perimeter of the rectangle is 10x - 16.

The perimeter of rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Plug the given values in the equation above

Perimeter = 2( l + w )

Perimeter = 2( (3x+ 1) + ( 2x - 9) )

We can go on and simplify.

Perimeter = 2( (3x+ 1) + ( 2x - 9) )

Perimeter = (6x+ 2) + (4x - 18)

Perimeter = 6x+ 2 + 4x - 18

Perimeter = 10x - 16

Given the length and width, the expression for the perimeter of the rectangle is 10x - 16.

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Answer:13

Step-by-step explanation:(2)²+3(3)=4+9=13

Answer:

2a^n+ 3b

Differentiate w.r.t a

2na^n - 1

= 13

[tex](\frac{-4}{5} )[/tex] in the form of Equivalent Fraction can be written as [tex]\frac{-4x}{15x}[/tex], where "x" is any integer.

As per the question statement, we are provided with a fraction, [tex](\frac{-4}{5} )[/tex].

We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.

To solve this question, we need to know what an equivalent fraction is.

Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.

For example, [tex](\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8})[/tex] all equate to [tex]\frac{1}{2}[/tex] when simplified.

Now, for this case, equivalent fractions of [tex](\frac{-4}{5} )[/tex] are [tex](\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...)[/tex], where

[tex]\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}[/tex]

i.e., the equivalent fractions of [tex](\frac{-4}{5} )[/tex] are in the form of  [tex]\frac{-4x}{15x}[/tex], where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)

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Answer:

Minimum z =22 at A =6, B=1

See the graph below variable A is on the horizontal axis and variable B on the vertical axis

Step-by-step explanation:

We can solve using the graphical method

Min z = 3A + 4B

s.t.

1A + 3B ≥ 9

1A + 1B ≥ 7

A, B ≥ 0

Draw two lines using the constraint equations

1A + 3B = 9

1A + 1B = 7

The feasible region for the inequality constraints is the region that satisfies all 4 constraints below

1A + 3B ≥ 9

1A + 1B ≥ 7

A, B ≥ 0

This is the heavily shaded region in the graph. The minimum will be at one of the corner points

There are three corner points on the graph

(0,7), (6,1) and (9,0)

Plug in these coordinate values with A being the first and B being second in the parentheses and see which set of values makes the objective function the minimum

Point (7,0) ==> z = 3(0) + 4(7) = 28

Point (6,1) ==> z = 3(6) + 4(1) = 22

Point (9,0) ==> z = 3(9)+4(0) = 27

Answer: 24

A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant, which is always greater than unity.

the fixed point is called the focus and the fixed line is directrix and the ratio is the eccentricity.

The general equation for the vertical hyperbola is

            [ (y-k)^2 / a^2 ] – [ (x-h)^2 / b^2 ] = 1

The conjugate axis of the vertical hyperbola is y = k

Length of the conjugate axis  = 2b

According to the question k = 2, h = -1, a = 4, b = 12

Length of the conjugate axis = 2b = 2 * 12  = 24

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The angles EFG and GFH are 71 and 109 degrees

The given parameters are:

EFG =2n + 25

GFH = 4n + 17

Linear pair angles are supplementary angles

So,we have

2n + 25 +4n + 17 = 180

Evaluate the like terms

6n= 138

Divide by 6

n = 23

Substitute n = 23 in EFG =2n + 25 and GFH = 4n + 17

EFG = 2 * 23 + 25 =71

GFH = 4 * 23 + 17 = 109

Hence, the angles EFG and GFH are 71 and 109 degrees

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Answer: 30

Step-by-step explanation: just do 6*5, 6 faces for five die is thirty faces

There are 30 faces on 5 dice in total.

Given that a standard die has 6 faces on it, we need to determine the number of the faces on 5 dice.

A standard die has 6 faces. If you have 5 dice, each with 6 faces, you can calculate the total number of faces by multiplying the number of dice by the number of faces on each die:

Total number of faces = Number of dice × Number of faces on each die

Total number of faces = 5 dice × 6 faces/die

Total number of faces = 30 faces

So, there are 30 faces on 5 dice.

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If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].

As per the question statement, we are provided with a mathematical expression in the form of a fraction which goes as [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex].

We are required to calculate an equivalent simplified form of the above mentioned expression.

To solve this question, we simply have to add the fractions in the denominator part and then perform a reciprocal of the overall fraction, and simplify it further in that format only, to obtain our final desired answer. The process is shown below as:

[tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\\=\frac{1}{\frac{(x+3)+(x+2)}{(x+2)(x+3)} } \\=\frac{1}{\frac{(2x+5)}{(x+2)(x+3)} }\\=\frac{(x+2)(x+3)}{(2x+5)} \\=\frac{x^{2}+3x+2x+6 }{2x+5} \\=\frac{x^{2}+5x+6 }{2x+5}[/tex]

Hence, If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].

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Answer:

the slope intercept form is 5y= -x+12

This sequence's explicit formula is [tex]a_n=-5+(n-1)*10[/tex]

What is a sequence?

The common distinction is equal to:

10

The sequence's total is equal to:

40

This sequence's explicit formula is:

[tex]a_n=-5+(n-1)*10[/tex]

This sequence's recursive formula is:

[tex]a_n=a_((n-1))+10[/tex]

Next terms:

-5,5,15,25,35,45,55,65,75,85,95...

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Number of student tickets sold = 84

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

Let the number student tickets sold = x

Let the number adult tickets sold = y

7x+10y = 3888 -----------i

y = 4x-6 ----------------------ii

Substituting eq ii in i

7x + 10 ( 4x -6) = 3888

7x + 40x - 60 = 3888

47x = 3888+60

x = 3948 / 47

     = 84

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Answer:

principle (p)= $200

interest (I) =$9

Rate (R) = 6%

time (T)= ?

we know,

Time(T) = I×100÷P×R

= 9×100÷ 200×6

= 3÷4 years

Answer:

Step-by-step explanation:

First I would begin by dividing both sides by 4

4(x+y) = 48     4/4 = 1      48/4 = 12

x + y = 12

next I'm going to assume this is needed in y = mx+b format so I will solve for y by subtracting the x:

y = -x + 12

this line has a slope of -1 and has a y-intercept at 12.

Answer: 6

Step-by-step explanation: 6 because then he would owe his parents 49 dollars

Julie is correct because:

[tex]\frac{\sin A}{\tan A}=\frac{a/c}{b/c}=a/b=\tan A \\ \\ \frac{\sin B}{\cos B}=\frac{b/c}{a/c}=b/a =\tan B[/tex]

Answer:

The first set is a set of linear equations.

The way to figure this out is pretty easy. If you want to see it visually, go search up desmos graphing calculator and put in these equations.

A linear equation is a function that has a constant slope, meaning that the rate it increases or decreases will never change. The first one is a set of linear equations because it is 2 equations with constant slopes, meaning that the slopes will never change no matter what y and x are.

The second set is not, because while the first equation is linear, the second is an inequality. While it is a straight line, it doesn't count as a linear equation.

The third set, both equations have exponents on the x, which means that the slope will change depending on x. This means that both of these are not linear equations.

The only set that is a linear set is the one that has only linear equations.

thirty-seven billion nine hundred five million

Answer:

hskekndndndokn jskjskiwijsnjskjskiwijsn kkskskskjd kdkdkdndndn

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}[/tex]

let's break it up :

now let's take [tex]{ \sf {3}^{(2n-4)}} [/tex] common here ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 27[/tex]

Answer:

Step-by-step explanation:

[tex]\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}[/tex]

[tex]\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}[/tex]

Simplify:-

[tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}[/tex]

Now, Factor:-

[tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}[/tex]

Now, let's simplify:-

Simplify:-

Apply the exponent rule:-

Therefore, your answer is 27.

______________________

Hope this helps!

Have a great day!

Answer:

10°C

Step-by-step explanation:

c = [tex]\frac{F - 32}{1.8}[/tex]  Plug in 50 for F and solve for C

c = [tex]\frac{50-32}{1.8}[/tex]

C = [tex]\frac{18}{1.8}[/tex] Divide

c = 10

Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality

The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.

Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.

Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality

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After solving the inequality we get the value of x as x ∈ (₋5,3)

Given the inequality is 2 |x + 1|  < 8

Divide both sides of the inequality by the coefficient of variable.

|x + 1| < 8/2

Reduce the fraction

|x + 1| < 4

Now convert the absolute inequality to standard inequality.

₋4 < x₊1 < 4

separate compound inequalities into system of inequalities.

x ₊ 1 > ₋4  (1)

x ₊ 1 < 4 (2)

for (1) x ₊ 1 > ₋4

rearrange variables to the left side of the equation.

x > ₋4 ₋1

calculate the sum.

x > ₋5

for (2) x ₊ 1 < 4  (2)

rearrange the terms.

x < 4 ₋ 1

x < 3

therefore ₋5 < x < 3

Hence we get the value ranging from (₋5 , 3)

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