calculate the area of this trapezium

In the given ΔDEF x is 17 units and y is 2 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, GH is the midpoint of ΔDEF and EF is the base of the ΔDEF with a length of 28 units.

We know the midpoint of ΔDEF is (1/2) EF.

∴ GH = (28/2) = 14 units.

Now GH = x - 3.

14 = x - 3.

x = 17.

Given DH and FH are equal.

∴ y + 8 = x - 7.

y + 8 = 17 - 7.

y + 8 = 10.

y = 2.

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Answer:

I got (-1,-4) and (3,0) When I graphed with Desmos.  I do no see that solution.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the median is a segment that goes from the vertex of a triangle to the midpoint of the opposite side.

Then Q is the midpoint of PR

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

use this formula to find the coordinates of Q

with (x₁, y₁ ) = R (0, 2b ) and (x₂, y₂ ) = P (2a, 0 )

Q = ( [tex]\frac{0+2a}{2}[/tex] , [tex]\frac{2b+0}{2}[/tex] ) = ( [tex]\frac{2a}{2}[/tex] , [tex]\frac{2b}{2}[/tex] ) = (a, b )

---------------------------------------------------

use the distance formula to find the lengths of median MQ and hypotenuse PR of Δ MRP

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = M (0, 0 ) and (x₂, y₂ ) = Q (a, b )

MQ = [tex]\sqrt{(a-0)^2+(b-0)^2}[/tex] = [tex]\sqrt{a^2+b^2}[/tex]

repeat with (x₁, y₁ ) = P (2a, 0 ) and (x₂, y₂ ) = R (0, 2b )

PR = [tex]\sqrt{(0-2a)^2+(2b-0)^2}[/tex]

     = [tex]\sqrt{(-2a)^2+(2b)^2}[/tex]

     = [tex]\sqrt{4a^2+4b^2}[/tex]

     = [tex]\sqrt{4(a^2+b^2)}[/tex]

     = 2[tex]\sqrt{a^2+b^2}[/tex]

then MQ is half PR

Simplification of the given expression ( a + b ) / ( a - b ) for the given values of a and b is equal to ( 4 / 1 ).

As given in the question,

Given expression:

( a + b ) / ( a - b )

Simplification of the given expression ( a + b ) / ( a - b ) for the value

a = 5 and b = 3 is given by,

( a + b ) / ( a - b ) we get,

( a + b ) / ( a - b )

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

= ( 8 ) / ( 2 )

= ( 4 × 2 ) / ( 2 )

= ( 4 / 1 )

Therefore, simplification of the given expression ( a + b ) / ( a - b ) for the given values of a and b is equal to ( 4 / 1 ).

The complete question is:

Simplify the given expression:

(a + b)/ (a -b) = ?

For a=5 and b=3

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The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.

The expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given will be illustrated as:

1/6x + 24 = -6

Collect like terms

x / 6 = -6 - 24

x/6 = -30

Cross multiply

x = -30 × 6

x = -180

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Answer:

9

Step-by-step explanation:

5 - 4 + 7 + 1 = 9/1 = 9

Answer:
30-2=28+542=570

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

if we x and y = 0

if we have 3x + 3y= 0

Check the picture below.

so in the parallelogram, the two triangles split by the side AC are congruents as you can see there by AAS, that means their sides and angles are congruent, that also includes the exterior angles.

since the exterior angles are also congruent, we can extend lines BC and AD as you see there in green and run an exterior angle at vertices A and C, since those two exterior angles are congruent and are also alternate interior ones, voila! it must be that BC || AD.

[tex]{ \purple{ \tt{x = 3}}}[/tex]

[tex]{ \blue{ \sf{ {6}^{2} - x - 12 = 0}}}[/tex]

[tex]{ \blue{ \sf{36 - x - 12 = 0}}}[/tex]

Take 12 as common

[tex]{ \blue{ \sf{ \cancel{12}(3 - x) { \cancel{-12} = 0}}}}[/tex]

[tex]{ \blue{ \sf{3 - x = 0}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \tt \overbrace{ \underbrace{x = 3}}}}}}[/tex]

Answer:

Step-by-step explanation: 9091.6

Answer:

9091.6

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5 + 2 = 7

7(3) = 21

_

5 + 16 = 21

The coordinates of the vertices of the points A and B are;

A(9, 7), B(15, 9)

A point on the coordinate plane is described by a pair of points known as an ordered pair.

The coordinates of the vertices of the identical rectangles are; (3, 5), (9, 5), (9, 9)

The length of (9 5) from A is the same as the length from (9, 9) to A.

The coordinate of the point A is therefore;

x-coordinate = 9

y-coordinate = 5 + (9 - 5)/2 = 7

The coordinate of point A is (9, 7)

The length of the sides of the rectangle are;

Length = 9 - 3 = 6

Width = 9 - 7 = 2

The coordinates of the point B are;

x-coordinate = 9 + 6 = 15

y-coordinate = 9

The coordinates of the point B is (15, 9)

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Answer: The answer is 10

Step-by-step explanation:

The number of gallons of gas which Mrs. Josey and her family would need is; 17.5 gallons of gas.

It follows from the task content that the quantity of gas in gallons needed by Mrs. Josey and her family to make it to Dallas is to be determined.

Therefore, since one gallon of gas is enough for 20 miles, It follows that the amount of gas required for 350 miles can be determined by proportion as follows;

20/1 = 350/x

x = 350 / 20

x = 17.5 gallons of gas.

Ultimately, the amount of gas needed for Mrs. Josey and her family to make it to Dallas is; 17.5 gallons of gas.

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The compound inequality is $176.40 ≤ t ≤ $352.80 if a construction worker earns an average bi-weekly net pay of $1,764.00 option (A) Is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

A construction worker earns an average bi-weekly net pay of $1,764.00.

= 10% of 1764

= (10/100)1764

= $176.4

= 20% of 1764

= (20/100)1764

= $352.8

Inequality will be: $176.40 ≤ t ≤ $352.80

Thus, the compound inequality is $176.40 ≤ t ≤ $352.80 if a construction worker earns an average bi-weekly net pay of $1,764.00 option (A) Is correct.

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Answer:

$382.20 ≤ t ≤ $764.40

Step-by-step explanation:

Hello, so first we would need to convert bi-weekly pay to monthly income.

First we would times $1,764.00 by 26

1764.00 × 26 = 45864

Then we would divide 45864 by 12

45864 ÷ 12 = 3822.

Then we calculate how much the worker can spend  if their monthly budget for food is in between 10% and 20%

3822 ×  10% = 382.20

3822 × 20% = 764.40

So, we can see the correct answer is $382.20 ≤ t ≤ $764.40.

Answer:2

Step-by-step explanation: I don’t have a explanation

Answer: 2

Step-by-step explanation:

You should be able to do this...

The sinusoidal equation for the graph in terms of Y, the temperature in degrees Celsius) and the time, T in hours is; Y = 3·sin((π/12)·(T + 6)) + 15

A sinusoidal equation or function is an oscillating and periodic function that is based on the sine of an angle.

The function of the graph is a sinusoidal function with the parts;

a = The amplitude

b = The frequency = 1/T

T = The period of the function

k = The vertical shift of the function

h = The horizontal shift of the function

From the graph, we have;

The minimum  point on the graph of the function = (1, 12)

The maximum point on the graph of the function = (13, 18)

The amplitude of the graph a is therefore; a = (18 - 12)÷2 = 3

The period of the graph = 1/b

1 cycle is completed in 24 hours, which indicates that the frequency of the function is; f = 2·π/24 = π/12 = b

The vertical shift, k from the parent function, y = sin(x) which is the distance the midline of the graph is raised above the x-axis is; k = 15

sin((π/12)·(0 - h)) = -1

((π/12)·(0 - h)) = -π/2

-h = 6

h = -6

The function, y = a·sin(b·(t - h)) + k, is therefore;

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Answer:

Step-by-step explanation:

300 grams-24 hour= 276 so i think u just need to keep doing this till it gets to 206.4

The equation which represents the number of hours will be ln(206.4) = 1200ln(0.014).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a candle weighs 300 grams (g). Each hour the candle is lit, it burns 4 g of its wax. a. Leth be the number of hours the candle burns.

The equation for the number of hours will be calculated as,
[tex]h=300\times (0.014)^h[/tex]

lnh= 300 x ln(0.014)

Therefore, the equation which represents the number of hours will be ln(206.4) = 1200ln(0.014).

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Answer: .01 fluid ounces.

Step-by-step explanation:

1,000 drops is 1 FL

100 drops is .1 FL

10 drops is .01 FL

The population variance of the given data is 3.2.

Given  Σ(x - 38)² = 64 .

We know that the population variance of the data is the square of the standard deviation.

Now the standard deviation for the population is given by

σ =√(Σ(x - 38)² / N)

Again variance = σ ²

Let us first calculate σ .

σ = √(64/20) = √3.2

variance

= σ ²

= (√3.2)²

= 3.2

Therefore the variance of the population is 3.2

In probability theory and statistics, variance is the predicted squared variation of a random variable from its population mean or sample mean. Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance.

A few ideas that use variance include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.

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Answer:0.0013

Step-by-step explanation:

Answer: the answer is on  the calclulator

Step-by-step explanation:

Answer:

Slope intercept form is achieved by isolating y to one side. 3x-6y=18: given. -6y=-3x+18: algebra. y=3/6x-3: simplifying.

Answer:

a = 30

Step-by-step explanation:

I am not exactly sure what the question is asking but if referring to right triangles, the Pythagorean theorem would work best.

Formula :

[tex]a^2 + b^2 = c^2\\\\[/tex]

Substitute values :

[tex]a^2 + 40^2 = 50^2\\a^2 + 1600 = 2500[/tex]

Solve for a:

[tex]a = \sqrt{2500 - 1600} \\a = 30[/tex]

** you could also use the 3:4:5 ratio

Answer:

  3 g

Step-by-step explanation:

You want to know the mass of thyme that must be added to 12 g of a spice mix that is 25% thyme in order to make it 40% thyme.

Let t represent the amount of added thyme (in grams). The amount of thyme in the augmented mix is ...

  0.25(12) + t = 0.40(12 +t)

Simplifying the equation gives ...

  3 +t = 4.8 +0.40t

  0.6t = 1.8 . . . . . . . . . subtract 0.40t +3

  t = 3 . . . . . . . . . . . divide by 0.6

3 grams of thyme must be added to the mix.

The key features of the exponential function modeled in terms of this situation and how can they be interpreted are;

1) The y-intercept is 15,000.

2) The y-intercept represents the number of bacteria when treatment began.

3) The asymptote indicates that as time increases, the number of bacteria approaches 0.

The general formula for an exponential function is;

y = aˣ

Now, an asymptote of a curve is defined as a line that exists in a way that the distance that exists between the curve and the line approaches zero as either one or both of the x or y coordinates approaches to infinity.

From the given graph, we can say that the y-intercept which is where the curve intersects the y-axis is 15,000 and this indicates the number of bacteria that existed prior to treatment.

The asymptote of the graph would likely be around x = 1 and it indicates that as time increases, the number of bacteria approaches 0.

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(i) The value of x is equal to 30 and the equation has one solution and it is neither identity nor contradiction.

(ii) This equation has infinite number of solutions and it is an identity.

(iii) This equation has no solutions and it is a contradiction.

What is identity and contradiction?

An identity is an equation that can be solved using any integer that can replace the variable in the equation in a meaningful way. A conditional equation is one that is met by some numbers but not by others, such as 2x = 4. A contradiction is an equation, such as x = x + 1, that cannot be solved.

We know that,

An equation having infinitely many solutions is called an identity equation.

An equation that having no solution is called a contradiction.

(i) 6x + 4x - 6 + 24 + 9x

Combining like terms

x = 30

Therefore, The value of x is equal to 30 and the equation has one solution and it is neither identity nor contradiction.

(ii) 25 - 4x = 15 - 3x +10 - x

Combining like terms

0 = 0

It means, The equation is true for all values of x.

Therefore, This equation has infinite number of solutions and it is an identity.

(iii) 4x + 8 = 2x + 7 + 2x - 20

Combining like terms

8 = -13

It means, The equation is not true for any value of x.

Therefore,  This equation has no solutions and it is a contradiction.

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Answer: PEMDAS

Parenthesis exponents multiplication Division addition subtraction

Step-by-step explanation:

solve (x+1) first then after just follow pemdas