Analyze the diagram below and complete the instructions that follow. Solve triangle EFD.

Answer:

1. 9 inches, 12 inches and 15 inches

2. 54 square inches

Step-by-step explanation:

1. The first part of this question would lead to a quadratic equation. Let the shorter leg be represented by x.

shorter leg = x

other leg = x + 3

hypotenuse = 15 inches

Applying the Pythagoras theorem, we have;

[tex]/15/^{2}[/tex] = [tex]/x/^{2}[/tex] + [tex]/x+3/^{2}[/tex]

225 = [tex]x^{2}[/tex] + [tex](x+3)^{2}[/tex]

225 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 6x + 9

       = 2[tex]x^{2}[/tex] + 6x + 9

2[tex]x^{2}[/tex] + 6x + 9 - 225 = 0

2[tex]x^{2}[/tex] + 6x - 216 = 0

divide through by 2 to have

[tex]x^{2}[/tex] + 3x - 108 = 0

From the quadratic formula;

x = (-b ± [tex]\sqrt{b^{2}-4ac }[/tex] ) ÷ 2a

but, a = 1, b = 3, c = -108

x = (-3 ± [tex]\sqrt{(3)^{2}-4(1)(-108)}[/tex]) ÷ 2

  = (-3 ± [tex]\sqrt{441}[/tex]) ÷ 2

= (-3 ± 21) ÷ 2

Thus,

x = (-3 + 21) ÷ 2 OR x = (-3 - 21) ÷ 2

x = 9 OR x = -12

So that, x = 9 inches

The shorter leg is 9 inches, and the other leg is 12 inches.

2. The area of the triangle can be determined by applying Heron's formula:

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is the average value of the sum of the three sides a, b, and c.

Let, a = 9, b = 12 and c = 15

s = [tex]\frac{a +b+c}{2}[/tex]

  = [tex]\frac{(9+12+15}{2}[/tex]

  = 18

A = [tex]\sqrt{18(18-9)(18-12)(18-15)}[/tex]

   = [tex]\sqrt{18*9*6*3}[/tex]

   = [tex]\sqrt{2916}[/tex]

A = 54

Area of the triangle is 54 square inches.

Answer:

g≥5

Step-by-step explanation:

Answer:

8 and 5

Step-by-step explanation:

8 - 5 = 3

8 + 5 = 13

Answer:

8 and 5

Step-by-step explanation:

8 - 5 = 3

8 + 5 = 13

Answer:

£1,920

Step-by-step explanation:

12 x 40=480 which is the weekly total

then times that by 4 which is how many weeks in a month

which gives you the total of 1920

Answer:

x=56°

Step-by-step explanation:

62x2=124 and 180-124=56

Answer:

B. x = -1 and x = 3

Step-by-step explanation:

I took the test on USATest Prep :)

I hope this helps!

Answer:

22/7 x d

22/7 x 28 = 88 units

The proportional relation between time and pushups is given by y = ( 1/6 )x

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

Let the number of pushups be y

Let the total time be represented as x

And , when x = 24 , y = 4

So , 4 = k ( 24 )

Divide by 24 on both sides , we get

k = ( 1/6 )

Therefore , the proportionality constant is k = ( 1/6 )

Hence , the equation is y = ( 1/6 )x

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ3

Answer: =187.45848

Step-by-step explanation:

Answer:

No, she isn't correct.

Step-by-step explanation:

If the domain is all the x-values in the relationship, then the domain is all values between -2 and 2. If the range is all the y-values in the relationship, then the domain is all values between -3 and 3. Tatiana got things all mixed up; the x-axis is horizontal and the y-axis is vertical.

Answer:

.05

Step-by-step explanation:

y is increasing by 0.05 as x is increasing by 1.

Answer:

The polynomial that represents the area of a rhombus is [tex]A = 2\cdot P^{2}-8[/tex].

Step-by-step explanation:

The area formula for the rhombus is defined below:

[tex]A = \frac{D\cdot d}{2}[/tex] (1)

Where:

[tex]A[/tex] - Area of the rhombus.

[tex]D[/tex] - Greater diagonal.

[tex]d[/tex] - Lesser diagonal.

If we know that [tex]d = (2\cdot P -4)[/tex] and [tex]D = (2\cdot P + 4)[/tex], then the area formula of the rhombus:

[tex]A = \frac{(2\cdot P - 4)\cdot (2\cdot P +4)}{2}[/tex]

[tex]A = \frac{4\cdot P^{2}-16}{2}[/tex]

[tex]A = 2\cdot P^{2}-8[/tex]

The polynomial that represents the area of a rhombus is [tex]A = 2\cdot P^{2}-8[/tex].

Answer:

10 is to 1

Step-by-step explanation:

First convert both the distances to the same unit. So,3 km = 3 × 1000 m = 3000 m. Thus,the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1.

Answer:

option A

Step-by-step explanation:

wkt 1km=1000m

3km=3000m

3000m:300m = 10:1

thus 3km:300m = 10:1

The answer u should date me <3

I love you I’m ur biggest fan ;)

Answer:

yes 1/8 =5/40 :)

Step-by-step explanation:

Answer: Yes

Step-by-step explanation: 1/8 2/16 3/24 4/32 5/40

1/8 x 5/5 = 5/40

Answer:

£69.75

Step-by-step explanation:

£75.00÷0.07=£5.25

£75.00-£5.25=£69.75

Answer:

80.25

Step-by-step explanation:

The sales tax is 7 percent so we want to add that to the full 100 percent. We then get 107 percent which we can just do by multiplying 75 by 107. Then move the decimal twice to the left and get 80.25

Answer:

294"

Step-by-step explanation:

168*1.75=294

Answer:

294 inches

Step-by-step explanation:

75%of168=126

168+126=294

Answer:

access?

Step-by-step explanation:

Answer:

The line on a graph that runs vertically (up-down) through zero.

It is used as a reference line so you can measure from it.

Step-by-step explanation:

Answer:

B is one of them

also D

Step-by-step explanation:

Answer:542.5

Step-by-step explanation:

Answer:

Scale factor(k) = 1/4, and centered at (5, -5).

Labelled the given figure as A, B and C.

The coordinates of the given triangle ABC are;

A = (-3, 7)

B = (-7, -5)

C = (9, 3)

To find the image of the figure after a dilation with scale factor 1/4 centered at (5, -5).

The rule of dilation with scale factor 1/4 and centered at (5, -5) is given by;

(x, y) \rightarrow (\frac{1}{4}(x-5)+5, \frac{1}{4}(y+5)-5)(x,y)→(

4

1

(x−5)+5,

4

1

(y+5)−5)

or

(x, y) \rightarrow (\frac{1}{4}x+\frac{15}{4}, \frac{1}{4}y-\frac{15}{4} )(x,y)→(

4

1

x+

4

15

,

4

1

y−

4

15

)

The coordinates of the image of the figure after dilation are;

A(-3, 7) \rightarrow A'(\frac{1}{4}(-3)+\frac{15}{4}, \frac{1}{4}(7)-\frac{15}{4} )A(−3,7)→A

′

(

4

1

(−3)+

4

15

,

4

1

(7)−

4

15

)

A(-3, 7) \rightarrow A'(3, -2)A(−3,7)→A

′

(3,−2)

B(-7, -5) \rightarrow B'(\frac{1}{4}(-7)+\frac{15}{4}, \frac{1}{4}(-5)-\frac{15}{4} )B(−7,−5)→B

′

(

4

1

(−7)+

4

15

,

4

1

(−5)−

4

15

)

B(-7, -5) \rightarrow B'(2, -5)B(−7,−5)→B

′

(2,−5)

and

C(9, 3) \rightarrow C'(\frac{1}{4}(9)+\frac{15}{4}, \frac{1}{4}(3)-\frac{15}{4} )C(9,3)→C

′

(

4

1

(9)+

4

15

,

4

1

(3)−

4

15

)

C(9, 3) \rightarrow C'(6, -3)C(9,3)→C

′

(6,−3)

As, you can see the graph as shown below in the attachment.

Answer: Not sure because you didn't attach a picture of the figure

Step-by-step explanation:

But something I did that worked for me was to multiply the coordinates by the factor (1/4) and it worked a few times to maybe try that!

Answer:

step below and graph

Step-by-step explanation:

y intercept: x=0      y = (-1/18) * 3 * (-3) * (-4) = - 2

y = -1/18 * (x³ - 4x² - 9x +36)    ... leading coefficient: (-1/18 x³)   -1/18

highest degree:( x³)  3

Answer:

24cm??

Step-by-step explanation:

Answer:

The work is on the picture

sorry was not letting write the work here

Step-by-step explanation:

Question attached

Answer:

130

Step-by-step explanation:

Number of students old donors can be calculated from the Pareto chart by adding number of blood donors on the different bars:

Type 0= 50

Type A= 35

Type B =30

Type AB =15

Therefore 50+35+30+15=130 blood donors

Answer:

Stranger things joining with X-MEN?

Step-by-step explanation:

Ok so I can say for sure that the second character is Cyclops (Marvel Character), and the fourth one looks like a cross between a Stranger Things character and the X-Men member Beast.

Answer:

Step-by-step explanation:

We see that the function has positive range and no restriction of domain.

A The range is the set of all real numbers less than 0.

B The domain is the set of all real numbers greater than-4.

C The range is the set of all real numbers greater than 0.

D The domain is the set of all real numbers less than-4.

Answer:

C is the correct answer!!

Step-by-step explanation:

hope this helped!!