Point E is on line segment DF. Given DE=2x, EF=2x-6, and DF=3x+5, determine the numerical length of EF.

Answer:

x = 5

Step-by-step explanation:

Given that y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion

To find k use the condition when y = 25 , x = 4 , then

25 = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

100 = k

y = [tex]\frac{100}{x}[/tex] ← equation of proportion

When y = 20, then

20 = [tex]\frac{100}{x}[/tex] ( multiply both sides by x )

20x = 100 ( divide both sides by 20 )

x = 5

Answer:

825x, X, 36500000x

Evaluate using scientific notation

PLZ let me know if im wrong!!!

Answer:

x=(-9)

Step-by-step explanation:

I'm pretty sure

The probability P(A or B) is equal to 5/10 = 0.5

P(A or B) is the probability that a randomly selected student plays either basketball of soccer.

On the diagram, we can see that there are a total of 10 students, such that 2 play only basketball and 3 play only soccer.

P(A or B) is equal to the quotient between the number of students that play one of the sports (here we don't count the ones that play both sports) and the total number of students.

Then we have:

P(A or B) = (2 + 3)/10 = 0.5

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Answer:

I think that it is 2

Step-by-step explanation:

I took the test.

Answer:

2

Step-by-step explanation:

Answer:

[tex]m =\frac{5}{3} \\\\m = 1\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-\left(-3\right)}{4-1}\\\\m = \frac{2+3}{4-1}\\ \\m =\frac{5}{3} \\\\m = 1\frac{2}{3}[/tex]

Answer:

The original cost of the butter cup was $91.

Step-by-step explanation:

Let x be the original price of the kitten butter cup.

Since Susan pays five out of seven of the original cos plus a fee of $24, the total amount she paid is 5x/7 + 24.

Now, this total amount equal the $89 she paid for the kitten butter cup. So,

5x/7 + 24 = 89.

We now solve this equation to find the original cost of the kitten butter cup.

So,

5x/7 + 24 = 89

Collecting like terms, we have

5x/7 = 89 - 24

5x/7 = 65

multiplying both sides by 7, we have

5x = 65 × 7

dividing both sides by 5, we have

x = 65 × 7 ÷ 5

x = 91

So the original cost of the butter cup was $91.

Answer:

x = 17 :)

Step-by-step explanation:

90-73=17

Answer:

17 degrees

Step-by-step explanation:

90 degree angle so 90-73=17

Answer:

6%

Step-by-step explanation:

Since the volume of the cylinder V = πr²h where r = radius of cylinder and h = height of cylinder and h = 2r, we have that r = h/2.

Substituting r into v, we have

V = πr²h

V = π(h/2)²h

V = πh³/4

Now let ΔV be the error in the volume and Δh be the error in the height.

Since h is raised to the power of 3,

ΔV/V = 3Δh/h

multiplying both sides by 100, we have

ΔV/V × 100 = 3Δh/h × 100

So, we have

ΔV/V × 100 = 3 × Δh/h × 100

since Δh/h × 100 = percentage error in height = 2%, and ΔV/V × 100 = percentage error in volume,

ΔV/V × 100 = 3 × 2% = 6%

So, the percentage error in volume is 6 %

Answer:

2

Step-by-step explanation

Rate of change is the slope, [tex]\frac{Y}{X}[/tex]

The distance from our y values which are -1 and 5 is 6.

The distance from our x values which 4 and 7 is 3.

Since its [tex]\frac{Y}{X}[/tex] The 6 would be over the 3 as 6/3 which simplifies to 2 or 2/1.

Answer:

Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?

A:

Perimeter = 2(L + W) 9 = 2(L+W) L+W = 4.5 L = 4.5-W Area = LW Area = (4.5-W)W A = 4.5W - W^2 You have a quadratic with a = -1 and b = 4.5 Maximum area occurs when W = -b/(2a) = 4.5/(2*-1) = 2.25  

Step-by-step explanation:

Dimension of the picture with 9ft strip of wood is

length = 2.25 ft  and width =2.25 ft

Given :

you want to frame a collage of picture with a 9ft strip of wood.

the perimeter of the frame is 9 ft

Perimeter of rectangle = 2(length +width )

Let 'l' be the length and 'w' be the width

[tex]Perimeter =2(l+w)\\9=2(l+w)\\Divide \; by \; 2\\l+w=4.5\\l=4.5-w[/tex]

Now we find the area

[tex]Area = length \cdot width \\Area= l \cdot w\\A= (4.5-w)(w)\\A=-w^2+4.5w[/tex]

Now we find out 'w' where area is maximum

[tex]w=-\frac{b}{2a} \\a=-1 and b=4.5\\w=-\frac{4.5}{2(-1)} =2.25[/tex]

Width =2.25 gives us maximum area

Now find out the length ,

[tex]Length = 4.5 -w\\w=2.25\\Length = 4.5-2.25=2.25[/tex]

Dimension of the picture is length = 2.25 ft  and width =2.25 ft

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Answer:

id say d

Step-by-step explanation:

The graph of the linear function y = 7.50x has a slope of 7.50 and a y-intercept is 0

The equation is given as:

y = 7.50x

The above equation is a linear equation

A linear equation is represented by y = mx + c

Where m represents the slope and c represents the y-intercept

By comparison, we have:

The slope is 7.50 and the y-intercept is 0

See attachment for the graph of y = 7.50x

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Answer:

a) The Metra will go 90 miles in 6 hours

b) It will take Amtrak 8 hours to travel 160 miles.

Step-by-step explanation:

From the question,

Metra travels 30 miles in 2 hours

a) To determine how far the Metra will go in 6 hours,

Let how far the Metra will go in 6 hours be x

Then,

If Metra goes 30 miles in 2 hours

Then, Metra will go x miles in 6 hours

x = (30 × 6)/2 miles = 90 miles

Hence, the Metra will go 90 miles in 6 hours.

b) To determine how long it will take Amtrak to travel 160 miles,

Let how long it will take Amtrak to travel 160 miles be y

From the question,

Amtrak travels 80 miles in 4 hours

Now,

If Amtrak travels 80 miles in 4 hours

Then, Amtrak will travel 160 miles in y hours

y = (160 × 4)/80 hours = 8 hours

Hence, it will take Amtrak 8 hours to travel 160 miles.

Answer:

[tex]x° + (3x + 60)° = 180° \: b. \: \boxed{combine \: like \: terms}

\\ 4x° + 60° = 180° c. \: \boxed{additive \: property \: of \: equality}

\\ 4x° = 120° d. \: \boxed{division \: property \: of \: equality}

\\ x° = 30° e. \: \boxed{division \: property \: of \: equality}[/tex]

Step-by-step explanation:

♨Rage♨

Answer:

28.5*40=1140

1140*52=59280

So the librarian makes an earning of $59,280 per year

Answer: $59,280

Step-by-step explanation:

multiply $28.5 by 40 to get how much she makes in a week= $1,140 multiply that by 52 because there are 52 weeks in a year and you get $59,280

Answer:

6x^6 + 9x^5 - 3x^4 + 10x^3 - 42x^2 +20x

Step-by-step explanation:

brainlest?

Answer:

6ft

Step-by-step explanation:

5.94 rounded up is 6

Answer:

6 feet

Step-by-step explanation:

If you round to the nearest foot, then You want to take the number before that one, and if it is above 5, then you can round the foot to the next number

Answer:

34

Step-by-step explanation:

Answer:

the answer is 1/2

Step-by-step explanation:

.79 2/3 1/2 .4

Answer:

5.328

Step-by-step explanation:

Answer:

Graph second down on the left

Step-by-step explanation:

Answer: The perimeter of rectangle M'N'O'P' =54 cm

Step-by-step explanation:

When we dilated a figure , then the image is the similar figure them the original.

For similar figures,

[tex]\dfrac{\text{Area of original figure}}{\text{Area of image}}=\dfrac{(\text{perimeter of original figure})^2}{(\text{perimeter of image})^2}[/tex]

As per given, Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm².

Area of M'N'O'P' =  126 cm²

then,

[tex]\dfrac{14}{126}=\dfrac{18^2}{(\text{(perimeter of M'N'O'P'})^2}\\\\\Rightarrow\ \text{(perimeter of M'N'O'P'})^2=\dfrac{324}{14}\times126\\\\\Rightarrow\ \text{(perimeter of M'N'O'P'})^2=2916\\\\\Rightarrow\ \text{perimeter of M'N'O'P'}=\sqrt{2916}=54[/tex]

Hence, the perimeter of rectangle M'N'O'P' =54 cm

Answer:

$4.99

Step-by-step explanation:

8(3.79)+5y=55.27

30.32 +5y=55.27

5y=24.95

y=4.99

Answer:

y=(x+1)^2-7

Step-by-step explanation:

y=x^2+2x-6=x^2+2x+1-7

y=(x^2+2*1*x+1^2)-7

y=(x+1)^2-7

vertex form equation is y=a(x-h)^2+k

of equation y=ax^2+by+c

so a is 1

h is -1 because (x+1)=(x-(-1))

k is -7

Answer:

33, 35, 37

Step-by-step explanation:

Let the tree consecutive odd integers be x, x +2 and x + 4

According to the given information:

Sum of the first and the third is 70

[tex] \therefore x + x + 4 = 70\\\\

\therefore 2x = 70 - 4\\\\

\therefore 2x = 66\\\\

\therefore x = \frac{66}{2}\\\\

\therefore x = 33\\\\

\implies x + 2 = 33 + 2 = 35\\\\

\& \hspace{25 pt}x + 4 = 33 + 4 = 37\\\\[/tex]

Thus, the three consecutive odd integers are 33, 35 and 37.

Verification: 33 + 37 = 70