In the diagram, the ratio of AB to AE is 1/2. What is the ratio of the length of DB to the length of CE?

Given:

In triangle ABC, [tex]AB=11x-25,DE=4x+1[/tex].

To find:

The measure of DE.

Solution:

From the given figure, it is clear that D is the midpoint of AC and E is the midpoint of BC. So, the line segment DE is the mid-segment of the triangle ABC.

According to the triangle mid-segment theorem, mid-segment of a triangle is equal to half of its base.

Using triangle mid-segment theorem, we get

[tex]DE=\dfrac{1}{2}AB[/tex]

[tex](4x+1)=\dfrac{1}{2}(11x-25)[/tex]

[tex]2(4x+1)=11x-25[/tex]

[tex]8x+2=11x-25[/tex]

Isolate the variable terms.

[tex]8x-11x=-2-25[/tex]

[tex]-3x=-27[/tex]

[tex]x=\dfrac{-27}{-3}[/tex]

[tex]x=9[/tex]

The value of x is 9. So,

[tex]DE=4x+1[/tex]

[tex]DE=4(9)+1[/tex]

[tex]DE=36+1[/tex]

[tex]DE=36+1[/tex]

[tex]DE=37[/tex]

Therefore, the length of DE is 37 units.

Answer:

1 ten and 5 ones

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

3(x-4)=2(-2x+1)

3x-12=-4x+2

3x-(-4x)-12=2

3x+4x=2+12

7x=14

x=14/7

x=2

Answer:

100 students

Step-by-step explanation:

10% of students in 7th grade ----- 10 students

Divide by 10 on both sides:

1% of students in 7th grade ----- 10 ÷10= 1 student

×100 on both sides:

100% of students in 7th grade ----- 1 ×100= 100 students

Answer:100

Step-by-step explanation:

Answer:

its 55

Step-by-step explanation:

Answer:

Formula: SA= 2B+Ph

This might not be an exact answer but it makes it easier

Answer:

76.5

Step-by-step explanation:

if the area is 76.5^2, then all you have to do is take the square root, and it is 76.5

Answer:

225

Step-by-step explanation:

Clockwise turn:

Southeast to South = 45

South to North = 180

Southeast to North = 180 + 45 = 225

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Angles.

The direction angle is :-

180° for South to North + 45° for South East to South

so total change in phase is ==> 180°+45° ==> 225°

hence, C.) option is correct

Answer:

x=60, y=30

Step-by-step explanation:

4x-7y=30

4x-5y=90

Subtract the equations

4x-7y=30-4x-5y=90

=2y=60

Solve 2y=60

Divide both sides by 2

2y/2=60/2

Simplify;

y=30

For 4x-7*30=30 for x

4x-7y*30=30

Multiply the numbers:7*30=210

4x-210=30

Add 210 to both sides

4x-210+210=30+210

Simplify;

4x=240

Divide both sides by 4

4x/4=240/4

Simplify

x=60

The solutions to the system of equations are:

x=60, y=30

Hope this helped!!!

Answer:

37

Step-by-step explanation:

q + q - r (p - q)

-4 + (-4) - 9[-9 - (-4)]

-8 - 9 (-5)

-8 + 45

37

Answer:

12 + 4y is the simplified version of 4(y+3). When you simplify you need to use the distributive property. So, 4 multiplied by y is 4y. 4 multiplied by 3 is 12.  So the answer will be 12 + 4y. Hence, they are equivalent.

Step-by-step explanation:

hope this helps and is right. p.s. i really need brainliest :)

if this is wrong then I am incredibly sorry!

Answer:

20.5g in protein

427.55mg in sodium

Step-by-step explanation:

Add the amount or proteins he ate first for all the food he ate, and then the sodium for the food and there is your answer.

Answer:

80+2x=180°{co-interior angle}

2x=180-80

2x=100

x=50°

hope it helps.

Answer:

There should be about 612 girls

Step-by-step explanation:

350 divided by 4 = 87.5

87.5 x 7 = 612.5

round 612.5 down, which gets 612

Answer:

I believe each person will run 10 and 1/4 miles

Answer:

 ∠BFC = 50

Step-by-step explanation:

∠AFC = 90

∠AFB + ∠BFC = 90

40 + ∠BFC = 90

           ∠BFC = 90 - 40

          ∠BFC = 50

Answer: B-C

Step-by-step explanation:

I believe it is the angle of B-C becuase B-E is a strieght line which equals 180. Also EFD looks the same as AFB so it is 40. And DFC is 90 becuase of the square. So we take 180-40-90=50. And the only one that is not solved is B-C

Answer:

Total amount spend on DVD = $87

Step-by-step explanation:

Given:

Total number of week = 6 week

Number of DVD purchase per week = 2

Cost of reduced price DVD = $5.50

Cost of regular price DVD = $9

Find:

Total amount spend on DVD

Computation:

Total amount spend each week = Cost of 1 reduced price DVD + Cost of 1 regular price DVD

Total amount spend each week = 5.5 + 9

Total amount spend each week = $14.5

Total amount spend on DVD = Total number of week x Total amount spend each week

Total amount spend on DVD = 6 x 14.5

Total amount spend on DVD = $87

Answer:

x = 6√2

Step-by-step explanation:

This is a right triangle, specifically a 45-45-90 one.  Using the Pythagorean Theorem, we get x^2 + x^2 = (12 cm)^2, or:

2x^2 = 144 cm^2, or

x^2 = 72 cm^2.

This comes out to x = 6√2

Answer:

Sorry it doesn't look like you attached any link for this.

Answer:

x = 128°

Step-by-step explanation:

180-83-45 = 52

180 - 52 = 128°

Answer:

(x+6)² + (y-6)² = 181

Step-by-step explanation:

equation of the circle in general is (x - a)² + (y - b)² = r²

center is (a, b) in our task a=-6 b=6

so equation of the circle is (x+6)² + (y-6)² = r²

we have point  (3,-4)​ ⇒ x=3 y=-4

put x y in equation of the circle ⇒  (3+6)² + (-4-6)² = r² ⇒r² =181

⇒The equation of a circle is (x+6)² + (y-6)² = 181

Answer:

x²+ y² - 109 = 0

Step-by-step explanation:

The coordinate of centre of circle = (-6 , 6)

Point through which it passes = (3 , -4)

So , Firstly find the distance between the centre and that point that will be equal to the radius . Using Distance Formula we have ,

⇒ D = √ [ ( x - x' )² + ( y + y')² ]

⇒ D = √ [ (3+6)² + (6+4)² ]

⇒ D = √ [ 9² + 10² ]

⇒ D = √ [ 81 + 100 ]

⇒ D = √ 181

⇒ D = 13.45 .

Now substituting the respective values in the general equation of circle .

⇒ ( x - h)² + (y - k)² = r²

⇒ { x - (-6) }² + { y - (6) }² = (13.45)²

⇒ ( x + 6 )² + ( y - 6)² = 13.45²

⇒ x² + 36 + 12x + y² + 36 -12x = 181

⇒ x² + y² + 72 = 181

⇒ x² + y² + 72 - 181 = 0

⇒ x² + y² - 109 = 0

Answer:1231.5

Step-by-step explanation:

volume of a cylinder = pie x r^2 x h

pie x 14 x 8 = 1231.5

Answer:

Sum of interior angles of a pentagon

Angles H and G are same as the trapezoid is isosceles

Answer:

no correlation

Step-by-step explanation:

because the teeth brushing had nothing to do with their grade, it would be no correlation.

Answer:

21.038 ft

Step-by-step explanation:

6.7x3.14=21.038

hope this helps

plz can  i get brainliest:)

Answer:

if your looking for radius it would be 3.35 if your looking for surface area its 3.14(3.35)^2  

Step-by-step explanation:

Answer:

[tex]\sqrt{80} \\OR \\ 5\sqrt{4}[/tex]

Step-by-step explanation:

pythagorean theorm

and then simplify with a factor tree or leave it as is.

BRAINLIEST PLEASE IF RIGHT