A farmer needs to enclose a section of land in the shape of a parallelogram by using one side of a barn for one side. The barn and the side opposite of the barn will both be 10 feet long. One of the other sides will be 6 feet long. What is the length of the last side?

Answers

Answer 1

Answer:

Answer: 6 feet

Step-by-step explanation:

Given: A farmer needs to enclose a section of land in the shape of a parallelogram by using one side of a barn for one side.

We know that in parallelogram opposite sides are equal.

Since, it is given that the barn and the side opposite of the barn will both be 10 feet long.

Therefore, if one of the other sides will be 6 feet long.

Then, the length of the last side must be 6 feet long because it is opposite to the 6 feet long side.

Answer 2

Answer: The other sides length is 6 feet

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In parallelogram ABCD, E is the midpoint of AB and F is the midpoint of DC . Let G be the intersection of the diagonal DB and the line segment EF . Prove that G is the midpoint of EF.

Answers

The midpoint of the line $\overline{EF}$ is the point that divides $\overline{EF}$ in two halves of the same length.

ΔDFG ≅ ΔBGE and $\overline{FG}$ ≅ $\overline{EG}$ by CPCTC, therefore, Gis the midpoint of $\overline{EF}$

Reasons:

The given parameters are;

The midpoint of AB in parallelogram ABCD = E

The midpoint of DC = F

Point of intersection of EF and DB = Point G

Required:

To prove that point G is the midpoint of EF.

Solution:

Statement ${}$ Reason

1. m∠BDC ≅ m∠ABD ${}$ 1. Alternate angles theorem

2. m∠DGF ≅ m∠BGE ${}$ 2.Vertical angles theorem

3. $\overline{DC}$ = $\overline {AB}$ ${}$ 3. Opposite sides of a parallelogram ABCD

4. $\overline{CF}$ ≅ $\overline{DF}$ ${}$ 4. Definition of midpoint of DC

5. $\overline{CF}$ = $\mathbf{\overline{DF}}$ ${}$ 5. Definition of congruency

6. $\overline{CF}$ + $\overline{DF}$ = DC ${}$ 6. Segment addition property

7. $\overline{CF}$ + $\overline{CF}$ = DC ${}$ 7. Substitution property

8. 2· $\overline{CF}$ = DC ${}$ 8. Addition

9. $\overline{CF}$ = 0.5· $\overline{DC}$ = $\overline{DF}$ ${}$ 9. Division property

Similarly;

10. $\overline{AE}$ = 0.5· $\overline{AB}$ = $\overline{EB}$ ${}$ 10. Division property

11. 0.5· $\overline{DC}$ = 0.5· $\overline{AB}$ ${}$ 11. Multiplication property of equality

12. $\overline{AE}$ = $\overline{EB}$ ${}$ 12. Substitution property

13. ΔDFG ≅ ΔBGE ${}$ 13. Angle-Angle-Side rule of congruency

14. $\overline{FG}$ ≅ $\overline{EG}$ ${}$ 14. CPCTC ${}$

15. $\overline{FG}$ = $\overline{EG}$ ${}$ 15. Definition of congruency

16. Point G is the midpoint of $\overline{EF}$ ${}$ 17. Definition of midpoint

Learn more about the midpoint of a line here:

brainly.com/question/5127222

Answer:

GF = GE that prove G is the mid-point of EF

Step-by-step explanation:

In the Parallelogram ABCD

∵E is the mid-point of AB

∵F is the mid-point of CD

∵AB = CD opposite sides in the parallelogram

∴EB = DF⇒(1)

∵AB // CD opposite sides in the parallelogram

∴m∠EBD = m∠FDB alternate angles ⇒(2)

∵BD intersects EF at G

∴m∠BGE = m∠DGF vertically opposite angles ⇒(3)

By using (1) , (2) and (3) you can prove:

ΔBGE is congruent to ΔDGF ⇒ AAS

∴GF = GE

∴G is the mid-point of EF

The volume of a solid right pyramid with a square base is v units3 and the length of the base edge is y units. which expression represents the height of the pyramid? units (3v – y2) units (v – 3y2) units units

Answers

we know that

The volume of a solid right pyramid with a square base is equal to

$V=(1)/(3)*[ area\ of\ the\ base]*height$

area of the base is the area of a square

$area\ of\ the\ base=y^(2)\ units^(2)\nV=v\ units^(3)$

Substitute the values in the formula of volume

$v=(1)/(3)*[ y^(2)]*height$

solve for the height

$v=(1)/(3)*[ y^(2)]*height\n \nheight=(3v)/(y^(2))\ units$

therefore

the answer is

$height=(3v)/(y^(2))\ units$

3v/y² units

Further explanation

Given:

The volume of a solid right pyramid with a square base is v units³
The length of the base edge is y units.

Question:

Which an expression represents the height of the pyramid?

The Process:

We will solve the problem of a geometric solid.

Let us recall the formula of volume of a right pyramid:

$\boxed{ \ V = (1)/(3) * base \ area * height \ }$

Because the base is square, we use the formula for square area, i.e., side times side.

Let us find out the height of the pyramid.

$\boxed{ \ Height = (3v)/(y * y) \ }$

Thus, an expression represents the height of the pyramid is $\boxed{\boxed{ \ (3v)/(y^2) \ }}$ units

Learn more

What is the volume of each prism? brainly.com/question/414021
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Keywords: the volume of a solid right pyramid, a square, the length of the base edge, an expression, represent, the height, the formula, a geometric solid, units

If Jennifer made a fruit juice using red and green grapes. Thirty percent of the grapes are green.If she used a total of 60 grapes , how many red grapes should she use?

Answers

$p\%=(p)/(100)\n\n30\%=(30)/(100)=0.30=0.3\n\n30\%\ of\ 60=0.3\cdot60=18\leftarrow\ number\ of\ green\ grapes\n\n60-18=\boxed{42}\leftarrow ANSWER$

Which phrase matches the algebraic expression below? (1 point) 3(x − 7) + 10 Three times the sum of x and seven plus ten Three times x minus seven plus ten Three times x minus the sum of seven and ten Three times the difference of x and seven plus ten

Answers

Answer:Three times the difference of x and seven plus ten

Step-by-step explanation:

James needs 50 tons of dirt for a large construction project. He already has 3 tons of dirt at the construction site. Each dump truck can transport 8 tons of dirt. How many trips does the dump truck need to take to reach 50 tons of dirt?A.
5
B.
6
C.
7
D.
8

Answers

If he already has 3 tons of dirt at the site, He needs 50-3=47 tons to be carried by the truck
Minimum number of trips the truck will need to take=47/8
=5.875
But since the truck cannot actually take 5.875 trips, it will take the next whole number of trips so it will take 6 trips.(B)

The value of a boat, in dollars, x years after its purchase is represented by the function.f(x)=10,000(0.73)^x

What is the average decrease in value per year between years 1 and 2?

Answers

Given the function f(x) = 10000(0.73)^x

Where y is The value of a boat, in dollars, x years after its purchase
at x = 1
f(1) = 10000(0.73)^1
f(1) = $7300
at x = 2
f(2) = 10000(0.73)^2
f(2) = $ 5329
so the decrease
D = $7300 - $ 5329
D = $ 1971

Answer:

The correct answer is $1971.

I just took the test and got it right.

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