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2 years ago

Complete the two-column proof. Given: ∠2 and ∠5 are supplementary Prove: l is parallel to m Need help quick

Mathematics

1 answer:

MakcuM [25]2 years ago

5 0

1) Statement: Angle 2 and angle 5 are supplementary

Reason: Given

2) Statement : Angle 2 and angle 3 are congruent.

Reason: Vertically Opposite Angles are always congruent.

3) Statement: If angle 2 is congruent to angle 3 and and angle 2 is supplementary to angle 5, then angle 3 is supplementary to angle 5.

Reason: Substitution Property

4) Statement: Line l is parallel to line m.

Reason: Converse of the the Same-Side Interior Angles Theorem (If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel.)

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You have a square flower garden that has an area of 400 square yards. What is the length of one side of the garden?

emmasim [6.3K]

Answer:

20 yards

Step-by-step explanation:

The area of a square is calculated by multiplying its height by its base. Because they are the same in a square, the area of a square is obtained by squaring one of its sides. Let's call the sides 'x'. Then we can express the area of the garden as x^2=400.

From here we simply need to square root both sides which gives us:

x=20

Therefore the length of one side of the garden is 20 yards.

Hope this helped!

7 0

2 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

You pack sandwiches for a mountain hike with your friends. Each sandwich takes 222 slices of bread, and each hiker eats one sand

Goryan [66]

Answer:

This question contains some errors; the correct question is:

You pack sandwiches for a mountain hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich. How many slices of bread are used for n hikers? Write your answer as an expression.

The answer is:

(2n) slices of bread for n hikers

Step-by-step explanation:

According to the question, sandwiches packed for a mountain hike with friends is made of two (2) slices of bread.

Each hiker gets one sandwich

This, n hikers will get n× 1 sandwich

= (n) sandwiches.

If 1 sandwich contains 2 slices of bread, then (n) sandwiches for n hikers will contain:

(2 × n) slices of bread

That is, (2n) slices of bread.

The expression is (2n).

4 0

2 years ago

The amounts of vitamin C (in milligrams) for 100g (3.57 ounces) of various randomly selected fruits and vegetables are listed. I

34kurt

Answer:

H0: sigma=12

H1:sigma≠12

This hypothesis test is a two tailed test.

Step-by-step explanation:

The null value described in the statement is 12 mg. So, the null hypothesis would be sigma=12. As the statement states that whether there is sufficient evidence to conclude that standard deviation differs from 12 mg, so the alternative hypothesis would be sigma ≠12. The alternative hypothesis contains inequality sign so, the hypothesis test is a two tailed test.

4 0

2 years ago

Rina is 6x+3/8 feet tall and Ryan is 5x+1/8 feet tall. How much taller is Rina than Ryan

worty [1.4K]

Answer:

Rina is 1/4 feet taller than Ryan

Step-by-step explanation:

(height of Rina)-(height of Ryan)

6x+3/8-(5x+1/8)

6x+3/8-5x-1/8

x+3-1/8

x+2/8

x+1/4

8 0

2 years ago