Given: p || q, and r || s.






Prove: ∠1 and ∠14 are supplementary angles.






What is the next step in the proof? Choose the most logical approach.




A.



Statement: ∠6 ≅ ∠14



Reason: For parallel lines cut by a transversal, corresponding angles are congruent.




B.



Statement: ∠6 ≅ ∠7



Reason: Vertical Angles Theorem




C.



Statement: ∠6 and ∠5 are supplementary.



Reason: Linear Pair Theorem




D.



Statement: m∠6 + m∠8 = 180°



Reason: angle addition

Answer:

Step-by-step explanation:

From what I understand about parabolic motion in the English system, the equation for flight is

[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]

where [tex]v_{0}t[/tex] is the initial upwards velocity and

[tex]h_{0}[/tex] is the initial height from which the object was launched.  Filling in that equation with those values gives you

[tex]s(t)=-16t^2+64t+3[/tex].  That's a.

In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function.  The absolute max is the heighest that the ball will go.  Completing the square is the way to solve this.  Begin by setting the equation equal to 0, the moving the 3 over by subtraction:

[tex]-16t^2+64t=-3[/tex]

Now factor out the -16 since the leading coefficient HAS to be a positive 1:

[tex]-16(t^2-4t)=-3[/tex]

Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:

[tex]-16(t^2-4t+4)=-3[/tex]

BUT since you added in a 4*-16 on the left you have to add it in on the right:

[tex]-16t^2(t^2-4t+4)=-3-64[/tex]

which simplifies to

[tex]-16(t-2)^2=-67[/tex]

Now bring the 67 over by addition and you have your vertex:

[tex]s(t)=-16(t-2)^2+67[/tex].

The vertex is (2, 67).  The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.

How long it will be in the air is found by factoring to find the zeros.  These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046

So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at

x = 4.05 seconds.  Which makes sense if you know anything about parabolic motion and physics.  The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark.  Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds.  And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters).  Sorry it's so long, but it's not a question that can be answered with just a few sentences.

Answer:

Step-by-step explanation:

m = megs age

v = vectors age

meg is 2 years older than vector   + 2

therefore

m = v +2

So if we have the number after the 36% increase in population, we would want to subtract that 36% from 51000.

36% of 51000 can be found by multiplying 51000 by 0.36 (0.36 is the decimal equivalent of 36%)

51000 x .36 = 18360

So you simply subtract 18360 from 51000, which is 32,640.

Answer:

  True

Step-by-step explanation:

The first power of the variable is what makes it a linear term.

Cosidering the ray BC.

It is clear that:

1) A ray starts from one point and extends infinitely in ONE direction.

2) The ray BC cannot be measured. But the line-segment BC can be Measured.

3) B and C are the only two points on the given ray.

Hence the statement: "There are only two points on the entire ray" is the correct one.

Hope it helps...

Regards;

Leukonov/Olegion.

The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered so options (A), and (D) are true.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given,

A ray is passing through points B and C.

(A) The ray extends infinitely in one direction which is True.

(D) There are only two points on the entire ray which is also true.

Hence, The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered.

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Final answer:

This question pertains to calculating the volume of a triangular pyramid using given measurements of the base edge, base height, and volume.

Explanation:

The subject of this question involves calculating the volume of a triangular pyramid and understanding its geometric properties. Given the volume (56 cubic centimeters), base edge (8 centimeters), and base height (7 centimeters), one can determine various other properties of the pyramid. In geometry, the formula to calculate the volume of a pyramid is V = (1/3)*Base Area*Height, where the Base Area for a triangular pyramid is ½ times the base length times the base height. The challenge here would involve determining the height of the pyramid based on the given volume and base dimensions.

Answer:

A

Step-by-step explanation:

Answer:

answer is A

Step-by-step explanation:

It seems that the boundary of [tex]M[/tex] is the circle [tex]x^2+y^2=49[/tex] in the plane [tex]z=0[/tex]. By Stokes' theorem,

[tex]\displaystyle\iint_M(\nabla\times\vec f)\cdot\mathrm d\vec S=\int_{\partial M}\vec f\cdot\mathrm d\vec r[/tex]

Parameterize [tex]\partial M[/tex] by

[tex]\vec r(t)=(7\cos t,7\sin t,0)[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the line integral is

[tex]\displaystyle\int_{\partial M}\vec f(x(t),y(t),z(t))\cdot\mathrm d\vec r=\int_0^{2\pi}(56\sin t,35\cos t,0)\cdot(-7\sin t,7\cos t,0)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(245\cos^2t-392\sin^2t)\,\mathrm dt=\boxed{-147\pi}[/tex]

The question involves computing the double surface integral of the curl of the given vector field over a specified surface. The curl of the vector field is found first using a determinantal formula, and the surface integral is then evaluated over the capped cylindrical surface. These concepts are fundamental in vector calculus and have applications in fields such as physics and engineering.

This question requires the application of vector calculus concepts, specifically surface integrals and the divergence theorem. Given the vector field f=(zx+z²y+8y, z³yx+5x, z⁴x²), your task is to compute the double surface integral of the curl of f over a capped cylindrical surface m, which is a union of a cylinder and a hemispherical cap.

To solve it, you will start by finding the curl of the vector field using the determinant of a special kind of 3x3 matrix, called the curl matrix, containing the unit vectors i, j, k, the coefficients of the derivatives in the Cartesian coordinate system, and the components of the vector field. Once you get an expression for the curl of f, you will set up and evaluate a double surface integral over the given region m to find the desired quantity.

The concept of surface integrals is prevalent in many fields including physics and engineering where it is used to calculate quantities like flux. The divergence theorem, also known as Gauss's theorem, connects the flux of a vector field through a closed surface to the divergence of this field in the volume enclosed by the surface.

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Answer:

  [4, 8]

Step-by-step explanation:

You want to find t such that ...

  T ≥ 69

  24t − 2t^2 + 5 ≥ 69

  t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2

  (t -4)(t -8) ≤ 0 . . . . . . . factor

The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...

  t ∈ [4, 8]

By the inscribed angle theorem,

[tex]12y-1=9y+11[/tex]

[tex]3y=12[/tex]

[tex]y=4[/tex]

So the angles have measure

[tex](12\cdot4-1)^\circ=\boxed{47^\circ}[/tex]

The measure of the angle is 47 degrees. Thus, the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angles at the periphery made by the same chord will be equal.

The equation is given as,

12y - 1 = 9y + 11

Simplify the equation, then we have

12y - 1 = 9y + 11

12y - 9y = 11 + 1

3y = 12

y = 4

Then the measure of the angle is given as,

Angle = 12 x 4 - 1

Angle = 48 - 1

Angle = 47

Thus, the correct option is B.

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Answer:18.66

Step-by-step explanation:

Answer:

[tex](x+3)^2 + y^2 =25[/tex]

Step-by-step explanation:

The general equation of a circle has the form:

[tex](x-h)^2 + (y-k)^2 =r^2[/tex]

Where the point (h, k) is the center of the circle and r is the radius

In this case the center is (-3, 0) and the radius is [tex]r=5[/tex]

So [tex]h=-3\\k=0[/tex]

Finally the equation of the circle is:

[tex](x-(-3))^2 + (y-0)^2 =5^2[/tex]

[tex](x+3)^2 + y^2 =25[/tex]

(X+3)^2 +y^2 =25

This is the correct answer

Check on Desmos

Answer:

$2950

Step-by-step explanation:

Add together the following three items:

Materials:  $2000 plus 15%, or 1.15($2000), or $2300

Labor:  $500

Equipment Rental:  $150

Total:  $2300 + $500 + $150 = $2950

To solve for Sydney's age, we used an equation based on the relationship that Devaughn is 11 years younger than Sydney and the sum of their ages is 83. Solving the equation 2S - 11 = 83, we found that Sydney is 47 years old.

To find Sydney's age, we need to set up and solve an equation based on the information given: Devaughn is 11 years younger than Sydney, and the sum of their ages is 83.

Let's let Sydney's age be represented by S and Devaughn's age be represented by D. Given that Devaughn is 11 years younger than Sydney, we can express Devaughn's age as D = S - 11.

The sum of their ages is given as 83, so we can write the following equation: S + D = 83.

Substituting Devaughn's age in terms of Sydney's age, we get: S + (S - 11) = 83. This simplifies to 2S - 11 = 83. Solving for S, we add 11 to both sides, resulting in 2S = 94, and then we divide by 2 to find S = 47.

Therefore, Sydney's age is 47 years old.

Answer:

2

Step-by-step explanation:

Kelly ran at an average speed of 8 miles per hour. If she finished the race in one and a half hours that means she ran 12 miles.

8=x

?=3/2x

12=x

We now know the road is 12 miles long. Ava has an average speed of 6 miles so she will finish it in 12/6 hours.

12/6=2

It takes Ava to finish the race in 2 hours.

Kelly ran at an average speed of 8 miles per hour.

If she finished the race in one and a half hours that means she ran 12 miles.

The average speed is the distance traveled divided by the time taken.

8=x

12=x

We now know the road is 12 miles long.

Ava has an average speed of 6 miles so she will finish it in 12/6 hours.

12/6=2hours

Therefore, It takes Ava to finish the race in 2 hours.

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Answer:

The solution is (-3, 10.8)

Step-by-step explanation:

While it's rather obvious that you want to solve this system of linear equations, you should share that instruction when you post the problem.

To solve this system using elimination by addition and subtraction, combine the two equations as shown below (to eliminate y):

-0.18x + y = -6.54

-2.8x - y = -2.4

--------------------------

-2.98x = -8.94

Dividing both sides by -2.98, to isolate x, yields:  x = -8.94 / (-2.98) = -3.

Then x = 3.  Find y from -2.8x - y = -2.4:  -2.8x + 2.4 = y, and here,

y = -2.8(-3) + 2.4 = 8.4 + 2.4 = 10.8

Then the solution is (-3, 10.8)

The expression 6(x − 5) means the product of 6 and the difference of x minus 5. If x = 7, the value of the expression is 12.

We can see that the number 6 to the left of the expression 6(x - 5), this means 6 times (x - 5), The reason we write it that way is because the multiplication symbol, ×, can be confused with the variable x, follow by (x - 5) which is the difference of x minus 5. All together is the product of 6 and the difference of x minus 5.

If x = 7, then:

6(7 - 5) = 6(2) = 12

Following are the solution to the given expression:

Given:

[tex]6(x-5) \\\\ x=7 [/tex]

To find:

value=?

Solution:

[tex]\to 6(x-5)\\\\ [/tex]

putting the x value into the above expression:

[tex]\to 6(7-5)\\\\ \to 6(2)\\\\ \to 12[/tex]

Therefore the final answer is "12".

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Answer:

Associative property of multiplication

Explanation:

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

Answer:

True

Step-by-step explanation:

A negative exponent turns into positive when it is put into fraction form.

5^-2 = 1/5^2

5^-2 = 1/25

Answer:

Step-by-step explanation:

It's true. A minus power means that you put the denominator in the numerator and the numerator in the denominator. For example

(5/3)^(-2) = (3/5)^2 = 9/25

Answer:

The length of MN is [tex]\sqrt{5}[/tex] units.

Step-by-step explanation:

The given Quadrilateral KLMN has vertices at K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4).

We use the distance formula to find the length of MN.

[tex]|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We plug in the values to get

[tex]|MN|=\sqrt{(-4--2)^2+(-4--5)^2}[/tex]

[tex]|MN|=\sqrt{(-2)^2+(1)^2}[/tex]

[tex]|MN|=\sqrt{4+1}[/tex]

[tex]|MN|=\sqrt{5}[/tex]

The length of MN is [tex]\sqrt{5}[/tex] units.

Answer:

B

Step-by-step explanation:

Answer:

$6.48

Step-by-step explanation:

There are no numbers here

Answer:

It is B because this triangle Q and R are congruent

Step-by-step explanation:

Answer:

B. 68

Step-by-step explanation:

Because the side lengths PQ and PR both equal 5 and are congruent, the angles opposite them (angle Q and angle R) are also congruent to each other.

Angle Q is 68, so angle R is also 68.

the answer is 3 I bet the oven is hot tbh

Title: The Infallible Logic of 1 + 1 = 2

Introduction:

The seemingly simple equation, 1 + 1 = 2, holds a profound and fundamental place in mathematics and logic. Its truth is evident, self-evident, and indisputable, serving as a cornerstone for mathematical reasoning and human understanding. In this essay, we explore the underlying principles and irrefutable logic behind the statement that 1 + 1 equals 2.

Body:

Basic Arithmetic Principles:

At its core, mathematics is a system of rules and principles that govern the manipulation of numbers and quantities. The equation 1 + 1 = 2 is a fundamental expression of these principles. It demonstrates the addition of two individual units (1) to form a collective sum (2). This is a foundational concept in arithmetic.

Axiomatic Truth:

In the realm of mathematics, certain statements are considered axioms—self-evident truths that do not require proof. 1 + 1 = 2 is one of these axioms. It is a statement that is true by definition and serves as a building block for more complex mathematical operations.

Logical Proof:

One way to understand why 1 + 1 equals 2 is through logical proof. We can start with the premise that we have one unit (1) and add another unit (1) to it. The result, by definition, is two units (2). This logical progression is simple and irrefutable.

Set Theory:

In set theory, a branch of mathematics that deals with sets and their relationships, the equation 1 + 1 = 2 is rigorously defined. In set theory, 1 represents a set containing a single element, and adding another set with one element results in a set with two elements. This is a formalized representation of why 1 + 1 equals 2.

Real-World Application:

The equation 1 + 1 = 2 has practical applications in various fields, including science, engineering, economics, and everyday life. It reflects the way we count and aggregate objects, making it essential for quantitative analysis and problem-solving.

Conclusion:

The equation 1 + 1 = 2 is not merely a mathematical expression; it is a reflection of the logical and axiomatic foundation upon which mathematics and much of human reasoning are built. Its undeniable truth serves as a testament to the precision and consistency of mathematics. The simple act of adding one to one resulting in two exemplifies the elegance and power of mathematical logic, making it an enduring principle in our understanding of the world. In a universe governed by mathematical laws, 1 + 1 will always equal 2, and this irrefutable truth is a testament to the beauty and reliability of mathematics.

ANSWER

4.1 units to the nearest tenth.

EXPLANATION

The graph of the two functions are shown in the attachment.

The coordinates of point A is (1.6,4.1).

The coordinates of point B is (7.1,6.1)

The x-axis represents the ground level.

The distance of point A from the ground level is how far the y-coordinate of this point is from the x-axis.

Which is |4.1-0|=4.1

In converting to spherical coordinates, we use

[tex]x=\rho\cos\theta\sin\varphi[/tex]

[tex]y=\rho\sin\theta\sin\varphi[/tex]

[tex]z=\rho\cos\varphi[/tex]

so that

[tex]\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

Then the integral is

[tex]\displaystyle\iiint_Ey^2\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^3\rho^4\sin^2\theta\sin^3\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta=\boxed{\frac{162\pi}5}[/tex]

To evaluate the expression using spherical coordinates, express the given solid hemisphere in spherical coordinates by replacing x, y, and z with r, θ, and φ. Substitute the volume element in spherical coordinates, and integrate over the limits specified by the solid hemisphere. Finally, evaluate the expression numerically.

To evaluate the expression ∫ey2dv using spherical coordinates, we first need to express the solid hemisphere in spherical coordinates. The given condition for the solid hemisphere is x2 + y2 + z2 ≤ 9 and y ≥ 0. In spherical coordinates, the equation for the solid hemisphere becomes r ≤ 3 and 0 ≤ θ ≤ π/2.

The volume element dv in spherical coordinates is dV = r2sinθdrdθdφ. Substituting this into the original expression, we have ∫ey2dv = ∫e(r*sinθcosφ)2r2sinθdrdθdφ. Since we are integrating over the solid hemisphere, the limits of integration for r, θ, and φ are r = 0 to r = 3, θ = 0 to θ = π/2, and φ = 0 to φ = 2π.

After substituting the expressions for y and dv in terms of spherical coordinates and integrating over the given limits, we can find the numerical value of the given expression.

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5 5/8= 45/8

1 1/2= 3/2

45/8 divided by 3/2

Or

45/8 times 2/3

15/4 or 3 3/4

Answer:

(10 yd) ............=x.....

Answer:

Final answer is E. 10

Step-by-step explanation:

Apply Pythagorean theorem to the given right triangle.

[tex]\left(Hypotenuse\right)^2=\left(Leg_1\right)^2+\left(Leg_2\right)^2[/tex]

[tex]\left(h\right)^2=\left(5\sqrt{2}\right)^2+\left(5\sqrt{2}\right)^2[/tex]

[tex]\left(h\right)^2=50+50[/tex]

[tex]\left(h\right)^2=100[/tex]

take square root of both sides

[tex]h=10[/tex]

Hence final answer is E. 10

ANSWER

E. 10

EXPLANATION

Using Pythagoras Theorem, which says the hypotenuse squared is equal to the sum of squares of the two shorter legs.

[tex] {h}^{2} = {(5 \sqrt{2} )}^{2} + {(5 \sqrt{2} )}^{2} [/tex]

Evaluate the squares on the RHS.

[tex] {h}^{2} = 25 \times 2 + 25 \times 2[/tex]

[tex] {h}^{2} = 50 + 50[/tex]

Simplify:

[tex] {h}^{2} = 100[/tex]

Take positive square root.

[tex]h = \sqrt{100} [/tex]

[tex]h = 10[/tex]

The hypotenuse is 10 units.

The correct answer is E