Which of the following completes the two-column proof below?

Given: ∠1≅∠2, p⊥r
Prove: q⊥r
Proof:

1. ∠1≅∠2 (Given)

2. p∥q (?)

3. p⊥r (?)

4. q⊥r (?)

The figure shows lines p and q and transversal r. The intersection of line p and transversal r forms four angles, the top right angle is labeled as a right angle, the top left angle is labeled as 1. The intersection of line q and transversal r forms four angles, the bottom right angle is labeled as 2.

In the case above, the side-side-angle (SSA) is no valid means for establishing triangle congruence.

Using the image attached:

m  angle A = M angle A

AB = A¹B¹

BC = B¹C¹

Looking at the image of both angles you will see that both are not congruence  because Two triangles can be regarded as congruent if and when all its three corresponding angles or sides are said to be equal and all the three corresponding angles are also said to have equal  measure.

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half the confidence interval is the answer.

The margin of error is a statistical measure that explains the difference between the actual and expected results of a random survey sample. Simply put, tolerances allow you to measure the level of unpredictability of your data and findings.

The margin of error is the amount added and subtracted in the confidence interval. The standard error is the standard deviation of the sample statistics when many samples of the same size can be obtained.

E = zs√n. The quantity E is called the margin of error. The margin of error is half the width of the confidence interval. The confidence interval may be given as ˉx ± E. For example, 9.95 ± 0.43.

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The closure property is defined below.

According to Closure Property, the set of numbers on which the mathematical operation like addition, subtraction, and multiplication are performed the result will be the number of the same set.

An example of this is if addition is done on two whole numbers the output will be a whole number.

The closure Property is valid for Whole numbers, Natural Numbers, Rational Numbers, Real Numbers, and Integers

For Natural Numbers: Addition of a + b = N

(a, b and N = natural numbers)

Thus, the closure property is defined.

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The expression which shows the amount of money, in dollars Maddie spent on mailing letters in March is 3.7 +0.74 y.

Given Maddie mailed y letters in January. She mailed 3 times as many letters in February. In March she mailed 10 letters more than half of what she mailed in January and February.

Expression  is combination of numbers, symbols, fraction, coefficients which are not found in equal to form.

Letters mailed in January=y

Letters mailed in February=3y

Letters mailed in March=10+(y+3y)/2

=10+2y

Amount of mailing of 1 letter=$0.37.

Amount of mailing of letters in March=0.37(10+2y)

=3.7+0.37*2y

=3.7+0.74y

Hence the expression which shows the amount of letters mailed in March is 3.7+0.74 y.

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The equation of the quadratic function that models the data is y = x^2 + 3x + 4

A quadratic function is represented as:

y = ax^2  +bx + c

Next, we enter the data values on the table to a graphing calculator.

From the graphing calculator, we have:

a = 1, b = 3 and c = 4

Substitute these values in y = ax^2  +bx + c

So, we have

y  = x^2 + 3x + 4

Hence, the equation of the quadratic function that models the data is y = x^2 + 3x + 4 and the scatter plot is (a)

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Answer:

Step-by-step explanation:

So if you look at the first photo I sent you'll see I marked three points. So the first point is going to be the two lines meet and the other two are going to be at 0 degrees and 48 degrees. After that you're going to draw a line to connect 2 of the dots to the middle one or the one connecting the two. After this you're going to put the protractor back on the triangle and line it up and then draw a point at 24 degrees (half of 48 degrees) and then draw a line to it. And this will be the bisector. And then after that label all the points. Also for the congruency thing just do the same thing except without an angle bisector through it.

The inequality of the bridge's legal limit 100000x + 34000y ≤ 700000

The given parameters are:

Represent the 6-axle trucks with x and the y-axle trucks with y.

So, we have the following inequality

100000x + 34000y ≤ 700000

The number of 6-axle trucks at one time

Here, we assume that y = 0.

So, we have:

100000x ≤ 700000

Divide by 100000

x ≤ 7

Hence, the number of 6-axle trucks at one time is 7

The number of 2-axle trucks at one time

Here, we assume that x = 0.

So, we have:

34000x ≤ 700000

Divide by 34000

x ≤ 20.58

Round down

x ≤ 20

Hence, the number of 2-axle trucks at one time is 20

See attachment for the inequality of 100000x + 34000y ≤ 700000

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Answer:

  (a)  The number of positive zeros is either 2 or 0. The number of negative zeros is either 2 or 0.

Step-by-step explanation:

The possible numbers of real zeros can be found using Descarte's Rule of Signs.

When signs of coefficients of terms of the polynomial are listed in order of decreasing degree, the number of sign changes can be counted. That number is the number of possible positive real zeros of the polynomial.

When the signs of odd-degree terms are changed, the number of sign changes becomes the possible number of negative real zeros.

The actual number of real zeros may be less by a multiple of 2. (The zeros may be complex, and complex zeros come in pairs.)

The signs of the terms in the given polynomial are ...

  + - + + + . . . . . 2 sign changes: 2 or 0 positive real zeros

When the signs of odd-degree terms are changed, they become ...

  + + + - + . . . . . 2 sign changes: 2 or 0 negative real zeros

Descarte's rule of signs lets us conclude ...

__

Additional comment

When we graph the function, we find there are no real zeros. All four of the zeros are complex.

Knowing which x-values would result in division by zero can help you avoid using certain x-values. Finding the domains of rational functions is therefore likely to be your initial step.

A function that measures two polynomials in comparison. Because one is divided by the other, just like a ratio, it is a "rational function."

All real numbers x, except those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.

For instance, the set of all real numbers other than x=0 is the domain of the parent function f(x)=1/x.

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There are 3 tolls where Stephanie pays $ 4.05.

The distance between two points is the length of the path connecting them.

Here,

Distance covered by Stephanie = 12 1/4 miles

                                                     = 12.25 miles

Distance between two toll tax = 3 1/2 miles

                                                   = 3.5 miles

Number of Tolls = Total distance covered / Distance between two tolls

                            = 12.25 / 3.5

                            = 3.5

                            ≈ 3 tolls.

Cost of 1 toll = $ 1.35

Total amount paid on toll = 3 X 1.35

                                          = $ 4.05

Thus, there are 3 tolls where Stephanie pays $ 4.05.

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Answer:

4 trees and 76 acorns.

Step-by-step explanation:

Let the amount of trees be x.

[tex]18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4[/tex]

There are 4 trees, and there are [tex]18x+4[/tex] acorns or 76 acorns.

Hope you have a nice day, and also you should mark brainliest :)

Answer:

76 acorns and 4 trees

Step-by-step explanation:

Let X be the number of acorns (a) Ms. Blue Jay plans to store.

We are told that she could hide 18 acorns (a) per tree (t) which we'll write as 18a/t.  This would result in 4 leftover acorns.

We then learn that if she hides 20 acorns per tree, 20a/t, she will have space for an extra four acorns.

There are t trees in both cases.  We can write these two scenarios as:

1)  18t + 4  = X [18 acorns are in each tree, t, plus there are 4 left over.]

2)  20t -4  = X [20 acorns per tree, t, with room to store 4 more]

These two are equal to each other:

18t + 4 = 20t - 4

2t = 8

t = 4

There are 4 trees.

Since 18t+4 = X, the total number of acorns is18*4+4 = 76 acorns and 4 trees.

Check to see if 76 acorns works for the second scenario:

Will hiding 20 acorns per tree leave room for 4 acorns if there are 76 acorns?

(4 trees)*(20 acorns/tree) = 80 acorns can be stored.  If Ms. Jay only has 76 acorns, there will be room for 4 more acorns.

Answer:

y = 3x + a (a > 0) - above the original line

y = 3x + b (b < 0) - below the original line

Step-by-step explanation:

Pick any number you want for a or b, as long as the number meets the condition I wrote down.

Answer:

y=3x+1 and y=3x-1

Step-by-step explanation:

y=3x+1 is above because it has a positive slope (3) while y=3x-1 is below because it has a negative slope (-3).

Answer:

12cm

Step-by-step explanation:

where:

c

is the hypotenuse, and

a

and

b

are the other two sides (legs).

Let

a

=

9 cm

Rearrange the equation to isolate

b

2

. Plug in the values for

a

and

c

, and solve.

b

2

=

c

2

−

a

2

b

2

=

(

15 cm

)

2

−

(

9 cm

)

2

Simplify.

b

2

=

225 cm

2

−

81

cm

2

b

2

=

144 cm

2

Take the square root of both sides.

b

=

√

144 cm

2

Simplify.

b

=

12 cm

The surface area of the planet is 103,184,713.4 miles².

A planet has the shape of a sphere.

The first step is to determine the radius of the planet from the circumference.

Radius = circumference / (π x 2)

18,000 / (3.14 x 2) = 2,866.24 miles

Surface area of a sphere = 4πr²

4 x 3.14 x ( 2,866.24²) = 103,184,713.4 miles²

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Answer: 4x^2 + 1

Step-by-step explanation:

I am assuming g(x) = x^2

4(x^2) + 1

4x^2 + 1

Answer:

[tex](fog)(x)=4x^2+1[/tex]

Step-by-step explanation:

Assume [tex]g(x)=x^2[/tex]

[tex](fog)(x)[/tex] is a composition of two functions such that [tex](fog)(x)=f(g(x))[/tex].

Consider the function:

[tex]f(x)=4x+1[/tex]

Replace [tex]x[/tex] with [tex]g(x)[/tex] into the equation:

[tex]f(g(x))=4\cdot g(x)+1[/tex]

Substitute [tex]g(x)=x^2[/tex] on the right side of the equation:

[tex]f(g(x))=4\cdot x^2+1[/tex]

Therefore, the expression for [tex](fog)(x)[/tex] is [tex]4x^2+1[/tex].

Option C) is correct z +3 is also an odd number

z- 3 is odd number,

odd number are given as 1, 3, 5, 7, 9,11,.. etc.

since z - 3 odd number

mean while
if we add 3 to z will also be the odd number cause subtracting 3 twice from z-3 returns the reverse value i.e.
so z + 3 also an odd number.

Thus, z +3 is also an odd number

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The picture of the drawing of triangle ABC with vertices at A(1,6), B (1,1) and C (5,1) is attached below.

A triangle is known to be a kind of a polygon that is made up of three edges and also made up of  three vertices.

It is regarded as a key shapes in geometry as its vertices is often denoted with A, B, and C.

The points will be taken as: A(1,6),  B(1,1) and C (5,1)

=AB + BC = AC

Therefore, The picture of the drawing of triangle ABC with vertices at A(1,6), B (1,1) and C (5,1) is attached below.

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Answer:

They used coordinates P(a,0), A(d,c), and R(b,c) instead of the given coordinates.

The volume of the spherical solid resulting of the drill is of 11,226 units³.

The volume of a sphere of radius r is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this problem, we have two spherical balls, one of radius 14 and other of radius 4, hence their volumes are given as follows:

[tex]V_1 = \frac{4\pi 14^3}{3} = 11494[/tex]

[tex]V_2 = \frac{4\pi 4^3}{3} = 268[/tex]

The volume of the resulting solid is the difference of the volumes, hence:

V = 11494 - 268 = 11,226 units³.

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Venn Diagram:

Neither a cat or dog: 37/100

A dog: (22+14)/100 = 36/100 = 18/50 = 9/25

A dog but not a cat: 22/100 = 11/50

The product of the given binomial is x⁴ -y².

FOIL stands for Firsts , Outsides , Insides , Lasts and while determining product of binomials this sequence is followed.

The binomials given are

( x² +y ) (x² -y)

x²  (x² -y)             + y * x² +              y* (-y)

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

Firsts  Outsides       insides             Lasts

After simplification

x⁴ - x²y +  x²y -y²

x⁴ -y²

The product of the given binomial is x⁴ -y².

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Answer:

y=250000

Step-by-step explanation:

y=ab^x

y=25*100^2

this is your answer

I hope you get your answer

[tex]3\sqrt{2} - 4 * (\sqrt{2})^2 = 3\sqrt{2} - 8[/tex]

Answer = [tex]3\sqrt{2} - 8[/tex]

The pattern on the table is x increases:

The functions on the table of values are:

sin(x), cos(x) and sin²(x) + cos²(x)

To describe the pattern, we simply observe how the values of the function change, as x increases.

As x increases, on the table:

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ANSWER :

= m - ( m of 47/100 )

(or)

= m of (53/100)

Mark BRAINLIEST

The algebraic expression for "m decreased by 47%" is m - 0.47m.

To translate "m decreased by 47%" into an algebraic expression, we first need to understand the meaning of the phrase. "Decreased by" indicates a subtraction operation, and "47%" represents 47 percent, which is equal to 0.47 in decimal form.

Let's break down the expression step by step:

"m" represents the original quantity we want to find.

"Decreased by" indicates subtraction.

"47%" is equivalent to multiplying the original value "m" by 0.47.

Combining all these elements, the algebraic expression for "m decreased by 47%" is:

m - 0.47m

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Hope this helped!

This is just what I drew. I believe the answer for B could be somewhat different than what I drew.

Have a nice day!

Using it's concept, it is found that the graph on top right represents the inverse function.

The inverse of the function is given by the set that contains point (y,x), that is, the coordinates are exchanged.

Considering the table given, the graph of the inverse function will contain these following points:

(4.4, -3), (0.6, -2), (-0.8, -1), (-1,0), (-1.2, 1), (-2.6, 2), (-6.4, 3).

Hence it is the top right graph.

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Answer:

y≤-x+1

Step-by-step explanation:

Since the line is slanted down and crossing through a point every one unit the slope is negative one. The line is also crossing 1 on the y-axis. This is the y-intercept. The last thing we need to know is which sign to use, less than, greater than, less than or equal to, greater than or equal to. We can immediately cross out less than and greater than because it is a solid line. The sign used on the graph is less than or equal to because it is a solid line shaded to the left. Now, we can use the formula with the information we have found to create the linear inequality.

Formula: y≤x+b

I put the less than or equal to sign there instead of the equal sign because the line graphed is less than or equal to. Plug in the information we have.

y≤-x+1

Using function notation.

f(x)≤-x+1

I have also attached a picture for you to see it is correct.

Hope this helps!

If not, I am sorry.