A line has a slope of 1/4. The line passes through the
point (4, 6). The line also passes through the point (12, k). What is the value of k?

A. 8
B. 9
C. 14
D. 18

Triangles ΔAEC, ΔECD are congruent.

Three angles and three sides, or the six measuring components, specify the requirements for the congruence of triangles. But if three of these are correctly satisfied, the other three are also satisfied automatically. Axioms for congruency are four such instances.

Triangles are said to be congruent if:

Congruent triangles under the SSS (Side Side Side postulate) condition.

Congruent triangles criterion according to the SAS (Side Angle Side postulate).

Congruent triangles are a requirement of the ASA (Angle Side Angle postulate).

The congruent triangles criterion of the AAS (Angle Angle Side postulate).

Given C is mid point of AD.

and, FE bisects the angle ∠AED.

By SAS Postulate we can say ΔAEC, ΔECD are congruent.

In triangles ΔAEC, ΔECD;

AC=CD (C is mid point)(S);

∠CEA=∠CED (Bisector)(A)

CE=CE (Common side)(S);

So by SAS theorem both are Congruent.

Triangles ΔAEC, ΔECD are congruent.

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Answer:

100<x<500

Step-by-step explanation:

We can create a system of inequalities by using the Triangle Inequality Theorem. This theorem states that the sum of two sides on a triangle is greater than the other sides.
1.) Figure out the first inequality. This would be 300+200>x, or x<500.

2.) Figure out the second inequality. This would be x + 200 > 300, or x>100.
3.) Figure out the third inequality. This would be x + 300 > 200, or x > -100.

4.) Combine these inequalities. By combining these inequalities, we would get 100<x<500.

The required value of y(7) is given as y (7)= 4412711.8.

Given that,
Given dy/dt=2y and y(2)=200.

The action of bringing concurrently shorter components into a single system that acts as one is known as integration.

Here,
dy/dt = 2y
dy/y = 2dt
integrate,
logy = 2t + c
[tex]y = e^{2t + c}[/tex]
put t = 2 and y = 200
C = 1.3
Now,
[tex]y= e^[2t + 1.3][/tex]
Substitute t = 7
[tex]y= e^[14 + 1.3]\\y = e^{15.3}[/tex]
y = 4412711.8

Thus, the required value of y(7) is given as y (7)= 4412711.8.

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The function in f(t) form that describes the amount of fuel in the plane at time t will be:

f(t) = 112.25t + 31.425.75

What is the Equation of line?

The equation of the line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

we have given that;

After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Now,

Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (32882 - 34902.5) / ((31 - 13)

m = 2020.5 / 18

m = 112.25

Thus, The equation of the line with slope 112.25 is,

⇒ y - 32885 = 112.25 (x - 13)

⇒ y - 32885 = 112.25x - 1459.25

⇒ y = 112.25x - 1459.25 + 32885

⇒ y = 112.25x + 31.425.75

Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be:

f(t) = 112.25t + 31.425.75

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The equation that represents the same relationship is equation 1: x-2y-1=0

We should know that an equation is a mathematical statement that shows the equality of two sides o a statement.

From the given equation:

x-2y-1=0

If we input the various values of x such as -5, 7,31,42 into the equation we are going to obtain the corresponding values of y as indicated in the table

x-2y-1=0

Rewrite the equation

x-1=2y

⇒2y=x-1

=2y=-5-1

y=-3

Also, 2y=7-1

2y=6

y=3

Input the value 31 into the equation or x

2y=31-1

2y=30

y=15

Input the value 45 or x in the equation

2y=45-1

2y=44

y=22

In conclusion, the equation x-2y-1=0 represents the the same relationship  in the table

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The quantity of food that would be needed to feed all the cubs for one year is 1825 kg

From the question, we are to determine how much food would be needed to feed all the cubs for one year

From the given information,

"Each cub eats 1.25 kg of food a day"

Assume there are 365 days in a year.

Since there are 4 cubs,

The quantity of food that would feed the cubs for one year = 365 × 4 × 1.25

The quantity of food that would feed the cubs for one year = 1825 kg

Hence, the quantity of food needed is 1825 kg

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By finding an evaluating a linear equation we will see that it takes 24 minutes to serve a group of 8 people.

Let's assume that the relation between the number of people and the time it takes to serve them is linear.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we have two points:

1 person, 10 minutes, written as (1, 10)

5 people, 18 minutes, written as (5, 18)

Then the slope is:

a = (18 - 10)/(5 - 1)

a = 8/4 = 2

Then the linear equation is:

y = 2x + b

To find the value of b, we can replace the values of one of the points, I will use (1, 10) so we will get:

10 = 2*1 +b

10 = 2 + b

10 - 2 = b

8 = b

The linear equation is:

y = 2x + 8

For 8 customers, the time will be:

y = 2*8 + 8

y = 24

It will take 24 minutes to serve 8 people.

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The Perimeter of the Pentagon in Figure 1 is 40ft

What is Pentagon?

A pentagon is a two-dimensional polygon having five sides and five angles. "Penta" means "five," and "gon" means "angles" in Greek, therefore when we mix the two words "penta + gon," we obtain the term "pentagon."

Solution:

Permieter of Pentagon = 5 * side

In Figure 1, the length of a side is 8 ft,

Then the Perimeter will be 8*5 = 40ft.

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Answer:

1.3,-12,16

Step-by-step explanation:

Answer: (6,2)

Step-by-step explanation:

(7,5)     (x,2)      m=3     x=?

y=mx+b

y=3x+b   (1)

To find the coefficient b we take the coordinate that belongs to this line (7,5): x=7    y=5

5=3(7)+b

5=21+b

5-21=21+b-21

-16=b

Thus, b=-16

Hence, y=3x-16

To find the x we take the coordinate that belongs to this line (x,2): y=2

2=3x-16

2+16=3x-16+16

18=3x

Divide both parts of the equation by 3:

6=x

Thus, x=6

Step-by-step explanation:

Note that the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Plug in the slope for m and the given coordinate for x and y:

9 = (7)(2) + b

9 = 14 + b

b = -5

y = 7x - 5

The equation in slope intercept form of the line that passes through the points (6,1) and (3,3) is y = - 2 / 3 x +5

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3) can be represented as follows;

let's find the slope

m = 3 - 1 / 3 - 6

m =  - 2 / 3

Hence, let's find the y-intercept as follows;

using (3, 3)

y = - 2 / 3 (x) + b

3 = - 2 / 3 (3) + b

3 + 2 = b

b = 5

Therefore, the equation of the line is y = - 2 / 3 x +5

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The critical points for the equation [tex]f(x)=(x^{2} +64)^{\frac{1}{11} }[/tex] is

[tex](x,f(x))[/tex] = [tex](0,2^{\frac{6}{11} })[/tex] = [tex](0,1.46)[/tex]. at x=0

The absolute maximum is at [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] =  [tex](9,1.6)[/tex], at x=9.

What is the absolute maximum of an equation?

The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) [tex]\geq[/tex] f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.

To find the critical points, we find the value of f'(x) and equate to 0.

[tex]\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0[/tex]

we get x=0.

We see that f'(x) exists for all x between [-8,9].

We also find the endpoints, that is -8 and 9.

Then we calculate f(x) at critical points and endpoints.

We calculate f(x) at 0, -8, and 9.

We get,

for x=0, f(x)= [tex]2^{\frac{6}{11} }[/tex]

for x=-8, f(x)= [tex]2^{\frac{7}{11} }[/tex]

for x=9, f(x)= [tex]\sqrt[11]{145}[/tex]

We see that the value is maximum at x=9, and f(x) becomes [tex]\sqrt[11]{145}[/tex].

Hence we get the absolute maximum is [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex]

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Knowing the history of the Earth is of the utmost importance to understand how it got to now and to know where we are going.

The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.

Knowing the history of the Earth is very important because:

¡Hope this helped!

Answer:

The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.

Answer:3.71 miles

Step-by-step explanation:

Answer:

  20%

Step-by-step explanation:

You want to know the tax rate if the added tax brings the cost of $45 purchase to a total of $54.

The multiplier applied to a purchase cost to add the tax is ...

   (1 +r)

where r is the tax rate.

Here, that means ...

  45(1 +r) = 54

  1 +r = 54/45 = 1.20

  r = 1.20 -1 = 0.20 = 20%

The tax rate Delia paid on the articles she bought was 20%.

Answer:

The “edge” effect of a tetrahedral container with edge length of 1,000 mm would be 2*r*√3 (r = radius of ball, see diagram below). For a ping pong ball with a diameter of 40 mm, the edge effect would be 2*20*√3 = 69.28 mm. Subtract that from 1,000 mm and you get 930.72 mm of “available space” along the bottom row. Divide 930.72 mm by 40 mm per ball and you get 23.27. So you wouldn’t be able to fit 24 balls along the base, you’d only be able to fit 23 balls. With 23 balls, the total number that a tetrahedron could contain (T) would be T = n(n+1)(n+2)/6 = 2,300 balls, not 2,600.

The additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.

What is quadrilateral ?

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Properties include: There are four vertices . There are four sides . 360° is the total of all interior angles. There are two diagonals in them.

Trapezium is one of the five unique quadrilateral shapes. Parallelogram. Rectangle. Rhombus. Square

These bisectors intersect each other at 90 degrees.

And it means that they are perpendicular.

Since they are perpendicular, we find that there 4 congruent triangles, XY is parallel to WZ, and WX is parallel to YZ.

Additionally, opposite angles are equal.

These two latter findings are the characteristics of the parallelogram.  

Hence, the additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.

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The probability of event A and event B of the independent events will be 0.05.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the conditional probability is given as,

P(A and B) = P(A) x P(B)

Event A and event B are independent events. The probability of event A is 0.50 and the probability of event B is 0.10.

Then the probability of event A and event B of the independent events is given as,

P(A and B) = P(A) x P(B)

P(A and B) = 0.50 x 0.10

P(A and B) = 0.05

The probability of event A and event B of the independent events will be 0.05.

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The graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.

What is the graph of the equation?

The graph of an equation is the group of all points on a number line or the coordinate plane that are solutions of an equation (= statement that two amounts are equal).

0 hours- $0

4 hours- $32

8 hours- $64

12 hours- $96

First find the equation of this problem to represent the relationship, which is y = 8x.

Next, you substitute the number of hours into x to get y, which is the amount of money.

Hence, the graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.

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The scale model of the sports arena has a height of 12 inches.

Unit rate is the amount of something at a rate of one amount to another amount.

If 2 inches = 30 feet, then a sports stadium's height is 180 feet.

A man can walk 6 kilometers in 2 hours.

A man can cover 3 miles by walking in an hour.

A machine can cut 10 potatoes in five minutes.

A machine can cut two potatoes in a minute.

30 feet equals 2 inches.

Add 30 to both sides.

1 foot equals 2/30 inches.

1 foot equals 2/30 inches today.

Add 180 to both sides.

180 feet equals 180 x 2/30 inches.

6 × 2 inches times 180 feet.

12 inches equal 180 feet

Since the height of the sports stadium is 180 feet, 2 inches would equal 30 feet.

The scale model of the sports arena has a height of 12 inches.

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Step-by-step explanation:

we know that the two angles with x are equal since they are made with the same lines

so

8x+36=5x+51

solve for x

a. subtract 36 from both sides

8x=5x+15

b. subtract 5x on both sides

3x=15

c. divide by 3

x=3

now to find z

we know a line equals 180

so

(8x+36)+z=180

plug in 3

8(3)+36+z=180

24+36+z=180

60+z=180

z=120

A total of 396 miles and 2.2 hours will pass between the two trains on the Long.

For additional information on how to handle rate-time-distance or motion problems, scroll down the page.

Moving away from one another are the two trains.

85x + 95x = 396

To solve you combine like terms. The like terms are 85x and 95x

85x + 95x = 180x

Right now, you

180x = 396

Now multiply by 180.

180 divided by 396 equals 2.2.

X= 2.2

That's how you do things, in my opinion.

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Answer:

yes youre right it is point D

Step-by-step explanation:

Using law of logarithm and exponent rules, the value of the unknown is 5

logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.

Logₐ x = n  or   aⁿ = x

Where b is the base of the logarithmic function.

This can be read as “Logarithm of x to the base b is equal to n”.

In this case, we just need to solve for the value of b

4 = logₐ(625)

4 = 1 / log625(a)

multiply both sides by log₆₂₅(x)

log₆₂₅(a) / 4 = 1/4

applying log rules

a = 5

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Answer:

137 cheap tickets sold, and 65 best seats sold

Step-by-step explanation:

x+y=202

50x+556y=42900

x=202-y

50(202-y)+556y=42900

10100-50y+556y=42900

10100+506y=42900

506y=32890

y=65

x=202-65

x=137

x= Cheap tickets, y= expensive tickets

a) His distances after each jump are given as follows:

b) He will jump exactly 16 meters.

In a geometric sequence, each term is obtained by the multiplication of the previous term by the common ratio.

In this problem, the sequence is given as follows:

8, 4, 2, ...

The common ratio is of:

q = 2/4 = 4/8 = 0.5.

Then the next jumps are given as follows:

The sum of the elements of an infinite geometric sequence is given as follows:

[tex]S = \frac{a_1}{1 - q}[/tex]

In which [tex]a_1[/tex] is the first element.

Hence for this problem, the sum is of:

S = 8/(1 - 0.5) = 16 meters.

Which means that he will reach exactly the desired distance.

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By the congruence property CD ≅ CX

Congruent examples include what?

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

Which five types of congruence are there?

If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).

Given that:

ΔECD ≅ ΔECX

so ED ≅ EX

CD ≅ CX

by the congruence property

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Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:

Arc QR = 48°

Arc RS = 96°

Arc QPS = 216°

Arc PSR = 186°

Arc SRQ = 144°

The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.

Find arc PSR:

Arc PSR = 2(93) [based on the inscribed angle theorem]

Arc PSR = 186°

Find arc QR:

Arc QR = 360 - arc PQ - arc PSR

Substitute

Arc QR = 360 - 126 - 186

Arc QR = 48°

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°

Arc QPS = 126 + 90

Arc QPS = 216°

Arc PSR = arc PS + arc RS

Arc PSR = 90 + 96

Arc PSR = 186°

Arc SRQ = arc RS + arc QR

Arc SRQ = 96 + 48

Arc SRQ = 144°

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Answer: 48 96

Step-by-step explanation:

Arc QR = 360 - 126 - 186

Arc QR = 48°

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°

Answer:

$23.02

Step-by-step explanation:

You add what she earned to what she had before

$14.27 + $8.75 = $23.02