Write an equation in slope-intercept form of the line that passes through $\left(-5,\ 19\right)$ and $\left(5,\ 13\right)$ .

The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

When two triangles ΔABC and ΔXYZ are similar then

                    AB/XY = BC/YZ = AC/XZ

Here we have

ΔABC and ΔOPQ which are similar and right-angled triangles

As we know in a right-angled triangle

=>  Hyp² = side² + side²  

From ΔABC,

AB² = AC² + BC²  

=> AB² = 6² + 4²

=> AB² = 100 = 10²

=> AB = 10 units

Since  ΔABC and ΔOPQ are similar

=>  AB/OP = BC/OQ = AC/PQ  

=>  10/OP = 4/ f = 6/ 6

Take 10/OP = 6/ 6  

=>  6(10) = 6(OP)

=>  OP = 10 units  

4/ f = 6/ 6  

=> f = 4 units    

Therefore,

The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units

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The equation of a line for y-intercept and the coordinate point is y=3x-1.

Given that, y-intercept is -1 and the line passes through the point (3, 8).

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Put, c=-1 and (x, y)=(3, 8) in y = mx+c, we get

8=m(3)-1

⇒ 3m=9

⇒ m=3

Substitute c=-1 and m=3 in y = mx+c, we get

y=3x-1

Therefore, the equation of a line for y-intercept and the coordinate point is y=3x-1.

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The rewritten expression will be 4a³ and the value of this expression is -500.

Given in the question:

(2a⁴)² / a⁰a⁵

We know that

(xy)ⁿ = xⁿ × yⁿ ... (i)

We can use equation (i) for the next step of our given expression.

In the case of the numerator:

(2a⁴)² = 2² × a⁸ = 4a⁸

Now, we know, any number to the power of zero is 1.

So, for the denominator, we get:

a⁰a⁵ = 1 × a⁵ = a⁵

We know,

pˣ / pʸ = y ⁽ˣ⁻ʸ⁾ ... (ii)

Using this equation, we can further simplify the given expression:

⇒ 4a⁸ / a⁵

⇒ 4 a⁽⁸ ⁻ ⁵⁾

⇒ 4 a ³ ... (iii)

Now, in the second part of the question, we need to find the value of the expression.

Given a = -5

Putting this value in equation (iii) we get:

4 a ³

⇒ 4 (-5) ³

⇒ 4 × (-125)

⇒ -500

Hence, the simplified expression is 4 a ³ and the value of the simplified equation is -500.

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Answer:

Two negatives, positive answer:

-3 - (-4) = 1

Two negatives, negative answer:

-45 - (-1) = -44

Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric.

What do you mean by ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

The total amount of fabric = 3 7/8 yards = 31/8 yards.

Amount of fabric needed to make 1 pair of shorts = 1 1/4 = 5/4 yards.

The number of shorts that can be made = 31/8 ÷ 5/4

⇒ 3.1 so it will be 3 because no relevance of decimal shorts.

Hence "Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric".

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Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.

Given that,
The coordinate pairs separated by a vertical distance of greater than 6 units is to be determined.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

here,
(A)
Since the x coordinate is the same in all the pairs, distance on the y axis can only be calculated.

(5.1, -3.3) and (5.1, 3.4)
y = 3.4 - (-3.3)
y = 6.7

Similarly distance,
(B) y = 6.8
(C) y = 5.6
(D) y = 3.5

Thus, Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.

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The probability of choosing 3 men and 3 women to form the committee is 0.4329 and the probability to select exactly 2 people from the human resources is 0.4545.

It is given that there are 12 employees.

The number of male employees is 6

number of female employees is 6

A committee of 6 is to be formed. We need to find the probability that out of 6, 3 are male and 3 are female.

Let A be the event of having 3 men and 3 women on the committee

The total number of ways to choose 6 people is

¹²C₆

Probability = number of favorable outcomes / total number of outcomes

n(A) = ⁶C₃   X  ⁶C₃

Therefore,

P(A) = (⁶C₃   X  ⁶C₃) / ¹²C₆

= (20  X  20) / 924

= 400/924

= 0.4329

It is given that the number of employees in human resources from the group is 4

Let B be the event to choose exactly 2 employees from the human resource

n(B) = ⁴C₂  X  ⁸C₄

P(B) = ⁴C₂  X  ⁸C₄ / ¹²C₆

= 6 X 70 / 924

= 420 / 924

= 0.4545

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Answer:

1 carton

Step-by-step explanation:

3 (7/10)= 21/10

1/3 of 21/10= 7/10

7/10=1 carton

The equation of the line in slope intercept form is y = 6x + 5

The given parameters are

Slope, m = 6

Points, (x₁, y₁) = (-2, -7)

A linear equation can be represented as

y = slope * x + y-intercept

i.e.

y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = 6(x + 2) - 7

Expand

y = 6x + 12 - 7

Evaluate the like terms

y = 6x + 5

Hence. the linear equation is y = 6x + 5

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The inverse function is given as s⁻¹ = [tex]\frac{t^2+4t-12}{t^2-9t+14}[/tex] and the equation represents the average sales each day for the real estate company would be [tex]s^{-1}=\frac{t+6}{t-7}[/tex].

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

A real estate company balances the books for its business on the first day of each month.

It hopes to sell houses every other day of the month.

The average number of houses, S, the company sells each day, t is represented by the inverse of the function given below.

               [tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}[/tex]

Then the inverse function can be written as

                   [tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}\\\\s^{-1}=\frac{t^2+6t-2t-12}{t^2-7t-2t+14}\\\\s^{-1}=\frac{(t+6)(t-2)}{(t-7)(t-2)}\\\\s^{-1}=\frac{t+6}{t-7}[/tex]

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Answer:

C. [tex]S=\frac{7t+6}{t-1}[/tex]

Step-by-step explanation:

I got it right on the exam.

First, take the equation and inverse it, replace and t with y and the y with t

[tex]y=\frac{t^{2}+4t-12}{t^{2}-9t+14} \\\\t=\frac{y^{2} +4y-12}{y^{2}-9y+14}[/tex]

Then, factor both the top and bottom

[tex]t=\frac{(y+6)(y-2)}{(y-7)(y-2)}[/tex]

You see that there is a duplicate of the (y-2) in the numerator and denominator, so they cancel out,

[tex]t=\frac{(y+6)}{(y-7)}[/tex]

Now you can start getting the y alone to make an equation,

[tex]t(y-7)=\frac{(y+6)}{(y-7)} (y-7)\\t(y-7)=(y+6)[/tex]

[tex]ty-7t=y+6\\ty-7t-y+7t=y+6-y+7t\\ty-y=7t-6\\y(t-1)=7t-6\\\frac{y(t-1)}{(t-1)} =\frac{7t-6}{t-1} \\y=\frac{7t-6}{t-1}[/tex]

The relationship between the number of weeks and cars are proportional since they are dependent on each other.

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.

This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.

Let;

y = 3x

At week 10, Alfred will have

y = 3(10) = 30 cars

After 10 weeks, Alfred will have 30 cars

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If its a 28 day month then 671088640

29 days 1342177280

30 days 2684354560

and 31 days 5368709120

The missing values that completes the table is shown in the attachment below.

To complete the table that is given in the table above, plug in the value of x into the equation and solve accordingly.

For x = 1, substitute the value of x into y = 3x² and y = 3^x:

y = 3(1)²

y = 3(1)

y = 3

y = 3^(1)

y = 3

For x = 2, substitute the value of x into y = 3x² and y = 3^x:

y = 3(2)²

y = 3(4)

y = 12

y = 3^(2)

y = 9

The complete table is shown below.

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For each of the arithmetic sequences, we have that:

a)

b)

c)

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the following rule:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

For the sequences in this problem, we have that:

Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.

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The greatest even integers that the 5 consecutive number has a sum of - 80 is - 12.

Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Therefore, even integers are integers that are even.

There are 5 consecutive even integers with a sum of –80.

let

x = first integers

Therefore,

x + x + 2 + x + 4 + x + 6 + x + 8 = - 80

5x + 20 = - 80

5x = -80 - 20

5x = - 100

divide both sides by 5

x = - 100 / 5

x = -20

Therefore,

greatest integer = - 20 + 8 = - 12

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Answer:

Step-by-step explanation:[tex]x2{12}5\\ =18[/tex]

Answer:

241

Step-by-step explanation:

9 x 12 = 108 m (area of square)

19 x 14 = 266 / 2 = 133 (area of triangle)

108 + 133 = 241

Answer:

v>3

Step-by-step explanation:

2v>7-1

2v>6

v>6/2

v>3

Directly proportional to x.

Acc to our question-

Hence,Directly proportional to x.

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∛128 is  the radius r and height h of the cylinder with minimal surface area .

What is Surface Area?

       V = πr²n

   128π = πr²n

        n = 128/r²

s = 2πrn + 2πr²

s = 2πr 128/r² +  2πr²

s = 256π/r + 2πr²

ds/dt = - 256π/r²  + 2πr

d²s/dt² = -256/(-2) r³ + 2π

d²s/dt² = 128/r³ + 2π

for maxima or minima

ds/dt = 0

- 256 π/r² + 2πr = 0

256 = 2r³

 r = ∛128

d²s/dt² = 128/(∛128)³  + 2π

           = 2π + 1

d²s/dt² > 0

so surface area is minimum

         a + r  = ∛128

  n = 128(∛128)²

   n = ∛128

r = ∛128  ,  n= ∛128

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Answer:

16.97

Step-by-step explanation:

It takes Lena to compress the accordion completely and then stretch it back out to a length of 50cm.

It takes Lena 4.1 seconds to compress the accordion completely and then stretch it back out to a length  of 50cm.

I am assuming the function without a T: [tex]A(t) = 25_{cos}(t)+65[/tex]

The function is graphed in the figure attached, and the blue line is [tex]y = 50cm[/tex].

From the graph we see that the accordion is completely stretched  (has minimum length) at [tex]t = \pi[/tex] seconds, and stretches back  to 50cm at [tex]t = 4.069s[/tex]; therefore, it takes Lena 4.069 seconds to stretch the accordion back again, which to the nearest tenth of a second is  4.1s.

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Answer: 1.3s

Step-by-step explanation:

If you're solving for  [tex]A(t)=25cos( \pi t)+65\\[/tex]

The solution to the system of equations will be;

⇒ (2, 0)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first equation is,

y = - 2x + 4

And, A line goes through (0, 4) and (2, 0).

Now,

For the second linear equation;

The coordinates are,

(-4, -3) (0, -1) , (2, 0) , (6, 2)

Hence, The equation of line passes through the points (-4, -3) and (0, -1).

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

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (0 - (-4))

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3)= 1/2 (x - (-4))

⇒ y + 3 = 1/2 (x + 4)

⇒ y = 1/2x + 2 - 3

⇒ y = 1/2x - 1

Now, We find the value of system of equations;

y = - 2x + 4

y = 1/2x - 1

Solve both above equation, we get;

1/2x - 1 = - 2x + 4

1/2x + 2x = 4 + 1

5/2x = 5

x = 2

And, y = 1/2 (2) - 1 = 0

Thus, The solution to the system of equations will be;

⇒ (2, 0)

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Answer:

A

Step-by-step explanation:

The distance from the top of the window to the base of the wall is 5.4 m.

According to the question,

We have the following information:

The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. And the window is 1 meter high.

Now, we know that the ladder, wall and base will make a right-angled triangle. We can use Pythagoras theorem to find height of the wall.

(Pythagoras theorem: square of hypotenuse = sum of squares of base and height)

Let's take height of the wall to be h meters.

[tex]h^{2}[/tex] = [tex](5.5)^{2} -(3.3)^{2}[/tex]

[tex]h^{2}[/tex] = 30.25-10.89

19.36

h = √19.36

h = 4.4 m

Now, the distance from the top of the wall window to the base of the wall is:

4.4 + height of the window

4.4+1

5.4 m

Hence, the distance from the top of the window to the base of the wall is 5.4 m.

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Answer:

4

Step-by-step explanation:

12÷3=4

Answer:

y=3+5x

Step-by-step explanation:

Add 5x to both sides.

Answer:

15/x

Step-by-step explanation:

x = fish tank

Oliver has to pay an amount of B: $90 with simple interest.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business.

The bank offered him an interest rate of 12% for 6 months.

P = $1500, r= 12% and t = 6 months or 1/2 or 0.5 years.

∴ SI = (1500×12×0.5)/100.

SI = 15×6.

SI = $90.

The amount of simple interest Oliver has to pay is $90.

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