Write the standard form of the line that passes through the given points using the steps below. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.

(6, 1) and (5, 4)



a) Using variables, write out the formula for the standard form of the equation.

b) Determine the slope of the line.

c) Write the point-slope form of the line.

d) Using the properties of algebra, rearrange the equation into the standard form.

Answer:

  (b) 150 feet

Step-by-step explanation:

You want to know the height of a kite at the end of 225 feet of string, flying at an angle of elevation of 45°.

The 45° angle in the given right triangle tells you this is one of the "special" right triangles. Its side lengths have the ratios ...

  1 : 1 : √2

where √2 is the hypotenuse.

That means the other two legs of this right triangle are ...

  (225 ft)/√2 ≈ 159.099 ft

Rounded to the nearest 50 feet, this is about 150 feet.

__

Additional comment

The sine function relates the angle value to the opposite side:

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse · Sin

  height = (225 ft)·sin(45°) = 225 ft/√2 ≈ 159.099 ft

Answer:

[tex]\sf y =\dfrac{-1}{5}x-\dfrac{1}{4}[/tex]

Step-by-step explanation:

Here, m is the slope and b is the y-intercept.

Substitute the values of m and b in the above equation.

  [tex]\sf m = \dfrac{-1}{5} \\\\b = \dfrac{-1}{4}[/tex]

       Slope y-intercept form:

              [tex]\sf \boxed{y=\dfrac{-1}{5}x - \dfrac{1}{4}}[/tex]

The value of side x is given by (C) 14.7 units approximately.

Given the triangle is a right angled triangle.

Now given also that, Height of triangle is = x units

Base of triangle is = 15 units

Hypotenuse of triangle is = 21 units

So by Pythagoras theorem, we get the sum of squares of base and height is equal to the square of hypotenuse. So,

[tex]x^2+15^2=21^2\\\Rightarrow x^2+225=441\\\Rightarrow x^2=441-225\\\Rightarrow x^2=216\\\Rightarrow x\approx14.7[/tex]

So the value of x is 14.7 units approximately.

Hence the correct option is (C).

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The unit rate for three dollars for 2 1/2 hours of work will be $1.2 using the concept of unitary method.

The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. The unitary technique is a method for determining the value of any necessary quantity by first obtaining the value of the unit (one) quantity.

Here,

$3 for 2.5 hours of work,

1 hour will cost $x,

3/2.5=x/1

2.5x=3

x=$1.2

Using the unitary technique, the unit rate for three dollars for two and a half hours of labour will be $1.2.

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The reason that proves the above conditions is option A. Definition of supplementary angles And Substitution property.

The pair of angles that gives 180° on adding is known as Supplementary angles. In other words, the sum of two supplementary angles is 180°. Two pairs of Supplementary angles will always form a linear pair.

Here we have

∠1,  ∠2,  ∠3, and ∠4 are formed by 2 intersecting lines

As we know      

∠1,  ∠2 is a linear pair and form supplementary angles

=> Sum of the ∠1,  ∠2 will equal 180°  

∠2,  ∠3 is a linear pair and form supplementary angles

=> Sum of the ∠2,  ∠3 will equal 180°  

Therefore,

By the Definition of supplementary angles ∠1+∠2= 180° and ∠2+∠3= 180°

From the above observations,

=> ∠1+∠2= 180° and ∠2+∠3= 180°

=> ∠1 + ∠2 = ∠2 + ∠3  

Therefore,

By the Substitution property ∠1 + ∠2 = ∠2 + ∠3  

Hence,

The reason that proves the above conditions is option A. Definition of supplementary angles And Substitution property

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1. The first figure posses the SSS property.

2. The second figure posses the ASA property.

3. The third figure posses the hypotenuse length property.

4. The fourth figure posses the SAS property.

Given:

1. The first figure shows the SSS property.

Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.

hence the two triangles are congruent.

2. The second figure posses the ASA property.

Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.

hence the two triangles are congruent.

3. The third figure posses the hypotenuse length properety.

RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.

hence the two triangles are congruent.

4. The fourth figure posses the SAS property.

Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.

hence the two triangles are congruent.

Hence we get the required answer.

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For the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 } .

As given in the question,

Given function is equal to :

h(x) = x² +5

Domain of the function h(x) = x² +5 maps by the set { -2, -1, 0, 1, 2 }

Range of the function h(x) = x² +5 is represented by the set as follow :

Substitute the value x = -2, -1, 0, 1, 2 in the function h(x) = x² +5 we get,

h(-2) = (-2)² + 5

       = 9

h(-1) = (-1)² + 5

       = 6

h(0) = (0)² + 5

       = 5

h(1) = (1)² + 5

       = 6

h(2) = (2)² + 5

       = 9

Range of the function is represented by the set : { 5, 6, 9 }

Therefore, for the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 }.

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Answer: -10.

Step-by-step explanation:

30/3 = 10.

However, there is a negative number in the expression.

A rule you need to remember is when you divide 2 numbers with different signs, the answer is negative. If you divide 2 numbers with the same sign, the answer is positive.

30/-3 = -10.

Answer:

Step-by-step explanation:

a. 6.17 , 5.5 , 4.375 , 4.3 , 3.75

b. Everyone except Micah.

C. Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have; 3.75+0.5=3.75 pounds. Then he would have got the coupon as a minimum of 4.25 pounds is required.

Answer:

20

Step-by-step explanation:

3x + 5 should be equal to 65

3x + 5 = 65

3x = 65 - 5

3x = 60

x = 60/3

x = 20

Answer:

y = 1/2x + 3

Step-by-step explanation:

first we change the first equation to slope-intercept form to find the reciprocal slope

2y - 4x = -10

add 4x to both sides

2y = 4x - 10

divide both sides by 2

y = 2x - 5

since perpendicular lines have reciprocal slopes the slope of our new line is 1/2

y = 1/2x + b

to find b we plug in the point

1 = 1/2(-4) + b

1 = -2 + b

add 2 to both sides

3 = b

___

our new line is

y = 1/2x + 3

Answer:

-83+8=19

Step-by-step explanation: how i figured this out is by guessing so i can get more points sorry guys.

Answer:

12oz box of cereal for $3.50 is the better buy

Step-by-step explanation:

12oz=$3.50

36oz = $10.50

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

18oz=$5.40

36oz=$10.80

12 is the marginal cost at the production level of 1000 units.

A differential equation is an equation that contains one or more functions with its derivatives.

The marginal cost represents the additional cost if 1 more unit is produced. So, we can find the marginal cost by computing C(1,001) and subtracting (1,000)

First, let's evaluate the cost at both x= 1,001 and x=1,000

C(1000)=0.002(1000)^2+8(1000)+6000

=0.002(1000000)+8000+6000

=2000+8000+6000

=16000

C(1001)=0.002(1001)^2+8(1001)+6000

=2004.002+8008+6000

=16012

The difference between these costs is $12.002. Rounding to the nearest cent, we find a marginal cost of $12 per unit. Let's see if we get a similar result from the derivative.

Hence 12 is the marginal cost at the production level of 1000 units.

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Answer:

4(y+3)(y+5)

Step-by-step explanation:

4y^2+32y+60 = 4(y^2+8y+15) = 4(y+3)(y+5)

y^2+8y+15 = (y+3)(y+5)

LCD = 4(y+3)(y+5)

Answer:

D

Step-by-step explanation:

the axis of symmetry is a vertical line with equation x = c

where c is the value of the x- coordinates the line passes through.

the line crosses the x- axis at the midpoint of the zeros

given (- 4, 0 ) and (6, 0 ) , that is

zeros are x = - 4 and x = 6

then equation of axis of symmetry is

x = (- 4 + 6) ÷ 2 = 2 ÷ 2 = 1 , that is

x = 1 ← axis of symmetry

Answer: 1/2

Step-by-step explanation: Divide both the numerator and denominator by the GCD (Greatest Common Denominator)

27 ÷ 27

54 ÷ 27      (its 27/54 divided by 27/27

Reduced fraction:

1/2

Therefore, 27/54 simplified to lowest terms is 1/2.

Answer:

c) divide both sides by 8

hope this helps!

Answer:

Its the 3 option

A z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.

Given:

z - score = 2.56

p value at z = 2.56 is:

p = 0.010467

The result is statistically significant: you can reject the null hypothesis and accept the alternative.

This decision is made at significance level α = 0.05.

Therefore a z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.

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An Integral transform that converts a function of a real variable to a function of a complex variable is a Laplace Transformation.

                                             F  =L (f)

We are interested in signal defined for t≥ 0.

The Laplace transformation of a signal function (f) if the function

                                            F = L(f)

                                  F(s) = ∫∞ ₀ f(t) e⁻ᵃᵇ dt

for those a ∈ C for which the integral makes sense.

Lets find Laplace transformation of f(t) =eᵃ

F(s) = ∫₀∞ eᵃ e⁻ᵃᵇ da

      = [ 1/1-a e⁽¹ ⁻ ᵃ⁾ ] = 1 / a-1

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Answer:

Step-by-step explanation:

Slope of a straight line is the gradient of that line.

Formula for gradient is rise over run. Meaning: m = (y2 - y1) / (x2 - x1)

To use this formula, you need 2 points of the straight line. They have already given you one: (8, -3). For the second one, we consider the equation of the line. The y-intercept is given too: -4.

Now, keep in mind, the y intercept is the point of the line that passes from x = 0. Meaning, the point where the line touches the y axis, and at y axis, x = 0. So our second point is (0, -4).

Now as we have 2 points, (8, -3) and (0, -4), we put the values in the formula: m = (y2 - y1) / (x2 - x1) = (-4 - (-3)) / (0 - 8) = -1 / -8 = 1 / 8

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Infinity is denoted by ∞.

∞ = 1/0

∞ times x is ∞

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Infinity is denoted by ∞.

∞ = 1/0

Now,

∞ times x = ∞

Whatever we multiply with infinity will always give us infinity.

Thus,

∞ times x is ∞

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Two approximations of the area of the region between the graph are

(9, 11)

Given;

To calculate two approximations of the area of the region between the graph of the function and the x-axis across the given interval, use the left and right endpoints and the specified number of rectangles. rectangles f(x) = 2x + 3, [0, 2], 4

The graph is positive and the width of each subinterval will be,

a = 0, b = 2, n = 4

Δx = b-a/n = 2-0/4

     = 0.5

Now for different values;

x → f(x) = 2x+3

x₀ = 0 → f(x₀ ) = 2x+3 = 2(0)+3 = 3

x₁ = 0.5 → f(x₁) = 2x+3 = 2(0.5)+3 = 4

x₂ = 1.0 → f(x₂) = 2x2+3 = 2(1) +3 = 5

x₃ =1.5 → f(x₃) = 2x+3 = 2(1.5)+3 = 6

x₄ = 2 → f(x₄) = 2x+3 = 2(2)+3 = 7

The area by using the approximation using 4 approximating rectangles and right endpoints is given by,

A ≈ R₄ = ∑f(x) Δx = ( ƒ(x1)Δx + ƒ (x2)Δx+ ƒ (x3)Δx + ƒ (x4)Δx)

          = 0.5 (4 + 5 + 6 + 7)

          = 0.5 × 22

          = 11

The area by using the approximation using 8 approximating rectangles and left endpoints is given by.

A ≈ L₄ = ∑f(x) Δx = ( ƒ(x0)Δx + ƒ (x1)Δx+ ƒ (x2)Δx + ƒ (x3)Δx)

          = 0.5 (3 + 4 + 5 + 6)

          = 0.5 × 18

          =9

Thus, 9 < Area < 11.

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The unit rate is 32.6 ft/s and approximately 0.03 s/ft.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

An object traveled 691.12 feet in 21.2 seconds.

So, the unit rate as feet per second.

= 691.12/ 21.2

= 32.6 ft/s

and, the unit rate as second per feet

= 21.2/ 691.12

= 0.03 s/ ft

Hence, the unit rate is 32.6 ft/s and approximately 0.03 s/ft

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Answer:

-2 ( 12x - 1 )

Step-by-step explanation:

1) Simplify the equation

To simplify the equation, we have to get rid of any brackets. To do this multiply the term to left of it with everything inside the bracket

Now we can plug these numbers into our equation

2) Collect like terms

The equation we are left with from the previous step would be 10-8-24x

The terms that are similar are 10 and -8.

To collect like terms simplify the terms down to one term

3) Find common factor and simplify

What we are left with from the previous step is -24x+2

To find the common factor you have to find a number that goes it both numbers which for 2 and 24 would be 12.

Hope this helps, have a great day!

The mean is 63.12 using the data given.

Given that,

Calculate the dataset's mean using the output from the following calculator, rounding to the nearest 100th if necessary.

1-Var-Stats

[tex]\bar x[/tex] = 63.1428571429

∑x = 442

∑x² = 28266

Sₓ = 7.71208081364

σₓ = 7.13999942834

n = 7

minX = 48

Q₁ = 58

Med = 66

Q₃ = 69

maxX = 69
​Mean value is defined as sum of all data values divided by the total number of data values

Using the given data output

We get,

Mean = 63.14 (rounded to 2 decimals)

Therefore, The mean is 63.12 using the data given.

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The equation in slope-intercept form that shows the relationship is y = 10x

From the question, we have the following parameters that can be used in our computation:

Rate of beating wings = 10 times per second

The equation in slope-intercept form of the relationship is then represented as

y = Rate of beating wings * x

Where

y is the number of times

x is the wings

So, we have

y = 10 * x

Evaluate

y = 10x

Hence, the equation is y = 10x

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The needed Sample size is 32.2 so that the confidence interval will have a margin of error of 0.06.

We have provided that , An article in a medical journal approx. 18% of operation results complications.

Using the estimate formula, for standard margin of error

Margin of error (E) = Z x √p(1-p)/n

where , E---> margin of error

Z---> estimate value

p----> sample proportion

n -----> Sample size

we have the value of E = 0.06 , p = 18% = 0.18

put all the values in above formula we get,

0.06 = Z × √0.18× 0.82/n

critical value or Z-value for sample proportion 0.18 is 0.91

Now, 0.06 = 0.91 × √0.18×0.82/n

=> √0.14/n= 0.065 => 0.14/n = 0.0043

=> n= 32.2

So, sample size is 32.2

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The value of x in the rectangle is  -5 + 5√3.

A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides are parallel to each other.

Therefore, the area of a rectangle can be found as follows:

area of a rectangle = lw

where

Therefore,

length = x + 10

width = x

Hence,

50 = x(x + 10)

50 = x² + 10x

x² + 10x - 50 = 0

using quadratic formula,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 1

b = 10

c = -50

Therefore,

x = [tex]\frac{-10+\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]  and x =  [tex]\frac{-10-\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]

Hence,

x = -5 + 5√3 and x = -5 - 5√3

Therefore, we can't use negative values

The value of x = -5 + 5√3

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After solving the word problem,  the change in the number of shares of stock he owns, is x-96.

In the given question we have to find  the change in the number of shares of stock he owns.

As given that Eric owns shares of a certain stock. If he sells off 8 shares each month for a year.

Let Eric owns x shares of a certain stock.

If he sells off 8 shares each months for a year.

So as we know that in a year have 12 months.

In 1 month = 8 shares sells

12 months = 12×8 shares sells

12 months = 96 shares sells

So in a year Eric sells 96 shares and he have total x shares.

So the remaining shares are x-96.

Hence, the change in the number of shares of stock he owns, is x-96.

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