How is slope formula and point-slope formula related

Answer:

The area of the enclosed gazebo is [tex]310.4\ ft^{2}[/tex]

Step-by-step explanation:

I assume that is a regular octagon (eight equal aides)

we know that

The area of a regular polygon is equal to

[tex]A=\frac{1}{2}(P)(a)[/tex]

where

P is the perimeter of the polygon

a is the apothem

Find the perimeter P (the octagon has 8 sides)

[tex]P=8(8)=64\ ft[/tex]

[tex]a=9.7\ ft[/tex]

substitute

[tex]A=\frac{1}{2}(64)(9.7)[/tex]

[tex]A=310.4\ ft^{2}[/tex]

=====================================================

Explanation:

The angle EQD is an inscribed angle that cuts off the arc from E to D (the shortest path). Note how central angle ECD also cuts off this same arc. By the inscribed angle theorem, we know that

inscribed angle = (1/2)*(central angle)

angle EQD = (1/2)*(angle ECD)

We can multiply both sides by 2 and flip the equation to get

angle ECD = 2*(angle EQD)

Now replace "angle EQD" with 5x+2

angle ECD = 2*(5x+2)

2*(5x+2) = angle ECD

Next, replace "angle ECD" with 104 as this is the measure of this central angle.

2*(5x+2) = angle ECD

2*(5x+2) = 104

From here, we solve for x

2*(5x+2) = 104

2*5x + 2*2 = 104

10x + 4 = 104

10x+4-4 = 104-4 ..... subtracting 4 from both sides

10x = 100

10x/10 = 100/10 ...... dividing both sides by 10

x = 10

Answer:

Option C. Graph C

Step-by-step explanation:

we have

[tex]y=(x-3)^{2}-25[/tex]

This is the equation of a vertical parabola open upward (vertex is a minimum)

The vertex is the point (3,-25)

therefore

The graph is C

The graph in the attached figure

Answer:c

Step-by-step explanation:

Answer:

29 red marbles

Step-by-step explanation:

Call R the number of red marbles and B the number of black marbles.

According to the second sentence, R = 2B + 3.

According to the third sentence, R + B = 42.

Now we have 2 equations, 2 unknowns. Sub the first into the second since it already has R isolated:

2B + 3 + B = 42

3B = 39

B = 13

Now sub this into either of the original equations (I'll use the first):

R = 2(13) + 3

R = 29

Answer:

Step-by-step explanation:

Put x = -7 to the equation -4x - 9y = -26, and solve it for y:

-4(-7) - 9y = -26

28 - 9y = -26            subtract 28 from both sides

-9y = -54           divide both sides by (-9)

y = 6

Answer:

x = 8

Step-by-step explanation:

Step 1 : Simplify the equation

3(x-5) + 7x = 65

3x - 15 + 7x = 65

Step 2 : Make x the subject

3x + 7x = 65 + 15

10x = 80

x = 80/10

x = 8

!!

Answer:

The answer is B

Step-by-step explanation:

The reasoning behind this is because in the second step, if you were to add all of the numbers you would get the solution of -5x or something like that.

Hope this helps!

Answer:

D. x + 5

Step-by-step explanation:

2x^4 + 20x^3 + 50x^2

= 2x^2 (x^2 + 10x + 25)

= 2x^2 (x + 5)^2

= 2x^2 (x + 5) (x + 5)

Answer

D. x + 5

For this case we have the following expression:

[tex]2x ^ 4 + 20x ^ 3 + 50x ^ 2[/tex]

It is observed that we can extract common factor [tex]2x ^ 2[/tex], since it is common in the three terms:

[tex]2x ^ 2 (x ^ 2 + 10x + 25) =[/tex]

If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.

Rewriting the expression we have:

[tex]2x ^ 2 ((x + 5) (x + 5))[/tex]

Thus, one of the factors of the original expression is[tex]x + 5[/tex].

Answer:

Option D

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{1}{2}[/tex] and (a, b) = (- 7, 2), hence

y - 2 = [tex]\frac{1}{2}[/tex] (x - (- 7)) → D

y - 2 = [tex]\frac{1}{2}[/tex](x + 7)

The point-slope form of the equation will be [tex]y-2 = \dfrac{1}{2}(x-(-7))[/tex]. The correct option is D.

In mathematics, slope refers to the measure of the steepness or inclination of a line or a curve. It quantifies the rate at which one variable changes with respect to another variable. The slope is commonly denoted by the letter "m."

Given that the slope of the line is 1/2. The point through which the line is passing is (-7,2).

The general form of the equation of the line passing through the point (-7,2) and the slope is 1/2 can be written as,

[tex]y-y_1 = m(x-x_1)[/tex]

The equation of the line in point-slope form can be written as,

[tex]y - y_1 = m(x-x_1)\\y-2=\dfrac{1}{2}(x-(-7))[/tex]

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Answer:

Let j = amount Jasmine spent, k = amount Karen spent, and m = amount Maggie spent.

m = 3k, k = (1/2)j

j + k + m = $60

2k + k + 3k = $60

6k = $60

k = $10, m = $30, j = $20

Jasmine spent $20, Karen spent $10, and Maggie spent $30.

Answer:

5e^(3x+7)=21

e^(3x+7)=4.2

(3x+7)lne=ln4.2

lne=1

3x+7=1.435

3x= -5.565

x= -1.855

To solve the equation [tex]5e^{3x}+7=21[/tex], isolate the exponential term, take the natural logarithm of both sides, and then solve for x. This results in x ≈ 0.3362.

To solve the equation [tex]5e^{3x}+7=21[/tex], follow these steps:

First, isolate the exponential term by subtracting 7 from both sides:

[tex]5e^{3x} = 14[/tex]

Next, divide both sides of the equation by 5:

[tex]e^{3x} =\frac{14}{5}[/tex]

Now, take the natural logarithm (ln) of both sides:

[tex]ln(e^{3x}) = ln(\frac{14}{5})[/tex]

Since the natural logarithm and the exponential function are inverse operations, the left side simplifies to:

[tex]{3x} = ln(\frac{14}{5})[/tex]

Finally, solve for x by dividing by 3:

[tex]x =\frac{1}{3}\times ln(\frac{14}{5})[/tex]

Using a calculator, this results in:

x ≈ 0.3362

Answer:

d

Step-by-step explanation:

i jut did it in google calculator (trust me)

Hello There!

First, our formula for finding the volume of a cylinder is Pi*radius^2*height

Now, let'd get into solving for the volume. First, we need to find the radius so in this problem, we are given the diameter so to find the radius, we just divid the diameter by 2. Once we divide, our radius comes out to 6.5.

Next, in our formula it says we have to square our radius so we would multiply 6.5 by 6.5 to get a product of 42.25.

Lastly, we need to multiply 42.25 by our height which is our last step in our formula. Once we multiply 42.25 by the height of the cylinder which is 11, we get a product of 464.75.

464.75 rounded to the nearest tenth is 464.8

Your answer is the first one

Answer:

6

Step-by-step explanation:

2 x 6 = 12/2 = 6

Answer:

A = 6 units ^2

Step-by-step explanation:

The area of a triangle is found by

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 (6) *2

A = 6 units ^2

[tex]0-(6+4i)=0-6-4i=-6-4i[/tex]

The additive inverse of the complex number 6+4i is -6-4i because it negates both the real and imaginary parts, resulting in a sum of zero when added to the original number.

The additive inverse of a complex number is a number that, when added to the original number, yields a sum of zero. For the complex number 6+4i, its additive inverse is found by changing the sign of both the real and the imaginary parts. Therefore, the additive inverse of 6+4i is -6-4i.

Answer:

[tex]\large\boxed{\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=3\ \text{and}\ x=5.\\(look\ at\ the\ picture)\\\\f(3)=1,\ f(5)=2\\\\\text{Substitute:}\\\\\dfrac{f(5)-f(3)}{5-3}=\dfrac{2-1}{2}=\dfrac{1}{2}[/tex]

Answer: D. Horizontal stretch by a factor of 3.

Step-by-step explanation:

Below are some transformations for a function [tex]f(x)[/tex]:

If [tex]f(x)-k[/tex], then it is shifted "k" units down.

If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.

If [tex]-f(x)[/tex], then it is reflected across the x-axis.

If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".

If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].

Based on this, the transformations done to the function [tex]f(x)=x[/tex]  to get the function [tex]g(x)=-3(x-4)-7[/tex] are:

- It is shifted 7 units down.

- It is shifted rigth 4 units.

- It is reflected over the x-axis.

- It is vertically stretched by a factor of 3.

Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex]  to get the function [tex]g(x)=-3(x-4)-7[/tex] is:

Horizontal stretch by a factor of 3.

Answer:

The farmer would need 80 posts.

Step-by-step explanation:

If one side of the garden is 10m long, and the garden is a square, we can assume that all 4 sides will be 10m. That makes it 40m in total. Times 40×2 and you get 80.

The simultaneous Equations for both total costs are;

Company A: y = 45x + 150

Company B: y = 50x + 125

Thus, both companies charge the same amount of money for food truck permits for 5 months

How to find the equation of the total charges?

We are told that;

Company A charges a one time fee of $150 and $45 per month.

Company B charges a one time fee of $125 and $50 per month.

Thus, using the concept of the equatiom of a line In slope intercept form, we have:

Company A: y = 45x + 150

Company B: y = 50x + 125

let's use the number 5 for x as an example

45(5) + 150 = 375

50(5) + 125 = 375

So both companies charge the same amount of money for food truck permits for 5 months.

Complete question is;

Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. Write an equation or a system of equations and explain what each solution tells you about the situation

Answer:

x = 25

Step-by-step explanation:

The 2 given angles form a straight angle and are supplementary, that is

2x + 2 + 5x + 3 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25

[tex]x^2<49\\x<7 \wedge x>-7\\x\in(-7,7)[/tex]

Answer:

130 degrees

Step-by-step explanation:

let the angle be x

2x+45+55=360(Sum of angles in quad)

2x=260

x=130

The measure of <Q is 130 degree.

There are four angles in a quadrilateral. Its inner angles add up to 360 degrees.

The angle sum property of a Quadrilateral states that the sum of all four inner angles is 360 degrees.

We have

<T = 55

<R= 45

let us consider the two angles are Equal.

Using angle sum Property

<T + <R + Q + <S = 360

45+ 55 + x + x = 360

100 + 2x = 360

2x = 260

x = 130

Thus, the measure of <Q is 130 degree.

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Answer:

[tex]-(4x^2)+6(x^4)y[/tex]

Step-by-step explanation:

Here apply the law of indices where ;

[tex]A^x*A^y=A^{x+y}[/tex]

Given;

[tex]\frac{48x^4y-72x^6y^2}{-12x^2y} \\\\\\\frac{-12x^2y(4x^2-6x^4y^2)}{-12x^2y} \\\\\\=-4x^2+6x^4y\\\\\\=-(4x^2)+6(x^4)y[/tex]

Final answer:

To rationalize the denominator and simplify the expression 6 / (5-3), multiply the numerator and denominator by 1/2. Then, simplify the expression to get 3/1 = 3.

Explanation:

To rationalize the denominator and simplify the expression 6 / (5-3), we can start by multiplying the numerator and denominator by a skillfully chosen factor. In this case, we can choose 1/2 as the factor.

The numerator becomes 6 * 1/2 = 3, and the denominator becomes (5-3) * 1/2 = 2/2 = 1.

Therefore, the simplified expression is 3/1 = 3.

Answer:

5/8

Step-by-step explanation:

first plug in for x & y, then solve. you should get 5/8

2 -2 +5 +0 / 2 +3 +5 -2

5/8

Answer:

125/32

Step-by-step explanation:

1box = 1400/7 = 200

200×3=600

1400+600=2000

Answer:

2000

Step-by-step explanation:

Given :Workers have packed 1,400 glasses in 7 boxes.

To Find :If they pack 3 more boxes, how many glasses will they have packed in all?

Solution:

Workers packed no. of glasses in 7 boxes = 1400

Workers packed no. of glasses in 1 box = [tex]\frac{1400}{7}[/tex]

Workers packed no. of glasses in 3 boxes = [tex]\frac{1400}{7} \times 3[/tex]

                                                                      = [tex]600[/tex]

So, initially they packed 1400 glasses

If they pack 3 more boxes so, the pack 600 glasses more

So, The total no. of glasses have packed by workers = 1400+600 = 2000

Hence they have packed 2000 glasses in all.

Answer:

10

Step-by-step explanation:

Range=big-small=34-16=18

Interquartile range=big number in box-small number in box= 29-21=8

The different between the two is 18-8=10

Answer:

The difference of range and interquartile range is 10.

Step-by-step explanation:

Consider the provided information.

From the box plot we can identify:

The lowest value is 16

The first quartile is 21

The 2nd quartile or median is 26

The 3rd quartile is 29

The highest value is 34

Range is the difference of the highest value and lowest value of the data set.

Range = 34 - 16 = 18

Interquartile range is the difference of the 3rd quartile from the 1st quartile.

IQR: 29 - 21 = 8

Thus, the difference of range and interquartile range is:

18 - 8 = 10

Hence, the difference of range and interquartile range is 10.

Answer: cubic meters : m³

Step-by-step explanation:

Cylinder volume is the product of area of the base by height.

Area of the base is the product of π·radius² = square meters : m²

Volume = square meters·meters =  m²·m = cubic meters : m³

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

Look to the attached file

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

g(x)=x^2+3

g(x)=(4^2)+3

g(x)=16+3=19

if g of x = x squared + 3, then 4 squared = 16, plus 3 = 19

Answer:

option(B)  g(4) =19.

Step-by-step explanation:

Given:If g(x) = [tex]x^{2}[/tex] + 3.

To find: g(4).

Solution: We have given that  

g(x) = [tex]x^{2}[/tex] + 3.

for x=4.

g(4) = [tex]4^{2}[/tex] + 3.

g(4) = 16+3

g(4) =19.

Therefore, option(B)  g(4) =19.