write the equation of the line that passes through (3, 4) and (2,-1) in point slope form

Answer:

The distance from Platform B to Platform C is 26.926 units

Step-by-step explanation:

The given parameters are;

The zip-line course distance from platform A to platform F are given;

On the given graph of the path of travel we have;

Coordinates of the point B = (-25, -20) and the coordinates of the point C = (-15, 5)

The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

Therefore, the distance between B and C is found by substituting (-25, -20) = (x₁, y₁) and (-15, 5) = (x₂, y₂)

Which gives;

[tex]l = \sqrt{\left (5-(-20) \right )^{2}+\left ((-15)-(-25) \right )^{2}} = 26.926 \ units[/tex]

The distance from points B to C = 26.926 units.

Answer:

D. 76

Step-by-step explanation:

a = 90°

a + b + 14 = 180°

90 + b + 14 = 180°

b = 180 - (90 + 14 )

b = 76°

The measure of ∠ b is 76°.

A Cyclic Quadrilateral is defined as a quadrilateral that is contained by a circle is referred to as a cyclic quadrilateral. This indicates that a circle connects the quadrilateral's four vertices. Concyclic vertices are referred to as such. Circumcenter and circumradius are terms used to describe the circle's center and radius, respectively.

According to given figure as:

Angle ∠ a = 90°

∠ a + ∠ b + 14° = 180°   ( three angles of triangle)

90 + ∠ b + 14 = 180°

∠ b = 180 - 90 - 14

∠ b = 180 - 104

∠ b = 76°

Hence, the measure of ∠ b is 76°.

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[tex]\frac{1}{3}x-1=\frac{3}{5}\\ \\5x-15=9\\\\5x=9+15\\\\5x=24\\\\x=\frac{24}{5}\\ \\x=4\frac{4}{5}[/tex]

Answer:

Hey there!

A pie graph is best used for looking at the percentages in each category.

Let me know if this helps :)

Answer:

Pie charts are used to show percentage or proportional data.

Answer:

[tex]\large\boxed{y=-\frac{3}{2}x+\frac{3}{2}}[/tex]

Step-by-step explanation:

Use the two-points slope equation: [tex]\boxed{m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]

Given the two coordinate points of [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex], implement these values into the equation and solve for m.

[tex]m=\frac{(3)-(6)}{(-1)-(-3)}\\\\m=\frac{(-3)}{(2)}\\\\m=-\frac{3}{2}[/tex]

The slope is then placed in the equation - y = -3/2x + b.

Then, insert a value for y and x from the same coordinate point to solve for b.

[tex]6=-\frac{3}{2}(-3)+b\\\\6=\frac{9}{2}+b\\\\\frac{3}{2}=b[/tex]

Then, plug it all in to get [tex]\large\boxed{y=-\frac{3}{2}x+\frac{3}{2}}[/tex].

Answer:

y=-3/2x  

Step-by-step explanation:

First, find the slope with y2-y1/x2-x1=m

3-6                      m=-3/2

--------- =

-1-+-3

Now plug it in to point slope form

Point slope form is y-y1=m(x-x1)

y-3=-3/2(x--1)       Distribute -3/2 to x and 1

y-3=-3/2x-3         Add three on both sides to get y alone

y=-3/2x                Three's cancel out. This is the final equation.

Answer: 12 miles

Step-by-step explanation:

Ok, we know that:

Distance = Time*Speed.

or:

D = T*S

The distance between the house and the school is constant, and suppose that T is the exact time such that you arrive just in time, then:

" If you  drive at an average speed of 45 mph, you arrive 1 min early  for the first bell. "

We can write this as:

D = (T - 1min)*45mi/h.

"If you drive at an average speed 40 mph,  you arrive 1 min late."

We can write this as:

D = (T + 1min)*40mi/h.

So we have a system of linear equations:

D = (T - 1min)*45mi/h.

D = (T + 1min)*40mi/h.

First, 1 hour has 60 mins, then 1 min = (1/60) hours.

We do this change because in the system of equations we have minutes and hours, and we can only work with one unit, now we can write the equations as:

D = (T - (1/60)h)*45mi/h.

D = (T + (1/60)h)*40mi/h.

now, we can write:

D = (T - (1/60)h)*45mi/h. = (T + (1/60)h)*40mi/h.

Now we can solve this for T.

(T - (1/60)h). = (T + (1/60)h)*(40/45)

T = (T + (1/60)h)*(40/45) + (1/60)h

T - T*40/45 = (1/60)h*(1 + 40/45) = 0.031 h

T*(1 - 40/45) = 0.031 h

T = 0.031h/(1 - 40/45) = 0.283... hours

Now, to find the distance to the school we can replace this time in one of the equations:

D = (T + (1/60)h)*40mi/h. = (0.283...h + (1/60)h)*40mi/h = 12 miles.

Answer:

[tex]L = 43[/tex]    and   [tex]M = 47[/tex]

Step-by-step explanation:

Given

[tex]L = 2x + 25[/tex]

[tex]M = 4x + 11[/tex]

Required

Determine the values of L and M

Since L and M are complementary, we have that

[tex]L + M = 90[/tex]

Substitute values for L and M

[tex]2x + 25 + 4x + 11 = 90[/tex]

Collect Like Terms

[tex]2x + 4x = 90 - 11 - 25[/tex]

[tex]6x = 54[/tex]

Divide both sides by 6

[tex]x = \frac{54}{6}[/tex]

[tex]x = 9[/tex]

Substitute 9 for x in the expressions of L and M

[tex]L = 2x + 25[/tex]

[tex]L = 2 * 9 + 25[/tex]

[tex]L = 18 + 25[/tex]

[tex]L = 43[/tex]

[tex]M = 4x + 11[/tex]

[tex]M = 4 * 9 + 11[/tex]

[tex]M = 36 + 11[/tex]

[tex]M = 47[/tex]

Answer:

45.57

Step-by-step explanation:

3 x 2.49 =7.47

4.65

5 x 0.67 = 3.35

5 x 6 = 30

7.47+ 4.65 + 3.35 + 30 = 45.47

One way to do it is by cleverly rewriting terms and using some basic algebraic identities:

[tex]4^n\cdot 2^{-18}=1[/tex].

[tex]2^{2n-18}=2^0[/tex].

[tex]2n-18=0[/tex].

[tex]n=18/2=\boxed{9}[/tex].

Another way would be to use logarithms, namely:

[tex]4^n\cdot2^{-18}=1\implies n=\log_4\Big({\frac{1}{2^{-18}}}\Big)=\boxed{9}[/tex].

Hope this helps.

Answer:

n = 9.

Step-by-step explanation:

4^n = 1 / 2^-18

4^n = 2^18

2^2n = 2^18

2n = 18

n = 9.

Answer:

Approximately 6.642 years

Step-by-step explanation:

The given parameters are;

The amount in the deposit account = $6,000

The time in which the money will have trebled at 11% compound interest, is given as follows;

[tex]A = P\times \left (1 + \dfrac{r}{n} \right )^{n\cdot t}[/tex]

Where;

A = The amount at the end of the period

P = The amount in the deposit = $6,000.00

r = The rate of interest = 11%

t =  The periods that elapsed

n = The number of times the interest is applied per period of time, t = 1

For the money to have trebled, the amount generated at the end of the period will be 200% the amount deposited

Therefore, we have;

Amount, A, at the end of period = 200/100× $6,000 = $12,000

Substituting the values into the formula for the formula, we have;

[tex]\$ 12,000 = \$ 6,000\times \left (1 + \dfrac{0.11}{1} \right )^{1\times t}[/tex]

Which gives;

[tex]\$ 12,000 = \$ 6,000\times \left (1 + {0.11} \right )^{t}[/tex]

[tex]\left (1 .11} \right )^{t} = \dfrac{ \$ 12,000}{\$ 6,000} = 2[/tex]

t = ㏒(2)/(㏒(1.11)) ≈ 6.642 years which is approximately 6 years, 7 months and 24 days

Step-by-step explanation:

i guess that is the correct answer

Answer:

C

Step-by-step explanation:

C on edge

Considering the discount and the sales tax, the equation that represents the situation is:

[tex]C(x) = 0.6955x[/tex]

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

Thus, the equation that represents the cost is:

[tex]C(x) = x \times 0.65 \times 1.07 = 0.6955x[/tex]

A similar problem is given at https://brainly.com/question/23721710

Answer:

[tex]70\sqrt{2}[/tex]

Step-by-step explanation:

Since angle A is 45, the height of the base BC is 10/[tex]\sqrt{2}[/tex] by 1-1-sqrt(2) triangles.

Then we can apply parallelogram area formula.

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

Explanation:

One formula you can use is

A = b*c*sin(theta)

where angle theta is between sides b and c

Note how angle A is between sides AB = 10 and AD = BC = 14.

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

Using that formula gives

A = b*c*sin(theta)

A = 10*14*sin(45)

A = 140*sin(45)

A = 140*sqrt(2)/2 ... use unit circle

A = (140/2)*sqrt(2)

A = 70*sqrt(2)

Answer:

10.3

Step-by-step explanation:

Pythagorean Theorem:

[tex]a^{2} + b^{2} = c^{2} \\[/tex]

a and b being the sides and c being the hypotenuse.

[tex]3.9^{2} + b^{2} = 11^{2}[/tex]

15.21 + [tex]b^{2}[/tex] = 121

[tex]b^{2}[/tex] = 121 - 15.21

[tex]b^{2}[/tex] = 105.79

b = [tex]\sqrt{105.79}[/tex]

b = 10.3

Hope that helped!!! k

Answer:

1)  -15·a·(5·b² + c)

2) h < 4

3) 4·x² - 9

4) 1792

5)  156°

6) 2t cm

7) 2·a·m·(2·m - 3)

8)  10 cm

9) 0.00051

10)  #47,250

11)  -10·p·q

12) 1.35 × 10⁻⁴

13) 320°

14) 20 cm

15) 12·x²·y²

16) 6.36 × 10⁵

17) 4 cm

18)  225°

19) 1034 cm²

20) 29

Step-by-step explanation:

1) The given expression is -75·a·b - 15·a·c

Which can be expressed as -15·a·(5·b² + c)

2) The height, h < 2 × 12/6 = 4

h < 4

3) (2·x - 3)·(2·x + 3) = 4·x² - 9

4) The selling price = 1.12 × 200 × 8 = 1792

5) The interior angle of a polygon is given by the relation;

(n - 2)×180/n for 15, we get;

(15 - 2)×180/15 = 156°

6) 2t cm

7) 4·a·m² - 6·a·m = 2·a·m·(2·m - 3)

8) Slant height = √(8² + 6²) = 10 cm

9) 51 × 10⁻⁵ = 0.00051

10) Cash price = #54,000 × (1 - 0.125) = #47,250

11) -40·p·q÷(-2)² = -10·p·q

12) 0.003 × 0.045 = 1.35 × 10⁻⁴

13) N40°W = 320°

14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm

15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²

16) 636,000 = 6.36 × 10⁵

17) 1/3·π·r²·h₁ = π·r²·h₂

h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3

h₂/12 =  1/3

h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm

18) The angle = 180 + 45 = 225°

19) The total surface area = 22/7×14²/4 +  22/7 ×14 × 20 = 1034 cm²

20) The number is 58/2 = 29.

Answer:

9) 51 × 10⁻⁵ = 0.00051

10) Cash price = #54,000 × (1 - 0.125) = #47,250

11) -40·p·q÷(-2)² = -10·p·q

12) 0.003 × 0.045 = 1.35 × 10⁻⁴

13) N40°W = 320°

14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm

15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²

16) 636,000 = 6.36 × 10⁵

17) 1/3·π·r²·h₁ = π·r²·h₂

h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3

h₂/12 =  1/3

h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm

18) The angle = 180 + 45 = 225°

19) The total surface area = 22/7×14²/4 +  22/7 ×14 × 20 = 1034 cm²

20) The number is 58/2 = 29.

Step-by-step explanation:

Answer:

8 1/3 %

Step-by-step explanation:

Since he bought for 240 and sold for 220, decrease is 20 Rupees.

20/240 = 1/12

100/12 = 8.33333 (Repeated)

0.33333 (repeated) = 1/3

8 1/3 %

Hope this helps!

Answer:

60%

Step-by-step explanation:

Cameras sold on Day 4 = 25, on Day 5 = 40

The difference in numbers of sold cameras = 40 - 25 = 15

The increase is 15 cameras.

Percentage increase:

Answer is 60% increase on Day 5 compared to Day 4

Answer:

Step-by-step explanation:

Given function in the vertex form is,

f(x) = (3x + 13)² + 89

    = [tex]9(x+\frac{13}{3})^{2}+89[/tex] --------(1)

Vertex of the parabola → [tex](-\frac{13}{3},89)[/tex]

If the standard equation of this function is,

f(x) = 9x² + 2x + 1

We will convert it into the vertex form,

f(x) = 9x² + 2x + 1

    = [tex]9(x^{2}+\frac{2}{9}x)+1[/tex]

    = [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}-(\frac{1}{9})^2]+1[/tex]

    = [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-9(\frac{1}{9})^2+1[/tex]

    = [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-(\frac{1}{9})+1[/tex]

    = [tex]9(x+\frac{1}{9})^2+\frac{9-1}{9}[/tex]

    = [tex]9(x+\frac{1}{9})^2+\frac{8}{9}[/tex] -------(2)

Vertex of the function → [tex](-\frac{1}{9},\frac{8}{9})[/tex]

Equation (1) and (2) are different and both the equations have different vertex.

Therefore, given equation doesn't match the equation given in the vertex form of the function.

Answer:568.58

Step-by-step explanation:

Tan(35)=h/1200

1200tan(35)=h

568.57766=h

568.58

Answer is b) 2/5

good luck

Answer:

x=2

Step-by-step explanation:

Answer: The correct answer is point and line. Explanation: These are two of the fundamental undefined terms in geometry. A line segment is a part of a line that has two defined points at each end; therefore "line" and "point" are used in the definition.

Step-by-step explanation:

The undefined terms which are needed to define a line segment are Point and line.

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Answer:

  A = 95238 (only)

Step-by-step explanation:

The question is equivalent to asking what n-digit number consisting only of the digit n will be divisible by n+1. Of the numbers 1, 22, 333, 4444, ... 999999999, the only one is 666666, which is divisible by 7.

The 5-digit integer A is 666666/7 = 95,238. There is only one instance of A.

Answer:

x = 0

Step-by-step explanation:

Hello!

2(x + 4) - 5 = 3x + 3

Distribute the 2

2x + 8 - 5 = 3x + 3

Combine like terms

2x + 3 = 3x + 3

Subtract both sides by 2x

3 = x + 3

Subtract both sides by 3

0 = x

The answer is x = 0

Hope this helps!

Answer: [tex]x=0[/tex]

Simplify both sides of the equation

[tex]2(x-4)-5=3x+3\\(2)(x)+(2)(4)+-5=3x+3(Distribute)\\2x+8+-5=3x+3[/tex]

[tex](2x)+(8+-5)=3x+3[/tex](Combine Like Terms)

[tex]2x+3=3x+3[/tex]

Subtract 3x from both sides

[tex]2x+3-3x=3x+3-3x\\-x+3=3[/tex]

Subtract 3 from both sides

[tex]-x+3-3=3-3\\-x=0[/tex]

Divide both sides by -1

[tex]-x/1=0/-1\\x=0[/tex]

Answer: [tex]3[/tex]

Add

[tex]19/8+5/8=24/8[/tex]

Divide

[tex]24/8=3[/tex]

Answer:

3

Step-by-step explanation:

To add these fractions, find the LCD (least common denominator). Then divide by 8. You get 3.

So your answer will be 3. Hope this helps!

Answer:

mBC ≈ 20.5

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Simply plug in it into the formula.

Step 1: Define variables

c = 16

C = 52°

A = 84°

BC = x

Step 2: Plug into formula

[tex]\frac{16}{sin51} =\frac{x}{sin84}[/tex]

Step 3: Solve

[tex]sin84(\frac{16}{sin51}) = x[/tex]

x = 20.4754

x ≈ 20.5

Answer:

25.

Step-by-step explanation:

I am assuming you only mean the small triangles, not the composite ones.

The  second  triangle set has 3 triangles on bottom row and 1 on the top - total 4.

The 3rd triangle set has 5 triangles on the bottom , 3 on the next up and 1 on the top  - total  9

Following the pattern 4th set will have the number of triaNGLES

7 + 5 + 3 + 1 = 16.

So the 5th will have 9 + 7 + 5 + 3 +1 = 25 triangles.

Answer:

[tex]|RS| = \sqrt[3]{19}[/tex]

Step-by-step explanation:

The computation of the magnitude is shown below:

Data provided in the question

Given points

R(3,7,-1), S(10,-4,0)

Now the distance lies between R and S

RS = (10 ,-4, 0) - ( 3 ,7, -1 )

     = (10 - 3, -4 - 7, 0 - (- 1))

     = (7, - 11, 1 )

After that, the magnitude is determined by using the following calculation part

[tex]|RS| = \sqrt{(7)^2 + (-11)^2 + (1)^2} \\\\ = \sqrt{49 + 121 + 1} \\\\ = \sqrt{121}\\\\ = \sqrt[3]{19}[/tex]

Answer:

  use the actual dimensions on your drawing

Step-by-step explanation:

"Full scale" simply means you use the actual object dimensions on your drawing of it.

If you don't know the meaning of "plan view", "front elevation", or "side elevation," you may need to consult your curriculum materials or any of numerous references on mechanical drawing.

For this object, I would say a "front elevation" is the view from the point marked "Y". A "side elevation" is the view from the point marked "X". A plan view is the view from above.

__

If you draw, on paper, patterns for cutting out the pieces that make up the object, you will be well on your way to making the required drawings. For example, the face ABCPEF would represent the front elevation. (The only thing added on the drawing of it is a dashed line representing hidden line RQ 1 cm below line AB.)

The side elevation is the shape of AQHGF on top of the shape EMLD. On your drawing of it, the line for EM is the same line as the line representing FG.

The top (plan) view is the shape CPNK with lines in the appropriate places to represent the edges EM, FG, and RQ.

__

Orthogonal views of an object like this are different from the kind of drawing you would make if you were trying to make a "net" for folding or calculating surface area. A net has every face actual size. Here, every face is represented the way it would be seen from a given direction. Slanted faces never show up actual size.

Answer:

cos 315°   =   45° reference angle in the 4th quadrant =  √2 /2

And sin 315°    is the negative of this

So  

z = (3) cos 315°  + ( 3i ) sin 315°  =

[   (3/2)√2  ,  - (3/2) √2 i  ]