How do I simplify the expression

Answer:

Procedure:

1) Form a system of 3 linear equations based on the two zeroes and a point.

2) Solve the resulting system by analytical methods.

3) Substitute all coefficients.

Step-by-step explanation:

A quadratic function is a polynomial of the form:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.

A value of [tex]x[/tex] is a zero of the quadratic function if and only if [tex]y = 0[/tex]. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: [tex]A(x,y) = (r_{1}, 0)[/tex], [tex]B(x,y) = (r_{2},0)[/tex] and [tex]C(x,y) = (x,y)[/tex]

Based on such information, we form the following system of linear equations:

[tex]a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0[/tex] (2)

[tex]a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0[/tex] (3)

[tex]a\cdot x^{2} + b\cdot x + c = y[/tex] (4)

There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

[tex]a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

And finally we obtain the equation of the quadratic function given two zeroes and a point.

Answer:

[tex]\frac{8}{5}[/tex]

Step-by-step explanation:

The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.

Usually represented with the variable [tex]k[/tex], it is given by:

[tex]\frac{y}{x}=k[/tex] for coordinates (x, y).

This relationship can be written as [tex]y=kx[/tex] which is also the layout for a proportional relationship.

Since coordinates are written (x, y), for point (5, 8), substitute [tex]x=5, y=8[/tex] to get the constant of variation:

[tex]8=5k,\\k=\boxed{\frac{8}{5}}[/tex]

Answer:

8/5

Step-by-step explanation:

Given that y varies directly with x , therefore ,

[tex]\implies y \propto x[/tex]

Let k be the constant . Therefore ,

[tex]\implies y = k x[/tex]

When the point is (5,8) ,

[tex]\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}[/tex]

Hence the constant of variation is 8/5.

Answer:

ayan po answer nasa picture po

Step-by-step explanation:

where

x

is the number you are trying to compute the (2/3) rds of

Answer:

wait whats your question

Step-by-step explanation:

Answer:

1/64 is 0.015625 in decimals

Answer:

y = -4/3 x - 1/3

Step-by-step explanation:

y = -4/3 x + b

5 = -4/3 (-4) + b

15 = 16 + 3b

b = -1/3

y = -4/3 x - 1/3

The equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.

To find the equation of line b, which is parallel to line a and passes through the point (-4,5), we need to use the fact that parallel lines have the same slope.

Given that line a has the equation y = (3/4)x - 3, we can determine its slope. The slope of line a is the coefficient of x, which is 3/4.

Since line b is parallel to line a, it will also have a slope of 3/4.

Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the slope and the coordinates (-4,5) into the equation to solve for the y-intercept, b.

5 = (3/4)(-4) + b

Simplifying, we have:

5 = -3 + b

Adding 3 to both sides, we find:

b = 8

Therefore, the equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.

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Answer:

5x+8x+17-9+2y

13x+8+2y

Answer:

13x+8+2y

Step-by-step explanation:

5x+8x=13x

17–9=8

2y=2y

Answer:

C

Step-by-step explanation:

Given

sinR = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

This is a 5- 12- 13 triangle with legs PQ = 5, QR = 12, hypotenuse PR = 13

cosR = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QR}{PR}[/tex] = [tex]\frac{12}{13}[/tex]

Answer:

1.likely. 11.likely

2. likely. 12.likely

3. likely. 13.likely

4. unlikely 14. unlikely

5. likely. 15. likely

6. likely

7. likely

8. likely

9. likely

10. likely

Step-by-step explanation:

im correct if I'm rwong

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\dfrac{(9 \times5) 2}{3}}[/tex]

[tex]\huge\boxed{9 \times 5 = \bf 45}[/tex]

[tex]\huge\boxed{ = \dfrac{45(2)}{3}}[/tex]

[tex]\huge\boxed{45(2) = \bf 90}[/tex]

[tex]\huge\boxed{= \dfrac{90}{3}} \\\\\huge\boxed{= \dfrac{90\div3}{3\div3}}\\\\\huge\boxed{= \dfrac{30}{1}}[/tex]

[tex]\huge\boxed{= \bf 30}[/tex]

[tex]\huge\boxed{\rm{Answer: 30}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

30

Step-by-step explanation:

Multiply 9 and 5 to get 45.

Multiply 45 and 2 to get 90.

Divide 90 by 3 to get 30.

Answer:

x=0.5

Step-by-step explanation:

10x-40-5x=2x+30

5x+10=25x

10=20x

x=0.5

Answer:

The surface area of the pyramid is 16.65 m^2.

Step-by-step explanation:

Answer:

24) x = 9.2

25) x = 30.8

Step-by-step explanation:

Given

See attachment for triangles

Solving (24)

To solve for x, we make use of cosine formula

i.e.

cos(40) = adjacent ÷ hypotenuse

So, we have:

cos(40) = x ÷ 12

Multiply both sides by 12

12 cos(40) = x

12 * 0.7660 = x

x = 9.2

Solving (25)

To solve for x, we make use of sine formula

i.e.

sin(25) = opposite ÷ hypotenuse

So, we have:

sin(25) = 13 ÷ x

Multiply both sides by

x sin(25) = 13

Divide by sin(25)

x = 13 ÷ sin(25)

Using a calculator

x = 30.8

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

1. a = 68

b = 112

c = 68

2. a = 127

3. a = 35

b = 40

c = 35

d = 70

4. a = 20

b = 70

c = 20

d = 70

e = 110

5. a = 90

b = 90

c = 42

d = 48

e = 132

6. a = 70

b = 55

c = 25

Answer:

5418.54 ft

Step-by-step explanation:

So sea level is 0, okay? So Nadia (her name is more than 3 letters and I'm lazy so from now on she'll be reffered to as "N") is at -19. 26 ft. N goes up 5,437.8 ft, so we add this value on.

-19. 26+ 5437.8= 5418.54

Now just add on the units!

Hope this helps!

Answer:

Answer:

5418.54 ft

Step-by-step explanation:

Answer:

5418.54 ft

Step-by-step explanation:

So sea level is 0, okay? So Nadia (her name is more than 3 letters and I'm lazy so from now on she'll be reffered to as "N") is at -19. 26 ft. N goes up 5,437.8 ft, so we add this value on.

-19. 26+ 5437.8= 5418.54

Answer:it’s C

Step-by-step explanation:

The system of inequalities can be used to determine, if The selling price of model A was less than $8,000, The selling price of model B was at most $10,000, are x < 8000 × 0.88, and y < 1000 × 0.85.

The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.

It is one of the most crucial things for a business to decide. It is significant since it determines whether it will survive. Sales of a product are directly impacted by its price.

Given:

The selling price of model A was less than $8,000,

The selling price of model B was at most $10,000,

The price of model A is decreasing at a rate of 12% each year,

The price of model B is decreasing at a rate of 15% each year,

Write the inequality as shown below,

Assume the selling price of A is x,

x < 8000

Assume the selling price of B is y,

y < 1000

The decreased selling price of A,

x < 8000 × (1 - 0.12) = x < 8000 × 0.88

The decreased selling price of B,

y < 1000 × (1 - 0.15) = y < 1000 × 0.85

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Answer:

-7

Step-by-step explanation:

63/9 but there is an odd number of negative numbers so negative answer

Answer:

divide 3 by the amount of feet to get to the yards

Step-by-step explanation:

For every three feet, there's always one yard

so to do this only given feet, we'll need to divide the amount of feet by 3 to represent the amount of yards

Answer:

The equation is:

Y=2x-1

Answer:

13

Step-by-step explanation:

Calculate the length using the distance formula

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

with (x₁, y₁ ) = (- 5, 4) and (x₂, y₂ ) = (7, - 1)

d = [tex]\sqrt{(7-(-5))^2+(-1-4)^2}[/tex]

   = [tex]\sqrt{(7+5)^2+(-5)^2}[/tex]

   = [tex]\sqrt{12^2+25}[/tex]

   = [tex]\sqrt{144+25}[/tex]

   = [tex]\sqrt{169}[/tex]

   = 13

Answer:

B) 67°C.

Step-by-step explanation:

Newton's Law of Cooling is given by:

[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]

Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.

We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.

And we want to find the temperature of the coffee after four minutes.

First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:

[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]

Take the integral of both sides:

[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]

Integrate:

[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]

Raise both sides to e:

[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]

The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:

[tex]\displaystyle T=Ce^{kt}+A[/tex]

We are given that A = 25. Hence:

[tex]\displaystyle T=Ce^{kt}+25[/tex]

Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:

[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]

Hence:

[tex]T=75e^{kt}+25[/tex]

We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.

So, T = 90 given that t = 1. Substitute:

[tex]90=75e^{k(1)}+25[/tex]

Solve for k:

[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]

Therefore:

[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]

Then after four minutes, the temperature of the coffee will be:

[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]

Hence, our answer is B.

Step-by-step explanation:

0.7 decimeter =

70,000,000 nanometers

Answer:

Step-by-step explanation:

1 . ( n + 4 ) / ( 2m - 3 )

The gradient (slope) is

= ( change in y direction ) / ( change in x direction )

= ( n - (-4) ) / ( 2m - 3 )

= ( n + 4 ) / ( 2m - 3 )

2.

A line parallel to the x-axis will always have the equation of y = #. This is because all along that line, every value of x, y will still equal the same number. For example, a line parallel to the x-axis that crosses the y-axis at 2, will be y = 2. If it is in the negative range, it's the same concept, for example if it crossed the y-axis at -4, the equation would be y = -4.

Example - Computational Knowledge Engine

3.

To understand the slope of a line parallel to y axis, let us consider the figure given below.

1 . The gradient (slope) is ( n + 4 ) / ( 2m - 3 )

2. n = -4

3. m is not defined.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

points (2m, n) and (3, -4).

1 . The gradient (slope) is

= ( change in y direction ) / ( change in x direction )

= ( n - (-4) ) / ( 2m - 3 )

= ( n + 4 ) / ( 2m - 3 )

2. A line parallel to the x-axis will always have the equation of y = x.

The line is therefore horizontal so gradient = 0

(n+4) / (2m-3)= 0

n = -4

(iii) Find the value of m if the line is parallel to the y-axis

(n+4) / (2m-3)= gradient

(n+4) / (2m-3)= 1

We know n = -4 from part (ii) then

(-4+4) /(2m-3)= 1

0/(2m-3) = 1

0 = 1 The 'm' vanishes

Hence, m is not defined.

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Step-by-step explanation:

Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)

= 200+625-1156 ÷ (2000)

= 1069 ÷2000

Cos A = 0.5345

A= cos inverse 0.5345

A = 57.7

Answer:

57.7

Step-by-step explanation:

took the test

Answer:

a= (π/4) + (kπ/2)

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

9514 1404 393

Explanation:

This is an identity.

  cos²(A) +cos²(A)cot²(A) = cot²(A)

Transforming the left side, we have ...

  = cos²(A)(1 +cot²(A))

  = cos²(A)csc²(A)

  = (cos(A)/sin(A))²

  = cot²(A)

Answer:

is there is no value of April

Step-by-step explanation:

so the value of the month April is zero