What is the slope of the line that passes through
the points (2,
-4) and (5, 2)? Write your
answer in simplest form.

Answer:

71

Step-by-step explanation:

The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).

An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.

A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.

predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.

By lagranier multi plur

of = hog

(2x, is, 22>= 25-47

8x=42

10x + 2 = 42

2

28

2x=4, 4= 2

=2

722 (4)

(4.9,2) = (4.2-8)

(4,2-8)= 84

Learn  more about constraints here https://brainly.com/question/6073946

#SPJ4

Answer:

[tex]-4\leq x[/tex] is what it looks like simplifed. In word form this means x is greater than all values equal to or greater than four. This means that the FOURTH graph is correct.

Step-by-step explanation:

[tex]13-2x\leq 37+4x = -24\leq 6x.[/tex]

Simplify this into [tex]-4\leq x[/tex] or [tex]x\geq -4[/tex]

This in words translates into x is greater than or equal to the value of four. Meaning all values larger than 4 and 4 are equal to x

Meaning the 4th graph is correct because it shows exactly what the word form says.

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

Have a great day,

Nish

The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.

Mixtures refers to substances which are composed of two or more substances physically combined together.

The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.

Let the volume of the 0.3 % concentration toothpaste required be x.

Final volume of toothpaste = (100 + x) mL

Amount of mixture = 0.8 * (100 + x)

100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)

solving for x

110 + 0.3x = 80 + 0.8x

110 - 80 = 0.8x - 0.3x

30 = 0.5x

x = 60

Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.

In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.

Learn more about mixtures at: https://brainly.com/question/2331419

#SPJ1

The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x

It is important to note that

sin A = opposite/ hypotenuse

cos A = adjacent/ hypotenuse

Then,

opposite = [tex]\sqrt{1} - x[/tex]

Hypotenuse = [tex]\sqrt{1} + x[/tex]

Let's find the adjacent side using the Pythagorean theroem

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

[tex]1 + x^2 = 1 - x^2 + x^2[/tex]

[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]

cos A = x/hypotenuse

[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]

cos A = √(1 + x²)/ (1 - x²) /√1 + x

Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x

Learn more about trigonometric identities here:

https://brainly.com/question/7331447

#SPJ1

The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

For given question,

We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]

We need to find the sum of given convergent series.

Given series is a geometric series with ratio r = sin(1)

The first term of the given geometric series is [tex]a_1=sin(1)[/tex]

So, the sum is,

= [tex]\frac{a_1}{1-r}[/tex]

= sin(1) / [1 - sin(1)]

This means, the series converges to sin(1) / [1 - sin(1)]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

= [tex]\frac{sin(1)}{1-sin(1)}[/tex]

= [tex]\frac{0.8415}{1-0.8415}[/tex]

= [tex]\frac{0.8415}{0.1585}[/tex]

= 5.31

Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

Learn more about the convergent series here:

https://brainly.com/question/15415793

#SPJ4

The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)

In this question we must find a kind of polynomial whose form offers the best approximation to the point set, that is, the least polynomial whose mean square error is reasonable.

In a graphing tool we notice that the least polynomial must be a cubic polynomial, as there is no enough symmetry between (10, 9.37) and (14, 8.79), and the points (6, 3.88), (8, 6.48) and (10, 9.37) exhibits a pseudo-linear behavior.

The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)

To learn more on cubic polynomials: https://brainly.com/question/21691794

#SPJ1

Answer:

18.0  cm to 1 decimal point.

Step-by-step explanation:

First  work out the unknown side (s) of the right triangle using the Pythagoras theorem:

s^2  = 13^2 - 5^2

       = 169 - 25 = 144

s = sqrt 144 = 12 cm.

Now consider the other triangle:

s = 12

The missing angle = 180 - 65 - 40 = 75 degrees.

By the Sine Rule:

x / sin 75 = 12 / sin40

x = 12 sin 75 / sin 40

  = 18.03

    -

Answer:

5x^2+22x-12         x cannot be -5, -4, -2

(x+5)(x+4)(x+2)

Step-by-step explanation:

In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:

x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)

x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)

Now that you have factored out the two quadratics, plug them into the equation.

    5x        -       3

(x+4)(x+2)      (x+5)(x+2)

Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.

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

(x+5)(x+4)(x+2)      (x+5)(x+4)(x+2)

Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:

5x^2+25x - (3x+12)     =    5x^2+22x-12         x cannot be -5, -4, -2

 (x+5)(x+4)(x+2)               (x+5)(x+4)(x+2)

The missing side length of the right triangle are as follows;

v = 1 units

u = 2 units

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Therefore,

tan 60 = opposite / adjacent

tan 60 = √3 / v

cross multiply

v = √3 / tan 6-

v = √3 / √3

v = 1

Hence,

sin 60 = opposite / hypotenuse

sin 60 = √3 / u

cross multiply

u = √3 / sin 60

u = √3 × 2 / √3

u = 2√3 / √3

u = 2

learn more on right triangle here: https://brainly.com/question/14324872

#SPJ1

The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.

The numeric value of an expression is found replacing each letter by it's attributed value.

In this problem, the expression is:

-a² - 2bc - |c|

The attributed values are:

a = -3, b = -5 and c = 2

Hence the numeric value will be given by:

-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.

More can be learned about the numeric value of an expression at https://brainly.com/question/14556096

#SPJ1

Answer: [tex]\displaystyle\\\frac{x^3}{y^7}[/tex].

Step-by-step explanation:

[tex]\displaystyle\\x^3y^{-7}=\frac{x^3}{y^7} .[/tex]

The standard form of the given quadratic equation in  factored form is

(x+2) (x-6) = x²-4x-12

(x-4) (x+3) = x²-x-12

(x-12) (X+1) = x²-11x-12

(x-3) (x+4) = x²+x-12

what are quadratic equations?

A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero

To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.

f(x) = (x+2) (x-6)

x²+2x-6x-12

x²-4x-12

similarly, the standard form of equations 2,3 and 4 are :

(x²-x-12)

(x²-11x-12)

(x²+x-12)

Learn more about quadratic function here:

brainly.com/question/4119784

#SPJ1

Answer:

B, D, A, C

Step-by-step explanation:

f(x) = (x + 2)(x – 6)

✔ B

f(x) = (x – 4)(x + 3)

✔ D

f(x) = (x – 12)(x + 1)

✔ A

f(x) = (x – 3)(x + 4)

✔ C

Answer: -9

Step-by-step explanation:  You might think that the smallest two numbers are 11 and 1 but there are negative numbers. 1 - (-9) is equal to 10. 1 x (-9) is -9.

Answer:

86.

Step-by-step explanation:

His total score is 99 + 85 + x where x is score on third test,

99 + 85 + x = 3 *90   (as his average must be 90, so:

184 + x = 270

x = 270 - 184

  =   86.

Answer:

86

Step-by-step explanation:

Let x be the required score for Lamar's third test in order to get an average of 90 or higher.

Start with the initial equation:

[tex]\frac{99+85+x}{3}\geq 90[/tex]

Simplify the numerator in the fraction:

[tex]\frac{184+x}{3}\geq90[/tex]

Multiply both sides by 3 to cancel out division on left side of equation:

[tex]184+x\geq 270[/tex]

Subtract 184 from both sides to isolate the x variable:

[tex]x\geq86[/tex]

Leaving us with x must be greater than or equal to 86.

Answer:

m = -x

Step-by-step explanation:

For the given function f(x) = 5x² + 2x - 3,

Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).

Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).

Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.

The x-intercepts of a function or equation are obtained at y = 0.

Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.

To calculate the x coordinate of vertex(h, k), use the formula mentioned below:

h = -b/2a

When the function is in the form of ax² + bx + c.

Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.

Thus, the required coordinates of the vertex are obtained as (h, k).

It is given that,

f(x) = 5x² + 2x - 3

Part A: Finding the x-intercepts:

Substituting y = 0 i.e., f(x) = 0;

⇒ 5x² + 2x - 3 = 0

On simplifying/factorizing,

⇒ 5x² + 5x - 3x - 3 = 0

⇒ 5x(x + 1) - 3(x +1) = 0

⇒ (5x - 3)(x + 1) =0

∴ x = 3/5 or x = -1

Thus, the x-intercepts are (3/5, 0) and (-1, 0).

Part B: Finding the vertex of the given function:

We have h = -b/2a

From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3

So, h = -2/2(5) = -1/5 = -0.2

Then, on substituting h = x = -0.2 in the function we get

k = 5(-0.2)² + 2(-0.2) - 3

k = -3.2

Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).

Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.

Part C: Steps to graph f(X):

Step 1: Plot the x-intercepts in the coordinate plane

Step 2: Plot the vertex of the function

Step 3: draw a curve line passing through them, opening towards up.

Thus, the graph of the given function is plotted as shown below.

Learn more about the x-intercepts of a function here:

https://brainly.com/question/12778829

#SPJ1

The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

The given coordinates on the graph are;

(-3, 0), (0, 3), (2, 4), and (5, 5)

The coordinates of the starting point of the graph = (-3, 0)

Shape of the graph = Extends from point (-3, 0), upwards and to the right

Therefore;

As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.

However, given that the graph is for a square root function, the correct option is option C;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

Learn more about functions and variables here:

https://brainly.com/question/8590101

https://brainly.com/question/14288182

https://brainly.com/question/13097291

#SPJ1

Applying the angle bisector and triangle proportionality theorem, the solutions are:

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6.

The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.

16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]

Cross multiply

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² - 3x² + 3x - 4 + 6x = 0

-2x² + 9x - 4 = 0

Factorize -2x² + 9x - 4

(−2x + 1)(x − 4)

-2x = -1

x = 1/2

or

x = 4

17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)

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

4x² + 8x + 4 = 4x² + 10x - 6

Combine like terms

4x² - 4x² + 8x - 10x = -4 - 6

-2x = -10

x = -10/-2

x = 5

18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]

Cross multiply

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

Expand

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize x² - 5x - 6 = 0

(x+1)(x−6) = 0

x = −1 or x = 6

Learn more about the angle bisector theorem on:

https://brainly.com/question/2478436

#SPJ1

The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

Learn more about Percentage here

https://brainly.com/question/843074

#SPJ1

The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind.  [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.

The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function

[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]

where x exists the increase in speed when the plane travels with the wind (tailwind).

The y-intercept exists at x=0, then

[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]

[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours

[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.

To learn more about y-intercept for the function refer to:

https://brainly.com/question/19552756

#SPJ4

An error exists in the distinction between the exact length of an object and its measured length.

The closest to the percent error for Diego's measurement exists at 4.3%.

An error exists in the distinction between the exact length of an object and its measured length.

Error = Actual length - Measured length

= 23cm - 22cm

= 1 cm

Percent error = Error/ Actual length × 100

= 1 /23 × 10

= 4.35%

Therefore, the closest to the percent error for Diego's measurement exists at 4.3%.

To learn more about percent error refer to:

https://brainly.com/question/1600371

#SPJ4

Answer:

b

Step-by-step explanation:

B

The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

A linear equation is given as:

y = mx + b

Where m represents the slope of the linear equation.

When the value of  is 0

i.e. m = 0, the equation becomes

y = 0 *x + b

Evaluate

y= b

The above equation is a horizontal line that passes through the y-axis at y= b

Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

Read more about linear functions at:

https://brainly.com/question/1884491

#SPJ1

Answer:

40 vanilla cookies

Step-by-step explanation:

Lets say that

N = No-bake cookies

V = Vanilla cookies

C = Cinnamon cookies

If the ratio is 2 : 2 : 2

And there are 40 no-bake cookies

It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same

( N : V : C )

( 40 : 40 : 40 )

Hope this helps  (๑ > ᴗ <)وxx

( I am so sorry if this is wrong!!)

Answer:

To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number. ∴ The biggest 4-digit number which is a perfect square = 9801.

Step-by-step explanation:

Answer:

9801

Step-by-step explanation:

well we know 100 squared is the first 5 digit square number so it must be 99 squared, which is 9801

The radius of the hemisphere is 9.5 inches.

The diameter of the hemisphere is 19 inches.

The surface area of the hemisphere is 850.2 inches²

circumference of a circle = 2πr

where

Therefore,

19π = 2πr

2r = 19

r = 19 / 2

r = 9.5 inches

diameter = 9.5 × 2 = 19 inches

Therefore,

surface area of an hemisphere = 3πr²

surface area of an hemisphere = 3 × 3.14 × 9.5²

surface area of an hemisphere = 850.155 inches²

surface area of an hemisphere = 850.2 inches²

learn more on hemisphere here: https://brainly.com/question/14076143

#SPJ1

Answer:

3 3/4 hour

Step-by-step explanation:

(3/4) ÷ (1/5) = (3*5) / (4*1)

= 15/4 hour

15/4 = 12/4 + 3/4 = 3 + 3/4 hour

= 3 3/4 hour

Answer:

x = 75

Step-by-step explanation:

Given information from the question:

x - 3y = 30

y = 15

We can substitute y = 15 into the equation to find x.

x - 3(15) = 30

x - 45 = 30

x - 45 + 45 = 30 + 45

x = 75

Answer:

75

Step-by-step explanation:

x-3y=30

x-3×15=30

x-45=30

x=30+45

x=75

Answer:

I x² +12x I = -32

Step-by-step explanation:

Absolute value equation:

  x = -4  ; x = -8

x + 4 = 0  and     x + 8 = 0

(x +4)(x + 8) = 0

x*x + x*8 + 4*x + 4*8 = 0

     x² + 4x + 8x  + 32 = 0

         x² + 12x   + 32   = 0

Absolute value equation:

  I x² + 12x I = -32