a = 63.5 rounded to 1 DP
b= 5.71 rounded to 2 DP
Find the minimum of a - b

Answer:

The slope of the line is 12

(Sorry for the bad quality image)

Explanation:

To find the average rate of change, calculate the change in y over the change in x.

m = 12

Answer:

Rate of change = 12
y-intercept = (0, 20)

Step-by-step explanation:

Part 1) Rate of Change
The rate of change (or slope) is found using the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
To use this formula, we must take the coordinates of two of the given points in the table and substitute them. For simplicity, I'll take the points (1, 32) and (4, 68).

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{68 - 32}{4 - 1} = \frac{36}3 = 12[/tex]

Therefore, the rate of change is 12.

Part 2) y-intercept
To find the y-intercept, we must find the value of the function where [tex]x = 0[/tex]. Since we have both the value of the function where [tex]x = 1[/tex] and we know that the rate of change is 12, we can simply subtract the rate of change from the y-value of the function at the point where [tex]x = 1[/tex].

The y-value of the function where [tex]x = 1[/tex] is 32, therefore, the y-value of the function at [tex]x = 0[/tex] is [tex]32 - 12 = 20[/tex]

The y-intercept is (0, 20).

The similar polygons, use proportion to find the value of each variable.

x= 40, y = 18

[tex]\frac{JK}{NM}[/tex] = [tex]\frac{KL}{ML}[/tex] = [tex]\frac{LJ}{LN}[/tex]

[tex]\frac{40}{16}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{45}{y}[/tex]

40*16 = 16*x

x= 40

40*y = 45*16

y = 18

In geometry, a polygon  may be a  plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or  the 2  together,  could also be  called a polygon.The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices (singular: vertex) or corners.  the inside  of a solid polygon is sometimes called its body. An n-gon  may be a  polygon with n sides; for example, a triangle  may be a  3-gon.

A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains  of straightforward  polygons and they often define a polygon accordingly. A polygonal boundary  could also be  allowed to cross over itself, creating star polygons and other self-intersecting polygons.

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The following inequality in slope-intercept form.

y≤-4x-15

Slope intercept form is y=mx+ c

what is a coordinate in geometry?

Coordinates are two numbers (Cartesian coordinates), or every so often a letter and a range of, that discover a particular point on a grid, called a coordinate aircraft. A coordinate aircraft has 4 quadrants and two axes: the x axis (horizontal) and y axis (vertical).

what is coordinate geometry instance?

In coordinate geometry,  lines are parallel if their slopes (m) are equal. for instance: the line y = ½ x - 1 is parallel to the line y = ½ x + 1 due to the fact their slopes are both the identical.

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Math reality is more restrictive and logical, physical reality is more "free" and well-behaved.

Mathematics are a logical construct, thus, everything in the "mathematical realty" must follow a certain logic.

For example, in math, always that you do a simplification (like rounding, applying a theorem, using an integration property, etc) you need to prove logically why you can do that.

While on physics we assume the reality is "nice" and we can always apply the simplifications. This is because most of the functions that represent physics are nice (continuous, differentiable, etc)  functions, in the same way, most of the matrices are square matrices, and so on.

Concluding, for example in math the number 4.99999 is exactly 4.9999

On physics, if that same number represents a measure, for example:

4.99999 meters is practically equal to 5 meters.

Math reality is more restrictive and logical, physical reality is more "free" and well-behaved.

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After solving, the factors of equation 3x² = 18x-24 are:

So,

Given equation: 3x² = 18x-24

Then,

Factors are: (x-4) and (3x-6)

Therefore, after solving, the factors of equation 3x² = 18x-24 is:

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Answer:[tex]\frac{-11x^2+135}{5}[/tex]

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

absolute value basically makes numbers positive

Answer:

32% of 200 is 64.

Step-by-step explanation:

Answer:

h = 0.01g

Step-by-step explanation:

[tex]{ \tt{g = kh + c}}[/tex]

When g is 0, h is 0 hence c is 0

[tex]{ \tt{g = kh}}[/tex]

when g is 1, h is 0.01

[tex]{ \tt{1 = 0.01k}} \\ { \tt{k = 100}} \\ { \boxed{ \tt{ equation \to \: {g = 100h}}}} \\ { \rm{or}} \\ { \boxed{ \tt{equation \to \: h = 0.01g}}}[/tex]

Answer:

A real number is a number that can take any value on the number line. They can be any of the rational and irrational numbers. Rational number is a number that can be expressed in the form of a fraction but with a non-zero denominator.

Based on the dimensions of the shape, the length of PR can be found to be 19.8 units.

The given triangle is an equilateral triangle which means that all the sides are equal.

PR = QR

This means that:

2n + 9 = 7n - 18

Solving for n gives:

7n - 2n = 18 + 9

5n = 27

n = 5.4

The length of PR is therefore:

= 2n + 9

= 2 (5.4) + 9

= 19.8 units

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The total amount that's is borrowed by Benjamin is $3.75.

It should be noted that from the information, Benjamin borrowed $0.75 from his friend cltyde five days last week to buy ice cream.

Therefore, the product will be:

= Amount borrowed × Number of times

= $0.75 × 5

= $3.75

The amount borrowed is $3.75.

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Answer:

2.45

Step-by-step explanation:

11x-2=25

11x=25+2

11x=27

11x/11=27/11

x= 2.45.

To check:

11x-2=25

11 × 2.45 - 2 = 24.95.

Round 24.95 to nearest whole number and you will get 25.

The number representing a constant from the expression will be 9. Then the correct option is D.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomial is given below.

⇒ 15x² + 2x + 9

If the power of the unknown is zero, then the term will be known as the constant term.

The polynomial can be written as,

⇒ 15x² + 2x + 9

⇒ 15x² + 2x + 9x⁰

The number representing a constant from the expression will be 9. Then the correct option is D.

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Answer:The answer would be negative.

Step-by-step explanation:There is already a negative balance of -$25 and you would add $23.-25+23=-2.So therefore the answer would be negative.

Please give brainliest if answer is correct.

The inequality that gat can be used to show the mobiles that are tolerable is w - 8 <= 0.3.

It should be noted that from the information, the

mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces.

Therefore, the mobiles are tolerable with an inequality will be:

w - 8 <= 0.3.

where w = weight of the mobiles.

In conclusion, the mobiles are tolerable with an inequality will be w - 8 <= 0.3.

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A particular mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Show which mobiles are tolerable with an inequality. ( W is the weight of the mobiles).

Answer:

if any number power of 0 is 1

so, (4)^0 =1

if any number power of -1 is equal to one divide this number.

like;

a^(-1) = 1/a

Therefore,

2^(-3) = 2^(-1) x 2^(-1) x 2^(-1)

= 1/2 x 1/2 x 1/2

Hence solution of 2^(-3). (4) ^0 is,

1/2 x 1/2 x 1/2 x 1

If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.

The inverse of the function is f⁻¹ = - (x² - 3/2)

Domain is 3/2 to positive infinity

Range is 0 to positive infinity.

The inverse function of a function f is a function that reverses the operation of f. The inverse of f exists if and only if f is bijective, and it is denoted by f⁻¹ if it exists.

A function's inverse is not always a function. To ensure that the inverse function is also a function, the original function must be a one-to-one function. A one-to-one function is one in which each second element corresponds to exactly one first element.

Let the given function be f(x) = √-2x+3

y = √-2x+3

simplifying the value of x, we get

x = √-2x+3

x² = -2y + 3

simplifying the above equation, we get

x² - 3 = -2y

y = - (x² - 3/2)

Therefore, the inverse function be f⁻¹ = - (x² - 3/2)

Domain is 3/2 to positive infinity because a negative number cannot be square-rooted.

Range is 0 to positive infinity.

f⁻¹ = - (x² - 3/2)

The domain of the inverse is negative infinity to positive infinity, which is not a mirror image of the range of the original equation.

Anything squared is a positive number or zero.

The minimum value of the range is

f⁻¹ = - (x² - 3/2)

f⁻¹ = -(-3/2)

f⁻¹ = 3/2

The range of the inverse is 3/2 to positive infinity, a mirror of the domain of the original equation.

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Carl made a mistake by multiplying the two values in the quotient rather than dividing them.

So, the result of 4 divided by 2 1/3 and an explanation of Carl's error:

Thus, if we divide 4 2/3 by 2 1/3, we get:

Carl made the error of assuming his quotient (2) was equal to the value of the terms it contained.

Therefore, Carl made a mistake by multiplying the two values in the quotient rather than dividing them.

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The length of the side of the equilateral triangle is 20.76 inches.

Here it is given that the length of the altitude of the equilateral triangle is 18 inches.

The formula of the altitude(h) of the equilateral triangle is

h = [tex]\frac{\sqrt{3} }{2}[/tex]a

Here a is the side of an equilateral triangle.

So we have

18 = [tex]\frac{\sqrt{3} }{2}[/tex]a

a = 18 × 2/[tex]\sqrt{3}[/tex]

For the rationalization of the fraction multiply numerator and denominator by [tex]\sqrt{3}[/tex].

a = [tex]\frac{18 * 2 * \sqrt{3} }{\sqrt{3}\sqrt{3} }[/tex]

  = [tex]\frac{18 * 2 * \sqrt{3} }{3}[/tex]

  = 6 × 2 × √3

  = 12×√3

  = 12 × 1.73

  = 20.76 inches

Therefore the length of the side of the triangle is 20.76 inches.

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The factoring of the expression 6 x²=5 x+6 is (2x-3) (3x+2)

By ordering the values, we get:

6 x² - 5x - 6

To solve this exercise, we have to follow the rules of factoring:

1. Factor 5 from 5x:

6 x² - 5x - 6

6 x² + (-9 + 4) x - 6

2. Apply the distributive property:

6 x² - 9x + 4x - 6

3. Groups the first two terms and the last two terms:

(6 x² - 9x) + 4x - 6

4. Factorize the greatest common denominator (GCM) of each group:

3x(2x - 3) + 2(2x - 3)

5. Simplify the common term (2x - 3) with the distributive property:

(2x-3) (3x+2)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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Answer:

mmmm

Step-by-step explanation:

!!!

Answer:

see explanation

Step-by-step explanation:

∠ CDF and 137° are a linear pair and sum to 180° , then

∠ CDF = 180° - 137° = 43°

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

the sum of the 3 angles in Δ CDF = 180° , then

∠ CFD + 43° + 32° = 180°

∠ CFD + 75° = 180° ( subtract 75° from both sides )

∠ CFD = 105°

then

∠ AFB = ∠ CFD = 105° ( vertically opposite angles are congruent )

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

∠ ABF= ∠ FCD = 32° ( alternate angles are congruent )

|x - 50| = 14 is the equation used to find the locations of the outer edges of the stage.

Absolute value function

The absolute function is defined by

 |x| = x, x≥0

 |x| = -x, x<0

It measures the distance of a point x to the origin, let's take some example

|-8| = 8

|-5| = 5

Here it is given that the center of the stage is on the 50-yard line, and the distance from the center to the outer edges is 14 yards.

So from this, we get an equation,

|x - 35| = 11

So the solution is given as follows:

First edge:

x - 50 = -14

x = 36 yards line

Second edge:

x- 50 = 14

x = 64 yard line

Therefore the equation used to find the location of the outer edges of the stage is |x - 50| = 14.

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Answer: The length of First piece = 6

The length of second piece = 18

The length of third piece = 30  

Step-by-step explanation:

Given data,

A 54-inch board is to be cut into three pieces.

so that the second piece is 3 times as long as the first piece and the third piece is 5 times as long as the first piece.

So, we can write,

Let us assume, first piece is represented by = x

Then,

second piece is 3 times as long as the first piece

So, we can write,

second piece is represented by = 3 ( first piece )

second piece is represented by = 3x

Then,

third piece is 5 times as long as the first piece

So, we can write,

third piece is represented by = 5 ( first piece )

third piece is represented by = 5x

So, we can find the all 3 pieces length,

we can solve it :
combine all three pieces = x + 3x + 5x

length of all three pieces = x + 8x

                                          = 9x

 Total board is to be cut into three pieces = 54

Hence,

                         9 x = 54

                          x = 54/9

                          x = 6

Now we know that the base length, x, is equal to 6.

From there, we can find the length of the all three pieces is :

The length of First piece = x = 6

The length of second piece = 3x

                                         = 3(6)

                                         = 18

The length of third piece = 5x

                                         = 5(6)

                                         = 30

Therefore,

The length of First piece = 6

The length of second piece = 18

The length of third piece = 30  

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Answer:

4

Step-by-step explanation:

15-2x=7

8=2x

4=x

---

HOPE THIS HELPS <3

Answer:

x=11

Step-by-step explanation:

let us name the unknown number: x

15 - 2x = 7

collect like terms,

-2x= 7 - 15

-2x= - 8

divide both sides by -2( coefficient of x)

-2x = -8

__ __

-2 -2

x= 4

Answer:

Solution:  x < -2 or x > 3

Interval notation:  (-∞, -2) ∪ (3, ∞)

Step-by-step explanation:

Given inequality:

[tex]||2x-1|-2| > 3[/tex]

Apply the absolute rule:

[tex]\textsf{If $|u| > a$, $a > 0$ \;then \;$u > a$ \;or \;$u < -a$}.[/tex]

Therefore:

[tex]\textsf{Case 1}: \quad |2x-1|-2 > 3[/tex]

[tex]\textsf{Case 2}: \quad |2x-1|-2 < -3[/tex]

Solve each case independently.

Isolate the absolute value on one side of the equation:

[tex]\begin{aligned}\implies |2x-1|-2& > 3\\\implies |2x-1| & > 5 \end{aligned}[/tex]

Apply the absolute rule:

[tex]\textsf{If $|u| > a$, $a > 0$ \;then \;$u > a$ \;or \;$u < -a$}.[/tex]

[tex]\begin{aligned}\underline{\textsf{Equation 1}} & & \quad \quad\underline{\textsf{Equation 2}}\\2x-1 & > 5 & 2x-1 & < -5\\2x& > 6 & 2x& < -4\\x& > 3 & x& < -2\end{aligned}[/tex]

Therefore, x < -2 or x > 3.

Isolate the absolute value on one side of the equation:

[tex]\begin{aligned}\implies |2x-1|-2& < -3\\\implies |2x-1| & < -1 \end{aligned}[/tex]

As an absolute value cannot be less than zero, there is no solution for x∈R.

Solution:  x < -2 or x > 3

Interval notation:  (-∞, -2) ∪ (3, ∞)

Answer:

0.9

Step-by-step explanation:

4n = 3.60

n = 3.60 / 4

n = 0.9

Answer: n = 0.9

Step-by-step explanation:

1. isolate the variable by dividing 4 from both sides

2. 3.60/4 = 0.9

Without knowing what the dropdown list shows for reasons, it's hard to pinpoint exactly what is expected here.

Angle ACD is congruent to angle BCD because they are corresponding angles between the congruent triangles ∆ACD and ∆BCD.

The triangle congruency is due to angle-angle-side (AAS) similarity:

• angles A and B are congruent - this is given

• angles CDB and CDA are congruent right angles - this is implied by the given detail that CD and AB are perpendicular

• the leg CD is common to both triangles, and CD is of course congruent to itself (reflexive property)

So angles ACD and BCD are congruent, which means they have the same measure, so by definition of angle bisector, CD bisects angle ACB.

QED

Answer:

[tex]\dfrac{\ln | \sec (x-b)- \ln | \sec (x-a)}{\sin (a-b)}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \sec(x-a) \sec (x-b)\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Trigonometric Identity}\\\\$\sec \theta=\dfrac{1}{\cos \theta}$\\\end{minipage}}[/tex]

Therefore:

[tex]\implies \displaystyle \int \dfrac{1}{\cos(x-a)} \cdot \dfrac{1}{\cos (x-b)}\:\text{d}x[/tex]

[tex]\implies \displaystyle \int \dfrac{1}{\cos(x-a)\cos (x-b)} \:\text{d}x[/tex]

[tex]\textsf{Multiply the integral by }\dfrac{\sin (a-b)}{\sin (a-b)}:[/tex]

[tex]\implies \displaystyle \int \dfrac{1}{\cos(x-a)\cos (x-b)} \cdot \dfrac{\sin (a-b)}{\sin (a-b)}\:\text{d}x[/tex]

Take the constant outside the integral:

[tex]\implies \displaystyle \dfrac{1}{\sin (a-b)}\int \dfrac{\sin (a-b)}{\cos(x-a)\cos (x-b)} \:\text{d}x[/tex]

Rewrite the numerator:

[tex]\implies \displaystyle \dfrac{1}{\sin (a-b)}\int \dfrac{\sin [(x-b)-(x-a)]}{\cos(x-a)\cos (x-b)} \:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identity}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\end{minipage}}[/tex]

Therefore:

[tex]\implies \displaystyle \dfrac{1}{\sin (a-b)}\int \dfrac{\sin(x-b) \cos (x-a)-\cos (x-b) \sin (x-a)}{\cos(x-a)\cos (x-b)} \:\text{d}x[/tex]

[tex]\implies \displaystyle \dfrac{1}{\sin (a-b)}\int \dfrac{\sin(x-b) \cos (x-a)}{\cos(x-a)\cos (x-b)} -\dfrac{\cos (x-b) \sin (x-a)}{{\cos(x-a)\cos (x-b)}}\:\text{d}x[/tex]

[tex]\implies \displaystyle \dfrac{1}{\sin (a-b)}\int \dfrac{\sin(x-b)}{\cos (x-b)} -\dfrac{\sin (x-a)}{\cos(x-a)}\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Trigonometric Identity}\\\\$\tan \theta=\dfrac{\sin \theta}{\cos \theta}$\\\end{minipage}}[/tex]

Therefore:

[tex]\implies \displaystyle \dfrac{1}{\sin (a-b)}\int \tan(x-b)-\tan(x-a)\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Integrating $\tan x$}\\\\$\displaystyle \int \tan x\:\text{d}x=\ln | \sec x|+\text{C}$\end{minipage}}[/tex]

Therefore:

[tex]\implies \dfrac{1}{\sin (a-b)}\left[ \ln | \sec (x-b)- \ln | \sec (x-a)\right]+\text{C}[/tex]

[tex]\implies \dfrac{\ln | \sec (x-b)- \ln | \sec (x-a)}{\sin (a-b)}+\text{C}[/tex]

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Answer:

The numbers are 4 and 7

Step-by-step explanation:

To start, we can set up two equations.

x + y = 11 and x - y = 3

We now need to solve for one of these variables in terms of the other. I am choosing to solve for x, but either way will work. I'm using the second equation and solving for x by adding y to each side, which gives me

x = 3 + y

Now that I have a value for x, I can plug this into my first equation

3 + y + y = 11

Combining like terms gives me

3 + 2y = 11

Subtracting 3 from both sides leaves

2y = 8

And dividing by 2 to solve for y gets

y = 4

We now know one number, and to solve for the other we can plug our y value into either equation

x + 4 = 11

Subtracting 4 from both sides yields the x value

x = 7

So the two numbers are 4 and 7