What are the factors of 4(m+6)

Answer:b = +7-6

Step-by-step explanation:

neverminding the jumbled lingo, is simply asking for the equation of the tangent line at that point, it says all tangents, well, there's only one passing there.

we can simply get the derivative of f(x) and take it from there.

\(f(x)=4-x^2+2x\implies \left. \cfrac{df}{dx}=-2x+2 \right|_{x=\frac{3}{2}}\implies -2(\frac{3}{2})+2\implies -1\)

since now we know the slope when x = 3/2, then we can just plug that into its point-slope intercept form, along with the coordinates.

\((\stackrel{x_1}{\frac{3}{2}}~,~\stackrel{y_1}{7})~\hfill \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-1}(x-\stackrel{x_1}{\frac{3}{2}}) \\\\\\ y-7=-x+\cfrac{3}{2}\implies y=-x+\cfrac{17}{2}\)

Answer:

As the given equation represents a quadratic function.

Thus, \(y\:=\:x^2-9x\) represents a function.

As we know that the function is just a relation in which each input has only one output.

Thus, \(y\:=\:x^2-9x\) represents a relation and function.

Step-by-step explanation:

Given the equation

\(y\:=\:x^2-9x\)

As the given equation represents a quadratic function.

Thus, \(y\:=\:x^2-9x\) represents a function.

As we know that the function is just a relation in which each input has only one output.

Thus, \(y\:=\:x^2-9x\) represents a relation and function.

We know that the domain of a function is the set of input or argument values for which the function is real and defined.

\(\mathrm{Domain\:of\:}\:x^2-9x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\)

We also know that the range of a function is the set of values of the dependent variable for which a function is defined.

\(\mathrm{Range\:of\:}x^2-9x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-\frac{81}{4}\:\\ \:\mathrm{Interval\:Notation:}&\:[-\frac{81}{4},\:\infty \:)\end{bmatrix}\)

The graph is also attached below. From the graph, it is clear that it represents a Parabola.

Answer: 60

Step-by-step explanation:

Always take care of what is in ( ) and [ ] first

28 - 2

26 + 4

30(2) i assume you are multiplying it?

60

9514 1404 393

Answer:

Step-by-step explanation:

"Periods" will be filled with the number of years (1) times the number of periods per year (quarterly = 4). periods = 4

"Rate" is likely filled with the rate of interest divided by the number of periods per year. rate = 4%/4 = 1%

Then the total amount is found by ...

  total amount = principal × (1 + rate)^(periods)

  = 575 × (1.01^4) = 598.35

The total interest is the difference between this amount and the principal.

  total interest = total amount - principal

  = 598.35 -575 = 23.35

_____

We believe we have made reasonable assumptions regarding the intent of the columns in the table. Your best bet is to compare this problem to the worked examples in your curriculum materials.

Answer: There is a picture below of my work. Sorry for my sloppy hand writing.

Answer:

Step-by-step explanation:

84

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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Lines AB, BC, and AC have an equal slope, with a slope value of 2/3.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a line AC that has an x-intercept of "2"

Since,

AB is part of line AC thus the slope of AB will be the same as the slope of line AC and the Slope of line BC.

For the slope of line AB:

Since there is no Additional data given on the problem we will assume that every square is a unit square in the graph

Thus, Coordinates of A = (-5, -2)

Since Point B is the x-intercept of line AB thus its coordinates = (-2, 0)

from the formula of the slope of a line:

m = (y₂ -y₁)/(x₂ - x₁)

Thus, the slope of line AB:

m = (0+2)/-2 +5)

m = 2/3

therefore, the slope of the line AB, BC, and AC are equal and the value of the slope is 2/3.

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Answer:Godo luck!

Step-by-step explanation:

Answer:

a)

(3-x)^2 = (3-x)(3-x) = 9 - 6x + x^2

(3x + 4y)^2 = (3x + 4y)(3x + 4y) = 9x^2 + 24xy + 16y^2

So, (3-x)^2 * (3x+4y)^2 = (9 - 6x + x^2) * (9x^2 + 24xy + 16y^2) = 144x^2 - 108x^3 - 192xy + 144y^2 + 9x^4 - 32y^2x^2 + 16y^4

b)

(7x - 5) (7x + 5)^2 = (7x - 5) (49x^2 + 70x + 25) = 343x^3 - 50x^2 - 175x - 125

c)

8x(x-4) - (x-6)(x+6) = 8x^2 - 32x - (x^2 - 36) = 7x^2 - 32x + 36

9514 1404 393

Answer:

  6

Step-by-step explanation:

Work backward.

If he has 24 after adding 6, he had 18 before that addition.

If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.

__

Note that this is the same process you would use if you started with an equation.

  3c +6 = 24 . . . . where c is the number of cards Johnny started with

  3c = 24 -6 = 18 . . . . . subtract 6 from the final number

  c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value

Johnny started with 6 cards.

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer:

Step-by-step explanation:

Let's take a look at the given angle 135°

The sketch of the angle which corresponds to \(-\dfrac{3\pi}{4}\) unit circle and can be seen in the attached image below;

The trigonometric ratios are as follows for an angle θ on the unit circle:

Trigonometric ratio           related ratio on coordinate axes

sin θ                                     \(\dfrac{y}{1}\)

cos θ                                    \(\dfrac{x}{1}\)

tan θ                                     \(\dfrac{y}{x}\)

csc θ                                     \(\dfrac{1}{y}\)

sec θ                                     \(\dfrac{1}{x}\)

cot θ                                      \(\dfrac{x}{y}\)

From the sketch of the image attached below;

The six trigonometric ratio for 135° can be expressed as follows:

\(sin (-\dfrac{3\pi}{4})= \dfrac{y}{1}\)

\(sin (-\dfrac{3\pi}{4})=- \dfrac{\sqrt{2}}{2}\)

\(cos (-\dfrac{3\pi}{4})= \dfrac{x}{1}\)

\(cos (-\dfrac{3\pi}{4})= -\dfrac{\sqrt{2}}{2}\)

\(tan (-\dfrac{3\pi}{4})= \dfrac{y}{x}\)

\(tan (-\dfrac{3\pi}{4})= \dfrac{-\dfrac{\sqrt{2}}{2}}{-\dfrac{\sqrt{2}}{2}}\)

\(tan (-\dfrac{3\pi}{4})= -\dfrac{\sqrt{2}}{2}} \times {-\dfrac{2}{\sqrt{2}}\)

\(tan (-\dfrac{3\pi}{4})= 1\)

\(csc (-\dfrac{3\pi}{4})= \dfrac{1}{y} \\ \\ csc (-\dfrac{3\pi}{4})=\dfrac{1}{-\dfrac{\sqrt{2}}{2}} \\ \\ csc=1 \times -\dfrac{2}{\sqrt{2}} \\ \\csc =-\sqrt{2}\)

\(sec (-\dfrac{3 \pi}{4})=\dfrac{1}{x} \\ \\ sec = \dfrac{1}{(-\dfrac{\sqrt{2}}{2})} \\ \\ sec = 1 \times -\dfrac{2}{\sqrt{2}} \\ \\ sec = - \sqrt{2}\)

\(cot(-\dfrac{3 \pi}{4}) = \dfrac{x}{y} \\ \\ cot(-\dfrac{3 \pi}{4}) = \dfrac{-\dfrac{\sqrt{2}}{2} }{-\dfrac{\sqrt{2}}{2}} \\ \\ cot(-\dfrac{3 \pi}{4})= -\dfrac{\sqrt{2}}{2} } \times {-\dfrac{2}{\sqrt{2}}} \\ \\ cot (-\dfrac{3 \pi}{4}) = 1\)

Answer:

41

Step-by-step explanation:

Answer:

y=10x+0.4

Step-by-step explanation:

I did the test too.

Answer:

y=10x+0.4

Step-by-step explanation:

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.

Hence:

Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.

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answer:

36

explanation to answer:

37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.

Equations can be categorized as identities or conditional equations.

w = (455.95-155.95)/(37.50)

=300/37.50

=8

So, number of weeks = 8

As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.

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Answer:

1 mile every 57 seconds I belive

Step-by-step explanation:

Answer:

XuY = { 3,5,6,9,10,12,15}

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

$102.81

Step-by-step explanation:

Time = 3.5

Rate = 5

Principal Amount = 587.50

Using the Simple Interest formula:

SI = \(\frac{P*R*T}{100}\) where

P -> Principal Amount,

R -> Rate, and

T -> Time

Substituting the given values into the formula:

SI =

\(\frac{587.50 * 5 * 3.5}{100}\\\\= \frac{10281.25}{100}\\\\= 102.8125\\\)

≈ $102.81

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Answer:

first box -1

second box 2

Step-by-step explanation:

Hope I helped!!