f(x) = -3x³ + x² - 3, find f(1).

Answer:

slope = - 32 , y- intercept = 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 32x + 5 ← is in slope- intercept form

with slope m = - 32 and y- intercept c = 5

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                          We have the equation [tex]\boldsymbol{\sf y=-32x+5}[/tex].

                          We need to know its slope and y-intercept.

                         If an equation has the y=mx+c form,  the slope is always

                         multiplied by x, the x co-ordinate. Such is the case here,

                          thereupon we note that the slope is [tex]\boldsymbol{\sf{-32}}[/tex].

                         As for the y-intercept, that's a constant. Do you remember

                         that constants have no variables attached to them?

                         Since the only number that has no variables attached to it is

                         5, we note that this is the desired value, the y-intercept.

done!!

[tex]\orange\hspace{300pt}\above3[/tex]

                        [tex]\large\boldsymbol{\sf{calligraphy}}[/tex]

Answer: 2

Step-by-step explanation:

     This system has 2 solutions because there are two points of intersection. See attached for where I pointed them out.

Step-by-step explanation:

Multiply the factors

[tex](x - 1)(x + 1)(x + 3)[/tex]

[tex]( {x}^{2} - 1)(x + 3)[/tex]

[tex]{x}^{3} + 3 {x}^{2} - x - 3[/tex]

The highest exponent is 3, so the degree is 3

Answer:

120 Vials

Step-by-step explanation:

160/1and1/3

160/4over3

Multiply top by 3

480/4

120

The number of vials in the case is given by the equation A = 120 vials

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of vials in the case be represented as A

Now , the equation will be

The total amount of med = 160 ounces

The amount of med in each vial = 1 1/3 ounces

The amount of med in each vial = 4/3 ounces

So , the number of vials in the case A = total amount of med / amount of med in each vial

Substituting the values in the equation , we get

The number of vials in the case A = 160 / ( 4/3 )

The number of vials in the case A = ( 160 x 3 ) / 4

The number of vials in the case A = 40 x 3

The number of vials in the case A = 120 vials

Therefore , the value of A is 120

Hence , the number of vials is 120

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Combine the fractions and factorize.

[tex]\dfrac{3a^2b}{a-b} + \dfrac{3ab^2}{b-a} = \dfrac{3a^2b}{a - b} - \dfrac{3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3a^2b - 3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3ab (a - b)}{a - b} \\\\ ~~~~~~~~ = 3ab[/tex]

Answer:

Each group will have 122

Step-by-step explanation:

It technically means divide 488 by 4

The point P could be located in quadrant I, quadrant IV and the x-axis

The coordinate of point P is given as:

P = (a, b)

Where a is positive

When a is positive, then the likely locations of P are:

Hence, point P could be located in quadrant I, quadrant IV and the x-axis

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I'm guessing you mean

[tex]S_{k+1} = S_k + a_{k+1}[/tex]

and that [tex]S_k[/tex] is the sum

[tex]S_k = 6 + 12 + 18 + \ldots + 6k = 6 (1 + 2 + 3 + \ldots + k) = 3 k (k+1)[/tex]

using the well-known formula

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

Then by substitution,

[tex]S_{k+1} = 6 (1 + 2 + 3 + \cdots + k + (k+1)) = 3 (k+1) (k+2)[/tex]

and hence

[tex]a_{k+1} = S_{k+1} - S_k[/tex]

[tex]a_{k+1} = 3 (k+1) (k+2) - 3k (k+1)[/tex]

[tex]a_{k+1} = 3 (k+1) \bigg((k+2) - k\bigg)[/tex]

[tex]\implies \boxed{a_{k+1} = 6 (k + 1)}[/tex]

Answer: AB = 90.7 meter

Given following:

Find angle A :

⇒ 180° - (104.6° + 14.4°)

⇒ 61°

Now, use sine rule:

[tex]\sf \dfrac{AB}{BC} = \dfrac{sin(C^{\circ })}{sin(A^{\circ \:})}[/tex]

[tex]\sf \dfrac{AB}{319} = \dfrac{sin(14.4) } {sin(61)}[/tex]

[tex]\sf AB = \dfrac{319 \ sin(14.4) } {sin(61)}[/tex]

[tex]\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)[/tex]

Answer:

4x -51

Step-by-step explanation:

m(n(x)) = m(x - 10) = 4(x-10) - 11 = 4x -40 -11 = 4x -51

Answer:

m[n(x)] = 4x - 51

Given following:

Solving steps:

Answer:

Not going to give answer, but let you solve

Step-by-step explanation:

You first have to start by drawing a number line and mark two integers between the fraction lines. Then you have to divide the section between the two integers in an equal number of parts which is equal to the denominator.

Hope I helped

The maximum concentration is greatest at; t = 4.926 hours

We are given the equation that represents the concentration as;

C = (3t² + t)/(50 + t³)

The maximum value of C is obtained when the slope of C' is zero (can be a local maxima too). So we are going to find solutions of C'.

C' = (-3t⁴ - 2t³ + 300t + 50)/(50 + t³)

At C' = 0, we have;

-3t⁴ - 2t³ + 300t + 50 = 0

Using online polynomial root calculator, the only valid root of this is;

t = 4.926 hours

Thus, the maximum concentration is greatest at t = 4.926 hours

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The equation which can be used to represent the total tolls Stephanie will pay is y = 1.35x

let

y = 1.35x

If the number of 3½ miles on the route is 5

Then, the total toll paid is

y = 1.35x

= 1.35(5)

= $6.75

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Differentiating both sides of

[tex]x^2 + 2xy - y^2 + x = 20[/tex]

with respect to [tex]x[/tex] yields

[tex]2x + 2y + 2x \dfrac{dy}{dx} - 2y \dfrac{dy}{dx} + 1 = 0 \\\\ \implies (2x-2y) \dfrac{dy}{dx} = -1 - 2x - 2y \\\\ \implies \dfrac{dy}{dx} = \dfrac{1 + 2x + 2y}{2(y-x)}[/tex]

At the point (3, 4) (so [tex]x=3[/tex] and [tex]y=4[/tex]), the tangent line has slope

[tex]\dfrac{dy}{dx} = \dfrac{1 + 2\times3 + 2\times4}{2(4-3)} = \dfrac{15}2[/tex]

Then the tangent line to (3, 4) has equation

[tex]y - 4 = \dfrac{15}2 (x - 3) \implies \boxed{y = \dfrac{15}2 x - \dfrac{37}2}[/tex]

Answer:

  $83,802

Step-by-step explanation:

The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.

The future value of an annuity due is given by the formula ...

  FV = P(1 +r)((1 +r)^t -1)/r

where P is the annual payment, r is the annual interest rate, and t is the number of years.

This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).

For P=$1000, r = 0.06, and t = 30, the future value is ...

  FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68

To the nearest dollar, the account value will be $83,802.

__

Additional comment

Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.

The difference based on the numbers given is -80.

The information given illustrates that the difference will be:

= (9 - 1) - (43) - (2 - 3) - 50

= 8 - 43 - (-1) - 50

= 8 - 43 + 1 - 50

= -80

Therefore, the difference or subtraction among the numbers given is -80.

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Answer:

Pints

Step-by-step explanation:

Answer:

Sanjay has more milk (12 pints)

Step-by-step explanation:

A quarter equals two pints

3 quarts = 3(2) = 6 pints

Lisa has 6 pints

Sanjay has 12 pints

Hope this helps

Answer:

2

Step-by-step explanation:

2.is best possible answer as it.says below 1000...

Answer:

the answer is

x^2 – 2y ≥ 7000

2x + 5y < 1000

so it would be the second option

Step-by-step explanation:

just took the test:)

Solve by elimination.

[tex](\vec A + 3\, \vec B) - (\vec A - \vec B) = (-3\,\vec\imath + \vec\jmath) - (\vec\imath - 2\,\vec\jmath)[/tex]

[tex]\implies 4\,\vec B = -4\,\vec\imath + 3\,\vec\jmath \implies \boxed{\vec B = -\vec\imath + \dfrac34\,\vec\jmath}[/tex]

[tex]\implies \vec A = \vec\imath - 2\,\vec\jmath + \vec B[/tex]

[tex]\implies \boxed{\vec A = -\dfrac54 \,\vec\jmath}[/tex]

The value of x from the given diagram is 16.6

In order to determine the value of x from the given figure, we will use the secant-secant theorem shown by the equation.

(6 +12) * 6 = (5 + x) * 5

Expand

36+72 = 25 + 5x

108 = 25 + 5x

5x = 108 - 25

5x = 83

x = 83/5

x = 16.6

Hence the value of x from the given diagram is 16.6

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Answer:

$1.26

Step-by-step explanation:

A 20% off means multiplying by 1-0.2=0.8

4.39*0.8=3.512

3.512-1=2.512

2.512-1.25=1.262

1.262 rounded to the nearest cent is $1.26

Answer:

(1,5)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect.

The two lines intersect at x=1 and y =5

The point of intersection is (1,5)

Answer: (1, 5)

Step-by-step explanation: Over to the right one, up five; I hope this helps!

Key: (xGraph, yGraph) If a number is positive on the x axis, go right, if negative, go left. The same applies to the y graph, if the number is positve, go up, if negative go down. Your solution is where the two lines meet.

Answer:

-9/11

Step-by-step explanation:

slope is change in y/change in x

change in y is 9 (12-3)

change in x is -11 (-17--8)

slope is -9/11

The probability that all men will be interviewed first is; 1/55

To solve this question we will make use of the probability combination formula which is;

nCr = n!/(r! * (n - r)!)

Thus, since we want to find the probability that all men will be interviewed first, then we will use the formula;

3(3!)/((11C1) * (10C1) * (9C1)) = 18/990

Simplifying that fraction  gives us; 1/55

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The relationship between temperature and the coffee sales is a negative exponential of temperature

relation is subject of order between to sets or how the connected to each other.

The temperature of liquid is essential in the  process of brewing because its affects the rate of evaporation or extraction. it refers to the test and matters that are dissolved from the coffee beans. The hot is the water, the quick it is to extract. At a high temperature, it’s tougher to control the rate of extraction. This can lead to over-evaporation of liquid, making your coffee taste too bitter since the heat strips away a lot of oxygen.

since the temperature varies over the year, which implies the taste of coffee also vary in a manner that in cold days people love coffees and in hotter days the people love to drink cold drinks instead of coffees
so in cold days the sales of coffees is grater in comparison with hot days

Thus the relationship between the sales of coffees and temperature is negative exponential of temperature.

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