A rectangular page is designed to contain 81 square inches of print. The margins at the top and bottom of the page are each 1 inches deep. The margins on each side are 1½ inches wide. What should the dimensions of the page be so that the least amount of paper is used?

Answer:

Step-by-step explanation:

go

Answer: 8 Remainder 4

Step-by-step explanation: Sum is the answer to addition so 5 plus 2 is 7 and 60 divided by 7 is 8 with a Remainder of 4

Answer:

  e^6 ≈ 403

Step-by-step explanation:

You want the value of e^(4x-2) when x = 2.

Put 2 where x is in the expression and do the arithmetic.

  e^(4·2 -2) = e^6 ≈ 403.429

The value of the expression is about 403.

The inequality using interval notation are (-7, -4).

An interval is represented on a number line using interval notation.

For the given expression;

-7 < x < -4

As, x > -7; x is not equal to -7.

x < -4; here also x is not equal to -4.

So, the is a condition of open interval where both vales are not taken.

Thus, the intervals are written as; (-7, -4).

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Answer:

C. =

Step-by-step explanation:

This is because 18% is 18/100. You could find the answer one of two ways. Divide by two or multiply by 2.

Answer:

Slope = (-7/4)

Step-by-step explanation:

Point 1: (-3, 4); Point 2: (1, -3)

            (x₁, y₁)               (x₂, y₂)

       y₂ - y₁        -3 - 4           -7           -7

m = ----------- = ----------- = ----------- = ------

       x₂ - x₁         1 - (-3)         1 + 3        4

I hope this helps!

Answer:

Step-by-step explanation: 6.140

The yearly interest rate percentage is 7%

The rate of interest can be found dividing the interest and  the product of the principal and time period which can be written as

R = I / PT

where R is the Rate of interest

          I is the Interest

          P is the Principal amount

          T is the time period.

Given values are

P = $5,875

 I = $1,675

 T = 4 years

Then,

R = I/PT

   = 1,645/(5,875 x 4)

   = 1645 / 23500

   = 0.07

The Yearly interest rate percentage is

 =0.07 x 100

 = 7%

Therefore, the yearly rate percentage is 7%

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The equation of the composite function h(x) is h(x) = -10x^2 + 40x

The functions are given as

f(x) = 2x – 8

g(x) = –5x

The equation of the composite function is given as

h(x) = f(x)g(x)

Substitute f(x) = 2x – 8 and g(x) = –5x in the equation h(x) = f(x)g(x)

So, we have

h(x) = (2x - 8) x (-5x)

Evaluate the product

h(x) = -10x^2 + 40x

Hence, the equation of the composite function h(x) is h(x) = -10x^2 + 40x

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The function which passes from (1,4) and (5,1) is y= -7/20x² + 27/20x   +3

and the net change between the indicated points is -3, whereas the average rate change is -3/4.

Given, from the graph, the function passes (1,4) and (5,1).

Let y = ax² + bx + 3

from point 1.

the equation is: a + b+ 3 = 4 eq(1)

from point 2.

the equation is 25a + 5b + 3 = 1 eq(2)

solving equation 1 and equation 2.

we get, 20b = 99-72

20b = 27

b = 27/20

substitute b value in equation 1.

a + 27/20 + 3 = 4

20a = -7

a = -7/20

hence y = -7/20x² + 27/20x +3

(a) net change = change in y coordinates.

net change = y₂ - y₁

net change = 1 - 4

= -3

(b) Average rate = change in y coordinates / change in x coordinates

= 1 - 4/5-1

= -3/4

hence  we get the required answers.

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Samuel's test score if he got 9 questions wrong=55

Samuel's test score if he got x questions wrong=45

Mean score: A mean scale score is the average performance of a group of students on an assessment. Specifically, a mean scale score is calculated by adding all individual student scores and dividing by the number of total scores. It can also be referred to as an average.

let y equal the number of questions

let's find how many total questions are there,

100=5y

divide by the coefficient of y which in the case is 5

20=y

so we have total of 20 questions each are worth 5 points

now, Samuel got 9 questions wrong and if we know they are 20 total questions

20-9=11

so, we know Samuel got 11 questions correct

let's use an expression to figure out his score

let x be the number of questions

5x

substitute

5(11)=55

his score if he got x questions wrong

20-11=9

9(5)=45

Samuel's test score if he got 9 questions wrong=55

Samuel's test score if he got x questions wrong=45

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By means of weighted averages, we conclude that an amount of 285 gallons are needed to prepare a 70 % salt solution.

In this problem we find two salt solutions with distinct concentrations, one with 80 % and another with 13 %, the latter in a quantity of 50 gallons. The required quantity of 80 % salt solution is determined by using weighted averages:

(80 / 100) · x + (13 / 100) · 50 = (70 / 100) · (x + 50)

0.8 · x + 13 / 2 = 0.7 · x + 35

0.1 · x = 57 / 2

0.2 · x = 57

x = 285

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The value of the given functions are:

(i) f + g = x² + x - 6

(ii) f - g = -x² + x - 4

(iii) f . g = x³ - 5x² - x + 5

(iv) f/g = ( x - 5)/(x +1)(x - 1)

(v) g(f(x)) = x² - 10x + 24

The two functions are given that

f(x) = x - 5

g(x) = x² - 1

We have to find

(i) f + g

f(x) + g(x) = ( x-5)  + (x² - 1)

                = x² + x -5 -1

               = x² + x -6

(ii) f - g

f(x) - g(x) = (x-5)- (x² - 1)

              = -x² + x -5 +1

              = -x² + x -4

(iii) f . g

f(x) . g(x) = (x-5)(x²-1)

              =x(x² - 1) -5(x² - 1)

              = x³ - x - 5x² + 5

              = x³ - 5x² - x + 5

(iv) f/g

f(x) / g(x) = (x-5) / ( x² - 1)

              = (x - 5) / (x+1)(x-1)

(v) g(f(x)) = - 1 + ( -5 + x )²

              = -1 + 25 + x² - 10x

              = x² - 10x + 24

Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.

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The complete question is:

F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).

Answer:

y = 2/3x + 9

Step-by-step explanation:

The equation of a line is defined as y = mx + b

with m being the slope, and b being he intercept.

So to figure out the equation for the line with a slope of 2/3 and an intercept of 9, we can just plug those values into our line equation!

So take y = (slope)*x + *(intercept)

and plug your values in and you get...

y = 2/3 * x + 9

Answer: the answers for the quiz are

1. What is the slope (rate of change) of the line in the graph show below? Answer is A. -2

2. Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1). Answer is D. 4/3

3. constant of variation of -4y=8x  answer is B. -2

4 the value of y when x=10 answer is B. 30

5. the equation for the line with slope 2/3 and y-intercept 9 answer is C. y=2/3x+9

6 is the equation in slope intercept form for the line that passes through the points (1, -3) and (3, 1) answer is D. y=2x-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the perimeter of each of the figures defined by the coordinates of their vertices. You are told to use the distance formula as necessary.

The first attachment shows the graph of the triangle. The distance formula is needed only for the length of the diagonal segment:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((3 -(-2))² +(-3 -3)²) = √(5² +(-6)²) = √61 ≈ 7.81

The lengths of the horizontal and vertical legs of the triangle are the difference of their x- and y-coordinates, respectively.

  CB = 3 -(-2) = 5

  CA = 3 -(-3) = 6

The perimeter is the sum of the side lengths:

  P = CA +CB +AB = 6 +5 +7.81 = 18.81

The perimeter of the triangle is 18.81 units.

The second attachment shows the graph of the parallelogram. As with the triangle, we only need to use the distance formula for the length of the diagonal side. Here is the length of ML.

  d = √((4 -2)² +(1 -(-2))²) = √(2² +3²) = √13 ≈ 3.606

The length of the horizontal legs is the difference of their x-coordinates.

  KL = 4 -(-1) = 5

Opposite sides are congruent, so the perimeter is double the length of two adjacent sides.

  P = 2(3.606 +5) ≈ 17.21

The perimeter of the parallelogram is about 17.21 units.

Answer:

1.  18.81 units

2.  17.21 units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Given vertices of ΔABC:

Plot the vertices on the given graph paper and join with line segments to create the triangle.

As points B and C share the same y-coordinate:

[tex]\implies BC = |x_B-x_C|=|3-(-2)|=5\:\: \sf units[/tex]

As points A and C share the same x-coordinate:

[tex]\implies AC = |y_A-y_C|=|3-(-3)|=6\:\: \sf units[/tex]

Use the distance formula to find the length AB:

[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-2))^2+(-3-3)^2}\\& =\sqrt{(5)^2+(-6)^2}\\& =\sqrt{25+36}\\& =\sqrt{61}\\\end{aligned}[/tex]

The perimeter of a two-dimensional shape is the distance all the way around the outside.

[tex]\begin{aligned}\textsf{Perimeter of $ABC$} & = AB + BC + AC\\& = \sqrt{61}+5+6\\& = 11+\sqrt{61}\\& = 18.81\:\: \sf units\:(nearest\:hundredth)\end{aligned}[/tex]

Given vertices of polygon KLMN:

Plot the vertices on the given graph paper and join with line segments to create the polygon.

As the y-coordinate of points K and L, and M and N are the same, KL and MN are parallel line segments.

As the difference between the x-coordinates of K and N, and L and M is 2 units, KN and LM are parallel line segments.

Therefore, the polygon is a parallelogram.

A parallelogram has two pairs of opposite sides that are equal in length.

Therefore, KL = NM and KN = LM.

As points K and L share the same y-coordinate:

[tex]\implies KL = |x_K-x_L|=|-1-4|=5\:\: \sf units[/tex]

Use the distance formula to find the length KN:

[tex]\begin{aligned}KN & =\sqrt{(x_N-x_K)^2+(y_N-y_K)^2}\\& =\sqrt{(-3-(-1))^2+(-2-1)^2}\\& =\sqrt{(-2)^2+(-3)^2}\\& =\sqrt{4+9}\\& =\sqrt{13}\\\end{aligned}[/tex]

The perimeter of a two-dimensional shape is the distance all the way around the outside.

[tex]\begin{aligned}\textsf{Perimeter of $KLMN$} & = 2\:KL + 2 \:KN\\& = 2 \cdot 5 + 2\cdot \sqrt{13}\\& =10 + 2\sqrt{13}\\& = 17.21\:\: \sf units\:(nearest\:hundredth)\end{aligned}[/tex]

Answer:

4 - 3x

Step-by-step explanation:

please mark me as brainliest

Answer:

3x-4= Y

Y= her dad's age.

2400mL is the amount of 60%acid solution to mix.

Let the amount of acid be mixed be x.

From the question, we get an equation that,

60%x + 35% × 600/ x + 600 = 55%

(Here x ≠ -600, as the denominator can never be 0.)

60%× x + 35% ×600 = 55%(x + 600)

Now we have to find the value of x to know the amount of acid that is mixed in a solution.

0.60x + 0.35 × 600 = 0.55(x+600)

0.60x + 210 = 0.55 + 330

0.05x = 120

x = 120/0.05

  = 2400

Therefore we get an amount of acid to be mixed is 2400mL.

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Answer:

only D is negative on the leading term

Step-by-step explanation:

even roots bounce at (0,0)

negative leading coefficient: initial graph descending to right, curve up

4 local extremes means remaining 5 degree of the function

[tex]\displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\hspace{5em}\stackrel{\textit{L'Hopital's rule}}{\lim_{x\to 44}~\cfrac{ ~~ \frac{d}{dx}[\sqrt{x+5}-7] ~~ }{\frac{d}{dx}[x-44]}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{d}{dx}[\sqrt{x+5}-7]\implies \cfrac{1}{2}(x+5)^{-\frac{1}{2}}(1)\implies \cfrac{1}{2\sqrt{x+5}} \\\\\\ \cfrac{d}{dx}[x-44]\implies 1 \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\implies \lim_{x\to 44}~\cfrac{ ~~ \frac{1}{2\sqrt{x+5}} ~~ }{1}\implies \lim_{x\to 44}~\cfrac{1}{2\sqrt{x+5}}\implies \cfrac{1}{2\sqrt{44+5}} \\\\\\ \cfrac{1}{2\sqrt{49}}\implies \cfrac{1}{2(7)}\implies \cfrac{1}{14}[/tex]

Answer: Here's the answer step by step

Step-by-step explanation: First, find the square root of 1000000 base to and leave your answer in base two

find the square root of 111 in base 2

simplify 342+134-233 in base 5

divide 100001 by 11 in base 2

convert 123.12 in base 3 to a number in base 10 and make sure you leave your answer in base 2

Last step: convert 3.875 in base 10 to a number in base 2

Answer:

[tex]\large\text{$y=ke^{\frac{1}{3}x^3+x}$}[/tex]

Step-by-step explanation:

Given differential equation:

[tex]\large\text{$\dfrac{\text{d}y}{\text{d}x}=y(x^2+1)$}[/tex]

Rearrange the equation so that all the terms containing y are on the left side, and all the terms containing x are on the right side:

[tex]\large\text{$\implies \dfrac{1}{y}\;\text{d}y=(x^2+1)\;\text{d}x$}[/tex]

Integrate both sides, remembering to add the constant of integration (C):

[tex]\large\begin{aligned}\implies \displaystyle \int\dfrac{1}{y}\;\text{d}y & =\int(x^2+1)\;\text{d}x\\\ln y & = \dfrac{1}{3}x^3+x+\text{C}\end{aligned}[/tex]

Rewrite C as ln k:

[tex]\large\text{$\implies \ln y = \dfrac{1}{3}x^3+x+\ln k$}[/tex]

Solve for y, applying:

[tex]\large\text{$ \implies e^{\ln y} =e^{\frac{1}{3}x^3+x+\ln k}$}[/tex]

[tex]\large\text{$ \implies y=e^{\ln k} \cdot e^{\frac{1}{3}x^3+x}$}[/tex]

[tex]\large\text{$\implies y=ke^{\frac{1}{3}x^3+x}$}[/tex]

Integration rules

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.1 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\\\(where $n$ is any constant value) \end{minipage}}[/tex]

Answer:

[tex]{ \tt{ \frac{dy}{dx} = y( {x}^{2} + 1) }} \\ [/tex]

- Simplify by collecting each term according to its corresponding d

[tex]{ \tt{ \frac{dy}{y} = ( {x}^{2} + 1) \: dx}} \\ [/tex]

- Integrate both sides;

[tex]{ \tt{ \int \frac{1}{y} \: dy = \int ( {x}^{2} + 1) \: dx }} \\ \\ { \tt{ ln(y) = \frac{1}{3} {x}^{3} + x + c }}[/tex]

- To make y the subject, you must remove the natural log;

[tex]{ \tt{ log_{e}(y) = \frac{1}{3} {x}^{3} + x + c }} \\ \\ { \tt{y = {e}^{( \frac{1}{3} {x}^{3} + x + c) } }} \\ [/tex]

Answer:

1) 60

2) 90

Step-by-step explanation:

Evaluate (f+2) (g+8), when f = 4 and g = 2

Solution

(f+2) (g+8)

Evaluate for f=4,g=2

(4+2)(2+8)

(4+2)(2+8)

=60

Evaluate 2Tu, when T = 5 and u = 9

Solution

2tu

Evaluate for t=5,u=9

(2)(5)(9)

(2)(5)(9)

=90

Answer:

Step-by-step explanation:

replace f and g for their values

(4+2)(2+8)

= 6*10

= 60

replace t and u for their values

2*5*9

= 10*9

= 90

Answer:

Step-by-step explanation:

                           [tex]\displaystyle\\\boxed {M_{AB}=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2} ) }[/tex]

1) E(-5,-3)      F(3,7)      M(x,y)=?

[tex]\displaystyle\\M(x,y)=(\frac{-5+3}{2} ),\frac{-3+7}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{4}{2} )\\\\ M(x,y)=(-1,2)\\\\Thus, \ M(-1,2)[/tex]

2) L(-8,11)     N(-3,12)      M(x,y)=?

[tex]\displaystyle\\M(x,y)=(\frac{-8+(-3)}{2} ,\frac{11+12}{2} )\\\\M(x,y)=(\frac{-11}{2},\frac{23}{2})\\\\ M(x,y)= (-5.5,11.5)\\\\Thus, M(-5.5,11.5)[/tex]

3) A(-4,6)    B(2,4)    M(x,y)=?

[tex]\displaystyle\\M(x,y)=(\frac{-4+2}{2},\frac{6+4}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{10}{2})\\\\ M(x,y)=(-1,5)\\\\ Thus,\ M(-1,5)[/tex]

Answer:

Step-by-step explanation:

330-250 =80

Answer:

The mean will move to the left as more affordable vehicles are introduced.

Step-by-step explanation:

It is given that a car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.

We need to find how will the distribution be affected if he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years.

Now, let us understand what is meant by mean;

What is the Mean ?

The mean of a set of data is its average value.

Further, It is given that the car salesman sells cars with prices ranging from $5,000 to $45,000.

Additionally, the salesperson has noticed that a lot of students are searching for vehicles around $5,000.

If he chooses to sell vehicles as well and anticipates selling 200 of them over the following ten years,

The histogram will deviate from its mean if cards with values less than $5,000 are also included in the data set.

The mean will move to the left as more affordable vehicles are introduced.

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The value of x is 13

From the diagram shown, we have that the line segments as;

NK = NM + ML + LK

Where;

Substitute the values into the equation

(x - 6) + 9 + 2x - 19 = 23

collect like terms

x + 2x -6 + 9 - 19 = 23

Add like terms

3x - 16 = 23

3x = 23 + 16

3x = 39

Divide both sides by 3

x = 39/ 3

x = 13

Thus, the value of x is 13

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√80 on the number line would be marked at (8.94, 0) on the number line.

Hope this graph helps!