A rental car company charges $63.41 per day to rent a car and $0.05 for every mile driven. Ella wants to rent a car, knowing that: She plans to drive 275 miles. She has at most $200 to spend. What is the maximum number of days that Ella can rent the car while staying within her budget?

to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]

[tex]\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}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]

Supplementary Angles:

[tex]\boxed{100°} and \boxed{80°}[/tex]

Arithmetically speaking, the closest 2 supplementary angles can get (in 3 and 2 digits respectively) is the upwritten.

Complementary Angles:

[tex]\boxed{45°} and \boxed{45°}[/tex]

Simply, in this case, for angles to be numerically as close as possible - make both the angles 45°.

[tex]a\cdot a^2+b\cdot a+c=a^3+ab+c[/tex]

Answer:

AB=CD and BC=AD because both of them are visually paired with the same longitude.

Answer:

AB = CD, BC = AD

Step-by-step explanation:

According to parallelogram properties,

Angle A = 180-Angle B; False
AB!=BC; False

AC==BD is only true when AB = BC, False
AB ==CD, BC == AD; True

After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent. [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We have:

A philanthropist pledges to donate 10% of a fund each year.

We can find the amount left after 7 years as follows:

A = 450000(1 - 0.1)⁷

10% of a fund each year.

Rate r = 10% = 0.1

A = 450000(0.9)⁷

A = $2152336.05

Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.

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The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)

From the question, we are to determine the solutions to the given system of equations

The given system of equations are

x + y = 3 ----------- (1)

y = x² - 9 ----------- (2)

From equation (1)

x + y = 3

We can write that

y = 3 - x -------- (3)

Substitute this into equation (2)

y = x² - 9

3 - x = x² - 9

x² +x -3 - 9 = 0

x² +x -12 = 0

Solve quadratically

x² +x -12 = 0

x² +4x -3x -12 = 0

x(x +4) -3(x +4) = 0

(x -3)(x +4) = 0

∴ x -3 = 0 OR x +4 = 0

x = 3 OR x = -4

Now, using equation (3)

When x = 3

y = 3 - x

y = 3 - 3

y = 0

When x = -4

y = 3 - -4

y = 3+4

y = 7

∴ When x = 3, y = 0; and when x = -4, y = 7

Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)

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the awnser is B x-2                    

Answer:

  (b)  domain: {-2, 0, 2}, range: {-1, 0, 1}

Step-by-step explanation:

For the function defined by the table ...

  [tex]\begin{array}{|cccc|}\cline{1-4}x&-2&0&2\\\cline{1-4}y&-1&0&1\\\cline{1-4}\end{array}[/tex]

we want the function's domain and range.

__

The domain is the list of x-values for which the function is defined. Here, that list is ...

  domain = {-2, 0, 2}

__

The range is the list of y-values the function produces. Here, that list is ...

  range = {-1, 0, 1}

_____

The domain and range sets are most conveniently listed in order, with duplicates removed.

Answer: 30

Step-by-step explanation:

     A LCD, or least common denominator, is the lowest common multiple of both denominators.

     Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...

     Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...

    We can see the LCD of 3/5 and 5/6 is:

           30

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The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal.  In this case, the problem is asking us to determine the LCD or least common denominator of two numbers.  We are provided with two fractions that we will use to help determine our solution.  However, before solving for the LCD let us first define what LCD means.

Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.

Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.

Answer:

Given:

Cylinder: height = 16 cm ; radius = 5 cm

cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³

Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³ 

The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos

A) The percentage of respondents who do not like both hamburgers and burritos is; 33/250 * 100% = 16.09%

B) Marginal relative frequency of all customers that like hamburgers will be the ratio of the sum of the customers that like hamburgers to the total number of respondents. Thus;

MRF = 134/205 = 0.65

C) Let us first find the ratio of all the four data with the total;

Ratio of those who like Hamburgers and burritos = 39/134 = 0.29

Ratio of those who like Hamburgers but not burritos = 95/134 = 0.71

Ratio of those who like burritos but not Hamburgers = 38/71 = 0.53

Ratio of those who do not like burritos or Hamburgers = 33/71 = 0.47

Thus, The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos

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The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that.  Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.

The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.

Distribute

After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.

Subtract 12 from both sides

The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h.  Then we will simplify the expression and that will give us our final answer.

Divide both sides by -2

Simplify the expression

We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.

Answer:

-∞ < y ∞

The range is all real numbers.

Answer:

Add and Divide.

Mean = 84

Step-by-step explanation:

Mean ( math word) and average (common usage word) tell us to ADD up the numbers in the list of data and DIVIDE by the number of pieces of data.

Here we add:

(80 + 84 + 88)

then divide by 3, because there's 3 numbers in this list.

(80 + 84 + 88)/3

= 252/3

= 84

The mean, or average is 84.

Answer:

see below

Step-by-step explanation:

You didn't include the choices but here is a solution

tan 68 = opp/adj = height / 13

13 Tan 68  = height of pole

Answer:

9

Step-by-step explanation:

[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]

Answer:

y = 3/2x + 7/2

Step-by-step explanation:

Slope-intercept form is when y is the subject. So we make y the subject:

Add 3x to both sides :

2y = 3x + 7

Now we divide both sides by 2 :

y = 3/2x + 7/2

This is our final answer.

Hope this helped and brainliest please

Hi student, let me help you out! :)

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We are asked to write the equation -3x+2y=7 in slope-intercept form.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's write this equation, -3x+2y=7, in slope-intercept form...

///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\///\\\////\\\///\\\///\\\////\\\\////\\\\

First, we add -3x to both sides of the equal sign:

[tex]\large\pmb{2y=7+3x}[/tex]

We can switch the order of the terms:

[tex]\large\pmb{2y=3x+7}[/tex]

This is starting to look like the slope-intercept equation. In fact, all we have to do is divide both sides by 2:

[tex]\large\pmb{y=(3x+7)\div2}[/tex]

Which simplifies to...

[tex]\large\pmb{y=\cfrac{3}{2}x+\cfrac{7}{2}}[/tex]

That's the equation in slope-intercept form.

Hope this helps you out! :D

Ask in comments if any queries arise.

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The solution to the system of equation is x = -7+√17/2 and -7-√17/2

Equations are expressions separated by an equal sign

Given the equation

x^2 = –7x – 8

Equate to zero

x^2+7x+8 = 0

Factorize

x = -7±√49-4(8)/2

x =  -7±√17/2

x = -7+√17/2 and -7-√17/2

Hence the solution to the system of equation is x = -7+√17/2 and -7-√17/2

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Answer:

Option 4

Step-by-step explanation:

The answer above is correct.

Answer:

As a fraction:

x | y

________

|

7/3 | 2

3 | 4

11/3 | 6

13/3 | 8

As a mixed fraction:

x | y

________

|

2 ⅓ | 2

3 | 4

3 ⅔ | 6

4 ⅓ | 8

As a decimal:

x | y

___________

|

2.33.. | 2

3 | 4

3.66.. | 6

4.33.. | 8

You should start with x values since the y values will be easier to plot. x's will not be easy to represent.

For example:

x | y

________

|

0 | -5

1 | -2

2 | 1

3 | 4

4 | 7

5 | 10

Answer:

h = 19

Step-by-step explanation:

The are is given so we can use the area to find the height because the area of a trapezoid is calculated by the following formula:

1/2 * (a+b)*h (a: base, b: base, h: height)

We already know the bases; 37 and 51

1/2*(37+51)*h = 836 first multiply both sides by 2

(37+51)*h = 1672 now divide both sides by 88 (sum of bases)

h = 19

There are 6 terms in the sequence greater than 1.

A geometric series is  sum of infinite numbers which has a common ratio between its successive terms.

The missing common ratio value is -1/2

It is given in the question that

the number of terms in the sequence = 300

Sum = a₁ (1-rⁿ)/(1-r)

nth term is given by

aₙ = a₁r⁽ⁿ⁻ ¹⁾

1337(1/2)^(n - 1) = 1

(1/2)^(n - 1)  = 1/1337

Applying log on both sides

log (1/2)^(n - 1) = log (1/1337)

(n - 1) log(1/2)  = log(1/1337)

n  = log (1/1337)/ log (1/2) + 1 ≈ 11.384

the 11th term  is 1337(-1/2)^(10)  ≈ 1.305

and

And the 12th term is 1337(-1/2)^11  =  -.653

As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.

Therefore there are 6 terms in the sequence greater than 1.

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -3 \\\\\\ \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}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10[/tex]

Answer:

d

Step-by-step explanation:

the length is how many units greater than twice the width ?

you skipped that information from us.

so, all we can say

length = 2×width + x

the perimeter is

2×length + 2×width

with width = w we get by using the first equating in the second :

2×(2×w + x) + 2×w = 4w +2x + 2w = 6w + 2x

so the right answer must be d.

it is the only option with "6w".

it means that 2x = 5 and x = 2.5.

so it was that the length is 2.5 units greater than twice the width

Answer:

3 teaspoons

Step-by-step explanation:

Three teaspoons are equivalent to one tablespoon

The correct answer is option C which is  [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

The multiplication of the matrix will be calculated as:-

M = [tex]\dfrac{1}{2}\left[\begin{array}{cc}12&64&\\78&30&\\\end{array}\right][/tex]

M  =    [tex]\left[\begin{array}{cc}\dfrac{12}{2}&\dfrac{64}{2}&\\\dfrac{78}{2}&\dfrac{30}{2}&\\\end{array}\right][/tex]

M =     [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

Therefore the correct answer is option C which is  [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^k~~ = ~~\cfrac{1}{x^{-1}}\implies x^k~~ = ~~x^1\implies k=1[/tex]

The summation notation is ∑ [tex](4^{n} -1)\\[/tex]/2.

The common ratio multiplied here to each term to get the next term is a non-zero number.

Given:  1/2+2+8+32+128

Using,

[tex]a_n= a_1r^{n-1}[/tex]

We have,

a1 =1/2 and r= 4

notation is : An= ∑ [tex](4^{n} -1)\\[/tex]/2

Hence, the notation is  An= ∑ [tex](4^{n} -1)\\[/tex]/2.

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Answer:

12 or 7??

Step-by-step explanation:

it depends if they are being spinned at the same time because then you can get for eg. 'A,1' 'A2' etc.

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5s^2}{s}[/tex]

[tex]\\ \rm\Rrightarrow 5s[/tex]