A rental car company charges $77.50 per day to rent a car and $0.10 for every mile driven. Sydney wants to rent a car, knowing that:
She plans to drive 275 miles.
She has at most $260 to spend.

Write and solve an inequality which can be used to determine xx, the number of days Sydney can afford to rent while staying within her budget.

[tex]\text{L.H.S}\\\\=\begin{vmatrix} 1 & bc& b+c\\ 1 & ca& c+a\\ 1 &ab&a+b\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & bc& b+c-(a+b+c)\\ 1 & ca& c+a-(a+b+c)\\ 1 &ab&a+b-(a+b+c)\end{vmatrix}~~~~~~~~~~~~~~~;c_3\rightarrow c_3 -(a+b+c)c_1\\\\\\=\begin{vmatrix} 1 & bc& -a\\ 1 & ca& -b\\ 1 &ab&-c\end{vmatrix}\\\\\\=\dfrac 1{abc}\begin{vmatrix} a & abc& -a^2\\ b & abc& -b^2\\ c &abc&-c^2\end{vmatrix}\\\\\\=-\dfrac {abc}{abc}\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\[/tex]

[tex]=-1\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\\\\\=-1 \times -1 \begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\text{R.H.S}\\\\\text{Showed.}[/tex]

Answer:

Hi,

Step-by-step explanation:

PR²=PQ²+QR²-2*PQ*QR*cos(51°)

=15²+12²-2*15*12*cos(51°)

=142,444659....

PR=11.9350...

PQ²=QR²+PR²-2*QR*PR*cos(R)

cos(R)=(12²+142.444...-15²)/(2*12*11.9350...)=0,21451112....

angle R=77,61315...°≈77.6°

angle P=180°-51°-77.6°≈51,4°

Answer:

Option A

Step-by-step explanation:

Remember the things.

In Q1

in Q2

in Q3

in Q4

Answer:

A. The x-coordinate is positive and the y-coordinate is positive.

Step-by-step explanation:

The Cartesian plane is divided into four regions by the x-axis and y-axis.

These regions are called "quadrants".

Quadrant I is the top right region, where x and y coordinates of points are positive.

From here, move in a counterclockwise direction.  

Therefore, Quadrant II is the top left region, where the x-coordinate is negative and the y-coordinate is positive.

Quadrant I → (x, y)

Quadrant II → (-x, y)

Quadrant III → (-x, -y)

Quadrant IV → (x, -y)

Answer:

200 KM/H

Step-by-step explanation:

A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.

let x=speed of wind

(840+x)=speed of plane with wind

(840-x)=speed of plane against wind

Travel time = distance/speed (same with and against the wind)

3120/(840+x)=1920/(840-x)

cross-multiply

3120*840-3120x=1920*840+1920x

3120*840-1920*840=1920x+3120x

5040x=1008000

x=200 km/hr

answer

Speed of wind=200 km/hr

Answer:

14.5 Meters

Step-by-step explanation:

1 centimeter= 0.01 Meters

1450 cm x 0.01 =14.5

Answer: x = 13

Step-by-step explanation: First, we simplify the equation to get 4x + 7 = 5x - 6. Then, from there, we subtract 7 on both sides to get 4x = 5x - 13. Then we subtract 5x from both sides, which would give us -x = -13. Finally, we can divide both sides by -1 (because remember, x = 1) to get that x = 13. Hope this helps!

Answer:

infinite number of solutions

Step-by-step explanation:

x + y = 1 → (1)

3y = - 3x + 3 ( add 3x to both sides )

3x + 3y = 3 ( divide through by 3 )

x + y = 1 → (2)

since the 2 equations are the same, this indicates the system has an infinite number of solutions

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Given that;

To determine how long it take to fill the dam, we say;

Time need = Amount of water needed ÷ Pump rate

T = A ÷ r

T = 30000 litres ÷ 75 litres/minute

T = 400 minutes

Note that; 60min = 1hrs

Hence,

T = 6hours 40minutes

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

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Answer:

 x = -1

y = 4

Step-by-step explanation:

Solving system of linear equations by elimination method.

    8x +  3y = 4 ---------------(I)

    2x  + y = 2 --------------(II)

Multiply the second equation by (-3) and then add them.Thus y will be eliminated and we will obtain the value of 'x'.

       (I)                8x  +  3y = 4

     (II)*(-3)         -6x - 3y = -6   {Now add}

                           2x         = -2

                                     x = -2/2

                           [tex]\sf \boxed{\bf x = -1}[/tex]

Plugin x = (-1) in any one of the equations. Here I have chosen equation (II)

2*(-1) + y = 2

    -2 + y  = 2

           y = 2 + 2

            [tex]\sf \boxed{\bf y = 4}[/tex]

The equation of the translation is y = sin(x - π/4)

The equation is given as:

y = sin(x)

The rule of translation to the right is:

(x,y) => (x - h,y)

This gives

(x,y) => (x - π/4,y)

So, we have:

y = sin(x - π/4)

Hence, the equation of the translation is y = sin(x - π/4)

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Answer:

5/6

Step-by-step explanation:

i'm not rly confident,, but i used a calculator and solved it,,

so im sry if im wrong. Good luck!!

Answer:

4/13 is the answer

total = 4+3+5+1= 13

let a be the event of getting red marbles= total is 4

probability=4/13

Step-by-step explanation:

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in

a) The compound interest equation is [tex]C = 4250 \cdot 0.9675^{t}[/tex].

b) There is an approximate loss of $ 987.16.

c) The stock will take approximately 12.979 to decrease by half.

Compound interest model represents the gain of a deposit as a function of the number of periods and initial amount. The model is represented below:

[tex]C = C_{o}\cdot (1+r)^{t}[/tex]     (1)

Where:

Capital decreases in time when interest rate is a negative number. The equation that models the situation is [tex]C = 4250 \cdot 0.9675^{t}[/tex] and the current capital after eight years is:

C = 4250 · 0.9675⁸

C = 3262.84

That represents an approximate loss of $ 987.16.

And the number of periods required to decrease the capital by half is:

[tex]2125 = 4250 \cdot 0.9675^{t}[/tex]

[tex]0.5 = 0.9675^{t}[/tex]

㏒ 0.5 = t · log 0.9675

t ≈ 20.979

The stock will take approximately 12.979 to decrease by half.

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Answer:

[tex]\normalsize \textsf{$x = -\dfrac{8}{3}$}[/tex]

Step-by-step explanation:

Given: [tex]\normalsize \textsf{$3(2x - 9) - 4(3x + 4) = 2(x - 12) + \dfrac{7}{3}$}[/tex]

1. Distribute

For 3:

[tex]\normalsize \textsf{$3(2x - 9)$}\\\normalsize \textsf{$3(2x) + 3(- 9)$}\\\normalsize \boxed{\textsf{$6x -27$}}\\[/tex]

For -4:

[tex]\normalsize \textsf{$-4(3x + 4)$}\\\normalsize \textsf{$-4(3x) + -4(4)$}\\\normalsize \boxed{\textsf{$-12x -16$}}\\[/tex]

For 2:

[tex]\normalsize \textsf{$2(x - 12)$}\\\normalsize \textsf{$2(x) + 2(-12)$}\\\normalsize \boxed{\textsf{$2x -24$}}\\[/tex]

Now we have: [tex]\normalsize \textsf{$6x - 27 - 12x -16 = 2x-24 + \dfrac{7}{3}$}[/tex]

2. Combine like terms:

[tex]\normalsize \textsf{$-6x -43 = 2x -\dfrac{72}{3} + \dfrac{7}{3}$}\\\\\normalsize \textsf{$-6x -43 = 2x -\dfrac{65}{3}$}\\\\[/tex]

3. Subtract 2x from both sides:

[tex]\normalsize \textsf{$-6x-2x -43 = 2x -2x -\dfrac{65}{3}$}\\\\\normalsize \textsf{$-8x -43 = -\dfrac{65}{3}$}\\\\[/tex]

4. Add 43 to both sides:

[tex]\normalsize \textsf{$-8x -43 +43 = -\dfrac{65}{3} + 43$}\\\\\normalsize \textsf{$-8x = -\dfrac{65}{3} + \dfrac{129}{3}$}\\\\\normalsize \textsf{$-8x = \dfrac{64}{3}$}[/tex]

5. Divide both sides by -8

[tex]\normalsize \textsf{$-8x = \dfrac{64}{3}$}\\\\\normalsize \textsf{$-8x \div 8 = \dfrac{64}{3} \div -\dfrac{8}{1}$}\\\\\normalsize \boxed{\textsf{$x = -\dfrac{8}{3}$}}[/tex]

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You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression

An extraneous solution is a solution that in obtained after completely solving an equation but it does not  work in the original given equation.

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression (Option D).

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Answer:

a=

b=8

Step-by-step explanation:

20-5=15 (admittance fee)

15-3=12 (food and drink)

12÷1.5=8 rides because 1.50 is price for every ride

Answer:

C

Step-by-step explanation:

The y-intercept if the graph is 2 and the slope is 2 so the rule is y=2x+2

The 5th term of the sequence is 27.98

The given parameters are:

The nth term of a geometric sequence is calculated using:

[tex]T_n = ar^{n-1[/tex]

So, we have:

[tex]T_5 = 1 * 2.3^{5-1[/tex]

Evaluate the difference

[tex]T_5 = 1 * 2.3^4[/tex]

Evaluate the product

[tex]T_5 = 27.98[/tex]

Hence, the 5th term of the sequence is 27.98

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Answer:

give clear image is next question

Step-by-step explanation:

i will give you the answer

Answer:

$113.64

Step-by-step explanation:

0.88 x $113.636364 = 100 euros

= $113.64

(Hope this helps ^-^)

Answer:

5;   2n + 5 ≤ 15

6;   n/5 ≤ 15

7;   5n ≥ 15

Step-by-step explanation:

"a number" means a variable denoted "n"

"product" means to multiply

"quotient" means to divide

"The sum" means to add

"is at least" means greater than or equal to or  ≥

"is no greater than" means less than or equal to or ≤

"Is at most" means less than or equal to or ≤

Answer:  p = 2 3/7

Step-by-step explanation:

7p+13 = 30

7p = 17

p = 17/7

p = 2 3/7

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The value of p as a fraction in its simplest form is 17/7

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example:

1/2, 1/3 is a fraction.

2/4 is a fraction but we can simplify further since there is a common factor of 2 with 2 and 4.

2/4 = 1/2 is a fraction.

4/16 = 4/(4x4) = 1/4 is a fraction.

We have,

7p + 13 = 30

Solve for p.

Subtract 13 on both sides.

7p + 13 - 13 = 30 -13

7p = 17

Divide both sides by 7.

p = 17/7

We can not further simplify the fraction as there are no common factors between 17 and 7.

Thus,

The value of p as a fraction in its simplest form is 17/7

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The income that's made based on the equation when 1 comb is sold is $0.5.

From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.

Therefore, the income by selling 1 comb will be:

y = 1/2

y = $0.5

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Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

Answer:

Step-by-step explanation:

Comment

It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.

The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.

Answer

product

12

Answer:

24.19

Step-by-step explanation:

[tex] \tan(x) = \frac{6.2}{13.8} \\ x = { \tan}^{1} \frac{6.2}{13.8} \\ x = 24.19320899[/tex]

or the value of x can be 24.20