A car rents for $230 per week plus $0.25 per mile. Find the rental cost for a three week trip of 600 miles.

Answer:

Part 1) The equation for the monthly charges for Runfast is [tex]y=8x+8[/tex] and for BA&D is [tex]y=4x+15[/tex]

Part 2) The solution of the system of equations is the point  (1.75.22)

Step-by-step explanation:

Let

x -----> the number of gig of data

y -----> the total monthly charges

we know that

Runfast Company

[tex]y=8x+8[/tex] -----> equation A

BA&D Company

[tex]y=4x+15[/tex] -----> equation B

Part 2) Use your mathematical skill to solve this system of equations using the substitution method

we have

[tex]y=8x+8[/tex] -----> equation A

[tex]y=4x+15[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]4x+15=8x+8[/tex]

[tex]8x-4x=15-8[/tex]

[tex]4x=7[/tex]

[tex]x=1.75\ Gb[/tex]

Find the value of y

[tex]y=8(1.75)+8=\$22[/tex]

so

The solution is the point (1.75.22)

That means

For the number of gig equal to 1.75 the monthly charge is equal to $22 in both company's

therefore

For a number of gigs less than 1.75 the company Runfast has the better pricing, while for a number of gigs greater than 1.75 the company BA&D has the better pricing

Answer:

m∠8 = 4x

Step-by-step explanation:

Angle 8 is the same angle measure of angle 1, which is m∠1 = 4x

Answer:

d = C /t

Step-by-step explanation:

C = td

We want to isolate d, so divide each side by t

C/t = td/t

C/t = d

d = C /t

Answer: c/d = t

Since d is being multiplied by t, to get d by itself we simply divide both sides of the equation by t and we have c/d = t which is our final answer.

Answer: 4 + (-1)^10 = 4+ 1 = 5

The tenth term of the sequence is 5.

Given to us,

Sequence, [tex]\bold{a_n=4+(-1)^n}[/tex]

For tenth term,

n = 10,

Subsituting the value of n we get,

[tex]{a_n=4+(-1)^n}\\a_{10}=4+(-1)^{10}\\a_{10} = 4 + 1\\a_{10} = 5[/tex]

Hence, the tenth term of the sequence is 5.

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Answer:

about 785.4

Step-by-step explanation:

The circumference of a circle is pi times the diameter:

C = πd

C = π·(250 ft) ≈ 785.4 ft

_____

Most scientific or graphing calculators have the value of π built in. If yours doesn't, a value good for at least 6 significant figures is the ratio 355/113.

The ferris wheel rotates approximately 785 feet in one complete turn. This was calculated using the circumference formula, 2πr, with the radius derived from the given diameter of 250 feet.

To solve this problem, we need to determine the circumference of the Ferris wheel as that would be equivalent to the distance the ferris wheel rotated in one complete turn. The formula to calculate the circumference of a circle (or ferris wheel in this case) is 2πr (2 times pi times the radius), where 'r' is the radius of the circle. However, since we're given the diameter of the Ferris wheel as 250 feet, we know that the radius 'r' would be half of the diameter. That would imply that the radius in this case is 250/2 = 125 feet. So, using the aforementioned formula, the circumference would therefore be 2 × π × 125, or approximately 785 feet. Therefore, with each complete turn, the Ferris wheel would rotate by about 785 feet.

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The answer is I. 8

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Answer:

-6x + 15 = - 69 which x = 14

Step-by-step explanation:

You cannot solve this equation. There is no equal sign anywhere. Either you mean

-6x = 15 in which case the answer is

-6x/-6 = 15/-6

x = - 2 1/2 or x= - 2.5

or you mean that you use the distributive property

- 3(2x + 5)

You may have left something out of this.

-6x + 15 = -  69

You can do it now that you have the complete equation. But you need the entire equation before you can answer the question.

Subtract - 15 from both sides.

-6x + 15 - 15 = -69 - 15

-6x = - 84

Divide by - 6

-6x/-6 = - 84/-6

x = 14

But what you want is

-6x + 15

-6*14 + 15

-84 + 15

-69

-6x + 15 = - 69

when x = 14 which is usually what you are asked.

Answer:

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1). This latter form can be more useful for many problems that involve polynomials.

Step-by-step explanation:

The quotient in polynomial division refers to the result of dividing one polynomial by another. When a polynomial S is divided by a polynomial P, the result is a quotient Q of a degree less than P. The quotient Q represents a rational function when it is derived from the division of two polynomials.

In terms of algebra, let's consider a polynomial P of degree n, and we divide another polynomial S with a degree less than 2n by P. The result is a quotient Q and a remainder R, both of which are polynomials and Q has a degree less than n. If P(x) has a degree higher than Q(x), one can use the method of long division to find the quotient. This quotient, Q, alongside the remainder, R, conforms to the relation S(x) = P(x)\Q(x) + R, where Q and R are of lesser degrees than P.

When dealing with rational functions, we often find ourselves in positions of evaluating expressions formed by dividing polynomials. These functions are called rational functions, which are essentially the quotient of two polynomials. Applying the quotient rule can simplify differentiable polynomial functions and is useful when finding limits or derivatives in calculus.

Answer:

the answer is D

Step-by-step explanation:

To solve the inequalities 3x + 1 ≥ 8 and 10x ≤ 15, we find that no x can satisfy both inequalities simultaneously. Thus, the solution set is empty and the correct answer is B. No solution.

Solving the System of Inequalities

We need to find the solution set for the system: 3x + 1 ≥ 8 and 10x ≤ 15.

3x + 1 ≥ 8

Subtract 1 from both sides: 3x ≥ 7

Divide by 3: x ≥ 7/3 x ≥ 2.33

10x ≤ 15

Divide by 10: x ≤ 1.5

For the two conditions x ≥ 2.33 and x ≤ 1.5 to both be true, there is no number x that satisfies both.

Therefore, the solution set is empty.

The correct answer is B. No solution.

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{4}{7}\right)^r=\dfrac{s}{343}\\\\\dfrac{4^r}{7^r}=\dfrac{s}{7^3}\to r=3\ and\ 4^r=s\\\\4^r=4^3=64\to  s=64[/tex]

Answer:

i believe it would be 1/27 or 0.037 depending on the form you need it in

Step-by-step explanation:

[tex] \bf \underline{Solution-} \\ [/tex]

[tex]\textsf{Given}\\[/tex]

[tex] \sf{ {9}^{ \frac{3}{2} } } \\ [/tex]

[tex] \longrightarrow{ \: ( {3}^{2} {)}^{ \frac{3}{2} } } \\ [/tex]

[tex] \longrightarrow{ \: {3}^ { \cancel2 \times \frac{3}{ \cancel2} } } \\ [/tex]

[tex] \longrightarrow{ {3}^{3} } \\ [/tex]

[tex] \longrightarrow{ \: 3 \times 3 \times 3} \\ [/tex]

[tex] \sf \longrightarrow{ \: 27 \: ans.} \\ [/tex]

[tex]\textsf{Hope this helps!!}\\[/tex]

A. f(-3) = -11

If the function is f(x) = 2x - 5, then just replace x with -3 to find f(-3).

f(-3) = 2(-3) - 5

Multiply 2 times -3.

f(-3) = -6 - 5

Subtract -6 minus 5.

f(-3) = 11

There’s the answer.

Answer:

-11

Step-by-step explanation:

If you substitute x with -3 in the equation then you will get -11. Have a good night/day!

=)

The value of the expression is 14.

Step-by-step explanation:

That means it is rotated 90° clockwise about the origin.

Answer:

90° clockwise rotation .

Step-by-step explanation:

Given  : Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x).

To find : Which is another way to state the transformation.

Solution : We have given that Quadrilateral ABCD

(x, y) → (y, –x).

It can be stated as it is as 90° clockwise rotation .

Therefore,  90° clockwise rotation .

Answer:

c. 10

Step-by-step explanation:

First of all, the sum can be simplified.

[tex]\sum\limits^6_{n=1} {(x-3n)}=\sum\limits^6_{n=1} {x}-3\sum\limits^6_{n=1} {n}\\\\=6x-3\cdot\dfrac{6\cdot 7}{2} =6x-63[/tex]

This result can be used in the equation ...

6x -63 = -3

6x = 60 . . . . . add 63

x = 10 . . . . . . . divide by 6

_____

Comment on the ∑n

The sum of numbers 1 to n is n(n+1)/2. We have used that fact here. For this problem, the sum is short enough you can simply add it up: 1+2+3+4+5+6 = 21.

[tex]\bf \displaystyle\sum\limits_{n=1}^{6}~(x-3n)=-3\implies \sum\limits_{n=1}^{6}~x-\sum\limits_{n=1}^{6}~3n=-3\implies \sum\limits_{n=1}^{6}~x-3\sum\limits_{n=1}^{6}~n=-3 \\\\\\ 6(x)~~-~~3\left[ \cfrac{6(6+1)}{2} \right]=-3\implies 6x~~-~~3[3(7)]=-3\implies 6x - 63 = -3 \\\\\\ 6x=60\implies x=\cfrac{60}{6}\implies x=10[/tex]

Answer:

Step-by-step explanation:

[tex]x^o\ \text{and}\ \left(\dfrac{2}{3}x\right)^o\ \text{are suplementary angles, therefore}\\\\x^2+\left(\dfrac{2}{3}x\right)^o=180^o\\\\x+\dfrac{2}{3}x=180\qquad\text{multiply both sides by 3}\\\\3x+2x=540\\\\5x=540\qquad\text{divide both sides by 5}\\\\x=108[/tex]

Answer:

hey can pay for 9 months

Step-by-step explanation:

585/65

Just simply divide 585 with 65 and you get number of months.

[tex]585\div65=\boxed{9}[/tex]

Tom can pay for 9 months for his gym membership.

Hope this helps.

r3t40

Answer:

$21.34

Step-by-step explanation:

You and 3 friends went out for dinner, total 4 people

The bill is $85.36

So

Each person owes = $85.36 / 4 = $21.34

Answer:28.45

Step-by-step explanation:divide 3 by 85.36

Answer:

637

Step-by-step explanation:

Ticket ending 00= £12 * 7 = £84  

Tickets ending 5 = £1.5 * 75 = £112.5  

£84+£112.5=£196.5  

Price money + Profit: £196.5+£163= 356

356/£0.5 = 719 total tickets sold

719- 82 (WINNING TICKETS) = 637 losing tickets sold

Tomas made £232.5 from the winning tickets. Subtracting his profit of £163, we see he made £69.5 from the losing tickets. At a price of £0.5 per ticket, that means he sold 139 losing tickets.

First, calculate the total amount Tomas made by selling all the winning tickets. There are ten tickets that end in '00' between 1 and 750, each valued at £12, i.e., £120. There are 75 tickets that end in '5' between 1 and 750, each valued at £1.50, i.e., total of £112.50. So, the total income from these tickets is £120 + £112.50 = £232.5.

Then, subtract Tomas's profit from the total income of the winning tickets to get the total revenue from the losing tickets. So, £232.5 - £163 = £69.5. Given each ticket costs 50p or £0.5, divide £69.5 by £0.5 to find the number of losing tickets sold. That is, £69.5/£0.5 = 139. Thus, Tomas sold 139 losing tickets.

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By buying 9 packs of 4 cartons and 2 single cartons, Lewis was able to spend the least amount of money to get the 38 cartons he needed. The total cost was £14.94.

The subject of this question is mathematics, specifically cost optimization and arithmetic. Lewis can buy single carton of juice for 45p or a pack of 4 cartons for £1.56. The goal is to minimize the cost. First, Lewis can start by buying packs of 4. The number of 4-carton packs he can buy is 38 divided by 4 which gives you 9 packs that include 36 cartons. He then needs to buy 2 more single cartons to reach 38. So, the total cost is 9 packs times £1.56/pack plus 2 single cartons times 45p/carton. Doing the arithmetic:

Convert 90p to pounds that is £0.90. Adding both gives £14.94. Therefore, Lewis spent a total of £14.94 on juice cartons.

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Answer:

∛4²

Step-by-step explanation:

A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.

To write an exponent in radical form , the denominator, or index goes in front of the radical, and the numerator goes inside of the radical. We raise the base to the power of the numerator

4 2/3

∛4².

The radical form of 4 2/3 is the cube root of 4 squared, denoted as √(4^2).

The radical form of the expression 4 2/3 means expressing the number as a radical, which refers to roots of numbers. In this case, the number 2/3 is the exponent in fractional form. To convert this into a radical, the numerator indicates the power and the denominator indicates the root. Therefore, 42/3 can be expressed as the cube root of 4 squared. The cube root is denoted by the radical symbol √ with a small three above or to the left of the radical. Thus, 42/3 = √(42).

Answer:

Final answer is [tex]P(B|A)=0.40[/tex].

Step-by-step explanation:

Given that P(A)= .50, P(B)=.80 , and P(A and B)=.20.

Now we need to find about what is the value of P(B/A).

So apply the formula of compound probability :

P(A and B) = P(A)*P(B/A)

Plug the given values into above formula

0.20 = 0.50*P(B/A)

0.50*P(B/A) = 0.20

[tex]P(B|A)=\frac{0.20}{0.50}[/tex]

[tex]P(B|A)=0.40[/tex]

Hence final answer is [tex]P(B|A)=0.40[/tex].

THE ANSWER ABOVE/ BELOW IS WRONG!!!

The correct answer is actually:

140

Answer:

140

Step-by-step explanation:

Answer:

option A

f(x) = (x – 1)2 + 3

Step-by-step explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

ANSWER

The vertex form is

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

EXPLANATION

The given function is

[tex]f(x) = 4 + {x}^{2} - 2x[/tex]

This is the same as:

[tex]f(x) = {x}^{2} - 2x + 4[/tex]

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} - 2x + {( -1 )}^{2} - {( -1 )}^{2} + 4[/tex]

[tex]f(x) = {x}^{2} - 2x + 1 - 1 + 4[/tex]

The first three term is a perfect square trinomial:

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

The vertex form is

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

Answer:

77 inches

Step-by-step explanation:

Given

1 inch = 3 miles in map

We are also given the actual distance between City A and City B = 231 miles.

In order to get the distance in inches = Distance between City A and City B in miles/ 3

We are dividing the distance by 3 to get the distance in inches.

So,

Distance on map = 231/3

= 77 inches

Answer: 77 inches.

Step-by-step explanation:

You know that this map uses this scale:

[tex]1in=3mi[/tex]

This means that 1 inch in the map represents 3 miles.

In this case, you know that the actual distance between City A and City B is 231 miles, then, to find the distance between the cities on the map, you can set up de following proportion:

[tex]\frac{1in}{3mi}=\frac{x}{231mi}[/tex]

Now, you need to solve for "x":

[tex](231mi)(\frac{1in}{3mi})=x\\\\x=77in[/tex]

ANSWER

Option D

EXPLANATION

The parent radical function is

[tex]f(x) = \sqrt{x} [/tex]

The transformed function is

[tex]g(x) = 2 \sqrt{x - 3} [/tex]

This is a transformation of the form.

[tex]y = a \sqrt{x - k} [/tex]

which shifts the parent function horizontally by k units to the right and stretches the parent function vertically by a factor of 'a'.

In this case a=2 and k=3,

there is a horizontal shift of 3 units to the right and a vertical stretch by a factor of 2.

The last choice is correct.

Answer:

[tex]x_1=-4\\\\x_2=\frac{1}{3}[/tex]

Step-by-step explanation:

Given the quadratic equation:

[tex]2x^2+14x-4=-x^2+3x[/tex]

You can follow these steps in order to solve it:

- Make the equation equal to 0:

[tex]2x^2+14x-4+x^2-3x=0[/tex]

- Now, add the like terms:

[tex]3x^2+11x-4=0[/tex]

- Finally, apply the Quadratic formula ([tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]):

In this case we know that:

[tex]a=3\\b=11\\c=-4[/tex]

Therefore, substituting values into the Quadratic formula and evaluating, we get:

[tex]x=\frac{-11\±\sqrt{11^2-4(3)(-4)} }{2(3)}\\\\x_1=-4\\\\x_2=\frac{1}{3}[/tex]

To find the solutions to the quadratic equation 2x^2+14x-4=-x^2+3x, we need to rearrange the equation and use the quadratic formula.

The quadratic equation is 2x^2+14x-4=-x^2+3x. To find the solutions, we need to rearrange the equation in the form ax^2 + bx + c = 0. Combining like terms, we get 3x^2 + 11x - 4 = 0. Now we can use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values a = 3, b = 11, and c = -4 into the formula, we can calculate the solutions.

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Answer:

Step-by-step explanation:

Just use the slope equation.

Answer:

Final answer is [tex]x=9[/tex].

Step-by-step explanation:

we know that if BD is angle bisector of angle B in triangle ABC then

[tex]\frac{AB}{BC}=\frac{AD}{DC}[/tex]

[tex]\frac{36}{28}=\frac{x}{DC}[/tex]

[tex]\frac{36}{28}=\frac{x}{16-x}[/tex]

[tex]\frac{9}{7}=\frac{x}{16-x}[/tex]

cross multiply

[tex]7x=9(16-x)[/tex]

[tex]7x=144-9x[/tex]

[tex]7x+9x=144[/tex]

[tex]16x=144[/tex]

[tex]x=\frac{144}{9}[/tex]

[tex]x=9[/tex]

Hence final answer is [tex]x=9[/tex].

Answer:

First of all, let's find the area of the upper rectangle. We have side lengths 5 and 6, so its area is 30.

Now to find the bottom. If we add our ten, and the five on top, we get a length of 15. We multiply this by 6, giving us 90.

Now we add.

90+30=120

Therefore, our answer is A) 120 square units.

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Step-by-step explanation: