Algebra 1: Write and solve two-variable linear equations: word problems

Riley plans to join a members-only speaker series for $50. As a member, she will pay just $12.50 for each event she attends.

Write an equation that shows how the total cost, y, depends on the number of events Riley attends, x.

Do not include dollar signs in the equation.

Inequality can be used to find the domain of f(x)  is  [tex]$\quad x \geq 20$[/tex]

Interval Notation: [tex]$[20, \infty)$[/tex]

What is Domain definition?

The domain of a function is the set of input or argument values for which the function is real and defined.

Find non - negative values for radicals: [tex]$x \geq 20$[/tex]

The function domain

[tex]$$x \geq 20$$[/tex]

Range of[tex]$\sqrt{\frac{1}{2} x-10}+3:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq 3 \\ \text { Interval Notation: } & {[3, \infty)}\end{array}\right]$[/tex]

Function range definition

The set of values of the dependent variable for which a function is defined

The range of an radical function of the form [tex]$c \sqrt{a x+b}+k$[/tex] is [tex]$f(x) \geq k$[/tex][tex]$k=3$[/tex]

[tex]$f(x) \geq 3$[/tex]

Axis interception points of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None

x - axis interception points of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None

y - axis interception point of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None

None

Extreme Points of [tex]$\sqrt{\frac{1}{2} x-10}+3: \quad$[/tex]Minimum (20,3)

First Derivative Test definition

Suppose that [tex]$x=c$[/tex] is a critical point of f(x) then, If [tex]$f^{\prime}(x) > 0$[/tex] to the left of [tex]$x=c$[/tex]and [tex]$f^{\prime}(x) < 0$[/tex] to the right of x=c then x=c is a local maximum. If [tex]$f^{\prime}(x) < 0$[/tex] to the left of [tex]$x=c$[/tex] and [tex]$f^{\prime}(x) > 0$[/tex] to the right of [tex]$x=c$[/tex] then [tex]$x=c$[/tex] is a local minimum. If [tex]$f^{\prime}(x)$[/tex] is the same sign on both sides of [tex]$x=c$[/tex] then [tex]$x=c$[/tex] is neither a local maximum nor a local minimum.

[tex]$$f^{\prime}(x)=\frac{1}{2 \sqrt{2} \sqrt{x-20}}$$[/tex]

Find intervals: Increasing:20 [tex]$ < x < \infty$[/tex]

Plug [tex]$x=20$[/tex] into [tex]$\sqrt{\frac{1}{2} x-10}+3: \quad 3$[/tex]

Minimum (20,3)

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Answer:

0

Step-by-step explanation:

Answer:

------------------------------------------

Find prime factors of 1265.

We see it is divisible by 5 since ends with 5:

253 is not divisible by 3 or 9 since the sum of digits is not divisible by 3 or 9. It is not divisible by 7 (since 25 - 3*2 = 19 is not divisible by 7) but divisible by 11, since the sum of digits in odd places is same as the digit in the even place (recall divisibility by 11):

23 is a prime number so no more factors.

Hence the prime factorization of 1265 is:

The probability that exactly two of thirteen fireworks are blue ones out of total 4 selections is 63/143.

The stated data;

You want 2 of the 7 items she selects to be blue, leaving 2 to be red.

Selecting 2 blue out of 7 blues is ⁷C₂ = 7!/(5!.2!)  =  21

Selecting 2 red out of 6 red = ⁶C₂ = 6!/(4!2!) = 15

Selecting total of 4 out of 13 ; ¹³C₄ = 13! / (9!.4!) = 715

Thus, probability that exactly two of them are blue ones;

P(2 blue) = 21 x 15 / 715

P(2 blue) = 63/143

Thus, probability that exactly two of them are blue ones out of total 4 selections is 63/143.

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Answer:

h = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] + h = [tex]\frac{5}{3}[/tex] ( subtract [tex]\frac{1}{3}[/tex] from both sides )

h = [tex]\frac{5}{3}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

The linear function models the given situation will be equal to f(x) = $3600 - $400(x).

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Original price of Machine = $3600

Price lost by the machine each year = $400

Then, the equation will be,

f(x) = $3600 - $400(x)

Here, x represents the number of years.

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Answer:

f(x) = −400x + 3600

So the exact length of the curve is given by [tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]

Given the equation of curve:

[tex]y = 3+ 4x^\frac{3}{2}[/tex]

The length of the curve is given by [tex]L= \int\limits^a_b {\sqrt{1+(y^[/tex]

Where y^ is derivative of y with respect to x

So [tex]y= 4*(3/2) * \sqrt{x}= > 6 \sqrt{x}[/tex]

Given a=1 and b=0

So [tex]L= \int\limits^1_0 {\sqrt{1+(6\sqrt{x})^2 } } \, dx[/tex]

[tex]L= \int\limits^1_0 {\sqrt{1+36x } } \, dx[/tex]

let 1+36x be t

36dx = dt

As the value of x changes after the substitution of the value.

So now the L changes as:

[tex]L= 1/36 \int\limits{\sqrt{t } } \, dt[/tex]

[tex]L=1/36* \left \{ {{t=37} \atop {t=1}} \right. \frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]

[tex](1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]

the min value of t=1 and max value of t=37

[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]

[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]

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Using 1 balls and bins, n balls are thrown into m bins; m and n are positive numbers. the probability of any given bin containing one ball is n/m n * (1 - (1 - 1/m)^n) / m^2

Given that n is the number of balls and m is the number of bins, the probability of any given bin containing one ball is n/m. Therefore, the variance of x is equal to the variance of a binomial random variable with n trials and probability of success p = n/m.

By the formula for the variance of a binomial random variable, the variance of x is equal to n * (1 - (1 - 1/m)^n) / m^2.

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Answer:

A. 276 miles apart

Step-by-step explanation:

We have the information that if two cities are 1 inch apart then the distance between them is 24 miles.

If it is 11.5 inches apart, then we should multiply the 24 miles per inch by 11.5

24 miles / 1 inch

(24 miles / 1 inch) * 11.5 inches

Inches cancel so you are left with

24 * 11.5 = 276 miles

Answer:15x3 /=divide 5 = 9

Step-by-step explanation:

because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!

After solving the two digit number is 45.

In the given question,

The 2 digit number which become 5 by 6th of itself when it digit are revered.

The difference in the digit of the number being 1, then we have to find the two digit number.

Let the two digit number = 10y+x

When we reversed the number then the number is 10x+y

As given that;

10y+x = 5/6(10x+y)

Multiply by 6 on both side, we get

60y+6x = 50x+5y

Subtract 5y on both side, we get

55y+6x = 50x

Subtract 50x on both side, we get

55y-44x = 0

Divide by 11 on both side, we get

5y-4x = 0

4x-5y = 0......................(1)

It is given that the difference between the number is 1.

x-y = 1..................(2)

Multiply by 4 in equation 2

4x-4y = 4.........................(3)

Now subtract equation 3 and 1, we get

y = 4

Now putting the value of y in equation 2

x-4 = 1

Add 4 on both side, we get

x = 5

Since the number is 10y+x. So

10y+x = 10(4)+5

10y+x = 45

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The equilibrium price is; $12

The quantity for the two equations is; 400

The equilibrium price formula is based on the demand and supply quantities; you will set quantity demanded (Qd) equal to quantity supplied.

The equilibrium price definition above is one that tells us that there is a price point that meets the needs of both supply and demand. In order to understand when those needs are met, we need to know how to find equilibrium price.

We are given;

Quantity supplied; S(p) = -200 + 50p

Quantity demanded; D(p) = 1060 - 55p

Thus, equilibrium price is p when;

S(p) = D(p)

-200 + 50p = 1060 - 55p

1060 + 200 = 55p + 50p

1260 = 105p

p = 1260/105

p = $12

S(p) = -200 + 50(12)

S(p) = 400

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Answer:

10 Child Tickets

Step-by-step explanation:

25 x 12 = 300

So we need 60

6 x 10 = 60

Step-by-step explanation:

25 x 13 = 300

300 + 60 = 360

Answer:

7

Step-by-step explanation:

4+3=7

7-4=3

7-3=4

Answer:

I hope the image helps!

Answer: This means that the range of values of k is k ∈ [-1/3, 1/3].

Step-by-step explanation: The quadratic equation (x+2)² +3k-1=0 can be written as (x+2)² = 1-3k. For the equation to have two real and distinct roots, the expression under the square root must be nonnegative. Therefore, we have the inequality 1-3k ≥ 0. Solving this inequality gives us -1/3 ≤ k ≤ 1/3. This means that the range of values of k is k ∈ [-1/3, 1/3].

A committee with 4 democrats and 2 republicans formed from a group of 7 democrats and 5 republicans can be created in a total of 350 ways. Therefore, the option C holds true.

The calculation of the same has been shown as below,

A group has 7 Democrats and 5 Republicans.

Committee with 4 Democrats and 2 Republicans = 7C4 x 5C2

7C4 x 5C2 = 7! / (4! 3!) x 5! / (2! 3!)

7C4 x 5C2 =(7×6×5 / 3×2×1) x (5×4 / 2×1)

7C4 x 5C2 = 35 × 10

7C4 x 5C2 = 350

Therefore, a committee can be created in 350 ways.

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Complete Question

In how many ways can a committee with 4 Democrats and 2 Republicans be formed from a group of 7 Democrats and 5 Republicans?

A 105

B 924

C 350

D 1680

To find the percent that 1.5 is of 7.5, we need to divide 1.5 by 7.5 and multiply the result by 100% to convert it to a percentage:

1.5 / 7.5 = 0.2

0.2 * 100% = 20%

Therefore, 1.5 is 20% of 7.5.

To find the percent that 5ft is of 37.5ft, we need to divide 5 by 37.5 and multiply the result by 100% to convert it to a percentage:

5ft / 37.5ft = 0.1333

0.1333 * 100% = 13.33%

Therefore, 5ft is 13.33% of 37.5ft.

Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

81 of [60-{(8*7)-(13-(3*5))}] =

81 of [60-{56}-(13-15)] =

81 of [60-{56}-(-2) =

81 of [60-{56}+2] =

81 of [6] =

81% of 6 = 4.86

Answer:

(18, -15)

Step-by-step explanation:

The vector AB is defined by its starting and endpoints. Usually, B would be at the end, but in this case A is. Since we are given its midpoint, that is, the point equidistant from both the coordinates A and B, we can find coordinate B by simply calculating the distance between A and the midpoint and reapplying this distance to the midpoint.

1. Finding the distance between the midpoint and A:

The distance between two coordinates, from what I can recall, is simply the final coordinate value minus the initial coordinate value, following the form (x2-x1, y2-y1). We know that A comes after the midpoint, because it is the endpoint (so it will be the final coordinate value). Applying this to the context of the question, (2-10, 13+1) = (-8,14).

2. Finding B using the distance between midpoint and A:

B will be the initial coordinate value because it comes before the midpoint. Therefore, giving B the values (x,y):   (10-x, -1-y) = (-8, 14). Separating into two equations (respective to each axis):

10-x=-8

-x=-18

x=18

-1-y=14

-y=15

y=-15

Therefore, the coordinate of B is (18, -15).

By using the property of division, it can be calculated that M = -21 divided by 0 is not possible

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

Anything divided by 0 is not possible.

M = -21 divided by 0 is not possible

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The linear equation on the table is the one in option D.

y = 25*x + 45

A general linear function is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know two points on the line, (x₁, y₁) and (x₂, y₂), the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Using the first two points, (0, 45) and (1, 70) we can get the slope:

a = (70 - 45)/(1 - 0) = 25

And because of the point (0, 45) we know that the y-intercept is b = 45, then the linear equation is:

y = 25*x + 45

So the correct option is D.

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Answer:

----------------------------

Divide the figure by three parts for easy calculation of its area:

Find each area and add up:

The blank is 75.

The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inchs then width is equal to 28 inch

What is length area and perimeter?

Firstly, the area of a shape is the surface or flat space that the shape covers whereas the perimeter of a shape represents the distance around its boundary. Secondly, the area is measured in square units, whereas the perimeter is measured in linear units.

given that the perimeter of a rectangle is 80 inch

we know that

perimeter = 2 ( L +B)

putting the values we get

80 = 2 ( 12 + B)

40= 12+B

B= 28

then the width is equal to 28inch

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Answer:

the angle would be 40 degrees

Step-by-step explanation:

using the alternative angle property the angle is 40