please help me with this geometry question

a) A linear equation that describes the relationship between the number of buses and the number of vans needed for 120 students is 24x + 8y = 120.

b) If the teachers rent 4 buses, the number of vans they will need to transport all the students is 3.

c) If the teachers rent 6 vans, the number of buses they will need to transport all the students is 3.

d) If the teachers rent only vans, the number of vans needed will be 15.

e) Suppose the teachers rented only buses, the number of buses needed will be 5.

A linear equation is an algebraic equation of the form y = mx+b.

A linear equation involves a constant and a first-order (linear) term, with m as the slope and b as the y-intercept.

The total number of students on the field trip = 120

The number of students a bus can seat = 24

The number of students a van can seat = 8

Let the number of buses = x and the number of vans = y

24x + 8y = 120

b) Renting 4 buses, the number of vans needed:

24(4) + 8y = 120

96 + 8y = 120

8y = 24

y = 3

c) Renting 6 vans, the number of buses will be:

24x + 8(6) = 120

24x = 48 = 120

24x = 72

x = 3

d) Renting only vans, the number needed will be:

24(0) + 8y = 120

8y = 120

y = 15

e) Renting only buses, the number needed will be:

24x + 8(0) = 120

24x = 120

x = 5

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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A characteristic of interest for the elements is called C) Variable.

A dataset is a grouping or set of data. This set is typically displayed in a tabular format. Each column provides information about a distinct variable. In accordance with the stated question, each row represents a certain component of the data set. The management of data includes datasets.

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

A qualitative variable, often known as a categorical variable, is one in which the variable categories are expressed verbally rather than as sets of numbers. Nominal and ordinal are the two subtypes of categorical data. Nominal variables don't have numerical values; they have "names."

Therefore, A characteristic of interest for the elements is called C) Variable.

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Answer:

y=x^2

Step-by-step explanation:

The area of the given figure would be = 508yd

The area of an object is defined as the total space that is being occupied by that object.

The are of the given shape above= area of a rectangle - area of square.

Area of the rectangle = length × width

= 36 × 18 = 648yd

Are of a square = length × width

= 10×14 = 140

Therefore, area of the figure, 648 - 140 = 508yd

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Answer:

Step-by-step explanation:

Answer:

Volume =936.3 ft³

Step-by-step explanation:

Solution Given:

The mathematics tells us that the cube of the ratio of the lengths is equal to the ratio of the volumes.

[tex]{(\frac{Side\: of\: bigger \: solid}{Side \: of \: smaller \: solid} )}^3 = \frac{volume\: of \: bigger \: solid}{volume \: of \: smaller \: solid} [/tex]

let volume of smaller solid be x.

by equation

[tex] {(\frac{12}{8} )}^3 = \frac{3160}{x} [/tex]

doing criss cross multiplication

12³*x=3160*8³

we get

[tex]x = \frac{3160 \times 8^3}{12^3} [/tex]

x= 936.296296296 ft³

The specified equations in the question are in logarithmic form. The exponential form of the equations are as follows;

The logarithmic form of an exponential equation is the form logₐ(c) = b

The exponential form from which the logarithmic form is obtained, is the form aᵇ = c

The form of the equations in the question are in the logarithmic form, the exponential form  of the equation are found as follows;

(1) 3 = logₓy

Therefore, x³ = y

(2) log₁₀100 = 2

Therefore, 10² = 100

(3) log₃27 = 3

Therefore, 3³ = 27

(4) log₁₀1 = 0

Therefore, 10⁰ = 1

(5) logₐa = 1

Therefore, a¹ = a

(6) log₁₀x = y

Therefore, [tex]10^y[/tex] = x

(7) log₅p = q

Therefore, [tex]5^q[/tex] = p

(8) [tex]log_yx=20[/tex]

Therefore, y²⁰ = x

(9) log₂16 = 4

Therefore, 2⁴ = 16

(10) log₅25 = 2

Therefore, 5² = 25

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Answer:

850

Step-by-step explanation:

Everything above 5 goes to the next tenth. Example:

17 = 20

Everything below 5 goes to the next below tenth. Example:

13 = 10

You get it or more expantion?

The solution to the inequality:

(1/2)*|x + 1| ≤ 6

is:

x ≤  11 or x ≥  -13

Here we want to solve the inequality below:

(1/2)*|x + 1| ≤ 6

To solve it we need to isolate x, so let's start by multiplying both sides by 2:

2*(1/2)*|x + 1| ≤ 2*6

|x + 1| ≤ 12

Now we can break the absolute value part into two inequalities:

(x + 1) ≤ 12

(x + 1) ≥ -12

Solving these two we will get:

x ≤ 12 - 1 = 11

x ≥ -12 -1 = -13

That is the solution.

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Answer:

S = 25

Step-by-step explanation:

Since it's stated as a square, that means all sides equal each other

In other words;

s+50 = 3s

To get S alone, we will first subtract 50 on both sides

s = 3s-50

Let's now subtract 3s from both sides

s-3s = -50, aka -2s = -50

Changing those to positive, 2s = 50

Last step is to divide both sides by 2

s = 25

The perimeter of five square and perimeter of rectangular cake is equal,

So, the perimeter of cakes is 600 cm.

The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle. Area and perimeter are the two major properties of a 2D shape, which describes them.

We have five square cakes of side 30cm.

the perimeter of one cake is =4a

                                                 =4×30

                                                 =120 cm

So, the perimeter of five cake = 5(120)

                                                    =600 cm

The perimeter of five square and perimeter of rectangular cake is equal,

So, the perimeter of cakes is 600 cm.

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Answer:

10

Step-by-step explanation:

PEMDAS

For the energy use to double it will take approximately 69.66 years.

To find out how many years it will take for the energy use to double, we can use the formula for exponential growth:

P = P₀ * (1 + r)^t

where P is the final amount of energy use, P₀ is the initial amount of energy use, r is the growth rate (1% per year in this case), and t is the number of years.

Setting P = 2 * P₀ and solving for t, we get:

2 * P₀ = P₀ * (1 + r)^t

Dividing both sides by P₀:

2 = (1 + r)^t

Taking the natural logarithm of both sides:

ln(2) = t * ln(1 + r)

Dividing both sides by ln(1 + r):

t = ln(2) / ln(1 + r)

Plugging in the values for r = 0.01 and using the natural logarithm function, we get:

t = ln(2) / ln(1 + 0.01) = 69.66 years

So it will take approximately 69.66 years for the energy use to double.

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The amount of gas used for 140 miles is 3.5 gallons and the inverse equation is g = m/40

From the question, we have the following parameters that can be used in our computation:

m = 40g

The number of miles is given as

m = 140

substitute the known values in the above equation, so, we have the following representation

40g = 140

Divide by 40

g = 3.5

Hence, the amount of gas is 3.5 gallons

Recall that, we have

m = 40g

Divide by 40

g = m/40

Hence, the inverse is g = m/40

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The equation of the line in slope intercept form is y = 8x -1.

What is slope intercept form?

The graph of the equation y = mx + b is a line with slope m and y-intercepts b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.

The slope, m, of a line indicates how steep it is. The gradient of a line is another name for the slope of a line. The y-intercept of a line is the y-coordinate of the location where the line's graph crosses the y-axis.

We are given two points which are (-1,-9) and (1,7).

First, we need to find the slope(m)

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]m=\frac{7 +9 }{1+1 }[/tex]

m = 16/2

m = 8

We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)

So,

⇒b = (-9) + 1(7 + 9)/(1+1)

⇒b = -9 + 8

⇒b = -1

The equation comes out to be

⇒y = mx + b

⇒y = 8x -1

Hence, the equation of the line in slope intercept form is y = 8x -1.

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There are 55 adults and 27 younglings attended the club.

let the number of adults attended the club be x

let the number of younglings  attended the club be y

total people attended the club = 82

so,

x + y = 82.....[1]

cost for the adult = $6

cost for the younglings = $4

so total amount collected = $438

so, equation formed is ,

6x + 4y = 438.......[2]

from equation [1]

x + y = 82

x = 82 - y

put this in equation [2]

6(82 - y) + 4y = 438

492 - 6y + 4y = 438

492 - 2y = 438

492 - 438 = 2y

2y = 54

y = 27

put this value in equation [1]

x + y = 82

x + 27 = 82

x = 82 - 27

x = 55

so, there are 55 adults and 27 younglings attended the club.

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$85000 is the prize money is awarded in total.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that  top four winners in a golf tournament share the prize money in the ratio 9:5:2:1.

The top prize winner receives $45,000

We need to find the prize money is awarded in total.

9+5+2+1=17

9/17 x = 45000

Divide both sides by 9/17

x=$85000

Hence, $85000 is the prize money is awarded in total.

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The function represents the domain of a function is x ≥ -2.

What is a graph of a quadratic function?

A graph of a quadratic function is a type of parabola, which is a symmetric, U-shaped curve that opens either upward or downward. The equation of a quadratic function is y = ax² + bx + c, where x and y are variables, and a, b, and c are constants.

The graph of a quadratic function is determined by the value of the coefficient a. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The vertex of the parabola is the highest or lowest point on the graph and it is the point of symmetry of the parabola. The x-coordinate of the vertex is given by -b/(2a) and the y-coordinate of the vertex is given by the value of the function at that point.

In the given figure, we can see that it is a parabola, and if we look towards the options, then the third option is a domain of the given function

x ≥ -2

So we can say this is the perfect match for the given figure.

Hence, the function represents the domain of a function is x ≥ -2.

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &120000\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=\textit{elapsed time}\dotfill &10\\ \end{cases} \\\\\\ A = 120000(1 + 0.014)^{10} \implies A \approx 137898.90 ~\hfill \boxed{A=120000(1.014)^t}[/tex]

Step-by-step explanation:

the vertex form of a quadratic function is

y = (x - h)² + k

with (h, k) being the vertex.

luckily for us the function is already defined in that form.

so, when we compare

y = (x + 4)² - 9

with the general form about (h, k) above we see

h = -4

k = -9

so, the vertex is (-4, -9).

Answer: 2 1/4

Step-by-step explanation: Exact Form:

9/4

Decimal Form:

2.25

Mixed Number Form: 2 1/4

Answer:

addition

Step-by-step explanation:

there's only one sign + so it means addition

Answer: addition

Step-by-step explanation:

The slope of the line is 0.93 and the y intercept is 100.54

Value of tempareture at time 30 mins = 1/2 hr = 101.01°

Value of tempareture at 1 hr is = 101.47°

Value of temperature at 90 mins  =1.5 hr = 101.935°

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A - > B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

As per the problem

at starting that is x =0 hrs The temperature y = 99.9°

at x = 10/60 = 1/6 , y = 100.7° and at x = 2 , y = 102.4°

The equation of the line is

y-y₁ = (y₂ - y₁)/(x₂ - x₁) * (x - x₁)

(y - 100.7) = (102.4 - 100.7)/(2 - 1/6) * (x - 1/6)

y = 0.93x + 100.54

The slope of the line is 0.93 and the y intercept is 100.54

Value of tempareture at time 30 mins = 1/2 hr = 101.01°

Value of tempareture at 1 hr is = 101.47°

Value of temperature at 90 mins  =1.5 hr = 101.935°

Temperature at 4 hrs past current time  = 104.26°

The domain of the function will be the time which can go upto infinite.

The range will be the temperature and have a fixed value between the range of a human body temperature as the body temperature can not exceed that temperature.

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Answer: 14

Step-by-step explanation: your correct

The solution is Option A.

The value of the modulus function is | x - 42.80 | = 12

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the modulus function be represented as A

Now , the equation will be

The amount James borrowed from Rita or Rita borrowed from James = $ 12

And , Let x be the amount of money James will have after he sees Rita

The amount of money with James in his wallet = $ 48

So ,

when James pays Rita , the equation will be

x = 42.80 - 12

On subtracting 42.80 on both sides of the equation , we get

x - 42.80 = -12   be equation (1)

And , when James receives the amount from Rita , the equation is

x = 42.80 + 12

On subtracting 42.80 on both sides of the equation , we get

x - 42.80 = 12   be equation (2)

Now , the modulus function will be

| x - 42.80 | = 12

Hence , the function is | x - 42.80 | = 12

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The equation of line with a gradient of 1 which runs through the point (0,4) is y = x + 4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

The point-slope form is expressed as;

y - y₁ = m( x - x₁ )

Given that, the slope of the line m = 1 and it passes through (0,4)

Plug the slope m = 1 and point  ( 0,4 ) into the point-slope form above and simplify.

y - y₁ = m( x - x₁ )

y - 4 = 1( x - 0 )

y - 4 = x - 0

y - 4 = x

Add 4 to both sides

y = x + 4

Therefore, the equation of the line is y = x + 4.

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The profit when n = 101/2 hours is $1,842.50.

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The equation that represents the number of hours on the second week will be x / 184 = 13 / 119.60.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation to Eric works 13 hours the first week and earns 119.60. the second week, he earns 184.

Let 'x' be the number of hours. Then the equation is given as,

x / 184 = 13 / 119.60

Simplify the equation, then we have

x / 184 = 13 / 119.60

x = 184 x 13 / 119.60

x = 2392 / 119.60

x = 20 hours

The equation that represents the number of hours on the second week will be x / 184 = 13 / 119.60.

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