a. Find the scale factor from triangle JKL to triangle PQR.

b. List all pairs of corresponding angles.

c. Write the ratios of the corresponding side lengths in a statement of proportionality.

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 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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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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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

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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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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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 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:

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 y intercept has been moved down, and the g(x) graph is less steep than the f(x) graph.

the fundamental duty of a family. Y = x or f(x) = x is the parent function for linear functions. Transformation: Modification of a figure's size or position. Child Function: The parent function is f(x) = x for all linear functions. y = x.

The simplest function in a family of functions that yet preserves the definition (or shape) of the entire family is known as a parent function in mathematics.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear.

Therefore, the correct answer is option C. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted down.

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

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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 the line which passes through the point (0,-4) and has a gradient of 0. 5 is (x-8)/2.

A straight line can be represented by the "Point-Slope" form of the line.

In point-slope form, we can deduce an equation of any line on the Cartesian coordinate system with the help of its slope/gradient "m" and a point through which it passes (x1,y1).

the equation of Point Slope form is,

(y-y1)=m(x-x1),

where, x and y are any general point on the line.

in the given question the value of the slope/gradient (m) is given as 0.5

and it passes across the point (0,-4)

so according to the equation of the point-slope form,

the equation of line must be,

(y-(-4))=0.5(x-(0))

= y+4=0.5x

= 2y+8=x

= 2y = x-8

= y = (x-8)/2

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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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Answer: 14

Step-by-step explanation: your correct

Answer:

y=x^2

Step-by-step explanation:

Answer: 2 1/4

Step-by-step explanation: Exact Form:

9/4

Decimal Form:

2.25

Mixed Number Form: 2 1/4

$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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[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]

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:

10

Step-by-step explanation:

PEMDAS

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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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).

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:

The value equivalent to the expression 2^3 + 3^4 is 19

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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Answer:

addition

Step-by-step explanation:

there's only one sign + so it means addition

Answer: addition

Step-by-step explanation: