A motorcycle consumes 5 gallons of gas for 300 miles and 7 gallons for 420 miles. Calculate the rate of change per gallon of gas.

The value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The question is:

Given the points (2,k) and (0,−6), for which values of k would the distance between the points be √5

[tex]\rm \sqrt{5}=\sqrt{(0-2)^2+(-6-k)^2}[/tex]

5 = 4 + (6 + k)²

After solving:

[tex]\rm 4+\left(6+k\right)^2-4=5-4[/tex]

(6 + k)² = 1

k = -5 or -7

Thus, the value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

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Answer:

x-intercept of f(x)=x²+3x-4 is (1,0) &(-4,0)

x-intercept of g(x)=x-4 is (4,0)

y-intercept of f(x)=x²+3x-4 is (0,-4)

y-intercept of g(x)=x-4 is (0,-4)

Step-by-step explanation:

[tex]f(x) = x {}^{2} + 3x - 4 \\ to \: find \: x \: intercept \: subistitute \: f(x) = 0 \\ 0 = x {}^{2} - 3x - 10 \\ x { }^{2} - 3x - 1 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5 \\ the \:equation \: x \: intercept \: are \: - 2and \: 5 \\ f(0) = 0 {}^{2} + 3(0) - 4 \\ - 4 \: is \: y \: intercept \: of \: f(x) = x {}^{2} + 3x - 4 \\ where \: as \: for \: g(x) = x - 4 \\ to \: find \: x \: intercept \: f(x) = 0 \\ 0 = x - 4 \\ - x = - 4 \\ x = 4 \\ 4is \: the \: x \: intercept \: and \: for \: the \: y \: intercept \\ g(0) = 0 - 4 \\ y = - 4is \: the \: y \: intercept.[/tex]

Answer:

Step-by-step explanation:

2x squared, denoted (2x)2, is equal to 4x2. In general, we can raise a product to a power using the following product rule for exponents: (ab)n = an

Answer:

(5a+5b+3ab)/15

Step-by-step explanation:

qquy đồng lên thôi !!

The quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(x-4)² – (x − 4) − 6 = 0

Let (x - 4) = u

u² - u - 6 = 0

Thus, the quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.

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Answer:Option D on edge 2022

Step-by-step explanation:

Step-by-step explanation:

Question 46.

[tex](2\sqrt{5}-\sqrt{2} )^2=(2\sqrt{5})^2-2*2\sqrt{5}*\sqrt{2} +(\sqrt{2})^2 } =4*5-4*\sqrt{2*5} +2=\\=20-4\sqrt{10}+2=22-4\sqrt{10}.[/tex]

Answer: E. None of these.

Question 47.

[tex]\frac{4\sqrt{5} }{\sqrt{3} } =\frac{4*\sqrt{5}*\sqrt{3} }{\sqrt{3} *\sqrt{3} } =\frac{4*\sqrt{5*3} }{3}=\frac{4\sqrt{15} }{3} .[/tex]

Answer: E. None of these.

Answer:

45) E 47) E

Step-by-step explanation:

45)

Remember the formula [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](2\sqrt5-\sqrt2)^2=(2\sqrt5)^2-2(2\sqrt5\times\sqrt2)+(\sqrt2)^2\\\\=20-2(2\sqrt{10})+4\\\\=24-4\sqrt{10}[/tex]

Hence E. None of these.

47)

[tex]\frac{4\sqrt{5}}{\sqrt3}=\frac{4\sqrt5\times\sqrt3}{\sqrt3\times\sqrt3}\\\\=\frac{4\sqrt15}{3}[/tex]

Hence E. None of these.

Have a nice day, also please mark brainliest thanks :)

[tex] \frac{?}{20} = \frac{6}{10} [/tex]

[tex] \frac{?}{2} = 6 \\ ? = 6\times 2 = 12[/tex]

Answer:

75 / 192

Step-by-step explanation:

When it comes to multiplying fractions, you just multiply them straightforward. Multiply the numerator with the numerator, and the denominator with the denominator

The total weight of the two pieces together is 6 pounds.

A piece of raw silk that is 100 yards long by 1.25 yards wide weights 38lb.

Then, a piece that is 12.5 yards long (and still 1.25 yards wide) will weight:

M = (12.5/100)*38lb = 4.75 lb

And a piece of habotai silk that is 100 yards long by 1.25 yards wide weights 12lb.

Then, a piece that is 12.5 yards long will weigh:

M' = (12.5/100)*12lb = 1.5 lb

If we add these two, we get a total weight of:

M + M' = 4.5lb + 1.5lb = 6lb

The total weight of the two pieces together is 6 pounds.

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Answer:

cant say you dont show

Step-by-step explanation:

id love to help but like send a picture next time

The true statements about the functions are:

The complete question is in the attached image

From the image, we have:

This means that the true statements about the functions are g(x) has the maximum greatest value and h(x) has a range of all negative numbers.

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Answer:

12

Step-by-step explanation:

just find the HCF, which will be

2² × 3 = 12

Answer: B , c, E

Step-by-step explanation:

Given that ,

∡J=90° , ∡k=30° , ∡L=60°

In the triangle ΔJKL,

 tan ∠L = tan 60°

⇒ JK÷JL= √3

⇒JK = √3JL

Thus, A is incorrect and B is correct

Again,

cos ∠L = cos60° =0.5

⇒JL/KL = 1÷2

⇒ JL = (1÷2)KL

⇒JL×2= KL

⇒ KL=2JL

Hence, F & D are incorrect and C is correct

Earlier we got,

JK = √3.JL

⇒JL=JK÷√3

and JL= (1÷2).KL

So, JK÷√3=(1÷2)KL

⇒JK÷√3×2 = KL

⇒2.JK= √3KL

⇒JK = (√3÷2).KL

hence E is correct

The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is [tex]a_1= -23, a_n = a_{n-1}+ 12,a_n=-23 +12(n-1)[/tex]

If first term of a arithmatic sequence is a₁ and the common difference is d then,

By Explicit Formula, the n-th term of the sequence is given by,

[tex]a_n=a_1+(n-1)d[/tex]

By Recursive Formula,

[tex]a_n=a_{n - 1}+d[/tex]

In the first choice: a₁ = -23 and

[tex]a_n=a_{n-1}+12[/tex]

Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.

and

[tex]a_n=-23+12(n-1)[/tex]

So by explicit formula it also suggests arithmatic sequence with first term -23 and common difference 12.

So it is one correct choice.

In second choice: a₁ = -100 and

[tex]a_n=a_{n-1}+1[/tex]

By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.

[tex]a_n=100-1(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 100 and common difference -1.

So it is not the correct choice.

In third choice: a₁ = -41 and

[tex]a_n=a_{n-1}+12[/tex]

By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.

[tex]a_n=12-41(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 12 and common difference -41.

So it is not the correct choice.

In fourth choice: a₁ = 50 and

[tex]a_n=a_{n-1}-4[/tex]

By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.

[tex]a_n=50+4(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 50 and common difference 4.

So it is not the correct choice.

Hence the option (A), the first choice is correct.

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The Big O notation of the composite function 5N^3 O(N^2) is c. O(N^3).

A composite function of two capabilities combines the given two functions inside the given order. i.e., for any given functions f(x) and g(x), there may be four composite functions: f(g(x)) that is substituting g(x) into f(x) g(f(x)) that's substituting f(x) into g(x).

A composite characteristic is a function that relies upon any other feature. A composite characteristic is created while one characteristic is substituted for another feature. For instance, f(g(x)) is the composite function that is fashioned whilst g(x) is substituted for x in f(x). f(g(x)) is studied as “f of g of x”.

In Maths, the composition of a character is an operation wherein two capabilities say f and g generate a brand new feature say h in one of these manners that h(x) = g(f(x)). It method right here feature g is implemented to the function of x. So, basically, a feature is carried out to the result of every other feature.

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Answer:

26.4

Step-by-step explanation:

Law Of Cosines:

    [tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]

    This should work for any side. This can generally be thought as:

   [tex]cos(\text{angle}) = \frac{\text{sum of squares of two other sides-opposite side squared}}{\text{2 times the product of the other two sides}}[/tex]

    If this is too confusing here's the formula for the other sides (which is essentially the same, just different variables)

   [tex]cos(B)=\frac{a^2+c^2-b^2}{2ac}[/tex]

   [tex]cos(C) =\frac{a^2+b^2-c^2}{2ab}[/tex]

Anyways now just plug in the known values into the equation

[tex]cos(A)=\frac{4^2+6^2-3^2}{2(6)(4)}\\[/tex]

Square and multiply values

[tex]cos(A)=\frac{16+36-9}{48}[/tex]

Add the values in the numerator

[tex]cos(A)=\frac{43}{48}[/tex]

Take the inverse of cosine on both sides

[tex]A=cos^{-1}(\frac{43}{48})[/tex]

calculate arccosine (inverse cosine) using a calculator

[tex]A\approx 26.384[/tex]

Round to nearest tenth

[tex]A\approx26.4[/tex]

Answer:

(1,0)

Step-by-step explanation:

I'm just gonna say that the point you want to be transformed is the origin. It will be moved to (1,0)

Answer:A.47.5 miles is 76

Step-by-step explanation:

in real life its like 76.44, but im rounding

Answer: 2   55   121

             22   5      11

Step-by-step explanation:

Answer:

b. 120

Step-by-step explanation:

3t2s

3(2)2(10)

6(20)

120

Answer:

Hello! The answer is 120.

Step-by-step explanation:

s = 10 and t = 2

Substitute:

(3)(2)(2)(10)

3 × 2 = 6

2 × 10 = 20

6 × 20 = 120

We must mix 240 liters of the 51 % solution and 10 liters of the 26 % solutions to produce 250 liters of 50 % solution.

Herein we have to prepare a solution with fertilizers by mixing two different solutions. The amount needed of the 51 % solution can be found by weighted averages:

(50/100) · (250 L) = (51/100) · x + (26/100) · (250 - x)

50 · 250 = 51 · x + 26 · 250 - 26 · x

24 · 250 = 25 · x

x = 240

We must mix 240 liters of the 51 % solution and 10 liters of the 26 % solutions to produce 250 liters of 50 % solution.

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By looking at the diagram, we can see that:

As you can see, the ray DE starts at point D and then passes through E, and then continues.

Then the only endpoint of that ray is D.

The ray GA starts at point G and goes through A (so it goes to the left of G).

The ray DF starts at point F and goes through F (So it goes to the right of D).

Then these two rays don't intersect, because D is at the right of G.

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The value of nickels is $76.80.

The height of each nickel is 6.25 / 100 = 0.0625 inches.

Divide 8 feet by 0.0625 inches to find that there are

8×12 / 0.0625 = 1536 nickels in an 8 ft stack.

Their value is $76.80.

Nickel is a chemical detail with the symbol Ni and atomic range 28. It is silvery-white lustrous steel with a mild golden tinge. Nickel belongs to the transition metals and is hard and ductile.

Pure nickel, powdered to maximize the reactive surface vicinity, indicates a widespread chemical interest, but large pieces are slow to react with air underneath fashionable conditions because an oxide layer paperwork at the floor stops further corrosion (passivation).

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Answer:

Angle C = 68.7°

Step-by-step explanation:

The largest angle es angle C ([tex]\beta[/tex])

[tex]26^{2} =22^{2} +24^{2} -2(22)(24)cos\beta[/tex]

[tex]676=484+576-1056cos\beta[/tex]

[tex]676-1060=-1056cos\beta[/tex]

[tex]\frac{-384}{-1056} =cos\beta[/tex]

[tex]\beta =cos^{-1} (\frac{-384}{-1056} )=cos^{-1} (.36363)=68.676=68.7^{o}[/tex]

Answer:

51.7661748226 degrees; 38.2338251774 degrees

Step-by-step explanation:

First, draw a diagram to illustrate this situation. Looking at angle A, Eric's height, 1.65 m, corresponds to OPPOSITE, and Eric's shadow, 1.30 m, corresponds to ADJACENT. Using SOH CAH TOA, the equation is:

tan(A) = 1.65/1.30

A = arctan(1.65/1.30)

A = 51.7661748226 deg

Looking at angle B, 1.65 m is ADJACENT and 1.30 m is OPPOSITE. Therefore, the equation is:

tan(B) = 1.30/1.65

B = arctan(1.30/1.65)

B = 38.2338251774 deg

The predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to 512.4 bacteria in 6 hours.

A continuous exponential growth model is used to determine the final value of a quantity (V), from an initial value of the quantity (V₀), at a rate of continuous growth per unit time (r), after the time (t), as:

[tex]V = V_0e^{rt}[/tex].

In the question, we are given that the number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 3% per hour.

We are asked, to find the predicted population after six hours when the initial population was 428 bacteria.

Thus, we take V₀ = 428, r = 3% = 0.03, and t = 6, in the equation:

[tex]V = V_0e^{rt}[/tex] ,

to find the predicted population (V) of bacteria after 6 hours.

Thus,

[tex]V = 428e^{0.03*6}\\\Rightarrow V = 428e^{0.18}\\\Rightarrow V = 428*1.1972173631218\\\Rightarrow V = 512.40903141613\\\Rightarrow V = 512.4[/tex]

Rounding to the nearest tenth.

Thus, the predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to 512.4 bacteria in 6 hours.

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The number of lighter boards and heavier boards in the truck is 216 and 192 boards respectively.

let

Light board = x

Heavy board = y

x = y + 24

x + y = 408

(y + 24) + y = 408

y + 24 + y = 408

2y = 408 - 24

2y = 384

y = 384 / 2

y = 192 boards

So,

x = y + 24

= 192 + 24

x = 216 boards

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The orthocenter of the triangles ABC are (2, 0) and (3, 3)

Question 8

The coordinates are given as:

A(2,0); B(2, 4); C(6,0)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 4)/(6 - 2)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1)  + y1

Where:

(x1, y1) = (2,0)

So, we have:

y = 1(x - 2) + 0

y = x - 2

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 0)/(6 - 2)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (2,4)

So, we have:

x = 2

Substitute x = 2 in y = x - 2

y = 2 - 2

y = 0

So, we have:

(x, y) = (2, 0)

Hence, the orthocenter of ABC is (2, 0)

Question 9

The coordinates are given as:

A(1,1); B(3, 4); C(6,1)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 4)/(6 - 3)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1)  + y1

Where:

(x1, y1) = (1,1)

So, we have:

y = 1(x - 1) + 1

y = x

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 1)/(6 - 1)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (3,4)

So, we have:

x = 3

Substitute x = 3 in y = x

y = 3

So, we have:

(x, y) = (3, 3)

Hence, the orthocenter of ABC is (3, 3)

Question 18 - 20

Line 2x and x+ 3 are congruent lines

So, we have:

2x = x +3

Solve for x

x= 3

Line 3x and 2x + 5 are congruent lines

So, we have:

3x = 2x +5

Solve for x

x = 5

Line 2x - 3 and x + 2 are congruent lines

So, we have:

2x - 3 = x + 2

Solve for x

x = 5

Question 21 - 23

Line x + 5 and 3x + 7 are congruent lines

So, we have:

x + 5 = 3x + 7

Solve for x

x = -1

Line x + 6 and 5x - 4 are congruent lines

So, we have:

x + 6 = 5x - 4

Solve for x

x = 2.5

Line x + 8 and 5x + 7 are congruent lines

So, we have:

x + 8 = 5x + 7

Solve for x

x = 1/4

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