If a cheetah can travel 120 meters in just 4 seconds, then how many meter can it travel in 25 seconds?

Answer:

14) Not a function 15) Function 16) Function

Step-by-step explanation:

The vertical line test is when you draw a line on the graph to see if it passes the function. The rule is that you can only have one intersection per line

for number 14, if you draw a line, it intersects the function twice each time

for 15, no matter what kind of vertical line you draw, each line will only intersect the function once and the same for 16 (except 16 is more of a linear function)

Answer:

Well a function can’t be on the same one as each other so thats why the vertical line test is used.

For number 14 if you’d draw a vertical line, you’d see there would be 2 answers So that can’t be a function.

For number 15, if you draw a vertical line, none of the given have 2 questions so number 15 is a function.

Whilst in number 16 if you’d draw a vertical line, there wouldn’t be anything that have 2 answers of that overlap. So it is a function

Answer:

-44

Step-by-step explanation:

Answer: -44

Step-by-step explanation: same as 36 + 8 and make the answer negative.

f(x)=(x+a)/b

or bf(x)=x+a

let f(x)=y

by=x+a

flip x and y

bx=y+a

or y=bx-a

or f^{-1}(x)=bx-a

also g(x) is inverse of f(x)

bx-a=cx-d

so b=c,a=d

again let g(x)=y

y=cx-d

flip x and y

x=cy-d

cy=x+d

y=(x+d)/c

or g^{-1}(x)=(x+d)/c

also f(x) is inverse of g(x)

so (x+a)/b=(x+d)/c

so a=d,b=c

so in either case a=d,b=c

take b=c=1

a=d=2

f(x)=(x+2)/1=x+2

g(x)=1x-2=x-2

so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0

g(x) with y-intercept -2 and slope 0

if we take b=c=2,a=d=3

f(x)=(x+3)/2=x/2+3/2

g(x)=2x-3

here f(x) is of slope 1/2 and y-intercept 3/2

g(x) is of slope 2 and y intercept -3

part 3.

f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d

An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.

Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2: g(x) = 3x - 2, the inverse.

Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.

An inverse function in mathematics exists function which "reverses" the another function.

TASK 1

Part 1

Let y = f(x) = (x + a) / b

x = g(y) = by-a = cy-d,

so c = b and d = a.

Let d = a = 2 and c = b = 3

f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2

y = f(x) = (x+2) / 3

3y = x+2  

x = 3y-2 = g(y)

so g(x) = 3x - 2, the inverse.

Part 3

g(f(x)) = 3

f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,

so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.

x       -2  -1        0    1     2

f(x)    0    1/3   2/3   1    4/3

g(x)  -8   -5      -2    1      4

Part 4

The graph is given below.

TASK 2

Part 1

(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5

(b) Let a=-1, b=2, c=3, d=4

(a) Multiply both sides by

[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]

[tex]$ x-36+30=-5 \sqrt{x }[/tex]

[tex]$ x-6=-5 \sqrt{x}$[/tex]

Square both sides:

[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].

Part 2

(a) So x=36 or 1 (apparently).

Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.

So x=36 is an extraneous solution.

substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.

(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.

Substitute x=1 in the original equation: -1+2+3=4 is true.

So x = 1 is the solution.

Part 3

(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].  

(b) the solution was simpler and there was no ambiguity.

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Answer:

21

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Answer:

x-intercept(s): (-2, 0), (6, 0)

y-intercept(s): (0, -6)

Step-by-step explanation:

An x-intercept represents the point(s) at which the parabola intersects the x axis.  A parabola can have 0, 1, or 2 x-intercepts.  

A y-intercept represents the point at which the parabola intersects the y axis.  A parabola always has exactly 1 y-intercept.

Hope it helps :) and let me know if you're still confused.

Step-by-step explanation:

16x²y⁵16x²y⁵ is the answer

Answer:

Your y intercept is 1.

Step-by-step explanation:

slope is y2-y1 over x2-x1, or 2.

slope intercept formula is y=mx+b, and if you plug values into formula you get 3=2(1)+b

and if you solve that, 2x1=2, 3-2=1.

then you get 1 as your y intercept.

Answer:

16 5c coins

34 10c coins

Step-by-step explanation:

(I prefer to use whole numbers)

5x + 10y = 420

x+y=50

multiply the bottom problem by -5

5x +10y =420

-5x -5y = -250

combine the problems

5y = 170

divide by 5

y = 34

that means x = 16

34 10c coins

16 5c coins

-- Gage Millar, Algebra 1/2 tutor

The number of 5 cent coins are 16 and the number of 10 cent coins are 34.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a trader has a mixture of 5 c and 10 c coins.

Let the the number of 5 c coins be x and the number of 10 c coins be y.

He has 50 coins in all, with a total value of $4.20.

So, x+y=50 ---------(I)

5x+10y=420 ---------(II)

Multiply equation (I) by 5, we get

5x+5y=250 ---------(III)

Subtract equation (III) from (II), that is

5x+10y-(5x+5y)=420-250

⇒ 5y=170

⇒ y=34

Substitute y=34 in equation (I), we get

x=16

Therefore, the number of 5 cent coins are 16 and the number of 10 cent coins are 34.

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Answer:the 3.38 answer

Step-by-step explanation:

Answer: Varies

Step-by-step explanation:

There would still be some Xs and Ys.

Answer:

Yamete Kodasai

Step-by-step explanation:

Thankyou sa pnts

Answer:

Step-by-step explanation:

a = -5 and b = -6

x² - (a +b)x + ab = 0

x² - (-5 - 6)x + (-5)*(-6) = 0

x² - (-11)x + 30 = 0

x² + 11x + 30 = 0

Answer:

Option 1:  y = (x - 2)² + 2

Step-by-step explanation:

Given the vertex, (2, 2), of an upward-facing parabola, and using the y-intercept of the graph, (0, 6):

The vertex form of the quadratic equations is:

y = a(x - h)² + k

where:

(h, k) is the vertex.

The sign of a  determines the direction of the graph's opening. The value of a also determines the vertical stretch or shrink of the graph.

Substitute the values of the vertex (2, 2) and the y-intercept, (0, 6) into the  vertex form to solve for the value of the coefficient, a:

y = a(x - h)² + k

6 = a(0 - 2)² + 2

6 = a(-2)² + 2

6 = 4a + 2

Subtract 2 from both sides

6 - 2 = 4a + 2 - 2

4 = 4a

Divide both sides by 4 to solve for a :

[tex]\displaytext\mathsf{\frac{4}{4} \:=\frac{4a}{4}}[/tex]

a = 1

Therefore, given the vertex, (2, 2) and a = 1, the quadratic equation in vertex form is: y = (x - 2)² + 2, thereby matching Option 1.

Answer:

Using the slope-intercept form, the slope is 4 4 .

Answer: Using the slope-intercept form, the slope is 4 4 .

Explanation: so your answer is 4 4.

Answer:

go to https://www.rcboe.org/cms/lib010/GA01903614/Centricity/Domain/1030/Ch.%203.3.pdf

Step-by-step explanation:

i think that will help

6p + 12 - 2 = 8p + 4

6p + 10 = 8p + 4

6p - 8p = 4 - 10

-2p = -6

2p = 6

p = 3

Answer:

p = 3

Step-by-step explanation:

First, simplify. Combine like terms. Like terms are terms with the same variable as well as same amount of said variable:

6p + (12 - 2) = 8p + 4

6p + (10) = 8p + 4

Isolate the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Addition

Subtraction

First, subtract 8p and 10 from both sides of the equation:

6p (-8p) + 10 (-10) = 8p (-8p) + 4 (-10)

6p - 8p = 4 - 10

-2p = -6

Next, isolate the variable, p, by dividing -2 from both sides of the equations:

(-2p)/-2 = (-6)/-2

p = -6/-2

p = 3

3 is your answer.

~

Answer:

y=6x+11

Step-by-step explanation:

The slope of y=3x+4 is 3 and the slope of y=6x+11 is 6.

Hope this helps :)

y = 3x + 4 is the steeper line with the slope 3

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two lines are y = 3x + 4 and y = 6x + 11

In the given line  y = 3x + 4

The slope of the line is 3

In the given line  y = 6x + 11

The slope of the line is 6

Among the two lines the line y = 3x + 4 has less slope. So the  the steeper line y = 3x + 4

Hence, y = 3x + 4 is the steeper line with the slope 3

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Answer:

x = 10

Step-by-step explanation:

Perimeter of a triangle = the sum of the three sided of the triangle.

In an isosceles triangle, there are two equal sides and  a base.

Perimeter = ( 3x - 6) + (3x - 6) + x

            58 = 7x - 12

            58 + 12 = 7x

                   70  = 7x

                    [tex]\frac{70}{7} = \frac{7x}{7}[/tex]

                    10 = x

Answer:

Julio: 65 soles

Agosto: 85 soles

Step-by-step explanation:

julio: x

agosto: x + 20

x + x + 20 = 150

2x + 20 = 150

2x = 130 x = 65

julio: x = 65

agosto: x + 20 = 85

verificacion: 65 + 85 = 150

julio [65] = 20 menos que agosto [85]

Answer:

Julio: 65 soles

Agosto: 85 soles

The consumption in July was 65 soles and the consumption in August was 85 soles.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Let's call the amount of consumption in July "C1" and the amount of consumption in August "C2".

We know that:

C1 + C2 = 150 (the total consumption for both months)

C2 = C1 + 20 (August consumption was 20 soles more than July)

We can substitute the second equation into the first equation to get:

C1 + (C1 + 20) = 150

Simplifying this equation, we get:

2C1 + 20 = 150

Subtracting 20 from both sides, we get:

2C1 = 130

Dividing both sides by 2, we get:

C1 = 65

So the consumption in July was 65 soles.

Using the second equation, we can find the consumption in August:

C2 = C1 + 20 = 65 + 20 = 85

So the consumption in August was 85 soles.

We can check that these values are correct by verifying that they add up to the total consumption of 150 soles:

65 + 85 = 150

Therefore,

The consumption in July was 65 soles and the consumption in August was 85 soles.

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The complete question:

Since the quarantine began, the consumption of electrical energy in my house has increased. It is because we are all at home without going out, using the computer, television and other devices at the same time. The last receipt came to us in July and August, since we could not go out to pay for the quarantine, but the receipt was lost. I can only remember that the total amount was 150 soles and that in July consumption was 20 soles less than in August. How much was our consumption in July and August? Check your answer.

Answer:

Answer → y = -7x + 12

Step-by-step explanation:

General equation of a line:

[tex] \hookrightarrow \: { \tt{y = mx + c}} \\ [/tex]

From the question;

m is -7

c is 12

[tex]{ \tt{y = - 7x + 12}}[/tex]

Answer:

There would be 10 more Girls.

Answer:

46 boxes of nails

Step-by-step explanation:

She has $187 to spend, the maximum.

187/4 = 46.75

Since she cannot buy 0.75 of a box of nails, she can only buy 46. So she is left with an extra $3 and buys 46 boxes of nails.

Hope this helps, and please mark me the brainliest! :D

Answer:

A)

y=1/3x +2

Step-by-step explanation:

equation of line is y=mx+c

so here the points are (0,2) and the gradient,m is 1/3

the y-intercept, c is 2

as when substituting the result is 2 for the y-intercept

y=mx+c (0,2)

2=1/3 (0) +c

c= 2

The equation of the line is y=1/3x +2 if a line passes through (0, 2) and has a slope of 1/3 option (A) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope-intercept form of the line is:

y=mx+c

The points are (0,2) and the gradient,m is 1/3

c= 2

y = x/2 + 2

Thus, the equation of the line is y=1/3x +2 if a line passes through (0, 2) and has a slope of 1/3 option (A) is correct.

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Answer:

THERE IS NO QUESTION

Step-by-step explanation:

Answer:

Option A: 0

Step-by-step explanation:

Given the multiplication of fractions, [tex]\huge\mathsf{\frac{1}{9} \:\times\frac{24}{25}}[/tex]:

Simply multiply the numerators (together), as well as the denominators.

In other words:

[tex]\huge\mathsf{\frac{1}{9} \:\times\frac{24}{25}\:=\frac{1\:\times\:24}{9\:\times\:25}\:=\:\frac{24}{225}}[/tex]

Since 24 and 225 do not have common multiples, then we cannot simplify the fraction into its lowest terms.

Next, in order to find out which is the closest value to the product, [tex]\huge\mathsf{\frac{24}{225}}[/tex], divide the numerator by the denominator, which gives you the following quotient:

[tex]\huge\mathsf{\frac{24}{225}\:=\:24\:\div\:225\:=\:0.1067}[/tex] or 0.11.

We must compare this quotient with the other options:

Option A) 0: This is a possible answer, since rounding 0.11 to the nearest ones (whole number) is 0.

Option B) 0.5:  Unlikely a valid answer, since the digit on the hundreths place is 0.11, and rounding it up to the nearest tenths will become 0.1.

Option C) 1: Definitely not a valid answer, according to the explanations provided in Options A and B.

For Option D) [tex]\huge\mathsf{\frac{21}{20}}[/tex] , we need to find its equivalent decimal form by dividing its numerator by the denominator:  [tex]\huge\mathsf{\frac{21}{20}\:=\:21\:\div\:20\:=\:1.05}[/tex]. Hence, it is also not a valid answer, according to the explanations provided in Options A and B.

Therefore, the closest value to  [tex]\huge\mathsf{\frac{24}{225}\:=\:0.11}[/tex] is Option A) 0.

Answer:

3 miles

Step-by-step explanation:

6 total miles

3 miles done

6 (total) = 3 (done) + x (unknown)

x = 6 - 3

x = 3

3 miles left to hike

Answer:

C

Step-by-step explanation:

m = -3

y = mx +b

y = -3x + b

Plugin x = -1 and y = 4

4 = -3*(-1) +b

4 = 3 + b

4-3 = b

b = 1

y = -3x + 1

Answer:

B, C, D

Step-by-step explanation:

The equation of a line in point slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 3 and (a, b ) = (- 1, 4 ) , then

y - 4 = - 3(x - (- 1) ) , that is

y - 4 = - 3(x + 1) → D

Distribute parenthesis

y - 4 = - 3x - 3 ( add 4 to both sides )

y = - 3x + 1 → C

Add 3x to both sides

3x + y = 1 → B

Answer:

Step-by-step explanation:

One

The exterior angles of a triangle add up to 360. You know two of them. Therefore you can find w.

125 + 90 + w = 360    Combine like terms on the left

215 + w = 360             Subtract 215 from both sides

w = 360 - 215              Combine

w = 145

Two.

The polygon has 4 exterior angles. They too should add up to 360.

88 + x + 108 + 115 = 360     Combine the left had side

x + 311 = 360                       Subtract 311 from both sides

x = 360 - 311                        Combine

x = 49

What have you learned? You should notice that all polygons have exterior angles that add up to 360