Mia records the distance traveled in x minutes in the table below, while Alexa uses a graph to record her distance traveled over the same time period.


Alexa’s Graph

A graph has time (minutes) on the x-axis and Distance traveled (miles) on the y-axis. A line goes through points (4, 3) and (8, 6).
Mia’s Table

A 2-column table with 4 rows. Column 1 is labeled Time (minutes) with entries 10, 18, 20, 26. Column 2 is labeled Distance Traveled (miles) with entries 5, 9, 10, 13.

Answer:

The solution for f(x) = g(x) are;

x = 1 and x = -1

Step-by-step explanation:

The given equations for the functions, g(x) are;

[tex]f(x) = \dfrac{1 + 2\cdot x}{x}[/tex]

g(x) = 2 + x

The solution for f(x) = g(x), is given by equating the equations of the two functions as follows;

When f(x) = g(x), we have;

[tex]\dfrac{1 + 2\cdot x}{x} = 2 + x[/tex]

By cross multiplication, we have;

1 + 2·x = x × (2 + x) = 2·x + x²

∴ x² + 2·x - 2·x - 1 = 0

x² - 1 = 0

(x - 1)·(x + 1) = 0

x = 1, or x = -1

f(x) = g(x) = 2 + 1 = 3, or 2 - 1 = 1

Therefore, the solution for f(x) = g(x) are;

f(x) = g(x) = 3 or 1 where x = 1 and x = -1.

Answer: a , b

Step-by-step explanation:

Answer:

11.67 Amperes

Step-by-step explanation:

From Ohm's law,

Ohm's law which state that a current

which flow through a conductor at a distance between two points is proportional directly to the voltage which is flowing across the two points.

I= V/R

Where

I= Current

V= potential difference =35v

R= resistance = 3 ohms

Then substitute the values we have

I = 35 / 3

I= 11.67 Amperes

Answer:

P=100(A-R)/RT

Step-by-step explanation:

A-R=PRT/100

100(A-R)=PRT

100(A-R)/RT=P

P=100(A-R)/RT

Answer:

-3

Step-by-step explanation:

[tex]\sqrt{25}[/tex] is equal to 5, so we can sub it in the equation.

This gives 12-3×5 or 12-15.

This solves to -3.

**This content involves simplifying surds, which you may wish to revise. I'm always happy to help!

Answer:

A1.) 87 + 63 =150

180 - 150 = 30

all the As is the same formula....

B1.) 180 - 123 = 57

57 + 82 = 139

180 - 131 = 41

Good question. It is supposed to be both the y-intercept and the x-intercept and is the only point on a graph that can be both. Something in wrong in that thing.

Answer:

126

Step-by-step explanation:

6 (14 + 7)

6 (21)

126

Answer:

[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]

Step-by-step explanation:

To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,

[tex]a^2+b^2=c^2[/tex]

Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,

[tex]a^2+b^2=c^2\\[/tex]

Substitute,

[tex]a^2+40^2=47^2\\[/tex]

Simplify,

[tex]a^2+1600=2209\\[/tex]

Inverse operations,

[tex]a^2=609[/tex]

[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]

Answer:

b = 9 mm

Step-by-step explanation:

Using Pythagoras; identity in the right triangle

b² + 40² = 41²

b² + 1600 = 1681 ( subtract 1600 from both sides )

b² = 81 ( take the square root of both sides )

b = [tex]\sqrt{81}[/tex] = 9 mm

Answer:

x = 2x - 1

x - 2x = -1

-x = - 1

x = 1

g = 1

Answer:

I dont see the question oh nvm

Step-by-step explanation:

Answer:

TRUE

Step-by-step explanation:

The Time of day is skip counting by ten each time

EX: 1000-1010-1020-1030-1040- so on

Answer: [tex]108^{\circ}[/tex]

Step-by-step explanation:

Given

The top left and right corners measures [tex]72^{\circ}[/tex] and the bottom right corner measures [tex]108^{\circ}[/tex].

Suppose the missing corner measures [tex]x[/tex]

So, the sum of the four angles of parallelogram is [tex]360^{\circ}[/tex]

[tex]\therefore x+72^{\circ}+108^{\circ}+72^{\circ}=360^{\circ}\\\Rightarrow x=360^{\circ}-252^{\circ}\\\Rightarrow x=108^{\circ}[/tex]

Therefore, the missing angle is [tex]108^{\circ}[/tex].

Answer:

x = 42°

Step-by-step explanation:

You can mark the opposite angle from 96° as 96° and the 2 other unknowns as y.

96 • 2 + 2y = 360

168 = 2y

y = 84

x is half of y.

84 ÷ 2 = 42

Answer:

[tex]x=42^{o}[/tex]

Step-by-step explanation:

Area of a triangle is 180 degrees

Here both the triangles are same so, form an equation:

[tex]x+x+96=180[/tex]

[tex]2x+96=180[/tex]

[tex]2x=180-96[/tex]

[tex]2x=84[/tex]

[tex]x=84/2[/tex]

[tex]x=42^{o}[/tex]

Answer:

C) 1/3

Step-by-step explanation:

if you have a 6 sided cube you have 1/6 of a chance of landing on any number.

But you only have a 2/6 chance of landing on 5 or greater.

2/6 is also equal to 1/3

Answer: square root property

Step-by-step explanation:trust me

Answer:

71. 8

Step-by-step explanation:

volume of a cylinder = 4/ 3 π r² h

=> 4817 = 4/ 3 × 22/ 7 × 4² × h

=> h = (4817 × 3 × 7)/ (4 × 22 × 4²)

=> h = 71.8

Answer:

∆ABC~=∆PQR

Angle BAC=QPR

Answer:

√2 ft.

Step-by-step explanation:

⇒ Area of square board = 2 ft.²

⇒ (Side of the board)² = 2 ft.²

⇒ Side of the board = √(2 ft.²)

⇒ Side of the board = √2 ft.

Answer:

[tex]\sqrt{15}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{3}[/tex] × [tex]\sqrt{5}[/tex] = [tex]\sqrt{3(5)}[/tex] = [tex]\sqrt{15}[/tex]

Answer:B

Step-by-step explanation:

Answer:

x= 4/3

y= -8

if you ment 3x + 2y = -12 in the second problem

Step-by-step explanation:

Answer:

x < [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Have a great summer :)

Answer:

someone answered this and its correct

Step-by-step explanation:

:D

Answer:

[tex]y=4(3)^{x}[/tex]

Step-by-step explanation:

Let the exponential function is,

f(x) = (b)ˣ

If this function has the base (b) = 3, function will be.

f(x) = (3)ˣ

If this function is transformed by a vertical stretch by a factor of 4,

New function will be,

g(x) = 4(3)ˣ

If the function 'g' is reflected across y-axis, new function will be,

h(x) = g(-x)

h(x) = [tex]4(3)^{x}[/tex]

Therefore, equation of the function will be,

[tex]y=4(3)^{x}[/tex]

Answer:

upper left graph:  y = 3/4x-3

lower right graph:  x = 3

Step-by-step explanation:

Answer:

196,836,571.6 miles²

Step-by-step explanation:

the earth is shaped like a sphere. the surface area of the earth can be determined by calculating the surface area of a sphere

surface area of a sphere = 4πr²

π= 3.14

r = 7,917.5 / 2 = 3958.75 miles

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

4 x 3.14 x 3958.75² = 196,836,571.6 miles²

Answer:

x = 1

AB = 9

BC = 9

AC = 18

Step-by-step explanation:

Given that B is the midpoint of AC, we can say that

AB = BC

x² + 8x = 4x + 5

subtract (4x+5) from both sides to make the equation equal to 0, enabling us to solve for x

x² + 4x - 5 = 0

Because 5 and -1 add to 4 (the coefficient to x in 4x) and 5 * (-1) = -5 ( the constant), we can factor this out into

(x+5)(x-1) = 0

Therefore, x² + 8x = 4x + 5 can be true at either x=-5. x=1, or both. Plugging these values in the equations to check, starting with x=-5, we get

-5²+8(-5) =4(-5) + 5

-15 = -15

As a line segment cannot have negative length, and  x² + 8x = 4x + 5  is negative when x=-5, x=-5 is not a viable solution

Next, for x=1, we get

1²+8(1) = 4(1) + 5

9=9

Therefore, x=1 is the only solution we have.

We have plugged this in for AB and BC, and 1²+8(1) = 4(1) + 5 = x² + 8x = 4x + 5 =  9 for both AB and BC

Next, AC is simply the sum of the two line segments that make them up, AB and BC, so AC = 9 + 9 = 18

Answer:

20

Step-by-step explanation:

By HL and CPCTC, GF = FI, so GI = 2FI = 2(10) = 20.

Answer:

[tex] {( \cos2A - \cos2B) }^{2} + {( \sin2A + \sin2 B }^{2}\\ = ( - 2\cos2A \cos2B + { \cos {}^{2} 2A } + \cos {}^{2} 2B) + (2 \sin2A \sin2B + \sin {}^{2} 2A + \sin {}^{2} 2B)\\ \\ { = - 2( \sin2A + \sin 2 B - \cos2 A - \cos2B) }\\ \\ { = - 2( - 4 \sin( A + B) \cos(A + B) } \\ \\ = {\tt{double \: angle \: of \: sine}}\\ \\ { = 2 \times 2(2 \sin (A + B) \cos(A + B)) }\\ \\ { = 4 \sin2(A + B)}[/tex]