Which expression is equivalent to 2x2x2x2x2

In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

Equation of a line:

The equation of a line is given by:

[tex]y = mt + b[/tex]

In which m is the slope and b is the y-intercept(value of y when x = 0).

This situation:

x between 0 and 10:

From here, we can take two points (t,y). I will take (0,0) and (10,10).

From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:

[tex]y_1 = mt[/tex]

To find the slope, when we have two points, it is given by change in y divided by change in t, so:

Change in t: 10 - 0 = 10

Change in y: 10 - 0 = 10

Slope: [tex]m = \frac{10}{10} = 1[/tex]

Thus, the first definition is:

[tex]y_1 = t, 0 \leq t < 10[/tex]

x between 10 and 20:

I will take the points (10,10) and (20,0).

First, we find the slope:

Change in t: 20 - 10 = 10

Change in y: 0 - 10 = -10

Slope: [tex]m = \frac{-10}{10} = -1[/tex]

Thus:

[tex]y_2 = -t + b[/tex]

For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So

[tex]0 = -20 + b[/tex]

[tex]b = 20[/tex]

Thus, the second definition is:

[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]

Write an equation for the graph.

We use the two definitions, that is:

[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]

So

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

A similar question can be found at https://brainly.com/question/16024991

Answer: 7 miles/h and 1 miles/h

Step-by-step explanation:

With the speed of current = x + 1

Against the speed of current = x - 1

ATQ

4(x-1) = 3(x+1)

4x-4 = 3x+3

4x - 3x = 3+4

x = 7

Speed of boat = 7miles/h

Current of river = 1 miles/h

please click thanks and mark brainliest if you like :)

Answer:

Hello,

Boat speed=7 miles/h

Current speed = 1 mile/h

Step-by-step explanation:

I am going to try to explain.

Let say V the speed of the boot (V like vitesse in french)

Let say v the speed of the current.

distance=24 miles

[tex]\left\{\begin{array}{ccc}V-v&=&\dfrac{24}{4} \\V+v&=&\dfrac{24}{3} \\\end{array}\right.\\\\\left\{\begin{array}{ccc}V-v&=&6 \\V+v&=&8 \\\end{array}\right.\\\\Adding\ the\ 2\ equations\ and\ substracting\ them \\\\\\\left\{\begin{array}{ccc}2V&=&14 \\2v&=&2 \\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}V&=&7 \\v&=&1 \\\end{array}\right.\\\\[/tex]

Boat speed=7 miles/h

Current speed = 1 mile/h

Answer:

y ≤ 2x-6

Step-by-step explanation:

First find the equation of the line

The y intercept is -6

The slope is 2

y = 2x-6

The line graphed is solid so we know that there is an equal sign

We are graphing below the line

y ≤ 2x-6

Answer:

Step-by-step explanation:

Answer:

A. 11.18

Step-by-step explanation:

(1, -2) will be x1 and y1.

(-9, 3) will be x2 and y2

The formula is

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

Substitute in all the variables.

[tex]\sqrt{(-9-1)^2+(3-(-2))^2}[/tex]

Solve.

[tex]\sqrt{(-10)^2+5^2}[/tex]

[tex]\sqrt{100+25}[/tex]

[tex]5\sqrt{5}[/tex]

11.18033988.....

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

X=7.9

Y=7.9

Step-by-step explanation:

We have that x=y

And form Pythagoras theorem we have

[tex]5 \sqrt{5} = \sqrt{x ^{2} + x ^{2} } \\ take \: the \: square \: of \: the \: two \: sides \\ 125 = 2x ^{2} \\ x {}^{2} = 62.5 \\ x = 7.9[/tex]

So x = y = 7.9

Answer:

Its AA similaroty theorem

Answer:

That is the graph for y = -|x| + 3

Answer:

65

Step-by-step explanation:

Because its a triangle,

P + Q + R = 180

So,

P + 70 + 45 = 180

P + 115 = 180

Subtract 115 on both sides

P = 65

Answer:

a)7, b)-40

Step-by-step explanation:

a) 5(x-1)=30

=>5x -5=30

=>5x=30+5

=>5x=35

=>x=35/5

so, x=7

b)3(x+10)-2(x-5)=0

=>3x+30-2x+10=0

=>x+40=0

so,x=-40

Answer:

absolute value

Step-by-step explanation:

Answer:

This shows the absolute value of an integer.

Step-by-step explanation:

When you see the lines | | around a number, it should always give you the answer of that number's positive integer. So lets say I out | -2 | the answer for this equation should be 2.

Step-by-step explanation:

(=) 1 ( x-5 ) > 6x-17

(=) x-5 > 6x -17

(=) -5x > -12

=> x < 12/5

Answer:

Step-by-step explanation:

I'm assuming that strange looking thing is a 9, so begin by multiplying both sides by that denominator to get:

[tex]x-9=\sqrt{x}+3[/tex] then subtract 3 from both sides to get

[tex]x-12=\sqrt{x}[/tex] and then square both sides to get

[tex]x^2-24x+144=x[/tex] and get everything on one side to solve for x by factoring:

[tex]x^2-25x+144=0[/tex] and factor that however it is you have learned to factor second-degree polynomials to get that

x = 16 and x = 9. We have to check for extraneous solutions because anytime you manipulate an equation, as we did by squaring both sides, you run the risk of these solutions that actually don't work when you plug them back into the original equation. Let's try 16 first:

[tex]\frac{16-9}{\sqrt{16}+3 }=1[/tex]  If 16 is a solution, then this statement will be mathematically true.

[tex]\frac{7}{4+3}=1[/tex]  and   [tex]\frac{7}{7}=1[/tex] so 16 works. Let's try 9:

[tex]\frac{9-9}{\sqrt{9}+3 }=1[/tex]  We know that one doesn't work, because 9-9 = 0 and 0 over anything = 0, not 1.

x = 16 is the only solution.

Answer:

x =  16

Step-by-step explanation:

[tex]\frac{x-9}{\sqrt{x}+3}=1[/tex]

Cross multiply,

x - 9 = √x + 3

Subtract 3 from both sides

x - 9 - 3 = √x

x - 12 = √x

Square both sides

(x -12)² = (√x)²

x² - 2 * x*12 + 12² = x

x² - 24x + 144 = x

x² - 24x + 144 - x = 0

x² - 25x + 144 = 0

Sum = -25

Product = 144

Factors = -9 , -16            {(-9)+(-16) = -25  & (-)*(-16) = 144}

x² - 25x + 144 = 0

x² - 16x - 9x + (-9)*(-16) = 0

x(x - 16) - 9(x - 16) = 0

(x - 16) (x - 9) = 0

x - 16 = 0     ; x - 9 = 0

x = 16          ; x = 9

x = 9 is  an extraneous solution.

When we plug in 9 in the LHS of the equation,

LHS = [tex]\frac{9-9}{\sqrt{9}+3}[/tex]

       [tex]= \frac{0}{3+3}[/tex]

        = 0 ≠ RHS

So, x = 16 is the only  solution

Answer:

BF = |4 – 1| = 3

FC = |4 – 0| = 4

Using the Pythagorean Theorem to find BC:

BC2  =  BF2 + FC2

BC2   =  32 + 42

BC2   =  9 + 16

BC  =  sqaure root 25

BC  =  5

Step-by-step explanation:

The length of BC is 5 unit.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We need to find the length of BC place point F at (4,4) and draw BF and FC now you have the right ∆BFC with BC as the hypotenuse find BC and FC using the coordinates of B,C, and,F then use the Pythagorean theorem to find BC.

Using the Pythagorean Theorem to find BC:

BC^2  =  BF^2 + FC^2

BC^2   =  32 + 42

BC^2   =  9 + 16

BC  =  √25

BC  =  5

So, BF = |4 – 1| = 3

FC = |4 – 0| = 4

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

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Answer:

it is <

Step-by-step explanation:

Answer:

Vertex is (-2.5, - 13.25) and x=(-5±sqrt(53))/2

Step-by-step explanation:

x^2+5x-7

x^2+5x+(2.5)^2-(2.5)^2-7

(x+2.5)^2-13.25. Vertex is (-2.5, - 13.25)

Solution of the functions are x=(-5±sqrt(53))/2

Answer:

x = 0.5

Step-by-step explanation:

When we add up the distance between the apartment and park with the distance between the park and the coffee shop, the total will equal nine miles.

Our equation will look like this:

(5x + 2) + (25x - 8) = 9

Add up the like terms

5x + 2 + 25x - 8 = 9

30x - 6 = 9

Add 6 to both sides

30x - 6 = 9

      + 6  + 6

30x = 15

Divide both sides by the coefficient, 30, to isolate the variable, x

30x/30 = 15/30

x = 15/30

Reduce

x = 1/2

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{2\sqrt{3} }{2}=\sqrt{3}[/tex]

I hope this helps!

pls ❤ and give brainliest pls

Answer:

Domain is the whole R and the range is R+. The domain is continuous

Answer:

c

Step-by-step explanation:

AB and CD are opposite sides of quadrilateral.

Answer:

30 centimeters

Step-by-step explanation:

true

Answer:

3/root8+root9

Step-by-step explanation:

3/root8+root9

Answer:

It's going to take you 17 min to travel 12 miles

assuming you are going with mph

Step-by-step explanation:

I looked at a speed calculator and calculated that to go 25 miles in 35 min, you were going 42 mph. so I changed the imput to 12 miles and I got my answer.

Answer:

[tex]{ \sf{ \int 4x \cos(2 - 3x) dx = {4x}^{2} \cos(2 - 3x) + c }}[/tex]

Step-by-step explanation:

From integration by parts:

[tex]{ \boxed{ \bf{ \int u \: \frac{dv}{dx} = uv - \int v \: \frac{du}{dx} }}}[/tex]

let u be cos(2-3x) and let dv/dx be 4x:

[tex]{ \sf{ \frac{du}{dx} = 3 \sin(2 - 3x) }} \\ \\ { \sf{ v = \int 4x = 2 {x}^{2} }}[/tex]

Substitute in formular box:

[tex]{ \sf{ = (2 {x}^{2} \times \cos(2 - 3x)) - \int 2 {x}^{2} .3 \sin(2 - 3x) dx}} \\ = { \sf{2 {x}^{2} ( \cos(2 - 3x) - 3 \int \sin(2 - 3x)dx }} \\ { \sf{ = 2 {x}^{2} ( \cos(2 - 3x) - 3( - \frac{1}{3} \cos(2 - 3x) ) + c}} \\ { \sf{ = {4x}^{2} \cos(2 - 3x) + c}}[/tex]

Answer:

A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.

Step-by-step explanation:

Answer:

A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.

Step-by-step explanation:

Sample response

Answer:

7.7 ft

Step-by-step explanation:

The third longest side is also the second shortest side.

The 14 ft side of quadrilateral ABCD corresponds to the 6 ft side of quadrilateral EFGH.

14/6 = 18/x

7/3 = 18/x

7x = 18 * 3

7x = 54

x = 54/7

x = 7.7

Answer: D. 7.7 feet

Answer:

Step-by-step explanation:

7.7

Hi there!

[tex]\large\boxed{y = \frac{x + 4}{7}}[/tex]

f(x) = 7x - 4

Rewrite f(x) with y:

y = 7x - 4

Swap the x and y variables:

x = 7y - 4

Solve for y:

x + 4 = 7y

y = (x + 4)/7

Answer: quit

Step-by-step explanation:

it’s really easy .

Answer:

Option C, 832 units²

Step-by-step explanation:

l = 8

w = 7

h = 24

Surface area = 2(wl+hl+hw)

=2×(7×8+24×8+24×7)

=832 units²

Answer: YO ITS ANSWER C)832 UNITS[tex]^{2}[/tex] !!!!