The diagram shows a map of three land masses, numbered region 1, region 2, and region 3, connected via bridges over water. Each bridge can be traversed in either direction. (diagram is attached)

Show that there are 10 walking routes that start and end in region 2, crossing over water exactly twice. Assume each bridge, when crossed, is fully traversed to the next land mass.

Answer:

f(x) = x^3 + 7x^2 + 7x -15

Step-by-step explanation:

f(x) = (x+5)(x+3)(x-1)

f(x) = (x^2 + 3x + 5x + 15)(x-1)

f(x) = (x^2 + 8x + 15)(x-1)

f(x) = x^3 + 8x^2 + 15x -x^2 -8x -15

simplify

f(x) = x^3 + 7x^2 + 7x -15

Answer:

[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].

Step-by-step explanation:

By the factor theorem, if a constant [tex]a[/tex] is zero of the polynomial [tex]f(x)[/tex], [tex](x - a)[/tex] would be a factor of this polynomial. (Notice how [tex]x = a[/tex] would indeed set the value of [tex](x - a)\![/tex] to [tex]0[/tex].)

For instance, since [tex](-5)[/tex] is a zero of the polynomial [tex]f(x)[/tex], [tex](x - (-5))[/tex] would be a factor of [tex]f(x)\![/tex]. Simplify this expression to get [tex](x + 5)[/tex].

Likewise, the zero [tex](-3)[/tex] would correspond to the factor [tex](x + 3)[/tex], while the zero [tex]1[/tex] would correspond to the factor [tex](x - 1)[/tex].

All three of these factors above are linear, and the degree of the variable [tex]x[/tex] in each factor is [tex]1[/tex]. Multiplying three such linear factors would give a polynomial of degree [tex]3[/tex].

Given the three factors, the expression of [tex]f(x)[/tex] in factored form would be:

[tex]f(x) = m\, (x + 5)\, (x + 3)\, (x - 1)[/tex] for some constant [tex]m[/tex].

When this expression is expanded, the constant [tex]m[/tex] would be the coefficient of the [tex]x^{3}[/tex] term (the leading term.) In other words, [tex]m\![/tex] is the leading coefficient of [tex]f(x)[/tex]. This question has required this coefficient to be [tex]1[/tex]. Thus, [tex]m = 1[/tex]. The expression of [tex]f(x)\![/tex] in factored form would be:

[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].

Answer:

i am just here for points

Step-by-step explanation:

Answer: yes squirrel is ?????

Answer: yes!

Step-by-step explanation:

Answer: As to what I am seeing i think you are doing fine

Step-by-step explanation:

Great Job

Answer

The armadillo and Glyptodon descended from a common ancestor.

Step-by-step explanation:

Answer:

R=11cm, r=3cm

Step-by-step explanation:

π(R²-r²) = π(121-9) = 112π cm² = 35.63cm².

hope this helps you.

The full installment price is $ 2200, and the annual interest rate is 10%.

Since Clare wants to buy a used wide-screen TV that sells for $ 2,000 cash, and she will make a down payment of $ 1,000 and then six monthly payments of $ 200, to determine what is the full installment price and the annual interest rate is due perform the following calculation:

Therefore, the full installment price is $ 2200, and the annual interest rate is 10%.

Learn more about maths in https://brainly.com/question/25866144

When a shape is rotated, it must be rotated through a point.

The vertices of the triangle would remain unchanged after both transformations

Assume the coordinates of triangle ABC is (x,y).

The first rotation is 90 degrees clockwise rotation.

The rule of this transformation is:

[tex](x,y) \to (y,-x)[/tex]

Next, the triangle is rotated 270 degrees clockwise.

The rule of this transformation is:

[tex](x,y) \to (-y,x)[/tex]

So, we have:

[tex](y,-x) \to (x,y)[/tex]

Hence, the vertices of the triangle would remain unchanged after both transformations

Read more about transformation at:

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Answer:

-75

Step-by-step explanation:

i had the exam so it is write

Answer:

120 [cm²].

Step-by-step explanation:

1) the required area is A=Area(ABCEFD)=Area(ABCD)+Area(CEFD);

2) Area of ABCD: Area(ABCD)=AB*BC=12*8=96 [cm²];

3) Area of CEFD: Area(CEFD)=0.5(CD+EF)*HD=0.5*(8+4)*4=24 [cm²];

4) finally, the required area is: A=96+24=120 [cm²].

all the details are provided in the attachment.

Answer:

A

Step-by-step explanation:

0 - 1400 = -1400 + 1400 = 0

Answer: 200 Students

Step-by-step explanation:

Answer:

Point C

Step-by-step explanation:

Trust me it is correct

make me brainiest because I answered first pls

Answer:

d = 146

Step-by-step explanation:

Answer:

d=146

Step-by-step explanation:

the sqrt of 2(2) is 4 which can be simplified to 2 and the 12 raised to the second power is 144 so 2+144 is 146

Step-by-step explanation:

this is not an isoceles triangle.

anyway, we need to remember 2 things :

1. the sum of all angles in a triangle is always 180°.

2. the sum of all angles around a single point on a line is 360° (as this point wound be the center of an invisible circle). and as the line cuts this circle in half, the angles on one side of the line around this point is therefore 180°.

so, the internal angle Q is then

180 = 50 + 55 + Q

Q = 180 - 50 - 55 = 180 - 105 = 75°

the exterior angle x at Q is then

180 = Q + x = 75 + x

x = 180 - 75 = 105°

Answer:

159

Step-by-step explanation:

10^2+(3+5)^2-5

First do the parentheses: 3+5 is 8

Now the equation is

10^2+8^2-5

Exponents:

10^2 is 100

8^2 is 64

100+64-5

Simplify and you would get 159

Thus the answer is 159

Hope this helps!

First thing we want to know is what it is asking us.

So, it is asking us to evaluate this expression. Which means to find the answer to it.

Second thing is the order of Operations.

P- (Parentheses)

E-Exponents

M Multiplication

D Division

A Add

S Sub

Now that we know what that means, we may now solve it.

you see a parenthesis, right? Do what is inside first

1.3+5=8

Now there is a exponent by the parentheses. We do that next

(Exponent means we times that number by the number. Like 4 to the power of 3 is really just 4x4x4)

2.8 to the power of 2 is 8x8 which is 64.

So, we got 64 down let's see our equation now.

10^2+64-5

Now, the next step in PEMDAS Is to do the exponents. 10 to the power of 2 is really just 10x10.

(A trick is that if you see the little number beside the 10, it means how many zeros there are like 10to the power of 2 is 100)

So, our new equation is

100+64-5.

Now all we have to do it add and sub right to left

100+64=164

Our new equation is 164-5 which is 159.

I hope this helps! If it's wrong blame me..

Answer:

Its ether 3 or 4.

Step-by-step explanation:

its more than likely its 4 but I wasn't %100 sure.

Answer:

  78.50°

Step-by-step explanation:

On either equinox, the sun is overhead at the equator. At 11.50 N, the sun will be at elevation ...

  90° -11.50° = 78.50°

The amount of broccoli needed to be ordered to prepare 50 portion of broccoli flower is 3.375 kg.

You need to prepare 50 portions of broccoli flowers.

A prepared portion weighs 0.090 kg.

Trimming accounts for 25% of the total weight.

Therefore, to find how much broccoli is needed to order can be calculated as follows:

Therefore,

the broccoli needed to be ordered = 0.0675 × 50 = 3.375 kg

learn more on percentage here: https://brainly.com/question/25304304?referrer=searchResults

Answer:

y= -4x + 2

Step-by-step explanation:

Y= mx + b is used to find the equation of the line

m=-4 a d b= 2

So, you put them into the equation.

The question is an illustration of system of equations

There are 14 problems worth 5 points and 15 problems worth 2 points

The system of equations is given as:

[tex]x + y = 29[/tex]

[tex]5x + 2y = 100[/tex]

Make x the subject in [tex]x + y = 29[/tex]

[tex]x = 29 - y[/tex]

Substitute 29 - y for x in [tex]5x + 2y = 100[/tex]

[tex]5(29 - y) + 2y = 100[/tex]

Open brackets

[tex]145 - 5y + 2y = 100[/tex]

Evaluate like terms

[tex]145 - 3y = 100[/tex]

Collect like terms

[tex]- 3y = 100-145[/tex]

Evaluate like terms

[tex]- 3y = -45[/tex]

Divide both sides by -3

[tex]y = 15[/tex]

Substitute 15 for y in [tex]x = 29 - y[/tex]

[tex]x = 29 - 15[/tex]

[tex]x = 14[/tex]

This means that there are 14 problems worth 5 points and 15 problems worth 2 points

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Answer:

circle tttdonuts

Step-by-step explanation:

d crystal

Answer:

x = 7

Step-by-step explanation:

[tex]\frac{3x-1}{5}[/tex] - [tex]\frac{x}{7}[/tex] = 3

Multiply through by 35 ( the LCM of 5 and 7 ) to clear the fractions

7(3x - 1) - 5x = 105 ← distribute parenthesis and simplify left side

21x - 7 - 5x = 105

16x - 7 = 105 ( add 7 to both sides )

16x = 112 ( divide both sides by 16 )

x = 7

To verify the answer substitute x = 7 into the left side of the equation and if equal to the right side then it is the solution

[tex]\frac{3(7)-1}{5}[/tex] - [tex]\frac{7}{7}[/tex]

= [tex]\frac{21-1}{5}[/tex] - 1

= [tex]\frac{20}{5}[/tex] - 1

= 4 - 1

= 3 = right side

Then x = 7 is the solution to the equation

Step-by-step explanation:

sorry I don't now but when I now I will tell you ok but mybe it 12×12×12

Answer:

300

Step-by-step explanation:

This question is pretty simple.

First, we just have to find 50% of 200.

So 50% is also 1/2.

1/2 of 200 is just 100. The question says that the truck is 50% LONGER than the car.

So 50% longer is 100 and 100+200(the length of the car) is 300.

The answer.

Answer:

NEED MORE

Step-by-step explanation:

Answer: Less likely since the number of cyan is quite lower or the lowest in comparison of magenta and yellow.

Answer:

m = [tex]\frac{-421}{6}[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

x

Step 1: Simplify both sides of the equation.

3m+3m=−7−12−18−(16)x(24)

3m+3m=−7+−12+−18+(−384)

(3m+3m)=(−7+−12+−18+(−384))(Combine Like Terms)

6m=−421

6m=−421

Step 2: Divide both sides by 6.

[tex]\frac{6m}{6} =\frac{-421}{6}[/tex]

m = [tex]\frac{-421}{6}[/tex]