Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure

f(x) = x³ – 2x² – x + 2

 0 = x3 – 2x2 – x + 2

 (x-2)(x-1)(x+1)=0

 x1=-1

 x2=1

 x3=2

For this case we must follow the steps below:

We factor the polynomial, starting by factoring the maximum common denominator of each group:

[tex]x ^ 2 (x-2) - (x-2)[/tex]

We factor the maximum common denominator[tex](x-2):[/tex]

[tex](x-2) (x ^ 2-1)[/tex]

Now, by definition of perfect squares we have:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

Where:

[tex]a = x\\b = 1[/tex]

Now, we can rewrite the polynomial as:

[tex](x-2) (x + 1) (x-1)[/tex]

To find the roots we equate to 0:

[tex](x-2) (x + 1) (x-1) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

Answer:

14

Step-by-step explanation:

Distance of the pathway around a park = 4 1/5 miles

Distances between lamppost = 3/20 miles

Numbers of 3/10 intervals

= 4 1/5 ÷ 3/10

= 21/5 x 10/3

= 14

Number of lamp posts = 14

28 because the number of spots in the pathway where the lampposts will be placed is 1/5 divided by 3/10=14. since each spot will have 2 lampposts, there will be 14*2=28 lampposts in all.

hope this helped!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

the function g(X) is a translation of [tex]f(x) = \sqrt{x}[/tex]

the range is {y|y≥-1}

the function g(x) can be translated 3 units right and 1 unit up to get the function [tex]f(x) = \sqrt{x}[/tex]

Step-by-step explanation:

Given the graph of a function g(x)

g(x) looks like a square root function

So parent function is [tex]f(x) = \sqrt{x}[/tex]

the function g(X) is a translation of [tex]f(x) = \sqrt{x}[/tex]

the domain is {x| x ≥ -3}

the range is {y|y≥-1}

The parent function [tex]f(x) = \sqrt{x}[/tex] starts at (0,0)

so g(x) is translated 3 units left and 1 unit down

the function g(x) can be translated 3 units right and 1 unit up to get the function [tex]f(x) = \sqrt{x}[/tex]

Answer:

The correct options are 1, 3 and 5.

Step-by-step explanation:

The given function is a continuous increasing curve which is increasing at decreasing rate. It means it is the graph of a radical function.

Parent radical function is

[tex]f(x)=\sqrt{x}[/tex]

It means function g(x) is the translation of function [tex]f(x)=\sqrt{x}[/tex]. Option 1 is correct.

Domain is the set of input values.

Function is defined for all x ≥ -3.

Domain = { x |  x ≥ -3 }

Option 2 is incorrect.

Range is the set of output values.

The values of the function are always greater than or equal to -1.

Range = { y |  y ≥ -1 }

Option 3 is correct.

The graph of parent function [tex]f(x)=\sqrt{x}[/tex] shifts 3 units left and 1 unit down to get the graph of g(x). So the function g(x) is defined as

[tex]f(x)=\sqrt{x+3}-1[/tex]

Option 4 is incorrect.

The function g(x) can be translated right 3 units and up 1 unit to create the function [tex]f(x)=\sqrt{x}[/tex].

Option 5 is correct.

Answer: Mine A

Step-by-step explanation: Mine A is further underground because elevation means height and when it’s shows a number that is negative that means underground. 225 is greater than 223. So Mine A is further underground.

Answer:

Step-by-step explanation:

Mine A, Mine B is not even a mine, its negative, not a hole

Answer:

m∠BPD = 120

mBC + mAD = 120°

Step-by-step explanation:

according to intersecting chord theorem: The measure of the angle formed by two chords  that intersect inside the circle is [tex]\frac{1}{2}[/tex] the sum of the chords' intercepted arcs.

m∠BPD = [tex]\frac{1}{2}[/tex] (M∠BD + M∠CA)

             = [tex]\frac{1}{2}[/tex]  (70 + 170)

             =  [tex]\frac{1}{2}[/tex] (240)

m∠BPD = 120

We know that a circle has a total of 360° around the center of circle. To find the measure of the remaining measure of angle of arcs, subtract them from the whole that is 360°

mBC + mAD = 360 - ( 70 + 170 )

                     = 360 - 240

mBC + mAD = 120°

Answer:

5; you add the two legs for the hypotenuse

Step-by-step explanation:

The length of the hypotenuse is 5 feet.

The hypotenuse is the opposite side of the right angle in the triangle. It’s also the longest side of the triangle.

The Pythagorean Theorem helps us calculate the hypotenuse of a right triangle if we know the sides of the triangle.

Here, a = 3 feet.

         b = 2 feet.

    Then hypotenuse will be = (√3 + √2) feet

                        = 5 feet.

The answer is 5 feet.

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Answer:

[tex]V=1,800\pi\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=10\ units[/tex]

[tex]h=18\ units[/tex]

substitute

[tex]V=\pi (10)^{2}(18)[/tex]

[tex]V=1,800\pi\ units^{3}[/tex]

Answer: C) 44

======================================

Work Shown:

P = 2*(L+W)

P = 2*(13+9) ... plug in given length and width

P = 2*22

P = 44

Answer:

Step-by-step explanation:

Answer:

10000000

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

13+(-29) = 13-29  = -16

Answer: -16

Step-by-step explanation:

Try Subtracting 13 from positive 29. This will help you out!

Answer:

circle

Step-by-step explanation:

Answer:

216 in²

Step-by-step explanation:

A cube has 6 congruent square faces, thus

area of 1 face = 6 × 6 = 36 in² and

area of 6 faces = 6 × 36 = 216 in²

Answer:

The vertex is (2,-16)

Step-by-step explanation:

The given function is [tex]f(x)=(x-6)(x+2)[/tex]

We expand to obtain;

[tex]f(x)=x^2+2x-6x-12[/tex]

[tex]f(x)=x^2-4x-12[/tex]

We complete the squares to obtain;

[tex]f(x)=x^2-4x+(-2)^2-12-(-2)^2[/tex]

[tex]f(x)=x^2-4x+(-2)^2-12-4[/tex]

[tex]f(x)=(x-2)^2-16[/tex]

The vertex form is [tex]f(x)=(x-2)^2-16[/tex]

Comparing this to

[tex]f(x)=a(x-k)^2+k[/tex]

The vertex is (h,k)= (2,-16)

Final answer:

The vertex of the quadratic function f(x) = (x - 6)(x + 2) is found by expressing the function in vertex form. After completing the square, the vertex of the function is determined to be at the point (2, -16).

Explanation:

To find the vertex of the quadratic function f(x) = (x
– 6)(x + 2), we first need to express the function in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Multiplying out the factors gives us f(x) = x² - 4x - 12. Completing the square allows us to transform this equation into vertex form.

First, Factor out the leading coefficient (which is 1 in this case, so this step is not needed), and then rewrite the function isolating the terms with x:

f(x) = x² - 4x + ____ - 12 + ____.

We complete the square by finding the value that makes x² - 4x + ____ a perfect square trinomial. This value is (-4/2)² = 4, so we add and subtract 4 inside the function:

f(x) = x² - 4x + 4 - 12 - 4.

Now we have f(x) = (x - 2)² - 16. Thus, the vertex form of the function is y = (x - 2)² - 16, and the vertex of the parabola is at the point (2, -16).

Answer:

Final answer is [tex]y=3x-13[/tex].

Step-by-step explanation:

Given that slope of the line is m=3

Plug the given point (4,-1) and the slope m=3 into point sloep formula:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-(-1)=3\left(x-4\right)[/tex]

[tex]y+1=3\left(x-4\right)[/tex]

[tex]y+1=3x-12[/tex]

[tex]y=3x-12-1[/tex]

[tex]y=3x-13[/tex]

Which looks like slope intercept form of line y=mx+b

Hence final answer is [tex]y=3x-13[/tex].

The answer is:

The equation in slope-intercept form is:

[tex]y=3x-13[/tex]

To solve the problem and find equation in slope-intercept form of the line, we need to use the following formula:

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

We are given the slope of the line, so, rewriting we have:

[tex]y=3x+b[/tex]

Then, to find "b" we need to substitute the given point into the equation, so, substituting we have:

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

[tex]-1=3*(4)+b[/tex]

[tex]-1=12+b[/tex]

[tex]b=-1-12=-13[/tex]

Therefore, writing the equation of the line, we have:

[tex]y=3x-13[/tex]

Have a nice day!

Cafeteria ratio of Swiss cheese to cheddar cheese is 15:17.

Perry’s ratio of Swiss chess to cheddar cheese is 5:7.

Wrong ratio because 5 * 3 = 15 but 7 * 3 does not equal 17.

For this case we have that by definition, it is known as proportion to the relationship of equality that exists between two reasons, that is, between two comparisons. That is: if [tex]\frac {a} {b}[/tex]is a ratio, then the equality [tex]\frac {a} {b} = \frac {c} {d}[/tex] will be a proportion.

Then, 15 cups of Swiss cheese for every 17 cheddar:

1[tex]5:17\\\frac {15} {17}[/tex]

We want to verify the proportion:

[tex]15:17 :: 5: 7\\\frac {15} {17} = \frac {5} {7}\\7 * 15 = 5 * 17[/tex]

Equality is not met!

Answer:

You are not using the correct proportion

Answer:

(−5, 8), (5, 8)

d = 10

(−2, −9), (−2, 4)

d = 13

(−12, −4), (−6, −4)

d = 6

Step-by-step explanation:

Answer:

(−5, 8), (5, 8)

d = 10

(−2, −9), (−2, 4)

d = 13

(−12, −4), (−6, −4)

d = 6

Step-by-step explanation:

Answer:

4.55 meters

Step-by-step explanation:

Answer:

Step-by-step explanation:

your answer is 4.55 :)

Answer:

see below

Step-by-step explanation:

The function is only defined for x < 1, and is undefined for x=1 or more. Thus the graph stops at x=1, with an open circle indicating the function is not defined there.

Answer:

The required graph is shown in figure 1.

Step-by-step explanation:

Consider the provided function f(x)=x if x<1

Here the sign of inequality is x<1.

That means the value of x can be anything less then 1.

Note the sign "<" indicates that the value x is strictly less than 1 also it is not equal to 1.

For x=1 the function is not defined.

For the inequity "<" and ">" we use an open dot or open circle which shows that the value is not included.

Now draw the table and substitute some value of x as shown.

Substitute x=0 in the provided equation.

f(x)=0

For x=0 the value of f(x) is also 0.

Substitute x=-1

f(x)=-1

For x=-1 the value of f(x) is also -1.

Substitute x=-2

f(x)=-2

For x=-2 the value of f(x) is also -2.

The required table is shown below:

x   0  -1  -2

f(x) 0  -1  -2

Now plot the above points and join them.

The required graph is shown in figure 1.

Answer: A large cube consists of smaller cubes. The more small cubes, the greater the large cube.

Step-by-step explanation:

I think the rule might be x-9

the answers are 15 times 4.

Answer:9.2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To solve this, we can plug in values to see which one works. Since it is a variable equals a variable, the answer is B(0,0)

Answer:

BC = 144 units

Step-by-step explanation:

It is given a line segment BC.

D is the point on the line segment.

To find the length of BC

BC = 8x

CD = 3x + 8  and BD = 4x + 10

BC = CD + BD

8x = 3x + 8 + 4x + 10

8x = 7x + 18

x = 18

BC = 8x = 8 * 18 = 144 units

Therefore the length of segment BC = 144 units

Segment BC is 144 units

Cos(90)= 0.00

It is only zero

The value of cosine  90°. or cos  90° is 0.

Trigonometric ratios are the ratios of the length of sides of a triangle.

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent.

We know that,

According to the trigonometric table the value of cos 90° is 0.

i.e.,  cos 90°.

This is because there is no horizontal component of the angle: The horizontal component of the angle is 0, so, the cosine of 90° is 0.

In other words,

the cosine of an angle tells the size of the adjacent side of a right triangle compared to the hypotenuse. Look at the unit circle to see why the adjacent side (the x axis) has a width of 0 when the angle between the initial arm and the terminal arm is a right angle.

Thus, value of cos 90 is 0.

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Answer:A) n=-6

Step-by-step explanation:

Answer:

n = -6

Step-by-step explanation:

3n + 14 = -4

Subtract 14 from both sides

3n = -18

Divide both sides by 3

n = -6

Answer:

0.5

Step-by-step explanation:

-1 + 0 + 1 + 2 = 2

2/4 = 0.5

Answer:

well its not 1 cuz i got it wrong

Step-by-step explanation:

let me know in the comments

The total cost of 1 pair of pants and 1 shirt is $18 . If s represents the cost of 1 shirt, which equation could you use to find .

For this case we propose a system of equations:

p: Variable representing the cost of a pair of pants

s: Variable representing the cost of a shirt

A pair of pants costs twice as much as a shirt, means:

[tex]p = 2s[/tex]

The total cost of 1 pair of pants and 1 shirt is $ 18:

[tex]p + s = 18[/tex]

We substitute the first equation in the second:

[tex]2s + s = 18\\3s = 18\\s = \frac {18} {3}\\s = 6[/tex]

Answer:

The following equation can be used:

[tex]2s + s = 18[/tex]

Answer: y=31

Step-by-step explanation

If x=5 and y=6x+1, you plug in 5 for x in the equation y=6x+1.

This would cause it to be y=6(5)+1.

Then you multiply 6*5, which equals 30. thatll turn into y=30+1

30+1=31, so y=31

Answer:

Y = 31

Step-by-step explanation:

Replace x with 5

Y = (6*5) + 1

Use PEMDAS

Parentheses

Exponent

Multiplication

Division

Subtraction

Addition

6 * 5 = 30

Y = 30 + 1

30 + 1 = 31

Y = 31

I hope I helped!

Let me know if you need anything else!

~ Zoe

Answer is B, Just some mutiplaction

Answer:C 30

Step-by-step explanation: They all divide evenly when divided by 30.