f(x) is graphed below. If g(x)=f(x+2)-4, what are the roots of g(x)?

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Explanation:

Set each factor equal to zero and solve for x. I'm using the zero product property which says A*B = 0 leads to either A = 0 or B = 0.

Let's apply that idea to the first factor.

x^2+4x+3 = 0

(x+1)(x+3) = 0

x+1 = 0 or x+3 = 0

x = -1 or x = -3  are two roots

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Do the same for the other factor as well.

x^2 - 4 = 0

(x-2)(x+2) = 0  .... difference of squares rule

x-2 = 0 or x+2 = 0

x = 2 or x = -2  are another two roots

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In total, the four roots are:

Side note: The term "root" is the same as the zeros of a polynomial. Visually, this corresponds to the x intercepts. Plugging any of those four items into p(x) will lead to p(x) = 0.

Answer:

Write full question

I cannot understand

Step-by-step explanation:

The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

Given that "Jane wrote all the natural numbers from 5 to k. Including 1 and k"

So Jane wrote k numbers.

lets take an example

if k = 10 , then natural numbers between 1 and 10 are 10 numbers that are 1 , 2 , 3 ,4 ,5 ,6 , 7 , 8 ,9 and 10.

Hence she write k numbers.

Jane wrote k - 4 natural numbers for the given condition.

Natural numbers are defined as which range from 1 to infinity and are the most fundamental sort of numbers. Commonly known as positive numbers or counting numbers, these numbers. Natural Numbers are represented by the symbol N.

Jane wrote all the natural numbers from 5 to k, including 5 and k.

So, she wrote the numbers as 5, 6, 7, 8, 9, ..., k.

To find out how many numbers Jane wrote, we have to subtract 4 from each of these numbers because 4 numbers (1, 2, 3, 4) come before 5.

1, 2, 3, 4, 5, ..., k-1

So, there are k-1 - 4 + 1 = k - 4 natural numbers between 5 and k, inclusive.

Therefore, she wrote k - 4 natural numbers.

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Answer:

A ratio table shows pairs of corresponding values, with an equivalent ratio between each pair.

Step-by-step explanation:

i have linked 1 picture of a ratio table example

hope this helped

Given that the total amount of land in acres is 538

The problem statements requires us to divide the total amount of land into 34 places, the number of whole parts is 15 acres

Mathematically we have

538/34 = 15.823

But we are required to return the whole parts, therefore, let us ignore the values that comes after the decimal point. we have 15

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Fraction 10/12 would be greater than 3/4

Answer:

380

Step-by-step explanation:

285 / x = 75 / 100

Cross multiply 28500 = 75x

Divide by 75  380

Answer:

6.5 x 10^(-7)

Step-by-step explanation:

When multiplied by 10, it is like multiplying by 10^1. We can use the exponent rule: 10^(-8) * 10^1 = 10^(-7).

Example:

1.3 x 10^2 multiplied by 10

This is the same as 130 multiplied by 10 which is equal to 1300.

1300 written in scientific notation is 1.3 x 10^3, which adds one more onto the exponent.

Answer:

Yes, it is a rotation!

Step-by-step explanation:

You know this because the shape rotated. It did not flip, change size, or remain the same.

I hope this helps!

Answers:

section A = 25,000 seats

section B = 14,200 seats

section C = 10,800 seats

Your teacher may want you to leave out the commas from each number.

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Work Shown:

A = B+C

A+B+C = 50,000

B+C+B+C = 50,000

2(B+C) = 50,000

B+C = 50,000/2

B+C = 25,000

C = 25,000 - B

25A + 20B + 15C = 1,071,000

25(B+C) + 20B + 15C = 1,071,000

25(25,000) + 20B + 15(25,000 - B) = 1,071,000

625,000 + 20B + 375,000 - 15B = 1,071,000

1,000,000 + 5B = 1,071,000

5B = 1,071,000 - 1,000,000

5B = 71,000

B = (71,000)/5

B = 14,200 is the number of seats in section B

C = 25,000 - B

C = 25,000 - 14,200

C = 10,800 is the number of seats in section C

A = B+C

A = 14,200 + 10,800

A = 25,000 is the number of seats in section A

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Check:

A+B+C = 25,000+14,200+10,800 = 50,000

Answer:

[tex]{ \rm{perimeter = side + side + side}} \\ \\ { \rm{perimeter = 3 \frac{1}{2} + 4 \frac{2}{3} + 5 \frac{1}{4} }} \\ \\ { \rm{perimeter = 13 \frac{5}{12} \: cm}}[/tex]

Answer:x=-1, y=2

Step-by-step explanation:

Summing these equations, we will obtain,

-7x =7

Therefore, x=-1

If we put x in the first equation,

(-3*-1)-5y=-7

3-5y=-7

-5y=-10

y=2

Answer:

x=-1, y=1

Step-by-step explanation:

-3x-5y=-7

-4x+5y=14

-7x=7

x=-1

-3x-5y=-7

-3(-1)-5y=-7

3-5y=-7

-5y=-10

y=2

Answer:

11

Step-by-step explanation:

-2 lies in the second range that begins with -2 and ends with 8

Answer:3

Step-by-step explanation:

It is because the letters in diagram A cannot go to 2 seperate numbers in diagram B

Answer:

f^-1(x) = (x+20) / 12

Step-by-step explanation:

f(x) = 4(3x-5)

Let y be the image of f.

y = 4(3x-5)

y = 12x-20

y+20 = 12x

x = (y+20) / 12

f^-1(y) = (y+20) / 12, so

f^-1(x) = (x+20) / 12

The desmos link is in the reply section below...

1.) y = 1.56x + 1.29

2.) the slope is 1.56

As the weeks are increasing, the student's balance is growing about 1.56 per week.

3.) y = 24.69

4.) 50 = 1.56x + 1.29

50 - 1.29 = 1.56x + 1.29 - 1.29

48.71 =1.56x

48.71 / 1.56

31.2

Answer:

  4.6 ft

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh

Fill in the given values and solve for the base.

  5.52 = 1/2b(2.4)

  5.52/1.2 = b = 4.6 . . . . divide by the coefficient of b

The base is 4.6 feet.

The probability of picking a marble that is not blue is 5/6

The proportions of the balls are given as:

[tex]Red = \frac 12[/tex]

[tex]White = \frac 13[/tex]

[tex]Blue = 6[/tex]

The probability of picking a ball that is not blue is:

[tex]P(Not\ Blue) = P(Red) + P(White)[/tex]

So, we have:

[tex]P(Not\ Blue) = \frac 12 + \frac 13[/tex]

Rewrite the fractions as equivalent fractions

[tex]P(Not\ Blue) = \frac 36 + \frac 26[/tex]

Take LCM

[tex]P(Not\ Blue) = \frac {3 + 2}6\\[/tex]

Add 3 and 2

[tex]P(Not\ Blue) = \frac {5}6[/tex]

Hence, the probability of picking a marble that is not blue is 5/6

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Answer:

c on edge YW

Step-by-step explanation:

The value of ∛4 × √3 is 2.75 or  [tex]\sqrt[6]{432}[/tex].

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given;

Expression,

product 3 sqrt 4 times sqrt 3.

In numerator form:

As per the given expression,

∛4 × √3

Simplifying,

∛4 × √3

= [tex]4^{1/3}[/tex] x [tex]3^{1/2}[/tex]

= [tex]4^{2/6}[/tex] x [tex]3^{3/6}[/tex]

= [tex]\sqrt[6]{16 + 27}[/tex]

= [tex]\sqrt[6]{432}[/tex]

= 2.749

= 2.75

Therefore, the product is 2.75 or  [tex]\sqrt[6]{432}[/tex].

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Using exponential functions, it is found that a = 1.5 would cause the function to stretch.

The exponential function given is:

[tex]y = \left(\frac{1}{3}\right)^x[/tex]

Hence, a = 1.5 would cause the function to stretch.

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Answer:

1.5 is the value of a in the exponential function below would cause the function to stretch

It should be noted that all the solids have the same volume.

Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. It should be noted that the definition of length is interrelated with volume.

Here, the three solids below have the same height. The cross-sections of the parallel planes have equal areas. They all have same volume.

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Answer:

The second one:

x 2-2 3-3

y 5 5 7 7

Step-by-step explanation:

Each domain value or x can only have one range, y, so, with that said, the second one is the answer.