x^2+6x+4 Which of the following is equivalent to the expression above? Justify your answer. A) (x+3)^2+5 B) (x+3)^2-5 C) (x-3)^2+5 D) (x-3)^2-5

Answer:

Step-by-step explanation:

[tex]Step 1: The- equation- of -a- circle- with -center -at- (h,k)- and- a -radius- of- r- is:\\(x-h)^2+(y-k)^2=r^2\\In -this -question ,h=3, k=1 and r=2, so- after- substituting- into- above -formula- we- get:\\(x-3)^2+(y-1)^2=2^2\\(x-3)^2+(y-1)^2 = 4\\ x^2-6x+9+y^2 -2y+1-4=0\\x^2-6x+y^2-2y+6=0[/tex]

Answer:

The constant of proportionality (k) is 24

Step-by-step explanation:

if y varies inversely as x

y = k × 1/x

and y = k/x

if y = 4 and x = 6

That means 4 = k/6

and k = 4 × 6

k = 24

Answer:

D

Step-by-step explanation:

A is not right as we don't know the formula used so we cant say the x intercept

B is not right as the function is not liner

C The function is not liner

That leaves D!

hope this helps!

Answer:

D

Step-by-step explanation:

Answer:

  O True

Step-by-step explanation:

If we substitute (x, y) = (0, 0) into both inequalities, we have ...

  0 < 2·0 +4   ⇒   0 < 4 . . . true

  0 > -2·0 -2   ⇒   0 > -2 . . . true

The point (0, 0) satisfies both inequalities, so is contained in the solution set.

Answer:

aₙ=  n²-6

Step-by-step explanation:

The sequence:

- 5, -2, 3, 10, 19, ...

The difference between terms:

3, 5, 7, 9

The next term would be: 19+11= 30

Let's work out the formula:

aₙ= a₁+n²-1= -5+ n²-1= n²-6

Let's test this formula for 5th and 6th terms:

So the nth term is:

Answer:

16ft

Step-by-step explanation:

Each side is 2 units long, 2^4 or 2x2x2x2 is 16.

Answer:

D.

Step-by-step explanation:

So angle 2 = 180 - angle 1

Angle 1 = angle 3 + angle 4.

Angle 2 = 180 - angle 3 - angle 4

So, you can come to the conclusion that (angle 1 + angle 2) = 180°

and (angle 3 + angle 4 + angle 2) = 180°

Answer:

Option D

Step-by-step explanation:

All the other expressions are correct but in Expression 3 , Sarah incorrectly multiplied 1/2(-6) while destroyed whole of her answer. She forgot to make 3 negative.

[tex]\sqrt{3x+10}=\sqrt{2x+3}\\\\\\\dfrac{\sqrt{3x+10}}{\sqrt{2x+3}}=1\\\\\\\sqrt{\dfrac{3x+10}{2x+3}}=1\\\\\\\dfrac{3x+10}{2x+3}=1\\\\\\3x+10 =2x+3\\\\x = -7[/tex]

Answer:

x=-7

Step-by-step explanation:

first simplify your equation to:

3x+10=2x+3

combine like terms

3x-2x=3-10

solve for x

x=-7

Answer:

Adult 36

Children 9

senior 27

Step-by-step explanation:

We have 3 types of tickets as seen from the question;

Adult, children and seniors tickets.

Now, looking at the question critically,

Since the ratio of adults to children and senior citizens stands at 4: a specific value, we can then conclude that the ratio of tickets sold is 4:1:3

where 1 and 3 represents the ratio for the children and seniors respectively

So let’s calculate the individual ratio now.

For the total, we have 4 + 1 + 3 = 8

Thus, for the adults, we have 4/8 * 72 = 36

For the children, we have 1/8 * 72 = 9

For the seniors, we have 3/8 * 72 = 27

Answer:

Step-by-step explanation:

Since none of the answer choices match the drawing of the gardener, we assume the question is referring to the drawing of the partner.

The gardener's drawing is 1/4 of actual size. So, in terms of the gardener's drawing, actual size is ...

  gardener's drawing = (1/4)actual size

  actual size = 4(gardener's drawing)

__

The partner's drawing is 1/20 of actual size, so is ...

  partner's drawing = actual size/20 = (4(gardener's drawing))/20

  partner's drawing = (4/20)(gardener's drawing)

  partner's drawing = (gardener's drawing)/5

__

Then the {length, width} of the partner's drawing are ...

  partner's drawing {length, width} = {15 in, 10 in}/5 = {3 in, 2 in}

The partner's drawing has a length of 3 inches and a width of 2 inches.

Answer: A—f(x)=1/(x-3)(x+3)

Step-by-step explanation:

The given graph is of the function :    

[tex]F(x) = \dfrac{1}{(x-3)(x+3)}[/tex]  
Hence, option (A) is correct.

Let’s draw the graphs for all the given options:

For option(A):

[tex]F(x) =\dfrac{ 1}{(x-3)(x+3)}[/tex]

For option (B):

[tex]F(X) = \dfrac{(x+3)}{(x-3)}[/tex]

For option(C):

[tex]F(x) = \dfrac{1}{x(x-3)}[/tex]

For option (D):

[tex]F(x) = \dfrac{1}{x(x-3)(x+3)}[/tex]

From all the attached graphs, we can infer that  the given graph is of the function   [tex]F(x) = \dfrac{1}{(x-3)(x+3)}[/tex]. This function is defined for all real numbers except x = 3 and x = -3. With having two vertical asymptotes at x = 3 and x = -3 because denominator is zero for these values. Here the degree of the numerator is 1 which is less than the degree of the denominator which is 2, there is a horizontal asymptote at y = 0 (the x-axis). As x approaches positive or negative infinity, the function approaches zero.

Hence, option (A) is correct.

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The probability that a student chosen randomly from the class plays basketball or baseball is 0.56. 

We are able to utilize the equation:

P(B or b) = P(B) + P(b) - P(B and b)

where

B speaks to playing ball

and b speaks about playing baseball.

From the given data, we have:

P(B) = 5/27 (the likelihood of playing ball)

P(b) = 12/27 (the likelihood of playing baseball)

P(B and b) = 2/27 (the likelihood of playing both sports)

Substituting these values into the equation, we get:

P(B or b) = P(B) + P(b) - P(B and b)

= 5/27 + 12/27 - 2/27

= 15/27

= 5/9

Hence, the likelihood that an understudy chosen haphazardly from the course plays ball or baseball is 5/9 or around 0.56. 

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Answer: [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

When any number has a negative exponent, all the negative exponent is doing is flipping the sides.

When we plug -3 in for x we get [tex]-3^{-2}[/tex].

Now just imagine the -3 in fraction form as [tex]\frac{-3}{1}[/tex]. And all you do now is just flip the sides to get [tex](\frac{1}{-3} )^{2}[/tex]

And now apply the exponent 2 to the 1 and negative 3.

1 to the power of 2 is just 1

-3 to the power of 2 is 9.

So your answer is [tex]\frac{1}{9}[/tex]

Answer:

10

Step-by-step explanation:

i have no flipping i think im wrong

Answer:

4600

Step-by-step explanation:

20*230=4600

I rounded it to tens

Answer:

answer is B

Step-by-step explanation:

............

Answer:

Lily would present after Edward

Step-by-step explanation:

Catherine must present after Ted. Therefore we have Ted, Catherine.

There must be one presenter between Bianca and Catherine, therefore we have: Bianca, x, Catherine. x is the name of the presenter between  Bianca and Catherine. Since Ted presents immediately before Catherine, x = Ted. This means we have Bianca, Ted, Catherine.

There must be at least two other people must present after Edward and before Ted. This means we have Edward, y, Bianca, Ted, Catherine. y is the name of the presenter between Edward and Bianca.. Since we have only five presenters, the only presenter remaining is Lily.

Therefore the presenters are arranged as:

Edward, Lily, Bianca, Ted, Catherine.

Lily is the second to present. Lily would present immediately after Edward and before Bianca

Answer:

m<M = 113 deg

m<N = 61 deg

Step-by-step explanation:

In an inscribed quadrilateral, opposite angles are supplementary.

m<M + m<K = 180

m<N + m<L = 180

m<M + 67 = 180

m<M = 113

m<N + 119 = 180

m<N = 61

Answer:

A.

Step-by-step explanation:

Count the arrows.  A has 1, B has 2, and C has 3.  D will have 4.  The pattern is also one vertical and one horizontal arrow being added alternately.

Answer:

x = 52

Step-by-step explanation:

You are given ratios, and the 1st ratio is being multiplied by 4 to get the second ratio. How did I find this? Divide 48 by 12 and you get 4. To find x, simply multiply 13 by 4 and you should get 52

Answer:

idk good luck have a nice day

Answer:

29:21

Step-by-step explanation:

The ratio of the diagonal to the base of ration is written as 58:42.

The ratio has the greatest common factor as 2.

58÷2:42÷2

29:21

The simplified ratio becomes 29:21.

Answer:

x = -1

Step-by-step explanation:

4x + 4 = 0

Subtract 4 on both sides.

4x = 0 - 4

4x = -4

Divide both sides by 4.

x = -4/4

x = -1

Answer:

So the value of x is -1

Step-by-step explanation:

4x+4=0

Subtracting 4 on both sides

4x+4-4=0-4

4x=-4

Dividing 4 on both sides

x=-4/4

x=-1

Answer: -2, 0 and 0, 2 and 2, 4

Step-by-step explanation:

The complete table of values for y = 2x² + x are (4, -2), (0, 0) and (2, 10)

Given:

y = 2x² + x

substitute the value of x to get the corresponding value of y

when x = -2

y = 2x² + x

= 2(-2)² + (-2)

= 2(4) - 2

= 6 - 2

= 4

(x, y) = (4, -2)

when x = 0

y = 2x² + x

= 2(0)² + 0

= 2(0) + 0

= 0 + 0

= 0

(x, y) = (0, 0)

when x = 2

y = 2x² + x

= 2(2)² + 2

= 2(4) + 2

= 8 + 2

= 10

(x, y) = (2, 10)

Therefore, the corresponding values of x and y is (4, -2), (0, 0) and (2, 10)

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Answer:

I think A

Step-by-step explanation:

I'm not really sure but I think it's A assuming the triangle is not an equilateral

Answer:

8.5 cm

Step-by-step explanation:

Angles of the triangle:

Right triangle as it has 90° angle

Sides are a, b and 19 cm

you can't factorize it in rational numbers

Answer:

The first choice.

Step-by-step explanation:

Direct variation is represented by y = kx where k is a constant and the graph passes through the origin.

Here k = 3..