What is the value of x in X² 9?

The answer is k = 7.

As the graph has been shifted down 7 units, the translation can be represented as :

g(x) = f(x) - 7

(0.5)x - k = (0.5)x - 7

k = 7

Answer:

B, C, A

Step-by-step explanation:

Don't really know how to explain this.

The number of quarts of orange juice did Rebecca use is 7

Given that 28 glasses with orange juice are filled for a camp breakfast

Each glass holds 1 cup of juice

We need to find the number of quarts of orange juice did Rebecca use  

We know that a quarts has 4 cups

We need to calculate the quarts from 28 glasses  

Let the number of the quarts be x

So the equation formed is

4x = 28

Where x is number of quarts and 28 are the number of glasses

x = 7

Hence the number of quarts is 7

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Answer:

14 units

Step-by-step explanation:

Oops, I was solving for the area in the picture.  You can still use  the picture to find the perimeter.  When I change the shape into a rectangle, you can see that the top and bottom lengths are 3 and the side lengths are 4.  3+3+4+4=14

The roots of the polynomial equation are -1.73, 1.73 and 0

The polynomial equation is given as:

[tex]x^4 + x^2 = 4x^3 - 12x + 12[/tex]

Next, we split the equation as follows:

[tex]y = x^4 + x^2[/tex]

[tex]y= 4x^3 - 12x + 12[/tex]

Next, we plot the equations on a graphing calculator

From the graph, we have the x-coordinates of the intersection points to be:

x = -1.73, 1.73 and 0

Hence, the roots of the polynomial equation are -1.73, 1.73 and 0

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Answer:

Question 1) 2/3

Question 2) -3

Step-by-step explanation:

Question 1)

The formula of a slope is (increase in y)/(increase in x), so in the graph, all we need to do is find two precise points and look at the distance difference.

1. The two points that I've found were (0,3) and (3,5). The change in y is 3 --> 5, which is 2. The change in x is 0 --> 3, which is 3.

2. The slope will be 2/3.

Question 2)

In this question, we can consider n as x and f(n) as y.

1. The two points I chose were (4, -31) and (7,-40). The change in y is -31 --> -40, which is -9. The change in x is 4 --> 7, which is 3.

2. The slope will be -9/3.

3. -9/3 can be simplified to -3 since we can divide both the numerator and the denominator by 3.

4. The final slope will be -3.

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.

Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.

We are required to find the number of bacteria present after 10 weeks.

let the number of bacteria present at t is x.

So,

dx/dt∝x

dx/dt=kx

1/x dx=k dt

Now integrate both sides.

[tex]\int\limits {1/x} \, dx[/tex]=[tex]\int\limits{k} \, dt[/tex]

log x=kt+log c----------1

Put t=0

log [tex]x_{0}[/tex]=0 +log c    ([tex]x_{0}[/tex] shows the population in beginning)

Cancelling log from both sides.

c=[tex]x_{0}[/tex]

So put c=[tex]x_{0}[/tex] in 1

log x=kt+log [tex]x_{0}[/tex]

log x=log [tex]e^{kt}[/tex]+log [tex]x_{0}[/tex]

log x=log [tex]e^{kt}x_{0}[/tex]

x=[tex]e^{kt}x_{0}[/tex]

We have been given that the population triples in a week so we have to put the value of x=2[tex]x_{0}[/tex] and t=1 to get the value of k.

2[tex]x_{0}[/tex]=[tex]e^{k} x_{0}[/tex]

2=[tex]e^{k}[/tex]

log 2=k

We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.

x=[tex]e^{20log 2}[/tex][tex]x_{0}[/tex]

x=[tex]e^{0.30*2}[/tex][tex]x_{0}[/tex]

x=[tex]e^{6}x_{0}[/tex]

x=403.42[tex]x_{0}[/tex]

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.

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The given question is incomplete as the question incudes the following:

Calculate the population after 20 weeks.

Answer:

20 units

Step-by-step explanation:

As you know that the quadrilateral is a square, you’ll just have to find the length of one side and multiply it by four. We can count and see that one side is 5 units.

5 * 4 = 20 units

You can also add the length of each of the four sides.

5 + 5 + 5 + 5 = 20

Hope that helps you! Please let me know if you need more help with this question. Have a great day!

The mean and the standard deviation of the following data are 35.75 and 11.6765 respectively.

First, we'll find the mean (X) of the data:

[tex]X =\dfrac{(\sum x \times f) } {\sum f}[/tex]

So, the approximate standard deviation for the monthly cell phone plan cost is 9.87.

The mean is given by

[tex]\mu =\frac{\sum xf}{\sum f}[/tex]

Where x is the midpoint of the class and f is the frequency.

The calculation of mean and the standard deviation is shown in the below table:

    Hence, the mean is calculated as:

mean is   [tex]\mu =\frac{2359.67}{66}[/tex]

                          =35.75

The standard deviation is calculated as:

Standard deviation =[tex]\sigma[/tex] =[tex]\sqrt{\Dfrac{\sum f(x-\bar{x})^2}{n-1}}[/tex]

=[tex]\sqrt{\dfrac{8862.12121}{65}}[/tex]

=11.6765

Thus, the mean and the standard deviation are 35.75 and 11.6765 respectively.

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The table of standard deviation is attached below.

Answer: [tex]y-1=\frac{3}{2}(x+1)[/tex]

Step-by-step explanation:

[tex]2x+3y-6=0\\\\3y=-2x+6\\\\y=-\frac{2}{3}x+2[/tex]

So, the slope of the given line is -2/3, meaning the slope of the line we want to find is 3/2.

Substituting into point-slope form, we get the equation of the line is

[tex]y-1=\frac{3}{2}(x+1)[/tex]

The volume of the oblique cylinder is 6867.18 cubic units

The given parameters are:

Height = 27

Radius = 9

The volume is calculated as:

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

So, we have:

[tex]V = 3.14 * 9^2 * 27[/tex]

Evaluate

V = 6867.18

Hence, the volume of the oblique cylinder is 6867.18 cubic units

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Applying the properties of kite, the measures are: SV = 41 units; QT = 21 units.

A kite is a quadrilateral that has 2 pairs of congruent adjacent sides, and has two diagonals where the longest one bisects the shorter one and divides it into equal segments.

The diagram given is a kite. Where TR = 17 units. Thus we would solve for x using the equation as shown below:

TR = RV [congruent adjacent sides of the kite]

Plug in the values

17 = 3x + 2

17 - 2 = 3x

15 = 3x

15/3 = x

x = 5

SV = TS = 9x - 4 [congruent adjacent sides of the kite]

Plug in the value of x

SV = 9(5) - 4

SV = 41 units

The length of segment QT is 41 units.

QT = QV = 4x + 1 [congruent adjacent sides of the kite]

Plug in the value of x

QT = 4(5) + 1

QT = 21 units

The length of segment QT is: 21 units.

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Answer:

SV: 41

QT:21

Step-by-step explanation:

The total amount of fencing they need = 38x + 10.

Perimeter for the rectangular fencing of the home = 160 yards

Perimeter for the square fencing of the pool = 40 yards

Perimeter of a rectangle = 2(length + width)

Perimeter of a square = 4(side length).

Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10

Perimeter for the square fencing of the pool = 4(2x) = 8x

The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.

If x = 5, then:

Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards

Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.

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Answer:

38
160
40

Step-by-step explanation:

Answer:

Cos² x

Step-by-step explanation:

    [tex]\sf Cos^2 \ x *Csc^2 \ x-Cos^2 \ x *Cot^2 \ x = Cos^2 \ x (Csc^2 \ x - Cot^2 \ x)[/tex]

                                                        [tex]\sf = Cos^2 \ x \left(\dfrac{1}{Sin^2 \ x} - \dfrac{Cos^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x \left(\dfrac{1-Cos^2 \ x}{Sin^2 \ x}\right)\\\\\boxed{\bf Indentity: \ 1 - Cos^2 \ x = Sin^2 \ x}\\\\\\= Cos^2 \ x \left(\dfrac{Sin^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x[/tex]

The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)

The functions are given as

f(x) =x^2

g(x) =3x^2

h(x) = -3x^2

Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2

g(x) =3f(x)

h(x) = -3f(x)

This means that the function f(x) is vertically compressed to form g(x)

Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)

See attachment for the functions g(x) and h(x)

Also, functions f(x) and g(x) have the same domain and range

While functions f(x) and h(x) have the same domain but different range

The complete table is:

x      -2    -1    0   1    2

g(x)  12    3    0    3   12

h(x)  -12    -3    0    -3   -12

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Answer:

Triangles MNP and QRS

Step-by-step explanation:

This is due to each corresponding line follows the same ratio of 1.5:1

e.g.

NP=6

RS=4

6:4

1.5:1

You can verify this by dividing 6 by 4 (6/4) which is 1.5

Answer:

2p-9>

Step-by-step explanation:

Hi

arithmetic serie mean that to change from a rank to an other, you add "r"

So :  if 6 is  S1, and  2 is  pace,    

then you need 8 hops to go from S1 to S9.

so you 'r going to add the reason 8 times.

so :  S9 = 6 + 8 * 2   =   6 + 16 = 22

conclusion :  S9 = 22

Answer:

you would look for them 3.5 meters away from the base

Step-by-step explanation:

so u do tan 86 =50/x

and u solve from there

Answer:

13.846153846

Step-by-step explanation:

Its easy Just 18:1.3=13.846153846

Answer:

Step-by-step explanation:

Givens

Line: y = 3x + 3

Point: (7,3)

Discussion

The easiest variation on line problems is one like this one. The reason is that all you need do is read the slope of the given line.

m = 3 of the given line. Also the slope of the new line.

What you have so far is

y = 3x + b

The point is used to find b -- the y intercept.

x = 7

y = 3

You are not given this, but what you want to think is that when x = 7, y = 3

Substitute into the new equation

3 = 3*7 + b

3 = 21 + b                         Subtract 21 from both sides.

3 - 21 = 21-21 + b

- 18 = b

Answer

y = 3x - 18

Answer:

-2/3x+23/3

Step-by-step explanation:

y= mx+c

where

m is the slope c is the y-intercept.

1-getting the slope:

we are given that the line we are looking for is parallel to the line

y=-2/3x+3

this means that the slope of the two lines are equal . comparing the general formula with the given line , we would find that the slope of the given lines -2/3.this means that the slope of the lines we are looking for is also -2/3

The equation of the line now becomes:y=-2/3x+c

2-getting the value of c

to get the value of c, we will use a point that belongs to the line (7,3),substitute in the equation and solve for c as follows:

y=-2/3x+c

3=(-2/3)(7)+c

3=-14/3+c

c=3+14/3

c=23/3

Based on the above, the equation of the line we are looking for is:

y=-2/3x+23/3

These two should be the points as then 2 points will remain on both sides

Slope

Equation in point slope form

When x=-15

Just above 7

Answer:

Distributive property

Step-by-step explanation:

In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.

Answer:

Option (1)

Step-by-step explanation:

See attached image.

The given measures form a acute angle triangle.

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Given that, a triangle with side lengths 10 in., 12 in., and 15 in.

We know that,

a²+b²=c²  then triangle will be right angled

a²+b²>c²  then triangle will be acute angled

a²+b²><c²  then triangle will be obtuse angled

Here, a=10 inches, b=12 inches and c=15 inches

10²+12²>15²

100+144>225

244>225

Therefore, the given measures form a acute angle triangle.

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Answer:

answer is (c)

May it help you

Option C. The inequality can then be written as  x² - 2y ≥ 5000 and 2x + 5y <1000

How to write the inequality

Stock = x² - 2y

Purchase = 2x + 5y

Stock is said to be at least 5000 dollars. We can write this as

x² - 2y ≥ 5000

Then the purchase is said to be below 1000. This is written as 2x + 5y <1000

The inequality can then be written as  x² - 2y ≥ 5000 and 2x + 5y <1000

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The next number in the series is 30.

It should be noted that series simply means the operation of adding values together in a data set.

In this case, it can be seen that the numbers are interchangeable between 30 and 31.

In this case, since 31 was the last number, the next number will be 30.

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Answer:

Answer: Option B

Just trust me that its right.

Answer:

The second option, 3x^2(x+3)(4x+1)

Step-by-step explanation:

Factor out the common term, which is 3x^2

This then becomes 3x^2(4x^2+13x+3)

Factor the inside term and it becomes

(3x^2)(x+3)(4x+1)