Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.

Answer:

3 both ways x = 3

EXPLANATION:

plug in inputs and do a little simplifying we get

x = 6 ± √(36-36) all of that over 2

So we simplify and we get 6±sqrt(0) / 2

Then we get 6/2 = 3

x-0 = x+0

thats why there is only one answer

Answer:

The value of X is 3

Step-by-step explanation:

x²-6x+9=0

x²- 3x - 3x + 9= 0

X(x-3) -3(x-3)=0

(x-3) (x-3)=0

(x-3)²=0

(x-3)=0

x-3 = 0

X= 3

Answer:

hey mate,

here is your answer. Hope it helps you.

C-(3,3)

Step-by-step explanation:

An equilateral triangle, which has three equal sides, has three lines of symmetry. This is because you can fold an equilateral triangle in  three halves and the are equal. Hence an equilataral triangle has three vertices and 3 lines of symmetry.

Now by using equation 1 in equation 2 we get,

Now upon using the value of y in equation 1, we get

Answer:

22.7

Step-by-step explanation:

ok so, First we need to find new values:

       96( 1 + 0.25) =120

       85( 1+0.2)=  102

Boys last year        girls last year      total this year

   96                             85                        181

Boys this year        girls this year        total this year

  120                         102                           222

   Find the overall increase:

181( 1+r)= 1.226519

THEN U SUBTRACT 1

r=0.226519

Multiply by 100 and round to nearest 10th

22.7%

Final Answer: 22.7%

HOPED IT HELPED:)

Answer:

[tex]x^{16}y^{22}[/tex]

Step-by-step explanation:

[tex]\frac{(x^{6}y^{8}) ^{3}}{x^{2}y^{2}}=\\\\x^{16}y^{22}[/tex]

Hope this helps!

Answer:

  (-2.60, -6.80)

Step-by-step explanation:

The new coordinates can be found by multiplying by the rotation matrix:

  [tex]\left[\begin{array}{c}x'&y'\end{array}\right]=\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right][/tex]

That is, ...

  x' = x·cos(175°) -y·sin(175°) = 2(-0.9962) -7(0.0872) = -2.60

  y' = x·sin(175°) +y·cos(175°) = 2(0.0872) +7(-0.9962) = -6.80

The new coordinates are ...

  (x', y') = (-2.60, -6.80)

Answer:

28.26 (Please mark as brainiest if you find it helpful )

Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.

Area of circle  =  pi * r ^ 2

⇒  3.14 * (3) ^ 2   →  3.14 * 9

⇒ 28.26

Answer: 20

Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.

Answer:

The first step is to determine how many times 2x goes into 8x^3

Step-by-step explanation:

The first step is to determine how many times 2x goes into 8x^3

                     4x^2

        --------------------------

2x-1  |  (8x3 – x2 + 6x + 7

           8x^3 -4x^2

Answer:

A

Step-by-step explanation:

i just took the test

Answer:

1.dotted, because it is not less than or equal to, but just less than.

2.below, because Y is less than the equation.

3. 0, -6

Step-by-step explanation:

// have a great day //

Answer:

15, 33

(if I'm not wrong, it should work this way)

Answer:

(1)0.0138

(2)A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

Nos 3-12: See Explanation

Step-by-step explanation:

Given the regression equation for the relation of dive duration (DD) to depth (D).

[tex]DD = 2.69 + 0.0138D\\$Where: Duration DD is measured in minutes\\epth D is in meters.[/tex]

(1)The slope of the regression lie =0.0138

(2)

When D=1, DD = 2.69 + 0.0138(1)=2.7038

When D=2, DD = 2.69 + 0.0138(2)=2.7176

2.7176-2.7038=0.0138

Therefore, If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

(3) When depth, D =200 meters

DD = 2.69 + 0.0138(200)=5.45 Minutes

(4) When depth, D =210 meters

DD = 2.69 + 0.0138(210)=5.588 Minutes

(5) When depth, D =220 meters

DD = 2.69 + 0.0138(220)=5.726 Minutes

(6) When depth, D =230 meters

DD = 2.69 + 0.0138(230)=5.864 Minutes

(7) When depth, D =240 meters

DD = 2.69 + 0.0138(240)=6.002 Minutes

(8) When depth, D =150 meters

DD = 2.69 + 0.0138(150)=4.76 Minutes

(9) When depth, D =160 meters

DD = 2.69 + 0.0138(160)=4.898 Minutes

(10) When depth, D =170 meters

DD = 2.69 + 0.0138(170)=5.036 Minutes

(11) When depth, D =180 meters

DD = 2.69 + 0.0138(180)=5.174 Minutes

(12) When depth, D =190 meters

DD = 2.69 + 0.0138(190)=5.312 Minutes

A regression line is only a single line that fits the data the best. It tells how steep it is, whereas the intercept reveals where it intersects an axis.

For question 1):

By calculating the slope of the regression line we get the slope value that is [tex]= 0.0138[/tex]

For question 2):

Describe whatever this slope means about this penguin's dives in precise terms.

The time spent under liquid increases by 0.0138 minutes whenever the diving depth is raised by one meter, which is equal to "Option A".

For question 3):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times200 = 2.69+2.76 = 5.45\ minutes[/tex]

For question 4):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times210 = 2.69 + 2.898 = 5.588\ minutes[/tex]

For question 5):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 220 = 2.69 + 3.036 = 5.726\ minutes[/tex]

For question 6):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times230 = 2.69 + 3.174 = 5.864 \ minutes[/tex]

For question 7):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times240 = 2.69 + 3.312 = 6.002\ minutes[/tex]

For question 8):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 150 = 2.69 + 2.07 = 4.76\ minutes[/tex]

For question 9):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 160 = 2.69 + 2.208 = 4.898\ minutes[/tex]

For question 10):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 170 = 2.69 + 2.346 = 5.036\ minutes[/tex]

For question 11):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 180 = 2.69 + 2.484 = 5.174 \ minutes[/tex]

For question 12):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 190 = 2.69 + 2.622 = 5.312\ minutes[/tex]

Find out more about the regression line here:

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Answer:

Step-by-step explanation:

mabey its c

The equation which is equivalent to [tex]2^{\frac{2}{3} }[/tex] will be equal to [tex]\sqrt[4]{2^3}[/tex]. Hence, option C is correct.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

[tex]2^{\frac{2}{3} }[/tex] = 1.68

Now, let's check the options,

A.

[tex](2^{\frac{1}{4} } )^{\frac{1}{2} }[/tex] = 1.09 ≠ 1.68, hence this is incorrect.

B.

[tex]2\frac{1}{4}*2\frac{1}{2}[/tex] = 9/4 × 5/2 = 5.625 ≠ 1.68, hence, this is incorrect.

C.

[tex]\sqrt[4]{2^3}[/tex] = 1.68 = 1.68, hence, this is correct.

D.

√8 = 2.82 ≠ 1.68, hence, this is incorrect.

To know more about arithmetic operations:

https://brainly.com/question/13585407

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Answer:

x=-2

Step-by-step explanation:

3 + -4x = 5+ -3x

-4x = 2 - 3x

-x = 2

x = -2

Answer:

C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale

Step-by-step explanation:

Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:

[tex]CV = \frac{\sigma_{x} }{\mu_{x} } * 100%[/tex]

Where [tex]\sigma{x}[/tex] is the Standard Deviation

and [tex]\mu_{x}[/tex] is the sample mean

From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.

Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.

The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.

Answer:

4 hours.

Step-by-step explanation:

Well we can simply divide 32 by 8 and we get 4 hours:

32 miles ÷ 8 miles = 4 hours

It takes the cyclist 4 hours.

Answer:

  4 hours

Step-by-step explanation:

As every speed limit sign tells you, ...

  speed = miles/hours

Solving for time and using generic distance units, we get ...

  time = distance/speed

Filling in the given values, we have ...

  time = 32 km/(8 km/h) = (32/8) h = 4 h

It takes the cyclist 4 hours to travel 32 km.

Answer:

7/8!

Step-by-step explanation:

They both can be divided by 10, so do just that. Then you are left with 7/8 which cannot be simplified.

The ratio 70:80 in its simplest form is equal to 7:8.

To simplify the ratio 70:80, we need to find the greatest common divisor (GCD) of the two numbers and then divide both numbers by the GCD.

Step 1: Find the GCD of 70 and 80:

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

The common factors of 70 and 80 are 1, 2, 5, and 10. The greatest common divisor (GCD) is 10.

Step 2: Divide both numbers by the GCD (10):

70 ÷ 10 = 7,

80 ÷ 10 = 8.

In summary, the ratio 70:80 can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 10. After simplification, the ratio becomes 7:8. Simplifying ratios involves dividing both parts of the ratio by the greatest common factor to express the ratio in its simplest and most concise form.

This makes it easier to understand and work with the relationship between the quantities being compared. In this case, the simplified ratio tells us that for every 7 units of the first quantity, there are 8 units of the second quantity.

To learn more about ratio click on,

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Answer:

Remember the formula for calculating volume is: Volume = Area by height. V = A X h.

For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.

So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h.

Step-by-step explanation:

Answer:

(a) [tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

(b)   After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

Step-by-step explanation:

The Markov Matrix can be interpret as :

[tex]M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]

From (a) ; we see that the initial population are as follows: 130 individuals in location 1, 300 in location 2, and 70 in location 3.

Le P represent the Population; So ;  [tex]P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]

The objective is to find How many are in each location after two time periods;

So, after two time period ; we have the population [tex]P_2 = [M]^2 [P][/tex]

where;

[tex][M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]

[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right][/tex]

[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right][/tex]

Now; Over to after two time period ; when the population [tex]P_2 = [M]^2 [P][/tex]

[tex]P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]

[tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?

After a long time; that is referring to an infinite time (n)

So; [tex]P_n = [M]^n [P][/tex]

where ;

[tex][M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty[/tex]

; if we determine the respective values of [tex][M]^2 , [M]^3 , [M]^4 .... \infty[/tex] we will always result to the value for [tex][M]^n[/tex]; Now if  [tex][M]^n[/tex] is said to be a positive integer; then :

After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

Answer:

Step-by-step explanation:

The following is the information provided

number of students is 5

The number of math major = 3

The number of statistic major = 2

Label math students as A, B, C

And statistic students as D, E

The total number of ways to select two students from 5 students is 10

The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}

Yes , in the sample space the events are equally alike

What is the probability that both selected students are statistics majors

The selected students of statistic major are DE

the probability that both selected students are statistics majors is [tex]\frac{1}{10}[/tex]

= 1/10

What is the probability that both students are math majors

The selected students of statistic major are AC,AB,BC

the probability that both selected students are math majors is [tex]\frac{3}{10}[/tex]

= 3/10

What is the probability that at least one of the students selected is a statistics major

Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}

the probability that at least one of the students selected is a statistics major is [tex]\frac{7}{10}[/tex]

7/10

What is the probability that the selected students have different majors

Number of ways to select students with different major is  {AD,AE,BD,BE,CD,CE,}

the probability that the selected students have different majors is [tex]\frac{6}{10}[/tex]

6/10

Answer:

Time = X = 37.14 minutes

Distance they covered= 33.42 miles.

Step-by-step explanation:

Distance= speed * time

And the distance traveled by the two need to be equal.

Speed of storm = 33 mph

Speed of van = 54 mph

But storm is 13 miles away from van.

So

54*x = 33*x+ 13

54x-33x = 13

21x = 13

X= 0.62 hours

X = 37.14 minutes

54 *0.62= 33.42 miles.

Answer:

The Pythagorean Theorum

Step-by-step explanation:

you can literally search it and see that it is right!

Answer:

y = 2cos5x-9/5sin5x

Step-by-step explanation:

Given the solution to the differential equation y'' + 25y = 0 to be

y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.

According to the boundary condition y(0) = 2, it means when x = 0, y = 2

On substituting;

2 = c1cos(5(0)) + c2sin(5(0))

2 = c1cos0+c2sin0

2 = c1 + 0

c1 = 2

Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given

y(x) = c1cos5x + c2sin5x

y'(x) = -5c1sin5x + 5c2cos5x

If y'(π) = 9, this means when x = π, y'(x) = 9

On substituting;

9 = -5c1sin5π + 5c2cos5π

9 = -5c1(0) + 5c2(-1)

9 = 0-5c2

-5c2 = 9

c2 = -9/5

Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation

y = c1 cos(5x) + c2 sin(5x) will give

y = 2cos5x-9/5sin5x

The final expression gives the required solution to the differential equation.

Answer:

D (4,11)

Step-by-step explanation:

Answer: it’s d

x is just going up by 1 and y is going up by 2

Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360

hope this helped

Answer:

D.

Step-by-step explanation:

Volume of cylinder = base area × height

25.5 = A × 4.8

A = 25.5/4.8

A = 5.3 inch ²

Answer:

y = 3x +1 (1)

2y = 6x +2  (2)

We can devide equation (2) by 2 and we got:

[tex] y =3x +1[/tex]   (3)

And since equations (1) and (3) are equal we can do this:

[tex] 3x +1 = 3x+1[/tex]

And that implies:

[tex] 0=0[/tex]

And for this case we will have infinite solutions for the sytem given since we have two lines equal

Step-by-step explanation:

For this case we have the following system of equations given:

y = 3x +1 (1)

2y = 6x +2  (2)

We can devide equation (2) by 2 and we got:

[tex] y =3x +1[/tex]   (3)

And since equations (1) and (3) are equal we can do this:

[tex] 3x +1 = 3x+1[/tex]

And that implies:

[tex] 0=0[/tex]

And for this case we will have infinite solutions for the sytem given since we have two lines equal

Answer:

A) 13/20

Step-by-step explanation:

65% in simplest form,

65/100

= 13/20 (Divided by five)

Answer:

[tex]\frac{13}{20}[/tex].

Step-by-step explanation:

We can begin by converting 65% to a fraction over 100. 65% converts to 0.65, or [tex]\frac{65}{100}[/tex].

We can simplify this down. Both 65 and 100 share a common factor of 5, which allows us to produce a new fraction:

[tex]\frac{65}{100} = \frac{13}{20}[/tex]

Therefore, the simplified version is [tex]\frac{13}{20}[/tex].

Step-by-step explanation:

I think there should be 5 capsicums because

4 times onions = 5 x 4 = 20

Then 5 capsicums = 20 + 5 = 25

Answer:

A large pizza has toppings of capsicum and onion. In total there are 36 pieces of both on the pizza .If there are 5 times as many onions pieces as capsicum pieces,how many of each vegetable are there on the pizza?

Step-by-step explanation:

Can you please help with this one