If f(x) = 3x² - 4 and g(x)= x+2, find (f - g)(x).

Answer:

it could help you so you don't have to count on your fingers

Step-by-step explanation:

5 divided by 2

5 times 2 = 10

so your answer would be 2

Answer: 163

Step-by-step explanation: y is vertical to 163, meaning that it is equal to 163

Therefore, the painting should be placed 5/4 feet on each side of the wall.

In the given problem, a 5-foot wide painting should be centered on a 15-foot wide wall. We can determine the length of each side of the painting by subtracting x from each side of the wall.

Therefore, the left side of the equation can be written as:

\(15 - x - 5 - x\)

The physical situation given is that the painting is to be centered on the wall. This means that each side of the wall will have the same amount of space as the painting.

Therefore, the length of each side of the painting can be determined by subtracting x from each side of the wall. The total width of the wall is 15 feet, and the painting is 5 feet wide.

Therefore, the total length of the space on each side of the painting is 5 + x.To find the value of x, we can equate the length of each side of the painting. Therefore, the equation can be written as:

\(15 -x - 5 - x = 5 + x + x\)

Simplifying the equation, we get:

\(10 - 2x = 2x + 5\)

Solving for x, we get:

\(4x = 5x = \frac{5}{4}\)

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{6.7}}}}}\)

Option C is the correct option.

Step-by-step explanation:

Let the points be A and B

Let A ( 7 , 8 ) be ( x₁ , y₁ ) and B ( 4 , 2 ) be ( x₂ , y₂ )

Finding the distance between these points

\( \boxed{ \sf{distance \: = \: \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{ {(4 - 7)}^{2} + {(2 - 8)}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{ {( - 3)}^{2} + { (- 6)}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{9 + 36}}} \)

\( \dashrightarrow {\sf{ \sqrt{45} }}\)

\( \dashrightarrow{ \sf{6.7 \: \: units}}\)

Hope I helped!

Best regards! :D

Answer:

\(\cos(T)\) =\(\frac{\sqrt{15}}{5}\)

Step-by-step explanation:

Given parameters.

\(TU = 4\sqrt 5\)

\(SU = 4\sqrt 2\)

\(ST = 4\sqrt 3\)

Required

Determine \(\cos(T)\)

Reference to \(\angle T\), we have:

\(Opposite = 4\sqrt 2\)

\(Adjacent = 4\sqrt 3\)

\(Hypotenuse = 4\sqrt 5\)

Apply trigonometry ratio of cosine

\(\cos(T)\) \(= \frac{Adjacent}{Hypotenuse}\)

Substitute values for Adjacent and Hypotenuse

\(\cos(T)\) \(= \frac{4\sqrt 3}{4\sqrt 5}\)

\(\cos(T)\) \(= \frac{\sqrt 3}{\sqrt 5}\)

Rationalize:

\(\cos(T)\) \(= \frac{\sqrt 3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}\)

\(\cos(T)\) =\(\frac{\sqrt{15}}{5}\)

Answer:

For this case we know that the random variable of interest would be X and the distribution for X is given by:

\( X \sim Bin (n,p)\)

And by properties of this distribution the expected value for this case is:

\( E(X)= np\)

And the variance :

\( Var(X)= np(1-p)\)

Step-by-step explanation:

For this case we know that the random variable of interest would be X and the distribution for X is given by:

\( X \sim Bin (n,p)\)

And by properties of this the expected value for this case is:

\( E(X)= np\)

And the variance :

\( Var(X)= np(1-p)\)

Answer:

63x-44

Step-by-step explanation:

7(9x - 6) - 2

63x-42-2

put the like terms together

63x-44

Answer:

1/2

Step-by-step explanation:

35+50+15 = 100

probability of the dance song = 50/100 = 1/2

Answer:50%

Step-by-step explanation:

35+15+50=100

50 divided by 100 is 0.5 or you can do it as a fraction and get 50/100

1) The intersection of sets A and B is; A ∩ B = {1, 3}

2) The complement of set A is; A' = {4, 5, 6, 9, 10}

We are given the sets;

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 7, 8}

B = {1, 3, 9, 10}

1) The intersection of sets A and B simply means the numbers that are common to both sets. Thus;

A ∩ B = {1, 3}

2) The complement of set A is defined as the set that contains the elements present in the universal set but not in set A. Thus;

A' = {4, 5, 6, 9, 10}

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Answer:

3/2

Step-by-step explanation:

Simplify the following:

((4 + 1/5)×5)/14

((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:

((4 + 1/5)×5)/14

Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:

(((5×4)/5 + 1/5) 5)/14

5×4 = 20:

((20/5 + 1/5)×5)/14

20/5 + 1/5 = (20 + 1)/5:

(((20 + 1)/5)×5)/14

20 + 1 = 21:

(21/5×5)/14

21/5×5 = (21×5)/5:

((21×5)/5)/14

((21×5)/5)/14 = (21×5)/(5×14):

(21×5)/(5×14)

(21×5)/(5×14) = 5/5×21/14 = 21/14:

21/14

The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:

Answer:  3/2

Answer:

\(^{}\) in a file

ly/3fcEdSx

bit.\(^{}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

−5 It can be written 9−5 = 9×2−5×2 = 18−10  9−5 = 9×3−5×3 = 27

−159−5 =

9×4

−5×4

​

=

36

−20

​

Therefore,  

18

−10

​

,

27

−15

​

 and  

36

−20

​

 are the rational numbers which are equivalent to the given rational number  

9

−5

​

.

Answer:

\(\boxed{-20i^2 -13ij+21j^2}\)

Step-by-step explanation:

\(\sf Plug \ in \ the \ values.\)

\((5i+7j) \cdot (-4i+3j)\)

\(\sf Expand \ brackets.\)

\(5i(-4i+3j)+7j(-4i+3j)\)

\(-20i^2 +15ij+-28ij +21j^2\)

\(\sf Combine \ like \ terms.\)

\(-20i^2 -13ij+21j^2\)

The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

From the question, we have the following parameters that can be used in our computation:

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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The transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4 will be C. The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.

The parent function f(x) = sin(x) has been transformed by replacing x with 3x in the argument of the sine function.

This results in a horizontal compression of the graph by a factor of 1/3. In addition, the graph of g(x) = sin(3x) is shifted upward 4 units, as indicated by the subtraction of 4 from the value of the sine function.

The correct option is C.

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\(\displaystyle\\\\Answer:\ \\x=\frac{3}{2} \pi +2\pi \mathbb N \\\\x=\frac{2}{3}\pi +2\pi \mathbb N\\\\x=\frac{4}{3} \pi +2\pi \mathbb N\)

Step-by-step explanation:

\(\displaystyle\\sin(2x)+sin(x)+2cos(x)+1=0\\\\2sin(x)cos(x)+sin(x)+2cos(x)+1=0\\\\2sin(x)cos(x)+2cos(x)+sin(x)+1=0\\\\2cos(x)(sin(x)+1)+(sin(x)+1)=0\\\\(sin(x)+1)(2cos(x)+1)=0\\\\a)\ sin(x)+1=0\\\\sin(x)=-1\\\\x=\frac{3}{2} \pi +2\pi \mathbb N\\\\b)\ 2cos(x)+1=0\\\\2cos(x)=-1\)

Divide both parts of the equation by 2:

\(\displaystyle\\cos(x)=-\frac{1}{2} \\\\x=\frac{2}{3}\pi +2\pi \mathbb N\\\\x=\frac{4}{3} \pi +2\pi \mathbb N\)

Answer:

Your answer would be 100! :)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(2^{60} =2^{2 \times 30} =(2^{2} )^{30}=4^{30}\)

For equation B → 2A, the rate of reaction becomes:

-Δ[B]/Δt = (1/2) Δ[A]/Δt

Correct option: c

The rate of reaction may be defined as the change in concentration of any of the products or reactants per unit of time. The pace at which reactants change into products is known as the rate of reaction or reaction rate. It goes without saying that the pace at which chemical reactions take place varies greatly.

The given reaction is:

B → 2A

rate of reaction in terms of A:

rate = (1/2) d[A]/dt

rate of reaction in terms of B:

rate = -d[B]/dt

So,

rate = -d[B]/dt = (1/2) d[A]/dt

Correct option: c

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Answer:

Here

Step-by-step explanation:

length = x

width = 2x - 3

Perimeter = 2length + 2 width

2x + 2(2x - 3) = 42

2x + 4x - 6 =42

6x - 6 = 42

Add 6 to both sides

6x = 48

Divide both sides by 6

x = 8

Length = 8 inches

Width = 2(8) - 3 = 16-3 = 13 inches

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

\((2^{\frac{1}{2}})^n=\frac{2^x}{2^{3y}}\\2^{\frac{1}{2}n}=2^{x-3y}\\\frac{n}{2}=x-3y\\n=2x-6y\)

The share of the whole bag of raisins individually of the friends get will be 1/12.

Algebra is the study of ideational symbols, while logic is the manipulation of all those opinions.

James had a large bag of raisins and he consumed 3/4 of it over the weekend. Then the share of raisins left is given as,

⇒ 1 - 3/4

⇒ 1/4

Monday he determined to share the remaining raisins with 2 friends so that individuals of the 3 of them fetches a fair share. Then the portion of the entire bag of raisins did separately of the friends get will be given as,

⇒ (1/4) / 3

⇒ 1 / (4 x 3)

⇒ 1 / 12

The share of the whole bag of raisins separately among the friends get will be 1/12.

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The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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To solve this problem we will need a system of equations.

Step 1. Find the first equation.

Using the statement "Emma rented a bike for 4 hours and paid £18", we will call the cost per hour h, and the flat fee f. Thus, the first equation is:

This is because Emma rented the bike for 4 hours but she had to pay a flat fee f, and the total was £18.

Step 2. Find the second equation.

We do the same but now with the statement "Louise rented a bike for 7 hours and paid £25.5". Remember that for our equation, h represents the cost per hour and f the flat fee. The second equation is:

Step 3. In summary, our system of equations is:

Step 4. To solve part a. we have to find the cost per hour "h".

To find it, we use the elimination method in our system of equations, which consists of adding or subtracting the equations in order to eliminate one variable.

Since we are interested in finding "h", we can subtract the second equation from the first one, and we get the following:

Applying the subtraction:

And we start subtracting 7h-4h, which results in 3h:

The next subtraction is f-f, which results in 0.

And then, subtract 25.5-18:

The equation we have as a result is:

Which is an equation we can use to solve for the cost per hour h.

Dividing both sides by 3:

The cost per hour is £2.5

Step 5. To find part b we need to find the rental feed, in our case, this means to find "h".

Using the first equation of the system:

And substituting the previous result:

We get:

Solving the operations:

And solving for f:

the flat fee is £8.

Step 6. To find part c, we consider the cost per hour and the flat fee.

Michael rented the bike for 2 hours.

Since the cost per hour is £2.5, and the flat fee is £8, he will pay:

Solving these operations:

It will cost £13.

Answer:

a. £2.5

b. £8

c. £13

The linear equation each graph is y = (1/5)x +3, y = 2x,  y = -3x+5 and y = (1/3)x +5 respectively

The equation of a line is of the form y = mx+c

Where m is the slope and c is the y-intercept

Graph 1

c = 3

m = 1/5 = 0.2

y = mx+c

Thus, the linear equation is y = (1/5)x + 3 or y = 0.2x + 3

Graph 2

c = 0

m = 2/1 = 2

y = mx+c

Thus, the linear equation is y = 2x+0 or y = 2x

Graph 3

c = 5

m = -3/1 = -3

y = mx+c

Thus, the linear equation is y = -3x+5

Graph 4

c = 5

m = 1/3 = 1/3

y = mx+c

Thus, the linear equation is y = (1/3)x+5 or y = 0.33x+5

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Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.