Given the following functions f(x) and g(x), solve (f+g)(2) and select the correct answer below:
f(x) = 6x - 2
g(x) = x - 1

A. 13
B. 11
C. 24
D. 30

Answer:

Step-by-step explanation:

they are both equal

Answer: They are not parallel because the two given alternate interior angles are not congruent

Step-by-step explanation:

Answer:

d 8x+12

Step-by-step explanation:

7x+3x+5-2x+7

combine 7x+3x-2x=8x

and 5+7=12

8x+12

Answer:

Step-by-step explanation:

7x+3x-2x=8x

5+7=12

8x+12

Answer:15/10

Step-by-step explanation:

You subtract the top of the fraction by 2

Answer:

   1 5/10  or  1 1/2

Step-by-step explanation:

You seem to have an arithmetic sequence, with each term 2/10 less than the one before.

2/10 less than 1 7/10 is 1 5/10. The fraction can be reduced to 1 1/2, but you may not want to.

Answer:

12 geese

10 dogs

Step-by-step explanation:

We are given;

We are required to determine the number of geese and dogs that Alex counted;

We need to know that;

Assuming he counted x number of geese and y number of dogs;

Then;

x + y = 22, and

2x + 4y = 64

Thus, solving the equation simultaneously;

we can multiply the first equation by 2, to get

2x + 2y = 44

2x + 4y = 64

Eliminating x (by subtracting the second eqn from the first eqn), we get;

-2y = -20

 y = 10

Solving for x;

   x = 22 - y

      = 22 - 10

  x  = 12

Therefore; he counted 12 geese and 10 dogs

Explanation: Calculation of the general sales taxes of Connecticut State for 2019 ... combined rates mentioned above are the results of Connecticut state rate (6.35%). There is no county sale tax for Connecticut. There is no city sale tax for the Connecticut cities. ... The Connecticut's tax rate may change depending of the type of purchase.

Answer:

0.84+1.00=1.84 +14=15.

Step-by-step explanation:

-x+2y=-6

x-2y=6

x=2y+6

substitute in 2x-3y=11 gives us 2(2y+6)-3y=11

4y+12-3y=11

y=-1

-x+2(-1)=-6

-x=-4

x=4

Answer:

  36 ft

Step-by-step explanation:

Let L represent the length of Louis's basement. The area is the product of length and width, so is ...

  A = L(L/3)

  432 = L²/3 . . . . . fill in area value

  1296 = L² . . . . . . multiply by 3

  36 = L . . . . . . . . . take the square root

The length of Louis's basement is 36 feet.

Answer:

[tex]\large\boxed{\dfrac{m^8}{25}}[/tex]

Step-by-step explanation:

[tex]\dfrac{m^6}{5}\div\dfrac{5}{m^2}\\\\\text{Divide by a fraction is the same as multiply by its reciprocal}\\\\=\dfrac{m^6}{5}\times\dfrac{m^2}{5}=\dfrac{m^6\times m^2}{5\times5}\\\\\text{use}\ a^n\times a^m=a^{n+m}\\\\=\dfrac{m^{6+2}}{25}=\dfrac{m^8}{25}[/tex]

1/3 banana hgfdsedcrtvfybgunhimjnyhtbgvfdcvfbgnhmij,omhnbvdcrmjytgvg

SEE IMAGE FOR A, B, C, D REFERENCE

A- 3

B- 3

C- 6

D- 3x+6

On the board you should have 6 of the orange + tiles and 3 of the orange x tiles.

Answer: 6

Step-by-step explanation: 12/2 because a pair is 2 people and there are 12 people in total.!

The number of different pairs of people who can have conversations at a round table with 12 people is 66. This is calculated using the combination formula C(n, 2).

The student asks about the number of different pairs of people who can have conversations at a round table with 12 people, assuming that everyone can talk to each other. The problem is a combinatorial one and can be solved by using the formula for combinations. The formula for the number of combinations of pairs from a set of n items is [tex]C(n, 2) = \frac{n! }{2! * (n - 2)!}[/tex], where n! (n factorial) is the product of all positive integers up to n, and C denotes the combination.

To find how many different pairs can have conversations, we plug in n = 12 into the combination formula:

[tex]C(12, 2) = \frac{12! }{2! * (12 - 2)!} = \frac{12 * 11}{2 * 1} = 66[/tex]

So, there are 66 different pairs of people that can have conversations at a round table with 12 people.

Final answer:

The correct solution to the equation 5x+10=24-2x is x=2, which is verified by substitution and results in an identity, confirming the solution is accurate.

Explanation:

The equation 5x+10=24-2x is a simple linear equation that can be solved by collecting like terms and isolating the variable x. Begin by adding 2x to both sides to get 7x + 10 = 24, then subtract 10 from both sides to obtain 7x = 14. Dividing both sides by 7 yields x = 2, which is the sole solution to the equation. Checking the solution, 24 - 2(2) does indeed equal 5(2) + 10, giving an identity of 20 = 20. This illustrates the solution is correct and verifies our process.

Because there are parentheses we distribute the negative signs:

3 - 20i + (-14) - 6i + (-8) + 2i

Next combine like terms:

3 + (-14) + (-8) and -20i - 6i + 2i

-19 -24i

Answer: 4z (to the 2 power) - 13z + 3

Step-by-step explanation:

If you are trying to find the equation of a line:

The equation of a line is y = mx + b   [m is the slope, b is the y-intercept or the y value when x = 0 --->  (0, y)  or the point where the line crosses through the y-axis]

Since you have m = -2, plug it into the equation

y = mx + b

y = -2x + b     To find b, plug in the point they gave you (3, -7)

-7 = -2(3) + b

-7 = -6 + b      Add 6 on both sides

-1 = b               Now that you have b, plug it into the equation

y = -2x - 1

Answer:

[tex] - 10 \div 9 = \frac{ - 10}{9} [/tex]

[tex]10 \div ( - 9) = \frac{10}{ - 9} [/tex]

[tex] - ( - 10 \div ( - 9)) = - (10 \div 9) = - \frac{10}{9} [/tex]

[tex] - \frac{10}{9} = \frac{10}{ - 9} = - \frac{10}{9} [/tex]

A and B are the correct choices.

We can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have one-third the sum of eleven and [p].

We can model the given question as -

y = (1/3)(11 + p)

Therefore, we can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)

To solve more questions on Equation Modelling, visit the link below -

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Answer:um where is the constant

Step-by-step explanation:

The expression 'x + 9/2' involves adding a variable 'x' to the fraction 9/2. In an example situation, if you substitute x with the number 5, the result would be 9.5. Remember, x can represent any number.

The expression you provided is x + 9/2. In mathematics, this is an algebraic expression which comprises of a variable x and a fraction 9/2. It means that you're adding the x variable to the fraction 9/2. For example, if you were to substitute x with a number, let's say 5, the answer would then be 5 + 9/2 = 9.5. It's important to remember that variables can represent any number, and in this case, the variable is x.

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Answer:

Hence (3, -3)   is  on the given line y = -2x + 3

Step-by-step explanation:

For a point on the Line, It must Satisfy the Equation of a line

Therefore for

[tex]y=-2x+3[/tex]

For (-2,-1)

Substitute x = - 2 and y = -1 in above equation

Left Hand Side = y

                         = -1

Right Hand Side = -2 × (-2) +3

                           = 4 +3

                           = 7

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-2,-1)  is NOT on the given line

For (3, -3)

Substitute x = 3 and y = -3 in above equation

Left Hand Side = y

                         = -3

Right Hand Side = -2 × (3) +3

                           = -6 +3

                           = -3

Left Hand Side = Right Hand Side

Satisfied

Hence (3, -3)   is  on the given line y = -2x + 3

For (3, 3)

Substitute x = 3 and y = 3 in above equation

Left Hand Side = y

                         = 3

Right Hand Side = -2 × (3) +3

                           = -6 +3

                           = -3

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (3,3)  is NOT on the given line

For (-3,-9)

Substitute x = -3 and y = -9 in above equation

Left Hand Side = y

                         = -9

Right Hand Side = -2 × (-3) +3

                           = 6 +3

                           = 9

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-3,-9)  is NOT on the given line

Only the point (3, -3) lies on the line y = -2x + 3. None of the other points satisfy the equation.

To determine which point lies on the line y = -2x + 3, we need to substitute the coordinates of each point into the equation:

(-2, -1): Substitute x = -2 into y = -2x + 3:

y = -2(-2) + 3 = 4 + 3 = 7. Since y = -1, this point does not lie on the line.

(3, -3): Substitute x = 3 into y = -2x + 3:

y = -2(3) + 3 = -6 + 3 = -3. Since y = -3, this point lies on the line.

(3, 3): Substitute x = 3 into y = -2x + 3:

y = -2(3) + 3 = -6 + 3 = -3. Since y = 3, this point does not lie on the line.

(-3, -9): Substitute x = -3 into y = -2x + 3:

y = -2(-3) + 3 = 6 + 3 = 9. Since y = -9, this point does not lie on the line.

The only point that satisfies the equation is (3, -3).

Complete question:

Which point is on the line y = -2x + 3?

A. (-2,-1)

B. (3, -3)

C. (3, 3)

D. (-3,-9)

By rounding each brother's weight to the nearest whole number and adding these, we get an estimate of 15 pounds. The actual total weight, 15 and one eighth pounds, is close to this estimate, indicating that Lucas' claim about his brothers' weight is reasonable. This demonstrates how estimation can be used to quickly verify the validity of a claim.

Estimation is a valuable mathematical tool that can be used to assess the reasonableness of a solution. In the case of Lucas' twin baby brothers' weight, you can use rounding to estimate their total weight. Let's start by rounding each brother's weight to the nearest whole number. In this scenario, Jackson, who weighs 6 and one fourth pounds could be estimated to weigh 6 pounds, and Jeremy, who weighs 8 and seven-eighths pounds, could be estimated to weigh roughly 9 pounds.

Adding these together gives a total of 15 pounds. The actual weight of the twins, 15 and one eighth pounds, is very close to this estimation, indicating that Lucas' claim about his brothers' weight is reasonable. This approach makes effective use of estimation as a means to quickly and simply verify a given claim's feasibility.

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Answer:

∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°

Step-by-step explanation:

i) AD = 9 cm

ii) DC = 3 cm

iii) ∠BCD = 35°

iv) Since AB is parallel to DC and ∠ABD = 90°  then we can conclude that ∠BDC = 90°.

v) [tex]\frac{BD}{DC} = \frac{BD}{3\hspace{0.1cm}cm} = tan(35)[/tex] = 0.6128      ∴ BD  = 3 [tex]\times[/tex] 0.6128 = 1.84 cm

vi) ∴ sin(∠ BAD ) = [tex]\frac{BD}{AD}[/tex]      ⇒     sin(∠ BAD ) = [tex]\frac{1.84}{9}[/tex] = 0.2044

     ∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°

Answer:

Step-by-step explanation:

Answer:

16.11(6)

Step-by-step explanation:

967/60=16 7/60

Answer:

5.7* 10 to the power of 4

Answer:

Step-by-step explanation:

[tex]\text{The scientific notation}:\\\\a\times10^k\\\\\text{where}\\\\1\leq a<10,\ k\in\mathbb{Z}\\\\================================[/tex]

[tex]57,000=5.7\times10000=5.7\times10^4\\\\-----------------------\\\\57000=5\underbrace{7000}_{\leftarrow4}=5\times10^4[/tex]

Answer:

[tex]\sqrt[3]{0.000004913}=0.017[/tex]

Step-by-step explanation:

Cubic Root

The cubic root of a number N is M, if

[tex]M^3=N[/tex]

It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.

Let's compute

[tex]M=\sqrt[3]{0.000004913}[/tex]

The argument can be expressed in scientific notation as

[tex]0.000004913= 4913\ 10^{-9}[/tex]

The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.

[tex]4913=17*17*17=17^3[/tex]

Thus our number is

[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]

We have then

[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]

Answer:

11.25 miles/hour

Step-by-step explanation:

Recall, speed = Distance ÷ Time

We are given :

Distance = 45 miles

Time = 4 hours

Hence,

Speed = Distance ÷ Time

= 45 miles ÷ 4 hours

= 11.25 miles/hour

Answer:

The functions which has the same horizontal asymptote y = -3 as given in the graph are,

f(x) = [tex]2^{x} - 3[/tex]  and

f(x) = [tex]2^{(x+2)} -3[/tex]

Step-by-step explanation:

The function that is graphed has horizontal asymptote as y = -3 .

As x → -∞  f(x) → - 3  for the second and fourth function. Hence the functions which has the same horizontal asymptote y = -3 as given in the graph are,

f(x) = [tex]2^{x} - 3[/tex]  and

f(x) = [tex]2^{(x+2)} -3[/tex]

Answer:

 [tex]4x+6y=34\\\\4x+3y=25[/tex]

Step-by-step explanation:

Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.

The cost of 4 hamburguers can be represented with this expression:

[tex]4x[/tex]

And the cost of 6 soft drinks  can be represented with this expression:

[tex]6y[/tex]

Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:

[tex]4x+6y=34[/tex]   [Equation 1]

 The following expression represents the the cost of 3 soft drinks:

[tex]3y[/tex]

According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:

[tex]4x+3y=25[/tex] [Equation 2]

Therefore, the Equation 1 and the Equation 2 can be used to determine the price of a hamburger and the price of a soft drink

Step-by-step explanation:

[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]

The answers are:

[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]

Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].

f(−x):

Replace x with −x in the function:

[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]

Simplify this expression:

[tex]f(-x)=3 x^2+2 x+5[/tex]

−f(x):

Multiply the entire function f(x) by −1:

[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]

Distribute the negative sign:

[tex]-f(x)=-3 x^2+2 x-5[/tex]

−f(−x):

Replace x with −x in the function f(x) and then multiply the whole expression by −1:

[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]

Simplify this expression:

[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]

Distribute the negative sign:

[tex]-f(-x)=-3 x^2-2 x-5[/tex]

Question:

For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).

Answer:

For the smaller rectangle: 9 x 19.8 = 178.2

For the bigger rectangle: 27 x 10.8 = 291.6