Coefficient of 5x/6?

Answer:

16.11(6)

Step-by-step explanation:

967/60=16 7/60

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

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

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:

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

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:

$158.74

Step-by-step explanation:

A sound system has a regular price of $249. Now, we have to find the total cost of it if there is a sale for 40% off and the sales tax is 6.25%.

Now, if there is 40% off on price $249, then the discounted price will be

[tex]249(1 - \frac{40}{100}) = 149.4[/tex] dollars.

Then the after-tax value of the sound system at the rate of 6.25% will be [tex]149.4(1 + \frac{6.25}{100}) = 158.74[/tex] dollars (Approximate)

(Answer)

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:

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:

  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]y=3(x+4.5)(x+2.8)[/tex] or  [tex]y=3x^2+21.9x+37.8[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola in factored form is equal to

[tex]y=a(x-x_1)(x-x_2)[/tex]

where

a is a coefficient

x_1 and x_2 are the roots or x-intercepts of the quadratic equation

In this problem we have

[tex]x_1=-4.5\\x_2=-2.8[/tex]

substitute

[tex]y=a(x+4.5)(x+2.8)[/tex]

Find the value of a

we have the y-intercept (0,37.8)

substitute the value of x and the value of y of the y-intercept in the equation and solve for a

[tex]37.8=a(0+4.5)(0+2.8)[/tex]

[tex]a=37.8/12.6\\a=3[/tex]

so

[tex]y=3(x+4.5)(x+2.8)[/tex]

Convert to expanded form

[tex]y=3(x^2+2.8x+4.5x+12.6)[/tex]

[tex]y=3x^2+21.9x+37.8[/tex]

Answer:

Go to the link below :)

Step-by-step explanation:

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The area of the gray portion in the room, after subtracting the area of the central linoleum from the total area of the room, is 112 sq. ft.

To calculate the area of the gray portion in the room, first subtract the area of the linoleum from the total area of the room. The area of the room is given as 12 x 16 sq. ft. and the linoleum is 8 x 10 sq. ft.. To find the total area of the room, multiply the length by the width (12 x 16 = 192 sq. ft.). Then do the same for the linoleum (8 x 10 = 80 sq. ft.). Subtracting the area of the linoleum from the total area of the room gives us the gray area (192 - 80 = 112 sq. ft.). Hence, the area of the gray portion is 112 sq. ft.

Answer:

D) 24.

Step-by-step explanation:

The solution is 24 routes. To determine the number of different routes we multiply the routes for each part of the trip. 4(3)(2) = 24 routes.

He can take 24 different routes for his trip

The correct option is option D)

What is permutation and combination?

an arrangement of objects in a definite order is known as permutation. The members or elements of sets are arranged here in a sequence.  a combination is a selection of items from a set which has distinct members, and the order of selection does not matter. even though the terms are used together they are different and formula for calculating them is also different

We are given that,

Jacksonville to Atlanta: 4 routes

Atlanta to Knoxville: 3 routes

Knoxville to Indianapolis: 2 routes

Also Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis

To find the different routes sammy can take can be computed as

4*3*2=24ways

Hence Sammy can take 24 routes

The correct option is option D)

To learn more about permutation please refer the following link

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Answer:

For the smaller rectangle: 9 x 19.8 = 178.2

For the bigger rectangle: 27 x 10.8 = 291.6

p = 32

Solution:

Given p represents the amount of air pressure in a tire.

t represents the time it takes for the tire to go flat and t = –8.

To find the value of p, if [tex]\frac{p}{t}=-4[/tex].

⇒ [tex]\frac{p}{t}=-4[/tex]

Substitute t = –8 in the above equation.

⇒ [tex]\frac{p}{-8}=-4[/tex]

Do cross multiply, we get

⇒ p = (–8) × (– 4)

⇒ p = 32

Hence, the value of p is 32 if the quotient [tex]\frac{p}{t}[/tex] is –4.

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: 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.

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:

[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]

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.

Answer:

Step-by-step explanation:

three angles measuring 40°, 70°, and 65 cannot create a triangle because sum of all the angles should be 180

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:

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.

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:

 [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

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: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:

#2 486

#3 25

#4 25

#5 1,000,000

Step-by-step explanation:

Sequences like this always have some rule that determines the next number, a pattern that needs to be followed. Sometimes the pattern is easy to find, sometimes really hard.

#2 One of the first things to check is the ratio of adjacent numbers. Here we have 2 then 6 then 18 then 54 etc.

The most prominent feature of these numbers is that the next number is always three times bigger than the previous. It's safe to assume that the missing number will be 162 • 3 = 486.

#3 Of course numbers can be arranged in the decreasing order as well. However, that does not change their ratio. In this example, carefully examining, we can see that each number in the sequence is exactly twice smaller than the previous:

800 -> 400 -> 200 -> 100  etc.

Following this pattern, we can say that the next number will be 50 / 2 = 25.

#4 Of course, ratio is not the only way to help us find the pattern. One of the very often used methods is also the difference between adjacent numbers. Let's subtract each adjacent pair:

4 - 1 = 3

9 - 4 =5

16 - 9 = 7

Longer the sequence is, greater are the chances to see the pattern, but from this we could conclude that the difference between adjacent numbers is always an odd number (3, 5, 7). We could say that the next odd number is 9, so the missing number is 16 + 9 = 25

There is another pattern that could be found. This sequence could also represent the sequence of squared numbers:

1^2, 2°2, 3°2, 4^2

In this case, the next number would be 5^2 which is also 25.

#5 Again, we can find a pattern established on the ratio of numbers, but this time with repetitive symbol L. After every L, the number is a thousand times bigger than the previous number:

0.001 -> 1 -> 1000

So, following this pattern, the missing number would be 1000 • 1000 which equals to 1000000 (a million).

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