A company did a quality check on all the packs of nuts it manufactured. Each pack of nuts is targeted to weigh 18.25 oz. A pack must weigh within 0.36 oz of the target weight to be accepted. Find the absolute value inequality that describes the situation and solve it to find the range of rejected masses, x.

 |x − 18.25| > 0.36; x < 17.89 or x > 18.61 |x − 0.36| + 18.25 > 0; x < 17.89 or x > 18.61 |x − 18.25| > 0.36; x < 18.25 or x > 18.61 |x − 0.36| + 18.25 > 0; x < 18.25 or x > 18.61

The phrase 'five more than twice the square root of four' is a mathematical expression which evaluates to 9. The operation uses addition, multiplication, and square root.

The student is asking for the result of a mathematical expression combining addition, multiplication, and square root operations. It can be written like "5 + 2(sqrt(4))". The square root of four (sqrt(4)) is two. So, the expression becomes "5 + 2*2", which equals 5 plus 4, resulting in 9. Therefore, five more than twice the square root of four equals nine.

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Answer:

your answers C

Step-by-step explanation:

The factored form of the expression [tex]27x^3+y^6[/tex] is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]. The correct answer of the factored expression is option A

Given the expression;

[tex]27x^3+y^6[/tex]

This can be expressed as the sum of cubes

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

The given expression can also be written as the sum of cubes as shown:

[tex]27x^3+y^6 = (3x)^3+(y^2)^3[/tex]

We can see that:

a = 3x

b = y²

Substituting the given parameters into the formula above;

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\(3x)^3+(y^2)^3=(3x+y^2)((3x)^2-3xy^2+(y^2)^2)\\(3x)^3+(y^2)^3=(3x+y^2)(9x2-3xy^2+y^4)\\[/tex]

Hence the factored form of the expression is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]

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answer is TT->T or a

Answer:

A)

Step-by-step explanation:

There are two ways you can approach this:

1) Factor [tex]\frac{5(x-1)(x+3)}{x+5}[/tex] this equals to [tex]\frac{5x^2+10x-15}{x+5}[/tex]

2) or divide which equals to 5x+35+[tex]\frac{160}{x+5}[/tex]

2. Linear Pair Postulate

4. 60° + m∠ACB = 180°

5. m∠ACB = 120°

6. definition of obtuse angle

First take not of the total sales and the cost of each ticket.

1,824 and 16

Now setup the equation

16x=1824

To solve this divide 1824 by 16 getting

X=144

x is the total tickets sold

Each ticket (t) costs $16. The band made a total of $1,824 from ticket sales, meaning that 16t=1,824, because the total amount of 16 dollar tickets sold is equal to the total made from ticket sales.

The equation is:

16t=1,824.

You are trying to find the amount of tickets sold by solving the equation.

t stands for the total amount of tickets sold.

Solving the equation:

16t=1,824

Divide both sides by 16.

t=114

114 tickets were sold. 114*16=1,824. This means that when 114 $16 tickets were sold, the band did make $1,824, which shows that 114 is the correct answer.

I hope this helps :)

The formula is

T=4B+10C

3° and 177°

supplementary angles sum to 180°

let x be an angle then the other angle is 59x

x + 59x = 180

60x = 180 ( divide both sides by 60 )

x = [tex]\frac{180}{60}[/tex] = 3

the angles are 3° and (59 × 3 )= 177°

To find the measures of two supplementary angles where one is fifty-nine times larger than the other, set up an equation x + 59x = 180, and solve for x. The smaller angle is 3 degrees, and the larger angle is 177 degrees.

The measure of an angle is fifty-nine times the measure of a supplementary angle. To solve this, we can set up an equation where x is the measure of the smaller angle, and therefore, 59x is the measure of the larger angle. Since angles are supplementary, their sum is 180 degrees. So, our equation is x + 59x = 180. Solving for x, we find that x = 3 degrees and 59x = 177 degrees.

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To do a two-column proof, you must know the definitions of the terms that are being used. Also, you must know the postulates and theorems you have learned so far. You look at the given information, and using the definitions, postulates, and theorems, you reason in your mind how to go from the given to the conclusion, step by step. You write each step and the accompanying reason that allows you to conclude each step.

Answer:

B- False

Step-by-step explanation:

that is very false bc the units mean alot

Final answer:

The car travels approximately 210 kilometers in 2 hours and 20 minutes by multiplying its speed of 90km/h by the time duration converted to hours (2.333 hours).

Explanation:

The student's question involves calculating the distance a car travels at a constant speed over a given period of time. In this case, the car drives at a speed of 90km/h for 2 hours and 20 mins. To find the distance, you can use the formula: distance = speed × time. First, convert 2 hours and 20 mins into hours, which is 2 hours + 20/60 hours = 2.333 hours.

Next, multiply the speed by the time to get the distance:

Distance = 90km/h × 2.333 hours = 209.97 km

So, the car travels approximately 210 kilometers in 2 hours and 20 minutes.

ANSWER=  +/- 5i sqrt2

sqrt=square root sign to solve you subtract 50 so x^2=-50 then get the square root on both sides and you're left with x=5isqrt 2 the i comes from the negative sign inside the square root

 +/- 5i sqrt2  is the solution

The average total cost of manufacturing scented candles is given by the formula A(b) = C(b)/b = (250 + 3b)/b, where b is the number of candles manufactured.

The concept of average total cost is key in the calculation. Given the function for total cost of the candles, C(b) = 250 + 3b, the average cost, A, can be calculated by dividing the total cost by the number of candles, b. Therefore, the function representing the average cost, A, in terms of b is given by A(b) = C(b)/b = (250 + 3b)/b. It's important to note that this function also signifies the 'economies of scale', stating as output number increases, the average cost falls.

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Every time you divide something by something else, you already have a fraction. A fraction is simply a different way to visualize a division. So, the following writings express the same concept:

[tex] 72\div 24 = \dfrac{72}{24} [/tex]

There's no conceptual difference between the two expressions, so you're not actuall "turning" 72 divided by 24 "into" a fraction, you're just writing it in another way.

Answer:

Dodecahedron

Step-by-step explanation:

Answer:

Distance Maria had to walk in the afternoon is [tex]2\frac{7}{8}[/tex]

Step-by-step explanation:

Lets take that Maria walked [tex]x[/tex] miles in the afternoon.

Distance walked in the morning + distance walked in the afternoon = [tex]10\frac{1}{8}[/tex]

⇒[tex]7\frac{2}{8} +x=10\frac{1}{8}[/tex]

[tex]\frac{58}{8} +\frac{8x}{8} =\frac{81}{8}[/tex]

[tex]\frac{58+8x}{8} =\frac{81}{8}[/tex]

[tex]58+8x=81[/tex]

[tex]8x=81-58\\[/tex]

[tex]8x=23[/tex]

[tex]x=\frac{23}{8}[/tex]

[tex]x=2\frac{7}{8}[/tex]

Answer is (3,1)

x + y = 4

2x + 3y = 9

We multiply the first equation by -2  to eliminate x

-2x - 2y = -8

2x + 3y = 9

-------------------(add both equations)

0 + y = 1

So y =1

Now plug in 1 for y in first equation

x + y = 4

x + 1 = 4

Subtract 1 on both sides

x = 3

Answer is (3,1)

B and D are both wrong. B has +4 outside the brackets. It is - 4

D is wrong because there is no 4 of any kind outside the brackets.

A is incorrectly represented inside the brackets as 16. That's not right

That only leaves  C. <<<< Answer

Graphs

Notice that the red parabola and the green one are the same thing.

Red: y = -4x^2 - 16x - 14

Green: y = -4(x + 2)^2 + 2

Hey there!!

Equation given :

2x² - 4x  = 0

Taking the common terms

2x ( x - 2 ) = 0

Divide by 2x on both sides

x - 2 = 0

Adding 2 on both sides ...

x = 2

And another answer would be zero as the whole equation is zero,

Hence the answer : ( 0 , 2 )

Hope it helps@+!!

The value x for equation 2x² - 4x = 0 is 2.

Given equation:

2x² - 4x = 0

Add 4x on both side,

2x² = 4x

Divide x on both side

2x = 4

Divide 2 on both side,

x = 2.

Therefore, the value x for equation 2x² - 4x = 0 is 2.

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The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (4, -5) and (0, -13).

Substitute:

[tex]m=\dfrac{-13-(-5)}{0-4}=\dfrac{-13+5}{-4}=\dfrac{-8}{-4}=2[/tex]

[tex](f+g)(x)=4x^2+\frac{3}{2}x-7[/tex]

Answer:

[tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]

Step-by-step explanation:

Given:  

[tex]f(x)=\dfrac{x}{2}-3[/tex]

[tex]g(x)=4x^2+x-4[/tex]

To find: (f+g)(x)

It is a composite function. Sum of f and g function.

[tex]h(x)=f(x)+g(x)[/tex]

[tex]h(x)=\dfrac{x}{2}-3+4x^2+x-4[/tex]

Combine the like term

[tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]

Hence, The sum of f(x) and g(x) would be [tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]

Answer: ∠Z = 117.2°

Step-by-step explanation:

∠X and ∠Y are isosceles so they are congruent (equal to each other)

5x + 33 = 33x + 42

-5x           -5x          

         33 = 28x + 42

        -42            -42

        -9   =  28x

        [tex]\frac{-9}{28} = \frac{28x}{28}[/tex]

        [tex]-\frac{9}{28} = x[/tex]

************************************************************

∠X + ∠Y + ∠Z = 180°                Triangle angle sum theorem

5x + 33 + 33x + 42 + ∠Z = 180°

38x + 75 + ∠Z = 180°

        -75              -75

38x          + ∠Z = 105°

38[tex](-\frac{9}{28})[/tex]      + ∠Z = 105°

-12.2         + ∠Z = 105°

+12.2                     +12.2

                     ∠Z = 117.2°

The first one is correct it is a Quadratic Polynomial.

The slope of the linear equation C(x) = 8x + 50 is 8, indicating an $8 charge per mile, and the y-intercept is 50, the flat towing fee. Similar service-based costs from other examples also follow this linear model, with their unique slopes and y-intercepts corresponding to the per-hour or per-mile charges and flat fees.

The function C(x) = 8x + 50 represents the cost of towing a vehicle, where C is the cost in dollars, and x is the number of miles the vehicle is towed. The slope of this line is 8, which indicates that the cost increases by $8 for every mile the vehicle is towed. The y-intercept is 50, representing the flat fee charged regardless of the distance towed, which is the cost when x (the number of miles) is 0.

Relating to the other examples provided, we can see a pattern in how these equations are structured for service-based costs. For instance, in Aaron's Word Processing Service, the total cost equation is y = 32x + 31.50, where the slope is 32 representing the hourly charge, and the y-intercept is 31.50, the fixed cost. Similarly, for Ethan's household appliance repairs, the equation is y = 20x + 25, with a slope of 20 and a y-intercept of 25. All these models illustrate how fixed fees and variable rates per service hour or mile can be represented in a linear equation format.

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The answer to the question is 10 + 9i, B.

Answer:

They will need 197 canoes.

Step-by-step explanation:

The first step is to find the ''3-people canoes'' that they filled.

Given that 273 people filled a certain number ''a'' of canoes that each hold 3 people, we know that is we multiply the number of canoes ''a'' by the number of people that can each canoe hold, we will obtain the number of people who

will take the canoe trip in the ''3-people canoes''. We write :

[tex]3a=273[/tex] ⇒

[tex]a=\frac{273}{3}=91[/tex]

We find that [tex]a=91[/tex] canoes. This means that 91 ''3-people canoes'' were filled each one with 3 people in order to hold 273 people in total.

The second step is to find the remaining people that won't take the ''3-people canoes''. We do this by subtracting 273 people to the total 485 people.

[tex]485-273=212[/tex]

We know that 212 people will travel in the ''2-people canoes''. Using a similar reasoning and defining as ''b'' to the total number of ''2-people canoes'' we write :

[tex]2b=212\\b=\frac{212}{2}=106\\ b=106[/tex]

We find that [tex]b=106[/tex] canoes is the total number of ''2-people canoes'' that we need If we want them to be filled up with 212 people.

The total number of canoes that the group will need is the sum of ''3-people canoes'' and ''2-people canoes'' :

[tex]Total=a+b=91+106=197[/tex]

The group of 485 people will need 197 canoes.