Which of the following is equivalent to 17g – 2g?

A.) (17 – 2) + g

B.) (17 – 2)g²

C.) (17 – 2) + g²

D.) (17 – 2)g

it SHOULD be a function, it looks like it at least. All domains are not duplicated so its a function

[tex]P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5[/tex]

If [tex]x+a[/tex] is a factor of [tex]P(x)[/tex], then [tex]-a[/tex] is a root of [tex]P(x)[/tex].

Therefore

[tex](-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0[/tex]

The toy company must sell more than 40 dolls to make a profit, taking into account the production cost of $20 per doll, a fixed promotion cost of $400, and a selling price of $30 per doll. The inequality that represents this problem is x > 40, where x is the number of dolls sold.

To determine how many dolls a toy company must sell to make a profit, we consider the cost of making each doll, the promotion cost, and the selling price per doll.

The company spends $20 to make each doll and has a fixed promotion cost of $400.

Each doll sells for $30.

The inequality representing the situation is:

30x - (20x + 400) > 0

Where x is the number of dolls sold. To find the breakeven point:

Calculate total cost: Total cost is the sum of the production cost for each doll and the promotion cost. If x is the number of dolls, then the total cost is 20x + 400.

Calculate total revenue: This is the selling price multiplied by the number of dolls, or 30x.

Set total revenue greater than total cost to find the breakeven point: 30x > 20x + 400.

Subtract 20x from both sides: 10x > 400.

Divide both sides by 10: x > 40.

The company must sell more than 40 dolls to make a profit. Thus, the inequality that represents this problem is x > 40.

Final answer:

The toy company must sell more than 40 dolls to make a profit. The cost of producing each doll is $20, and they are sold for $30 each, with a fixed promotional cost of $400. The inequality representing the situation is 30x > 20x + 400, where x is the number of dolls sold.

Explanation:

The question asks about the number of dolls a toy company must sell to make a profit. To calculate this, we must establish the costs and revenues involved in the production and sale of the dolls. The cost per doll is $20 and there is an additional fixed promotional cost of $400. Each doll is sold for $30.

Let's denote the number of dolls sold as x. The total cost for x dolls would be $20x (variable cost) plus $400 (fixed cost). The total revenue from selling x dolls would be $30x. To make a profit, the total revenue must be greater than the total costs.

Using this information, we can write the inequality for profit as follows:

Total Revenue > Total Cost
$30x > $20x + $400

To find the breakeven point where the company begins to make a profit, we must solve for x:

$10x > $400
x > 40

So, the company needs to sell more than 40 dolls to start making a profit.

For this one, there are a few steps that will make it easier towards the end.

First lets solve for y

y+3x=8

subtract 3x from both sides

y=-3x+8

Now you are ready to plug in each of the x values and solve for y.

x vaues: -1, 0, 3

Here is what it would look like for each:

y=-3(-1)+8

y=3+8

y=11

y=-3(0)+8

y=8

y=-3(3)+8

y= -9+8

y=-1

So your final answer would be y= {-1, 8, 11}

~be careful putting it into the system, that one is sensitive~

Hope this helps!

dude its b thats easy and yes im sure 4 units down and sense its not reflection then thats the answer

Hello!

Solve for y.

[tex]2x +4y =12[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

First you had to add by -2x from both sides of the equation.

[tex]2x+4y+-2x=12+-2x[/tex]

[tex]4y=-2x+12[/tex]

Then divide by 4 from both sides of the equation.

[tex]\frac{4y}{4}=\frac{-2x+12}{4}[/tex]

Simplify it should be the correct answer.

[tex]y=\frac{-1}{2}x+3[/tex]

Answer⇒⇒⇒⇒⇒⇒y=-1/2x+3

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

The formula of a distance between two points A and B:

[tex]|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]

We have A(6, 6) and B(2, 9).

Substitute:

[tex]|AB|=\sqrt{(2-6)^2+(9-6)^2}=\sqrt{(-4)^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex]

Total number of pizzas Juan ordered [tex]20[/tex]

Since, [tex]45\%[/tex] of pizzas have [tex]8[/tex] slices.

Therefore, number of pizzas with [tex]8[/tex] slices are: [tex]45\%\times(20)[/tex]

                                                                                          [tex]=\frac{45}{100} \times(20)[/tex]

                                                                                          [tex]=\frac{45}{10} \times(2)[/tex]

                                                                                          [tex]=\frac{90}{10}[/tex]

                                                                                          [tex]=9[/tex] pizzas

Also, since, [tex]55\%[/tex] of pizzas have [tex]12[/tex] slices.

Therefore, number of pizzas with [tex]12[/tex] slices are: [tex]55\%\times(20)[/tex]

                                                                                          [tex]=\frac{55}{100} \times(20)[/tex]

                                                                                          [tex]=\frac{55}{10} \times(2)[/tex]

                                                                                          [tex]=\frac{110}{10}[/tex]

                                                                                          [tex]=11[/tex] pizzas

Now, there are [tex]9[/tex] pizzas with [tex]8[/tex] slices and [tex]11[/tex] pizzas with [tex]12[/tex] slices.

Therefore, total number of slices of pizza are: [tex]=(9)(8)+(11)(12)[/tex]

                                                                            [tex]=72+132[/tex]

                                                                            [tex]=204[/tex] slices

Answer:

I hope this helped! <3

Step-by-step explanation:

Number of pizzas with 8 slices:  9

Number of pizzas with 12 slices:  11

45% of the pizzas have 8 slices each. In total, there are  72  slices in these pizzas.

55% of the pizzas have 12 slices each. In total, there are  132  slices in these pizzas.

Altogether, there is a total of 204  slices of pizza.

7.5y - z/9 + 50 + 2y

Okay, so it would be best to organize and simplify this expression: 9.5y -z/9 + 50

Alright, now let's eliminate some answers.

True or false: The constant is 7.5. This is false. 7.5 is a coefficient, 50 is a constant.

True or false: The coefficients are 7.5 and -9. This is false. Sure, 7.5 is a coefficient, but -9 is not. Actually, z/9 is also equal to (1/9)z, so technically 1/9 is the coefficient.

True or false: The variables are x and y. This is false. Where is x? Nonexistent.

True or false: The like terms are 7.5y and 2y. This is true. When we simplified the equation, we first combined like terms. 7.5y and 2y are like terms and therefore able to be combined. That's how we got 9.5y.

The answer, I believe, is D. Hope this helps!

The formula that can be used to describe the sequence is:

               [tex]f(x)=-3\cdot (\dfrac{-1}{5})^{x-1}[/tex]

We are given a sequence of numbers as:

[tex]-3\ ,\ \dfrac{3}{5}\ ,\ \dfrac{-3}{25}\ ,\ \dfrac{3}{125}\ ,\ \dfrac{-3}{625}[/tex]

Hence, we could observe that the series is a series with alternating sign such that the power of 5 is increasing in the denominator and there is no change in the numerator i.e. the power of 3 remain unchanged.

Hence,third and last option are discarded.

Also, in first option each of the terms of the digit will be negative and not alternating and hence option (1) is also discarded.

    Hence, the function that represent this sequence is:

        [tex]f(x)=-3\cdot (\dfrac{-1}{5})^{x-1}[/tex]

Let x represent the number of ounces of vinegar

Let y represent the number of ounces of lemon juice

Oil required = 8 oz

Container can hold = 16 oz

So the inequality equation will be :

[tex]x+y+8\leq16[/tex]

Answer:

9

Step-by-step explanation:

0.9 per cent of 1000 = 0.9(1000)/100 = 0.9(10) =9

ANSWER

The set of the intersection  of {[tex]2,3,5,7[/tex]} and {[tex]2,5,11,13[/tex]} is

{[tex]2,5[/tex]}

EXPLANATION

Let [tex]A=[/tex]{[tex]2,3,5,7[/tex]}

and

[tex]B=[/tex]{[tex]2,5,11,13[/tex]}.

The intersection of the two sets are the elements that are in both set A and set B.

The elements that are common to both sets are 2 and 5. So, we write;

[tex]A \cap B=[/tex]{[tex]2,5[/tex]}

Therefore the correct answer is C

The intersection of the sets {2,3,5,7} and {2,5,11,13} is the set {2,5}, which has the elements common to both sets. Therefore option c is correct

The intersection of two sets is the set of elements common to both sets. In the provided sets {2,3,5,7} and {2,5,11,13}, the common elements are 2 and 5. Therefore, the intersection of these two sets is {2,5}. So, the correct answer is C. {2,5}.

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Follow this as an example

An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of

10 m

and a depth of

1.4 m

. Suppose water is pumped into the pool at a rate of

11 m3

per hour. How many hours will it take to fill the empty pool?

Use the value

3.14

for

π

, and round your answer to the nearest hour. Do not round any intermediate computations.

The formula for the volume of a cylinder is  ∏r2h.  The problem gives d=10m, so r=5m.

The pool holds  (3.14)*52*1.4 m3 = 109.9 m3 of water.

At a rate of 11 m3 per hour:

            ( 109.9 m3 ) / (11 m3/hr)  = 9.990909 hr.

              rounding to the nearest hour, this is 10 hours

The pool has a volume of approximately 47.97 cubic meters. The pump can fill 11 cubic meters per hour. Therefore, rounding up, it will take roughly 5 hours to fill the pool.

The volume of the swimming pool shaped like a cylinder can be calculated using the formula for the volume of a cylinder which is V = πr2h, where r is the radius, h is the height (or depth in this case) and π is a constant whose value we'll take as 3.14. Therefore, the volume of the pool is V = 3.14 * (6/2)2 * 1.7.

Once we have the volume, we can divide this by the rate of water being pumped in, in terms of how many cubic meters it pumps per hour, to find out how many hours it would take. So the time taken to fill the pool, in hours, is Time = Volume / Rate.

By substituting the numbers we have into these formulas, we get V = 3.14 * 9 * 1.7 = 47.97 m3, and Time = 47.97 m3 / 11 m3/hour = approximately 4.36 hours. Since we need to round up to the nearest hour, the pool will take about 5 hours to fill.

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The domain is all of the x-values.  The x-values are also considered the input values.

Side Note: the range is all of the y-values, which represent the output values.

Answer: A

To solve this problem you must apply the proccedure shown below:

1. You can use the following formula for calculate the volume:

[tex]V=(\frac{a+b}{2})(h)(l)[/tex]

Where:

[tex]a=6m\\b=12m\\h=8m\\l=3m[/tex]

2. Now, you must substitute the values above into the formula:

[tex]V=(\frac{a+b}{2})(h)(l)\\V=(\frac{6m+12m}{2})(8m)(3m)\\V=216m^{3}[/tex]

Therefore, the answer is the last option: D. 216 m³.

Final answer:

The cable company had approximately 866.67 regular subscribers.

Explanation:

To find the number of regular subscribers, we need to set up a proportion using the given ratio. The ratio of regular subscribers to premium subscribers is 10:3, which can be written as 10/3. Let x represent the number of regular subscribers.

We can set up the proportion:

10/3 = x/260

Cross-multiplying, we get:

3x = 260 * 10

3x = 2600

Dividing both sides by 3, we find:

x = 2600 / 3

Therefore, the cable company had approximately 866.67 regular subscribers.

ANSWER

Each side of the chip is 5 centimeters long.

EXPLANATION

The chip is in the form of a square.

The formula for finding the area of a square is

[tex]Area=l^2[/tex]

We were given in the question that, the area is 25 square centimeters. This means that,

[tex]25=l^2[/tex]

We take the square root of both sides to get,

[tex]\sqrt{25}=l[/tex]

[tex]\Rightarrow 5=l[/tex]

Hence the length of the square technology chip is 5 centimeters

answer is equal to 168/144

7/6feet

Answer:

Option C

Step-by-step explanation:

Given a quadratic equation

x^2+10x+24 =0

We can use either formula or factorization method to solve this equation.

The last term is 24, it is a product of 6 and 4. Sum =6+4 =10

Hence factoring can be done easier

Split the middle term as 6x +4x

x^2+6x+4x+24 =0

x(x+6)+4(x+6)=0

(x+4)(x+6)=0

Either x+4 =0 or x+6 =0

x=-6 or x =-4

Thus solution for this equation is option C

In general, any equation like [tex] ax=b [/tex] (assuming [tex] a \neq 0[/tex]) is solved by

[tex] x= \dfrac{b}{a} [/tex]

So, in your case, the solution is

[tex] x = \dfrac{\frac{1}{5}}{\frac{3}{4}} [/tex]

Dividing by a fraction means to multiply by the inverse of that fraction:

[tex] \dfrac{\frac{1}{5}}{\frac{3}{4}} = \dfrac{1}{5} \cdot \dfrac{4}{3} = \dfrac{4}{15} [/tex]

The slope-point formula:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (0, 3) and (-10, 4)

Substitute:

[tex]m=\dfrac{4-3}{-10-0}=\dfrac{1}{-10}\\\\y-3=-\dfrac{1}{10}(x-0)\qquad|\text{add 3 to both sides}\\\\y=-\dfrac{1}{10}x+3\to\boxed{A.}[/tex]

5/8 is the answer. I just x the numerator and denominator by 2 to be 6/8-1/8=5/8

I believe it is A.  I did this awhile ago.

Intercept form is: y = a(x - p)(x - q)  

It is given that:  p = 14, q = -6, x = 14, y = 4

4 = a(14 - 12)(14 - (-6))

4 = a(2)(20)

4 = 40a

[tex]\frac{4}{40} = \frac{40a}{40}[/tex]

[tex]\frac{1}{10} = a[/tex]

Answer: y = [tex]\frac{1}{10}[/tex](x - 14)(x + 6)

The perimeter of △ABC is approximately 25.93 units. The area of △ABC is approximately 28.62 square units.

Given that △ABC has m∠A=60°, m∠C=45°, and AB=9, we can use trigonometry to find the missing side lengths and then use them to calculate the perimeter and area of the triangle.

First, we can use the fact that the sum of the angles in a triangle is 180° to find m∠B:

m∠A + m∠B + m∠C = 180°

60° + m∠B + 45° = 180°

m∠B = 75°

Next, we can use the law of sines to find the length of side BC:

sin 60° / 9 = sin 75° / BC

BC = sin 75° * 9 / sin 60°

BC ≈ 8.14

Finally, we can use the fact that the sum of the side lengths of a triangle is its perimeter to find the perimeter of △ABC:

Perimeter = AB + BC + AC

Perimeter = 9 + 8.14 + AC

To find AC, we can use the fact that the angles in a triangle add up to 180°:

m∠A + m∠B + m∠C = 180°

60° + 75° + m∠C = 180°

m∠C = 45°

Now we can use the law of sines again to find AC:

sin 45° / AC = sin 60° / 9

AC = sin 45° * 9 / sin 60°

AC ≈ 7.79

Substituting this value into the equation for the perimeter, we get:

Perimeter = 9 + 8.14 + 7.79

Perimeter ≈ 25.93

Therefore, the perimeter of △ABC is approximately 25.93 units.

To find the area of △ABC, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

We can use the fact that △ABC is a right triangle (since m∠C = 45°) to find the height:

sin 45° = height / 9

height = sin 45° * 9

height ≈ 6.36

Substituting the values for the base and height into the formula for the area, we get:

Area = 1/2 * 9 * 6.36

Area ≈ 28.62

Therefore, the area of △ABC is approximately 28.62 square units.

Perimeter of △ABC: 20.67 units,

Area of △ABC: 20.11 square units.

In △ABC, we are given that ∠A = 60°, ∠C = 45°, and AB = 9 units. To find the perimeter, we need to calculate the length of side BC. Using the angles, we can determine that ∠B = 180° - ∠A - ∠C = 75°. Now, applying the Law of Sines, we find BC ≈ 8.21 units. The perimeter, therefore, is the sum of the three sides: 9 + 8.21 + BC ≈ 20.67 units.

For the area, we can use the formula A = 0.5 * AB * BC * sin(∠C). Substituting the known values, we get A ≈ 0.5 * 9 * 8.21 * sin(45°) ≈ 20.11 square units.

Explanation:

In the main answer, we first addressed the perimeter by finding the length of side BC through the Law of Sines. The perimeter is then calculated by summing the three sides.

Moving on to the area, we employed the formula for the area of a triangle involving two sides and the sine of the included angle. Substituting the given values, we obtained the area of △ABC as approximately 20.11 square units.

These calculations showcase the application of trigonometric principles in solving geometric problems involving angles and side lengths. The Law of Sines and the area formula for triangles provide a mathematical framework for determining these essential properties.

P<1.5

Step-by-step explanation: