Is (0,0) a solution to this system?

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.

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]

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.

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]

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

Answer:

The equation [tex]35x+93\frac{3}{4} =190[/tex] gives average time spent on 35 rehearsals.

Step-by-step explanation:

We are supposed to find that what question does the equation [tex]35x+93\frac{3}{4} =190[/tex] finds answer of.

We can see that 35x represents time spent on 35 rehearsals and [tex]93\frac{3}{4}[/tex] is time spent on other responsibilities related to play. The sum of these times equals to total time spent on preparing the play.

Now let us solve our equation step by step.

[tex]35x+\frac{375}{4} =190[/tex]

After subtracting [tex]93\frac{3}{4}[/tex] hours from 190 hours we will get time spent on 35 rehearsals.

[tex]35x =190-\frac{375}{4}[/tex]

[tex]35x =\frac{760-375}{4}[/tex]

[tex]35x =\frac{385}{4}[/tex]

Time spent on 35 rehearsals is 96.25 hours and we are told that each rehearsal took different amount of time. Dividing 96.25 by 35 we will get average time spent on each rehearsal.

[tex]x =\frac{96.25}{35}=2.75[/tex]  

Therefore, equation [tex]35x+93\frac{3}{4} =190[/tex] finds average time spent on 35 rehearsals.

Answer:

What was the average length of each rehearsal?

Step-by-step explanation:

Khan Academy

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.

answer is equal to 168/144

7/6feet

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

the answer is b f(x)=-4/x-5

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.

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

The salesman needs to sell $5000 worth of products or services to earn a $1000 commission, calculated by dividing the desired commission by the percentage of commission he retains from sales.

To find out how much a salesman needs to sell to earn $1000 as a commission, we need to consider that he keeps 20% of his sales as commission. Since 20% is the part of the sales that corresponds to the commission, we can set up the following equation: 0.20 x sales = $1000.

To solve for sales, we divide both sides of the equation by 0.20:

sales = $1000 / 0.20

sales = $5000

Therefore, the salesman must sell $5000 worth of products or services to earn a $1000 commission.

First, subtract 90 from his total

159 - 90 = 69

Next, divide the remainder with 10%

Note that 10% = 0.10

69/0.10 = 690

$690 is your answer

hope this helps

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]

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]

Answer:

y3 - 4 y2 + 2 y - 5

Step-by-step explanation:

The correct expansion of (y + 1)(y² + 2y + 3) is y³ + 3y² + 5y + 3, achieved through the FOIL method and combining like terms.

The correct expansion of (y + 1)(y² + 2y + 3) is obtained by multiplying each term in the first polynomial by each term in the second polynomial and then simplifying the result. This process is known as FOIL (First, Outer, Inner, Last), which is an acronym that stands for multiplying the first terms, the outside terms, the inside terms, and the last terms of each binomial.

To expand (y + 1)(y² + 2y + 3), we perform the following steps:

Now, add up all the products: y³ + 2y² + y² + 2y + 3.

Combine like terms to simplify: y³ + (2y² + y²) + (2y) + 3

The final answer is y³ + 3y² + 5y + 3.

Final answer:

The expression that results from using the distributive property on 2(5 + r) is 10 + 2r.

Explanation:

The expression that results from using the distributive property on 2(5 + r) is 10 + 2r.

The distributive property allows us to multiply a number or variable by each term inside parentheses.

In this case, we multiply 2 by both 5 and r.

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!

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!

The slope-point form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

The slope-intercept form of a line:

[tex]y=mx+b[/tex]

1.

[tex]m=6,\ (4,\ 1)\to x_0=4,\ y_0=1[/tex]

Substitute

[tex]y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}[/tex]

2.

[tex]m=-5,\ (6,\ -3)[/tex]

Substitute

[tex]y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}[/tex]

3.

[tex]m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}[/tex]

4.

[tex]m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}[/tex]

(- 5, - 6 )

for x- coordinate x + 5 = 0 ⇒ x = - 5

given f(x) ± c , the value of c translates the graph vertically up/down by ± c

here c = - 6 , thus graph is shifted down by - 6

thus the vertex = (- 5, - 6)

P<1.5

Step-by-step explanation:

Answer:

(x - 2) is not a factor of f(x)  = 3x^5 - 7x^3 -  11x^2 + 2

Step-by-step explanation:

According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).

So first we will divide f(x) by (x - 2) using long division to get:

(3x^5 - 7x^3 -  11x^2 + 2) / (x - 2)

= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)

= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)

= [tex]\frac{-2 + 3x^{5} - 7x^{3} - 11x^{2} + 2x}{x - 2} - 2[/tex]

Therefore the remainder is -2.

Now check x = 2 for 3x^5 - 7x^3 -  11x^2 + 2:

3(2)^5 - 7(2)^3 -  11(2)^2 + 2 = -2

The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.

So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .

Answer:

Answers to the Complex Zeroes of a Polynomial Function Quiz Part 1 (I tried to signify each question)

Step-by-step explanation:

1. C, f(x) is a polynomial function. The degree is 5... -7

2. A, f(x)=7x^9-3x^2-6

3. C,D

4. Written

5. Rational Zero Theorem, B

6. Written

7. B, -5,-2, 3

8. A, (4 + 6i, -2 -11i)

9. D, (2,3, plus minus sqrt 5i)

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