Trenton works for a company that is promoting its line of LED lightbulbs. He is selling boxes of the lightbulbs at a local store. A box of 60-watt bulbs costs $7. 00, and a box of 100-watt bulbs costs $12. 0. During the promotion, Trenton wants to sell more than 100 boxes total and make at least $1,000. The graph and the system of inequalities represent this situation, where x represents the number of boxes of 60-watt bulbs sold and y represents the number of boxes of 100-watt bulbs sold. 7x 12y ≥ 1,000 x y > 100 Which solution is valid within the context of the situation? A. (90,25) B. (40,64. 50) C. (30,80) D. (200,-10).

The equation of the directrix for the parabola y = 18 · x² - 4 · x + 41 is y = 2935 / 72.

In this question we find the case of the equation of a parabola in standard form:

y = a · x² + b · x + c

Where:

This equation must be changed into vertex form:

y - k = C · (x - h)²

Where:

Where the vertex constant is:

C = 1 / (4 · p)

Where p is the distance between focus and vertex.

And the equation of directrix is:

y = k - 1 / (4 · C)

First, write the quadratic equation in standard form:

y = 18 · x² - 4 · x + 41

Second, use algebra properties until vertex form is obtained:

y = 18 · [x² - (2 / 9) · x + 41 / 18]

y = 18 · [x² - (2 / 9) · x + 1 / 81] + 18 · (367 / 162)

y = 18 · (x - 1 / 9)² + 367 / 9

y - 367 / 9 = 18 · (x - 1 / 9)²

Third, find the equation of the directrix:

y = 367 / 9 - 1 / (4 · 18)

y = 2935 / 72

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Answer:

11. 34

Step-by-step explanation:because you have to add all the whole numbers together and add the fractions expect the 1-2 because is a Improper fraction and have to simply it

Answer:

18%

Step-by-step explanation:

540$ is 18% of what he put towards the loan :))

Answer:

many sides

unique shape

Answer:

The probability that Chang gets dressed with a white shirt and tan pants is 25%.

Step-by-step explanation:

Given that Chang has 2 shirts, a white one and a black one, and he also has 2 pairs of pants, one blue and one tan, to determine what is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants the following calculation must be performed:

Each shirt = 50% chance

Each pants = 50% chance

0.50 x 0.50 = X

0.25 = X

Therefore, the probability that Chang gets dressed with a white shirt and tan pants is 25%.

Answer:

a) (f + g)(x) = 8x + 2

b) (f - g)(x) = 4x - 6

Step-by-step explanation:

Given:

a) Find (f + g)(x):

a. (f + g)(x) = f(x) + g(x)

⇒ (f + g)(x) = (6x - 2) + (2x + 4)

⇒ (f + g)(x) = 6x + 2x - 2 + 4

⇒ (f + g)(x) = 8x + 2

b) Find (f - g)(x):

b. (f - g)(x) = f(x) - g(x)

⇒ (f - g)(x) = (6x - 2) - (2x + 4)

⇒ (f - g)(x) = 6x - 2x - 2 - 4

⇒ (f - g)(x) = 4x - 6

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Answer:

<YMX=33 degrees

Step-by-step explanation:

<YMX=<YMW---<WMX

         =90-57

         =33

Answer:

Option D:  <YMX = 33°

Step-by-step explanation:

Given that < WMX = 57°, and <WMY = 90°,  then:

< YMX = < WMY - < WMX

< YMX = 90° - 57°

< YMX = 33°

Answer:

0.125

Step-by-step explanation:

Simplified:

1/8

Answer:

0.125

Step-by-step explanation:

The area of the given circle is 36π square meters.

What is the area of a circle?

The region encircled by a circle is known as the area of a circle in geometry. The area of a circle is π multiplied by the square of the radius r. Here, the Greek letter π stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

Given,

 Diameter of the circle = 12 metres

Radius of the circle = Diameter/2 =12/2 = 6 metres

Area of circle = πr² = π ×6² = 36 π square meters

Therefore the area of the given circle is 36π square meters.

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Answer:

40%

Step-by-step explanation:

assuming you actually mean 10^5 and 10^6, to find percentages you do

part/total x percent/100

you have (6x10^5/1.5x10^6) x (x/100)

cross multiply, and you have 6x10^7=1.5x10^6x

divide on both sides by 1.5x10^6

x=40

so the answer is 40%

Answer:5x+7

Step-by-step explanation:

Answer:

I’m pretty sure that #1 is D because their are 4 different degrees making it a quadratic

Step-by-step explanation:

Answer:

12) 26x^2+22x+25

13) -15x^2-21x-11

14) x^2+32x+18

15) 9x^6+10x^5-15x^4+14

Step-by-step explanation:

Answer:

12. 26x² + 22x + 25

13. -15x² - 21x - 11

14. x² + 32x + 18

15. \(9x^6+6x^5-15x^4+14\)

Step-by-step explanation:

12. To add the polynomials we must combine like terms ( like terms are terms that have the same variable ( represented by a letter ) and the same exponent )

( 19x² + 12x + 12 )  + ( 7x² + 10x + 13 )

19x² and 7x² both have x as a variable and an exponent of 2 which means that they are like terms

Therefore we combine them

19x² + 7x² = 26x²

12x and 10x both have x as a variable and no exponent therefore the are like terms

So we combine them

12 + 10x = 22x

13 and 12 have no variable nor do they have a exponent therefore they are like terms so we combine them

13 + 12 = 25

We would then have 36x² + 22x + 25

None of the terms in the polynomial have the same variable and exponent therefore this is the answer.

We do the same process with 13 -15

13. (4x² - 6x + 7 ) + ( -19x² - 15x - 18 )

4x² - 19x² = -15x²

-6x - 15x = -21x

7 - 18 = -11

-15x² - 21x - 11

14. (20x² + 15x + 13 ) +  ( -19x² + 17x + 5 )

20x² -19x² = x²

15x + 17x = 32x

13 + 5 = 18

x² + 32x + 18

15. \((9x^6-4x^5)(10x^5-15x^4+14)\)

-4x^4 and 10x^4 are the only like terms so those are the only two numbers we combine

\(-4x^5+10x^5=6x^5\)

\(9x^6+6x^5-15x^4+14\)

The present value is $7,307.31.

To calculate the present value, we can use the formula: PV = A / (1 + r/n)^(n*t) where PV is the present value, A is the future value, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have A = $35,000, r = 15% = 0.15, n = 4 (since it is compounded quarterly), and t = 10.

Plugging these values into the formula, we get:

PV = $35,000 / (1 + 0.15/4)^(4*10)

PV = $35,000 / (1.0375)^40

PV = $35,000 / 4.79

PV = $7,307.31

Therefore, the present value is $7,307.31.

I ignored the "Ineedarim?" part of the question as it is irrelevant to the calculation.

$7,307.31.

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Answer: B i think

Step-by-step explanation:

The amount Arianna sold 80 milkshakes last week, and 35% of them had whipped cream on top. This means 28 milkshakes had whipped cream.

Arianna sold 80 milkshakes last week and 35% of them had whipped cream on top. This means that 35% of the total number of milkshakes, 80, had whipped cream. To calculate the amount of milkshakes with whipped cream, we must multiply the total number of milkshakes (80) by 35%. 35% of 80 is 28, so 28 milkshakes had whipped cream. To find the percentage, we divide the amount of milkshakes with whipped cream (28) by the total number of milkshakes (80). When we divide 28 by 80, we get 0.35, which is the same as 35%. Therefore, 35% of the milkshakes sold by Arianna last week had whipped cream on top.

Total milkshakes: 80

Milkshakes with whipped cream: 28

Percentage: 28/80 = 0.35 = 35%

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Since the sides RS and QT are parallel, these triangles are similar by case AA.

So we can write the following proportion between corresponding sides:

So the length of PT is 35 units.

Answer:

4

Step-by-step explanation:

the time it takes for a plane to travel a distance varies directly as the speed of the plane because ts=16,200

Answer: -2

Step-by-step explanation: 4-8= -4 then it ends up being -2r-4=0

Then you add 4 to 0 so -2r=4 then divide

The particular solution that satisfies the differential equation and the initial condition f(0) = a is: f(x) = -sin(x) + C1x + a.

To find the particular solution that satisfies the differential equation f''(x) = sin(x) and an initial condition, we need to integrate the equation twice and apply the initial condition.

1. First Integration:

Integrating the differential equation f''(x) = sin(x) with respect to x once gives us:

f'(x) = -cos(x) + C1

where C1 is the constant of integration.

2. Second Integration:

Integrating f'(x) = -cos(x) + C1 with respect to x again gives us:

f(x) = -sin(x) + C1x + C2

where C2 is another constant of integration.

3. Applying the Initial Condition:

To apply the initial condition, we need to use the given information about the problem. Let's say the initial condition is given as f(0) = a, where 'a' is a specific value.

Substituting x = 0 and f(x) = a into the equation, we get:

a = -sin(0) + C1(0) + C2

a = 0 + 0 + C2

C2 = a

Therefore, the particular solution that satisfies the differential equation and the initial condition f(0) = a is:

f(x) = -sin(x) + C1x + a

In this particular case, the initial condition f(0) = a determines the value of the constant C2, which becomes C2 = a. The resulting particular solution incorporates the constant C1 from the first integration and the constant a from the initial condition.

Note that without a specific initial condition or boundary condition, the constants C1 and C2 remain arbitrary and can be adjusted to fit different situations or additional information if provided.

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Answer:

I think it C if it not please don't report me

Answer:

0.4875

Step-by-step explanation:

Long division process:

       _0.4875__

800|39.00000

      -3200

          7000

         -6400

             6000

            -5600

               4000

              -4000

                      0

Answer:

487.8

Step-by-step explanation:

According to Siegler, the pattern of learning math concepts involves a gradual development and refinement of strategies. Siegler's theory, known as the overlapping waves model, suggests that learners use multiple strategies simultaneously and gradually shift towards more efficient ones over time. This process allows for a better understanding and application of math concepts, ultimately leading to improved problem-solving skills.

According to Siegler, the pattern of learning math concepts involves a gradual progression from using counting strategies to more efficient and accurate strategies. Children initially rely on counting strategies to solve math problems, such as counting fingers or objects. As they progress, they begin to use more advanced strategies, such as decomposition or mental math, which allow them to solve problems more quickly and accurately. Siegler also emphasizes the importance of practice and repetition in developing math skills and the role of feedback and instruction in promoting learning. Overall, Siegler's theory suggests that children's math skills develop through a combination of innate abilities and environmental factors, including exposure to math concepts and opportunities for practice and instruction in time.

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Answer:

The graph is a translation 3 left and 1 up from the function f(x) = x3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Vertex: (2,4)

Focus: (2, 63/16)

Axis of Symmetry: x=2

Answer:

TAKEN FROM GOOGLE

Step-by-step explanation:

The reciprocal of a number is the number that the initial number can be multiplied by to get the product 1. Therefore, the reciprocal of .8 is 1.25, since those two factors when multiplied together created a product of 1, or 1.000. The easiest way to find a reciprocal is to write the initial number as a fraction ( in this case, 8/10) and then "flip it" (making it 10/8) and simplifying. (10/8 = 1 and 1/4, or 1.25)

\(f(x) = x^3/3 + 7x + 30\) is  f such that the given conditions are satisfied.

Given that \(f'(x) = x^2 + 7\)  and f(0) = 30.

We need to find the function f which satisfies the given conditions.

Using the Fundamental Theorem of Calculus, we can solve the problem.

Fundamental Theorem of Calculus

Let f(x) be a continuous function and let a be any fixed number in its domain.

Then the function g defined by g(x) = ∫[a,x] f(t) dt is continuous and differentiable for all x in its domain, and g′(x) = f(x)

Consider \(f(x) = x^2 + 7\)and f(0) = 30

Using the Fundamental Theorem of Calculus, we can write:

                                     f(x) = ∫f'(x) dx

                               =\(∫(x^2 + 7) dx = (x^3/3) + 7x + C\) where C is a constant of integration.

We know that f(0) = 30Therefore, 30 = 0 + 0 + C ⇒ C = 30

Hence, f(x) = x^3/3 + 7x + 30.

Therefore, the correct answer is option D. f(x) = x^3/3 + 7x + 30.

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Answer:

\(x = 2\)

Step-by-step explanation:

Using the pythagorean theorem in the right triangle:

\(1^2 + 2^2 = c^2\\1 + 4 = c^2\\c = \sqrt5\)

Using the pythagorean theorem in the left triangle:

\(x^2 + (\sqrt5)^2 = 3^2\\x^2 + 5 = 9\\x^2 = 4\\x = 2\)

the pattern of the numbers 1,3,6,10,15,21,28,36. What is the 5857th triangular number: The unit digit of the 5857th triangular number is 8.

A series of numbers known as triangular numbers might be demonstrated as the amount of a series of positive whole numbers. The condition Tn = (n(n+1))/2 yields the nth triangular number. The initial not many triangular numbers, for example, are 1, 3, 6, 10, 15, etc. Numerous numerical and non-numerical applications exist for triangular numbers. They can be found, for example, in the investigation of math, combinatorics, and number hypothesis. They are used in calculations for information looking and arranging in fields like software engineering, where they have reasonable applications.

The nth triangular number is given by the recipe:

Tn = (n(n+1))/2

For the given arrangement 1,3,6,10,15,21,28,36, the units digit are:

1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, ...

The worth of 5857 is compatible with 7 modulo 10.

Consequently, the unit digit is the seventh number in the cycle above, which is 8.

Thus, the unit digit of the 5857th triangular number is 8.

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the complete question is:

Here is the sequence of numbers called triangular numbers: 1,3,6,10,15,21,28,36, Notice the pattern -the numbers increase by one more each time. What is the unit's digit of the 5857th triangular?

Answer:

(45÷9) - 3

5-3

=2 is a required answer

hope it is helpful to you