Chris bought 5 tacos and 2 burritos for $13. 25.


Brett bought 3 tacos and 2 burritos for $10. 75.


The price of one taco is $


The price of one burrito is $

The total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

To find the total area of the solid figure, we need to determine the areas of each face and then add them together.

The solid figure consists of a rectangular prism with dimensions 3" x 3" x 6" and a pyramid on top with an equilateral triangle base.

First, let's find the area of the rectangular prism. The rectangular prism has two identical square faces with side length 3" and four rectangular faces with dimensions 3" x 6". The total area of the rectangular prism can be calculated as:

Area of the square faces: 2 * (3" * 3") = 2 * 9 square inches

Area of the rectangular faces: 4 * (3" * 6") = 4 * 18 square inches

Total area of the rectangular prism: 2 * 9 + 4 * 18 = 18 + 72 = 90 square inches.

Next, let's find the area of the triangular pyramid. The base of the pyramid is an equilateral triangle with side length 3". The height of the pyramid is 3". The formula to find the area of an equilateral triangle is (sqrt(3) / 4) * (side length)^2. Plugging in the values, we have:

Area of the triangular pyramid: (sqrt(3) / 4) * (3" * 3") * 3" = (sqrt(3) / 4) * 9 * 3 = (sqrt(3) / 4) * 27 = 27sqrt(3) / 4 square inches.

Now, we can find the total area of the solid figure by adding the area of the rectangular prism and the area of the triangular pyramid:

Total area = Area of rectangular prism + Area of triangular pyramid

Total area = 90 square inches + 27sqrt(3) / 4 square inches.

Thus, the total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

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Answer:

2

Step-by-step explanation:

Answer:

b = 4a

Step-by-step explanation:

Given

a = \(\frac{1}{4}\) b

Multiply both sides by 4 to clear the fraction

4a = b

Answer:

510 votes

Step-by-step explanation:

we multiply 680 by 75% and to do so we make 75 percent in a decimal by dividing it by 100

0.75 and now multiply

0.75x680

510 votes

Hopes this helps please make brainliest

Answer:

510 votes

Step-by-step explanation:

you can change 75% to 0.75 and multiply it by 680 to get 510

or you can change 75% to 3/4 and multiply it by 680 to get 510

Typically, high-end and specialized machines such as servers, supercomputers, and mainframes have a larger flat fee just to log in.

These machines require advanced hardware and software configurations, as well as highly skilled IT professionals to maintain and operate them, which ultimately increases their cost.

Moreover, these machines often run critical and high-performance applications that require dedicated resources and security measures, hence the higher fees to access them.

Conversely, personal computers and standard laptops have a lower flat fee to log in as they are designed for individual use and do not require the same level of resources and security.

In summary, the more advanced and specialized the machine is, the higher the flat fee to log in.

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The coordinates of the points after dilation is D'(-5/3,1),  E'(1,-2/3), F'(5/3,-1), and C'(-1,-4/3)

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given that the scale factor is 1/3. The coordinates of the points after dilation is,

D(-5,3) = D'(-5/3,1)

E(3,-2) = E'(1,-2/3)

F(5,-3) = F'(5/3,-1)

C(-3,-4) = C'(-1,-4/3)

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The 63.5% of the students who do not exercise is the wrong percentage because 70% of the students do not exercise.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Miguel thinks that his data do not support the article's claim because 63.5% of the students who made the honor roll at his school do not exercise.

The percentage of the students who do not exercise will be

\(\rm P = \dfrac{112}{160} \times 100\\\\P = 70\%\)

The 63.5% of the students who do not exercise is the wrong percentage because 70% of the students do not exercise.

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Answer:

6

Step-by-step explanation:

No, we cannot measure 3 gallons of water using 2 jugs of size 100 and 98 gallons. But, we can measure 4 gallons of water using these jugs.

Let's call the two jugs A and B, with A being the 100-gallon jug and B being the 98-gallon jug.

To measure 3 gallons of water, we need to have one jug that is smaller than 3 gallons and another jug that is larger than 3 gallons.

However, both of these jugs are larger than 3 gallons.

This means that it is impossible to measure 3 gallons of water using these jugs.

To measure 4 gallons of water, we can follow these steps:

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 2 gallons of water in jug A.

Pour the water from jug B down the drain, then pour the 2 gallons from jug A into jug B.

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 96 gallons of water in jug B, with 4 gallons of water in jug A.

Thus, we can measure 4 gallons of water using these jugs.

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Answer:

A and B

Step-by-step explanation:

A is correct because the three terms are x², 5yz, and -8.

B is 100% correct I guarantee it.

C is incorrect because ² is not a coefficient.

D is incorrect because there are three factors in that multiplication term: 5, y, and z.

The otter takes approximately 12.10 seconds to get to the other side if it swims directly across the river. The current will have carried the otter approximately 30.25 meters downstream when it reaches the other side. The otter's velocity, relative to the bank from where it started, is 0.25 m/s.

a) To find the time it takes for the otter to get to the other side, we can use the concept of relative velocity. The otter's swimming speed is 2.75 m/s, and the current velocity is 2.5 m/s. Since the otter is swimming directly across the river, its swimming speed and the current speed are perpendicular. Using the Pythagorean theorem, we can find the resultant velocity of the otter:

Resultant velocity = √(swimming velocity² + current velocity²)

= √(2.75² + 2.5²)

≈ √(7.5625 + 6.25)

≈ √13.8125

≈ 3.72 m/s (rounded to two decimal places)

The time it takes to cross the river is given by the distance divided by the resultant velocity:

Time = Distance / Resultant velocity

= 45.0 m / 3.72 m/s

≈ 12.10 seconds (rounded to two decimal places)

b) To find how many meters downstream the current carries the otter when it gets to the other side, we can calculate the distance using the time it takes to cross and the current velocity.

Distance downstream = Time × Current velocity

= 12.10 s × 2.5 m/s

= 30.25 m

c) The otter's velocity, relative to the bank from where it started, can be calculated by subtracting the current velocity from the otter's swimming velocity.

Relative velocity = Swimming velocity - Current velocity

= 2.75 m/s - 2.5 m/s

= 0.25 m/s

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Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Answer:

8

Step-by-step explanation:

Isn't it simple because all other numbers are less than 4?

Step-by-step explanation:

This is a word problem that we must translate to mathematical expression before we can solve.

let the individual saving be the first letters of the names

Jada= J

Lin= L

Elena= E

1. Jada saved $20 less than Lin

    J=L-20

2. Lin saved 3 times as much money as Elena

   L= 3E

3. Hence Elena saved

   E

Together they saved $120.

hence

(L-20)+3E+E= 120

L-20+3E+E= 120

collecting like terms we hav

L+4E=120+20

L+4E= 140

but we know that L= 3E

3E+4E= 140

7E= 140

divide both sides by 7 we have

E= 140/7

E= $20

This means Elena saves $70

also  L= 3E

L= 3*20

L= $60

this means that Lean saved $60

also  J=L-20

J= 60-20

J= $40

This means that Jada saved $40

(b) By solving the dual problem graphically, we find that the optimal solution occurs at the vertex (0, 2) with a minimum value of W = 10. The shadow price for resource 1 (x1 + x3 ≤ 3) in the primal problem is 10. This means that an additional unit of resource 1 would increase the objective function value by 10. The shadow price for resource 2 (x2 + 2x3 ≤ 5) in the primal problem is 0. This indicates that the optimal solution is not sensitive to changes in resource 2.

(a) To construct the dual problem, we will assign dual variables y1 and y2 to the constraints of the primal problem and convert the objective function to the dual form. The dual problem has two constraints corresponding to the resources in the primal problem. The objective function in the dual problem represents the costs or prices associated with the resources.

(b) To solve the dual problem graphically, we will plot the feasible region and find the optimal solution.

Constraint 1: y1 + y2 ≥ 2

Rearranging the inequality, we get:

y2 ≥ 2 - y1

Constraint 2: y1 + 2y2 ≥ 6

Rearranging the inequality, we get:

y2 ≥ (6 - y1) / 2

The feasible region is the intersection of the two constraint inequalities, taking into account the non-negativity constraints y1 ≥ 0 and y2 ≥ 0.

Now, let's plot the feasible region on a graph:

Starting with the y-axis, plot points (0, 2) and (0, 3) to represent the non-negativity constraint y2 ≥ 0.

Next, draw a line with a slope of -1 passing through the point (0, 2).

Draw another line with a slope of -0.5 passing through the point (0, 3).

The feasible region is the area bounded by these two lines and the y-axis.

To find the optimal solution, we need to evaluate the objective function at the vertices of the feasible region.

Vertices of the feasible region:

(0, 2)

(0, 3)

Now, substitute these vertices into the objective function:

For (0, 2):

W = 3(0) + 5(2) = 10

For (0, 3):

W = 3(0) + 5(3) = 15

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a) The utility depends on both health (H) and consumption of other goods (X).

b) The coefficient is negative, indicating a negative relationship between two variables.

c) Health (H) is greater than zero, suggesting a positive value for health.

d) Health (H) is a function of a variable denoted as 'm'.

e) The variable 'm' is greater than zero and the coefficient is negative.

f) The product of two variables, 'm' and 'm', is negative.

a) The expression in (a) is reasonable as it acknowledges that utility is influenced by both health and consumption of other goods. It recognizes that happiness or satisfaction is derived not only from health but also from other aspects of life.

b) The expression in (b) suggests a negative coefficient and a negative relationship between the variables. This could imply that an increase in one variable leads to a decrease in the other. The reasonableness of this relationship would depend on the specific variables involved and the context of the theoretical framework.

c) The expression in (c) states that health (H) is greater than zero, which is reasonable as health is generally considered a positive attribute that contributes to well-being.

d) The expression in (d) indicates that health (H) is a function of a variable denoted as 'm'. The specific nature of the function or the relationship between 'm' and health is not provided, making it difficult to assess its reasonableness without further information.

e) The expression in (e) states that the variable 'm' is greater than zero and the coefficient is negative. This implies that an increase in 'm' leads to a decrease in some other variable. The reasonableness of this relationship depends on the specific variables involved and the theoretical context.

f) The expression in (f) suggests that the product of two variables, 'm' and 'm', is negative. This implies that either 'm' or 'm' (or both) are negative. The reasonableness of this expression would depend on the meaning and interpretation of the variables involved in the theoretical framework.

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The exercise highlights that converting the dual problem into standard form and applying the primal simplex method does not yield the same algorithm as the dual simplex method. By considering a specific standard form problem and its dual, it is shown that the primal simplex method applied to the dual problem may require one or more changes of basis, unlike the dual simplex method where termination occurs immediately due to the specific structure of the problem.

In the given exercise, we have a standard form problem and its dual:

Primal Problem:

minimize 21x1 + 22x2

subject to x1 = 1

x1, x2 ≥ 0

Dual Problem:

maximize P1 + P2

subject to P1 < 1

P2 < 1

P1, P2 ≥ 0

Since there is only one possible basis in this case, the dual simplex method terminates immediately because of the specific structure of the problem.

However, if we convert the dual problem into standard form and apply the primal simplex method to it, one or more changes of basis may be required. This is because the primal simplex method operates differently from the dual simplex method and may encounter different pivot elements and entering/leaving variables during the iterations. These differences in the algorithm can lead to changes in the basis during the primal simplex method's execution.

Therefore, it is evident that converting the dual problem into standard form and applying the primal simplex method does not result in the same algorithm as the dual simplex method. The primal simplex method may require one or more changes of basis during its execution, unlike the dual simplex method, which terminates immediately in this specific problem due to the singular structure of the basis.

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If m∠ABP is 6n°, m∠ABC is a straight angle, which is always equal to 180°.

The angle bisector of ∠ABC divides the angle into two congruent angles, so we have:

m∠ABP = m∠CBP

Since these are angles on a straight line, we also have:

m∠ABP + m∠CBP = 180°

Substituting the given value for m∠ABP, we get:

6n° + m∠CBP = 180°

Solving for m∠CBP, we get:

m∠CBP = 180° - 6n°

Since ∠ABC is the sum of ∠ABP and ∠CBP, we have:

m∠ABC = m∠ABP + m∠CBP

Substituting the above expressions for m∠ABP and m∠CBP, we get:

m∠ABC = 6n° + (180° - 6n°) = 180°

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Complete question is:

The angle bisector of ∠ABC is BP. If m∠ABP is 6n°, what is m∠ABC?

\(3.05 \times 10 ^{8} m/s\)

\(3.15 \times 10 ^{7} \)

\(\rule{300pt}{3pt}\)

Multiply the speed of light with seconds in a year

*Note:- We will not change the values because speed of light is in m/s and the time is also given in seconds.

\(\rule{300pt}{3pt}\)

\(3.08 \times 10 ^{8} \times 3.15 \times 10 ^{7} \)

\((3.05 \times 3.15) \times (10 ^{8} \times 10 ^{7} )\)

\(9.4675 \times 10 ^{15} \)

\( \tt9.46 \: Trillion \: Kilometers\)

If the discriminant is negative, then neither of the solutions is a real number.

Since the discriminant is a negative number 7, then there is/are no real solutions to the quadratic equation.

Answer:

its A

Step-by-step explanation:

-x²+x+(4x²-x-1)

-x²+x+4x²-x-1

-x²+4x²-1

3x²-1

Answer:

Hey there!

Our equation can be: 2y+3=4y+2

Hope this helps :)

Answer:

2y+3=4y+2

I hope you got it..

Easy! The slope represents the rate of change or the steepness of a line. In this case, the population is decreasing by 300 people per year. Since the population is decreasing, the slope would be negative.

Therefore, the slope would be -300 (people per year).

The angles formed when two lines cross each other sum over one line 180º:

Then, if one part of the angle is 32º the other part is:

Hope this helps, have a nice day!!!

Our answers are

1 4/7 and 1 5/9

Answer:

26

Step-by-step explanation:

Read it as a row that gives you the answer

Answer:  A

Step-by-step explanation:

Notes: Dividing by a fraction means to multiply by its reciprocal.

           The denominator cannot equal zero.

\(\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}\)

Answer:

x = ±2\(\sqrt[]{2}\)-2

Step-by-step explanation:

x^2+4x-4=0

x^2+4x=4

x^2+4x+4=4+4

(x+2)^2=8

x = ±2\(\sqrt[]{2}\)-2

GD DAY AND NIGHT EMMANUEL MUDIAY