Determine if the rates are equivalent. Explain your reasoning.5 cans of soup for $3.75; 8 cans of soup for $6.00

The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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None of the ordered pairs (1, 0), (-1, 1), (2, 2), and (0, 3) make both inequalities true.

To determine which ordered pair makes both inequalities true, we can substitute the given values into the inequalities and check for validity:

1. (1, 0):

  For y > -3x + 3: 0 > -3(1) + 3 -> 0 > 0, which is not true.

  For y < 2x - 2: 0 < 2(1) - 2 -> 0 < 0, which is not true.

  Therefore, (1, 0) does not satisfy both inequalities.

2. (-1, 1):

  For y > -3x + 3: 1 > -3(-1) + 3 -> 1 > 6, which is not true.

  For y < 2x - 2: 1 < 2(-1) - 2 -> 1 < -4, which is not true.

  Therefore, (-1, 1) does not satisfy both inequalities.

3. (2, 2):

  For y > -3x + 3: 2 > -3(2) + 3 -> 2 > -3, which is true.

  For y < 2x - 2: 2 < 2(2) - 2 -> 2 < 2, which is not true.

  Therefore, (2, 2) does not satisfy both inequalities.

4. (0, 3):

  For y > -3x + 3: 3 > -3(0) + 3 -> 3 > 3, which is not true.

  For y < 2x - 2: 3 < 2(0) - 2 -> 3 < -2, which is not true.

  Therefore, (0, 3) does not satisfy both inequalities.

None of the given ordered pairs satisfy both inequalities simultaneously.

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The final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

What is the interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.

We have,

F and H are sets of real numbers defined as follows.

F = { v l v < 4}

H = { v l v ≥ 7}

F is the set of all real numbers that are less than or equal to 4.  H is the set of real numbers greater than 7.

F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:

F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets.  Hence the answer is the empty set, Ø:

F ∩ H = Ø

F ∩ H = [7, 4]

F ∪ H = [-∞, ∞]

Hence, the final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

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Answer:

21

Step-by-step explanation:

Answer:

Its 21

Step-by-step explanation:

The motion of the skier from point A to point B, then to point C, and then point D, indicates that the distances and displacement traveled are;

a) The distance from A to C is 280 meters

b) The distance from point A to point D is 360 meters

c) The displacement of the skier from point B to point C is 120 meters.

Displacement is the change in the position or location of the object.

The possible diagram of the skier in the question can be presented as follows;

A \({}\)                            C                                                   D                          B

t = 0 min      \({}\)         t = 2 min                                       t = 3 min            \({}\)t = 1 min

ʂ         \({}\)                     ʂ                                                     ʂ                           ʂ

-|-------|------|------|------|-----|------|-----|------|------|-------|-------|--------|-------|-------|-----

0           \({}\)   20           40         60          80            100    120    140           160

The above diagram indicates that we get;

a) The distance from point A (t = 0 min) to point C(t = 2 min) is can be found as follows;

The skier moves from point A to point B then from point B to point C, therefore,

The distance from point A to point B = 160 m - 0 m = 160 m

The distance from point B to point C = 160 m - 40 m = 120 m

The distance from point A to point C is therefore;

b) The distance from point A to point D = The distance from point A to point C + The distance from point C to point D as follows;

AD = AC + CD

CD = 120 m - 40 m = 80 m

Therefore;

AD = 280 m + 80 m = 360 m

c) The displacement of the skier from point B (t = 1 min) to C (t = 2 min) can be found as follows;

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Answer:

The answer to the question is B or 8

Step-by-step explanation:

this is because ther is 3x meaning three time what ever the answer is and because 8x3=24 it is equal to 24 so 24 is less than or equal to 24 hence the corr6 answer is 8.

Answer:

the answer is 8

Alex spend $1507.92 in total to buy this stock at 3% charges on each shares.

Shares represent equity ownership in a corporation or financial asset, owned by investors who exchange capital in return for these units.

Alex buys 30 shares of Walmart at the close price of $48.80.

His broker charges him 3% of each share.

Purchasing of 30 shares =48.80 *30

                                         =$1464

Now we have to find the 3% of total purchasing of shares.

So,

Broker's fees =\(\frac{3}{100}*1464\)

                      = 0.03 * 1464

                      = 43.92

So, total cost of stock= 1464+43.92

                                   = 1507.92

Hence, Alex spend $1507.92 in total to buy this stock.

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The polynomial with complex coefficients of the smallest possible degree is found as: P(x) = x⁴ + 17x² + 16.

The given zeroes for the polynomial is-

4i and 1i.

From the conjugate zeroes theorem, for the polynomial having eal coefficients.

Then, -4i and -i is also the zeroes of the polynomial.

Thus, forming the polynomial P(x).

P(x) = (x + i)(x - i).(x + 4i)(x - 4i)

Using the property.

P(x) = (x² - i²).(x² - (4i)²)

We know that, i² = -1

P(x) = (x² + 1).(x² + 16)

Simplifying the equation;

P(x) = x⁴ + 17x² + 16

In which the coefficient of the highest power (x⁴) is 1.

Thus, the polynomial with complex coefficients of the smallest possible degree is found as: P(x) = x⁴ + 17x² + 16.

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Given statement solution is :- a) The area of one semi-circle at one end is  58.09 square feet.

b) The area of the garden is 274.42 square feet.

c) The area in square metres is approximately 58.09 square feet.

The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.

Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.

Now we can calculate the area of the semi-circle:

A = (π * 4.3²) / 2

A ≈ 58.09 square feet

b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.

Area of the rectangular portion = length * width

Area of the rectangular portion = 18.4 feet * 8.6 feet

Area of the rectangular portion ≈ 158.24 square feet

Area of the two semi-circles = 2 * (area of one semi-circle)

Area of the two semi-circles ≈ 2 * 58.09 square feet

Area of the two semi-circles ≈ 116.18 square feet

Total area of the garden = area of the rectangular portion + area of the two semi-circles

Total area of the garden ≈ 158.24 square feet + 116.18 square feet

Total area of the garden ≈ 274.42 square feet

c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.

Area in square meters = Total area of the garden * (0.3048)²

Area in square meters ≈ 274.42 square feet * 0.3048²

Area in square meters ≈ 25.49 square meters

Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

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Answer:

148 children and 140 adults were admitted.

Step-by-step explanation:

Given that the admission fee at an amusement park is $ 3.50 for children and $ 13.00 for adults and on a certain day, 288 people entered the park, and the admission fees collected totaled $ 2,338.00, to determine how many children and how many adults were admitted you must be perform the following calculation:

13 - 3.5 = 9.50

288 x 3.50 = X

1.008 = X

2338 - 1008 = 1330

1330 / 9.5 = 140

288 - 140 = 148

148 x 3.5 + 140 x 13 = X

2338 = X

Therefore, 148 children and 140 adults were admitted.

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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Answer:

it is one

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

Answer:

15 dollars

Step-by-step explanation:

Answer:

B. 14,525

Step-by-step explanation:

If a tablet costs $35 and the school is purchasing tablets for every student, then the total cost to buy tablets for the whole school would be:

$35 x 415 = $14,525

Therefore, the answer is B. $14,525.

There are zero possible triangles.

There are basically six different types of triangles with respect to the length and measure of the lines and angles of a triangle, respectively.

In general, there will be 0 or 2 potential triangles if the supplied angle is opposite the shorter of the two specified sides.

If the sides-to-angle ratio is smaller than the sine of the angle, then there are no triangles that could possibly exist. There are two possible triangles if the ratio of sides is higher. There is only one feasible triangle if the specified angle is opposite the longer of the two given sides. If the specified angle is between the two given sides, the same holds true.

Here, 32/65 ≈ 0.4923

sin(79°) ≈ 0.9816.

The ratio of sides is smaller, so there are zero possible triangles.

Thus, the number of triangles ABC possible with the given parts is zero.

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Answer:

6555

Step-by-step explanation:

Again you can you Distributive property to answer this question here is how-To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Answer:

6555

Step-by-step explanation:

The vector component along the horizontal direction is 1.77 m/s and along the vertical direction is 1.77 m/s.

To find the vector components along the horizontal and vertical directions for a, we can use the Pythagorean theorem and basic trigonometry. The hypotenuse of the triangle formed by the vector is 2.5 \(m/s^2\), and the angle is 45°. We can use the Pythagorean theorem to solve for the horizontal component, which would be 1.77 m/s. We can then use basic trigonometry to solve for the vertical component, which also comes out to be 1.77 m/s.

Hence, the vector component along the horizontal direction is 1.77 m/s and along the vertical direction is 1.77 m/s.

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The bearing here is given as 54.89 degrees degrees

The distance that the puffin flies is 38 km due to the east

Then the distance is 54 km due to the north

We would have the height h = √(p²+b²)

We would have to solve this out such that :

=√54²+38²

h = 66.03 units

From here we would have to solve for sine θ

sin θ = 54 / 66.03

sine θ = 0.818

θ = sin ⁻¹0.818

= 54.89 degrees

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Answer:

B. 78

Step-by-step explanation:

78 It is the most frequent data (2)

Hope this helps

The linear function is V(x) = 800x + 2400.

Given,

The cost of computer when purchased (the initial book value), V = 2400 (x = 0)

Company chooses to depreciate for 3 years using straight line method.

The book value after 3 years = 0 (x = 3)

We have to write a linear function that expresses the book value of the computer as a function of its age V(x).

Here, the value is depreciating over 3 years.

That is 2400 in 3 years = 2400/3 = 800

That is depreciating $800 in a year.

Now we can write the equation as:

V(x) = 800x + 2400

When we consider slope-intercept form, we can check that the above given equation of a line passes through two points: (0, 2400) and (3, 0)

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Step-by-step explanation:

51x + 23y = 116 ……….. (i)

23x + 51y = 106 ………… (ii)

Subtracting (ii) from (i)

28x – 28y = 10

28(x – y) = 10

⇒ (x – y) = 10/28 = 5/14

The solution of the expression x- y is 5/14.

Given Equation:

Equation 1: 51x + 23y = 116

Equation 2: 23x + 51y = 106

Now, multiply 23 in equation 1 and 51 in equation 2 gives

Equation 3: 1173x + 529y = 2,668

Equation 4: 1173x + 2601 y = 5406

Solving the Equation 1 and (3) gives

2601y - 529y = 5406 - 2668

2072y= 2738

y = 37/28.

Substituting the value of y= 37/28 in Equation 1 gives

51x + 23(37/28)= 116

51 x= 2397/28

x= 47/28

So, the value of x-y

= 47/28 - 37/28

= 10/28

= 5/14

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Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

9514 1404 393

Answer:

  x = {7, 1, -4}

Step-by-step explanation:

Dividing the given factor from the polynomial using synthetic division, we get ...

  f(x) = (x -7)(x^2 +3x -4)

Factoring the quadratic* gives ...

  f(x) = (x -7)(x -1)(x +4)

The zeros are the values of x that make these factors be zero:

  x = {7, 1, -4}

_____

* The constants in the binomial factors are factors of -4 that have a sum of +3. Those are (-1)(4) = -4. -1+4 = 3.

Answer:

1 out of 3 people vote for junior

Step-by-step explanation: