1. Use the elimination strategy to solve this linear system:
(1) 12c + 28d = 12 (2) -20c + 16d = 168

2. Determine the number of solutions of this linear system:
(1) 7x − 3y = 43 (2) 7x - 3y = 13 ​

Answer:

4.4 ounces/ 4 ounce (if rounded)

Step-by-step explanation:

There are 16 ounces in a pound, therefore the equation 12/16 will be useful since 16 ounces in a pound can be divided by 12, in conclusion 12/16=0.75 which is how much an ounce costs.

Then you will take $3.30 and divide it by 0.75 to get your answer for how many ounces you can buy for $3.30 which will equal 4.4 ounces but if you were to round it would be 4 ounces

Hope this helps!

Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2

Step-by-step explanation:

You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about

for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'

in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)

as such the line x = 4 will cut the function f(x) in 'half'

a.) a possible coordinate for the third vertex is (3.67, 0) or (-3.67, 0).

b.) No, there is no other point that could be the third vertex.

a. To find a possible coordinate for the third vertex, we need to consider the distance between the two given points and the given perimeter of the triangle. The two given points are (0, 0) and (3, 0), which means they lie on the x-axis.

Since the triangle has a perimeter of 11 units, we can calculate the length of one side by dividing the perimeter by 3, since a triangle has three sides of equal length.

The length of one side is 11 / 3 = 3.67 units (rounded to two decimal places). Since the two given points lie on the x-axis, the third vertex must lie somewhere on the line parallel to the x-axis and at a distance of 3.67 units away from either of the given points.

Let's consider the point (0, 0). If we move 3.67 units in either the positive or negative direction on the x-axis, we get two possible coordinates for the third vertex: (3.67, 0) or (-3.67, 0). These points complete the triangle with the given perimeter of 11 units.

Therefore, a possible coordinate for the third vertex is (3.67, 0) or (-3.67, 0).

b. No, there is no other point that could be the third vertex. Since the two given points are on the x-axis, any other point on the grid would either increase the perimeter of the triangle or create a degenerate triangle with zero area.

If we choose a point above or below the x-axis, it would increase the distance between that point and the x-axis, resulting in a longer side length and a larger perimeter than 11 units.

If we choose a point on a different line parallel to the x-axis, the distance between the two given points and the third point would be different, resulting in sides of unequal band an unequal perimeter.

Therefore, the only possible points for the third vertex are (3.67, 0) and (-3.67, 0) in order to satisfy both the given perimeter of 11 units and the condition that the triangle is non-degenerate.

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The calculated value of y in the diagram is (b) 80

From the question, we have the following parameters that can be used in our computation:

DE ia parallel to XY

Using the above as a guide, we have the following equation

y + 100 = 180

Evaluate the like terms

y = 80

Hence, the value of y is (b) 80

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In order to find restrictions in math, you need to find the values of the variable that would make the expression undefined.

This is usually done by setting the denominator of a rational expression equal to zero and solving for the variable.

For example, the expression

(x+2)/(x-1) is undefined when x=1, because the denominator is equal to zero. Therefore, x cannot be equal to 1.

In general, to find restrictions in math, you need to follow these steps:

Identify the expression that you want to find the restrictions for.

Set the denominator of the expression equal to zero.

Solve the equation for the variable.

The solutions to the equation are the values of the variable that would make the expression undefined.

It is important to note that not all expressions have restrictions.

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To add or subtract numbers using compensation,

We can adjust one or more of the numbers to make the calculation easier.

Let's use compensation to add 468 and 59:

Identify a friendly number to compensate with. A friendly number is one that is easy to work with mathematically. In this case, we can use 2.

Step 1: Identify a friendly number to compensate with.

A friendly number is one that is easy to work with mentally. In this case, we can use 60 as a friendly number.

Step 2: Compensate the numbers.

Since we are adding 468 and 59, we'll use the friendly number 60 to compensate for the difference.

Add or subtract the friendly number to one of the numbers to make the calculation easier. Let's add 2 to 468

468 + 2 = 470

Add or subtract the same amount from the other number. Since we added 2 to 468, we also add 2 to 59:

59 + 2 = 61

Perform the adjusted calculation:

470 + 61 = 531

Therefore, using compensation, we find that 468 + 59 is equal to 531.

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In the given graph, the diagram Z is not a function. A function is a set of ordered pairs where each x-value has only one y-value. The correct answer is (D) diagram Z is not a function.

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Answer:

B and F

Step-by-step explanation:

[Note: Work for this problem is shown in the image attached to this answer]

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Using the intermediate value theorem on the function f(x) = (x² + x)/(x - 3) on the interval [13/2,8] the value of c = 7.

The Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b] with its domain having values f(a) and f(b) at the endpoints of the interval, then the function takes any value between the values f(a) and f(b) at a point inside the interval.

Now, given the function f(x) = (x² + x)/(x - 3) on the interval [13/2,8] where f(c) = 14, we want to show using the intermediate value theorem that there is a value c such that 13/2 < c < 8

So, we proceed as follows.

Since  f(x) = (x² + x)/(x - 3)

Substituting x = c into the equation, we have that

f(c) = (c² + c)/(c - 3)

Now, f(c) = 14

So, we have that

14 = (c² + c)/(c - 3)

14(c - 3) = c² + c

Expanding the brackets, we have that

14c - 48 = c² + c

Re-arranging, we have that

c² + c - 14c + 48 = 0

c² - 13c + 48 = 0

Factorizing, we have

c² - 6c - 7c + 48 = 0

c(c - 6) - 7(c - 6) = 0

(c - 6)(c - 7) = 0

c - 6 = 0 or c - 7 = 0

c = 6 or c = 7

Since 6 does not lie in the interval [13/2, 8], we choose c = 7

So, the value of c = 7.

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The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The triangles in the coordinate plane are congruent to triangle A are: Triangles D and F

Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are the same size. These triangles can be moved, rotated, flipped, and flipped to make them look identical. When repositioned, they match each other.

The postulates of congruency follows:

SAS - Side Angle Side Congruency Postulate

SSS - Side Side Side Congruency Postulate

ASA - Angle Side Angle Congruency Postulate

AAS - Angle Angle Side Congruency Postulate

HL - Hypotenuse Leg Congruency Postulate

Looking at the attached image, the only two triangles that are congruent to Triangle A ae D and F.

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The effective rate of interest for 1 year with a principal of $15,500 and an interest rate of 12% compounded quarterly is 12.55%.

The effective annual interest rate (APY) is used to calculate the return on an investment after one year, including any compounding that occurs over the year. It is a crucial tool for determining the actual interest rate paid or earned on an investment. In this question, we will use the given information to calculate the APY or effective rate of interest for 1 year.
Given information:
Principal amount (P) = $15,500
Annual Interest rate (r) = 12%
Compounding periods per year (n) = 4 (since interest is compounded quarterly)
Time (t) = 1 year
Formula to calculate APY or effective rate of interest:
APY = (1 + r/n)ⁿ - 1
where r is the annual interest rate, n is the number of compounding periods in a year, and t is the time period for which interest is calculated.
Substituting the values, we get:
APY = (1 + 12%/4)⁴ - 1
APY = (1 + 0.03)⁴ - 1
APY = 1.1255 - 1
APY = 0.1255 or 12.55%
Therefore, the effective rate of interest for 1 year with a principal of $15,500 and an interest rate of 12% compounded quarterly is 12.55%.

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With a pound of flour costing $12 and considering that there are 16 ounces in a pound, the cost per ounce is $0.75. Thus, for $3.30, you can purchase 4.4 ounces of flour.

To find out how many ounces of flour can be purchased for $3.30, we need to determine the cost of one ounce of flour.

Given that a pound of flour costs $12, we know that there are 16 ounces in a pound (since there are 16 ounces in 1 pound). So, the cost of one ounce of flour can be calculated as:

Cost of one ounce of flour = Cost of one pound of flour / Number of ounces in one pound

Cost of one ounce of flour = $12 / 16 ounces

Cost of one ounce of flour = $0.75

Therefore, the cost of one ounce of flour is $0.75.

To determine how many ounces of flour can be purchased for $3.30, we divide the total amount of money by the cost of one ounce of flour:

Number of ounces of flour = Total money / Cost of one ounce of flour

Number of ounces of flour = $3.30 / $0.75

Number of ounces of flour ≈ 4.4 ounce

Therefore, for $3.30, approximately 4.4 ounces of flour can be purchased.

In summary, with the given cost of $12 for a pound of flour, and knowing that there are 16 ounces in a pound, we find that one ounce of flour costs $0.75. Thus, for $3.30, approximately 4.4 ounces of flour can be purchased.

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Answer:  y-intercept = (0, -3)

               x-intercepts: (-3,0), (1/2, 0) and (-1/2, 0)

Step-by-step explanation:

An y-intercept occurs when x=0 and you get (0,y)

Plug x=0 into function:

f(x)=(x+3)(4x²−1)

f(0) = (0+3) (4(0)²-1)

f(0) = (3)(-1)

f(0)= -3

y-intercept = (0, -3)

An x-intercept occurs when y=0 and you get (x, 0)

f(x)=(x+3)(4x²−1)

0 =(x+3)(4x²−1)                 >set each parentheses =0 to solve for x

(x+3)=0        and        (4x²−1)=0

x = -3          and            4x² = 1

                                     x² = 1/4

                                     x = ±(1/2)

There are 3 x-intercepts: (-3,0), (1/2, 0) and (-1/2, 0)

The distance between point T (-5, 1) and point I (-1, 1) is 4 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's apply this formula to find the distance between point T (-5, 1) and point I (-1, 1):

x1 = -5, y1 = 1 (coordinates of point T)

x2 = -1, y2 = 1 (coordinates of point I)

Plugging these values into the formula, we have:

Distance = √((-1 - (-5))² + (1 - 1)²)

        = √(4² + 0²)

        = √(16 + 0)

        = √16

        = 4

Therefore, the distance between point T (-5, 1) and point I (-1, 1) is 4 units.

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The sequence is geometric, with a common ratio of 1/3, and the missing terms are 12 and 4.

To determine if the sequence is arithmetic, geometric, or neither, let's examine the given terms: 972, 324, 108, 36.

To find the missing terms of the sequence, let's look for a pattern in the numbers:

If we divide each term by 3, we get:

972/3 = 324

324/3 = 108

108/3 = 36

It seems that each term is obtained by dividing the previous term by 3.

Now, let's check if the sequence is arithmetic or geometric:

If we calculate the common difference between consecutive terms, we see that there is no constant difference. For example:

324 - 972 = -648

108 - 324 = -216

36 - 108 = -72

Since the differences are not constant, the sequence is not arithmetic.

If we calculate the common ratio between consecutive terms by dividing a term by its previous term, we find that the ratio is constant:

324/972 = 1/3

108/324 = 1/3

36/108 = 1/3

The common ratio is 1/3, which indicates that the sequence is geometric.

The missing terms in the sequence are:

(36/3) = 12

(12/3) = 4

The complete sequence is: 972, 324, 108, 36, 12, 4.

The sequence is geometric, with a common ratio of 1/3, and the missing terms are 12 and 4.

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The missing dimensions of the given expressions are as follows:

1. 2x + 24 (81) → 24x2. (82) → 16 3. 2x (83) → 83x4. (84) → 42x

Given expressions are:1. 2x + 24 (81)2. (82) 3. 2x (83)4. (84) Let’s find the missing dimensions of the given expressions one by one:

1. 2x + 24 (81)We know that perimeter = 2 × length + 2 × breadth.

The given expression represents the perimeter of the rectangle. Here, the breadth of the rectangle is 24.

Therefore, length of the rectangle = 2x/2 = x.

So, the missing dimension is x. Dimension of the rectangle = x × 24 Expression of the rectangle as a product = 24x 2. (82)

The given expression represents the area of the rectangle.

Therefore, the two dimensions of the rectangle are (8) and (2). Dimension of the rectangle = 8 × 2 Expression of the rectangle as a product = 16 3. 2x (83)

The given expression represents the area of the rectangle.

Therefore, the two dimensions of the rectangle are (2) and (83/2). Dimension of the rectangle = 2 × 83/2 Expression of the rectangle as a product = 83x4. (84)

We know that perimeter = 2 × length + 2 × breadth The given expression represents the perimeter of the rectangle.

Here, the length of the rectangle is 84/2 = 42.

Therefore, breadth of the rectangle = 2x/2 = x.

So, the missing dimension is x.

Dimension of the rectangle = 42 × x

Expression of the rectangle as a product = 42x

Hence, the missing dimensions of the given expressions are as follows:

1. 2x + 24 (81) → 24x2. (82) → 16 3. 2x (83) → 83x4. (84) → 42x

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If the public swimming pool is open, then people may swim or dive into the pool. Therefore, if the time is between 8:00 a.m. and 6:00 p.m., then people may swim or dive into the pool

Based on the given statements, the conclusion would be:

"If the time is between 8:00 a.m. and 6:00 p.m., then people may swim or dive into the pool."

This conclusion follows logically from the premises given, as it combines the conditions stated in the first two statements.

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The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

The congruent linear pair angles ∠ADC and ∠BDC indicates that the measure of the angle ∠BDC is half of 180° or m∠BDC = 90°

Please find attached the drawing of the flow chart to prove that the measure of the angle ∠BDC = 90°

Linear pair angles are adjacent angles that share a arm, with the other arm of each angle forming a straight lines. These are adjacent angles that have a sum of 180°.

The completed flow chart can be presented as follows;

The label corresponding to the linear pear theorem is; mADC is supplementary to m∠BDC

The label corresponding to; definition of supplementary angles is the option; mADC + m∠BDC = 180°

The label corresponding to substitution property of equality is the option; 2·m∠BDC = 180°

The label corresponding to division property of equality is the option; m∠BDC = 90°

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The statements are completed as;

3. sin A = -cos B

4. The relationship between the acute angles of a right triangle is that the angles are complementary

5. sin A = 1/cosec A

6. tan A = cot B

7. tan A = opposite/adjacent

First, we need to know that the six trigonometric identities are given as;

The relationship between these identities are;

tan θ =sinθ/cosθ

cot θ = cos θ/sin θ

sec θ= 1/cos θ

sin θ = 1/cosec θ

The relationship between the acute angles of a right triangle is that the angles are complementary

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The sum of the first 19 terms of the sequence is 1254.From the given options, the correct answer is (3) 1254.

To find the sum of the first 19 terms of the sequence, we need to identify the pattern and use the formula for the sum of an arithmetic series.

Looking at the given sequence, we can see that each term is obtained by adding 7 to the previous term. So, the common difference is 7.

The formula for the sum of an arithmetic series is:

Sn= (n/2)(2a + (n-1)d),

where Sn is the sum of the first n terms, a is the first term, and d is the common difference.

In our case, the first term a is 3, and the common difference d is 7.

Plugging these values into the formula, we have:

S19 = (19/2)(2(3) + (19-1)(7)).

Simplifying the equation:

S19 = (19/2)(6 + 18(7)).

S19 = (19/2)(6 + 126).

S19 = (19/2)(132).

S19 = 19(66).

S19 = 1254.

Therefore, the sum of the first 19 terms of the sequence is 1254.From the given options, the correct answer is (3) 1254.

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