Higher Order Thinking Determine the
number of solutions for this system of
equations by inspection only. Explain.
3x - 4y = 6
12x - 16y= 24

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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The z-score of the datum 75.4 is approximately -1.31. Option b is the correct answer.

To calculate the z-score of the datum 75.4, we can use the formula: z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. Given that μ = 78.2 and σ = 2.13, we can substitute these values into the formula:

z = (75.4 - 78.2) / 2.13

Calculating this expression, we get:

z ≈ -1.31

Therefore, the z-score is approximately -1.31. Hence, option b is the correct naswer.

The z-score is a measure of how many standard deviations a particular data point is away from the mean. To calculate the z-score, we subtract the mean from the data point and divide the result by the standard deviation. In this case, the mean (μ) is 78.2 and the standard deviation (σ) is 2.13. By substituting these values into the z-score formula and performing the calculation, we find that the z-score for the datum 75.4 is approximately -1.31. This negative value indicates that the datum is about 1.31 standard deviations below the mean.

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Answer:

The answer would be $12. You would need to change the 30% to 0.3 then multiply by $20. Then take the -$6 and subtract it by $20.

The area of the sector is 11.75 metres squared.

The area of the sector can be calculated as follows:

area of a sector = ∅ / 360 × πr²

where

Therefore,

r = 3 metres

∅= 150 degrees

Therefore,

area of the sector = 150 / 360 × 3.14 × 3²

area of the sector = 150 / 360 × 3.14 × 9

area of the sector = 4239 / 360

area of the sector = 11.775 metres squared

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When a graph is non-proportional, it will always satisfy the condition mentioned in option D: the graph will not pass through the origin (0, 0). This means that option D is the correct answer choice.

A non-proportional graph represents a relationship where the dependent variable does not vary directly with the independent variable. In other words, the ratio of the dependent variable to the independent variable is not constant. This implies that the graph will not pass through the origin (0, 0) since a proportional relationship would require the origin to be included.

Options A and B are incorrect because the slope of a non-proportional graph can be positive, negative, or even zero. It is not restricted to any particular sign. Option C is also incorrect because a non-proportional graph may or may not pass through the origin. Therefore, the correct answer is option D: the graph will not pass through (0, 0).

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To draw the image of quadrilateral ABCD under a translation by 1 unit to the right and 4 units up, we will move each point of the quadrilateral in the specified direction.

Let's assume the coordinates of the original quadrilateral ABCD are as follows:

A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), D(x₄, y₄)

To perform the translation, we will add the given values to the x-coordinates and y-coordinates of each point:

A'(x₁ + 1, y₁ + 4), B'(x₂ + 1, y₂ + 4), C'(x₃ + 1, y₃ + 4), D'(x₄ + 1, y₄ + 4)

Now, plot the original quadrilateral ABCD and then move each point to its corresponding new position.

For example, if point A had coordinates (2, 3), after the translation, it will move to (2 + 1, 3 + 4) = (3, 7). Similarly, you can calculate the new coordinates for points B, C, and D using the same process.

Once you have the new coordinates for each point, connect them to form the image of the quadrilateral ABCD under the translation.

The new quadrilateral A'B'C'D' will be a shifted version of the original quadrilateral, 1 unit to the right and 4 units up.

It's important to note that the scale and proportions of the quadrilateral will remain the same after the translation. Only its position in the coordinate plane will change.

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Answer:

x=75

Step-by-step explanation:

Knowing that

a=72 and that

b=33 you add both to get 105

and because triangles entire angle is 180 you subtract 180 to 105

Answer:1.f=2-(20)

2.21 ---2=F

Step-by-step explanation:Dats my answer in my paper

Answer:

12.40

Step-by-step explanation:

\(223.20 \div 18\)

that will give you the answer of 12.40 for each unit.

Answer:

Step-by-step explanation:

1 box costs x amount

18 boxes cos 223.20

Cross multiply

223.20 * 1 = 18 x

Divide by 18

223.20 / 18 = 18x / 18

x = 12.40

Cost of 1 box is 12.40

The similarity statement that would be true for the given figure is;

A. ∆ DAB ~∆ DAC

Similar triangles are those triangles that have the same proportionate side lengths as well as related angle measurements.

here, we have,

Two triangles are said to be similar if their corresponding angles and sides have the same ratio. Similar triangles will possess the same form but may or may not have the same size.

The SAS similarity rule states that If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then it means that the two triangles are similar.

The Side-Side-Side (SSS) similarity rule states that If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

In this question, when we analyze the triangles well, it is clear that;

DA is congruent to itself by reflexive property of congruence.

Thus, we can say that ΔDAB is similar to ΔDAC,

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\(\dfrac{5-i}{4+3i}=\dfrac{(5-i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{20-15i-4i-3}{16+9}=\dfrac{17-19i}{25}=\dfrac{17}{25}-\dfrac{19}{25}i\)

The equation for breaking even is, 2x + 15 = 5x.

We have, Sandra makes and sells bracelets. It costs her $2 to make each bracelet, plus a one-time cost of $15 for supplies. She plans to sell each bracelet for $5.

Therefore we have,

The number of bracelets that Sandra needs to sell in order to break even can be solved by equating the total cost to her total revenue.

If the x represents the number of bracelets,

The total cost would be, 2x + 15.

Her total revenue from sales is expressed as 5x.

Thus, the equation for breaking even is,

                                       2x + 15 = 5x

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Answer:

1

Step-by-step explanation:

Answer:

hope it will helpful for uhh

make me brainliest plz

Answer:

x = 6

Step-by-step explanation:

3x - 2 = 2x + 4

First, we need only 1 set of x, so I'll subtract the smallest x from the other.

-2x both sides.

x - 2 = 4

Next, add +2 to both sides. (In these types of questions always do the inverse!)

And so your answer is:

x = 6

Answer:

x = 6

Step-by-step explanation:

1. Add  2  to both sides of the equation

3x - 2 = 2x + 4

3x - 2 + 2 = 2x + 4 + 2

2. Simplify  

3x = 2x + 6

3. Subtract 2x from both sides of the Equation

3x - 2x = 2x  + 6 - 2x

4. Simplify

x = 6

Answer: 13 (simplified)

Step-by-step explanation: 9 + 4= 13, minus 9  equals 4

Answer: Question: x-9=4

Step-by-step explanation: X is 13

Within the third step of the control process, management by exception is a principle that states that managers should be informed of a situation only if data show a significant deviation from standards.

The third step of the process of controlling is to compare the actual performance of the organization with the established standards. By comparing the actual performance with the standards, an organization can determine the deviation between them.

The final step of the control process is the correction of deviations to improve the performance so that in the future it matches with the plan. Establishing standards and methods for measuring performance. Measuring performance. Determine if performance is up to par. take corrective action. The marginal rate of return reduction is set to reduce the factor's marginal rate of return.

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Answer:

135 m

Step-by-step explanation:

Draw a diagram, set your calculator to degrees and solve.

Answer:

\(y = -3+ rx\)

Step-by-step explanation:

Given

\(Base = -3C\)

\(Time = x\)

Required

Determine the equation (y)

Let the steady rate be represented with r.

So, the equation (y) can be determined using:

\(y = Base + Rate * Time\)

\(y = -3+ r* x\)

\(y = -3+ rx\)

Using the triangle sum theorem and other definitions, the measures of the other numbered angles are:

m∠5 = 68°

m∠3 = 35°

m∠4 = 112°

m∠7 = 145°

m∠2 = 77°

In a triangle, all the three interior angles will add up to give a sum of 180 degrees according to the triangle sum theorem.

The alternate interior angles theorem states that any two angles that lie alternate to each other, they will have the same angle measure

Given the angle measures:

m∠1 = 68°

m∠6 = 35°

Therefore:

m∠5 = m∠1 [alternate interior angles theorem]

m∠5 = 68°

m∠3 = m∠6 [alternate interior angles theorem]

m∠3 = 35°

m∠4 = 180 - m∠5 [definition of linear pair]

m∠4 = 180 - 68

m∠4 = 112°

m∠7 = 180 - m∠6 [definition of linear pair]

m∠7 = 180 - 35

m∠7 = 145°

m∠2 = 180 - m∠5 - m∠6 [triangle sum theorem]

m∠2 = 180 - 68 - 35

m∠2 = 77°

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Answer:

O.225

Step-by-step explanation:

Two negatives = positive

Answer:

.255

Step-by-step explanation:

.255

Answer:

4 pairs cost $64

Step-by-step explanation:

16*4=64$

Answer:

MIT economics professor Richard Bookstaber put it simply in his book “The End of Theory”: “No man is better than a machine, and no machine is better than a man with a machine.” ... Humans are too emotion-driven and susceptible cognitive biases, while machines lack an understanding of human thinking.

Answer:

yesThe Liverpool researchers estimate that the robot is able to work 1,000 times faster than a human scientist, and highlight that it is “unlikely a human researcher would have persevered with this multivariate experiment using manual approaches given that it might have taken 50 experiments or 25 days

Step-by-step explanation:

T : S

5 : 95

1 : 19

Tu : S

6. : 48

1. : 8

10 : 80

There are 19 students per teacher.

There are 8 students per teacher.

The school will need 10 tutors if there is 80 students.

A rate ratio  two groups' incidence, person-time, or mortality rates. The two groups are often distinguished by demographic traits or by exposure to a suspected causal agent, similar to how the risk ratio distinguishes them.

The jar contains nine quarters, three dimes, and one nickel, for a ratio of nine to three to one. As a result, the ratio of pennies to quarters is 6: 7. c. Sum up the pennies to quarters ratio. The amount of dime coins to all the coins should be written down.

How should a rate ratio be written?

A ratio can be expressed as a fraction 35, 3:5, or with a colon. In contrast, a rate is a comparison of two quantities that may have several units. A rate might be, for instance, 5 miles every 3 hours or 34 dollars per square foot.

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Answer:

\(1.9 \sqrt{3} \)

Step-by-step explanation:

3.8 is 2x 3.8/2 is 1.9

Answer:

(3,60)

Step-by-step explanation:

Marc is walking at a rate of 20 minutes per 1 mile; therefore, at that rate he can walk 3 miles in 60 minutes.

Answer: the answer is 13.6 units

Step-by-step explanation:

Answer:

C. 13.6 units

Step-by-step explanation:

i took the quiz on edge

Answer:

1064

Step-by-step explanation:

Answer: 1064

Step-by-step explanation: