What is the correct classification of the system of equations below?
14x + 2y= 10
y+ 7x=-5
A.
parallel
B.
coincident
C.
intersecting

Answer:

sin(30)° = \(\frac{10}{x}\)

Step-by-step explanation:

By applying sine rule in the given triangle,

sin(30)° = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

sin(30)° = \(\frac{10}{x}\)

\(\frac{1}{2}= \frac{10}{x}\)

x = 2 × 10

x = 20

Therefore, answer will be sin(30)° = \(\frac{10}{x}\).

Answer:

1. (n-5)÷2 2. (n×2-8)+5 3. 5÷(8+n×2) 4. 8-(5×n) 5. 2÷(5-n) 6. (-n-5)² 7.

Answer: 31.5

The square root of 993 with one digit decimal accuracy is 31.5.

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Answer:

Step-by-step explanation:

C. 319 meters

Answer:

8d+20

Step-by-step explanation:

Just multiply whatever is outside the bracket in this case 4 by whatever is in the bracket (2d+5)

Answer:

value of x = 12

value of y = 8

Solving this will reveal that it will take more than 8hours for the temperature to reach this level.

Let t represent the duration in hours since the temperature began to rise. After t hours, the mercury will have risen by 2.5t degrees Celsius because the temperature is rising by 2.5°C every hour.

The inequality that indicates the number of hours needed for the average temp to rise over 20°C is as follows:2.5t + 0 > 20. When we simplify this inequality, we obtain:2.5t > 20 .

By multiplying equal parts by 2.5, we obtain:t > 8. As a result, it will take longer than eight hours for it temperature to exceed 20 °C.

We can express the hours required for the temperatures to exceed 20°C as the equation 2.5t > 20. Solving this imbalance will reveal that it will take more than 8hours for the temperature to reach this level.

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Answer:

420

Step-by-step explanation:

Take the the amount of pages(60) multiply it by the number of days (7)

you will get 420

Answer:

I think the answer is 4 because AP is congruent with PC

Answer:

P (greater than 3) = 1/2

Step-by-step explanation:

A standard number cube has 6 sides, numbered 1 through 6.

We want to find the probability of rolling a number greater than 3. To find this probability, create a fraction. The numerator is the amount of numbers greater than 3 and the denominator is the total amount of numbers.

P(greater than 3)= numbers greater than 3/ total numbers

There are 3 numbers that are greater than 3 (4, 5 and 6).

There are 6 total numbers (1, 2, 3, 4, 5, and 6)

P (greater than 3) = 3/6

This fraction can be simplified. Both the numerator and denominator can be divided by 3.

P (greater than 3) = (3/3) / (6/3)

P (greater than 3)= 1/ (6/3)

P(greater than 3) = 1/2

The probability of rolling a number greater than 3 is 1/2.

Here, we want to use the given number of 3's to get the answer of 5

Mathe matically, we can have this as;

By adding what we have above , we get 6

Dividing this by 3, we get 2

Then consequently, we add this to 3 and we get 5

The percentage of error in Pansy's measurement is 14.67%

In the given statement is :

Pansy measured the height of a window frame as 5.12 feet, but the actual height was 6 feet.

We know that

Percentage error can be calculated using the formula: (what was measured - the actual measurement) / actual measurement × 100%.

Thus:

The height that was measured = 5.12 feet

Actual measurement of the height = 6 feet

Percentage error = (6 - 5.12) / 6 × 100

Percentage error = 14.67

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The 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. 8: No masks or costumes were worn by contestants .

The possibility of an event occurring is described by the concept of probability. In real life, we frequently have to make predictions about the future. We might know about the result of an occasion.

We declare that there is a possibility that the event will take place when this occurs.

In conclusion, probability can be used in a lot of great ways in business, entertainment, and this new area of artificial intelligence.

By simply dividing the total number of possible outcomes by the favorable number, the probability of an event can be calculated using the probability formula.

n(A)=31 and n(B) = 20 and n(AB) =9

50-42 = 8

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Answer:

9.2oz

Step-by-step explanation:

Answer:

The stone will be in flight for 3 seconds

Step-by-step explanation:

Given the equation;

d = -16t^2 + vt + h

Where;

v = the initial velocity

h = the initial height

Given;

v = 48 ft/s

h = 0

Substituting into function d;

d = -16t^2 + 48t + 0

d = -16t^2 + 48t

At the point of launch and the point of landing d = 0.

We need to calculate the values of t for d to be equal to zero.

d = -16t^2 + 48t = 0

-16t^2 + 48t = 0

Factorising, we have;

16(-t+3)t = 0

So,

t = 0 or -t+3 = 0

t= 0 or t =3

Change in t is;

∆t = t2 - t1 = 3 - 0

∆t = 3 seconds.

The stone will be in flight for 3 seconds.

Answer:

2x²  +  3x  - 1   - 5/(5x +2)

Step-by-step explanation:

               2x²  +  3x  - 1  

             __________________            

  5x + 2 |   10x³ + 19x² + x - 7

             |  -10x³ -   4x²  

             |              15x² + x

             |            - 15x² - 6x  

             |                     - 5x  - 7

             |                      5x   +2

             |                             - 5

2x²  +  3x  - 1   - 5/(5x +2)

Answer:

414 have a great day :)

Step-by-step explanation:

(54−32)(9.2)

=(54−9)(9.2)

=(45)(9.2)

We can get heads for 200 times if we flipped the dime for 200 times.

What do you mean by Probability?

Probability is a mathematical measurement to measure the possibility of happening a particular incident or event mathematically.

Also, from the definition of probability, Probability is the ratio of the Number of Favorable event points to the number of total event points with respect to a particular event or incident.

\(Probability=\frac{Number of Favorable event Points}{Number of Total event Points}\)

According to the given problem,

The probability of getting heads is 1.

Total number of flip of dime is 200

so, we can get heads from 200 flips \(=200*1=200 Times\)

Hence, we get 200 heads from 200 flips of dime.

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Answer:

1. 128=x

2.37=x

3. 55=x

4. 15=x

5. 76=x

Step-by-step explanation:

Therefore, for spheres of different sizes, we need to use different measuring units, unlike prisms and pyramids, where a unit cube can be used as a standard unit for all shapes with the same base and height.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the measure of the total amount of space that an object takes up. The standard unit of volume is the cubic meter (m³) in the International System of Units (SI), but other units such as cubic centimeters (cm³) and cubic inches (in³) are also commonly used. The volume of an object can be calculated using different formulas depending on its shape and dimensions.

Here,

A unit sphere is not a good unit of volume measurement for all spheres because spheres come in various sizes and diameters. The unit sphere has a radius of 1, and while it can be used to measure the volume of spheres with radii equal to 1, it cannot be used to measure the volume of spheres with different radii.

For example, if we want to find the volume of a sphere with a radius of 2, we cannot use the unit sphere as a measuring unit. Instead, we would need to use a larger sphere with a radius of 2 as our measuring unit.

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Answer:

10 and 2

Step-by-step explanation:

10+2=12

10 is even

2*2=4  10-4+6

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The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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The general solution to the given differential equation is z(t) = C1*\(e^{(3t)}\) + C2*\(e^{(-3t)}\)

The given differential equation is a second-order linear homogeneous differential equation, which can be written as:

z'' + z' - 9z = 0

To find the general solution, we first need to solve the characteristic equation:

\(r^2\) + r - 9 = 0

By factoring or using the quadratic formula, we find the roots r1 and r2:

r1 = 3
r2 = -3

Since we have two distinct real roots, the general solution of the differential equation is:

z(t) = C1 * \(e^{(r1t)}\) + C2 * \(e^{(r2t)}\)
z(t) = C1 * \(e^{(3t)}\) + C2 * \(e^{(-3t)}\)

where C1 and C2 are arbitrary constants determined by initial conditions.

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The following are the formulas for the equired figures:

Rectangular Prism = l·w·h

l: length

w: width

h: height

Sphere = 4/3 ·π·r³

r: radius

Cylinder = π·h·r²

h: height

r: radius of the base

Cone = 1/3·π·r²·h

r: radius of the base

h: height

Triangular prism = 1/2·b·h·l

h: height

l: length

b: base

The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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Answer:

Direct Observation

Step-by-step explanation:

Some of the most common qualitative data collection techniques include open-ended surveys and questionnaires, interviews, focus groups, observation, case studies, and so on.

There are many methods used to collect or obtain data for statistical analysis. Three of the most popular methods are: Direct Observation • Experiments, and • Surveys. A survey solicits information from people; e.g. Gallup polls; pre-election polls; marketing surveys.

The alternative Hypothesis is that at least one of the mean total cholesterol levels is different from the others in the four groups of subjects.

A researcher can use an analysis of variance (ANOVA) parametric statistical method to determine if the mean total cholesterol level of the population is the same for four groups of subjects (Group 1 = Diet Restriction; Group 2 = Exercise; Group 3 = Both Diet and Exercise; Group 4 = None).

a. Statistical Test is ANOVA.
b. Null Hypothesis is that the mean total cholesterol level of the population is the same for all four groups.
c. Alternative Hypothesis is that the mean total cholesterol level of the population is different for at least one group.

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Answer:

105 mm

Step-by-step explanation:

The leaf is 10.5 centimeters, and every centimeter equals 10 milimeters, so you multiply the leaf's length by 10 to convert it.

10.5 * 10 = 105, and that's the result.