Solve this system of equations by graphing. First graph the equations, and then type the solution.
3x-y=-6
y=x+4
The solution is (_,_)

The expression represents the area of the room not covered by the rug is A(x) = 2x² - 22x + 144.

Area of room = 3x² + 2x

Area of rug = x² + 24x - 144

We have to find the area of the room not covered by the rug.

Area of the room not covered by the rug = Area of the room - Area of rug

= (3x² + 2x) - (x² + 24x - 144)

= 3x² + 2x - x² - 24x + 144

= (3x² - x²) + (2x - 24x) + 144

= 2x² - 22x + 144

Hence, 2x² - 22x + 144 is the required expression for the area of the floor not covered by the rug.

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The particle is at the point (-1.112,3.909) after traveling for 20 microseconds.

We have been given a circle,

(x-3)²+(y-4)²=25

whose center is (3,4)

and with a radius of 5 units.

The particle starts at (3,-1) which is the 6 o'clock position in the circle, and ends at (8,4) after 7 microseconds which are at the 3 o'clock position in the circle.

So, the particle traveled 1/4 of the circumference of the circle in 7 microseconds

therefore according to the unitary method it will travel 5/7 of the circumference of the given circle.

so it will subtend 2π×5/7 of the circle from (3,-1)

from the polar form of the circle and the shifting of center of the circle we can conclude

that it's location will be

(5 × cos (10π/7) - 3 , 5 × sin (10π/7) - 4)

= (-1.112,3.909)

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Answer: 0.35x + 12.00 = 14.35

Explanation: You would make sure to include the x since we are unsure of how many apples to bought, we know the total it will be at the other side of the equal sign, she spent 12 on her groceries so we would add that to the number of apples she got.

Answer:

A. C(x) = 495,000 (1.0325)^ x

Step-by-step explanation:

c(x) = 495,000 x (1+3.25%)^x

= 495,000(1.0325)

For x = 0, the sides of parallelogram are equal.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are six crucial parallelogram characteristics to be aware of:

Congruent sides are those when AB = DC.

Congruent opposite angels are D = B.

(A + D = 180°) Consecutive angles are supplementary.

All angles are correct if just one of them is.

A parallelogram's diagonals cut each other in half.

A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides.

As the sides of parallelogram are parallel and equal,

2x + 15 = x + 15

2x = x

x = 0

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The solution of a system of equations for a graph that intersects at (0, 6) is given by the ordered pair (0, 6).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines representing a system of linear equations cross each other (intersect), which is depicted by an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.

By critically observing the graph of the lines representing the system of linear equations, you would notice that the correct solution set lies on Quadrant I and it represents the y-intercept of the graph.

In conclusion, the ordered pair (0, 6) represents the point of intersection and solution set to the system of linear equations represented by the graph.

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The new pair of basketball shoes become a "desire" because Frankie already owns a pair that he can use for the tryout. Frankie's new basketball shoes would be viewed as a "need" if he didn't already have a pair for the tryout.

When referring to possessing or acquiring specific commodities, people frequently use the terms "want" and "need" interchangeably. In terms of economics, a need is what a person needs in order to survive. If a certain need is not met, a person may get sick or perhaps pass away. On the other hand, a desire is something that a person hopes to achieve in the near or distant future. In the first instance, Frankie is able to attend the tryout in a pair of basketball shoes that he already has. He could wear the shoes he already owns, thus the new pair of shoes would be his desire. In contrast, Frankie needs a new pair of sneakers in the second scenario because he doesn't have any basketball shoes for the tryout.

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The equation for Tomas and Emilio birthday party's celebration is 200 = 45.99 + 17p

In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal.

Here we have know that seven friends accept the invitation to the twins' birthday party.

Where the possible equation that can be set up will have the total budget equal to total expenses.

So it can be written as the Total Cost of party is 200,

Then the amount can be divided as

=> Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

Let us consider that if p people attend the party, then the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.

Hence the equation will be written as

=> 200 = 45.99 + 12.50p + 4.50p

=> 200 = 45.99 + 17p

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The reflected function is the one below:

g(x) = -√x

This function is represented by the last table.

For a general function y = f(x), we define a reflection over the x-axis as:

g(x) = -f(x)

In this case f(x)=  √x, then the reflected function will be:

g(x) = -f(x) = -√x

Now we can evaluate this function to get some pairs of values.

Then when x = 1

g(1) = -√1 = -1

g(2) = -√2 = -1.41

And so on.

Then the correct option is the last table.

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By distributive property (5k + 2m)(3p + 4s) this we get   15kp + 20 ks + 6mp +8ms.

It is possible to multiply a single value by two or more values enclosed in a set of parenthesis using the distributive property, an algebraic property.

According to the distributive property, it is necessary to multiply each of the two terms by the factor when adding two terms to a factor. Only then may the addition operation be done. The following is a symbol for this property:

A (B+ C)=AB + AC

When there are three distinct values for A, B, and C.

Example : (5k + 2m)(3p + 4s)

Apply FOIL method:

(a + b) (c + d) = ac + ad + bc + bd

(5k + 2m)(3p + 4s) = 5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s

5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s

Simplify 5k . 3p + 5k . 4s + 2m .3p + 2m .4s : 15kp + 20 ks + 6mp +8ms

= 15kp + 20 ks + 6mp +8ms.

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45 percent of the 8th graders estimated they spend less than an hour a day on social media. The solution has been obtained by using concept of frequency.

What is frequency?

The frequency of a specific value in a set of data is how frequently it appears. Typically, we would keep track of data frequency in a frequency table.

We are given that 17 8th graders spent more than an hour a day on social media and 14 8th graders spent less than an hour a day on social media.

The total 8th graders who spent time on social media is 14 + 17 = 31

The percentage of the 8th graders estimated they spend less than an hour a day on social media is

= 14*100/31

= 45.16%

= 45%

Hence, 45 percent of the 8th graders estimated they spend less than an hour a day on social media.

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Answer: a-4b

Step-by-step explanation:

Combine like terms

4a-6b-3a+2b

1a-6b+2b

a-6b+2b

a-4b

Answer:

Step-by-step explanation:

I think it's 6 but I am not positive. I would double check it

Answer:

30

Step-by-step explanation:

Because it is an isosceles triangle, then only two sides of the triangle are of the same length and since it said one angle of the triangle is 120° there are still 60° left, so split that into two, and it equals 30° for both equal sides

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Answer:

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

What factors determine if one relationship is proportional?

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

What are the two proportional relationships principles?

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Step-by-step explanation:

The expected value for each set of 50 items that Sammi sells is $1.82.

The expected value can be calculated by multiplying the profit from each successful sale by the probability of making that sale, and then subtracting the expected cost of each defective item.

Expected value = (Profit from each successful sale * Probability of making that sale) - (Expected cost of each defective item)

Let's assume that Sammi plans to sell 50 items. So, the probability of a successful sale is 49/50 = 0.98. The expected cost of each defective item is $7.

Expected value = ($2 * 0.98) - ($7 * 1/50) = $1.96 - $0.14 = $1.82

So, the expected value for each set of 50 items that Sammi sells is $1.82.

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Answer:

because they are not equal in size

The value of the variables 'x' and 'y' will be 47° and 27°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

The equations are given below.

2y = 180° - 126°

2y = 54°

y = 27°

2x + 1 = 180° - 85°

2x + 1 = 95°

2x = 94°

x = 47°

The value of the variables 'x' and 'y' will be 47° and 27°, respectively.

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Answer: 30$

Step-by-step explanation:

To find the slope of the equation, you can use the formula (y2-y1)/(x2-x1). Plugging the points the question gives us we can get:

(205-100)/(5-2)

= 105 / 3

= 35

Plugging this information along with a point into the formula y = mx + b:

100 = 35*2 + b

100 = 70 + b

b = 30

y = 35x + 30

To double check this is correct:

y = 35 * 5 + 30

y = 175 + 30

y = 205

(5,205) is a point therefore y = 35x + 30 is the equation

Because the x of the graph represents the number of months, the initial membership fee would be when x = 0.

y = 35*0 + 30

y = 30$

In the given parallelogram, the value of g is 116 degrees and that of h is 64 degrees.

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a type of quadrilateral with opposite pairs of sides that are parallel and equal. The diagram depicts a parallelogram ABCD with AB II CD and AD II BC. In addition, AD = BC and AB = CD. Non-Example: A trapezium is a parallelogram's non-example.

Here,

Since the given figure is parallelogram. Opposite angles are equal.

g=116 degree

h=64 degree

The value of g is 116 degrees and that of h is 64 degrees in the given parallelogram.

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Answer:d

Step-by-step explanation:

The equation of a circle with center located at (5,2) and that is tangent to the y-axis is given as follows:

C. x² + y² - 10x - 4y + 4 = 0.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Considering the center, we have that:

(x - 5)² + (y - 2)² = r².

The circle is tangent to the y-axis, meaning that it passes through the point (0, 2), thus the radius is obtained as follows:

r² = 25.

Then the equation in standard form is given as follows:

x² - 10x + 25 + y² - 4y + 4 - 25 = 0.

x² + y² - 10x - 4y + 4 = 0.

Meaning that option C is correct.

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The distance between G and H on the number line  -12 and -2 is -10.

What is Distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language .

The phrase is widely used metaphorically to refer to a measurement of the degree of difference between two similar objects since spatial cognition is a rich source of conceptual metaphors in human thought.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.  

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that each real number and each point on a number line relate to one another.

We are given two point G and H which are represented on number line;

The value G = -12 and H = -2

We have to find the distance between them;

So , we can simply subtract these two values of  G and H to get the distance between them;

distance = -12-(-2)

             = -12 + 2

             = -10

Therefore, the distance between G and H on the number line  -12 and -2 is -10.

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     A variable whose value is decided by a random process or experiment is known as a random variable.

    Depending on how the experiment or random process turns out, it may have a range of distinct numerical values. Random variables come in two varieties: discrete and continuous. A continuous random variable can take on any value within a specific range, such as real numbers, but a discrete random variable can only take on a countable number of values, such as integers.

This random variable has the following distribution and is discrete in nature:

P(X=0) = probability of red or white = P(red) + P(white)

P(X=1) = probability of green or blue = P(green) + P(blue)

P(X=2) = probability of yellow or violet = P(yellow) + P(violet)

P(X=x) must have a sum of all possible values of 1, which indicates that

   P(red) + P(white) + P(green) + P(blue) + P(yellow) + P(violet) = 1

    Therefore ,with a probability  of 1/3 for each value, this random variable has a discontinuous uniform distribution over the set of values 0, 1, and 2.

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The energy in the pendulum as it swings from point A to point B

Potential energy is converted to kinetic energy.

Now, According to the question:

Energy is defined as the ability of an object to do work. Energy can be classified in two different types of energy, Kinetic and potential energy. This two may be the principal ones, but we can see how energy manifests in different ways in nature, like heat, chemical potential energy, solar energy, electric potential energy, and so on.

Energy is constantly changing from kinetic to potential energy, and vice-versa in a pendulum. At the lowest point of the pendulum swing, the pendulum will have reach a state of maximum kinetic energy. This due to it attaining the maximum speed the pendulum can reach due to it's movement. As the pendulum start to rise again, it will start to lose kinetic energy and will gain potential energy. This loss in kinetic energy will cause the pendulum to slow down until it reaches it's max height. At this point the pendulum will have converted all of it's kinetic energy to potential energy.

Hence, Potential energy is converted to kinetic energy.

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Answer:

125,664 mm³/s

Step-by-step explanation:

V = (4/3)πr³

dV/dt = (4π/3) × 3r² × dr/dt

dV/dt = 4πr² × dr/dt

dr/dt = 4 mm/s

d = 100 mm; r = 50 mm

dV/dt = 4π(50 mm)² × 4 mm/s

dV/dt = 125,664 mm³/s

The relation as a set of ordered pairs is expressed below.

The domain of the relation is {0, 1, 2, 3, 4, 5}.

The range of the relation is {8, 11, 12, 23, 28}.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:

Mathematically, the set of ordered pairs which represents the relation include the following:

Based on the mapping diagram (see attachment), the domain and range of the relation is given by:

Domain = {0, 1, 2, 3, 4, 5}.

Range = {8, 11, 12, 23, 28}.

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The responses to the survey question are quantitative, as the respondents were asked to provide a numerical answer.

Out of the 79,659 respondents, 79,659 said that they expect driverless cars to be common in the next years.

Out of the 79,659 respondents, 15,030 answered in the range of years. This means that 15,030 respondents provided a numerical answer that was within the range of years.

It is important to note that the survey question was quantitative, so the responses provided by the respondents were numerical. This means that the responses were not categorical, as categorical responses would have been in the form of words or phrases.

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