Select the statement that correctly describes the solution to this system of equations:
5x
4y=-3
y=-3x+5

The perimeter, in miles, of the rectangle formed by connecting the points representing the cabana, beach, water slide, and roller coaster will be 22 miles.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given, a coordinate system where 1 unit = 1 mile

Lets,

First, calculate the linear distance between adjacent points as displayed in the graph.

Distance between car to cabana = 4 units = 4 miles

Distance between cabana to beach = 6 units = 6 miles

Distance between beach to water slide = 5 units = 5 miles

Distance between water slide to roller coaster = 6 units = 6 miles

Distance between roller coaster to cabana =5 units = 5 miles

Thus,

1) the perimeter, in miles, of the rectangle formed by connecting the points representing the cabana, beach, water slide, and roller coaster:

Perimeter = 6 + 5 + 6 + 5

Perimeter = 22 miles

2) the total distance in miles from the car to the cabana and then from the cabana to the beach:

Distance = 4 + 6

Distance = 10 miles

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The given function, f(x)=-3x^(2)+4, has three types of symmetry: 1. Symmetry with respect to the y-axis (even symmetry).
2. Symmetry with respect to the x-axis (odd symmetry). 3. Symmetry with respect to the origin (rotational symmetry)

To check for symmetry with respect to the y-axis, we can substitute (-x) for x in the function and see if it is equal to the original function.

f(-x)=-3(-x)^(2)+4=-3x^(2)+4

Since f(-x)=f(x), the function is symmetric with respect to the y-axis.

To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the function and see if it is equal to the original function.
-3x^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the x-axis.

To check for symmetry with respect to the origin, we can substitute (-x) for x and (-y) for y in the function and see if it is equal to the original function.
-3(-x)^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the origin.

Therefore, the given function f(x)=-3x^(2)+4 has symmetry with respect to the y-axis, but does not have symmetry with respect to the x-axis or the origin.

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The decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.

The number 2.998 x [tex]10^8[/tex] m/s represents the scientific notation of a very large number. It is a shorthand way of writing a number that is expressed as the product of a decimal number between 1 and 10 and a power of 10. In this case, the decimal number is 2.998 and the power of 10 is 8.

To convert this number to decimal form, we need to multiply the decimal number by 10 raised to the power of the exponent. So, we have:

2.998 x [tex]10^8[/tex] = 2.998 * 10,000,000

Multiplying 2.998 by 10,000,000, we get:

2.998 * 10,000,000 = 29,980,000

Therefore, the decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.

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B

B=G-11 and B+G=28 could be used to solve the problem

Answer:

  45

Step-by-step explanation:

You want the area of triangle RST using the area formula A=1/2bh, given the points R(-2, 7), S(-5, 1), and T(7, -5).

A plot of the points is shown in the first attachment. By counting grid squares, you can see that segment RS has a "rise" of 2 grid squares for each 1 to the right. The total (run, rise) is ...

  R -S = (-2, 7) -(-5, 1) = (-2 +5, 7 -1) = (3, 6)

The length of RS is found using the Pythagorean theorem (distance formula). It is ...

  RS = √(3² +6²) = √45 = 3√5

Similarly the length of segment ST is ...

  T -S = (7, -5) -(-5, 1) = (7 +5, -5 -1) = (12, -6)

  ST = √(12² +(-6)²) = √180 = 6√5

We note that the slopes of these segments are opposite inverses of each other:

  slope RS = 6/3 = 2

  slope ST = -6/12 = -1/2

This means the segments are at right angles. One of them can be considered to be the "base" and the other the "height" of the triangle.

Using the area formula, we find the area to be ...

  A = 1/2bh

  A = 1/2(6√5)(3√5) = (1/2·6·3)(√(5·5)) = 9·5 = 45

The area of ∆RST is 45 square units.

__

Alternate solution

When the coordinates of a polygon are given, there are several other ways to find its area. One of these is illustrated in the second attachment.

The method illustrated here computes successive "determinants", then finds the area as half the absolute value of their sum. (The sign of the sum will depend on the order in which the points are listed around the figure. Here, it is counterclockwise.) As you can see, we get the same result. You can also see that a spreadsheet is useful for doing the repetitive math.

  Area ∆RST = 45 square units

__

Additional comment

The distance formula for the length of the segment between two points is ...

  d = √((x2-x1)² +(y2-y1)²)

Above, we calculated the differences (x2-x1, y2-y1) separately, then used the "root sum squares" formula for the distance. This has the advantage that (y2-y1)/(x2-x1) is the slope of the segment, and we needed to make sure the segments were perpendicular.

15000 rational numbers from (-1,1) interval using black

Answer: Code for the given mathematical function# Python code for plotting sine and cosine functions import matplotlib.py plot as plt import numpy as npa = [0.25, 1, 3] # given set of valuesx = np.linspace(-15, 1, 15000) # from (-1, 1) interval and 15000 rational numbersb = 2.5c = 1.6fig, ax = plt.subplots()# Plotting the graph with different colorsplt.plot(x, a[0]*np.cos(b*x)+ (1-a[0])*np.sin(c*x), color='black', label='a=0.25')plt.plot(x, a[1]*np.cos(b*x)+ (1-a[1])*np.sin(c*x), color='red', label='a=1')plt.plot(x, a[2]*np.cos(b*x)+ (1-a[2])*np.sin(c*x), color='blue', label='a=3')# Adding labels and titlesplt.xlabel('x-axis')plt.ylabel('y-axis')plt.title('Plot of given mathematical function')plt.legend()# Displaying the plotplt.show()Graphical output for the given mathematical function:Here, the above code gives a line plot of the given mathematical function for all a € (0.25k: 1 ks 3,k e Z+), and x € {x € R:-15x 1), where b=2.5, C = 1.6 by creating 15000 rational numbers from (-1,1) interval using black, red, and blue colors for respective k values.

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It is a unique variety of quadrilateral called a parallelogram that has both pairs of opposite sides parallel and equal.

A polygon with has four sides, four angles, and four vertices is called a quadrilateral. The Latin words 'Quadri', which denotes four, and latus, which means side, were combined to form the English word quadrilateral.

Given, Height of the Parallelogram = 2 units

Each segment on the grid is represented as = 1 unit.

So, One side of the Parallelogram = 3 units

Properties of Parallelogram

a. Opposite sides are equal.

b. Opposite sides are parallel.

c. Diagonals Bisect each other.

Also, Every Rectangle is a Parallelogram.

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The dimension of a vector space is equal to the number of linearly independent vectors in its basis.

In the given basis B = {(0,2,1),(0,2,1),(1,0,0)}, we can see that the first two vectors (0,2,1) and (0,2,1) are identical and therefore not linearly independent. Therefore, the dimension of the vector space is equal to the number of linearly independent vectors in the basis, which is 2.

So, the dimension of the vector space whose basis are B = {(0,2,1),(0,2,1),(1,0,0)} is equal to 2.

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Answer:

B, D, E

Step-by-step explanation:

52= -4(2n+1)

= -8n-4

52= -8n-4

8n= -4-52

8n= -56

n= -7

-8n= 52+4

= 56

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Slope would approximately be -1/8

Step-by-step explanation:

The first point that it looks like it touches would be (0,100) then from what I can see the next point would be (400,50). To get from the first point to the second, the slope would have to drop 1 block and move to the right 8 blocks. This means the slope would be -1/8

Answer:

y(x)=2*(x+-2)^2+5

Step-by-step explanation:

The answer of function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].

A 6th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function[tex]y=(x-3)^4(x+1)^2[/tex].

This is because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times, and the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

Therefore, the values of a, b, and c in the function y=(x-3)^(a)(x-b)^(c) are:

a = 4, because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times.

b = -1, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

c = 2, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

So, the function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].

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The correct answer is c: Initial value: 1, rate of change 5 over 3. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5).

A linear equation is an equation that describes a straight line when it is graphed. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. Linear equations are used to describe many real-world situations, such as the height of a ball thrown in the air, the distance traveled by a car, or the height of a person over time.

This question is asking for the initial value and rate of change for a linear equation. The initial value is the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is 1, so the initial value is 1. The rate of change is the slope of the line, which can be found by calculating the change in y over the change in x. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5). Therefore, the rate of change is 5 over 3, so the correct answer is c: Initial value: 1, rate of change 5 over 3.

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Answer:

y = x+5

x+2y=16

x+2(x+5)=16

x+2x+10=16

3x+10=16

16. 3x + 10 = 16

3x+10=16

    -10  -10

3x=6

Divide 3 from both sides

x=2

y=x+5

y=2+5

y=7

17. (2,7)

The set builder nοtatiοn wοuld be {(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}

A set builder nοtatiοn is a cοncise way οf representing a set οf elements based οn a rule οr cοnditiοn. In set builder nοtatiοn, we use braces { } tο enclοse the set οf elements, and a vertical bar | οr a cοlοn : tο separate the cοnditiοn frοm the elements. The general fοrmat οf a set builder nοtatiοn is:

{elements | cοnditiοn}

Using this nοtatiοn, we can represent the set οf οrdered pairs (x, y) given in the questiοn as:

{(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}

This nοtatiοn reads as "the set οf all οrdered pairs (x, y) such that x takes οn the values 1/125, 1/25, 1/5, 1, 5, 25, and 125, and y takes οn the values -3, -2, -1, 0, 1, 2, and 3."

Hence, the set builder nοtatiοn wοuld be {(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}

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Step-by-step explanation:

3.

the sum of all internal angles in a quadrilateral is always 360°.

so, the internal angle at x is given by

360 = 40 + 80 + 110 + inner angle

inner angle = 360 - 40 - 80 - 110 = 130°

an inner and an outer angle combined are together always 180°.

so,

130 + x = 180

x = 50°

4.

first, again, the sum of all inner angles is 360°.

this is a parallelogram. that means the diagonally opposing angles are equal.

so, the angle opposite of the 38° angle is also 38°.

that leaves

360 - 38 - 38 = 284°

for the 2 (again equal) remaining angles :

284 = 2 × angle

each of these remaining angles is then

284/2 = 142°

the angle JML is one of them.

so,

angle JML = 142°

The equation of total time taken by the commuter in travelling is 14x + 11, thus the correct option (b).

An algebraic equation can be defined as a mathematical statement in which two expressions are equivalent. Algebraic equations usually consist of variables, coefficients and constants .

Algebraic equations are also called polynomials because they contain polynomials on both sides of the equality sign. Algebraic equations consist of variables, coefficients, constants, and algebraic operations such as addition, subtraction, multiplication, division, and exponentiation.

According to the question:

(4x + 13) + (10x - 2) = 4x + 10x + 13 - 2

                               = 14x + 11

Thus, the equation for the total time taken is 14x + 11.

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Shante rides at an average speed of 9.33 miles per hour.

We need to determine how many miles Shante rode per hour. We can set up an equation to solve this problem:

3 hours x M (miles per hour) = 29 miles

7 hours x M = 65 miles

We can then solve this equation to find out the number of miles she rode per hour:

3M = 29

M = 29/3

M = 9.67 miles per hour.

Therefore, Shante rode at an average rate of 9.67 miles per hour.

Now, we can find her average speed by dividing the total distance she has traveled by the total time she has traveled:

Therefore, Shante rides at an average speed of 9.33 miles per hour.

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200% of number 13 is 26.

A percentage is a number expressed as a fraction of 100, with the symbol % (percent) added. For example, 50% is the same as 50/100 or 0.5.

To find the number that is 200% of another number, we need to divide the given number by 200% (or 2) and then multiply by 100%. So, to find the number that is 200% of another number that is equal to 26, we can use the following equation:

200% of x = 26

We can simplify this equation by dividing both sides by 200% or 2:

x = 26 ÷ 2

x = 13

Therefore, the number that is 200% of 13 is 26.

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Answer:

marcy added 20 instead of equating that -20

8m-20=36

8m=36+20

8m÷8=56÷8

m=7

15 - 60%

x - 100%

1500 = 60x

x = 25

∴ There are 25 students in the class in all.

The value  of x for the given  triangle  is x = 8.4 units. 2. For the given triangle the value of x is 2941.17 m.

The opposing angles created by the junction of two lines are known as

vertical angles

or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are

supplementary angles

, meaning their sum is 180 degrees.

The given triangle is a right triangle.

Using the trigonometric functions we have:

tan (35) = opposite / adjacent = x / 12

0.7 (12) = x

x = 8.4

Hence, the value of x for the given triangle is x = 8.4 units.

For the second figure, using the alternate interior angles we have angle corresponding to the segment x as 10 degrees.

Using the trigonometric function we have:

sin (10) = opposite / hypotenuse = 500/x

x = 500/0.17

x = 2941.17

Hence, the value of x is 2941.17 m.

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Answer:

Step-by-step explanation:

The llsab have to be divided by the number quotient and then once your sllab get hot then you answer.

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Answer:

We would need to know the percentage of discount offered during the sale to determine the sale price of the polo shirt. Here's an example calculation for a 25% discount:

If the discount offered is 25%, Bert will only need to pay 75% of the original price. We can calculate this as:

Sale price = (100% - 25%) x $20

Sale price = 75% x $20

Sale price = 0.75 x $20

Sale price = $15

Therefore, if the discount offered during the sale is 25%, Bert will pay $15 for the polo shirt. However, if the discount is different, the sale price will be different.

Therefore , the solution of the given problem of fraction comes out to be -3 5/8 as a result.

Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction.

Here,

=> 9 1/4 = (4 x 9 + 1)/4 = 37/4

=> 12 7/8 = (8 x 12 + 7)/8 = 103/8

4 and 8 have the same shared factor, which is 8.

=> 37/4 - 103/8 = (2 x 37)/(2 x 4) (2 x 4) - 103/8

=> 74/8 - 103/8

=> -29/8

There is no simpler way to describe the outcome.

Since the outcome is already an incorrect fraction, we can change it back to a mixed integer as follows:

-29/8 = -3 5/8

9 1/4 - 12 7/8 Equals -3 5/8 as a result.

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The expected value of this scenario is 4.19.

The Expected value (EV), which is based on a random variable's probability distribution, describes the long-term average level of that variable. The expected value of a stock or other investment is a crucial factor in investing and is taken into account while performing scenario analysis.

To calculate the expected value, we need to multiply each outcome xi by its respective probability P(xi), and then add up all of these products. So, we have:

Expected value = 1(0.24) + 2(0.22) + 3(0.31) + 4(0.01) + 5(0.16) + 6(0.29)

Expected value = 0.24 + 0.44 + 0.93 + 0.04 + 0.80 + 1.74

Expected value = 4.19

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Answer:

Let's first calculate the number of compounding periods in a year, given that the interest is compounded quarterly:

Number of compounding periods in a year = 4 (since there are 4 quarters in a year)

Next, let's use the formula for compound interest to find the annual interest rate:

A = P (1 + r/n)^(nt)

Where:

A is the balance after t years

P is the principal (initial balance)

r is the annual interest rate (what we are looking for)

n is the number of compounding periods in a year

t is the time in years

We know that P = $1250, A = $1406.08, n = 4, and t = 9/12 years (since the interest is earned for 9 months).

Plugging these values into the formula, we get:

$1406.08 = $1250 (1 + r/4)^(4/3)

Dividing both sides by $1250 and taking the cube root of both sides, we get:

1 + r/4 = (1406.08/1250)^(3/4)

1 + r/4 = 1.038

Subtracting 1 from both sides, we get:

r/4 = 0.038

Multiplying both sides by 4, we get:

r = 0.152

Therefore, the annual interest rate is 15.2%.

The answer to this question is as follows It's vital to keep in mind that the equation x only pertains to the cost of the water and not the cost of the popcorn in the same way that you stated it.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

To calculate Theodore's overall spending, use the following expression:

3x + 4.50

This is due to the fact that he also spent $4.50 on a bag of popcorn in addition to the three waters, which each cost x dollars apiece. His whole expenditure may be calculated by adding these two charges.

When we condense the formula 3x + 4.50, we get:

the 7.50x

It's vital to keep in mind that the x only pertains to the cost of the water and not the cost of the popcorn in the same way that you stated it.

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Let's assume the number to be x.

According to the problem statement, the sum of a number and its reciprocal is 2 1/6 or 13/6.

So we can set up the equation:

x + 1/x = 13/6

Multiplying both sides by 6x, we get:

6x^2 + 6 = 13x

Bringing all the terms to one side, we get:

6x^2 - 13x + 6 = 0

We can solve for x using the quadratic formula:

x = [13 ± sqrt(13^2 - 4(6)(6))] / (2*6)

x = [13 ± sqrt(169)] / 12

x = [13 ± 13] / 12

So, x can be either 2/3 or 3/2. Therefore, the number is either 2/3 or 3/2.