AB || CD, and the coordinates are A(-4, -6), B(0, -2), C(-4, 0), and D(0,y). What is the value of y?

The solution to the linear function M(x) = 180 is of x = -5.

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

In this problem, the function is defined as follows:

M(x) = 120 - 12x.

M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.

The domain of the situation is given as follows:

x ≥ 0. {discrete}

As the number of tickets cannot assume negative neither decimal values.

The equation is:

M(x) = 180.

The solution is calculated as:

120 - 12x = 180

12x = -60

x = -60/12

x = -5.

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Answer:

$0.99

Step-by-step explanation:

15x0.066=0.99

The correct answer is b. we know the standard deviation of the population.

The Nearly Normal condition, also known as the Central Limit Theorem, states that the sampling distribution of the sample mean tends to be approximately normal, even if the population distribution is not normal, under certain conditions. One way to meet the Nearly Normal condition is by knowing the standard deviation of the population.

When the standard deviation of the population is known, the sample size does not have to be large for the sampling distribution of the sample mean to be approximately normal. This is because the standard deviation provides information about the variability of the population, allowing for a more accurate estimation of the sample mean distribution.

While the other options (a, c, and d) may be relevant in specific scenarios, they are not directly related to meeting the Nearly Normal condition as defined by the Central Limit Theorem.

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The given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

According to the given question.

We have two planes

2x - 4y + 3z = 5

and,

x + 8y + 10z = 3

Since, two planes are perpenicular if

\(a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0\)

Where \(a_{1}\), \(b_{1}\) and \(c_{1}\) and \(a_{2}\), \(b_{2}\) and \(c_{2}\) are the direction ratios of planes.

And the two planes are parallel to each other if

\(\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }\)

Here, the direction ratios of plane 2x + 4y + 3z = 5 are 2, -4, and 3  and the direction ratios of plane x + 8y + 10z = 3 are 1, 8, and 10

Now,

2(1) + (-4)(8) + 3(10)

= 2 - 32 + 30

= 0

Since, the sum of the product of the direction ratios of  the two palnes is 0. Therefore, the given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

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36ft^2 square feet of outdoor carpet we will need for this hole.

Big square: Length = 6 ft ; Width = 4 ft

Small square: Length = 6 ft ; Width = 2 ft

Area = L x W

Big square: 6 * 4 = 24 ft^2

Small square: 6 * 2 = 12ft^2

On adding both, we get

Total area = 24 + 12 = 36ft^2

36ft^2 square feet of outdoor carpet we will need for this hole.

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Answer:

A

Step-by-step explanation:

TR=\(\sqrt{60^{2} -48^{2} }\)

TR=36

36/60=AR/36

AR=21.6

TA=\(\sqrt{36^{2} -21.6^{2} }\)

TA=28.8

the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer: men: 120 men, 310 women, and 170 children

600*0.2=120

600*0.35=310

600-120-310=170

If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.

There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.

There are 3! ways to find the three songs are liked by which pair of girls.

In total, there are ⁴C₃×3! possibilities for the first "3-songs".

There are "3-cases" for fourth song, let that song be "D".

Case 1: Song "D" is disliked by all three girls means there is only one possibility.

Case 2: Song "D" is liked by exactly one girl means there are three possibility.

Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.

However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.

Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.

In total, there are 3×12=36 over-lapped possibilities,

Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.

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Answer: 20% does chores but don't get allowance (me)

Step-by-step explanation: 5 is 20% of 25.

Answer:

20%

Step-by-step explanation:

5 is 20% of 25

Answer:1y+7x

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

11 y - 2 x - 10 y - y + 6 x . (Subtract all the y's first then the x's)

4x

Answer:

t=8p

Step-by-step explanation:

Basically, you need to determine the total length the pieces by multiplying the length of the string by the number of pieces of string there are. If you were to find the length of a piece of string you could just do p+p+p+p+p+p+p+p but to simplify it you would use the above stated answer.

Answer:

Undefined.

Step-by-step explanation:

Slope is the Rise/Run of a straight line.  Run is the change in the value of y for a change in x.  The graph shows all values are possible for y even when there is zero change in x.  All Values/0 = Undefined.

Answer:

I WILL SAY THE 2 ONE

Step-by-step explanation:

To give your daughter $50,000 towards her college education in 15 years, you must set aside approximately $14,803.42 today.

To calculate the amount of money you need to set aside today, we can use the concept of future value of a lump sum. The future value is the amount of money an investment will grow to in the future, given a certain interest rate and time period.

In this case, we want to determine the present value (the amount you need to set aside today) to achieve a future value of $50,000 in 15 years, assuming an annual interest rate of 9 percent. The formula to calculate present value is:

Present Value = \(Future Value / (1 + Interest Rate)^T^i^m^e\)

Plugging in the values, we have:

Present Value = \($50,000 / (1 + 0.09)^1^5\)

Present Value ≈ $14,803.42

Therefore, you would need to set aside approximately $14,803.42 today in order to accumulate $50,000 for your daughter's college education in 15 years, assuming an annual interest rate of 9 percent.

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Answer:

$109.53

Step-by-step explanation:

first, let's find 16.7% of 131.49:

131.49(0.167) = 21.95883

next, subtract the percentage from the sale, leaving the remainder for the company:

131.49 - 21.95883 = 109.53

hope this helped!

Answer:

v=-1

Step-by-Step Explanation:

Answer:

\(v=-1\)

Step-by-step explanation:

\(6\left(6v+6\right)-5=1+6v\)

Use the distributive property to multiply 6 by 6v+6:

\(36v+36-5=1+6v\)

Subtract 5 from 36 = 31

\(36v+31=1+6v\)

Subtract 6v from both sides:

\(36v+31-6v=1\)

Combine like terms:

\(36v\) and \(-6v\) \(=30v\)

\(30v+31=1\)

Subtract 31 from both sides:

\(30v=-30\)

Divide both sides by 30:

\(\cfrac{30v}{30}=\cfrac{-30}{30}\)

\(v=-1\)

_________________________

Answer:

La opción correcta es;

C) 30, 80

Step-by-step explanation:

Deje que el número de preguntas buenas sea X y el número de preguntas malas sea Y,

Se nos da que X = 3Y ............... (1)

y X + Y = 40 .................................. (2)

Por lo tanto;

Poniendo X = 3Y en la ecuación (2), tenemos;

3Y + Y = 40

4Y = 40

Y = 40/4 = 10

X = 3Y = 3 × 10 = 30

Por lo tanto, la buena pregunta respondida = 30

Dado que las buenas preguntas reciben 3 puntos y las malas preguntas reciben -1 punto, tenemos;

Puntaje total = Preguntas buenas × Punto otorgado + Preguntas malas × Puntos otorgados

Puntuación total = 30 × 3 + 10 × - 1 = 90 - 10 = 80

To find the volume of the empty space, we need to find the volume of the cube and the pyramid and then find the difference between both values.

VOLUME OF CUBE:

The volume of a cube is calculated as

The length of the cube is 18. Therefore, the volume is given to be

VOLUME OF PYRAMID:

The formula to calculate the volume is

Where

Since the base is an 18 unit square, and the height of the pyramid is 18 units as well, we can calculate the volume to be

VOLUME OF THE EMPTY SPACE:

The volume of the empty space can be calculated by subtracting the volumes of the cube and pyramid:

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

32.94%

Step-by-step explanation:

Hope this helps

Answer:

\(\frac{1}{2^{10}} \ and\ \frac{1}{1024}\)

Step-by-step explanation:

Given

\((2^{5})^{-2}\)

Required

Find the equivalent;

To find the equivalent of the given expression, we make use of laws of indices;

Using the following law of indices;

\((a^m)^n = a^{m*n}\)

So;

\((2^{5})^{-2}\) becomes

\((2^{5})^{-2} = 2^{5*-2}\)

\((2^{5})^{-2} = 2^{-10}\) ------------ This is one equivalent

Solving further;

Using the following law of indices;

\(a^{-m} = \frac{1}{a^m}\)

So;

\((2^{5})^{-2} = 2^{-10}\) becomes

\((2^{5})^{-2} = \frac{1}{2^{10}}\)

\(2^10 = 1024\)

Hence;

\((2^{5})^{-2} = \frac{1}{1024}\)

Conclusively; the equivalents of \((2^{5})^{-2}\) are \(\frac{1}{2^{10}} \ and\ \frac{1}{1024}\)

Answer:

B

Step-by-step explanation:

took the pretest! good luck!

Answer:

---------------------------

Make x the subject in steps below:

2. EFGH is a parallelogram. 3. EFGH is a rectangle.4. EFGH is not a square.5. the length of EF is √(2.25+2.25) = √(9) = 3.

A quadrilateral is a polygon with four sides and four vertices. It is a 2-dimensional shape that can be either convex or concave. The sum of the interior angles of a quadrilateral is always equal to 360 degrees.

There are many types of quadrilaterals, including rectangles, squares, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique properties and characteristics.

2. To determine if Quadrilateral EFGH is a parallelogram, we need to check if opposite sides are parallel. We can calculate the slope of each side using the coordinates:

EF: slope = (6-3)/(0-2) = -3/2

FG: slope = (-4-6)/(3-0) = -10/3

GH: slope = (-1+4)/(-1-3) = -3/4

HE: slope = (3-(-1))/(2-(-1)) = 4/3

We can see that opposite sides EF and GH have the same slope, and opposite sides FG and HE have the same slope. Therefore, EFGH is a parallelogram.

3. To determine if Quadrilateral EFGH is a rectangle, we need to check if all angles are right angles. We can calculate the slope of each side using the coordinates and use the fact that perpendicular lines have negative reciprocal slopes:

EF: slope = -3/2, so a line perpendicular to EF has slope 2/3

FG: slope = -10/3, so a line perpendicular to FG has slope 3/10

GH: slope = -3/4, so a line perpendicular to GH has slope 4/3

HE: slope = 4/3, so a line perpendicular to HE has slope -3/4

We can see that the lines perpendicular to EF and GH have the same slope, and the lines perpendicular to FG and HE have the same slope. Therefore, all angles of EFGH are right angles, and EFGH is a rectangle.

4. To classify EFGH as a square, we need to check if it is both a parallelogram and a rectangle, and if all sides are congruent. We have already established that EFGH is a parallelogram and a rectangle. To check if all sides are congruent, we can calculate the distance between each pair of opposite vertices:

EF: distance = √((0-2)² + (6-3)²) = √(10)

FG: distance = √((3-0)² + (-4-6)²) = 5√(2)

GH: distance = √((-1-3)² + (-1+4)²) = 5

HE: distance = √((2-(-1))² + (3-(-1))²) = √(29)

We can see that all four sides have different lengths, so EFGH is not a square.

5. To draw a right triangle EFR with hypotenuse EF, we need to find the coordinates of R. We can use the midpoint formula to find the midpoint of EF:

Midpoint of EF = ((2+0)/2, (3+6)/2) = (1, 4.5)

We can then use the distance formula to find the length of ER and RF:

ER = √((1-2)² + (4.5-3)²) = √(2.25) = 1.5

RF = √((1-0)² + (4.5-6)²) = √(2.25) = 1.5

Therefore, the length of EF is √(2.25+2.25) = √(9) = 3.

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1) In 1910, Halley's Comet was 21.37 million kilometers close to Earth.

2) Given that Halley's Comet orbits the sun at about 75 years, and that the last time it passed near the Earth was in 1986, the years in which it will happen again will be 2061, 2136 and 2211.

3) Earth is 794 times larger in diameter than Halley's Comet.

Since in 1910, Halley's Comet traveled close to Earth about 1/7 of the distance from the Earth to the Sun, and Earth's distance from the Sun is 149.6 million kilometers, to determine 1) how close was Halley's Comet to Earth in 1910, 2) estimate the next 3 years when Halley's Comet will appear, and 3) if the core of Halley's Comet is oblong in shape, with its longest dimension 16 km long, and Earth's diameter is about 12,700 km, how many times larger in diameter is Earth than Halley's Comet, the following calculations must be performed:

1)

2)

3)

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The relationship between Halley's comet and the earth is an illustration of proportions

The given parameters are:

(a) The distance

The distance which Halley's comet get to is calculated using:

\(d = \frac 17 \times 149.6\ million\ km\)

So, we have:

\(d = 21.37\ million\ km\)

Hence, Halley's comet was 21.37 million kilometers close to the earth in 1910.

(b) The next three years it will appear

From the complete question, the comet is visible every 74 years.

It appears in 1910.

So, the next three years are:

\(Year\ 1 = 1910 + 74 = 1984\)

\(Year\ 2 = 1984 + 74 = 2058\)

\(Year\ 3 = 2058 + 74 = 2132\)

Hence, the comet will appear in 1984, 2058 and 2132.

(c) The number of times the earth is larger

The diameter of the earth is given as: 12700 km, while the longest dimension of the oblong shaped comet is 16 km.

So, the number of times (n) which the earth is greater than the comet is:

\(n = \frac{12700}{16}\)

\(n = 794\) --- approximated

Hence, the diameter of the earth is 794 times larger than Halley's Comet.

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Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).

"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.

Here, The formulae are as follows:

=>y = -z + 2      ...(1)

=> y = -2x² + z + 1  ...(2)

Equation (1) can be substituted for equation (2) to find the value of z:

=> Z = x² + 1/2 - z + 2 = -2x² + z + 1

=> 2z = 2x² + 1

We can now enter this value of z into equation (1) and find the value of y:

=> y = -z + 2

=> y = -(x² + 1/2) + 2

=> y = -x² + 3/2

As a result, the equation system can be expressed as:

=> z = x² + 1/2

=> y = -x² + 3/2

When x=0:

=> z = 0² + 1/2 = 1/2

=> y = -0² + 3/2 = 3/2

Therefore, there is no answer for the ordered pair (0, 3/2).

When x=1:

=> z = 1² + 1/2 = 3/2

=> y = -1² + 3/2 = 1/2

The answer is the ordered pair (1, 1/2).

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We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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