Select the equation of a straight line that is perpendicular to the line y = 3x - 2.
A y = 3x - 5
B 3y=x+2. C y=- -3x-2 D y= -x/3+2 E y=1\3x-2

The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

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Answer: 3

Step-by-step explanation:

We can solve this problem by recognizing that z is the geometric mean of 9 and 9+4. This property is outlined in the following formula:

[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]

where hypotenuse is the longest side of the triangle, leg is the side of the triangle we are calculating for, and part is the part of the hypotenuse on the side of the leg.

Here, the hypotenuse is 13, or 4 + 9. The leg is z, as it is the side of the triangle we are trying to find. Finally, the part is 9. It is the part of the hypotenuse that is on the side of the leg.

Let's plug in these values:

[tex]\frac{13}{z}=\frac{z}{9}\\117=z^2\\z=\sqrt{117}[/tex]

117 is the product of 9 and 13. Since 9 is a perfect square, we can take it out from the square root.

[tex]z=\sqrt{9*13}\\z=\sqrt{9}*\sqrt{13}\\z=3\sqrt{13}[/tex]

The "?" must be a 3.

The equation of the line is y = 2/3x + 4

The points on the line are given as:

(zero, four) and (negative six, zero).

Rewrite the points properly as

(0, 4) and (-6, 0)

The slope of the line is calculated using:

m =(y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (0 - 4)/(-6 - 0)

Evaluate

m = 2/3

The equation of the line is then calculated as:

y = mx + b

This gives

y = 2/3x + b

So, we have:

4 = 2/3 * 0 + b

Evaluate

b = 4

Substitute b = 4 in y = 2/3x + b

y = 2/3x + 4

Hence, the equation of the line is y = 2/3x + 4

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Correct option is D) and E)

(3,7π/6),(3,11π/6)

Point of intersection is the point where two lines or two curves meet each other.

The point of intersection of two lines of two curves is a point.

If two planes meet each other then the point of intersection is a line.

The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.

let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

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I understand that the question you are looking for is:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

A) -3,7/6

B) (-3,11/6)

C) (3,7/6)

D) (3,11/6)

1. The 100 prisoner experiment: 100 prisoners are about to be executed (you can use paper stick figures to model 100 prisoners, or you can do about 10), but the warden has agreed to allow all prisoners to be commuted to a 6-month sentence if they can pass one game. The game states that 100 pieces of paper with each of the prisoner's numbers are to be randomly shuffled into boxes that have random prisoner's numbers (where the number on the paper does not match the number on the boxes.) Each prisoner is allowed to open 50 boxes to find their number such that they have a [tex]\frac{1}{2}[/tex] chance of finding their number. If you find your number, you are cleared to another room to wait. If you don't, then you've messed up huge. If even one prisoner does not find their number, all the prisoners die. If all of the prisoners find their numbers, they all get 6-month sentences instead. The chance of all the prisoners randomly finding their numbers is [tex](\frac{1}{2})^{100}[/tex], which is about a 0.0000000000000000000000000000008% chance. 30 zeros after the decimal placement. For reference, two people have a better chance of picking up the same grain of sand from any of the beaches in the world than finding their numbers randomly.

The Vickrey Auction can be modeled into an experiment by testing people's psychological thinking. You can do this with any of your friends. In a Vickrey auction, you put your bids into a closed letter. For an item, the highest bidder wins the auction, but does not pay what he or she put their bid under in the auction, but rather pays what the second bidder had bidded. It teaches people to be more honest, because if you bid the highest and win, you pay the second-highest bidder's payment, which could also be almost equally as high and could cost you a fortune for an undervalued item.

Another great experiment you can do is to measure the different unsynchronizations of analog clocks that are not close together. Scientists have measured atomic clocks that are just a millimeter apart that start ticking in different measures.

2. I select the 100-prisoner experiment.

3. A curved graph like -x^2 would fit perfectly.

4. A quadratic function would fit my experiment the best. The best graph to use would be [tex]y = -x^2[/tex]. An equation with a large curve would be the best for this type of experiment to graph success and failure. More than three quarters of my graph wouls be full of failure and maybe a little more than 10% would be full of success if repeated over 100,000 times. I am not too sure though.

The logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

The logarithmic equation is given as:

f(x) = log₈(x + 1) + 4

The parent function of the logarithmic equation is

y = log₈(x)

When the logarithmic equation is translated 1 unit left, we have:

y = log₈(x + 1)

When the logarithmic equation is translated 4 units up, we have:

y = log₈(x + 1) + 4

This means that the logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

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Answer:

10

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]4x=2x+20 \\ \\ 2x=20 \\ \\ x=10[/tex]

tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.

The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.

The dimensions are the sides of a geometric shape.

The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.

If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:

The width of the garden with a length of 6 ft [tex]= \dfrac{36}{6} = 6\ ft[/tex]

The width of the garden with a length of 9 ft [tex]= \dfrac{36}{9} = 4\ ft[/tex]

The width of the garden with a length of 6 ft [tex]= \dfrac{36}{12} = 3\ ft[/tex]

The parameters are calculated as:

The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft

The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft

The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft

The least of the parameter is of the garden with dimensions (6 ft, 6 ft).

Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.

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Answer:

-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)  (the last choice).

Step-by-step explanation:

Im ignoring the 2^2 in the equation

The equation transforms to

2x^2 - 3x - 5 = 0    (standard form)

So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)

Answer:

5 and 5

Step-by-step explanation:

[tex]AB = BC =\sqrt{(4-0)^2+(3-0)^2}=5[/tex]

Answer:

AB = 5

BC = 5

Step-by-step explanation:

The formula to find the distance between two points is: [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

AB: 5

The two points are A(-4,0) and B(0,3).

In the formula, it will be expressed as:

[tex]\sqrt{(0-(-4))^2+(3-0)^2}[/tex]

-->  [tex]\sqrt{4^2+3^2}[/tex] .

-->  [tex]\sqrt{16+9}[/tex]

-->  [tex]\sqrt{25}[/tex]

--> 5

BC: 5

The two points are: B(0,3) and C(4,0)

In the formula, it will be expressed as:

[tex]\sqrt{(4-0)^2+(0-3)^2}[/tex]

-->  [tex]\sqrt{(4)^2 + (-3)^2}[/tex]

-->  [tex]\sqrt{16 + 9}[/tex]

-->  [tex]\sqrt{25}[/tex]

--> 5

So both AB and BC is 5.

The solution to the inequality 4 ≥ b is represented in the graph

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Inequality shows the non equal comparison between two or more numbers and variables.

Given the inequality:

4 ≥ b

Rearranging gives:

b ≤ 4

The solution to the inequality 4 ≥ b is represented in the graph

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The required minimum sample size to construct a 95% confidence level for the population mean is 267.

In this question,

In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.

The population standard deviation, σ = 25

Confidence level for the population mean = 95%

Margin of error = ±3

Let n be the sample size of the population

The z-score for the confidence level of 95% for the population mean is 1.96.

The formula of margin of error is

[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]

Now, the sample size of the population can be calculated as

[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]

On substituting the above values,

⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]

⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]

⇒ [tex]n=(16.33)^{2}[/tex]

⇒ n = 266.77 ≈ 267

Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.

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Applying the angle bisector and triangle proportionality theorem, the solutions are:

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6.

The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.

16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]

Cross multiply

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² - 3x² + 3x - 4 + 6x = 0

-2x² + 9x - 4 = 0

Factorize -2x² + 9x - 4

(−2x + 1)(x − 4)

-2x = -1

x = 1/2

or

x = 4

17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)

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

4x² + 8x + 4 = 4x² + 10x - 6

Combine like terms

4x² - 4x² + 8x - 10x = -4 - 6

-2x = -10

x = -10/-2

x = 5

18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]

Cross multiply

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

Expand

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize x² - 5x - 6 = 0

(x+1)(x−6) = 0

x = −1 or x = 6

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Answer:

 [tex]h(x)=7(1.3)^x[/tex]

Step-by-step explanation:

Since this is an exponential equation we will use

[tex]h(x)=a(b)^x[/tex]

[tex]a[/tex] Is your starting value, 7

[tex]b[/tex] Is your percentage of change, remember its not 0.3, as that would hint the population is decreasing by thirds exponentially, instead we will use 1.3 as our percent of change, as the 1 maintains the original value and the 0.3 adds 30%, now all we have to do is put it all together!

[tex]h(x)=7(1.3)^x[/tex]

Answer:

Step-by-step explanation:

[tex]We\ summarize\ (1) \ and\ (2),\ \ (2) \ and\ (3):\\\displaystyle\\\left \{ {{2x\geq -6\ |:2} \atop {-2x\geq -6\ |:(-2)}} \right. \ \ \ \ \ \left \{ {{x\geq -3} \atop {x\leq 3}} \right. \ \ \ \ \ \Rightarrow\ \ \ \ x\in[-3;3].\\[/tex]

[tex]2)\ We\ subtract\ equation\ (2) \ from \ equation (1),[/tex]

The equation represents the parabola shown on the graph is  x^2 = - 8y . Option D

We were given the following parameters;

The standard for a parabola is given as;

y² = 4ax

It can also be written as;

x² = 4ay

Given the focus as ( -2, 0), we have the value of 'a' to be -2

Now, let's substitute the value into the standard equation of a parabola

x^2 = 4ay

x^2= 4 × -2 × y

Multiply through

x^2 = - 8y

The equation of the parabola is x^2 = - 8y

Thus, the equation represents the parabola shown on the graph is  x^2 = - 8y . Option D

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Answer:

b

Step-by-step explanation:

trust

Answer:

34 L

Step-by-step explanation:

there are four 100 km(s) in 400 km

so

8.5 * 4 is what you need to do to find your answer

8.5 * 4 = 34

34 L is your answer

The function to represent the problem is f(x)=6x+24 and the range is 30[tex]\leq[/tex]y[tex]\leq[/tex]48.

If the terms of a sequence differ by a constant, we say the sequence is arithmetic. If the initial term ([tex]a_{0}[/tex]) of the sequence is a and the common difference is d, then we have,

[tex]a_{n}[/tex]=a+(n-1)d

Initial number of clients=30

Number increase per week= 6

So, we can make an arithmetic sequence fir six weeks

30,36,42,48

Here, first term, a=30

Common difference, d=6

Range is [30,48]

The explicit formula of an arithmetic sequence is

[tex]a_{n}[/tex]=a+(n-1)d

Put a=30, d=6, n=x

[tex]a_{x}[/tex]=30+(x-1)6

[tex]a_{x}[/tex]=30+6x-6

[tex]a_{x}[/tex]=6x+24

Therefore, The function to represent the problem is f(x)=6x+24 and the range is 30<=y<=48

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Answer:

Resistance

Step-by-step explanation:

Answer:

(28.36)

Step-by-step explanation:

Answer:

$149.25

Step-by-step explanation:

The discount is 15% of $995

[tex]15\%\times995[/tex]

Note that percentages can also be written as that number over 100.

[tex]\frac{15}{100}\times995[/tex]

Simplify the fraction

[tex]\frac{3}{20}\times995=\frac{2985}{20}=149.25[/tex]

Therefore the discount is $149.25.

Answer:

$149.25

Step-by-step explanation:

The cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

We have to estimate the cofactors of each entry in the first row of the matrix.

A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.

Thus the cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

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The area of the baseball diamond is 8192 sq. units.

We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).

The side of the square can be computed using the distance formula,

D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).

Thus, the side of the square,

a = √((x₂ - x₁)² + (y₂ - y₁)²),

or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,

or, a = √(64² + (-64)²),

or, a = √(4096 + 4096),

or, a = 64√2 units.

Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.

Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.

Thus, the area of the baseball diamond is 8192 sq. units.

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Answer:

1. 36 liters

2. 3 kg

Step-by-step explanation:

because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters

also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)

Answer:

1.) 36 litres

2.) 3 kg

Step-by-step explanation:

In this case there is a ratio of 1:3 of mass to volume.  If we know the mass, the volume is 3 times that.  If we know the volume, the mass is that divided by 3.

Answer:

-2n+15>3

Step-by-step explanation:

Answer:

1/2.x+3(x-1)-5=30

1/2.x+3x-3-5=30

(1/2+3)x-8=30

7/2.x-8=30

7/2.x=38

7x=76

x=76/7

CMIIW

The rate at which battery charges is 10 percent per minute.

According to the statement

we have given that the charging capacity of battery in the graphical representation.

And we from this we have to find the percentage by which battery charges.

And the graphical representation given is :

The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.

A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes.

And according to this representation it is clear that the percentage by which battery charges is 10 percentage per minute.

So, The rate at which battery charges is 10 percent per minute.

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Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

The height of the prism is h = 19 mm

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

A regular pentagonal prism has a volume of 2,850 millimeters³

The pentagonal base has side edge labeled 12 millimeters.

And , Apothem from center to a base edge is labeled 5 millimeters

Area of a regular polygon =  (A x P) / 2

where A = side / (2 * Tan (π / N))

and , N = Number of sides, A = Apothem,  P = Perimeter

h = 2850 / 150

On simplifying , we get

h = 19 mm

Hence , the height is 19 mm

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