What value of b will cause the system to have an
infinite number of solutions?
6
y = 6x-b
+3x+12y=-3
-3x + y = -3
b =

other

other

therefore, the order from least to greatest is:

The equation of the table is y = 28x

The slope intercept equation of a linear equation is as follows:

y = mx + b

where

Therefore, let's find the slope using (1, 28)(2, 56)

m = slope = 56 - 28 / 2 - 1 = 28

Therefore, let's find the y-intercept as follows:

using (1, 28)

28 = 28(1) + b

b = 28 - 28

b = 0

Hence, the equation of the table is y = 28x

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Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

The equation of the line in slope - intercept form is -

y = - 5x + 77.

The equation of a straight line in slope - intercept form is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation as -

77 - y = 5x

We have the equation in the slope - intercept form as -

77 - y = 5x

y = 77 - 5x

y = - 5x + 77

Therefore, the equation of the line in slope - intercept form is -

y = - 5x + 77.

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Answer:

so what do i do

Step-by-step explanation:????????????

Answer:

B, C, and F

Step-by-step explanation:

Answer:

f(x) has a greater slope.

Step-by-step explanation:

The slope of the image line

= difference in y coordinates / difference in x coordinates

= (7-3) / (3-2)

= 4.

The  slope of f(x) = 6x + 1 is  6.

The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

What is mean by straight line?

A straight line is a combination of endless points joined on both sides of the point.

Given that;

The function, f(x) = 6x + 1

And the function g(x) is a linear function which passes through the points (2 , 3) and (3, 7).

Since, The slope 'm' of any straight line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

And, m = d/dx (f(x))

So, The slope of function f (x) will be;

f(x) = 6x + 1

M = d/dx (f(x))

M = d/dx (6x + 1)

M = 6

And, Slope of linear function which passes through the points (2 , 3) and (3, 7) is;

m = (7 - 3) / (3 - 2)

m = 4/1

m = 4

Thus, The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

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The measure of ∠D is equal to 120°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image attached.

We can write -

{8x}° + {4x}° + ∠B = 180°

∠B = 180° - {8x}° - {4x}°

∠B = 180 - 40 - 20

∠B = 120°.

∠B = ∠D = 120°      [Opposite angles of a ||gm are equal}

Therefore, the measure of ∠D is equal to 120°.

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Answer:

The valedictorian is the person who has the highest academic achievements in their graduating class not to mention they get to deliver the valedictory speech.

Step-by-step explanation:

Step-by-step explanation:

according to Oxford learner's dictionary:

the student who has the highest grades in a particular group of students and who gives the valedictory speech at a graduation ceremony compare salutatorian.

it means to have quality speech

Answer:

Form: Linear Direction: Positive Strength: Moderate

Step-by-step explanation:

The scatter plot for the Cost of Airplane Ticket versus the number of Miles Flown is attached below.

It can be easily seen that the plot is moving in an upward directions. An upward moving scatter plot represents a positive relationship between the two variables.

Similarly, the scatter plot here represents a positive relationship between cost of airplane ticket and the number of miles flown.

Now consider the points plotted on the graph.

If we form a line of best by joining any two points it can be seen that the rest of the points are close to this line but not very close.

Thus, implying that there is a moderately strong relationship between the two variables.

Thus, the statement accurately describing the data is:

Form: Linear Direction: Positive Strength: Moderate

Answer:

D.

Step-by-step explanation:

The graph of the linear equation, x = 6, is shown in the image attached below.

The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.

Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.

Thus, the graph of the linear equation, x = 6, is shown in the image attached below.

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Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer: 2/3

Step-by-step explanation:   y1-y2    3-(-1) = 4       simplify  4/6=2/3

                                               x1-x2     4-(-2)= 6

Slope is described as "the rise over the run," meaning that it's the fraction of "the change in the y-values compared to the change in the x-values."

In this situation
    - the change in the y-values is 3 - (-1) = 4.
    - the change in the x-values is 4 - (-2) = 6.
so the fraction is 4/6 or 2/3.

As a general formula, the formula for slope is \(m = \dfrac{y_2-y_1}{x_2-x_1}\).

      \(m = \dfrac{3-(-1)}{4-(-2)}=\dfrac{4}{6}=\dfrac{2}{3}\)

Answer: c. estimated OLS values are not BLUE

Step-by-step explanation:

Regression of ordinary least squares (OLS) is a statistical analysis technique that estimates the relationship between one or more independent variables and a dependent variable. The method estimates the relationship between the observed and predicted values of the relationship by minimizing the sum of the squares.

Answer:

non lo so

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

3a = 3×7 = 21

2b = 2×5 = 10

c = 5

3a +2b+c = 21+10 +5 = 36

the square root of 36 is 6

√36 = 6

answer = 6

hope this answer helps you.....

Answer:

Rs. 18936.54

Step-by-step explanation:

Given data

Discount=15%

VAT= 13%

Amount paid= Rs.19,323

The amount of VAT

=13/100*19323

=0.13*19323

= Rs. 2511.99

The amount of discount

=15/100*19323

=0.15*19323

= Rs.2898.45

The marked price is

=19323+2511.99-2898.45

=21834.99-2898.45

=Rs. 18936.54

Answer:

\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.

Step-by-step explanation:

Elliptic curve cryptography (ECC) makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.

ECC is a type of public-key cryptography that is based on the difficulty of solving the elliptic curve discrete logarithm problem (ECDLP), which is a variant of the discrete logarithm problem in which the group operation is performed on points on an elliptic curve.

ECC is particularly useful in settings where computational resources are limited, such as mobile devices and smart cards, as it provides the same level of security as other public-key cryptographic systems but with smaller key sizes.

ECC also offers other advantages over traditional public-key cryptography such as faster computation times, lower power consumption, and smaller message sizes.

ECC is widely used in a variety of applications, including digital signatures, encryption, and key exchange. It is implemented in many cryptographic standards, such as the Transport Layer Security (TLS) protocol used to secure internet communications, and is considered to be one of the most promising cryptographic techniques for the future.

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Complete question is:

___________ makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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Answer:

A. Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (StartFraction pi over 2 EndFraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).

Step-by-step explanation:

edge

The supplementary relationship between sine and cosine  

to write sin(x + y) is  sin x cos y + cos x sin y. and correct steps are

Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (Start Fraction pi over 2 End Fraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).

Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.

What is Sin(a + b) Identity in Trigonometry?

Sin(a + b) is the trigonometry identity for compound angles. It is applied when the angle for which the value of the sine function is to be calculated is given in the form of the sum of angles. The angle (a + b) represents the compound angle.

sin (a + b) = sin a cos b + cos a sin b

According to the question

sin(x+y)

= cos (\(\frac{\pi }{2} - (x+y)\))

Now as (cos (x-y) = cosx cosy - sinx siny )

=  Cos (\(\frac{\pi }{2}-x\))cos(-y) - sin(\(\frac{\pi }{2}-x\))sin(-y)

By using identity sin(–y) = –sin(y) and cos(–y) = cos(y)      

=  Cos (\(\frac{\pi }{2}-x\))cos(-y) - sin(\(\frac{\pi }{2}-x\))sin(-y)  

=  sin x cos y - cos x sin(-y)  

= sin x cos y + cos x sin y

Hence, the supplementary relationship between sine and cosine  

to write sin(x + y) is  sin x cos y + cos x sin y. and correct steps are

Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (Start Fraction pi over 2 End Fraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).

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Answer:

I believe the answer is 11.25 forgive me if I'm wrong.

Step-by-step explanation:

Answer:

Hypotenuse Formula = a^2 + b^2 = c^2

Step-by-step explanation:

6.75^2 + 9^2 = x^2

45.5 + 81 = 126.5

√126.5 = 11.25

I'm not from the US or UK. So, My method of answering this maybe different

Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

Answer:

(V + W) * 5 = 175     boat traveling downstream

(V - W) * 7 = 189       boat traveling upstream

V + W = 35

V - W = 27

2 V = 62    

V = 31 = speed of boat

2 W = 8

W = 4    speed of water

Upstream  7 * (31 - 4) = 189

Downstream 5 * (31 + 4) = 175

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: Number of people that support the candidate.

You need to calculate the sample size to estimate the population proportion of supporters given a confidence level of 99% and a margin of error of 4%

The margin of error of the confidence level for the population proportion is

d= \(Z_{1-\alpha /2}\) * \(\sqrt{\frac{p'(1-p')}{n} }\)

From this formula you have to clear the value of n:

\(\frac{d}{Z_{1-\alpha /2}}\)= \(\sqrt{\frac{p'(1-p')}{n} }\)

\((\frac{d}{Z_{1-\alpha /2}})^2\)= \(\frac{p'(1-p')}{n}\)

\(n*(\frac{d}{Z_{1-\alpha /2}})^2\)= \(p'(1-p')\)

n= \(p'(1-p') * (\frac{Z_{1-\alpha/2}}{d} )^2\)

\(Z_{1-\alpha/2}= Z_{0.995}= 2.586\)

sample proportion "p'" since there is no sample information, nor any previous information is known, you have to consider it as the "worse case scenario" and use the value of p'= 0.50

d= 0.04

\(n= p'(1-p') * (\frac{Z_{1-\alpha/2}}{d} )^2= 0.5*0.5*(\frac{2.586}{0.04} )^2= 1044.9= 1045\)

She has to take a sample of 1045 people to estimate the population proportion of her supporters with a confidence level of 99% and a margin of error of 4%

I hope this helps!

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.