Write the equation of the line that passes through the point (-6,1) and has a slope of 1/2 in slope-intercept form.

For the angles to be parallel, the value of x is of x = 28, and the angle is of 132º.

The angles need to have the same measure. Their measures are of 3x + 48 and 6x - 36, hence:

3x + 48 = 6x - 36

3x = 84

x = 84/3

x = 28.

Hence the measure of the angle is:

3x + 48 = 3 x 28 + 48 = 132º.

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Answer:

I think the answer is 3:5

Answer:

3.5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

72.25 in^2

The minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².

The equation of the circle is the equation that is used to represent the circle in the algebraic equation form with the value of the center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

\((x-h)^2+(y-k)^2=r^2\)

Here (h,k) is the center of the circle, and (r) is the radius of the circle.

A company produces circular drink coasters. the equation which represents the size of a coaster is,

\(x^2+y^2=18.06\)

The units are in inches. This equation can be written as,

\(x^2+y^2=(280/16)\)

\(x^2+y^2=(17/4)^2\)

Compare it with the equation of the circle, we get,

h=0

k=0

r=17/4 inch

The radius of the circular coaster is 17/4. Its diameter of it is,

\(d=2\times \frac{17}{4}\\ \\d=\frac{17}{2}\)

Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.

a=d=17/2 inch

The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,

A=a^2

A=(17/2)^2

A=75.25inch^2

Thus, the minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².

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Answer:

Below

Step-by-step explanation:

Earnings, e, will be divided by 4  friends to equal 12

e/4 = 12      multiply both sides of the equation by 4

4 * e/4 = 12 * 4

    e = 48

Answer:

i) it is not possible for the student to receive an A in the class

ii) 119 points

iii) 84points

Step-by-step explanation:

Total exam scores = 350points

homework scores of 7, 8, 7, 5, and 8

Let the third exam score =y

Exam scores = 81, 80, x

i) To know if the student would get an A in class, we would find the third exam score

(Scores received by a student)/ (total scores) = least of the grade percentage to get an A

(7 + 8 + 7 +5 + 8 + 81 + 80 + x)/350 = 0.9

(196+x)/350 = 0.9

196+x = 350 × 0.9

196+x = 315

x = 315-196

x = 119

119 > 100

Since the maximum grade for each of the exam score is 100points, it is not possible for the student to receive an A in the class.

ii) Since the least of the grade percentage that would guarantee an A is 0.9, the minimum score on the third exam that will give an A = 119points

iii) (Scores received by a student)/ (total scores) = least of the grade percentage to get a B

(7 + 8 + 7 +5 + 8 + 81 + 80 + x)/350 = 0.8

(196+x)/350 = 0.8

196+x = 350 × 0.8 = 280

x = 280-196

x = 84

The minimum score on the third exam that will give a B = 84points

The estimated cost for constructing the house in New Orleans, Louisiana of the given square feet is option A. $113,750.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that, construction rate per square feet is $65.

We have to find the estimated cost for a two-story home of 950 ft2 on the first floor and 800 ft² on the second floor.

Total area of the plot = 950 ft² + 800 ft²

                                   = 1750 ft²

Estimated cost can be calculated by multiplying total area with the construction rate per square feet.

Estimated cost = 1750 ft² × $65

                         = $113,750

Hence the estimated cost is $113,750.

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To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Answer:

Let m be the minimum value of original data set.

Given -

Therefore, the range of new data set is 96-m.

Now, we can find the difference between two ranges by subtracting the ranges -

\( \\ \implies \sf \: (96 - m) - (84 - m) \\ \\ \\ \sf \footnotesize \: using \: \: distributive \: \: property \: - \\ \\ \\ \bf \: it \: \: will \: \: be \: \: equal \: \: to \: \: 12. \\ \)

Therefore, the range of the new data set must be greater than the range of original data set.

Step-by-step explanation:

2+5=7 = 19-3+3=13

5-3=2

6+5=11-21+3= -33

8+5= 13= 1

4+5= 9

The system of equations that does not satisfy the ordered pair is

6m -21n = -33  

9m + 4n = 5

3m = 9 + 6n

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the ordered pair ( m , n ) = ( 5 , 3 )

The value of m = 5

The value of n = 3

Now , the equation will be

a)

The equation is

2m = 19 - 3n

Substituting the values , we get

2 x 5 = 19 - 3 x 3

10 = 19 - 9

10 = 10

The equation satisfies for the ordered pair

b)

The equation is

m - n = 2

Substituting the values , we get

5 - 3 = 2

2 = 2

The equation satisfies for the ordered pair

c)

The equation is

6m -21n = -33

Substituting the values , we get

6 x 5 - 12 x 3 = -33

30 - 36 = -33

-3 = -33

The equation does not satisfy the ordered pair

d)

The equation is

8m = −23 + 21n

Substituting the values , we get

8 x 5 = -23 + 21 x 3

40 = -23 + 63

40 = 40

The equation satisfies for the ordered pair

e)

The equation is

4m − 3n = 11

Substituting the values , we get

4 x 5 - 3 x 3 = 11

20 - 9 = 11

11 = 11

The equation satisfies for the ordered pair

f)

The equation is

2m + 5 = 5n

Substituting the values , we get

2 x 5 + 5 = 5 x 3

10 + 5 = 15

15 = 15

The equation satisfies for the ordered pair

g)

The equation is

9m + 4n = 5

Substituting the values , we get

9 x 5 + 4 x 3 = 5

45 + 12 = 5

57 = 5

The equation does not satisfy the ordered pair

h)

The equation is

3m = 9 + 6n

Substituting the values , we get

3 x 5 = 9 + 6 x 3

15 = 9 + 18

15 = 27

The equation does not satisfy the ordered pair

Hence , the equations 6m -21n = -33  ,  9m + 4n = 5 and 3m = 9 + 6n   does not satisfy the given ordered pair ( m , n ) = ( 5 , 3 )

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The equation written in slope-intercept form is y = (1/3)x -9

A linear equation is that which can be represented in the form of y =mx +c , m is the slope and c is the intercept.

The given equation is

y+6 = 1/3(x-9)

To determine the slope and the intercept this equation needs to be solved

y+6 = (1/3)x - 3

y = (1/3)x -9

Therefore this is the slope intercept format , here

the slope = 1/3

intercept = -9

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Answer:

Consider that it is a triangle ABC which means:

AB = 23; AC =? ; BC = 31

AC + AB = BC

AC = BC- AB

AC = 31-23

AC = 8

I hope it will help you :)

Step-by-step explanation:

The corresponding values of g(x) \(g(x)=-3(\frac{1}{2} )^x\) are -12, -6, -3, and -1.5.

A graph of each of the point of g(x) is shown in the image below.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the corresponding y-values of g(x) for each x-values given in the table as follows;

When the x-value = -2, the corresponding y-values of g(x) is given by:

\(g(-2)=-3(\frac{1}{2} )^{-2}\)

g(-2) = -3 × 4

g(-2) = -12.

When the x-value = -1, the corresponding y-values of g(x) is given by:

\(g(-1)=-3(\frac{1}{2} )^{-1}\)

g(-1) = -3 × 2

g(-1) = -6.

When the x-value = 0, the corresponding y-values of g(x) is given by:

\(g(0)=-3(\frac{1}{2} )^{0}\)

g(0) = -3 × 1

g(0) = -3.

When the x-value = 1, the corresponding y-values of g(x) is given by:

\(g(1)=-3(\frac{1}{2} )^{1}\)

g(1) = -3 × 0.5

g(1) = -1.5.

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Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

Answer:

21/32

Step-by-step explanation:

Convert \(-1+i\) to polar form.

\(z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}\)

By de Moivre's theorem,

\(\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)\)

QED

Hello!

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

(a) y = 36° and x = 36°

DAB = 90°

so y = 90° - 54° = 36°

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

AB // DC

so x and y are alternate-internal

so x = y = 36°

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

(b) y = 73° and x = 68°

SPQ = 90°

so yPQ = 90° - 51° = 39°

the sum of the angles of the triangle PQR = 180°

so y = 180° - (39° + 68°) = 73°

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

PSy = 90°

the sum of the angles of the triangle PSy = 180°

so PyS = 180° - (51° + 90°) = 39°

SyxR is a flat angle = 180°

so x = 180° - (39° + 73°) = 68°

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

(c) y = 36° and x = 54°

The center of the triangle is K.

So the triangles NKO, MKP, MNK, POK are isosceles

NKO = MKP and MNK = POK

MKP and NKO are opposed

so MKP = NKO = 72°

K is a full angle = 360°

so MKN and PKO = 360° - (72° + 72°) = 216°

so MKN = PKO = 216°/2 = 108°

PMN = y so because MKN is isoscel.

so we know x + y = 90° because PMN = 90°

and so we know PON = OPM = y

and so we know KNO = KON = x

the sum of the angles of the triangle KNO = 180°

so KNO and KON = 180° - 72° = 108°

so x = 108°/2 = 54°

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

the sum of the angles of the triangle MKN = 180°

so KMN and KNM = 180° - 108° = 72°

so y = 72°/2 = 36°

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

The correct options regarding the confidence intervals are given as follows:

2. B. (0.0361, 0.0973); The manufacturer can be 90% confident that the population proportion of discs that give an error message lies between 3.61% and 9.73%.

3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0472 and 45.0928 lbs.

4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The variables used to calculated these bounds are listed as follows:

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.9}{2} = 0.95\), so the critical value is z = 1.645.

The sample size and the estimate for item 2 are given as follows:

\(n = 180, \pi = \frac{12}{180} = 0.0667\)

Hence the lower bound of the interval is of:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0667 - 1.645\sqrt{\frac{0.0667(0.9333)}{180}} = 0.0361\)

The upper bound is of:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0667 + 1.645\sqrt{\frac{0.0667(0.9333)}{180}} = 0.0973\)

Hence option B is correct.

For item 3, we have that:

Hence the lower bound of the interval is of:

\(45.07 - 1.96\frac{0.09}{\sqrt{60}} = 45.0472\)

The upper bound is of:

\(45.07 + 1.96\frac{0.09}{\sqrt{60}} = 45.0928\)

Hence option D is correct.

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Answer:

Just make the equation and solve. Easy, isn't it?

Step-by-step explanation:

(18+m)/2= 5m

=>18+m= 10m

=>9m=18

=>m=2

hope it helped!

Answer:

Step-by-step explanation:

What is 20 as a decimal? To write 20 as a decimal you have to divide numerator by the denominator of the fraction. 20 is not a fraction so it is a decimal already. And finally we have: 20 as a decimal equals 20

Answer: 2x(8-+7) is true I believe

Step-by-step explanation:

my answer

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(m=\boxed{-\frac{4}{5}}\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Recall that the slope formula is:}}\\\\\frac{y_2-y_1}{x_2-x_1}\\\\(x_1,y_1), (x_2,y_2)-\text{Points}\)

⸻⸻⸻⸻

\(\boxed{\text{Finding the Slope:}}\\\\\rightarrow m=\frac{5-1}{-2-3} \\\\\rightarrow m=\frac{4}{-5}\\\\\rightarrow \boxed{m= -\frac{4}{5}}\)

⸻⸻⸻⸻  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The equation shows that the number of toys that must be bought for them to have equal profit will be 212 toys.

From the information, it should be noted that the equation that can be used to represent the information about Jaclyn company will be:

= 2125 + (49.99 × x)

= 2125 + 49.99x

The equation that can be used to represent the information about Richie company will be:

= (39.95 × x)

= 39.95x

Therefore, we will equate both equations:

2125 + 49.99x = 39.95x

49.99x - 39.95x =2125

10.04x = 2125

x = 212

Therefore, the number of toys that must be bought for them to have equal profit will be 212 toys.

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Answer:

x^2+12x=-11

Step-by-step explanation:

Answer:

(-1, 12) and (-11, 132)

Step-by-step explanation:

Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.

Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:

Unused yearly pass income = Modern cost x Modern amount requested

Unused yearly pass income = $25.25 x 2482 = $62,678.50

We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:

Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income

Alter in yearly pass income = $62,678.50 - $62,500 = $178.50

Subtract m + ? from m:

11-7 = 4

12-8 - 4

16-12 = 4

21-17 - 4

All the differences are identical, so the rule is to add 4 to m.

The expression would be m + 4

Answer: 162

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

51 = 11b – 15

66 = 11b

b = 6

      Statement              Reason

1.      LQ ║NP                  Given

2.     ∠Q ≅ ∠N                 ASA Theorem

3.     ∠L ≅ ∠P                   Alternate Interior Angles

4.    ΔLMQ ~ ΔPMN         ASA Similar Theorem

Similar shapes are enlargements of each other using a scale factor.

All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

The scale factors for length, area and volume are not the same.

From the given diagram,

 Statement              Reason

1.      LQ ║NP                  Given

2.     ∠Q ≅ ∠N                 ASA Theorem

3.     ∠L ≅ ∠P                   Alternate Interior Angles

4.    ΔLMQ ~ ΔPMN         ASA Similar Theorem

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3 root 2

root 3 x root 6 = root 18

to write it in its simplest form, we have to reduce the number to a situation, where we have a product that includes a perfect square and and another number

let me break that down

let us use another example;

root 8

we think of the largest perfect square that is also a factor of 8

then, we conclude to our answer; 4

next, we think of the number that multiplies with 4 to give is 8 and that is 2

so, we bring the 4 outside by square rooting it and everything gives us

2 root 2

to open this, we just square the 2 outside and multiply it by the 2 inside to give us root 8

if we apply this example to our question,

root 18 = root 9 * 2

this is because 9 is the largest square and factor of 18 and 2 multiplies with 9 which gives us root 9 * 2

then, we square root 9 to give us 3 and we bring this 3 out to give us

3 root 2

hope this helps.

if you do not understand, just send me a message

thank you