In △ABC,c=9, m∠B=65°, and a=105. Find b.

Answer:

The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.

Step-by-step explanation:

A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.

Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:

[tex]2\cdot \alpha = 120^{\circ}[/tex]

[tex]\alpha = 60^{\circ}[/tex]

The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])

[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]

[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]

[tex]\beta = 180^{\circ}-\alpha[/tex]

[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]

[tex]\beta = 120^{\circ}[/tex]

The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.

Answer:  see below

Step-by-step explanation:

[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]

P(x) ÷ Q(x)

[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]

P(x) + Q(x)

[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]

P(x) - Q(x)

[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]

P(x) · Q(x)

[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]

Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

Step-by-step explanation:

The cylinder is given by A = pi/4 the volume of the prism or π/4  x (4r²h) or π x r² x h

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Area circle is A = πr²

Area square with side s = s²

The side of the square is equal to the diameter of the circle

Area square = D²

A diameter of square is always twice the radius

Area square = (2r)² = 2²r² = 4r²

So , on simplifying , we get

Area circle/Area square = (πr²)/(4r²)

Area circle/Area square = π/4

Now , The volume Prism = Area Square x h

Volume Prism =  4r²h

Volume of Cylinder= Area Circle x h

Volume of Cylinder = π x r² x h

So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h

Volume of Cylinder/Volume of Prism = π/4

Volume of Cylinder = π/4 x Volume Prism

And , The volume of Cylinder = π/4  x (4r²h)

Hence , the volume of cylinder is V = π/4  x (4r²h)

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Answer:

f(x) = 60(2)ˣ

Step-by-step explanation:

f(x) = a(b)ˣ

After one month:

120 = a(b)¹

After four months:

960 = a(b)⁴

Divide the second equation by the first:

8 = b³

b = 2

Plug into either equation and find a.

120 = a(2)¹

a = 60

Therefore, f(x) = 60(2)ˣ.

ANSWER :

6i - (1-i)

Step - by - step explanation:

( 4 + 2i ) - ( 1 - i )

( 4 + 2 × i) - ( 1 - i )

( 6× i ) - ( 1 - i )

= 6i- (1-i)

Hope this helps and pls mark as brainliest :)

Answer:

Blue paint=21 ounces

Step-by-step explanation:

3/4 cup=6 ounces

1 cup=8 ounces

3/4 cup of blue paint=6 ounces of blue paint

1 cup of white paint= 8 ounces of white paint

Ava has 28 ounces of white paint

Find the required blue paint

Let the required blue paint=x

Blue paint ratio white paint

6:8=x:28

6/8=x/28

Cross product

6(28)=x(8)

168=8x

x=168/8

x=21 ounces

Answer:se

Step-by-step explanation:

Answer:

 A-2, B-DNE*, C-3, D-DNE, E-4, F-1

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

The first attachment shows the solutions to A and C.

The second attachment shows the solutions to E and F.

There are no real number solutions to systems B and D.

_____

In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.

A.

 (3-x) +12 = x^2 +x

 15 = x^2 + 2x

 16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root

 ±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A

__

B.

 (x -1) -15 = x^2 +4x

 -16 = x^2 +3x

 -13.75 = x^2 +3x +2.25 = (x +1.5)^2

roots are complex: -1.5 ±i√13.75

__

C.

 (1-2x) +5 = x^2 -3x

 6 = x^2 -x

 6.25 = x^2 -x + .25 = (x -.5)^2

 ±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C

__

remaining problems are done in a similar way.

_____

* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.

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

Hope this helps!

Brainliest would be great!

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

With all care,

07x12!

Answer:

Step-by-step explanation:

2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

0.10512

Step-by-step explanation:

Given the following :

Mean number of calls(μ) in 2 hours = 14

2 hours = 60 * 2 = 120 minutes

Average number of calls in 45 minutes :

= (45 / 120) * 14

= 0.375 * 14

= 5.25

Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)

Using the poisson probability formula:

P(x, μ) = [(e^-μ) * (μ^x)] / x!

Where :

e = euler's constant

μ = 5.25

x = 0, 1, 2

Using the online poisson probability calculator :

P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)

P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.

Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.

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Answer:

(28/33+28 ) *100

Step-by-step explanation:

(28/33+28 ) *100

(28/61)*100

Answer:

it's 2

Step-by-step explanation:

I did it before

Answer:

The cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Step-by-step explanation:

Let the:

Cost to rent a chair = x

Cost to rent a table = y

We would form an algebraic equation.

The total cost to rent 2 chairs and 3 tables is $31

2x + 3y = 31 ...... Equation 1

The total cost to rent 6 chairs and 5 tables is $59

6x + 5y = 59 ......... Equation 2

We solve the above equation above using elimination method

Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2

Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1

Hence, we have:

2x + 3y = 31 ...... Equation 1 × 6

6x + 5y = 59 ......... Equation 2 × 2

12x + 18y = 186........ Equation 3

12x + 10y = 118 .…...... Equation 4

Subtracting Equation 4 from Equation 3

= 8y = 68

y = 68/8

y = 8.5

Therefore, the cost to rent a table = $8.50

Substituting 8.5 for y in Equation 1 to get the value of x

2x + 3y = 31 ...... Equation 1

2x + 3(8.5) = 31

2x = 31 - 3(8.5)

2x = 31 - 25.5

2x = 5.5

x = 5.5/2

x = 2.75

The cost to rent a chair = $2.75

Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Answer:

160 adults and 80 students

Step-by-step explanation:

With the information from the exercise we have the following system of equations:

Let x = number of students; y = number of adults

I want to maximize the following:

z = 3 * x + 6 * y

But with the following constraints

x + y = 240

y / 2 <= x

As the value is higher for adults, it is best to sell as much as possible for adults.

So let's solve the system of equations like this:

y / 2 + y = 240

3/2 * y = 240

y = 240 * 2/3

y = 160

Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.

You did not give any options but i will try to answer.

y < -lxl basically means that the value of y is less than the absolute value of x time - 1.

So if x = 2, then y is any number less than -2.

And if x is -3. then y is any number less than -3.

Happy to help!

Answer:

The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.

Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

Answer:

The value of  annuity is  [tex]P_v = \$ 7929.9[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 250[/tex]

     The  interest rate  is   [tex]r = 5\% = 0.05[/tex]

     Frequency at which it occurs in a year is  n = 4 (quarterly )

      The number of years is  [tex]t = 10 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)

 substituting values

             [tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]

             [tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]

             [tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]

            [tex]P_v = \$ 7929.9[/tex]

Answer:

4 plants

Step-by-step explanation:

If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4

(8 * 4 is 32)

She will have one dollar left but she can't buy another plant since that's not enough.

Answer:

4 plants

Step-by-step explanation:

Take the amount of money she has and divide by the cost per plant

33/8

The amount is 4 with 1 dollar left over

4 plants

Hello!

Answer:

Table B.

Step-by-step explanation:

An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:

We can use points on the table:

[tex]f(x)[/tex] = (7, 21)

The inverse of this function would 7 as its y value, and 21 as its x value:

[tex]f^{-1} (x)[/tex] = (21, 7)

The only table shown that correctly shows this relationship is table B.

Answer:

13, 21

Step-by-step explanation:

Add 8 to the next number from the left to the right.

Answer:

The next three numbers in the sequence are: 13, 21, 29.

Step-by-step explanation:

Common Pattern: +8

-27 +8 = -19

-19 + 8 = -11

-3 + 8 = 5

5 + 8 = 13

13 + 8 = 21

21 + 8 = 29

Answer:

In 10 years she'll have approximately $21865.4 in her account.

Step-by-step explanation:

When an amount is compounded continuously its value over time is given by the following expression:

[tex]v(t) = v(0)*e^{rt}[/tex]

Applying data from the problem gives us:

[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]

In 10 years she'll have approximately $21865.4 in her account.

Answer:

21,865.43

previous answer left out the last digit

Step-by-step explanation:

Answer:  width = 2.4 in, length = 5

Step-by-step explanation:

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.

Let the length and width of the rectangle be x and y.

Then Area of the rectangle = xy

Now, from the triangle we can conclude that

[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]

Put the value of y in Area we get

[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]

Differentiating it w.r.t x we get

[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]

Put A'(x)=0 for maximum /minimum value

[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]

Now, [tex]A''(3)=-\frac{8}{3} &lt;0[/tex]

Therefore the area of the rectangle is maximum for x=3 inch

Now,

[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]

Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.

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Answer:

the length of DF = 3/4 AC

see below for explanation

Step-by-step explanation:

ABC is said to be approximately equal to DEF

The scale factor from ABC to DEF = 3/4

From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.

We can deduce from the question, ΔABC was dilated to form ΔDEF

In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.

In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :

AB, BC and AC

ΔDEF has 3 sides : DE, EF and DF

If AB corresponds to DE

BC corresponds to EF

AC corresponds to DF

Then:

length DE = scale factor × AB = 3/4 AB

length EF = scale factor × BC = 3/4 BC

length DF = scale factor × AC = 3/4 AC

Therefore, the length of DF = 3/4 AC

Answer:

The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation

Answer:

200,000

Step-by-step explanation:

The current population: 50,000

Doubling time:70

Population after 280 years=?

280/70=4

50,000*4=200,000

Hope this helps ;) ❤❤❤

Answer: 800,000

Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.

Answer:

x + 1 - ( 4 / x³ + 3x² + 8 )

Step-by-step explanation:

If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area  [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.

Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

They're making me write something here so I can post the answer:

p(p + 12)