I
5) From a sector of a circle subtending an angle of 135º and radius 14cm, a cup in form of a cone is made

Use it
Determine:

a) the radius of the conical cup.
(3 marks)

b) the volume of the cup​

Answer:

point slope form: y-3=[tex]-\frac{3}5}[/tex](x+2)

slope-intercept form: y=[tex]-\frac{3}{5}[/tex]x+[tex]\frac{9}{5}[/tex]

Step-by-step explanation:

so to find point-slope form, you first have to find the slope of the line

--slope =[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]=[tex]\frac{0-3}{3+2} =-\frac{3}{5}[/tex] (you have to use the two points shown: (-2,3) and (3,0) to plug in for y1, y2, x1, and x2 to find the slope.)

so your slope is [tex]-\frac{3}{5}[/tex].

Now all you have to do is use one of the points (-2,3) to sub in for y1 and x1 in the point-slope form equation.

Therefore, you get y-3=[tex]-\frac{3}{5}[/tex](x+2) for point-slope form.

Now for slope-intercept form, you already have the slope because you found it to complete the equation for point slope form

slope = [tex]-\frac{3}{5}[/tex]

Now slope intercept form is y=mx+b, where m is the slope and b is the y-intercept.

So, far we have y=[tex]-\frac{3}{5}[/tex]x+b

the easiet point to use for the x and y values is (3,0)

so, lets substitute: 0=[tex]-\frac{3}{5}[/tex](3)+b, which becomes 0=[tex]-\frac{9}{5}[/tex]+b

add [tex]-\frac{9}{5}[/tex] to both sides to get b=[tex]\frac{9}{5}[/tex]

Now you have both the slope and the y-intercept so you can now write the line in slope-intercept form.

You get [tex]y=-\frac{3}{5}x +\frac{9}{5}[/tex].

Answer:

k = 77/10

Step-by-step explanation:

The jar consist of blue, red and green marbles . The probability of each of them can be described as follows.

probability of blue marbles = 2/7

probability of red marbles = 3/k

probability of green marbles = 5/2k

The sum of the individual probability is equals to 1. Therefore,

2/7 + 3/k + 5/2k = 1

collect like terms

(6 + 5)/2k = 1 - 2/7

11/2k =(7 - 2) /7

11/2k = 5/7

cross multiply

10k = 77

divide both sides by 10

k = 77/10

Answer:

solution,

Let the points be A and B

A(-4,-8)--->(X1,y1)

B(-4,12)---->(x2,y2)

Now,

[tex]ab = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \: \: \: = \sqrt{ {( - 4 - ( - 4)}^{2} + 12 - ( - 8) ^{2} } \\ \: \: \: \: = \sqrt{ {( - 4 + 4)}^{2} + {(12 + 8)}^{2} } \\ = \: \: \: \: \sqrt{ {(0)}^{2} + {(20)}^{2} } \\ \: \: \: \: = \sqrt{0 + 400} \\ \: \: \: = \sqrt{400} \\ \: \: = \sqrt{ {(20)}^{2} } \\ \: \: = 20 \: units[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

Step-by-step explanation:

m=[tex](5,\frac{25}{4} )[/tex]

midpoint line between A and B

The midpoint is halfway between the two end points:

Its x value is halfway between the two x values

Its y value is halfway between the two y values

Answer: C

Step-by-step explanation:

Simplify(Subtract 2)

x > 0

Greater than is represented by a open circle with an arrow pointing right.  Because x is greater than 0, the point must be on 0.

Hope it helps <3

Answer:

C

Step-by-step explanation:

The inequality is x+2 > 2

x > 0 means that x is positive

so the graph must start from 0 and then should grow towrd the positive value

since we have x > 0 then 0 should be excluded

the graph that fits our solution is c where 0 is excluded

Answer:

2.5

Step-by-step explanation:

The median is the middle value of the data set. If there is no exact middle value then it is the average of the 2 values either side of the middle.

0  ,  1  ,  2  ,  3  ,  4  ,  5

                 ↑ middle of data

Thus median = [tex]\frac{2+3}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5

Answer:  The answers are in the steps

Step-by-step explanation:

x         y        value of y/x

-3        -3            1

1           1             1

3           3             1

Answer:

Step-by-step explanation:

To factorise this, we find the equality ( common factor).

Here this is 4.

So the factores version = 4(t+11)

Answer: x = -3/4 can not be a rational zero of the polynomial.

Step-by-step explanation:

We have the polynomial:

6x^5 + ax^3 -bx -12 = 0.

The theorem says that:

If P(x) is a polynomial with integer coefficients, and p/q is a zero of P(x) then p is a factor of the constant term (in this case the constant term is -12) and q is a factor of the leading coefficient (in this case the leading coefficient is 6.).

The factors of -12  (different than itself) are (independent of the sign).

1, 2, 3, 4 and 6.

So p can be: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6.

The factors of 6 are:

1, 2 and 3, so q can be 1, -1, 2, -2, 3, -3.

Then the option that can not be a zero of the polynomial is

x = -3/4

because the number in the denominator must be a factor of the leading coefficient, and 4 is not a factor of six.

Answer:

Step-by-step explanation:

[tex]\dfrac{|AC|}{\sin B}=\dfrac{|AB|}{\sin C}\\\\\dfrac{9}{\sin38^o}=\dfrac{11}{\sin C}\\\\\dfrac{\sin38^o}9=\dfrac{\sin C}{11}\\\\\sin C=\frac{11}9\sin38^o =\frac{11}9\cdot0,6157=0,7525(2)\\\\\sin C\approx0,7525\quad\iff\quad |\angle C|\approx48^o48'\\\\|\angle A|=180^o-|\angle B|-|\angle C|\\\\|\angle A|=180^o-38^o-48^o48'\\\\|\angle A|=93^o12'\approx93^o[/tex]

Answer: D

Step-by-step explanation:

Answer:

the answer is "C"

Step-by-step explanation:

i just took the test

Answer:

True

Step-by-step explanation:

In order to inscribe a circle in a triangle, the circle's center must be placed at the in center of the triangle, is true. the in center also is a point where the bisectors of the angles meet.

It would be irrational.

Reasoning:

A rational number is any number that can be expressed as a fraction of two integers provided that the denominator is not zero.

π is an irrational number because its approxiamation is [tex]\frac{22}{7}[/tex] is not the exact value of π. Additionally, we know that the quotient of irrational numbers can be rational or irrational. Here is the case where we have [tex]\frac{\pi }{2}[/tex], an irrational number divided by a rational number giving a quotient that is irrational.

Answer: irrational

Step-by-step explanation:

Apart from multiplying by 0 or dividing by pi, nothing can make pi rational. pi/2 is the same thing as 1/2pi, which is irrational, because it cannot be simplified into a repeating or terminating decimal

Answer:

A) P(10 on three rolls) = 1/1728 = 0.0005787

B) P(10 in two of three rolls) = 11/1728 = 0.0063657

Step-by-step explanation:

Each die has 6 possible values, so a pair of dice have a total of 6*6=36 outcomes.

To find a sum of 10, the cases are:

(4,6), (5,5) and (6,4).

So to have a sum of 10 we have 3 cases among the 36 possible, therefore the probability is:

P(10) = 3/36 = 1/12

A)

If we want the sum of 10 in each of the three rolls, the probability is:

P(10 on three rolls) = P(10)^3 = (1/12)^3 = 1/1728 = 0.0005787

B)

If the sum is 10 in two of three rolls, in one roll we need the probability of the sum not being 10:

P(not 10) = 1 - P(10) = 1 - (1/12) = 11/12

So we have:

P(10 in two of three rolls) = P(10)^2 * P(not 10) = (1/12)^2 * (11/12)

P(10 in two of three rolls) = 11/1728 = 0.0063657

Answer:

t =5

g = 15

Step-by-step explanation:

t = tennis balls

g = golf balls

70 = 5t+3g

85 = 2t+5g

Multiply the first equation by -2

-2(70 = 5t+3g)

-140 = -10t -6g

Multiply the second equation by 5

5(85 = 2t+5g)

425 = 10t + 25g

Add these new equation together to eliminate t

-140 = -10t -6g

425 = 10t + 25g

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

285=0t+19g

Divide by 19

285/19 = g

15 = g

Now find t

85 = 2t+5g

85 = 2t +5(15)

85 = 2t + 75

10= 2t

t =5

Let the cost of a can of tennis balls be $x and that of a sleeve of golf balls be $y.

5x + 3y = 70

2x + 5y = 85

(5x + 3y) x 2 = 70 x 2

10x + 6y = 140

(2x + 5y) x 5 = 85 x 5

10x + 25y = 425

10x + 25y -10x - 6y = 425 - 140

19y = 285

y = 15

2x + 5y = 85

2x + 75 = 85

2x = 10

x = 5

Therefore the cost of a sleeve of golf balls is $15 and that of a can of tennis balls is $5.

Answer:

30 persons

Step-by-step explanation:

Let's create a proportion using the following setup:

persons/rice=persons/rice

We know that 12 persons can eat 8 kilograms of fried rice.

12 persons/ 8 kg of rice= persons/rice

We also know that x (unknown) persons can eat 20 kilograms of fried rice.

12 persons/ 8 kg of rice= x persons/ 20 kg of rice

12/8=x/20

x is being divided by 20. The inverse of division is multiplication. Multiply both sides of the equation by 20.

20(12/8)=(x/20)20

20*12/8=x

20*1.5=x

30=x

30 persons can eat 20 kilograms of fried rice.

Answer:

30 people

Step-by-step explanation:

1) Set up a proportion, 8kg/12 = 20kg/x

2) Do cross multiplication to solve for x

3) x = 30 people

Answer:

1 * 10^11

Step-by-step explanation:

Take the gulf of mexico and divide by the rate to get the number of seconds

2,434,000,000,000,000 / 16790

Change each to scientific notation

2 * 10 ^15/ 1.6 *10^ 4

Rounding

2 * 10^15 / 2 * 10^4

Dividing the numbers 2/2 =1

Dividing the exponents means subtracting the powers = 10 ^(15-4) = 10 ^1

1 * 10^11

Answer:

(A) [tex]1157,625$ cm^3[/tex]

Step-by-step explanation:

s = 10,5 cm.

Volume do cubo = [tex]s^3[/tex]

[tex]=10,5^3\\=1157,625$ cm^3[/tex]

O volume do cubo é  [tex]1157,625$ cm^3[/tex]

Answer:

A

Step-by-step explanation:

T is the dependent variable

a dependent variable means it depends on something so if a number changes it will change the end result for T.

T is dependent on P since if the weight on the elevator changes the total weight will change. That is what makes it dependent.

Answer:

They are both dependent variables.

Step-by-step explanation:

I did this on Khan Academy and it worked.

Answer: 18.75 pints per month

Step-by-step explanation:

Answer:

6√2

Step-by-step explanation:

Gm = √a×b

= √4×18

= √72

= √36×2

= √6²×2

= 6√2

Answer:

growth

Step-by-step explanation:

Exponential equations are in the form

y = a * b^x

a is the initial value

b is the growth or decay

b>1 is growth b-1 rate  of growth

b <1 decay  1-b rate of decay

y = 4(5.6)^x

5.6 is greater than 1 so it is growth

Answer:

the first step to eliminate d is to multiply equation B by 5

second :(m,n) (-6,-11)

value of a can be substituted into equation D to solve the system of equations is 7b-1

Step-by-step explanation:

first equation:

4c=d-8 or 4c-d=-8

c=5d+8 or c-5d=8

so the first step to eliminate d is to multiply equation B by 5

second equation :

n=3m+7 or n-3m=7

n-2m=1

n-3m=7

solve :

1-eliminate n by subtracting two equation : : n-2m-(n-3m)=1-7

-2m+3m=-6

m=-6

substitute m: n-3(-6)=7 , then n+18=7

n=7-18=-11

third :

a=3b+6 or a-3b=6

a=7b-1

find a

a-3b=6

value of a can be substituted into equation D to solve the system of equations is 7b-1

Answer:

39.8°

Step-by-step explanation:

We know slope is rise over run. That would mean our right triangle would have a horizontal leg of 6 and a vertical leg of 5. From there we use tan∅ to help solve ∅:

tan∅ = 5/6

∅ = tan⁻¹(5/6)

∅ = 39.8056

Answer:

144

Step-by-step explanation:

Abigail wants to produce a tapestry that will be in the shape of a parallelogram

The tapestry is 24 inches across the bottom and 36 inches tall

She pieces smaller simlar parallelograms that are 2 inches wide and 3 inches tall

The first step is to find the area of the whole tapestry

Area = base × height

Base= 24 inches

Height= 36 inches

Area= 24×36

= 864 square inches

The next step is calculate the area of the smaller pieces

Area= base × height

Base= 2 inches

Height= 3 inches

Area= 2×3

= 6 square inches

Therefore, the value needed to produce the tapestry can be calculated by dividing the area of the whole tapestry by the area of the smaller pieces

= 864/6

= 144

Hence Abigail will need 144 smaller similar parallelograms to make the tapestry.

Answer:

144

Step-by-step explanation:

Answer:

x intercepts are : (1,0)(4,0),(-3,0)

Step-by-step explanation:

x intercepts are : (1,0)(4,0),(-3,0)

plot only the x values

hope it helps

Answer:

  1. [tex]\dfrac{2y^3}{3}[/tex]

  2. 9,765,625

Step-by-step explanation:

The relevant exponent laws are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

  a^-b = 1/a^b

__

1)

  [tex]\dfrac{3x^3y^5\cdot 8xy^4}{(6x^2y^3)^2}=\dfrac{(3\cdot 8)x^{(3+1)}y^{5+4}}{6^2x^4y^6}=\dfrac{2}{3}x^{4-4}y^{9-6}=\boxed{\dfrac{2y^3}{3}}[/tex]

__

2)

  [tex]5^3\div 5\cdot(5^2)^4=5^3\cdot 5^{-1}\cdot 5^8=5^{3-1+8}\\\\=5^{10}=\boxed{9\,765\,625}[/tex]  

Answer:

29 square yards

Step-by-step explanation:

see attachment for the graph

Vertices of rectangular pool are A(3,2),B(7,8),C (4,10), and D (0,4).

AB=[tex]\sqrt{(7-3)^{2}+(8-2)^{2}}= \sqrt{16+36}=\sqrt{52}[/tex] yard=CD

BC= [tex]\sqrt{(7-4)^{2}+(8-10)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]yard=DA

In order to find the area of rectangular pool =Length × Breadth

                                        =√52 ×√13=13×2=26 sq. yard

Vertices of triangle given are: P(5,2),Q(7,2) and R(7,5).

PQ= 2 units, QR= 3 units

Area of right triangle PQR=1/2 ×PQ×PR

                                           =1/2×2×3= 3 sq. yards

Next is to find total material needed to cover( that includes bot rectangular pool and triangular hot tub)

       = Area of rectangle + Area of right triangle

       =26+3=29 square yards

Answer:

29

Step-by-step explanation:

I just did my homework