Martin is an artist who molds plaster into unique shapes.
How much plaster can Martin fit into the mold shown?

Answer:

B. 44°

Step-by-step explanation:

Central angle = 3x + 10°

Inscribed angle = 2x - 17°

Now

Central angle = 2 * inscribed angle

( Central angle is double of the inscribed angle standing on same arc)

3x + 10° = 2 ( 2x - 17°)

3x + 10° = 4x - 34°

4x - 3x = 34 ° + 10°

x = 44°

Hope it will help :)❤

Answer:

Step-by-step explanation:

h

Answer:

a. x = 180 - (j + k)

b.

j + k = (5x - 2) + (2x - 2) = 7x - 4

l = x

x = 180 - (7x - 4)

x = 180 - 7x + 4

8x = 184

x = 184/8

x = 23

l = 23°

j = 5x - 2

j = 5 × 23 - 2

j = 115 - 2

j = 113°

k = 2x - 2

k = 2 × 23 - 2

k = 46 - 2

k = 44°

or k = 180 - (23 + 113) = 180 - 136 = 44°

Answer:

[tex]Length = Width = 6\ units[/tex]

Step-by-step explanation:

Given

[tex]Area=36[/tex]

Required

The least possible material

Sandboxes usually, are rectangles or squares.

Using the above assumption, the area is calculated as:

[tex]Area= Length * Width[/tex]

[tex]Area= L* W[/tex]

[tex]L * W = 36[/tex]

Make L the subject

[tex]L = \frac{36}{W}[/tex]

The material of the outer edge is calculated by the perimeter.

[tex]Perimeter = 2 * (L +W)[/tex]

[tex]P = 2 * (L + W)[/tex]

Substitute [tex]L = \frac{36}{W}[/tex]

[tex]P = 2 * (\frac{36}{W} + W)[/tex]

Open bracket

[tex]P = \frac{72}{W} + 2W[/tex]

[tex]P = 72W^{-1} +2W[/tex]

To get the minimum material needed, we differentiate P

[tex]P' = -72W^{-2} + 2[/tex]

Set: [tex]P' = 0[/tex]

[tex]-72W^{-2} + 2 = 0[/tex]

Collect like terms

[tex]72W^{-2} = 2[/tex]

Divide both sides by 72

[tex]W^{-2} = \frac{2}{72}[/tex]

[tex]W^{-2} = \frac{1}{36}[/tex]

Rewrite as:

[tex]\frac{1}{W^2} = \frac{1}{36}[/tex]

Take positive square roots of both sides

[tex]\frac{1}{W} = \frac{1}{6}[/tex]

Cross multiply

[tex]W = 6[/tex]

Recall that: [tex]L = \frac{36}{W}[/tex]

So, we have:

[tex]L =\frac{36}{6}[/tex]

[tex]L = 6[/tex]

Hence, the dimension with the littlest material as possible is:

[tex]Length = Width = 6\ units[/tex]

Answer:

B

Step-by-step explanation:

Use the definition of a logarithm,  log b ( x ) = y  ⟹  b y = x , to convert from the logarithmic form to the exponential form. 10^ 4 = x

The exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x

When you raise a number with an exponent, there comes a result.

Lets say you get [tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.

Log with base 10 is written as [tex]\log(x)[/tex] simply.

The given logarithmic equation is;

[tex]\log x = 4[/tex]

Since, log with base 10 is written as [tex]\log(x)[/tex] simply, therefore, we have:

[tex]\log_{10} x = 4[/tex]

Using the definition of logarithm, we get;

[tex]x = 10^4[/tex]

Equivalently, [tex]10^4 = x[/tex] (option B).

Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x

Learn more about logarithm here:

https://brainly.com/question/20835449

Answer:

540

Step-by-step explanation:

area of trapezium is b×h

Answer:

540 Sq m

Step-by-step explanation:

Area of parallelogram EFGH

= base * height

= 30 * 18

= 540 Sq m

Answer:

5 / 8

Step-by-step explanation:

Total possible outcomes = (1, 2, 3, 4, 5, 6, 7, 8)

Odd outcomes = (1, 3, 5, 7)

Outcomes > 7 = 8

Required outcomes = (1, 3, 5, 7, 8)

Number of required outcomes = 5

P(pointer stops on odd or number > 7) = required outcome / Total possible outcomes

P(pointer stops on odd or number > 7) :

= 5 / 8

Answer:

-2

Step-by-step explanation:

Given equation

x - 2y = 4

2y = x - 4

y = ( x - 4 ) / 2

y = x/2 - 4 /2

y = x/2 - 2

Comparing with y = mx + b

y-intercept (b) = - 2

Hope it will help :)❤

Answer:

-3 = D

Step-by-step explanation:

A really smart freind of mine says this is the answer.

Answer:

the answer is D :)

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{9-10}{6-4}[/tex]

Answer: 1

Step-by-step explanation:

Answer:

[tex]x^2+y^2=9[/tex]

Step-by-step explanation:

Equation of a circle (when centred at the origin):

[tex]x^2+y^2=r^2[/tex] where r is the radius of the circle

Plug in the point (0,3) to solve for the radius squared

[tex]0^2+3^2=r^2\\9=r^2[/tex]

Plug r² back into the original equation

[tex]x^2+y^2=9[/tex]

I hope this helps!

Answer:

She has completed 4 problems

Step-by-step explanation:

Take the total number of problems and multiply by the percent completed

20 * 20%

20 * .20

4

She has completed 4 problems

Answer:

4

Step-by-step explanation:

Answer:

$20.30  plus tax

Step-by-step explanation:

You multiply 28 x .30 and that is your discount.

Answer:

$20.30

Step-by-step explanation:

Answer:

hello your question has a missing diagram attached below is the missing diagram

answer :  

Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )

Step-by-step explanation:

when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between  the given circles and then construct a line through it

Answer:

Mark the point of intersection S of circles R and P, and construct line QS.

Step-by-step explanation:

This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points.  If your in FLVS, it would be in lesson 7.04.  I also got this right on my test.  Good luck!

Answer: 9.

Step-by-step explanation:

6 large rooms which will add up to 18

9 small rooms which will also add up to 18 totaling the 36 guests.

The no. of small and large rooms in the hotel are 9 and 6 respectively.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, Emily is blocking off several rooms in a hotel for guests coming to her wedding.

Let us assume that small rooms be x and large rooms to be y.

Emily booked a total of 15 rooms which is x + y = 15...(i).

which can accommodate 36 guests altogether which is 2x + 3y = 36...(ii)

Now if we multiply eqn(i) by 2 it'll be 2x + 2y = 30...(iii)

Now subtracting eqn(iii) from eqn(ii) we get y = 6.

substituting the value of y in eqn(iii) we get x = 9.

So, the number of small rooms is 9 and no. of large rooms is 6.

learn more about linear equations here :

https://brainly.com/question/13738061

#SPJ2

Answer:

Area:12.5663706            Circumference: 12.5663706

Step-by-step explanation:

Answer:

Volume of cylinder = 12,560 feet³

Step-by-step explanation:

Given:

Height of cylinder = 40 ft

Radius of cylinder = 10 ft

Find:

Can its volume be 10 ft ?

Computation:

Volume of cylinder = πr²h

Volume of cylinder = (22/7)(10)²(40)

Volume of cylinder = (3.14)(10)²(40)

Volume of cylinder = (3.14)(100)(40)

Volume of cylinder = 12,560 feet³

Volume of this cylinder never be 10 feet

Answer:

A

Step-by-step explanation:

I am to determine the future value of Thomas' deposit with annual compounding

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

840 x (1.075)^5 = 1205.93

I am to determine the future value of Sherill's deposit in 5 years using simple interest

The amount that would be in the account = amount deposited + interest earned on deposit

interest earned on deposit can be determined by determining the simple interest

Simple interest = amount deposited x time x interest rate

1250 x 0.069 x 5 = 431.25

Amount that would be in her account after 5 years = 1250 +  431.25 =  1681.25

Sheril's money is higher by - 1681.25 -  1205.93 = 475.32

Answer:

216

Step-by-step explanation:

(6 to the -4th) * (6 to the 7th)

Complete Question

Tyrone is making 52 cookies for a party. Some will be a pecan cookies and some will be honey ginger. The ratio of pecans to a honey ginger is 7:6. How many of each kind of cookie will he make

Answer:

28 pecan cookies and 24 Honey ginger cookies

Step-by-step explanation:

From the above question

Pecans : Honey ginger = 7:6

Sum of Proportion = 7 + 16 = 13

Total number of cookies = 52

Number of pecans

= 7/13 × 52 = 28 pecans cookies

Number of Honey ginger

= 6/13 × 52 = 24 Honey ginger cookies

Therefore, we have:

28 pecan cookies and 24 Honey ginger cookies

Tn = a + (n-1) d

= 3 + (n-1) (-4)

= 3 -4n +4

= 7-4n

hope it helped you dear