Find the measure of angle C of a triangle ABC, if: d m∠A = 60°+α, m∠B = 60°−α

Answer:

Step-by-step explanation:

P = 2w + 2l

l = 3 + w

38 = 2w + 2(3 + w)

38 = 2w + 6 + 2w

38 - 6 = 4w

32 = 4w

w = 32 : 4

w = 8 inches

l = 3 + w

l = 3inches + 8inches

l = 11 inches

Answer: 46

Step-by-step explanation:

Given that the coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5).

You need to find length GA, GD, RA and RD by using the formula

L = sqrt[ ( X2 - X1)^2 + ( Y2 -Y1 )^2 ]

Length GA will be

L = sqrt [ ( 8-3 )^2 + ( 4+8 )^2 ]

L = sqrt ( 5^2 + 12^2 )

L = sqrt(25 + 144)

L = sqrt (169)

L = 13.

Length GD will be

L = sqrt [ ( -5-3 )^2 + ( -2+8 )^2 ]

L = sqrt ( -8^2 + 6^2 )

L = sqrt(64 + 36)

L = sqrt (100)

L = 10.

Length RA will be

L = sqrt [ ( 10-4 )^2 + ( 0-8 )^2 ]

L = sqrt ( 6^2 + 8^2 )

L = sqrt(36 + 64)

L = sqrt (100)

L = 10.

Length RD will be

L = sqrt [ ( 10+2 )^2 + ( 0+5 )^2 ]

L = sqrt ( 12^2 + 5^2 )

L = sqrt(144 + 25)

L = sqrt (169)

L = 13.

The perimeter P will be

Substitute all the parameters into the formula below

P = GA + GD + RA + RD

P = 13 + 10 + 10 + 13

P = 46

Answer:

360

Step-by-step explanation:

Given

Digits: 0 to 5

Required

Number of 4 digit passcode that can be generated.

First, we need to get the number of usable digits.

Digits 0 to 5 = 0,1,2,3,4,5

Number of digits = 6

To make a 4 digit passcode;

The first digit can be taken from any of 6 digits

The second digit, any of the remaining 5 digits

The third digit, any of the remaining 4 digits

The fourth digit, any of the remaining 3 digits

Number of passcode = 6 * 5 * 4 * 3

Number of passcode = 360

Answer:

The blue point will be at (4, 3)

Step-by-step explanation:

Numbers inside the parenthases only affect x, but are revered. If it is -4, move right 4. lf it is 4, move left 4.

Numbers after the patentheses affect the movement of y. When the point is at (4, 0), move up 3.

Question

Points A, B and C are all on the

circumference of the circle. O represents the centre. DA and DB are tangents to the circle. Angle BDO = 31°

Work out the size of angle x

Answer:

62°

Step-by-step explanation:

To solve for the above question, we would be using circle theorems.

Step 1

Angle OBD = 90° This is because a radius and a tangent meet at 90°

Step 2

The sum of Angles in a triangle = 180°

180° = Angle OBD + Angle BDO + Angle BOD

180° = 90° + 31° + Angle BOD

Angle BOD = 180° - (90° + 31°)

= 180° - 121°

Angle BOD = 59°

Step 3

Angle BOD = Angle AOD because they are congruent ,therefore, Angle AOD = 59°

Step 4

The sum of angles of a straight line = 180°

Angle BOD, Angle AOD and Angle x are angles on a straight line

Hence,

180° = Angle BOD + Angle AOD + Angle x

180° = 59° + 59° + x

x = 180° - ( 59 + 59)°

x = 180° - 118°

x = 62°

Therefore Angle x = 62°

Answer:

Permuation; 210 possibilites

Step-by-step explanation:

With permutations we care about the order of the elements, whereas with combinations we don’t. For this question order matters, because you have two different positions you want to fill (captain, and co-captain).

This would be written as 15p2

To find the number of possibilities we want to use the permuation equation.

(,)=!(−)!

P=permutation

n= the set or population (15 soccer players)

r= subset (1 captain and 1 co-captain, total of 2)

(,)=(15,2)

=15!(15−2)!

= 210

If u are confused about !(factorial) in the equation here is a quick explanation

Many calculators have a factorial key (look for the ! symbol). This function of the calculator will automate the multiplications, but if you do not have a calculator that can compute factorials you just have to go like this

1! = 1

2! = 2 x 1 = 2

3! = 3 x 2 x 1 = 6

4! = 4 x 3 x 2 x 1 = 24

5! = 5 x 4 x 3 x 2 x 1 = 120

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362880

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

etc

Hope this helps!!

The number of possibilities in choosing captain and co-captain are 210 ways.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, a team of 15 soccer players needs to choose a captain and a co-captain.

Number of captains can be choose from 15 players.

Number of co-captains can be choose from 15-1=14 players.

So, the number of possibilities= 15×14

= 210 ways

Therefore, the number of possibilities in choosing captain and co-captain are 210 ways.

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Answer:

$16

Step-by-step explanation:

Let x=number of cars washed when y=allowance. We know she got $4 as a result of washing the car. She ends with $12, and we want to find the amount before washing the car.

$12 - $4 = $8

So, Coral had $8 before washing the car. Since she spent half of her allowance already playing golf, we know that $8 is only half of her total weekly allowance. Double this.

($8)2 = $16

Therefore, her weekly allowance is $16.

We can check this. She spent half playing golf, $16 / 2 = $8. She washes a car for $4. $8 + $4 = $12, which is what she ended with. So our answer is correct.

Answer:

-35 dollar net loss

Step-by-step explanation:

Since the gambler won $65 but still lost $100, we can see that we would still have a negative net loss.

Answer:

No it’s not a translation

Step-by-step explanation:

No it’s not a translation because a translation is when you are just moving a shape not resizing or rotating the shape.

Answer:

A. x is all real numbers.

Step-by-step explanation:

The domain is the input values for the function, in this case the x values

As we can see in the graph, x can be any real value

Answer:

A) x is all real numbers

Step-by-step explanation:

Domain = x

In the graph, x seems to continue infinitely in both directions. This means that x is all real numbers.

Answer:

Step-by-step explanation:

x=✓25*9

x=✓5^2*3^2

x=5*3

x=15

Answer:

The volume of the composite figure is:

Step-by-step explanation:

To identify the volume of the composite figure, you can divide it in the known figures there, in this case, you can divide the figure in a cube and a pyramid with a square base. Now, we find the volume of each figure and finally add the two volumes.

VOLUME OF THE CUBE.

Finding the volume of a cube is actually simple, you only must follow the next formula:

So:

VOLUME OF THE PYRAMID.

The volume of a pyramid with a square base is:

Where:

B = area of the base.

h = height.

How you can remember, the area of a square is base * height, so B = 6 ft * 6 ft = 36 ft^2, now we can replace in the formula:

Finally, we add the volumes found:

Answer:

x=36

Step-by-step explanation:

x×4/9=16

x=16×9/4=36

Answer:

666.70 at the end of every six months.

Step-by-step explanation:

At the end of  every six months deposit amount is 666.70

Compound interest is the interest paid on both principal and interest, compounded at regular intervals.

Formula of compound interest :

[tex]A = P(1+\frac{r}{100} )^{n}[/tex]

where,

A = final amount

P = initial principal

n = time in years

r = rate per annum

According to the question

Final Amount needed for a special vacation (A) = ​$4000

Time in years needed to collect Amount (n) =  3 years

Rate per compounded semiannually (r) = 4.5​%

Substituting values in formula for six months

Now time (n) = 3 * 6 = 18 years

using formula of compound interest

[tex]A = P(1+\frac{r}{100} )^{n}[/tex]

[tex]4000 = P(1+\frac{4.5}{100} )^{18}[/tex]

[tex]4000 = P(1.045 )^{18}[/tex]

now,

P = 666.70

Hence, at the end of  every six months deposit amount is 666.70

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Answer:

x = 18

Step-by-step explanation:

We can use Alternate Exterior Angles Theorem to find the angle above x. It would equal 94°. We then use Supplementary Angles to find x:

5x - 4 + 94 = 180

5x + 90 = 180

5x = 90

x = 18

Answer:

I am in 6th, doing 7th grade math, but can get up to 12th grade math lol.

x = 18

Step-by-step explanation:

First step: 5x - 4 + 94 = 180

Second step: 5x + 90 = 180

Last step: 5x = 90

So, therefore, your correct answer is: x = 18

Answer:

area = 25.12

Step-by-step explanation:

area of circle = pi(r)^2

area = 3.14 (4)^2 /2

area = 3.14 (16) / 2

area = 50.24 / 2

area = 25.12

Answer:

A = 78.9568350285

Step-by-step explanation:

A = TTr^2/2

A = TT4^2/2

A = 12.5663706^2/2

A = 157.913670057/2

A = 78.9568350285

Answer:

(-2, 0), (-1, 0), (1, 0), (2, 0)

Step-by-step explanation:

The x-intercept of function can be defined as the values of x at which the graph of the function intercepts the x-axis, or where the values of the function, y, is equals to zero.

As it is already given that the graph crosses x-axis at points (-2, 0), (-1, 0), (1, 0), and (2, 0), and as we know that the point where the graph crosses x-axis has the value of the function equal to zero, so the x-intercepts of the given function are (-2, 0), (-1, 0), (1, 0), and (2, 0)

Answer:

(–3, 0) and (1,0)

Step-by-step explanation:

on edge

Answer:

The answer is below

Step-by-step explanation:

We have a vector with a magnitude of 50 miles and a direction of 240 °.

To draw it, the first thing is to make a Cartesian plane, the first thing is to know in which quadrant it would be, 240 ° is in the third quadrant (180 ° - 270 °), that is, it would be 30 ° (270 ° - 240 °) with respect to to the y axis negative.

Knowing this angle, we calculate the value of x and y, knowing that the magnitude of the vector is 50 miles, that is, this value would be the hypotenuse.

The value on the x-axis can be calculated using the sine of the angle, like this:

sin 30 ° = x / 50

x = sin 30 ° * 50

x = 25, how is the third quadrant would be -25

Now to calculate the value on the y-axis it would be by means of Pythagoras and it would be:

y ^ 2 = 50 ^ 2 - 25 ^ 2

y ^ 2 = 1875

y = 43.3, -43.3 because it must be located in the fourth quadrant

Which means that to draw the vector that we are asked to do, we must draw a point from origin (0,0) to (-25, -43.3).

Then I leave a sketch of what it would be:

The chord of a circle is, LG

We have to given that,

A circle with center C is shown in figure.

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

And, The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle.

Hence, By given figure,

Chord of a circle is,

⇒ Line segment LG

Thus, Option 2 is true.

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Answer:

Approximately 55 students

Step-by-step explanation:

13% of 420 is 54.6 which you can then round up to 55

Hope this helped!

Answer:

55 students

Step-by-step explanation:

Take the percent and multiply by the number of students

13% * 420

.13 * 420

54.6

Rounding up

55 students

Answer: C) d-6.5 units: M(0.5, 8.5.-2)

Step-by-step explanation:

Distance between points [tex](x_1,y_1,z_1)[/tex] and [tex](x_2,y_2,z_2)[/tex]  :

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]

The midpoint of the line joining [tex](x_1,y_1,z_1)[/tex] and [tex](x_2,y_2,z_2)[/tex] is given by :-

[tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2},\dfrac{z_1+z_2}{2})[/tex]

The given points : (3,8, 0) and (-2,9,-4)

Distance between points (3,8, 0) and (-2,9,-4):

[tex]D=\sqrt{(-2-3)^2+(9-8)^2+(-4-0)^2}\\\\=\sqrt{25+1+16}\\\\=\sqrt{42}=6.48074069841\approx6.5\text{units}[/tex]

The midpoint of the line joining (3,8, 0) and (-2,9,-4) :

[tex](\dfrac{3+(-2)}{2},\dfrac{8+9}{2},\dfrac{0+(-4)}{2})=(\dfrac{1}{2},\dfrac{17}{2},-2)\\\\=(0.5, 8.5.-2)[/tex]

Hence, the correct answer is C) d-6.5 units: M(0.5, 8.5.-2).

Answer:

Step-by-step explanation:

eq. of any line parallel to y=1/2 x-4 is

y=1/2 x+a,where a is constant.

∵ it passes through (4,5)

5=1/2(4)+a

5=2+a

a=5-2=3

so reqd. eq. is y=1/2 x+3

Answer:

Equation of the line is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

[tex]y = \frac{1}{2} x - 4[/tex]

comparing this equation with the above formula

Slope or m is 1/2

Since the lines are parallel their slope are also the same

That's

m = 1/2

Equation of the line using point (4,5) is

[tex]y - 5 = \frac{1}{2} (x - 4) \\ y - 5 = \frac{1}{2} x - 2 \\ y = \frac{1}{2} x - 2 + 5 \\ y = \frac{1}{2} x + 3[/tex]

Hope this helps you.

Answer:

571.392 cm3

Step-by-step explanation:

Answer:

a) he would have 27500 won

b) changbin and han would have 70 lightsticks

Step-by-step explanation:

a)

multiply 45 rings by 500 won to get the total expense

45 x 500 = 22500

then subtract 22500 won from 50000 to get the amount left after the purchase

50000 - 22500 = 27500

this results in 27500 won total

b)

subtract 75 from 145 to get the amount left

145 - 75 = 70

Answer:

Hyunjin has 27,500 left.

Changbin & Han have 70 lightsticks left.

Step-by-step explanation:

A) 45 × 500 = 22500      50,000 - 22500 = 27500

B) 145 - 75 = 70

Answer:

B. Is the Answer 100 m²

Step-by-step explanation:

The ratio of the two solid is 729/125  

The ratio of the surface area = (729/125)^(2/3)=81/25  

Surface area = 25 * 324 / 81 = 100 m²

Answer:

The type of sampling method used is:

Step-by-step explanation:

A simple random sampling is a method where the pollster, in this case, the company, from a finite or infinite population (the costumers in the database) takes a representative sampling (in this case 100 costumers) to apply the survey and obtain data that can be used to deduce the way of thinking of all the costumers, though to actually identify this way of thinking, the sampling must be proportional to the size of the population, on the contrary, the data obtained won't be useful to reveal the real level of the satisfaction (In this case securely the database is 10,000 costumers or less, then the sampling is at least the 1% of the population). Another characteristic is all the people in the population should have the same opportunity to be part of the sampling, this is identified in the paragraph where says that the selection was random.

Answer:

B. simple random sampling

Step-by-step explanation:

right on edge

Answer:

4/3

Step-by-step explanation:

y = kx

4 = k(3)

4/3 = k3/3

4/3 = k

The constant proportion is 4/3.

Answer:

the correct answer is 20 just took

the test

Answer:

The correct answer would be D.

Step-by-step explanation: