Three friends share 2 bags of trail mix equally.

What fraction of a bag of trail mix does each friend get?

Answer:

38

Step-by-step explanation: subtraction:

Input interpretation: x: 105-67=

Ratio in lowest terms: 38

Division:

105/67= 1.56...=1 38/67---1R 38= 1 with the remainder of 38. So just 38.

The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

By the above theorem, the equation is written as,

x + 67 = 107

Simplify the equation, then we have

x + 67 = 105

x = 105 - 67

x = 38°

The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.

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Answer:

pq - 12r

step by step explanation:

Answer:

Considere una secuencia cuyos primeros cinco términos son: 4, 8, 16, 32, 64.

¿Qué función (con dominio todos los enteros n 2 1) podría usarse para definir y continuar esta secuencia?

A f(n) = 4(n-1)

® f(n) = 4(2)"-1

f(n) = 4n2

f(n) = 4n

Step-by-step explanation:

Answer:

1. [tex] \theta = 61.9^\circ [/tex]

2. [tex] x = 23.7~cm [/tex]

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]

[tex] \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} [/tex]

[tex] \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} [/tex]

[tex] \sin \theta = 0.88176 [/tex]

[tex] \theta = \sin^{-1} 0.88176 [/tex]

[tex] \theta = 61.9^\circ [/tex]

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]

[tex]\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}[/tex]

[tex]x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}[/tex]

[tex] x = 23.7~cm [/tex]

The circle with center (0,6) containing the point (74,2) has an equation of x² + (y - 6)² = 74.1²

The equation of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the center and r is the radius.

The circle with center (0,6) containing the point (74,2). Hence:

[tex]Radius=\sqrt{(2-6)^2+(74 -0)^2}=74.1\ unit[/tex]

The equation is:

x² + (y - 6)² = 74.1²

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Answer:

A.12x2 −6; 21 inches

Step-by-step explanation:

The perimeter  of the triangle is 21inches and the expression can be used to find the perimeter of the triangle is 12x^2 −6

The perimeter of a triangle is the sum of all its sides as shown

P = s1 + s2 + s3

Given the following

s1 = 4x^2 - 3

s2 =4x^2 - 2

s3 = 4x^2 - 1

x = 1.5

Take the sum of the sides

P = 12x^2 - 6

Substitute x = 1.5

P = 12(1.5)^2 - 6

P = 21 inches

Hence the perimeter  of the triangle is 21inches and the expression can be used to find the perimeter of the triangle is 12x^2 −6

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Answer:

18.84

Step-by-step explanation:

Answer:

18.8495559215

Step-by-step explanation:

In order to find circuference we use the formula

C= 2π(r)

c= circumference

r= radius

since they gave you the diameter, you first have to find the radius so you would divide the diameter by two since radius is half of a circle so 6 divided by 2 is 3. From here we would plug in 3 for "r" in the formula I wrote above. So C= 2π(3). then type this into a calculator to get the answer I wrote above. Then round as directed

Answer:

th answer is 324

Step-by-step explanation:

i took the test

Answer: 10

Step-by-step explanation:

We can get this is a right triangle with a hypotenuse of c and legs equal to the height and radius.

So, the hypotenuse is c and the legs are 6 and 8.

This means that c=10

Answer:

[tex] \sf \: Proved \: \angle \: OAD \: = \angle \: OCD[/tex]

Step-by-step explanation:

Given:

Mn is diameter of circle having centre O

and BD = OD,

To prove that:

[tex]\angle \: OAD \: = \angle \: OCD[/tex]

Solution:

Join the points O and B and draw OB,

On joining the line,

in ∆OCD and ∆OBD,

OC =OB → (Radius of same circle)

BD =CD → (from given)

OD =OD → (Common side in both the triangles)

Hence ∆OCD and ∆OBD are congruent from SSS property.

so we can say that,

[tex]\angle \: OBD \: = \angle \: OCD[/tex]

Consider above prove as statement A

Corresponding angles of congruent traingle.

in ∆ OAB,

OA = OB (radius of same circle)

hence ∆OAB is an isosceles traingle.

We know that opposite angle of isosceles traingle are always equal. hence,

[tex]\angle \: OBD \: = \angle \: OAB \\ \angle \: OAB \: = \angle \: OAD (same \: angles) \\ \angle \: OBD \: = \angle \: OAD[/tex]

Consider above prove as statement B

From Statement A & B we can say that

[tex]\angle \: OAD \: = \angle \: OCD[/tex]

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Answer:

  16666.25

Step-by-step explanation:

For rounded values, the minimum value they could have been rounded from is the given value less half its least-significant digit.

That means the minimums are ...

  a: 340 ⇒ 340 -5 = 335

  b: 49.8 ⇒ 49.8 -0.05 = 49.75

Then the minimum product would be ...

  (335) × (49.75) = 16666.25

Answer:

£10200

Step-by-step explanation:

Amount borrowed (P) = £6000

Rate of interest (R) = 7%

Time (T) = 10 years

First, let us calculate the simple interest (SI) for 10 years.

Formula for simple interest is given as:

[tex]S.I.=\frac{PRT}{100}[/tex]

Plugging the values of P, R and T in the above formula, we find:

[tex]S.I.=\frac{6000(7)(10)}{100}[/tex]

S.I.= £4200

Total money paid back at the end of the 10 years

= £6000 + £4200

= £10200

Answer:

A. 2086 yd²

Step-by-step explanation:

SA = 2lw + 2wh + 2lh
SA = 2*17*20 + 2*20*19 + 2*17*19
SA = 680 + 760 + 646
SA = 2086
Hope this helps :)

Answer:

the answer is B 0.760

Step-by-step explanation:

i did the test.

The angle measure of minor arc KM is 41 degrees

From the given diagram, we have the following parameters

mKLM = 82 degrees

Required

arcKM

Since the angle at the vertex is twice that of the intercepted arc, then:

<KLM = 2(arcKM)
arcKM = <KLM/2

arcKM = 82/2

arcKM = 41 degrees

Hence the angle measure of minor arc KM is 41 degrees

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Answer:

V = 8 cm³

Step-by-step explanation:

the volume (V) of a cube is calculated as

V = s³ ( s is the side length )

here s = 2 , then

V = 2³ = 8 cm³

Answer:

8 cm

Step-by-step explanation:

Answer:

Straight along the horizontal axis

Step-by-step explanation:

Hope this helped :)

Answer:

Sarpong is 11.

Quartey is 39.

Step-by-step explanation:

Let Sarpong's age now = s.

Let Quartey's age now = q.

Now:

q + s = 50

In five years, their ages will be

Sarpong: s + 5

Quartey: q + 5

q + 5 = 4s

We have a system of two equations in two variables.

q + s = 50

q + 5 = 4s

We will use the substitution method.

Solve the second equation for q.

q = 4s - 5

Substitute 4s - 5 for q in the first original equation and solve for s.

4s - 5 + s = 50

5s = 55

s = 11

q + s = 50

q + 11 = 50

q = 39

Answer:

Sarpong is 11.

Quartey is 39.

Answer: converse alternate exterior angles theorem

Step-by-step explanation:

The angles are alternate exterior angles.

Answer:27.712812921102

Step-by-step explanation:

24*32=x*x

√768=√x²

27.712812921102=x

Geometric mean formula

a=24

b=32

Find GM

On rounding

Answer:

8,070 meters

Step-by-step explanation:

First we add :)

410 + 370 = 780

Now we subtract :)

8,850 - 780 = 8070

Have an amazing day!!

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Answer:

Step-by-step explanation:

This is a logical question that can be d=solved thus;

To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.

1. Using simple interest formula of ( P X R X T)/ 100

Since p  = 1500, r  = 2.5%,  T = 3

1500 x 2.5% x 3  / 100  =  1500 x 0.025 x 3 / 100

112.5 / 100 = 1.125

to find amount  = 1.125 + 1500 = 1501.25 for the three 3years.

2. Using compound interest formula of ( P ( 1 + r/n)∧nt

1 + (2%/3) ∧3(3)

1500( 0.02/3) ∧ 9

1500  x 0.006 ∧9

1500 x 2.60 = 3900

A = 3900 + 1500 = 5400

SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS

Given the data from the question, the best account to use is:

A high interest savings account, with 2.5% simple interest annually (Option 1)

I = PRT / 100

A = I + P

Where

A = P(1 + r/n)ⁿᵗ

Where

I = PRT / 100

I = (1500 × 2.5 × 3) / 100

I = $ 112.5

Thus

A = I + P

A = 112.5 + 1500

A = $ 1612.5

A = P(1 + r/n)ⁿᵗ

Since n = 1,

A = P(1 + r)ᵗ

A = 1500(1 + 0.02)³

A = $ 1591.8

SUMMARY

The amount at the end of 3 years using:

Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)

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Answer:

  a) CD = 7.25

  b) BC = 5.25

Step-by-step explanation:

The parallel lines mean the triangles are similar. ΔADC ~ ΔAEB. Corresponding sides are proportional, so ...

  AD/AE = DC/EB

  10.5/4.2 = CD/2.9

  CD = 2.9(5/2) = 7.25

__

Corresponding sides are proportional, so ...

  BC/AC = ED/AD

  BC = AC(ED/AD) = 8.75(10.5 -4.2)/10.5 = 8.75(3/5) = 5.25

Answer:

The points are in the form (x,y) this means you count x (right) if positive and left if negitive, for y up is positive and down negitive. for example the point (3,-2) would be three to the right two down

Step-by-step explanation:

The points are in the form (x,y) this means you count x (right) if positive and left if negitive, for y up is positive and down negitive. for example the point (3,-2) would be three to the right two down

Answer:

  3x³ and 6x³, y and 7y

Step-by-step explanation:

Like terms have variables with the same exponents. This fact eliminates choices A, C, D.

The like terms are ...

  3x³ and 6x³, 7y and y . . . . . . choice B

Answer:

Maximum

Step-by-step explanation:

At the vertex the function is at aits maximum value.

Answer:

C. (25,20)

Step-by-step explanation:

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Good luck and remember (yall that take edge) , you can get through the day no matter how hard it may seem. I have faith In you guys :).

If number of hours worked is less than 20, 500 flat rate is preferable

and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

In the first scenario, where there is a $500 flat rate regardless of the number of hours worked, the pay per hour remains constant at $500 divided by the number of hours worked.

So, the graph for this scenario would be a horizontal line at a height of $500.

In the second scenario, where the contractor is paid $20 per hour worked, the pay per hour is fixed at $20.

let the number of hours be worked be x.

Then, 20x < 500

x< 25

So, if number of hours worked is less than 20, 500 flat rate is preferable

and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.

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Answer:

[tex]\displaystyle Dependency\:[Infinitely\:Many\:Solutions][/tex]

Explanation:

In the bottom equation, moving [tex]\displaystyle -2x[/tex]to the oppocite side will give you the linear standard equation above it, therefore numerous solutions will occur.

I am joyous to assist you at any time.

Answer:

the sum of a number

Step-by-step explanation:

0.017