Mark currently works part time with a salary of $8000 per year mark plans to quit working and attend college for four years if his college cost will total $64,000 how long will it take Mark to recover his investment assuming he has a salary of $32,000 upon graduating

Answer:

13/48

Step-by-step explanation:

1 7/16 - 1 1/6

Make improper fraction

23/16 - 7/6

Common Denominator

69/48 - 56/48

Subtract

13/48

Hope that helped!!! k

Answer:

13/48

Step-by-step explanation:

1 7/16=1+7/16

1 1/6=1+1/6

So: 1 7/16 - 1 1/6=

1+7/16-(1+1/6)=

1+7/16-1-1/6=

7/16-1/6= (48 common denominator)

(7×3-8)/48=

(21-8)/48=

13/48

Part (a)

BC = opposite side (furthest leg from the reference angle)

AB = adjacent side (closest leg from the reference angle)

AC = hypotenuse (always opposite the 90 degree angle)

=============================================

Part (b)

i. False. Angle B is 90 degrees as shown by the square angle marker.

ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.

iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.

iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.

==============================================

Part (c)

cos(theta) = adjacent/hypotenuse = AB/AC

tan(theta) = opposite/adjacent = BC/AB

Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.

==============================================

Part (d)

The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.

sin(C) = opposite/hypotenuse = AB/AC

cos(C) = adjacent/hypotenuse = BC/AC

tan(C) = opposite/adjacent = AB/BC

Note the tangent ratio is the reciprocal of what we found back in part (c).

Answer & Step-by-step explanation:

(a)

The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))

The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)

The opposite is on the line CB (this is opposite the given angle)

(b)

i.   false (b is a right angle)

ii.  false (the side opposite C is BA)

iii. true

iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)

(c)

cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]

tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]

The cosine and tangent ratios of the given angle:

[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]

(d)

Remember SOH-CAH-TOA:

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Using the angle C, plug in the appropriate sides:

[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]

:Done

Answer:

27500

Step-by-step explanation:

meters are 100 times more than kilometers hope this helps:)

[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]

☃️ Refer to the trigonometric table....

Then, proceeding

⇛ tan 60 ° = √3

⇛ tan 60° = tan (a + b)

⇛ 60° = a + b

Flipping it,

⇛ a + b = 60° --------(1)

And,

⇛ tan 30° = 1 / √3

⇛ tan 30° = tan (a - b)

⇛ 30° = a - b

Flipping it,

⇛ a - b = 30° ---------(2)

Now adding eq.(1) and eq.(2),

⇛ a + b + a - b = 60° + 30°

⇛ 2a = 90°

⇛ a = 90° / 2

⇛ a = 45°

Putting value of a in eq.(1),

⇛ 45° + b = 60°

⇛ b = 15°

☄ So, Our Required answers:

━━━━━━━━━━━━━━━━━━━━

Answer:

obtuse

Step-by-step explanation:

because obtuse triangle would provide more support that acute or right as its bigger.

Answer:

A = 8%, B = 5%

Step-by-step explanation:

Let

a=concentration of solution A (in percent)

b=concentration of solution B (in percent)

Given

2a+4b = 0.06*(2+4)  ...........(1)

4a+2b = 0.07*(4+2)  ...........(2)

2(1) - (2)

4a-4a +8b-2b = 6 (2*0.06-0.07)

6b = 6(0.05)

b = 0.05  .............(3)

Substitute (3) into (1) and solve for a

2a+4(0.05) = 0.36

2a = 0.16

a = 0.08

Answer:

2(x-4) (x+9)

Step-by-step explanation:

Answer:

[tex]x^\frac{9}{5}[/tex]

Step-by-step explanation:

[tex]\sqrt[5]{x}[/tex] is the same thing as [tex]x^{\frac{1}{5}}[/tex].

Now if we have [tex]x^{\frac{1}{5}}[/tex] to the power of 9, the exponents are multiplied.

[tex]x^{\frac{1}{5} \cdot9} = x^{\frac{9}{5} }[/tex].

Hope this helped!

Answer:it’s the top right box

Step-by-step explanation: what I did was I added 24+24 and 19+19 which gives you 86ft

Answer:It is left side 21ft and top 22ft Step-by-step explanation:

Answer:

Domain x ≥ 0 Range y ≤ 0

Step-by-step explanation:

Answer:

[tex]Domain = \{x\,|\,x\geq 0\}[/tex]

[tex]Range=\{\,y\,|\,y\leq 0\}[/tex]

Step-by-step explanation:

Notice that the Range of the function (x-values for which the function exists) is limited by the possible values of x inside the square root. For [tex]\sqrt{x}[/tex] to exist, x must be larger than or equal to zero ([tex]x\geq 0[/tex])

So this gives us the description for building the Domain (what is called "set builder notation":

[tex]Domain = \{x\,|\,x\geq 0\}[/tex]

Now for the Range, let's look into all the possible values that these  [tex]x\geq 0[/tex] values of x can render:

[tex]x\geq 0\\\sqrt{x} \geq 0\\x\,\sqrt{x} \geq 0[/tex]

but now, if we multiply both sides of the inequality by "-4", the direction of the inequality changes rendering;

[tex]-4\,x\,\sqrt{x} \leq 0[/tex]

Since these are the possible values of the "y-coordinate", then we right the Range in set builder notation as:

[tex]Range=\{\,y\,|\,y\leq 0\}[/tex]

Answer:

x = -9

Step-by-step explanation:

subtract 3 from both sides

x = -9

Answer:

x = -9

Step-by-step explanation:

x + 3 = -6

Subtract 3 from both sides.

x + 3 - 3 = -6 - 3

x = -9

Answer: Answers are in the steps.

Step-by-step explanation:

The coefficients are 3, -5, and 1  

The terms are, 3m, -2,-5n and p

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

Answer:

A

Step-by-step explanation:

Option A is correct. Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations.

Answer: Correct

Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations above the mean and Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean.

Step-by-step explanation: No clue:)

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]h(x)=5/2x+4 \\\\x=(h^{-1}o})(x)=(hoh^{-1})(x)=h(h^{-1}(x))=\dfrac{5}{2h^{-1}(x)+4}\\\\<=> 2h^{-1}(x)+4=\dfrac{5}{x}\\\\<=> h^{-1}=\dfrac{\dfrac{5}{x}-4}{2}\\\\<=>h^{-1}=\dfrac{5-4x}{2x}[/tex]

Thank you.

Answer: 49 cm^2

Step-by-step explanation:

The length of the small pink square box will be:

L^2 = 9

L = sqrt( 9 )

L = 3

The length of the big pink square box will be:

L^2 = 16

L = sqrt( 16 )

L = 4

The length of the yellow square box will be:

4 + 3 = 7

The area of the third square box will be

A = 7^2

A = 49 cm^2

Answer:

18

Step-by-step explanation:

30-60-90 triangles have a set of x values that you can plug your numbers into.

we know that the side length opposite to 30 is x

the side length opposite to 60 is xsqrt3

the side length opposite to 90 is 2x

from this we can gather that y=2x where x=9 therefore y=18

Answer:

3 times the percent for the balance to be $221

Step-by-step explanation:

Answer:

a) true

Step-by-step explanation:

$4.65. >$7.45.

Answer:

500

Step-by-step explanation:

A = the unknown number that we need to find

A x 13/100 = 65

=> A x 13 = 6500

=> A = 6500 / 13

=> A = 500

13% of 500 is 65.

Let's check whether the answer is correct or not.

=> 500 x 13/100

=> 5 x 13

=> 65.

So, the number whose 13% is 65 is 500

Answer:

Step-by-step explanation:

Let the number be x,

Then,

13% of x =65

Or, 13/100 of x =65

Or,x=6500/13

:.x=500

Answer:

Hey there!

1 gallon=400 square feet

2 3/8 gallon= 400 (2 3/8) square feet

2 3/8 gallon= 950 square feet.

Let me know if this helps :)

Answer:

4 and 34/63

Step-by-step explanation:

we know that he has to walk 8 and 2 thirds of an kilometer to school. so far he has ran 1 10/11 of a kilo.

To solve this you would have to divide 8 2/3 by 1 10/11.

you would have to make them into improper fractions so 26/3 divided by 21/11

your answer will be 4 34/63

Alan covers he distance by walking is   6+25/33 km.

distance is a scaler quantity which means it only have magnitude and no direction if any person or any thing moves from place A to B then it will show the distance between A and B

Given that Alan's school a distance is 8+2/3 km which is 26/3 km,

and he ran one and ten elevenths kilometers

means 1+10/11 = 21/11 km

and walks rest

let distance covered by walking be x

total distance for Alan school = distance covered by running + distance covered by walking

26/3 = 21/11 +x

x = 26/3 - 21/11

x = 223/33 = 6+25/33

Hence rest walking distance for Alan is 6+25/33

Learn more about Distance

https://brainly.com/question/15317318

#SPJ3

Answer:

$5,000 per week

Step-by-step explanation:

Ruri is a 30 year old female.

there are about 4 weeks per month

there are about 52 weeks per year

52*5000 = 260,000

She would get 260,000 per year and lets see how much she would have at 40.

260,000*10

at 40 she would have 2,600,000

2,600,000*10

at 50 she would have 26,000,000

at 50 she already has earned more money that the $20 million.

She should go with the $5000 per week if she would like more money.

Answer:

1/25 or 0.04

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

5 to the 4th power (5 × 5 × 5 × 5) is 625.

5 to the 6th power (5 × 5 × 5 × 5 × 5 × 5) is 15625.

625/15625 = 0.04.

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer:

intersection of the lines drawn to bisect each vertex of the triangle

Step-by-step explanation:

trust

Answer:

[tex]D=-5y^2[/tex]

Step-by-step explanation:

We have the equation:

[tex]\displaystyle -15y^4=D(3y^2)[/tex]

And we want to find D such that the equation is true.

So, we can divide both sides by 3y². This will yield:

[tex]\displaystyle D=\frac{-15y^4}{3y^2}[/tex]

We can split this into:

[tex]\displaystyle D=\frac{-15}{3}\cdot\frac{y^4}{y^2}[/tex]

Simplify. Hence:

[tex]D=-5y^2[/tex]

Answer:

5 5/7

Step-by-step explanation:

Convert it to fractions:

30/7 and 4/3

Now multiply.

120/21

Simplify it:

5 5/7

Answer:

8 cm

Step-by-step explanation:

The maximum length of the string will be the greatest common divisor of  32 , 16 , 8

32 = 2 * 2 * 2 * 2 * 2

16 = 2 * 2 * 2 * 2

8 = 2 * 2 * 2

GCD = 2* 2 * 2 = 8

The maximum length of the string = 8 cm

Answer:

3 or at least i think

Step-by-step explanation:

Answer:

a= 138/59 - 8√5b B=69√5/1180 - a√5/40

Step-by-step explanation:

yuh

Answer:

2 1/3 cupcakes

Step-by-step explanation:

A cupcake can make 3 four cups of flour

In 8 fourteen cups of flour, require (14 X 4)/(3 X 8) of cupcakes

  = 56/24 = 2 1/3 cupcakes