Skylar is answering the following math problem: The value of an investment decreased by 10%. The original amount of the investment was $75.00. What is the current value of the investment? Skylar said 10% of $75.00 is $7.50, and since the investment decreased by that amount, you have to subtract $7.50 from $75.00 to arrive at the final answer of $67.50. Create one algebraic equation that can be used to arrive at the final answer of $67.50. Solve the equation to prove it results in an answer of $67.50. Be prepared to explain your thought process to the class.

Answer:

10%

Step-by-step explanation:

5/50 = 10/100

10/100 = 10%

Answer:

5 gallons is 10% capacity.

Step-by-step explanation:

5 gallons accounts for 10% of a container which holds 50 gallons.

[tex](\frac{1}{10} )*50=5[/tex]

Answer:

5.50

Step-by-step explanation:

5 = whole number

.

5 = Tenths

0 = Hundreths

5.50

Answer: -3

Step-by-step explanation:

[tex]\frac{27}{-9} = -3 \\[/tex]

We can check our work my multiplying -3 by -9 and see that it equals 27

[tex]-9*[\frac{27}{-9} = -3 ]* -9\\27 = 27[/tex]

Answer:

31 is the answer of this question

Answer:

31 and my day was good how was yours?

Step-by-step explanation:

Answer:

y= 2x -2

Step-by-step explanation:

Answer:

[tex]x = 6[/tex]

Explanation:

Given:

[tex]Area = 24cm^2[/tex]

See attachment for shape

Required

Find x

The attached shape is a rectangle.

So:

[tex]x * 4 = 24[/tex]

[tex]4x = 24[/tex]

Divide both sides by 4

[tex]\frac{4x}{4} = \frac{24}{4}[/tex]

[tex]x = \frac{24}{4}[/tex]

[tex]x = 6[/tex]

Answer:

A

Step-by-step explanation:

We have the equation:

[tex]x^2-2x-2=0[/tex]

We can use the quadratic formula. In this case, a = 1, b = -2, and c = -2. Hence:

[tex]\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{2\pm\sqrt{12}}{2}[/tex]

Simplify:

[tex]\sqrt{12}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}[/tex]

Hence:

[tex]\displaystyle x=\frac{2\pm2\sqrt{3}}{2}[/tex]

Divide:

[tex]x=1\pm\sqrt3[/tex]

The correct answer is A.

The interest rate for his account was r ≈ 1.375% .

Answer:

x = 5.26 m

Step-by-step explanation:

Given that,

The angle of inclination = 20°

The vertical height of the ramp, h = 1.8 m

We need to find the length of the ramp. Let it is x.

We can find it using trigonometry. So,

[tex]\sin\theta=\dfrac{P}{H}[/tex]

We have,

P = 1.8 m, H = x

[tex]\sin20=\dfrac{1.8}{x}\\\\x=\dfrac{1.8}{\sin20}\\\\x=5.26\ m[/tex]

So, the length of the ramp is 5.26 m.

Answer:

AB ≈ 5.6 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{12}[/tex] ( multiply both sides by 12 )

12 × cos62° = AB , then

AB ≈ 5.6 cm ( to 1 dec. place )

Answer:

x= −11 2 + 5 2 √5 or x= −11 2 + −5 2 5

Step-by-step explanation:

Answer:

D on edg

Step-by-step explanation:

Answer:

Not apportionment

Step-by-step explanation:

Apportionment can be described as a way of sharing out or dividing out in the best fair method.

If a family of 10 leave the house at the same time and have to share just two bathrooms, the time allocation should not be based on age rather should be based on how early each person wakes up in the morning.

Answer:

It means that x = 20

Step-by-step explanation:

Answer:

$1,078.68

Step-by-step explanation:

Here, we want to calculate the balance

That would be adding interest plus deposit plus balance minus withdrawals

That would be;

618.21 + 466.26 + 4.31 - 10.10 = $1,078.68

Answer:

The line will not pass through the first quadrant.

Step-by-step explanation:

Since the y-intercept is negative, and the slope is negative, the line will start in the second quadrant, pass through the third quadrant to intercept the y-axis, then pass through the fourth quadrant. It will never touch the first quadrant.

Answer:

Answer A=48

Step-by-step explanation:

Took the test got it right.

The expression (2w - 2)³ × (8w⁶) is equivalent to :

64w⁹ - 64w⁶ - 192w⁸ + 192w⁷.

Given is the expression as -

(2w - 2)³ × (8w⁶)

The given expression is -

(2w - 2)³ × (8w⁶)

{2(w - 2)}³ × (8w⁶)

8(w - 1)³ × (8w⁶)

(a+b)³ = a³ - 3a²b + 3ab² - b³

So, on expanding, we will get -

8(w³ - 1 - 3w² + 3w) x (8w⁶)

(8w³ - 8 - 24w² + 24w )(8w⁶)

64w⁹ - 64w⁶ - 192w⁸ + 192w⁷

Therefore, the expression (2w - 2)³ × (8w⁶) is equivalent to :

64w⁹ - 64w⁶ - 192w⁸ + 192w⁷.

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Answer:

Equation is [tex]x+\frac{16}{3}=\frac{15}{2}[/tex] where [tex]x[/tex] denotes number of cups of orange juice needed by Sam.

[tex]x=\frac{13}{6}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] denotes number of cups of orange juice needed by Sam.

Number of cups needed to make punch [tex]=7\frac{1}{2} =\frac{15}{2}[/tex]

Number of cups with Sam [tex]=5\frac{1}{3}=\frac{16}{3}[/tex]

Therefore,

[tex]x+\frac{16}{3}=\frac{15}{2}\\\\x= \frac{15}{2}-\frac{16}{3}\\\\x=\frac{45-32}{6}\\\\x=\frac{13}{6}[/tex]

Answer:

34

Step-by-step explanation:

3rd square number is 9

5th square number is 25

9+25= 34

Answer:

Domain: (-∞, ∞) or All Real Numbers

Range: (0, ∞)

Asymptote: y = 0

As x ⇒ -∞, f(x) ⇒ 0

As x ⇒ ∞, f(x) ⇒ ∞

Step-by-step explanation:

The domain is talking about the x values, so where is x defined on this graph? That would be from -∞ to ∞, since the graph goes infinitely in both directions.

The range is from 0 to ∞. This where all values of y are defined.

An asymptote is where the graph cannot cross a certain point/invisible line. A y = 0, this is the case because it is infinitely approaching zero, without actually crossing. At first, I thought that x = 2 would also be an asymptote, but it is not, since it is at more of an angle, and if you graphed it further, you could see that it passes through 2.

The last two questions are somewhat easy. It is basically combining the domain and range. However, I like to label the graph the picture attached to help even more.

As x ⇒ -∞, f(x) ⇒ 0

As x ⇒ ∞, f(x) ⇒ ∞

Answer:

EBC and CBF are supplementary.

EBD=66

Step-by-step explanation:

Since vertical angles are congruent, ABE=CBF

ABE=40-x

40-x + 6x-30=90

5x+10=90

5x=80

x=16

16(6)-30=66

Answer:

85 inches

Step-by-step explanation:

Using pythag.  A^2 + B^2 = C^2  

(68*68) + (51*51) = 7225^2

Thus if you square root 7225, you get your answer - 85 inches.

Cylinder's volume = 1330.5 cm^3

Step-by-step explanation:

radius, r = diameter, d / 2

= 11/2

= 5.5 cm

Volume = π r^2 h

= π × 5.5^2 × 14

= 423.5π

= 1330.5 cm^3

Answer:

Step-by-step explanation:

[tex]d=vt-\frac{at^2}{2} \\ \\ a=\frac{2(d-vt)}{t^2} \\ \\ a=\frac{2(500-300(20)}{20^2} \\ \\ a=-27.5 \frac{m}{s^2}[/tex]

The acceleration of the tram is 1 m/s^2.

To find the acceleration of the tram, we can use the following equation:

acceleration (a) = (change in velocity) / (time taken)

First, let's convert the initial velocity to m/s:

Initial velocity = 300 m/minute

To convert to m/s, we need to divide by 60 (since there are 60 seconds in a minute):

Initial velocity = 300 m/minute ÷ 60 seconds/minute = 5 m/s

Now, let's find the final velocity. The tram travels a distance of 0.5 km in 20 seconds.

Distance traveled = 0.5 km = 500 m (since 1 km = 1000 m)

Time taken = 20 seconds

Now, we can find the final velocity (v) using the formula:

v = (change in distance) / (time taken)

v = 500 m / 20 seconds = 25 m/s

Next, we can find the change in velocity:

change in velocity = final velocity - initial velocity

change in velocity = 25 m/s - 5 m/s = 20 m/s

Finally, we can calculate the acceleration:

acceleration (a) = (change in velocity) / (time taken)

acceleration (a) = 20 m/s / 20 seconds = 1 m/s^2

So, the acceleration of the tram is 1 m/s^2.

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Answer:

u uninstalled ♭ that ↓ t sugar rx

Step-by-step explanation:

utajtt kytisau

Answer:

104

155

180

Step-by-step explanation:

an easy way is to solve what is in the parenthesis then multiply by the outside number

but if you need to use the distributive property:

1. 4 x (20 - -6)

(4 x 20) - (4 x -6) = 80 - -24 = 80 + 24 = 104

2. -5 x (24 - -7)

(-5 x 24) - (-5 x -7) = -120 - 35 = 155

3. 12 x (-30 + 45)

(12 x -30) + (12 x 45) = -360 + 540 = 180

Step-by-step explanation:

must calculate the number in ( ) first before calculate the number in [ ]

- - > +

+ + > +

+ - > -

- + > -

Answer:

KR

Step-by-step explanation:

First, you can see the right angle and the 30 degrees. Those are the same, so we can flip the triangle on the right to match the one on the left. The line that is similar is KR.

Answer:

1.) 18

2.) 55

3.)43

Step-by-step explanation: