Question
Which of the following equations is equivalent to 8x - 6y = 12?
y = ³x - 1²/2 3
y=x-2
y = 2x - 12
y = 8x - 6

The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.

The future values of the savings account are calculated in two installments.

The first installment is for 10 years when the account earns 6% compounded semiannually.

Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.

Future values can be determined using the future value formula or an online finance calculator, as follows:

N (# of periods) = 20 (10 years x 2)

I/Y (Interest per year) = 6%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $3,612.22

Total Interest $1,612.22

N (# of periods) = 32 (8 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)

PMT (Periodic Payment) = $0

Results:

FV = $5,816.85

Total Interest $2,204.63

Thus, the value of the account after 18 years was $5,816.85.

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Answer:

x - 2, if x > 5

Step-by-step explanation:

The vertical lines either side of the expression mean absolute value.

The absolute value of a number is its positive numerical value.

if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive.  Therefore, we can disregard the absolute value.

Therefore:  

x - 2,  if x > 5

To find the range (output values) of the expression, substitute x = 5 into the expression:

⇒ 5 - 2 = 3

Therefore, |x - 2| > 3,  if x > 5

Answer:

3

Step-by-step explanation:

2+ (-2/3)^2 ÷ 1/3

make -2/3 postive because its being raised by an even exponent

you never divide by fractors so make 1/3 into 3 and make it multiplication

2+ (2/3)^2 × 3

raise the fraction to the power of 2

2+ (4/9)× 3

cancel out the GCF

2+ 4/3

add

10/3

simplify

3.3 ≅ 3

Answer:

8

Step-by-step explanation:

120/14.25=8.4 rounded off to a whole number is 8

Answer:

Step-by-step explanation:

e^-6 = 1/e^6 = about 0.00248

The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y

Inequality for number of videos Sarita uploaded:

v - 500 < y

Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y

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Answer:

- v < 500

Step-by-step explanation:

Answer:

28/57

Step-by-step explanation:

odds in favor of event occurring = (probability event occurs)/(probability event does not occur)

Let p = probability event occurs.

Then the probability the event does not occur is 1 - p.

Let the odds = a/b.

a/b = p/(1 - p)

a(1 - p) = bp

a - ap = bp

bp + ap = a

p(a + b) = a

p = a/(a + b)

p = 28/(28 + 29)

p = 28/57

As per the given scenario, the probability of event E is 28/57 or approximately 0.4912.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

If the odds in favor of an event E are "a to b," then the probability of E is given by:

P(E) = a / (a + b)

In this case, the odds in favor of E are 28 to 29, which means that there are 28 favorable outcomes for E and 29 unfavorable outcomes against E.

So, using the formula above, we can compute the probability of E as:

P(E) = 28 / (28 + 29)

P(E) = 28 / 57

Therefore, the probability of event E is 28/57 or approximately 0.4912.

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All values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1

The inequality expression is given as:

2x+2/x+7 >= 0

Multiply both sides by x + y

2x+2 >= 0

Subtract 2 from both sides

2x > -2

Divide both sides by 2

x >= -1

Hence, all values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1

See attachment for the number line of x >= -1

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Answer:

[tex](17x)^{\frac{2}{4}}[/tex]

Step-by-step explanation:

There's not much work to show for this problem, but I'll explain it for you

Use the exponent rule for roots to combine the 4 and the 2 like a fraction

2 on the top and 4 on the bottom

[tex](17x)^{\frac{2}{4} }[/tex]

That's it!  Pretty easy

Good Luck!

pls mark brainliest

Answer:

approximately 2 lb

Step-by-step explanation:

Juan: 31/7

Ari: 19/3

Juan's fraction is close to 32/8 = 4

Ari's fraction is close to 18/3 = 6

6 - 4 = 2

Answer: approximately 2 lb

Answer:

Step-by-step explanation:

The amount of each brand can be found by writing and solving an equation that makes use of the given relations.

Let x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...

  0.55x +0.30(160 -x) = 0.45(160)

Subtracting 0.30(160), we have ...

  x(0.55 -0.30) = 160(0.45 -0.30)

  x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x

96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.

__

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Answer:

1.24

Step-by-step explanation:

because 1.24>1.215>0.365>0.095

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.

Length

2.6 x 40 = 260

260 cm = 2.6 m

Width

4.5 x 40 = 180

180 cm= 1.8 m

Area

1.8 x 2.6 = 4.68 m

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

your mother i swear

Step-by-step explanation:

ask yo mom

Answer:

Cube Root Calculator

Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

It will help you alot.

Step-by-step explanation:

It looks like you have

[tex]\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}[/tex]

Substituting these in to the plane equation, we have

[tex]4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2[/tex]

When [tex]t=-2[/tex], we get the point

[tex]\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}[/tex]

The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)

The information that completes the question are added as an attachment

The question requires that we determine the intervals which the original function f(x) concave down

From the attached graph, we have the following turning points

(-2, -4) and (3, 2)

From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)

So, we have:

(-5, 0), (-2, -4), (3, 2) and (5, 0)

Remove the y coordinates

x = -5, -2, 3 and 5

Express as intervals

(-5, -2) and (3, 5)

Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)

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Answer:

Step-by-step explanation:

9.05737

The length of the radius of the cone to the nearest foot is 5 feet.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The surface area of a cone is 216π sq units and the height of the cone is  (5/3) times of the radius.

∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.

∴ πrl = 216π.

√{(34/9)r³ = 216.

1.9r³ = 216.

r³ = 113.7.

r = 4.8 feet Or 5 feet.

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Answer:

Step-by-step explanation:

.11x = 55

11x = 5500

x = 500

Answer:

BC 1

AC 2

AABC 3

Step-by-step explanation:

BC=16

AC = 15

AABC= 15

Answer: C, B, A

Step-by-step explanation: It just is

Answer:

R=i

Step-by-step explanation:

R=i×100÷p×t

r=30105×100÷6570×12

r=3010500÷78840

r=38.18

Separate the variables.

[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]

Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].

[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]

[tex]\ln|y| = \frac12 \ln|u| + C[/tex]

[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]

[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]

[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]

Using separation of variables, the solution to the differential equation is:

y = ksqrt(x² + 11)

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is:

(x² + 11)y' = xy

Applying separation of variables, we have that:

y'/y = x/(x² + 11)

[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]

[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]

[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]

[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]

Hence the solution is:

y = ksqrt(x² + 11)

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The linear equation that represent the left balance of sanjaya’s y after visiting x number of days is:

y = 10x + 500.

A linear function is modeled by:

y = mx + b

In which:

From the data given, we have that:

Hence the balance is given as follows:

y = 10x + 500.

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The number sets that each number belong too are given as follows:

1. Rational.

2. Irrational.

3. Rational.

4. Whole.

5. Whole.

6. Integer.

It is a terminating decimal, hence it is a rational number.

The square root of 5 is not exact, hence it is a non-terminating decimal, meaning that is an irrational number.

It is a fraction, hence it is a rational number.

It is a positive non-decimal number, hence it is a whole number.

The square root of 16 is of 4, which is a positive non-decimal number, hence it is a whole number.

The result of the division is of -4, which is a negative non-decimal number, hence it is an integer number.

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Answer:

120

Step-by-step explanation:

5 rings 5 colors

for the first ring there are 5 colors to choose from

4 colors for the second

3 for the third

2 for the fourth

1 for the last one

so 5! = 120

2 angles that have the same angle measure are congruent.

Given that the two angles have the same angle measure.

Congruence is a term reserved for geometry. Two metrics are congruent when you can perfectly map to each other by mirroring, rotating, and translating without distortion.

We know that two shapes or objects are congruent if they have the same shape and the same size. For two angles to be congruent, they must coincide when they are overlapped. This is only possible if the two angles are equal.

Therefore, if two angles have the same measure, then they are said to be congruent.

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The inequalities that represents the third side of the triangle is  c ≥ 4 or c ≤ 20

The triangle inequality theorem states that that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the two sides of the triangle are 12 cm and 8 cm.

A triangle with sides a, b and c follows the principle below;

a + b ≥ c.

Therefore,

let

c = third sides

12 + 8 ≥ c

20 ≥ c

c + 8 ≥ 12

c ≥ 4

c + 12 ≥ 8

Therefore, the third third should be greater than or equals to 4 or less than or equals to 20

c ≥ 4 or c ≤ 20

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The two missing numbers in the pattern are 10 and 1

The sequence is given as:

100 000 , 10 000 , 1000 , 100 , A , B

From the above sequence, the next term is the quotient of the current term and 10.

So, we have:

A = 100/10 = 10

B = A/10 = 10/10 = 1

Hence, the two missing numbers in the pattern are 10 and 1

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