what is (6x-5) + (8x-50)

we have

x^2+24x=50

complete the square

(x^2+24x+12^2-12^2)=50

x^2+24x+144=50+144

(x+12)^2=194

therefore

Using compound interest, it is found that:

a) Pietro will have $1,719.49 in his account after 5 years.

b) The interest rate is of 8.19%.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Item a:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(5) = 1500\left(1 + \frac{0.0275}{2}\right)^{2(5)}\)

\(A(5) = 1719.49\)

Pietro will have $1,719.49 in his account after 5 years.

Item b:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(1.5(1500) = 1500\left(1 + \frac{r}{4}\right)^{20}\)

\(1.5 = (1 + \frac{r}{4}\right)^{20}\)

\(\sqrt[20]^{(1 + \frac{r}{4}\right)^{20}} = \sqrt[20]{1.5}\)

\(1 + 0.25r = 1.02048015365\)

\(0.25r = 0.02048015365\)

\(r = \frac{0.02048015365}{0.25}\)

\(r = 0.0819\)

The interest rate is of 8.19%.

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(a) At t = 1.11 s, the distance from the particle to the origin is 3.15 m. (b) The speed of the particle at t = 1.11 s is 1.86 m/s. (c) The magnitude of the acceleration at t = 1.11 s is 0.32 m/s². (a) At t = 3.4 s, the x-coordinate of the particle is 11.56 m. (b) The y-coordinate of the particle at t = 3.4 s is 17.14 m. (c) The speed of the particle at t = 3.4 s is 4.48 m/s.


(a) To find the distance from the particle to the origin, we use the formula for the magnitude of a vector: distance = √(x² + y²). Plugging in the given values at t = 1.11 s, we calculate the distance to be 3.15 m.
(b) The speed of the particle can be found by taking the magnitude of its velocity vector: speed = √(v_x² + v_y²). Plugging in the given values at t = 1.11 s, we calculate the speed to be 1.86 m/s.
(c) The magnitude of the acceleration can be found using the formula: magnitude of acceleration = √(a_x² + a_y²). Plugging in the given values at t = 1.11 s, we calculate the magnitude of the acceleration to be 0.32 m/s².
For the second scenario, the x-coordinate at t = 3.4 s can be found by plugging the given values into x(t) = a*t + b, which gives us 11.56 m. Similarly, the y-coordinate at t = 3.4 s can be found using y(t) = c*t² + d, which gives us 17.14 m. The speed of the particle at t = 3.4 s can be calculated using the same method as in (b), resulting in a speed of 4.48 m/s.

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Answer:

v=1

Step-by-step explanation:

Answer:

V = 1

Hope this helped :)

Answer:

The answer to your questions is 96.

The area of the square is 144 \(cm^{2}\).

Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.

We know, both these perimeters are equal. Hence,

4x = 3(x+4)

To further simplify the above equation.

4x = 3x + 12

x = 12

Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:

Area = \((side)^{2}\)

Area = 12 * 12

Area = 144 \(cm^{2}\)

Hence, the Area of the Square is 144 \(cm^{2}\)

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Answer:

36 3/4

Step-by-step explanation:

12 1/4 + 12 1/4 + 12 1/4 = 36 3/4 :)

Answer:

36 3/4

Step-by-step explanation:

12 1/4 + 12 1/4 + 12 1/4 = 36 3/4 :)

The polynomial (6x³ + 5x² - 9)/(x³) can be written as the sum of fractions: 6 + (5x² - 9)/(x³)

To divide the polynomial (6x³ + 5x² - 9) by the monomial denominator (x³), we can write it as the sum of fractions.

(6x³ + 5x² - 9)/(x³)

We divide each of the three terms of the numerator by the denominator:

6x³/x³ + 5x²/x³ - 9/x³

by simplification of each term;

6 + 5/x - 9/x³

Now, we can combine these terms as;

6 + (5/x - 9/x³)

Finally, we simplify further:

6 + (5x² - 9)/(x³)

Therefore, the polynomial (6x³ + 5x² - 9)/(x³) can be written as the sum of fractions: 6 + (5x² - 9)/(x³)

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Answer: the answer is approximately 41.65428, not rounded (maybe re do all the steps just in case)

Step-by-step explanation:

1. label the space between X and W the unknown.

2. You will be using SOH-CAH-TOA

3. Label the X as the opposite because it is the opposite side of where your degree is located.

4. Label five as adjacent because it’s next to the degree.

5. You will use TOA since you have adjacent and opposite values.

6. Write the equation tan58=x/5, the unknown goes on the top because O is first, the five goes on the bottom because A is last on TOA.

7. After you have the equation time 5 on both sides leaving you out with (5)tan58=x

8. On your calculator time (5)tan58 which will give you x.

Answer:

the figure is in cuboidal shape.

volume of cuboid=length ×width ×height

volume of cuboid=12mi×5mi×4mi

volume of cuboid=240mi³

Answer:

A i believe

Step-by-step explanation:

The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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The cups of smoothie mixture should be fruit is 2.4

To find how many cups of the smoothie mixture should be fruit when 4 cups of smoothie are to be made, we can use proportions.

Let's call the number of cups of fruit needed x.

So, we have

x = percentage of fruit * number of cups

Substitute the known values in the above equation, so, we have the following representation

x = 60% * 4

Evaluate

x = 2.4

Hence, 2.4 cups of the smoothie mixture should be fruit to make 4 cups of smoothie with a 60% fruit and 40% water ratio.

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The 98% confidence interval is (433.5866,854.6934)

What is a confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contains the parameter's true value is what is meant by the confidence level.

Given n = 14

Mean x = 644.14

standard deviation is s = 297.29

here α= 0.02

t(α</2,-1) = 2.65

The 98% confidence interval for mean is given by

z = x'- u / α(/√n) = (23-24/5.5/√5) =

x'-u / α(/√n) ≤ µ ≤ x'+u / α(/√n)

⇒(433.5866≤µ≤854.6934)

Hence, The 98% confidence interval is (433.5866,854.6934)

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Answer:

g(x) = 4rx + 4r - 4x - 4

Step-by-step explanation:

g(x)= -(x+1)(r-1)(-4)

Answer:

False Bri Please mark me as brainlist answer. I am in search of 1 brainlist answer.

Answer: Read the step by step explanation

Step-by-step explanation:

Since sin A = , we can use the Pythagorean identity to find cos A:

cos A = √(1 - sin²A) = √(1 - ( )²) = √(1 - ) = √()

Since A is in Quadrant I, both sin A and cos A are positive. Therefore, we can use the definition of secant to find sec A:

sec A = 1/cos A = 1/√() = √()/

To simplify the expression, we can rationalize the denominator by multiplying both the numerator and denominator by √():

sec A = (√()/)(√()/√()) = √()/ =

Therefore, the exact secant of A in simplest radical form using a rational denominator is .

Answer:

B

It's the only set that matches the line shown above, when plotted.

Hope this helps!

To determine the missing amounts in each situation, let's analyze the given information.Situation a: Supplies available-prior year end: $3,578

Supplies purchased during the current year: $675

Total supplies available: $4,725

To find the missing amount, we can subtract the known values from the total supplies available:

Missing amount (Situation a) = Total supplies available - (Supplies available-prior year end + Supplies purchased during current year)

                           = $4,725 - ($3,578 + $675)

                           = $4,725 - $4,253

                           = $472

Therefore, the missing amount in Situation a is $472.

Situation b:

The missing amount is already provided in the question as $12,165.

Situation c:

Supplies available-current year-end: $3,041

Supplies expense for the current year: (unknown)

To find the missing amount, we need to determine the supplies expense for the current year. However, based on the given information, there is no direct indication of the supplies expense. It is not possible to determine the missing amount in this situation without additional information.

Situation d:

Supplies available-current year-end: $5,400

Supplies expense for the current year: $24,257

To find the missing amount, we can subtract the known supplies expense from the supplies available at the current year-end:

Missing amount (Situation d) = Supplies available-current year-end - Supplies expense for the current year

                           = $5,400 - $24,257

                           = -$18,857 (negative value indicates a loss)

Therefore, the missing amount in Situation d is -$18,857 (indicating a loss of $18,857).

In summary, we were able to determine the missing amounts in Situations a and d, while Situations b and c already provided the missing amounts in the question.

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The area enclosed between the functions f(x) = 22 - 2x + 3 and g(x) = 2x^2 - 1-3 can be calculated by finding the definite integral of their difference. The result will give us the area of the region between the two curves.

To find the area between the curves, we need to determine the points where the curves intersect. Setting f(x) equal to g(x), we can solve the equation 22 - 2x + 3 = 2x^2 - 1-3. Simplifying, we get 2x^2 + 2x - 19 = 0. Using quadratic formula, we find the values of x where the curves intersect.

Next, we integrate the difference between the functions over the interval between these x-values to calculate the area. The definite integral of [f(x) - g(x)] will give us the area of the region enclosed by the two curves.

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Answer:

x = 140

Step-by-step explanation:

5% = 5/100 = 0.05

0.05x + 9 = 16

0.05x = 16-9

x = 7/0.05

x = 140

Answer:

Number that can be definitely defined, like 3.75, not 3.777....

Hope that helps!

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

f(4) = 4(4) - 3 = 16 - 3  =  13

g(-5) = -2(-5) + 10  =  10 + 10  =  20

13 + 20 = 33

Answer:

30 feet of chain link and 50 feet of rope

Step-by-step explanation:

Let's call the amount of chain link as x and the amount of rope as y. We can write:

x + y = 80 -- Equation 1

2x + 1.5y = 135 -- Equation 2

2x + 2y = 160 -- Equation 3 (Multiply Equation 1 by 2)

0.5y = 25 (Subtract Equation 2 from Equation 3)

y = 50 (Divide by 2)

x + 50 = 80 (Substitute y = 50 into Equation 1)

x = 30 (Subtract 50)

Answer:

Step-by-step explanation:

The mathematical translation of the statement:

\(\sqrt{121} = \sqrt{11 *11}\)

        \(= \sqrt{11^{2}}\)

        \(= (11^{2}) ^{\frac{1}{2} }\)

The indices will cancel each other out completely:

        \(= 11\)

OR:

\(\sqrt{121} = \sqrt{(-11)*(-11)}\)

        \(= \sqrt{(-11)^{2} }\)

        \(= [(-11)^{2}] ^{\frac{1}{2} }\)

        = -11

Answer:

The last option.

Step-by-step explanation:

Because, x*5 each time, gets you y.