can anyone solve this for me

Answer:

Step-by-step explanation:

The greatest common factor of 9x and 36 is 9. So factored it would be 9(x+4)

Carlos buy 35 number of angelfish and 360 number of parrotfish.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

x represents the number of angelfish Carlos bought and the variable y represents the number of parrotfish he bought.

Carlos bought 405 tropical fish for a museum display.

x + y = 405            ..(1)

As he bought 8 times as many parrotfish as angelfish.

⇒ y = 8x                ..(2)

Plug y = 8x in equation (1)

x + 8x = 405

     9x = 405

       x = 45

Plug x = 45 in equation (2)

y = 8(45)

y = 360

Hence, Carlos bought 35 number of angelfish and 360 number of parrotfish.

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In a primitive Pythagorean triple, the sides a, b, and c are all integers, and they satisfy the equation a^2 + b^2 = c^2.

Now, let's assume that neither x nor y is divisible by 3. This means that x and y can only be 1, 2, 4, 5, 7, or 8 modulo 3. Therefore, x^2 and y^2 can only be 1 or 4 modulo 3. Now, let's consider the equation a^2 + b^2 = c^2 mod 3. If a and b are both 1 or both 2 modulo 3, then their squares will add up to 2 modulo 3, which is not a quadratic residue. Therefore, one of a and b must be 0 modulo 3, and hence, c must also be divisible by 3. We assumed that neither x nor y is divisible by 3. We then looked at the possible residues of x and y modulo 3 and saw that they can only be 1, 2, 4, 5, 7, or 8 modulo 3. We then used the fact that the sum of two quadratic residues is not a quadratic residue modulo 3, and concluded that one of a and b in the Pythagorean triple must be divisible by 3.

In conclusion, either x or y in a primitive Pythagorean triple must be divisible by 3. This is a result of the fact that the sum of two quadratic residues is not a quadratic residue modulo 3.

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Step-by-step explanation:

6x^2 - 14x >= -4

6x^2 - 14x +4  >= 0

Use Quadratic Formula to find

(x-2)(x-1/3) >= 0       If both +   this is true

                                If both neg this is true

(- inf , 1/3]    U    [2 , + inf )      is x

Rounding to the nearest 10th, the length of the missing leg is approximately 7.2.

Using the Pythagorean theorem, we can solve for the missing leg:

a² + b² = c²

where a and b are the legs of the right triangle, and c is the hypotenuse.

Substituting the given values, we get:

12² + b² = 14²

Simplifying:

144 + b² = 196

Subtracting 144 from both sides:

b² = 52

Taking the square root of both sides:

b = 7.211

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The required measure of the angle measured by using a protractor is 70°

Given situation : A protractor is used on an angle

A ray is passed through this angle

we have to find the measure of the total angle

Let the angle is passed through an angle ∠ABC

and the ray be BD

thus the two angles which will be formed will be

∠ABD and ∠DBC

Now let one of the angles , say angle ∠ABD be 13°

and ∠DBC be 57°

Thus the whole angle would be ∠ABD + ∠DBC = ∠ABC

∠ABC = 57 + 13 = 70°

Thus the required measure of the angle is 70°

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Answer:

$5,000

50%

Step-by-step explanation:

$1,000×100=10,000

10,000÷2,000= 500

500×10= 5,000

Answer:

2 pounds per hour

Step-by-step explanation:

there is 24 hours in a day so 48 divided by 24 = 2

So they make 2 pounds per hour

The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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The volume of the resulting solid is (26π/3) cubic units.

To find the volume of the solid generated by rotating the region bounded by the curves x = (y - 6)², x = 25, about the axis y = 1, we will integrate the cylindrical shells along the y-axis.

The limits of integration for y are from y = 1 to y = 11, as determined earlier.

The differential volume of a cylindrical shell is given by dV = 2πrh dy, where r is the distance from the axis of rotation to the curve, h is the height of the cylindrical shell, and dy is the thickness of the shell.

In this case, the radius of the cylindrical shell is r = 1, and the height of the cylindrical shell is h = x₁ - x₂ = 25 - (y - 6)².

Thus, the differential volume becomes dV = 2π(1)(25 - (y - 6)²) dy.

We can now integrate this differential volume over the range of y = 1 to y = 11 to find the total volume V:

V = ∫[1,11] 2π(25 - (y - 6)²) dy

Expanding and simplifying the integral:

V = 2π ∫[1,11] (25 - (y - 6)²) dy

V = 2π ∫[1,11] (25 - (y² - 12y + 36)) dy

V = 2π ∫[1,11] (25 - y² + 12y - 36) dy

V = 2π ∫[1,11] (-y² + 12y - 11) dy

Integrating the terms individually:

V = 2π [-y³/3 + 6y² - 11y] |[1,11]

V = 2π [-(11³/3) + 6(11²) - 11(11)] - [-(1³/3) + 6(1²) - 11(1)]

V = 2π [-1331/3 + 726 - 121] - [-1/3 + 6 - 11]

V = 2π [-1331/3 + 726 - 121 + 1/3 - 6 + 11]

V = 2π [-604/3 + 616 + 1/3]

V = 2π [13/3]

Simplifying further:

V = (26π/3)

Therefore, the volume of the resulting solid is (26π/3) cubic units.

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Answer:

i am pretty sure the answer is d.

Step-by-step explanation:

let me know if this is wrong

Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

y 10

Step-by-step explanation:

Answer

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

12°

Step-by-step explanation:

The angles of the shape should all add to 360°.

We divide this by 30, because the shape has 30 angles.

360° ÷ 30 = 12°.

This is the measure of each angle, and also the degree of rotation. The shape will look like the original figure each time it is rotated 12°.

Answer: 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)\)

The factored form of an equation is done by rewriting the equation in simpler forms.

The completely factored form of \(x^3 - 64x\) is \(x(x-8)(x + 8)\)

The expression is given as:

\(x^3 - 64x\)

Factor out x from the expression, \(x^3 - 64x\)

\(x^3 - 64x = x(x^2-64)\)

Express 64 as 8^2

\(x^3 - 64x = x(x^2-8^2)\)

Express the expression as a difference of two squares

\(x^3 - 64x = x(x-8)(x + 8)\)

Hence, the completely factored form of \(x^3 - 64x\) is \(x(x-8)(x + 8)\)

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Answer:

\(m=\frac{7}{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-4, 19)

Point (4, 9)

Step 2: Find slope m

Answer 18

Solve 5+5+4+4=18

Answer: 23 spools of thread

Step-by-step explanation:

0.2 times 9 = 1.8 spools of thread

25 - 1.8 = 23.2 spools of thread

Answer:

22

50

Step-by-step explanation:

Crowding out refers to the phenomenon where increased government spending or borrowing reduces private sector spending or investment.

In this scenario, income taxes fall by $20 billion, leading to an increased deficit. As a result of the increased deficit, interest rates rise, which reduces investment expenditures by $15 billion.

To determine the extent of crowding out, we need to consider the relationship between changes in government spending and changes in private sector spending. The marginal propensity to consume (MPC) measures the fraction of additional income that is spent.

In this case, the MPC is given as 0.9, which means that for every additional dollar of income, individuals spend 90 cents and save 10 cents. With a high MPC, a decrease in income taxes (increase in disposable income) is expected to result in a significant increase in consumer spending.

However, the increase in the deficit and subsequent rise in interest rates can have a dampening effect on private sector investment. The higher interest rates make borrowing more expensive, reducing the incentive for businesses to invest.

Based on the given information, it can be inferred that the crowding out effect is incomplete (option c). While the decrease in income taxes stimulates consumer spending, the subsequent increase in interest rates partially offsets this effect by reducing investment expenditures. The overall impact on private sector spending is not fully negated (complete crowding out) nor completely unaffected (zero crowding out).

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Han's retirement account earns $247,163.25 in simple interest.

To find the simplest interest, we need to use the formula:

Simple Interest = Principal × Rate × Time

In this case, the Principal is $410,000 and the Rate is $15,785 per year. We don't know the time period, but we can solve for it using the formula:

Time = Simple Interest ÷ (Principal × Rate)

Plugging in the values, we get:

Time = $15,785 ÷ ($410,000 × 1) = 0.0385 years

Therefore, the simplest interest is:

Simple Interest = $410,000 × $15,785 × 0.0385 = $247,163.25

So Han's retirement account earns $247,163.25 in simple interest.

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The given statement newton's root finding method always converge to the root at a quadratic convergence rate is False.

Newton's root finding method does not always converge to the root at a quadratic convergence rate. While the method can exhibit quadratic convergence under certain conditions, such as when the initial guess is close to the root and the function satisfies certain smoothness properties, it is not guaranteed in all cases.

The convergence rate of Newton's method depends on the behavior of the function and the initial guess. It can vary from quadratic convergence (the fastest rate) to linear convergence or even slower convergence in some cases. Factors such as multiple roots, singularities, or oscillatory behavior of the function can affect the convergence rate and stability of Newton's method.

Therefore, it is not accurate to claim that Newton's root finding method always converges to the root at a quadratic convergence rate.

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The maximum profit per day is $600, and the soft-drink vendor must sell 1,500 cans to achieve this maximum profit.

The profit function for the soft-drink vendor is given by P(x) = -0.001x^2 + 3x - 1800. To find the maximum profit per day and the number of cans to sell for maximum profit, follow these steps:

1. Identify the quadratic function: In this case, it's P(x) = -0.001x^2 + 3x - 1800.

2. Find the vertex of the parabola, which represents the maximum profit point. The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a and b are the coefficients of the quadratic function (a = -0.001, b = 3).

3. Calculate the x-coordinate of the vertex: x = -3 / (2 * -0.001) = -3 / -0.002 = 1500.

4. Substitute the x-coordinate back into the profit function to find the maximum profit: P(1500) = -0.001(1500)^2 + 3(1500) - 1800 = $600.

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Answer:

58

Step-by-step explanation:

72 + 1 - 5 x 3

= 72 + 1 - 15

= 73 - 15

= 58

Answer:

15 Packages

Step-by-step explanation:

Let number of packages = x

For Nic

Nic sells advertising packages for a radio station. The company pays him $ 150 per week and they also pay him $ 75 for every package he sells.

Equation =

150 + 75x

His friend Asia works for the same radio station but she receives a salary only, which is $ 1 , 275per week.

We solve by equating

150 + 75x = 1275

75x = 1275 - 150

75x = 1125

x = 1125/75

x = 15 Packages

Answer:

8

Step-by-step explanation:

Answer:

8mph

Step-by-step explanation:

Because it took Ruthene 1/4 of an hour or 15 minutes to run two miles, if she were to run for an entire hour she would go 4 times as far, or 8 miles. This means that Ruthene had an average speed of 8mph.