Graph the ellipse with equation x squared divided by nine plus y squared divided by sixteen = 1

Final answer:

The two integers that satisfy the conditions of being twice of each other and having a product of 32 are either (4, 8) or (-4, -8).

Explanation:

The two integers as x and y, with y being 2 times x (y = 2x). According to the problem, the product of these two integers is 32 (x * y = 32). If we substitute y in the equation with 2x, we obtain the following: x * 2x = 32. Simplifying this equation gives us a quadratic equation, x² = 16.

To find x, we take the square root of both sides. The square root of 16 is 4, so x can be either 4 or -4. Consequently, y can be either 8 or -8, depending on whether x is positive or negative.

Therefore, the two sets of integers that satisfy the equation x*y = 32 are (4, 8) and (-4, -8), as both pairs have a product of 32 and one integer is exactly twice the other.

An equation regarding the length of the sides of an isosceles right triangle is required.

The required equation is [tex]2x^2=h^2[/tex]

The length of the legs of triangle which are equal in length is [tex]x[/tex]

The length of the hypotenuse is [tex]h[/tex]

From the Pythagoras theorem we have

[tex]x^2+x^2=h^2\\\Rightarrow 2x^2=h^2[/tex]

Hence, in the above equation the length of the legs and the hypotenuse lengths are related.

Learn more:

https://brainly.com/question/15138986

https://brainly.com/question/343682

Final answer:

The expression that results in a rational product is √10 times √10, as this simplifies to the rational number 10.

Explanation:

To find which expression results in a product that is a rational number, we need to identify which pair of square roots can be multiplied to produce a non-radical number.

Multiplication of square roots is analogous to the multiplication of exponents. When the same base is multiplied, the exponents are added. Utilizing this property, we know:

√7 × √10 = √(7 × 10) = √70 (which is irrational since 70 is not a perfect square).

√8 × √10 = √(8 × 10) = √80 (which is irrational since 80 is not a perfect square).

√9 × √10 = √(9 × 10) = √90 (which is irrational since 90 is not a perfect square).

√10 × √10 = √(10 × 10) = √100 = 10 (which is rational since 100 is a perfect square).

Therefore, the expression that results in a rational product is √10 × √10, which simplifies to 10.

Final answer:

Jose should rent a truck from Company A if he plans to drive more than 55 miles, as it will charge less than Company B beyond this mileage.

Explanation:

To determine for what mileages Company A will charge less than Company B, we set up an inequality comparing the total cost for each company and solve for m (the number of miles driven).

The cost for Company A is a flat rate of $108, so it does not depend on mileage. The cost for Company B includes an initial fee of $75 plus $0.60 per mile. We set up the inequality as follows:

Company A \< Company B

$108 < $75 + $0.60m

$108 - $75 < $0.60m

$33 < $0.60m

$33 / $0.60 < m

55 < m

Therefore, Company A will charge less than Company B for any number of miles greater than 55. So, if Jose plans to drive more than 55 miles, he should choose Company A for a cheaper rate.

Answer:

The answer is .......D

Step-by-step explanation:

d. 480

You have to remember that The answer is D

The student's equation simplifies to 9v + 10 = 9v + 9. Upon further simplification, it becomes apparent that the equation is a contradiction and has no solution.

The student is asking about the solution to the equation (3x6÷2)v+10=3²v+9. The first step in solving this equation is to simplify the terms. We start by simplifying the multiplication and division in the first part of the equation (3x6÷2), which equals 9 since 3 times 6 is 18 and 18 divided by 2 is 9. Therefore, the equation simplifies to 9v + 10 = 3²v + 9. Next, we simplify 3², which is 3 raised to the power of 2, meaning 3 times itself, which results in 9. The equation now reads 9v + 10 = 9v + 9.

With the equation simplified, we notice that the terms containing v are equal on both sides of the equation. This indicates that we may be dealing with an identity or a contradiction depending on the constants. Subtracting 9v from both sides yields 10 = 9, which is clearly not true. Therefore, we conclude that the equation is a contradiction, and there is no solution for v that would make the equation true.

Final answer:

To solve the equation (3x6÷2)v+10=3²v+9, we need to follow the order of operations and solve for the variable v. However, the equation is inconsistent and has no solution.

Explanation:

To solve the equation (3x6÷2)v+10=3²v+9, we need to follow the order of operations and solve for the variable v. Let's break it down step by step:

Start by performing the division 3x6÷2 = 18÷2 = 9.

Now rewrite the equation as 9v+10=9v+9.

Subtract 9v from both sides of the equation to isolate the constants: 10 = 9.

Since 10 is not equal to 9, the equation is inconsistent and has no solution.

Therefore, there is no value of v that satisfies the equation.

To find the positive difference between the solutions of the quadratic equation x^2-4x-14=3x+16, we simplify it to x^2-7x-30=0 and use the quadratic formula. Calculating the solutions, we get 10 and -3, and the positive difference between these solutions is 13.

To find the positive difference between the solutions of the quadratic equation x2-4x-14=3x+16, we first need to simplify the equation by subtracting 3x and 16 from both sides to set it equal to zero.

x2 - 7x - 30 = 0

Now, we use the quadratic formula, which is x = ∛(-b ± √(b2 - 4ac))/(2a), to find the solutions for x, where a = 1, b = -7, and c = -30.

∛(-(-7) ± √((-7)2 - 4*1*(-30)))/(2*1)

The solutions are:

Calculating the square root and simplifying, we find:

The solutions then become:

The positive difference between the solutions 10 and -3 is:

10 - (-3) = 13

Therefore, the positive difference between the solutions is 13.

The positive difference between the two solutions is 13.

Start by rearranging the equation [tex]\(x^2 - 4x - 14 = 3x + 16\)[/tex] into standard quadratic form:

[tex]\[ x^2 - 4x - 14 = 3x + 16 \][/tex]

Combine like terms:

[tex]\[ x^2 - 4x - 14 - 3x - 16 = 0 \][/tex]

[tex]\[ x^2 - 7x - 30 = 0 \][/tex]

Now, to find the solutions to this quadratic equation, we can use the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

For the equation [tex]\(x^2 - 7x - 30 = 0\)[/tex], the coefficients are:

[tex]\[ a = 1, \quad b = -7, \quad c = -30 \][/tex]

Let's substitute these values into the quadratic formula:

[tex]\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(-30)}}{2(1)} \ \\\\\\[ x = \frac{7 \pm \sqrt{49 + 120}}{2} \ \\\\\\[ x = \frac{7 \pm \sqrt{169}}{2} \ \\\\\\[ x = \frac{7 \pm 13}{2} \][/tex]

So, the solutions are:

[tex]\[ x = \frac{7 + 13}{2} = 10 \ \\\\\\[ x = \frac{7 - 13}{2} = -3 \][/tex]

The positive difference between these solutions is:

[tex]\[ \text{Positive difference} = |10 - (-3)| = |10 + 3| = 13 \][/tex]

Therefore, the positive difference between the two solutions is 13.

To find the dimensions of the rectangle, we set up an equation using the area formula and solve for 'x'.

Let's assume that the width of the rectangle is 'x' yards. Since the length is 5 yards less than twice the width, we can express the length as (2x - 5) yards. The area of a rectangle is given by the formula A = length * width, so we can set up the equation:

A = (2x - 5) * x = 52

Expanding the equation:

2x^2 - 5x - 52 = 0

Using the quadratic formula or factoring, we can solve for 'x'. Once we find the value of 'x', we can substitute it back into the expressions for length and width to find the dimensions of the rectangle.

Dimensions of the rectangle: Width = x yards, Length = (2x - 5) yards

https://brainly.com/question/31677552

#SPJ3

I would be $3.41 first you figure out how much one cost by dividing 0.93 by 6 then you multiply your answer by 22

Joe is positive 986 yards

Ziggy is negative 118 yards

the total difference is 986 +118 = 1,104 yards

Answer:

[tex]\sqrt{31}[/tex]

Step-by-step explanation:

A.[tex]-5 \frac{4}{11} =\frac{-59}{11}[/tex]

Since it in in p/q form so it is a rational number

B. [tex]\sqrt{31} =5.5677643.......[/tex]

Since it cannot be represented in the form of p/q . So, it is irrational number .

C. 7.608

[tex]\frac{7608}{1000}[/tex]  

Since it can be represented in p/q form . So, it is rational number.

D. 18.46...

18.4666.. Since 6 is repeating in decimal place . So, 18.46.. can be written in p/q form .

Hence Option B sqrt of 31 is not a rational number .

To evaluate the line integral, calculate the arclength element and substitute it into the integral. Expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.

To evaluate the line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1, we need to find the arclength element ds and substitute it into the integral. The arclength element ds can be calculated using the formula ds = sqrt(dx^2 + dy^2 + dz^2). In this case, dx = dt, dy = 2t dt, and dz = 3t^2 dt. Substituting these values into the arclength element formula, we get ds = sqrt(dt^2 + 4t^2 dt^2 + 9t^4 dt^2) = sqrt(1 + 4t^2 + 9t^4) dt.

Substituting ds into the line integral, we get the integral of (2x+9z) * sqrt(1 + 4t^2 + 9t^4) dt. To evaluate this integral, you can expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.

However, it seems that there might be a typo in the original question regarding the curve parametrization. The curve given by x=t, y=t^2, z=t^3 is actually a parabolic curve, not a line. If you need further clarification or assistance, please let me know.

Answer:

990

Step-by-step explanation:

Answer:

the answer is A which is 14. help this helps

Step-by-step explanation:

A piecewise equation to model the total weekly pay for an engineering technician who earns different rates for hours within and beyond 40 hours is P(h) = {25h if h ≤ 40, 1000 + 32(h - 40) if h > 40}.

The question asks for a piecewise equation to model the total weekly pay of an engineering technician who makes $25 per hour for the first 40 hours and $32 an hour for each hour over 40 hours. The piecewise function is made up of two parts:

When written as a piecewise function, it will look something like this:

P(h) =
 \{
 \begin{array}{ll}
 25h & \text{if } h ≤ 40,\\
 1000 + 32(h - 40) & \text{if } h > 40.
 \end{array}
 \}

In an area that is 5 km by 3 km, with an ocotillo population density of 15 plants per square kilometer, we would expect to find 225 ocotillo plants.

The student's question pertains to calculating the expected number of ocotillo plants in a given area based on the known population density. First, we need to find the total area of the region in question, which in this case is a desert area that measures 5 km by 3 km. We calculate the area by multiplying the length by the width: 5 km x 3 km = 15 km2.

Since the population density of ocotillo is given as 15 plants per square kilometer, we can find the total number of ocotillos by multiplying the density by the total area:

15 plants/km2 x 15 km2 = 225 plants.

Therefore, in an area that is 5 km by 3 km, we would expect to find 225 ocotillo plants.