Write the quadratic equation given the roots 0 and -3. Can someone answer this please

Answer:

x=63

Step-by-step explanation:

hope that helped

Answer:

a) See attachment

b) P has coordinates of (5,7)

Step-by-step explanation:

Answer:

6.4

Step-by-step explanation:

5/4x=8

1.25x=8

x=6.4

Answer:

1064.8 km³

Step-by-step explanation:

The triangular base of the prism can be divided into a right triangle and an isosceles triangle. The right triangle has legs of 10 km and 8.8 km, while the isosceles triangle has two sides of 12 km and an altitude of 8.8 km.

To find the area of the triangular base, we can use the formula for the area of a triangle:

Area = ½ * base * height

For the right triangle, the base is 10 km and the height is 8.8 km, so the area is:

Area = ½ * 10 km * 8.8 km = 44 km²

For the isosceles triangle, the base is 12 km and the height is also 8.8 km, so the area is:

Area = ½ * 12 km * 8.8 km = 52.8 km²

The total area of the triangular base is the sum of the areas of the two triangles:

Total Area = 44 km² + 52.8 km² = 96.8 km²

To find the volume of the prism, we can multiply the area of the base by the height of the prism:

Volume = Base Area * Height

Volume = 96.8 km² * 11 km = 1064.8 km³

Rounding to the nearest tenth, the volume of the prism is 1064.8 km³.

The volume of the given triangular prism is 975.7 km³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

The figure is a triangular prism, with a triangular base and three rectangular faces.

To calculate the volume of the prism, we will use the formula V = Bh, where B is the area of the base and h is the height of the prism.

The area of the base can be calculated using Heron's formula:

Area = √s(s-a)(s-b)(s-c)

where a, b, and c are the side lengths of the triangle and s is the semi perimeter (half of the perimeter).

For this figure, the side lengths are 10 km, 12 km, and 13 km, and the semi perimeter is (10 + 12 + 13)/2 = 35/2 = 17.5 km.

Substituting these values into Heron's formula, we get:

Area = √(17.5)(7.5)(5.5)(4.5) = 88.7 km²

Now that we have the area of the base, we can use the formula V = Bh to calculate the volume of the prism:

V = 88.7 km² × 11 km = 975.7 km³

Therefore, the volume of the given triangular prism is 975.7 km³.

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Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.

To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.

1. Critical Points:

To find the critical points, we need to find the points where the gradient of the function is zero or undefined.

The gradient of f(x, y) is given by:

∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).

Setting the partial derivatives equal to zero, we get:

2x + 2xy + 2x = 0          (Equation 1)

2y + x² + 8y + x² = 0      (Equation 2)

Simplifying Equation 1, we have:

2x(1 + y + 1) = 0

x(1 + y + 1) = 0

x(2 + y) = 0

So, either x = 0 or y = -2.

If x = 0, substituting this into Equation 2, we get:

2y + 0 + 8y + 0 = 0

10y = 0

y = 0

Thus, we have one critical point: (0, 0).

2. Evaluate Function at Critical Points and Boundary:

Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.

(i) Critical point:

f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4

       = 0 + 0 + 0 + 0 + 0 + 4

       = 4

(ii) Boundary points:

- At (1, 1):

f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4

       = 1 + 1 + 1 + 4 + 1 + 4

       = 12

- At (1, -1):

f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, 1):

f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, -1):

f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4

          = 1 + 1 + 1 + 4 + 1 + 4

          = 12

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Given that the particle moves along the curve y=e^(2x) and the magnitude of its velocity is v=5ft/s.A particle moving along a curve is given by:y = e^(2x)Taking the derivative of this function with respect to time t will give the velocity function as follows;dy/dt = 2e^(2x) dx/dt ............................... (1)We know that the magnitude of velocity is constant v = 5ft/s.

Therefore, we can use the velocity function to solve for dx/dt and dy/dt as shown below;dx/dt = v/√(4e^(4x)) = v/(2e^(2x)) ................ (2)Substituting equation (2) into (1), we get;dy/dt = 2e^(2x) dx/dt = 2e^(2x) * v/(2e^(2x))=v = 5 ft/sHence, the y-component of velocity when the particle is at y = 8 ft is 5 ft/s.

Therefore, we can use the slope of the curve at point y = 8 ft to find the angle of the slope, then use trigonometry to solve for the x-component of velocity.

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Answer:

Step-by-step explanation:

1593/13

122.538

answer: 122.5

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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The pH of a solution that is 0.25 M NH3 and 0.35 M NH4Cl is 9.25.To calculate the pH of a solution that is 0.25 M NH3 and 0.35 M NH4Cl, we need to consider the ionization of the weak base NH3, which will result in the formation of NH4+ and OH- ions.

The pH of the solution is equal to the negative logarithm of the concentration of H+ ions in the solution. The steps to calculate the pH of a solution are as follows:

Step 1: Write the balanced equation of the reaction NH3 + H2O ⇌ NH4+ + OH-

Step 2: Write the ionization constant of the base NH3Kb = [NH4+][OH-]/[NH3]Kb

= (x)(x)/0.25-xKb

= x^2/0.25-x

Step 3: Calculate the concentration of NH4+ ionsNH4+ = 0.35 M

Step 4: Calculate the concentration of OH- ionsOH-

= Kb/NH4+OH-

= (0.025x10^-14)/(0.35)OH-

= 1.79 x 10^-15 M

Step 5: Calculate the concentration of H+ ions[H+]

= Kw/OH-[H+]

= (1.0x10^-14)/(1.79x10^-15)[H+]

= 5.59 x 10^-10 M

Step 6: Calculate the pH of the solutionpH = -log[H+]pH

= -log(5.59 x 10^-10)pH

= 9.25

Therefore, the pH of a solution that is 0.25 M NH3 and 0.35 M NH4Cl is 9.25.

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The value of Y(s) is  Y(s) = 12/(s⁴ + 4s²) + (4s + 2)/(s⁴ + 4s²) and the value of y(t) is y(t) = (2/s²)(2sin(2t) + 7). Given differential equation is y" + 4y = 12t, y(0) = 4, y(0) = 2. We need to find the value of Y(s) and y(t).

a. Laplace Transform of given differential equation is

L{y"} + 4L{y} = 12L{t}

=> s²Y(s) - sy(0) - y'(0) + 4Y(s)

= 12/s² (since L{t} = 1/s²)

Given y(0) = 4 and y'(0) = 2,

s²Y(s) - 4s - 2 + 4Y(s) = 12/s²

=> Y(s) = 12/(s⁴ + 4s²) + (4s + 2)/(s⁴ + 4s²)

b. Y(s) = 12/(s⁴ + 4s²) + (4s + 2)/(s⁴ + 4s²)

=> Y(s) = (4s + 14)/(s⁴ + 4s²)

=> Y(s) = (2/s²)(2s/(s² + 2²) + 7/s²)

We know that inverse Laplace Transform of 2s/(s² + a²) = sin(at)

Therefore, inverse Laplace Transform of Y(s) is y(t)= L⁻¹{Y(s)}= (2/s²)(2sin(2t) + 7)

Therefore, the value of Y(s) is  Y(s) = 12/(s⁴ + 4s²) + (4s + 2)/(s⁴ + 4s²) and the value of y(t) is y(t) = (2/s²)(2sin(2t) + 7).

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Answer:

a) 4\(x^{6}\)

b) 2\(w^{4}\)

Step-by-step explanation:

a) multiply the coefficients and add the exponents

(4)(1) · \(x^{3+3}\) = 4\(x^{6}\)

b) divide the coefficients and subtract the exponents

(14 ÷ 7) · \(w^{6-2}\) = 2\(w^{4}\)

The kWh a house uses in a year is 11050 kWh

From the question, we have the following parameters that can be used in our computation:

Average in 4 weeks = 850 kWh

There are 52 weeks in a year

So, the kWh used in a year is calculated as

kWh used = Average in 4 weeks * Number of weeks in a year/4

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

kWh used = 850 kWh * 52/4

Evaluate

kWh used = 11050 kWh

Hence. the kWh used is 11050 kWh

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Answer:

Step-by-step explanation:

The answer would be 120 because you have to add all numbers.

The answer is B 24°.

The midpoint formula is used to find the center point of a line segment, given the coordinates of the two endpoints. The formula is as follows:

Midpoint = ( (x₁+ x₂) / 2, (y₁ + y2) / 2 )

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.

To find the missing coordinate using the midpoint formula, you would need to have the coordinates of one endpoint, as well as the coordinates of the midpoint. Then, you can use the formula to solve for the missing coordinate.

For example, if you have the coordinates of one endpoint as (3, 5) and the coordinates of the midpoint as (4, 6), you can use the formula to solve for the missing endpoint:

Midpoint = ( (3 + x₂) / 2, (5 + y₂) / 2 )

(4, 6) = ( (3 + x₂) / 2, (5 + y₂) / 2 )

So, by solving above equation we can get the missing coordinate

(x₂, y₂) = (5,7)

In conclusion, the midpoint formula can be used to find the missing coordinate of a line segment by using the coordinates of one endpoint and the midpoint. It is a simple and efficient way to find the missing coordinate when working with geometric shapes.

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The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The confidence interval = 95%

And, Size of sample = 17

Now,

Since, The confidence interval = 95%

And, Size of sample (n) = 17

Hence, The degree of freedom (n - 1) = 16

Thus, The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

Therefore, The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

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━━━━━━━☆☆━━━━━━━

▹ Answer

C = 3215.36

▹ Step-by-Step Explanation

A = πr²

A = 3.14(32)²

A = 3215.36

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

The integral ∫∫ r √4 −x2−y2da where r = {(x, y) : x2 y2≤ 4, x ≥ 0} conversion to polar coordinates the value of the integral is (4/3)π.

To convert the integral to polar coordinates, we need to express the limits of integration in terms of the polar coordinates.

Recall that in polar coordinates, x = r cosθ and y = r sinθ, where r is the radial distance from the origin and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin to the point (x, y).

In this case, the region r is defined by \(x^2 + y^2\) ≤ 4 and x ≥ 0. In polar coordinates, this corresponds to the region 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. To see why, note that x ≥ 0 implies 0 ≤ θ ≤ π/2, and \(x^2 + y^2 = r^2\), so r ≤ √4 = 2.

So we have:

∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) ∫(r=0 to 2) r√(4-\(r^2\)) dr dθ

To evaluate this integral, we can use the substitution u = 4 - \(r^2\), du = -2r dr, which gives:

∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) ∫(u=4 to 0) -1/2 √u du dθ

Now we can evaluate the inner integral:

∫(u=4 to 0) -1/2 √u du = [-1/3 u^(3/2)](u=4 to 0) = (1/3)(8 - 0) = 8/3

Substituting this back into the original integral, we have:

∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) (8/3) dθ = (8/3) (π/2 - 0) = (4/3)π

Therefore, the value of the integral is (4/3)π.

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The differential operator that annihilates e sin 2x is (A) (D+1)(D-2), the differential operator that annihilates 3et+2 cos x is (E) None of these, and the differential operator that annihilates 5+x+3e +xe is (C) D(D-2).

To find the differential operator that annihilates a given function, we need to apply the operator to the function and check if it evaluates to zero. For the function e sin 2x, applying the operator (D+1)(D-2) to it yields zero, indicating that this operator annihilates the function.

However, for the function 3et+2 cos x, none of the given options in (B), (C), (D), or (E) result in zero when applied to the function. Similarly, for the function 5+x+3e +xe, only the operator D(D-2) evaluates to zero, indicating that it is the differential operator that annihilates the function.

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Answer:

Find the equivalent ratio for the total shapes:

Total Black Shapes : Total White Shapes = 5 : 11

Multiply by 2:

Total Black Shapes: Total White Shapes = 10 : 22

Step-by-step explanation:

Answer:

608 hours

Step-by-step explanation:

64% as a decimal is 0.64.

950(0.64) = 608

Macy had 3 appointments.

Logan had 5 appointments.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, which is written in the form of "ax^2 + bx + c = 0", where x is the variable and a, b, and c are constants. The solutions to a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.

Part A:

Let x be the number of appointments Macy had.

We know that the total income (60x + 40) must equal 220.

Therefore, the equation representing the situation is:

60x + 40 = 220

To solve for x, we can subtract 40 from both sides:

60x = 180

Finally, we divide both sides by 60 to get:

x = 3

Macy had 3 appointments.

Part B:

Let y be the number of appointments Logan had.

We know that the total profit (70y + 50 - 20y) must equal 300.

Therefore, the equation representing the situation is:

50y + 50 = 300

To solve for y, we can subtract 50 from both sides:

50y = 250

Finally, we divide both sides by 50 to get:

y = 5

Logan had 5 appointments.

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The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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The particular solution of the given differential equation with the initial condition x(0) = 4.

Any mathematical equation that connects a function and its derivatives to one or more independent variables is known as a differential equation. Many different physical phenomena, including as the behaviour of particles, fluids, and electrical circuits, are modelled using differential equations. They are used extensively in physics, engineering, and other disciplines. Differential equations' solutions frequently provide light on the behaviour of complicated systems and can be used to forecast how they will behave in the future.

Step 1: Write down the given differential equation and initial condition.
\(dx/dt = 4x\\x(0) = 4\)

Step 2: Rewrite the differential equation in a separable form.
\((1/x)dx = 4dt\)

Step 3: Integrate both sides of the equation.
\(\int\limits {x} \, dx (1/x)dx = \int\limits {x} \, dx 4dt\)

Step 4: Find the antiderivatives.
\(ln|x| = 4t + C\)

Step 5: Solve for x.
\(x = e^(4t + C)\\x = e^(4t) * e^C\)
Step 6: Apply the initial condition x(0) = 4.
\(4 = e^(4*0) * e^C\\4 = e^C\)

Step 7: Write the general solution, substituting the value of e^C.
\(x(t) = e^(4t) * 4\)

That's the particular solution of the given differential equation with the initial condition x(0) = 4.

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Answer:

B

Step-by-step explanation:

(20)/(6)-(5)/(2)

Hope this helps!!!

Answer:

an enlargement or a reduction of the figure

a slide of the figure

a turning of the figure about some fixed point

a mirror image of the figure

The best description of a dilation of a figure is a slide of the figure.

What is dilation?

A dilation is a transformation that changes the size of a figure. It can become larger or smaller but the shape of the figure does not change.

Now,

The best description of a dilation of a figure is a slide of the figure.

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In Python, the double asterisk (**) operator is used for exponentiation or raising a number to a power.

When you write 5 ** 2, it means "5 raised to the power of 2", which is equivalent to 5 multiplied by itself.

The base number is 5, and the exponent is 2.

The double asterisk operator (**) indicates exponentiation.

The number 5 is multiplied by itself 2 times: 5 * 5.

The result of the expression is 25.

So, 5 ** 2 evaluates to 25.

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Answer:

4 2/7 - 6/7 = 24/

7

= 3 3/

7

Step-by-step explanation:

Conversion a mixed number 4 2/

7

to a improper fraction: 4 2/7 = 4 2/

7

= 4 · 7 + 2/

7

= 28 + 2/

7

= 30/

7

To find a new numerator:

a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7/

7

= 28/

7

b) Add the answer from previous step 28 to the numerator 2. New numerator is 28 + 2 = 30

c) Write a previous answer (new numerator 30) over the denominator 7.

Four and two sevenths is thirty sevenths

Subtract: 30/

7

- 6/

7

= 30 - 6/

7

= 24/

7

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 7) = 7. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 7 = 49. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirty sevenths minus six sevenths = twenty-four sevenths.