Write the quadratic equation whose roots are - 5 and -4, and whose leading coefficient is 3.

Answer:

Step-by-step explanation:

It is the turning point, (100,0)

Answer:

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry

Step-by-step explanation:  it is the center so it would be 100

The solution of the system of equations is (x, y) = (1/3, 1/3).

To solve the given system of equations, we can use any of the following three methods; the substitution method, the elimination method (also known as the addition/subtraction method), and the graphical method. Below, we will solve it using each of these methods.

1. Substitution method:

We will use the substitution method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2) From equation (1), we have

Y + 2x = 3y ...(3)Now substitute equation (3) into equation

(2)2y = 3x - 2 ...(2)Y + 2x = 3y ...(3)2(3y - 2x) = 3x - 2

Multiplying both sides by 2:

6y - 4x = 3x - 2 Grouping like terms:

6y - 3x = 2 Adding 3x to both sides:

6y = 3x + 2Dividing both sides by 6:

y = (3/6)x + 2/6y = (1/2)x + 1/3

Therefore, the solution of the system of equations is (x, y) = (1/3, 1/3).

2. Elimination method:

We will use the elimination method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2)Multiplying equation (1) by 2,

we get;2Y = 6y - 4x ...(3)Multiplying equation (2)

by -3, we get;-6y = -9x + 6 ...(4) Adding equations (3) and (4),

we get;-4x = -9x + 8

Simplifying;-4x + 9x = 8x = -8x = -2

Therefore, we found the value of x, which is -2.

Substitute the value of x in either equation (1) or (2);

If we substitute x = -2 in equation (1), we get;

Y = 3y - 2(-2)Y = 3y + 4Y - 3y = 4Y = 4/2Y = 2Substitute the value of y in equation (1)

;Y = 3y - 2xY = 3(2) - 2(-2)Y = 6 + 4Y = 10

Therefore, the solution of the system of equations is (x, y) = (-2, 10/2).3.

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Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

1/4 = 3/12

1/6 = 2/12

3 + 2 = 5/12

12/12 - 5/12 = 7/12

7/12 is shaded

Evaluating the expression we will get the simpified fraction -2/3, or -0.66 as a decimal.

First, remember that for the quotient between two fractions

(a/b)÷(c/d)

We can rewrite it as:

(a/b)*(d/c)

Now, our expression is:

(1/3)÷(-11/7) + (-15/33)

Now, using the rule above, we can rewrite this as:

(1/3)*(-7/11) + (-15/33)

(-7/33) + (-15/33) = (-7 - 15)/33 = -22/33

Now we can simplify it, divide both numbers by 11.

-22/11 = -2

33/11 = 3

Then:

-22/33 = -2/3 = -0.66

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Answer:

Column 1 should be titled “Time,” and Column 2 should be titled

“Velocity.” ⇒ 1st answer

Sorry for being super late

Step-by-step explanation:

B. Four less than a number.

The given function is F(x) = (x - 3)³(x + 1)(x - 6)²(x² + 49). To find out how many roots (not necessarily distinct) does this function have, we will use the concept of multiplicity of roots for polynomial functions.

Multiplicity of RootsThe multiplicity of a root refers to how many times a factor occurs in the factorization of a polynomial. For instance, if we factor the polynomial x³ - 6x² + 11x - 6, we get (x - 1)(x - 2)². Here, 1 is a root of multiplicity 1 since the factor (x - 1) occurs once. 2 is a root of multiplicity 2 since the factor (x - 2) occurs twice. The total number of roots of a polynomial function is equal to the degree of the polynomial function.

Hence, in this case, we have a polynomial of degree 9. So, it has a total of 9 roots (not necessarily distinct). Hence, the number of roots (not necessarily distinct) that the given function F(x) = (x - 3)³(x + 1)(x - 6)²(x² + 49) has is equal to 9.

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Answer:

Answer is in the photo below.

Slope= 0.1

Step-by-step explanation:

In a high-quality coaxial cable, the power drops by a factor of 10 approximately every 2.75 km. This means that for every 2.75 km of cable length, the signal power decreases to one-tenth (1/10) of its original value.

Given that the original signal power is 0.45 W (4.5 x 10^-1), we can calculate the power at different distances along the cable. Let's assume the cable length is L km.

To find the number of 2.75 km segments in L km, we divide L by 2.75. Let's represent this value as N.

Therefore, after N segments, the power would have dropped by a factor of 10 N times. Mathematically, the final power can be calculated as:

Final Power = Original Power / (10^N)

Now, substituting the values, we have:

Final Power = 0.45 W / (10^(L/2.75))

For example, if the cable length is 5.5 km (which is exactly 2 segments), the final power would be:

Final Power = 0.45 W / (10^(5.5/2.75)) = 0.45 W / (10^2) = 0.45 W / 100 = 0.0045 W

In conclusion, the power in a high-quality coaxial cable drops by a factor of 10 approximately every 2.75 km. The final power at a given distance can be calculated by dividing the distance by 2.75 and raising 10 to that power. The original signal power of 0.45 W decreases exponentially as the cable length increases.

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The statement supported the graph is

The axis of symmetry is x = 3

The coordinates of the y-intercept are (0,7)

A line that divides an object into two equal halves and produces a mirror-like reflection of each side of the object is known as an axis of symmetry.

1. The axis of symmetry is x = 3

The axis of symmetry is the central axis of the graph, which signifies the middle point of the graph. It is evident that this graph is centered on x = 3.

2. The coordinates of the y-intercept are (0,7)

The y intercept is the point where the graph meets the y-axis, that is, the value of y on the graph when x=0.

From the graph, the coordinates of the y-intercept is (0, 7)

3. The X-intercept is located at (-3,0)

The x intercept is the point where the graph meets the x-axis, that is, the value of x on the graph when y=0.

From the graph the curve x axis at x= 1.5 and x= 4.5

So, the x-intercept is truly located at (1.5, 0) and (4.5,0)

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Answer:

x=10

Step-by-step explanation:

First square root 36 cm^2

Then you square both 8 and 6

Then you square root the sum of the two numbers.

This is called Pythagorean Theorem, which can be shown as a^2 + b^2 = c^2

The northbound car has traveled approximately 8.4 kilometers distance (rounded to the tenth decimal place).

Distance is the amount of space between two points or objects. It can be measured in various units such as kilometers, miles, meters, feet, etc. In mathematics, distance is often calculated using the Pythagorean theorem or other distance formulas, depending on the context of the problem.

We can use the Pythagorean theorem to solve this problem. Let's call the distance traveled by the northbound car "d". According to the Pythagorean theorem:

d² + 3²=\(9^{2}\)

Simplifying this equation, we get:

d² + 9 = 81

Subtracting 9 from both sides, we get:

d² = 72

Taking the square root of both sides, we get:

d = \(\sqrt{72}\) = 6\(\sqrt{2}\)

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Answer:

n ≥ 75

Step-by-step explanation:

-81 ≥ -6 -n

+6    +6

-75 ≥ -n

divide both sides by negative 1 to get rid of the negative sign in front of the n

75 ≥ n

flip the sign because you divided by a negative

75 ≤ n

or

n ≥ 75

Hope this helps!!!

For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is given by the values of x.

In this problem, the function is defined between x = -4 and x = 4, hence the domain is [-4,4].

The zeros are the values of x for which f(x) = 0, that is, when it crosses the x-axis.

Hence, for this problem, the zero is at (0,0).

The function is positive when it is above the x-axis, and negative when it is below, hence:

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Given:

Answer:

240 yd

Step-by-step explanation:

Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.

Consider the figure in the attached file.

We need to find the total distance traveled by Betsy.

The distance covered by Betsy is

length of segment AB length of segment BC length of segment CD length of segment DA.

To find the distance AB, we need to find the distance from A to B on y-axis.

So, length of segment AB units

To find the distance BC, we need to find the distance from B to C on x-axis.

So, length of segment BC units

To find the distance CD, we need to find the distance from C to D on y-axis.

So, length of segment CD units

To find the distance DA, we need to find the distance from D to A on x-axis.

So, length of segment DA units

Hence, the total distance covered is units

It is given that 1 unit equals 10 yd, so distance traveled by Besty is yd

For the entire independent-measures experiment 24 individuals are participated.

Different participants are utilized in each condition of the independent variable in an experimental design known as an independent measures design, or between-groups. This indicates that a different group of participants is present for each condition of the experiment. A research strategy known as an independent measures design uses numerous experimental groups with subjects only being assigned to one group. Throughout the experiment, each participant is solely exposed to one independent variable condition. A drug trial for a novel medicine would serve as an example. This has the benefit of preventing order effects, which occur when participants behave differently as a result of the order in which conditions are done, often as a result of factors like boredom or exhaustion.

We are given the value  t(22) = 5.30, p < .01

So here degree of freedom (df) is 22 and it is independent so there is two samples,

so df= n₁+n₂-2

⇒ 22 =  n₁+n₂-2

⇒ n₁+n₂ = 24.

Thus for the entire experiment 24 individuals are participated.

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The unique equation of the given parabola in the form of f(x) = (x - a)(x - b) is given by, f(x) = x(x + 6).

The y intercept of the parabola is at (0,0).

Zeros of the parabola are at x = 0, -6.

Given the model equation for the parabola is f(x) = (x - a)(x - b)

It is the standard equation of a parabola with zeros x = a, b.

Here from the graph we can see that at x = -6, 0 the value of y reaches 0 that is the parabola has zeros at x = 0, -6.

So, a = 0 and b = -6

So, f(x) = (x - 0)(x - (-6))

f(x) = x(x + 6)

From the graph we can also see that the parabola is downward negative Y axis.

At y intercepts x = 0

So, the equation becomes in that case,

f(x) = 0.

So (0, 0) is the only y intercept of the parabola.

Hence, the equation of the unique parabola is, f(x) = x(x + 6) and Y intercept is at (0, 0) and zeros are at x = 0, -6.

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The question is incomplete. The complete question will be -

"The second part of the new coaster is a parabola.

Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros."

The correct answer is option D.which is -4 ≤ x ≤ 1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

in the graph, we can see that the value of x is increasing from -4 coordinate of x to the 1 coordinate of x so the interval will be given as -4 ≤ x ≤ 1.

Therefore the correct answer is option D.which is -4 ≤ x ≤ 1.

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The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:

The equation is in the form  

dy/dx +P(x)y=Q(x)yⁿ,  where P and Q are functions of x or constants, this is called Bernoulli's equation.

Now, we have to substitution using 

\(v = {y}^{1 - n} \)

Differentiating both side with respect to 'x'

\(v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'\)

we get,

\(= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)\)

Now, by using 

\(v' = {y}^{1 - n} \)

The given equation is expressed as:

\(v + (1 - n)p(x)v = (1 - n)q(x)\)

or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)

The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.

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Answer:

y = -3x + 2.5

Step-by-step explanation:

3x + 2y = 5

-3x              -3x

2y = 5 -3x

/2     /2

y = -3x + 2.5

Answer:

3/4 is equivalent to 9/12

Step-by-step explanation:

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The worth of the 100 dollar worth if groceries in 3 years is

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential a base is the transcendental number e, which is approximately equal to 2.71828.

Using the formula:

P(t) = P(o) e ^kt

k =7/100 = 0.07

t = 3years

P(o) = $100

P(t) = 100 e^0.07×3

P(t) = 100e^0.21

P(t) =100×1.23

P(t) = $123

therefore the worth of the $100 groceries in 3 years is $123

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Answer:

no

Step-by-step explanation:

Answer:

43.98

Step-by-step Explanation:

Equation I use: 2(3.14)r

2 · 3.14 · 7 = 43.98

Answer:

0.000000207 in scientific notation = 2.07 × 10^-7

Remember it has to have one number before the decimal.

8.2 * 10^-7 in standard form = 0.00000082

YOu have to move the decimal back.

In the first box the answer is 2.07 × 10^-7.

In the second box the answer is 0.00000082.

If arc ce measures 126 degrees, point b lies on circle a, the measure of angle cde is 54 degrees. Correct option is D.

In a circle, if two tangent lines intersect at a common point on the circle, then the angles formed by these tangent lines at the point of intersection are equal.

In this case, lines cd and de are tangent to circle a and intersect at point d. Therefore, the angles formed by these lines at point d are equal. Let's call this angle x.

Also, arc ce measures 126 degrees, which means that the central angle that corresponds to this arc (angle cbe) measures 126 degrees as well.

Since angle cbe and angle cde form a linear pair (they share a common side and their non-common sides form a straight line), we can find the measure of angle cde by subtracting the measure of angle cbe from 180 degrees:

angle cde = 180° - angle cbe

angle cbe = 126° (given)

angle cde = 180° - 126° = 54°

Therefore, Option D is correct answer.

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Complete question is:

Lines cd and de are tangent to circle a: lines cd and de are tangent to circle a and intersect at point d. arc ce measures 126 degrees. point b lies on circle a. if arc ce is 126°, what is the measure of  cde?

A) 126

B) 63

C) 117

D) 54