The quadratic function f(x) = a(x - h)^2 + k is in standard form.
(a) The graph of f is a parabola with vertex (x, y) =

Answer:

Multiply the radius by 2 to get the diameter.

Multiply the result by π, or 3.14 for an estimation.

That's it; you found the circumference of the circle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the straight sides are just 4.5 *2 = 9 cm

the arcs are  2\(\pi\)r * Ф/360

where Ф= 50 for this problem

and r = 8

the inner arc is  2\(\pi\)(3.5) *50/360 = 3.05432

the outer arc is 2\(\pi\)(8)*50/360 = 6.98131

total is 19.0356

to 3 sig figs is 19.036  :)

Answer:

Step-by-step explanation:

Answer:

second part is: "greater than"

Step-by-step explanation:

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Answer:

Triangle ABC is congruent to triangle DFE.

Answer:

2,-1/4

you can use the calculator to find the answer .

depending on your calculator you can find it in different ways but the most common one that works on most of tge calculators is pressing mode button the press 5 then 3. then put a as tge coeffcient of x^2 and b as coefficient of x and c as the number without any x

The number of bacteria produced is a function of time in hours.

In Mathematics, a function simply refers to a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically shows the relationship between input values (x-values or domain) and output values (y-values or range) of a data set, as well as showing how the elements in a table are uniquely paired (mapped).

Based on the information provided above, we can reasonably infer and logically deduce that the bacteria's population increases with respect to time (number of hours).

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The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.

For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.

The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.

Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.

Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.

This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.

Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.

The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.

Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.

Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the  answer is (b) S = 2231.

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

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The first partial derivatives of the function f(x, y) = x^4 - 6xy^5 are ∂f/∂x = 4x^3 - 6y^5 and ∂f/∂y = -30xy^4.

The first partial derivatives of the function f(x, y) = x^4 - 6xy^5 with respect to x and y can be found as follows.

The partial derivative with respect to x (denoted as ∂f/∂x) can be obtained by treating y as a constant and differentiating the function with respect to x. In this case, the derivative of x^4 with respect to x is 4x^3. The derivative of -6xy^5 with respect to x is -6y^5, as the constant -6y^5 does not depend on x. Therefore, the first partial derivative of f(x, y) with respect to x is ∂f/∂x = 4x^3 - 6y^5.

Similarly, the partial derivative with respect to y (denoted as ∂f/∂y) can be found by treating x as a constant and differentiating the function with respect to y. The derivative of -6xy^5 with respect to y is -30xy^4, as the constant -6x does not depend on y. Thus, the first partial derivative of f(x, y) with respect to y is ∂f/∂y = -30xy^4.

In summary, the first partial derivatives of the function f(x, y) = x^4 - 6xy^5 are ∂f/∂x = 4x^3 - 6y^5 and ∂f/∂y = -30xy^4. These derivatives represent the rates at which the function changes with respect to each variable individually.

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So the answer here is approximately 95% of housing prices are between a low price of  $143000 and a high price of $171000.

The empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, is a statistical principle that asserts that, with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.

The Empirical Rule indicates that 99.7% of data that are seen to have a normal distribution fall within 3 standard deviations of the mean.

According to this criteria, 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within  three standard deviations of the mean.

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Answer:

144 oz

Step-by-step explanation:

Answer:  If i'm not mistaking its 144 oz.  If that's what the question is asking you.  Hope this helps <3.

Hi!

(5+d)+(-8)=(5+d)-8

Hence, this is the required solution.

~SparklingFlower :)

No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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The given conditions cannot form a triangle. A triangle cannot be formed if the sum of three angle measurements does not equal 180°.

A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's internal angles equals 180 degrees, which is its most important property. This is known as the angle sum property of a triangle.

A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it. Another method for calculating a triangle's exterior angle is to subtract the angle of the vertex of interest from 180°.

A protractor is the most convenient tool for measuring angles. If you don't have a protractor, you can use the basic geometric principles of triangles to determine the size of an angle. To solve the equations, you'll need a scientific calculator.

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the weight of the substance after 28 years is 8 grams.

We have that the half life of a substance is defined as the time required for the substance to decrease by half

The formula for calculating the half - life of a material is given as;

\(N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }\)

Where

Substitute into the formula

N(t) = 128 × (0. 5) ^28/ 7

N (t) = 128 × ( 0. 5) ^ 4

N(t) = 128 × 0. 0625

N(t) = 8 grams

Thus, the weight of the substance after 28 years is 8 grams.

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The amount of commission that Joan earns this month on sales will be $480.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Joan earns an 8% commission on her sales this month Joan had $6000 in sales.

Let 'x' be the commission. Then the equation is given as,

x / $6,000 = 0.08

x = 0.08 · $6,000

x = $480

The amount of commission that Joan earns this month on sales will be $480.

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When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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The final expression is given as ln|S| = 8t / √πS(0) + ln|S(0)|.

A spherical weather balloon is being inflated at a rate of 5 cm/s. If we want to express the surface area of the balloon as a function of time t (in seconds), then we have to use the formula for the surface area of a sphere which is given as S = 4πr².

Here, the radius of the balloon is increasing at the rate of 5 cm/s.

So we can say that dr/dt = 5 cm/s, where dr is the rate of change of radius with respect to time.

We can differentiate the formula of surface area of the sphere w.r.t time, we get: dS/dt = d/dt (4πr²) => dS/dt = 8πr (dr/dt)We know, r = (1/2)Sqrt(S/π)So, we can substitute the value of r in the above expression, dS/dt = 4πS (ds/dt) / Sqrt(πS)

On simplifying this, we get: dS/dt = 4S (ds/dt) / √πSNow, if S = S(0) at t = 0, then we can integrate both sides of the equation to get the surface area of the balloon as a function of time t.S(0) is the initial surface area of the balloon.

Substituting, we get:∫ dS/S = ∫ 4(dt/√πS(0))We get:ln|S| = 8t / √πS(0) + CWhere C is the constant of integration.At t = 0, S = S(0),

so we get:ln|S(0)| = CBy substituting this value of C in the above expression, we get:ln|S| = 8t / √πS(0) + ln|S(0)|

On simplifying this expression, we get the surface area of the balloon as a function of time t.

We derived the expression of surface area of the balloon as a function of time t when the radius of the balloon is increasing at the rate of 5 cm/s. We used the formula of surface area of a sphere and the derivative of radius w.r.t time to derive the expression of surface area. The final expression is given as ln|S| = 8t / √πS(0) + ln|S(0)|.

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Solution -:

\( \bold{ \underline{ \underline{Given}}}\)

-3x7x7x7x7x7x7

\(\bold{\underline {\underline{lets \: begin}}}\)

We have,,

\( -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} \)

As like example→ 2⁴

here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.

Answer:

68 in^2

Step-by-step explanation:

Leonie made a 125% profit on the cost of the coat.To determine Leonie's percentage profit on the cost of the coat, we need to calculate the original cost of the coat and then determine the profit made on that cost.

Let's start by finding the original cost of the coat. We know that the hat cost £6 and Leonie made a 300% profit on the hat. A 300% profit means she sold the hat for 4 times its original cost (£6 * 4 = £24).

Next, we can calculate the total cost of the hat and coat. Since Leonie made a 125% profit on the total cost, the total cost represents 100% + 125% = 225% of the original cost.

To find the original cost, we can divide the total cost (£45) by 225% (or 2.25 in decimal form): £45 / 2.25 = £20.

Now we can calculate the profit made on the coat. The total cost of the hat and coat was £20, and Leonie sold both items for £45, so the profit made is £45 - £20 = £25.

To find the percentage profit on the cost of the ccoatoat, we can divide the profit (£25) by the original cost of the coat (£20) and multiply by 100: (£25 / £20) * 100 = 125%.

Therefore, Leonie made a 125% profit on the cost of the coat.

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I think it's going to cost 300

Answer:

D

Step-by-step explanation:

y = m(x - x1) + y1

y = -7(x - 8) + 5

y - 5 = -7(x - 8)

Answer:

k(x) = -40

i(x) = -15

n(x) = 71

d(x) = 17

Step-by-step explanation:

This is exactly the same deal as the most recent question you asked.

"Evaluate each function for x = 8". In other words, this is saying, calculate the result for each function, replace x with 8. So, that means for every function, you are going to replace x with 8.

k(x) = -5x turns into k(x) = -5(8)

Then you just solve, -5(8) = -40

Since I have answered this question similarly, I ask that you go back to the answer and detailed explanation I gave you earlier.

Answer:

true

Step-by-step explanation:

true

the answer is true mommy

Answer:

I think 84 but you may need to check just to be sure :)

Answer:

Step-by-step explanación

0.02

When the mean number of points scored per game next season is 60, the model predicts that the mean home attendance will be 11902

The function that predicts the attendance is given as:

\(y = -7628+325.5x\)

When the mean number of points scored per game next season is 60, it means that the value of x is 60

i.e. x = 60

Substitute 60 for x in the function

So, we have:

\(y = -7628+325.5 \times 60\)

Evaluate the product

\(y = -7628+19530\)

Add -7628 and 19530

\(y = 11902\)

Hence, the model predicts that the mean home attendance will be 11902

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Answer:

Can you insert pictures of the graph? I might be able to help you then.

Step-by-step explanation: