The price of an iteam has been reduced by 75%. The original price was $45. What is the price of the item now?

Answer with Step-by-step explanation:

We are given that:

f(x)=ax²+bx+c

also at x=0 f(x)=15

Putting x=0 in f(x)

a×0+b×0+c=15

⇒ c=15

now, f(2)=15.5

⇒ a×2²+b×2+c=15.5

⇒ 4a+2b+15=15.5

⇒ 4a+2b=0.5  -------(1)

f(4)=17

⇒ a×4²+b×4+c=17

⇒ 16a+4b+15=17

⇒ 16a+4b=2     --------(2)

equation (2)- 2×equation(1)

⇒ 16a+4b-8a-4b=2-2×0.5

⇒ 8a=2-1

⇒ 8a=1

⇒ a=1/8

⇒ a=0.125

Putting value of a and c in equation (1)

⇒ 4×0.125+2b=0.5

⇒ 0.5+2b=0.5

⇒ 2b=0

⇒ b=0

Hence

a=0.125

b=0

c=15

and f(x)=0.125x²+15

There is a vertical asymptote at x = 0 (because the denominator becomes 0). We need to further analyze the behavior at x = 3 to see if it's a hole (cancellation) or the function is continuous there (Option A or B might be the answer).

Step 1: Identify Potential Discontinuities

A rational function (like f(x)) is discontinuous when its denominator is zero. So, we need to find the values of x that make the denominator 0:

Denominator = 4x^2 - 12x = 0

Factor the denominator: 4x(x - 3) = 0

This gives us two possible values for x: x = 0 and x = 3.

Step 2: Verify Discontinuity Type at Each Point

Check if the function is defined (has a value) at these points.

x = 0: If we plug x = 0 in the original function, we get 0/0, which is indeterminate. This suggests a potential vertical asymptote at x = 0.

x = 3: If we plug x = 3 in the original function, the expression doesn't become 0/0. The function might have a hole or be continuous at x = 3.

Step 3: Analyze for Holes (Optional):

To further investigate x = 3, we can try to simplify the function by factoring the numerator (possible because the denominator is already factored). If the simplification gets rid of the term that causes the 0/0 at x = 3, it creates a hole.

Answer:

D - 45

Explanation:

Hope you have a great day!

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

a = 4

b = - 131

c = 480

Answer:

The correct answer is 3 1/24

Step-by-step explanation:

because I did all the math

Answer:

3 1/24

Step-by-step explanation:

Answer:

B) 46

Step-by-step explanation:

What you have to do here is plug in the numbers 2, 3, 4, and 5 in for i in the equation and then add the sums together:

3(2) + 1 = 7

3(3) + 1 = 10

3(4) + 1 = 13

3(5) + 1 = 16

Add those together and they equal 46

To determine how many tickets Dan bought, we calculate the price per ticket from Amy's purchase as £3.50 each. Then we subtract Amy's payment from the total to find Dan's payment of £38.50, and finally, we divide Dan's payment by the price per ticket to find that Dan bought 11 tickets.

The question involves finding out how many tickets Dan bought for a concert, using the total amount paid by both Amy and Dan and the price Amy paid for her tickets.

First, we need to find out the price per ticket from the information provided about Amy's purchase:

Amy pays £24.50 for 7 tickets.

To find the price per ticket, we divide £24.50 by 7:

Price per ticket = £24.50 / 7 = £3.50

Next, we use the total amount paid to find out how much Dan spent:

Total amount paid by Amy and Dan = £63

Amount paid by Amy = £24.50

So, the amount paid by Dan = Total amount - Amount paid by Amy

Amount paid by Dan = £63 - £24.50 = £38.50

To find out how many tickets Dan bought, we divide the amount he paid by the price per ticket:

Number of tickets Dan bought = £38.50 / £3.50

Number of tickets Dan bought = 11 tickets

Answer:

Octagon

Step-by-step explanation:

It has 8 sides

The number of BTUs does 1 cubic foot of propane yield is 684,000 BTUs/ft³ (in thousand)

Since we know that

The volume of the spherical tank is

[tex]V=4\div 3\pi r^3[/tex]

Now the volume of the tank will be:

[tex]V=4\div 3\times \pi \times (10/2)^3[/tex]

=523.59877756

= 523.6 ft³

Now the number should be

= [total amount] ÷ [total volume]

=358,000,000 ÷ 523.6

=683,728.0367 BTUs/ft³

= 684,000 BTUs/ft³ (in thousand)

Therefore, The number of BTUs does 1 cubic foot of propane yield is 684,000 BTUs/ft³ (in thousand)

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Answer: 134.95 to be exact

you multiply the zscore with the standard deviation and add the mean

The formula for calculating the z-score:

z = (x - μ) / σ
Where

μ - mean

σ = standard deviation

The x-score that corresponds to a z-score of 2.33 is 134.95.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Iq test scores are normally distributed:

Mean = 100

Standard deviation = 15
z-score = 2.33

The formula for calculating the z-score:

z = (x - μ) / σ

Where

μ - mean

σ = standard deviation

Now,

2.33 = (x - 100) / 15

Multiply 15 on both sides.

2.33 x 15 = x - 100

34.95 = x - 100

Add 100 on both sides.

34.95 + 100 = x

x = 134.95

Thus,

The x-score that corresponds to a z-score of 2.33 is 134.95.

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Answer:

Without exponents, we can write the term as:  [tex]27(n)(n)(n)[/tex]

Step-by-step explanation:

The given term is :

[tex](3n)^{3}[/tex]

This can be written as:

[tex](3n)(3n)(3n)[/tex]

= [tex]27n^{3}[/tex]

= [tex]27(n)(n)(n)[/tex]

Hence, without exponents, we can write the term as:  [tex]27(n)(n)(n)[/tex]

To find the distance from the plateau's base, use the tangent function with the given height and angle of elevation.

We can use trigonometry to determine the distance from the base of the plateau. The vertical height of the table (opposite side) is 70 m, and the elevation angle to the top of the plateau (theta) is 60 degrees. We can use the tangent function to find the distance (adjacent side) from the table's base: tan(theta) = opposite/contiguous. Solving for the space, we get: adjacent = contrasting/tan(theta). Plugging in the values, the distance from the plateau's base is approximately 40 m.

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The solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.

Trigonometric functions are periodic functions, cosine function has a standard period of 2π radians. There are two approaches to solve the expression given, an analytical one and a graphical one. Now we proceed to show each approach:

Analytical method

Now we proceed to apply algebraic handling and inverse trigonometric functions to solve the expression for t:

7 · cos 2t = 3

cos 2t = 3/7

2 · t = cos⁻¹ (3/7)

There are two solutions:

2 · t₁ ≈ 0.359π + 2π · i  ∨   2 · t₂ ≈ 1.641π + 2π · i

t₁ ≈ 0.180π + π · i   ∨ t₂ ≈ 0.821π + π · i

t₁₁ ≈ 0.180π ∨ t₁₂ ≈ 1.180π ∨ t₂₁ ≈ 0.821π ∨ t₂₂ ≈ 1.821π

The solutions of the trigonometric equations in [0, 2π] are approximately 0.18π, 0.82π, 1.18π and 1.82π.

Graphical approach

First, we add the definition of the following two functions (f(x) = 7 · cos 2t and g(x) = 3) and plot in the calculator through a graphing tool. The solutions of this trigonometric function are the points of intersection of the two functions.

According to the image attached below, the solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.

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