Find X:
X + 25% x X = -1,25

Answer:

10, 9, 12

Step-by-step explanation:

Answer:

See Below.

Step-by-step explanation:

We want to show that the normal line to the parabola:

[tex]y^2=8x[/tex]

At the point (2, 4) meets the parabola again at (18, -12).

First, find the tangent line to the parabola at the point (2, 4). We can take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[ y^2\right]=\frac{d}{dx}\left[8x\right][/tex]

Implicit differentiation:

[tex]\displaystyle 2y\frac{dy}{dx}=8[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{8}{2y}=\frac{4}{y}[/tex]

Then the slope of the tangent line to the point (2, 4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{y=4}=\frac{4}{(4)}=1[/tex]

Thus, the slope of the normal line is -1.

And since it passes through the point (2, 4), by the point-slope form:

[tex]y-(4)=-1(x-2)[/tex]

Simplify:

[tex]y=-(x-2)+4[/tex]

By letting x = 18:

[tex]y=-(18-2)+4=-16+4=-12[/tex]

So, the normal line indeed passes through (18, -12).

Answer:

answer is in the picture.

Answer:

h = [tex]\frac{V}{\pi r^2}[/tex]

Step-by-step explanation:

Given

V = πr²h ( isolate h by dividing both sides by πr² )

[tex]\frac{V}{\pi r^2}[/tex] = h

Answer:

C

Step-by-step explanation:

When ever a problem gives information about parallel lines, look for Alternate Interior angles.

Answer:

A

Step-by-step explanation:

Answer:

4.2

Step-by-step explanation:

The length of the arc of each slice of cake will be 4.18 inches if Khali shares the cake between him and 5 friends equally.

The circumference is the length of the outer boundary of the circle. It can be calculated as under:

Circumference=2πr

We have been given that the diameter of the cake is 8 inches So, the radius becomes 4 inches. We have to calculate the circumference of the cake. so the circumference becomes:

Circumference=2π(4)=8π

=8*22/7

=25.1

Then we have to divide it into 6 people so it will be 25.1/6=4.18 inches.

Hence the length of the arc will be 4.8 inches.

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Answer:

Oval frames = 17

Rectangular frames = 51

Step-by-step explanation:

Given that :

Paintings on wall are either oval or rectangular ;

Let :

Oval painting = x

Rectangular painting = y

According to the information given :

x + y = 68 - - (1)

Rectangular frames = 3 times oval frames

y = 3x - - - (2)

Put y = 3x in equation (1)

x + 3x = 68

4x = 68

x = 68/4

x = 17 frames

From :

x + y = 68

17 + y = 68

y = 68 - 17

y = 51

Oval frames = 17

Rectangular frames = 51

9514 1404 393

Answer:

  a, c

Step-by-step explanation:

There are 3 linear factors, so the function is odd degree (cubic). The coefficients of x are all positive, so the function has the general shape of an increasing function, left-to-right. The three linear factors mean that the curve crosses the x-axis 3 times, changing sign each time.

The x-intercepts are the values of x that make the factors zero: -7, 3/2, 5. The shape of the function tells you it will be negative for x < -7. Between -7 and 3/2, it will be positive, since it changes sign at x=-7. It changes sign again at x=3/2, so will be negative for 3/2 < x < 5.

In short, the function will be negative at any point that has an odd number of function zeros to its right (taking multiplicity into account).

The function is negative on intervals (a) and (c).

Step-by-step explanation:

I cannot really identify and read the provided answer options.

the solution to the sequence 2, 6, 10, 14, 18, ... is

an = 4×(n-1) + 2

recursive that is

a1 = 2

an = an-1 + 4

please pick the right option in your original problem definition that fits to this solution.

The recursive formula that represents the given sequence is:

[tex]a_n = a_{n-1} + 4[/tex]

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant value to the previous term.

This fixed value is called the common difference, and it is the same for all terms in the sequence.

We have,

The given sequence has a common difference of 4 between its consecutive terms.

To represent this sequence using a recursive formula, we can start with the first term and use the common difference of 4 to find each subsequent term.

Let's assume that the first term of the sequence is a1. Then, we can represent the second term [tex]a_2[/tex] as:

[tex]a_2 = a_1 + 4[/tex]

Similarly, we can represent the third term (a3) as:

[tex]a_3 = a_2 + 4[/tex]

Substituting the value of a2 from the above equation, we get:

[tex]a_3 = (a_1 + 4) + 4 = a_1 + 8[/tex]

We can continue this pattern to find the recursive formula for the nth term of the sequence:

[tex]a_n = a_{n-1} + 4[/tex]

where [tex]a_1[/tex]= 2

Thus,

The recursive formula for the given sequence is:

[tex]a_n = a_{n-1} + 4[/tex]

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The number of times that the band played an encore at 7 out of the next 14 shows.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.

We may use the following percentage to determine how many of the following 14 performances will likely have an encore:

1/2 = x/14

14 = 2x

x = 7

Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.

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Answer:

D. [tex]4^{15}[/tex]

Step-by-step explanation:

[tex]=(4^3)^5[/tex]

Multiply the exponent inside the parenthesis with the exponent outside.

[tex]=4^{15}[/tex]

Hope this helps.

Answer:

4^15

Step-by-step explanation:

Ok, so lets replace the base, 4, with x so we don’t get confused by it:

(X^3)^5

When we raise a power to a power, we multiply them , so:

(X^15)

Remember x is 4, so:

4^15 is the answer

Answer:

f(x,y) = [tex]e^{xy}[/tex] is maximum at x = 2 and y = 2 and f(2,2) = [tex]e^{4}[/tex]

Step-by-step explanation:

Since f(x,y) = [tex]e^{xy}[/tex] and x³ + y³ = 16, Ф(x,y) = x³ + y³ - 16

df/dx = y[tex]e^{xy}[/tex], df/dy = x[tex]e^{xy}[/tex], dФ/dx = 3x² and dФ/dy = 3y²

From the method of Lagrange multipliers,

df/dx = λdΦ/dx and df/dy = λdΦ/dy

y[tex]e^{xy}[/tex] = 3λx² (1) and  x[tex]e^{xy}[/tex] = 3λy² (2)

multiplying (1) by x and (2) by y, we have

xy[tex]e^{xy}[/tex] = 3λx³ (4) and  xy[tex]e^{xy}[/tex] = 3λy³ (5)

So,  3λx³ = 3λy³

⇒ x = y

Substituting x = y into the constraint equation, we have

x³ + y³ = 16

x³ + x³ = 16

2x³ = 16

x³ = 16/2

x³ = 8

x = ∛8

x = 2 ⇒ y = 2, since x = y

So, f(x,y) = f(2,2) = [tex]e^{2 X2}[/tex] = [tex]e^{4}[/tex]

We need to determine if this is a maximum or minimum point by considering other points that fit into the constraint equation.

Since x³ + y³ = 16 when x = 0, y is maximum when y = 0, x = maximum

So, 0³ + y³ = 16

y³ = 16

y = ∛16

Also, when y = 0, x = maximum

So, x³ + 0³ = 16

x³ = 16

x = ∛16

and f(0,∛16) = [tex]e^{0X\sqrt[3]{16} } = e^{0} = 1[/tex].

Also, f(∛16, 0) = [tex]e^{\sqrt[3]{16}X0 } = e^{0} = 1[/tex].

Since f(0,∛16) = f(∛16, 0) = 1 < f(2,2) = [tex]e^{4}[/tex]

f(2,2) is a maximum point

Answer:

45 miles in 1 hour

Step-by-step explanation:

1 hour is 60 minutes

22.5 miles / 30 minutes  * 2/2 = 45 miles / 60 minutes = 45 miles in 1 hour

Answer:

He drove 22.5 miles in 60 min. He drove 45 miles in 1 hour

Step-by-step explanation:

22.5 miles in 30 min

1 hour= 60 min

30+30=60

22.5+22.5=45 miles

Answer:

A and B are exhaustive.

Step-by-step explanation:

Given

[tex]A = \{1,2,4\}[/tex]

[tex]B = \{2,3,4,5,6\}[/tex]

[tex]C =\{3,4\}[/tex]

[tex]D = \{2,4,5\}[/tex]

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

[tex]S = P(X\ n\ Y)[/tex]

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]

and the sample space is:

[tex]S = \{1,2,3,4,5,6\}[/tex]

By comparison;

[tex]A\ n\ B = S[/tex]

Hence, A and B are exhaustive.

Answer:

(15x + 120) ft³

Or

15(x + 8) ft³

Step-by-step explanation:

The prism can be decomposed into a rectangular prism and a triangular prism

The volume of the prism = volume of the rectangular prism + volume of the triangular prism

✔️Volume of rectangular prism = L*W*H

L = 5 ft

W = 4 ft

H = 6 ft

Volume = 5*4*6 = 120 ft³

✔️Volume of triangular prism = ½*b*h*l

b = x ft

h = 6 ft

l = 5 ft

Volume = ½*x*6*5 = 15x ft³

✔️Volume of the prism = (15x + 120) ft³

Answer: 24 years

Step-by-step explanation:

Based on the information given, we've been given,

Principal = #250

Interest = #120

Interest rate = 2%

Time = Unknown

Interest = PRT/100

120 = (250 × 2 × Time)

Cross multiply

120 × 100 = (250 × 2 × T)

12000 = 500T

Time = 12000/500

Time = 24

It will take 24 years.

Answer:

[tex]M = (0,0)[/tex]

Step-by-step explanation:

Given

[tex](4,-5)[/tex] and [tex](-4,5)[/tex]

Required

The midpoint (M)

This is calculated as:

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

So, we have:

[tex]M = \frac{1}{2}(4-4,-5+5)[/tex]

[tex]M = \frac{1}{2}(0,0)[/tex]

[tex]M = (0,0)[/tex]

Answer:

15 days

+

Step-by-step explanation:

A

200 pages / (8 pages / day) =

= 200 pages days / 8 pages =

= 200 days / 8 = 25 days

B

200 pages / (5 pages / day) =

= 200 pages days / 5 pages =

= 200 days / 5 = 40 days

40-25 = 15 days

A will finish 15 days sooner than B.

A will finish her report 15 days sooner than B.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Writer A averages 8 pages a day,

Number of pages per day written by writer A = 8 per day

Writer A will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (8 pages / day)

⇒ 200 pages days / 8 pages

⇒ 200 days / 8

⇒ 25 days

Writer B averages 5 pages a day

Number of pages per day written by writer B = 5 per day

Writer B will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (5 pages / day)

⇒  200 pages days / 5 pages

⇒  200 days / 5

⇒  40 days

Difference between both of time when they finished their report = 40-25 = 15 days

Hence, A will finish her report 15 days sooner than B.

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Answer:

y

Step-by-step explanation:

In function notation, f(x) is another way of saying y. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

Tables, symbols, and graphs can all be used to represent functions. Every one of these interpretations has benefits. Tables provide the functional values of certain inputs in an explicit manner. How to compute direct proportionality is succinctly stated in symbolic representation.

The function is represented as,

y = f(x)

In function notation, f(x) is another way of saying y. Then the correct option is A.

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Answer:

B. The nominal level of measurement is most appropriate because data cannot be ordered.

Step-by-step explanation:

Nominal scale is used when there is no specific order scale and data can be arranged according to name. Ordinal scale requires variables to be arranged in specific order. For fast food restaurant the best scale used is nominal scale as variables can be arranged according to their name without specific order.

Answer:

The solution to the inequality is [tex](-\infty, 0) \cup (3, \infty)[/tex]

Step-by-step explanation:

We have a product, which is positive if both terms is positive or if both is negative.

Both positive:

[tex]x > 0[/tex]

[tex]x - 3 > 0 \rightarrow x > 3[/tex]

Then the intersection of these two is: [tex]x > 3[/tex]

Both negative:

[tex]x < 0[/tex]

[tex]x - 3 < 0 \rightarrow x < 3[/tex]

Then the intersection of those two is: [tex]x < 0[/tex]

Then:

Union of two solutions:

[tex]x < 0[/tex] or [tex]x > 3[/tex]

Then

[tex](-\infty, 0) \cup (3, \infty)[/tex]

Answer:

8

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

The function given in the table is a linear function:

f(x) = 3x+2

Answer:

let's use a sample set.

8+8, 8+4, 8+5, 8+6, 8+7

4+8, 4+4, 4+5, 4+6, 4+7

5+8, 5+4, 5+5, 5+6, 5+7

6+8, 6+4, 6+5, 6+6, 6+7

7+8, 7+4, 7+5, 7+6, 7+7

There is 25 sums.

[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]

[tex] \sf \: p(y) = 2 + y + 2y {}^{2} - y {}^{3} [/tex]

[tex] \sf \: p(o) = 2 + (o) + 2(o) {}^{2} - (o) {}^{3} = 2 + 0 + 0 - 0 = 2 [/tex]

[tex] \sf \: p(1) = 2 + (1) + 2(1) {}^{2} - 1 {}^{3} = 2 + 1 + 2 - 1 = 4 [/tex]

[tex] \sf \: p(2) = 2 + 2 + 2(2) {}^{2} - 2 {}^{3} = 4 + 8 - 8 = 4 [/tex]

Answer: lil t j

Step-by-step explanation:

I’m not a goat but I fit the description we walk around with then bands in my pocket

Answer:

y - 4 = (2/5)(x + 2)

Step-by-step explanation:

point slope form is

y - y₁ = m(x - x₁)

(x₁, y₁) is a point on the line and m is the slope

------------------------

Given (x₁, y₁) = (-2, 4) and m = 2/5

y - 4 = (2/5)(x + 2)

Answer:

Step-by-step explanation:

Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]

Answer:

[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]

Explanation is attached to the picture

Hope this helps you.

Answer:

The gain percent is 33.3 %

Step-by-step explanation:

Let the selling price of 1 m cloth is p.

Cost of 33 m = 33 p

gain = cost of 11 m = 11 p  

The gain percentage is given by

[tex]\frac{11 p}{33 p}\times 100\\\\= 33.3 %[/tex]

The gain percent is 33.3 %.

Answer: hello the exercise is missing from your question below is the missing exercise for reference

answer:

0.1745

Step-by-step explanation:

Determine  P ( Y > 3 )

Given that y follows Poisson distribution with mean

P( Y = y ) = [tex]\frac{e^{-1} }{y!}[/tex]

assuming that yi represents number of autos that will enter the tunnel and

also let A represent Y > 3 at one of the ten two-minute interval

step 1 : hence finding  P(A )

= P(Y > 3 ) = 1 - P( Y≤ 3 )

= 1 - [ [tex][\frac{e^{-1} }{0!} +\frac{e^{-1} }{1!} +\frac{e^{-1} }{2!} +\frac{e^{-1} }{3!} ][/tex]

= 0.018988

since the ten observations are independent

P(X≥ 1 ) = 1 - P( X = 0 )

            = 1 -  [tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right][/tex]  * (0.018988)^0 ( 1 - 0.018988)^10-0

            = 1 - 0.8255 = 0.1745