A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse? startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 5 2nd row y = startfraction 14 over 81 endfraction (x minus 2) squared minus 6 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 25 2nd row y = startfraction 14 over 81 endfraction (x minus 2) squared minus 6 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 5 2nd row y = negative startfraction 14 over 81 endfraction (x 7) squared 8 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 25 2nd row y = negative startfraction 14 over 81 endfraction (x 7) squared 8 endlayout

It exists not linear the curve indicates that the rate of change exists not constant.

Linear functions exist as those whose graph exists as a straight line. A linear function exists that can be characterized by the equation

y = mx + c, Where m exists the slope and c exists the intercept on the

y-axis. A linear function contains one independent variable and one dependent variable.

Therefore, the correct answer is option c) No, because the curve indicates that the rate of change is not constant.

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Answer:

[tex]x=\frac{P^2t}{(m-t^3)}[/tex]

Step-by-step explanation:

[tex]P^2=\frac{mx}{t} -t^2x\\\\P^2+t^2x=\frac{mx}{t}\\\\t(P^2+t^2x)=mx\\\\P^2t+t^3x=mx\\\\P^2t=mx -t^3x\\\\P^2t=x(m-t^3)\\\\\frac{P^2t}{(m-t^3)} =\frac{x(m-t^3)}{(m-t^3)} \\\\\frac{P^2t}{(m-t^3)}=x[/tex]

Step-by-step explanation:

In a Mathematics lab. There are some cubes and cuboids of following measurements

(i) One cube of side 4 cm

(ii) One cube of side 6 cm

(iii) 3 cuboids each of dimensions 4cm ×4 cm ×6cm

(iv) 3 cuboids each of dimensions 4cm ×6 cm ×6cm

A student wants to arrange these cubes and cuboids in the form of big cube. Is it

possible to arrange them in the form of big cube? If yes, then find the length of side of

Answer:

here's your answer step by step explanation

Step-by-step explanation:

page 6 is missing comment me i will send you page 6

Answer:

B

Step-by-step explanation:

using the tangent ratio on the triangle on the right and the exact value

tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex]  = [tex]\sqrt{3}[/tex] ( multiply both sides by h )

11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

11[tex]\sqrt{2}[/tex] = h

using the sine ratio in the triangle on the left and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

x = 22

Answer:

16 pi/ 9 inches should be the right one.

Answer:

(4) (x + 6)(x - 1)

Step-by-step explanation:

Given expression

[tex]x { }^{2} + 5x - 6[/tex]

Find numbers when they are multiplied gives 6 and when they are added which gives 5.

Thus, these numbers are -1 & 6.

[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]

Can also check the multiplied values of these two values.

Hope it helps!

Answer:

(4)

Step-by-step explanation:

Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).

Multiples are: +6 and -1

input the two multiples in place of the middle term (+5x)

=x^2+6x-1x-6

Collect like terms

=x(x+6)-1((x+6)

Answer= (x+6)(x-1)

Confirm answer above:

Open bracket

x(x-1)+6(x-1)

x^2-x+6x-6

x^2+5x-6 (initial equation).

Answer:

k = 33

Step-by-step explanation:

Terminating decimal numbers:  Decimals that have a finite number of decimal places.

For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5.  As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.

Prime factorization of 660:

⇒ 660 = 2 × 2 × 3 × 5 × 11

⇒ 660 = 2² × 3 × 5 × 11

Therefore:

[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]

The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out.  To do this, their lowest common multiple must be the numerator:

⇒ LCM of 3 and 11 = 3 × 11 = 33

[tex]\implies \sf \dfrac{33}{660}[/tex]

[tex]\implies \sf k=33[/tex]

Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.

Answer:

33

Step-by-step explanation:

the train travels at 45 meters per each second

this question can be rewritten into the equation d = 45t, where d represents the distance traveled and t represents the time elapsed.

we are given two seperate times, so we can replace the variable t with each respective time. this leaves us with only one missing variable, so we can successfully isolate to find the other.

for i), we substitute t for 30 seconds, shown as follows

d = 45t

d = 45(30)

d = 1350m

for ii), we know that there are 60 seconds in every minute, so in multiplying 60 seconds by two we get the total amount of seconds in two minutes, which is 120.

we can now use 120 to substitute t in our equation

d = 45t

d = 45(120)

d = 5400m

hope this helps!!

Answer:

i) 1350 m

ii) 5400 m

Step-by-step explanation:

To calculate the distance traveled by the train, we can use the formula:

[tex]\large\boxed{\sf Distance=Speed \times Time}[/tex]

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula for distance:

[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 30\;s\\& = \sf 1350\:m\end{aligned}[/tex]

Therefore, the train travelled a distance of 1350 meters in 30 seconds.

[tex]\hrulefill[/tex]

Given values:

As the time is given in a different unit of time than the speed, we must first convert the time into seconds. As 1 minute = 60 seconds, then:

[tex]\sf 2\; minutes = 60 \;s \times 2 = 120 \;s[/tex]

Substitute the given values into the formula for distance:

[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 120\;s\\& = \sf 5400\:m\end{aligned}[/tex]

Therefore, the train travelled a distance of 5400 meters in 2 minutes.

The option that explains the point (1, 1400) is (c) the person surveyed took a day trip

From the graph, we have the following representations:

The point (1,1400) implies that

x = 1 and y = 1400

This means that

The number of days on vacation is 1 and the total cost of vacation is 1400

Hence, the option that explains the point (1, 1400) is (c) the person surveyed took a day trip

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The product of the given expression is 7x/24y²

Given the product of the fractions below

3x/6y * 7/12y

Simplify

x/2y * 7/12y

Multiply the numerator and denominator to have:

7x/24y²

Hence the product of the given expression is 7x/24y²

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Answer:

[tex]644cm^2[/tex]

Step-by-step explanation:

First we'll work out the surface area of the pink figure.

That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.

However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.

The above works out to [tex]2\times(30+100+120)-72=428 cm^2[/tex].

Then we'll work out the surface area of the purple figure.

This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.

That's [tex]2\times(24+48)+72=216cm^2[/tex].

So the total surface area is [tex]428+216=644cm^2[/tex].

The correct option is B.

The value will be  = 25

What is the Angles of the triangle?

The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.

∠ACE = (2x+2)°

∠ECB = (5x+ 3)°

Angles ACE and ECB are additional angles according to the linear postulate, as seen in the attached diagram.

Therefore:

∠ACE+∠ECB = 180°

(2x+2)+(5x+3) = 180

2x+ 5x+ 2+ 3 = 180

7x + 5 = 180

7x = 175

x= 175/7

x = 25

Thus the value will be  = 25

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I understand that the question you are lookin for is :

Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x?

A.12

B. 25

C. 38

D. 52

Answer:

[tex]\textsf{Midpoint rule}: \quad \dfrac{2\pi}{\sqrt[3]{2}}[/tex]

[tex]\textsf{Trapezium rule}: \quad \pi[/tex]

[tex]\textsf{Simpson's rule}: \quad \dfrac{4 \pi}{3}[/tex]

Step-by-step explanation:

Midpoint rule

[tex]\displaystyle \int_{a}^{b} f(x) \:\:\text{d}x \approx h\left[f(x_{\frac{1}{2}})+f(x_{\frac{3}{2}})+...+f(x_{n-\frac{3}{2}})+f(x_{n-\frac{1}{2}})\right]\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Trapezium rule

[tex]\displaystyle \int_{a}^{b} y\: \:\text{d}x \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Simpson's rule

[tex]\displaystyle \int_{a}^{b} y \:\:\text{d}x \approx \dfrac{1}{3}h\left(y_0+4y_1+2y_2+4y_3+2y_4+...+2y_{n-2}+4y_{n-1}+y_n\right)\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Given definite integral:

[tex]\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x[/tex]

Therefore:

Calculate the subdivisions:

[tex]\implies h=\dfrac{2 \pi - 0}{4}=\dfrac{1}{2}\pi[/tex]

Midpoint rule

Sub-intervals are:

[tex]\left[0, \dfrac{1}{2}\pi \right], \left[\dfrac{1}{2}\pi, \pi \right], \left[\pi , \dfrac{3}{2}\pi \right], \left[\dfrac{3}{2}\pi, 2 \pi \right][/tex]

The midpoints of these sub-intervals are:

[tex]\dfrac{1}{4} \pi, \dfrac{3}{4} \pi, \dfrac{5}{4} \pi, \dfrac{7}{4} \pi[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2}\pi \left[f \left(\dfrac{1}{4} \pi \right)+f \left(\dfrac{3}{4} \pi \right)+f \left(\dfrac{5}{4} \pi \right)+f \left(\dfrac{7}{4} \pi \right)\right]\\\\& = \dfrac{1}{2}\pi \left[\sqrt[3]{\dfrac{1}{2}} +\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}\right]\\\\ & = \dfrac{2\pi}{\sqrt[3]{2}}\\\\& = 4.986967483...\end{aligned}[/tex]

Trapezium rule

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} &&&&&\\ x & 0 & \dfrac{1}{2}\pi & \pi & \dfrac{3}{2} \pi & 2 \pi \\ &&&&&\\\cline{1-6} &&&&& \\y & 0 & 1 & 0 & 1 & 0\\ &&&&&\\\cline{1-6}\end{array}[/tex]

[tex]\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2} \cdot \dfrac{1}{2} \pi \left[(0+0)+2(1+0+1)\right]\\\\& = \dfrac{1}{4} \pi \left[4\right]\\\\& = \pi\end{aligned}[/tex]

Simpson's rule

[tex]\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(0+4(1)+2(0)+4(1)+0\right)\\\\& = \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(8\right)\\\\& = \dfrac{4}{3} \pi\end{aligned}[/tex]

Concluding, the end behavior is:

as x ⇒ ∞, f(x) ⇒ -∞

as x ⇒ -∞, f(x) ⇒ ∞

Here we have the function:

[tex]f(x) = -2*\sqrt[3]{x}[/tex]

When we evaluate the function in x that tends to positive infinity, the cubic root also tends to infinity, while because of the negative factor that multiplies it, we conclude that the end behavior is:

as x ⇒ ∞, f(x) ⇒ -∞

When x tends to negative infinity, the opposite happens:

as x ⇒ -∞, f(x) ⇒ ∞

Concluding, the end behavior is:

as x ⇒ ∞, f(x) ⇒ -∞

as x ⇒ -∞, f(x) ⇒ ∞

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Answer:

2/3 or 66%

Step-by-step explanation:

there are 3 odd numbers on a 6 sided die

3 + 1 = 4

4/6 = 2/3

B. number of dogs owned versus number of plane tickets bought

Answer:

20 cm

Step-by-step explanation:

The volume, V, of a cone with radius r and height h is given by the formula

V = [tex](1/3) \pi r^2 h[/tex]

Since it is given that the ratio of h to r is 3/4 we have the relationship

h/r = 3/4 ==> h = (3/4)r

Substituting for h in the volume equation gives us an expression in terms of r

[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]

So the expression simplifies to[tex](1/4)\pi r^3[/tex]

We are given that this volume is 2000π cm³

So

(1/4)πr³ = 2000π

Eliminating π on both sides and multiplying by 4 on both sides gives

r³ = 8000

r = ∛8000 = 20 cm   Answer

D box plot correctly represents the data

A box plot or boxplot is a technique for illustratively displaying the localization, dispersion, and skewness groups of numerical data through their quartiles.

Using a five-number summary (the minimum, first quartile (Q1), median, third quartile (Q3), and "maximum"), a boxplot is a common method of visualizing data distribution.

The median value for the provided data will be the sixth data point's value, or 3.

The median of the data's lower half is now the first quartile. The third data point's value of 1 will therefore be in the lower quartile.

The median of the data's upper half is now referred to as the upper or third quartile. This means that the value of the ninth data point, which is 6, will represent the upper quartile.

Thus, box-plot D effectively displays the data from above.

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Answer:

The answer is D.

Edg 2023.

It should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity.

It should be noted that an identity simply means an equation that is always true no matter the values that are substituted.

In this case, should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity. It's simply the inverse of the sine function.

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Answer:

25 / 4

Step-by-step explanation:

To find the left sum, you need to....
1.) Find Δx

2.) Find [tex]x_{k-1}[/tex]

3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx

4.) Solve for the left sum

Answer:

5 un^2

Step-by-step explanation:

the liens from (0, 0) to (1, 3) and (1, 3) to (4, 2) are perpendicular meaning that the angle at (1, 3) is a right angle

to find the lengths of the sides we must use the pythagorean theorem

a^2 + b^2 = c^2

for the leftmost side

we have 1^2 + 3^2 = c^2

1 + 9 = 10

c^2 = 10

c = sqrt(10)

for the top side

we have

the same thing

1^2 + 3^2 = c^2

1 + 9 = 10

c^2 = 10

c = sqrt(10)

you must multiple sqrt(10) by sqrt(10) and then by 1/2

sqrt(10) * sqrt(10) is 10

10 * 1/2 is 5

the area is 5 un^2

Answer:

youre answer is here I hope it's right

x=24

Equivalent to tan A =[tex]\frac{y}{x}[/tex]

Equivalent to tan A:

A right triangle ABC so that m∠C = 90°

The lengths are:

                           Side a is opposite ∠A,

                           Side b is opposite ∠B,

                           Side c (the hypotenuse) is opposite ∠C

Because cos A = x, therefore

[tex]x =\frac{b}{c}[/tex]  => [tex]b = cx[/tex]                  (1)

Because sin A = y, therefore

[tex]y =\frac{a}{c}[/tex] => [tex]a = cy[/tex]                 (2)

By definition,

tan A = a/b

         [tex]=\frac{cy}{cx}[/tex]

        [tex]=\frac{y}{x}[/tex]

Equivalent to tan A =[tex]\frac{y}{x}[/tex]

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Step-by-step explanation:

step 1: multiply [tex]2^m[/tex] by [tex]3^n[/tex]

2 × 3 = 6

to times power you must add them

[tex]2^m[/tex] × [tex]3^n[/tex] = [tex]6^{m+n}[/tex]

step 2: rearrange

[tex]6^{m+n}[/tex] = 108

can you do this step by yourself

Answer:

choice d

Step-by-step explanation:

I hand this question

The conclusion can be made from the given information

The volume of the triangular prism is equal to the volume of the cylinder

Given that there are two figures

1. A right triangular prism

2. Right cylinder

The area of the cross-section of the prism is equal to the Area of a cross-section of the cylinder.

Let this value be A.

Also given that the Height of prism = Height of cylinder = 6

The volume of a prism is will be :

[tex]V _{prism} = cross section area \times height[/tex]

[tex]V _{prism} = A \times 6 = 6A[/tex]  (1)

The Cross section of the cylinder is a circle.

hence the Area of the circle will be:

Area of cross-section, A = [tex]\pi \times r^2[/tex]

so, the Volume of the cylinder will be :

[tex]V _{cylinder} = \pi \times r^2 \times h[/tex]

[tex]V _{cylinder} = A \times h = A \times 6 = 6A[/tex]  (2)

From equations (1) and (2) we can say that

The volume of the triangular prism is equal to the volume of the cylinder.

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The probability that out of 8 newly hired people is 3.2.

According to the statement

we have given that the some conditions and based on these conditions we have to find the probability that out of 8 newly hired people.

So, For this purpose,

we have given that the

new employee in a fast-food chain still being with the company at the end of the year is  0.5

Now, we See that is probability of remaining with the company.

There is only one is 0.5.

According to the probability law

P + Q = 1

and this become

Q = 1 - 0.60.

And the probability of one people hired is Q.

Then

Q = 0.4

And probability that out of 8 newly hired people is

8Q = 0.4 * 8

it become 3.2.

So, The probability that out of 8 newly hired people is 3.2.

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Answer:

y = - 2x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2

y = - 2x + c ← is the partial equation

to find c substitute (3, 2 ) into the partial equation

2 = - 6 + c ⇒ c = 2 + 6 = 8

y = - 2x + 8 ← equation of perpendicular line

Answer:

1/9

Step-by-step explanation:

For each of the first die's 6 outcomes, the second die also has a possible 6 outcomes.

6 × 6 = 36

There are 36 different outcomes from

1, 1

1, 2

1, 3

...
6, 6

Many outcomes have the same sum. For example, 3, 4 and 4, 3 both add to 7.

How many outcomes add to 9?

3, 6

4, 5

5, 4

6, 3

4 different outcomes out of a possible 36 different outcomes add to 9.

p(sum of 9) = 4/36 = 1/9