a kite has diagonals 9.8 ft and 7 ft what is the are of the kite?
33.6ft^2
34.3ft^2
68.6ft^2
8.4ft^2

Answer:

B) 0.972

Step-by-step explanation:

To be able to calculate the correlation coefficient of the model you just have to divide the number of one year by the number of the next year. TO make it clearer you can do it with the years 2002 and 2003:

Correlation Coefficient= [tex]\frac{14.5}{15.1}[/tex]=.960 and since the closest to that number is the .972 that´s the one that is the correct answer.

well the intercepts are  (8,0) and (-4,0) its a lot of math so you need to find it i would show you but i have a quiz

im not sure tho soo

Answer:

The x-intercepts of the quadratic function are 8 and -4.

Step-by-step explanation:

The given function is

[tex]f(x)=x^2-4x-32[/tex]

Equate the function f(x) equal to 0, to find the x-intercepts of the quadratic function.

[tex]f(x)=0[/tex]

[tex]x^2-4x-32=0[/tex]

The middle term can be written as -8x+4x.

[tex]x^2-8x+4x-32=0[/tex]

[tex]x(x-8)+4(x-8)=0[/tex]

Take out the common factors.

[tex](x-8)(x+4)=0[/tex]

Using zero product property,

[tex]x-8=0\Rightarrow x=8[/tex]

[tex]x+4=0\Rightarrow x=-4[/tex]

Therefore the x-intercepts of the quadratic function are 8 and -4.

360 - 130 = 230

Measure of CAR = 230/2.

CAR = 115

The line of music which shows a translation is b.

Translation means moving.

The Second line of music shows a translation from all the lines.

The translation is defined as the sliding of an object without changing its shape and size.

In this figure, the second option shows the exact translation operation. but the first and third line doesn't represent a translation.

In the first option, the translation does not take place, the music lines are inverted.

In the third option, the music lines are just interchanged which doesn't prove the translation.

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Answer:

see below

Step-by-step explanation:

The opposite of 2 is -2. The opposite of that is -(-2) = 2. The graph shows 2 on the number line.

Answer:

-2

Step-by-step explanation:

When it comes to negatives and positives, both are the opposite of each other because they are on the opposite sides on the number line. For example, the opposite of 9 would be -9. Or, the opposite of -9 is 9.

[tex] - 4 \sqrt{3} x - 2 + 6 = 22 \\ - 4 \sqrt{3}x + 4 = 22 \\ - 4 \sqrt{3}x = 18 \\ x = \frac{18}{ - 4 \sqrt{3} } = \frac{ - 18 \sqrt{3} }{12} = \frac{ - 3 \sqrt{3} }{2} = - 1.5 \sqrt{3} [/tex]

HOPE THIS WILL HELP YOU

The solution depends on the argument of the square root. Please be more precise and less ambiguous when writing your questions.

You could either mean:

[tex]-4\sqrt{3}x-2+6=22,\quad -4\sqrt{3x}-2+6=22,\quad -4\sqrt{3x-2}+6=22[/tex]

In the first case, we have

[tex]-4\sqrt{3}x-2+6=22 \iff -4\sqrt{3}x= 18 \iff x = -\dfrac{18}{4\sqrt{3}}[/tex]

In the second case, we have

[tex]-4\sqrt{3x}-2+6=22 \iff \sqrt{3x}=-\dfrac{9}{2}[/tex]

which has no solution, because a square root can't be negative

In the third case, we have

[tex]-4\sqrt{3x-2}+6=22 \iff -4\sqrt{3x-2}=16 \iff \sqrt{3x-2}=-4[/tex]

which again has no solution, for the same reason.

Set up a ratio for the area.

Area is squared so find the square root of the scale

√64/169 = 0.61538

Volume is cubed so cube the scale factor:

0.61538^3 = 0.23304

Multiply that by the volume:

4394 x 0.23304 = 1024

The volume of the smaller figure is 1,024 m^3

Answer:

Step-by-step explanation:

We know:

The ratio of the surface of two similar figures is equal to the square of the similarity scale. The ratio of the volume of two similar figures is equal to the cube of the similarity scale.

Therefore

k - similarity scale

[tex]k^2=\dfrac{64}{169}\to k=\sqrt{\dfrac{64}{169}}=\dfrac{\sqrt{64}}{\sqrt{169}}=\dfrac{8}{13}\\\\\dfrac{V}{4394}=\left(\dfrac{8}{13}\right)^3\\\\\dfrac{V}{4394}=\dfrac{512}{2197}\qquad\text{cross multiply}\\\\2197V=(512)(4394)\qquad\text{divide both sides by 2197}\\\\V=(512)(2)\\\\V=1024\ m^3[/tex]

Answer:

Step-by-step explanation:

Please, share the possible answer choices next time.

The graph of a parabola y = x^2 has its vertex at the origin, (0, 0), and opens up.  By replacing x with (x - 3), we translate the graph 3 units to the right.

Answer:

the answer is c

Step-by-step explanation:

Answer:

2.3744 ft

Step-by-step explanation:

11.54/(2.7*1.8)

(9/18)(9/18) = 81/324. The probability that Amy takes out pink chips in both draws is 81/324.

In this example we will use the probability property P(A∩B), which means given two independent events A and B, their joint probability P(A∩B) can be expressed as the product of the individual probabilities P(A∩B) = P(A)P(B).

The total number of chips of different colors in Amy's bag is:

8 blue chips + 9 pink chips + 1 white chip = 18 color chips

Amy takes out a chip from the bag randomly without looking, she replaces the chip and then takes out another chip from the bag.

So, the probability that Amy takes out a pink chip in the first draw is:

P(A) = 9/18 The probability of takes out a pink chip is 9/18 because there are 9 pink chips in the total of 18 color chips.

Then, Amy replaces the chip an takes out another which means there are again 18 color chips divide into 8 blue chips, 9 pink chips, and 1 white chip. So, the probability of takes out a pink chip in the second draw is:

P(B) = 9/18  The probability of takes out a pink chip is 9/18 because there are 9 pink chips in the total of 18 color chips.

What is the probability that Amy takes out a pink chip in both draws?

P(A∩B) = P(A)P(B)

P(A∩B) = (9/18)(9/18) = 81/324

Probability of taking out pink chip in both draws is equal to [tex]9[/tex] over [tex]18[/tex]multiplied by [tex]9[/tex] over [tex]18[/tex] equals [tex]81[/tex] over [tex]324[/tex].

" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes."

Formula used

Probability [tex]= \frac{n(F)}{n(T)}[/tex]

[tex]n(F)=[/tex] Number of favourable outcomes

[tex]n(T)=[/tex] Total number of outcomes

For independent events

[tex]P(A\cap B) = P(A) \times P(B)[/tex]

According to the question,

Given,

Total number of chips [tex]= 18[/tex]

Number of pink chips [tex]= 9[/tex]

[tex]'A'[/tex] represents the event of taking out pink chip first time

[tex]'B'[/tex] represents the event of taking out pink chip second time

Probability of taking out pink chip first time [tex]'P(A)' = \frac{9}{18}[/tex]

After replaces the chips again number of chip remain same

Probability of taking out pink chip second time [tex]'P(B)' = \frac{9}{18}[/tex]

Both the events are independent to each other

Substitute the value in the formula of probability of independent event we get,

Probability of taking out pink chip in both draw

[tex]P(A \cap B) = \frac{9}{18} \times \frac{9}{18}[/tex]

               [tex]= \frac{81}{324}[/tex]

Hence, probability of taking out pink chip in both draw is equal to [tex]9[/tex] over [tex]18[/tex]multiplied by [tex]9[/tex] over [tex]18[/tex] equals [tex]81[/tex] over [tex]324[/tex].

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Answer:

Step-by-step explanation:

answer:   27/159

The experimental probability of rolling a four is [tex]27 \div 159[/tex]

A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times.

The experimental probability should be [tex]27 \div 159[/tex]

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ANSWER

[tex]x = 2 \: \: or \: \: x = 15[/tex]

Or

[tex]x = - 2 \: \: or \: \: x = - 15[/tex]

EXPLANATION

The given polynomial is

[tex] f(x) = {x}^{2} + kx + 30[/tex]

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

[tex]m + n = - \frac{b}{a} = -k [/tex]

and the product of roots is

[tex]mn = \frac{c}{a} = 30[/tex]

The square difference of the zeroes is given by the expression.

[tex]( {m - n})^{2} = {(m + n)}^{2} - 4mn [/tex]

From the question, this difference is 169.

This implies that:

[tex]( { - k)}^{2} - 4(30) = 169[/tex]

[tex]{ k}^{2} -120= 169[/tex]

[tex] k^{2} = 289[/tex]

[tex] k= \pm \sqrt{289} [/tex]

[tex]k= \pm17[/tex]

We substitute the values of k into the equation and solve for x.

[tex]f(x) = {x}^{2} \pm17x + 30[/tex]

[tex]f(x) = (x \pm2)(x \pm 15)[/tex]

The zeroes are given by;

[tex] (x \pm2)(x \pm 15) = 0[/tex]

[tex]x = \pm2 \: \: or \: \: x = \pm 15[/tex]

The force used by Randy is 40 N.

When a force moves anything over a distance, it is said to be doing work.

Work = Force * Displacement

Work done given in the question = 200 N.m

Distance moved by the piano = 5m

W = F * d

200 = F * 5

F = 40N

Hence, the force used by randy is 40N.

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Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25

Step-by-step explanation:

The Rational Roots Theorem states that, given a polynomial

[tex]p(x) = a_nx^n+a_{n-1}x^{n-1}+\ldots+a_2x^2+a_1x+a_0[/tex]

the possible rational roots are in the form

[tex]x=\dfrac{p}{q},\quad p\text{ divides } a_0,\quad q\text{ divides } a_n[/tex]

The rational root theorem is used to determine the possible roots of a function.

The true statement about [tex]f(x) = 25x^7 - x^6 - 5x^4 + x - 49[/tex] is (c) Any rational root of f(x) is a factor of =-49 divided by a factor of 25.

For a rational function,

[tex]f(x) = px^n + ax^{n-1} + ...................... + bx + q[/tex]

The potential roots by the rational root theorem are:

[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]

By comparison,

p = 25, and q = -49

So, we have:

[tex]Roots = \pm\frac{Factors\ of\ -49}{Factors\ of\ 25}[/tex]

Hence, the true statement about [tex]f(x) = 25x^7 - x^6 - 5x^4 + x - 49[/tex] is (c)

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ANSWER

405m

EXPLANATION

We know the opposite side of of the right triangle to be 4629m and the given angle is 85°.

Since we want to find the adjacent side which is x units, we use the tangent ratio to obtain,

[tex] \tan(85 \degree) = \frac{opposite}{adjacent} [/tex]

[tex] \tan(85 \degree) = \frac{4629}{x} [/tex]

Solve for x.

[tex]x = \frac{4629}{\tan(85 \degree)} [/tex]

x=404.985

To the nearest meter, x=405m

Answer: 405m

Step-by-step explanation:

Answer:

336

Step-by-step explanation:

The average rate of change is Δy/Δx.

On the interval [5, 7]:

(1469 - 549) / (7 - 5) = 460

On the interval of [2, 4]:

(287 - 39) / (4 - 2) = 124

The difference is:

460 - 124

336

Answer:

A [tex]\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.[/tex]

Step-by-step explanation:

The equation [tex]12x^3-5x=2x^2+x+6[/tex] have in both sides expressions [tex]12x^3-5x[/tex] and [tex]2x^2+x+6.[/tex]

Therefore, the system of two equations

[tex]\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.[/tex]

has the solution (x,y), where x is the solution of the equation above.

ANSWER

[tex]y = 12 {x}^{3} - 5x[/tex]

{

[tex]y= 2 {x}^{2} + x + 6[/tex]

EXPLANATION

The given equation is

[tex]12 {x}^{3} - 5x = 2 {x}^{2} + x + 6[/tex]

To find the system of equations, we just have to equate each side of the equation to y and form two different equations.

The left sides gives one equation,

[tex]y = 12 {x}^{3} - 5x[/tex]

The right side also gives,

[tex]y= 2 {x}^{2} + x + 6[/tex]

Hence the correct choice is A

Answer:

He correctly determines that she has 300 nickels and 330 dimes.

Step-by-step explanation:

I'll first explain how Mark got that system of equations. Then I'll solve the system of equations to find the numbers of coins.

Moira has a collection of nickels and dimes. We don't know the number of nickels and the number of dimes she has.

First, we define two variables to represent the unknowns in this problems, the numbers of coins.

Let n = number of nickels.

Let d = number of dimes.

The sum of the numbers of coins is n + d. We are told she has 630 coins, so the first equation is

n + d = 630

Since we have two unknowns, we need two equations. Now we write an equation based on the values of the coins. A nickel is worth $0.05. A dime is worth $0.1. n nickels are worth 0.05n, and d dimes are worth 0.1d. The total value of the coins is 0.05n + 0.1d. We are told the value of the coins is $48. Now we can write the second equation.

0.05n + 0.1d = 48

Our system of equations is:

n + d = 630

0.05n + 0.1d = 48

These are the same equations Mark got.

Now we solve the system of equations. We will use the substitution method. First, we solve one equation for one variable. Then we substitute that into the other equation.

Let's solve the first equation for n:

n + d = 630

Subtract d from both sides:

n = 630 - d

Now that we know that n is the same as 630 - d, we replace n of the second equation with 630 - d.

0.05n + 0.1d = 48

0.05(630 - d) + 0.1d = 48

Distribute the 0.05:

31.5 - 0.05d + 0.1d = 48

Combine the terms in d:

0.05d + 31.5 = 48

Subtract 31.5 from both sides.

0.05d = 16.5

Divide both sides by 0.05.

d = 330

Now that we know d is 330, we substitute d with 330 in the first original equation and solve for n.

n + d = 630

n + 330 = 630

Subtract 330 from both sides.

n = 300

Since we let n = the number of nickels, and d = the number of dimes, now we can fill in the blanks.

n = number of nickels = 300

d = number of dimes = 330

Answer: He correctly determines that she has 300 nickels and 330 dimes.

*******************************************************************

The question is already answered, but we can check with the given information to confirm that our answer is correct.

We check the number of coins:

300 nickels + 330 dimes = 630 coins (the number of coins checks out.)

Now, we check the value of the coins:

300 * $0.05 + 330 * $0.1 = $15 + $33 = $48 (the value of the coins checks out.)

Since both the number of coins and the value of coins check correctly, our answer, 300 nickels and 330 dimes, is correct.

To find the number of nickels and dimes Moira has, start by simplifying the system of equations and solve for the variables. The solution to the given system of equations reveals that Moira has 300 nickels and 330 dimes.

The subject of this question is about solving a system of equations. The system in this case is given as {n+d=630 & 0.05n+0.10d=48}, where n represents the number of nickels Moira has and d represents the number of dimes she has.

First, we clear the decimals in the second equation by multiplying every term by 100, which gives us 5n + 10d = 4800. This can be simplified to n + 2d = 960 after dividing each term by 5.

Now, we have a new system of equations: {n + d = 630 & n + 2d = 960}. Subtraction of the first equation from the second will give us d = 330. Substituting d = 330 into the first equation will give us n = 300. Therefore, Moira has 300 nickels and 330 dimes.

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Answer:

275 miles

Step-by-step explanation:

Let x be the number of miles Alan has to drive to get the same cost for tha two plans.

1 plan: total cost

[tex]55+0.50x[/tex]

2 plan: total cost

[tex]0.7x[/tex]

Equate them:

[tex]55+0.5x=0.7x\\ \\55=0.2x\\ \\550=2x\\ \\x=275[/tex]

Answer:

275 miles

Step-by-step explanation:

You can express the cost of each plan as follows:

Plan 1: 55+0.50x

Plan 2: 0.70x

x is the amount of miles driven

As you need to find the amount of miles where the two plans cost the same, you can equate them and solve for x:

55+0.50x= 0.70x

55= 0.70x-0.50x

55= 0.2x

x= 55/0.2

x= 275

Alan needs to drive 175 miles for the two plans to cost the same.

Answer:

I think its C) 43. Let me know what you get

Answer:

it's 43

Step-by-step explanation:

i got the answer right

the point estimate typically is in the middle of the interval, so it would be at (1/2)(0.52+0.80) or 0.66.

Find the volume of the lake:

37 x 30 x 2 = 2,220 cubic miles.

Now find 65% of the total volume:

2,220 x 0.65 = 1,443 cubic miles

Divide the number of fish by the volume of the lake:

115, 200 fish / 1,443 cubic miles = 79.83 fish per cubic mile.

Rounded to the nearest fish = 80 fish per cubic mile.

Answer:

80 fish per cubic mile.

Answer:

(x - 8)² + (y - 13)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre is located at the midpoint of the endpoints of the diameter.

Use the midpoint formula to find the centre

[[tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex] ]

with (x₁, y₁ ) = (5, 9) and (x₂, y₂ ) = (11,17)

centre = ( [tex]\frac{5+11}{2}[/tex], [tex]\frac{9+17}{2}[/tex] ) = (8, 13)

The radius is the distance from the centre to either end of the diameter

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 13) and (x₂, y₂ ) = (5, 9)

r = [tex]\sqrt{(5-8)^2+(9-13)^2}[/tex]

  = [tex]\sqrt{(-3)^2+(-4)^2}[/tex]

  = [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5 ⇒ r² = 25

Hence

(x - 8)² + (y - 13)² = 25

Answer:

the answer should be f(x)=-4

Substitute x=-3 in the equation

F(x)= -2(-3)^2 -3(-3) +5

-18+9+5=-4

The answer is -4

Answer:

[tex]\frac{b+3}{3}[/tex]

Step-by-step explanation:

[tex]\frac{b+3}{b} \div\frac{3}{b}[/tex]

We need to solve the above equation.

We replace the division sign by multiplication and reciprocated the second term

[tex]=\frac{b+3}{b} *\frac{b}{3}[/tex]

Multiplying both fractions:

[tex]=\frac{(b+3)*b}{3b}[/tex]

Cancelling b from numerator and denominator.

[tex]=\frac{(b+3)}{3}[/tex]

So, answer is:

[tex]\frac{b+3}{3}[/tex]

ANSWER

[tex]\frac{b + 3}{3}[/tex]

EXPLANATION

The given expression is

[tex] \frac{b + 3}{b} \div \frac{3}{b} [/tex]

We multiply the first fraction by the multiplicative inverse of the second fraction.

[tex]\frac{b + 3}{b} \times \frac{b}{3}[/tex]

We now cancel out the common factors to get:

[tex]\frac{b + 3}{3} [/tex]

Therefore simplified form is:

[tex]\frac{b + 3}{3} [/tex]

Answer:

d is your answer

Step-by-step explanation:

Answer:

Option D.

Step-by-step explanation:

The given system of equations is

[tex]y=2x[/tex]         ....(i)

[tex]y=x^2-15[/tex]         ...(ii)

From (i) and (ii) we get

[tex]x^2-15=2x[/tex]

[tex]x^2-2x-15=0[/tex]

[tex]x^2-5x+3x-15=0[/tex]

[tex]x(x-5)+3(x-5)=0[/tex]

[tex](x-5)(x+3)=0[/tex]

Using zero produc property we get

[tex]x-5=0\Rightarrow x=5[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

If x=5, then

[tex]y=2(5)=10[/tex]

If x=-3, then

[tex]y=2(-3)=-6[/tex]

The solutions of the given system of equations are (-3,-6) and (5,10).

Therefore, the correct option is D.

Answer:

The cost of 1 jar of peanut butter is $2.50 ⇒ answer B

Step-by-step explanation:

* Lets change the story problem to equations to solve it

- The cost of a jar of peanut butter is p dollars

- The cost of a jar of jelly is j dollars

- Winston purchased 3 jars of peanut butter and 2 jars of jelly for $11.50

- Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00

* Lets write the equations

∵ The cost of a jar of peanut butter is p dollars and the cost of a jar

   of jelly is j dollars

∵ Winston purchased 3 jars of peanut butter and 2 jars of jelly for $11.50

∴ 3p + 2j = 11.50 ⇒ (1)

∵ Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00

∴ 2p + 4j = 13.00 ⇒ (2)

- Lets solve this system of equation by using elimination method

- Multiply equation (1) by -2

∴ -6p - 4j = - 23 ⇒ (3)

- Add equations (2) and (3)

∴ -4p = -10 ⇒ divide both sides by -4

∴ p = 2.5

∵ p is the cost of 1 jar of peanut butter

* The cost of 1 jar of peanut butter is $2.50

Final answer:

Using a system of equations based on the purchases of Winston and Peter, the price of one jar of peanut butter is calculated to be $2.50.

Explanation:

To determine the cost of one jar of peanut butter, we can set up a system of equations based on the information provided. Let p represent the price of one jar of peanut butter, and j represent the price of one jar of jelly.

The system of equations based on the purchases made by Winston and Peter are:
1) 3p + 2j = 11.50
2) 2p + 4j = 13.00

To solve for p, we can multiply equation 1) by 2 and equation 2) by 3 to eliminate j when we subtract one equation from the other.

2*(1): 6p + 4j = 23.00
3*(2): 6p + 12j = 39.00

Subtracting the first equation from the second, we get:

6p + 12j - (6p + 4j) = 39.00 - 23.00
8j = 16.00
j = 2.00

Now, substitute j = 2.00 into equation 1) to find p:

3p + 2(2.00) = 11.50
3p + 4.00 = 11.50
3p = 7.50
p = 2.50

Therefore, one jar of peanut butter costs $2.50, which corresponds with option B.

Answer:

The coordinates for the location of the center of the platform are (-1 , 2)

Step-by-step explanation:

* Lets revise the equation of the circle

- The equation of the circle of center (h , k) and radius r is:

  (x - h)² + (y - k)² = r²

- The center is equidistant from any point lies on the circumference

 of the circle

- There are three points equidistant from the center of the circle

- We have three unknowns in the equation of the circle h , k , r

- We will substitute the coordinates of these point in the equation of

 the circle to find h , k , r

* Lets solve the problem

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ Points D (-2 , -4) , E (1 , 5) , F (2 , 0)

- Substitute the values of x and y b the coordinates of these points

# Point D (-2 , -4)

∵ (-2 - h)² + (-4 - k)² = r² ⇒ (1)

# Point E (1 , 5)

∵ (1 - h)² + (5 - k)² = r² ⇒ (2)

# Point (2 , 0)

∵ (2 - h)² + (0 - k)² = r²

∴ (2 - h)² + k² = r² ⇒ (3)

- To find h , k equate equation (1) , (2) and equation (2) , (3) because

  all of them equal r²

∵ (-2 - h)² + (-4 - k)² = (1 - h)² + (5 - k)² ⇒ (4)

∵ (1 - h)² + (5 - k)² = (2 - h)² + k² ⇒ (5)

- Simplify (4) and (5) by solve the brackets power 2

# (a ± b)² = (a)² ± (2 × a × b) + (b)²

# Equation (4)

∴ [(-2)² - (2 × 2 × h) + (-h)²] + [(-4)² - (2 × 4 × k) + (-k)²] =

  [(1)² - (2 × 1 × h) + (-h)²] + [(5)² - (2 × 5 × k) + (-k)²]

∴ 4 - 4h + h² + 16 - 8k + k² = 1 - 2h + h² + 25 - 10k + k² ⇒ add like terms

∴ 20 - 4h - 8k + h² + k² = 26 - 2h - 10k + h² + k² ⇒ subtract h² and k²

  from both sides

∴ 20 - 4h - 8k = 26 - 2h - 10k ⇒ subtract 20 and add 2h , 10k

  for both sides

∴ -2h + 2k = 6 ⇒ (6)

- Do the same with equation (5)

# Equation (5)

∴ [(1)² - (2 × 1 × h) + (-h)²] + [(5)² - (2 × 5 × k) + (-k)²] =

  [(2)² - (2 × 2 × h) + k²

∴ 1 - 2h + h² + 25 - 10k + k² = 4 - 4h + k²⇒ add like terms

∴ 26 - 2h - 10k + h² + k² = 4 - 4h + k² ⇒ subtract h² and k²

  from both sides

∴ 26 - 2h - 10k = 4 - 4h  ⇒ subtract 26 and add 4h

  for both sides

∴ 2h - 10k = -22 ⇒ (7)

- Add (6) and (7) to eliminate h and find k

∴ - 8k = -16 ⇒ divide both sides by -8

∴ k = 2

- Substitute this value of k in (6) or (7)

∴ 2h - 10(2) = -22

∴ 2h - 20 = -22 ⇒ add 20 to both sides

∴ 2h = -2 ⇒ divide both sides by 2

∴ h = -1

* The coordinates for the location of the center of the platform are (-1 , 2)

Answer:

The coordinates for the location of the center of the platform are (-3.5,1.5)

Step-by-step explanation:

You have 3 points:

D(−2,−4)

E(1,5)

F(2,0)

And you have to find a equidistant point (c) ([tex]x_{c}[/tex],[tex]y_{c}[/tex]) from the three given.

Then, you know that:

[tex]D_{cD}=D_{cE}[/tex]

And:

[tex]D_{cE}=D_{cF}[/tex]

Where:

[tex]D_{cD}[/tex]=Distance between point c to D

[tex]D_{cE}[/tex]=Distance between point c to E

[tex]D_{cF}[/tex]=Distance between point c to D

The equation to calculate distance between two points (A to B) is:

[tex]D_{AB}=\sqrt{(x_{B}-x_{A})^2+(y_{B}-y_{A})^2)}[/tex]

[tex]D_{AB}=\sqrt{(x_{B}^2)-(2*x_{B}*x_{A})+(x_{A}^2)+(y_{B}^2)-(2*y_{B}*x_{A})+(y_{A}^2)}[/tex]

Then you have to calculate:

*[tex]D_{cD}=D_{cE}[/tex]

[tex]D_{cD}=\sqrt{(x_{D}-x_{c})^2+(y_{D}-y_{c})^2}[/tex]

[tex]D_{cD}=\sqrt{(x_{D}^2)-(2*x_{D}*x_{c})+(x_{c}^2)+(y_{D}^2)-(2*y_{D} y_{c})+(y_{c}^2)}[/tex]

[tex]D_{cD}=\sqrt{(-2^2-(2(-2)*x_{c})+x_{c}^2)+(-4^2-(2(-4) y_{c})+y_{c}^2)}[/tex]

[tex]D_{cD}=\sqrt{(4+4x_{c}+x_{c}^2 )+(16+8y_{c}+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}-x_{c})^2+(y_{E}-y_{c})^2}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}^2)-(2*x_{E}*x_{c})+(x_{c}^2)+(y_{E}^2)-(2y_{E}*y_{c})+(y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(1^2-2(1)*x_{c}+x_{c}^2)+(5^2-2(5)+y_{c}+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2)}[/tex]

[tex]D_{cD}=D_{cE}[/tex]

[tex]\sqrt{((4+4x_{c}+x_{c}^2)+(16+8y_{c}+y_{c}^2))}=\sqrt{(1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2)}[/tex]

[tex](4+4x_{c}+x_{c}^2)+(16+8y_{c}+y_{c}^2)= (1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2)[/tex]

[tex]x_{c}^2+y_{c}^2+4x_{c}+8y_{c}+20=x_{c}^2+y_{c}^2-2x_{c}-10y_{c}+26[/tex]

[tex]4x_{c}+2x_{c}+8y_{c}+10y_{c}=6[/tex]

[tex]6x_{c}+18y_{c}=6[/tex]

You get equation number 1.

*[tex]D_{cE}=D_{cF}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}-x_{c})^2+(y_{E}-y_{c})^2}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}^2-(2+x_{E}*x_{c})+x_{c}^2)+(y_{E}^2-(2y_{E} *y_{c})+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{((1^2-2(1)+x_{c}+x_{c}^2)+(5^2-2(5)y_{c}+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(1-2x_{c}+x_{c}^2 )+(25-10y_{c}+y_{c}^2)}[/tex]

[tex]D_{cF}=\sqrt{(x_{F}-x_{c})^2+(y_{F}-y_{c})^2}[/tex]

[tex]D_{cF}=\sqrt{(x_{F}^2-(2*x_{F}*x_{c})+x_{c}^2)+(y_{F}^2-(2*y_{F}* y_{c})+y_{c}^2)}[/tex]

[tex]D_{cF}=\sqrt{(2^2-(2(2)x_{c})+x_{c}^2)+(0^2-(2(0)y_{c}+y_{c}^2)}[/tex]

[tex]D_{cF}=\sqrt{(4-4x_{c}+x_{c^2})+(0-0+y_{c}^2)}[/tex]

[tex]D_{cE}=D_{cF}[/tex]

[tex]\sqrt{(1-2x_{c}+x_{c}^2 )+(25-10y_{c}+y_{c}^2)}=\sqrt{(4-4x_{c}+x_{c}^2 )+(0-0+y_{c}^2)}[/tex]

[tex](1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2 )=(4-4x_{c}+x_{c}^2)+(0-0+y_{c}^2)[/tex]

[tex]x_{c}^2+y_{c}^2-2x_{c}-10y_{c}+26=x_{c}^2+y_{c}^2-4x_{c}+4[/tex]

[tex]-2x_{c}+4x_{c}-10y_{c}=-22[/tex]

[tex]2x_{c}-10y_{c}=-22[/tex]

You get equation number 2.

Now you have to solve this two equations:

[tex]6x_{c}+18y_{c}=6[/tex] (1)

[tex]2x_{c}-10y_{c}=-22[/tex] (2)

From (2)  

[tex]-10y_{c}=-22-2x_{c}[/tex]

[tex]y_{c}=(-22-2x_{c})/(-10)[/tex]

[tex]y_{c}=2.2+0.2x_{c}[/tex]

Replacing [tex]y_{c}[/tex] in (1)

[tex]6x_{c}+18(2.2+0.2x_{c})=6[/tex]

[tex]6x_{c}+39.6+3.6x_{c}=6[/tex]

[tex]9.6x_{c}=6-39.6[/tex]

[tex]x_{c}=6-39.6[/tex]

[tex]x_{c}=-3.5[/tex]

Replacing [tex]x_{c}=-3.5[/tex] in

[tex]y_{c}=2.2+0.2x_{c}[/tex]

[tex]y_{c}=2.2+0.2(-3.5)[/tex]

[tex]y_{c}=2.2+0.2(-3.5)[/tex]

[tex]y_{c}=2.2-0.7[/tex]

[tex]y_{c}=1.5[/tex]

Then the coordinates for the location of the center of the platform are (-3.5,1.5)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x-4y=4\\x+2y=18&\text{multiply both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x-4y=4\\2x+4y=36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=40\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=8}\\\\\text{Put the value of x to the second equation:}\\\\8+2y=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}[/tex]

[tex]\text{Put the values of x and y to the expression}\ x^2+y^2+xy:\\\\8^2+5^2+(8)(5)=64+25+40=129[/tex]

Answer:

j(t)=230600(1.009)^t

Step-by-step explanation:

Increasing at a rate of 0.9\%0.9%0, point, 9, percent means the expected number of jobs keeps its 100\%100%100, percent and adds 0.9\%0.9%0, point, 9, percent more, for a total of 100.9\%100.9%100, point, 9, percent.

So each year, the expected number of jobs is multiplied by 100.9\%100.9%100, point, 9, percent, which is the same as a factor of 1.0091.0091, point, 009.

If we start with the initial number of jobs, 230{,}600230,600230, comma, 600 jobs, and keep multiplying by 1.0091.0091, point, 009, this function gives us expected number of jobs in radiology ttt years from 201420142014:

j(t)=230600(1.009)^t

Answer:

[tex]J(t) =230600(1.009)^t[/tex]

Step-by-step explanation:

Given,

The initial number of jobs ( or jobs on 2014 ), P = 230,600

Also, the rate of increasing per year, r = 0.9% = 0.009,

Thus, the number of jobs after t years since 2014,

[tex]J(t)=P(1+r)^t[/tex]

[tex]=230600(1+0.009)^t[/tex]

[tex]=230600(1.009)^t[/tex]

Which is the required function.