If x2 + y2 = 14 and xy = 5, find the value of
(x + y)2
and
(X-y)2

The high temperatures in City B are more spread out than the high temperatures in City A.

The difference between the means of the two cities is 12 degrees Fahrenheit. This is equivalent to about 4 mean absolute deviations in City A or 5 mean absolute deviations in City B. This means that the high temperatures in City B are more spread out than the high temperatures in City A.

To put it another way, the high temperatures in City A are more likely to be close to the mean, while the high temperatures in City B are more likely to be further away from the mean.

Here is a table summarizing the data:

City Mean high temperature Mean absolute deviation

City A 59°F                             3.2°F

City B 71°F                                     2.9°F

The high temperatures for City A are more tightly clustered around the mean, while the high temperatures for City B are more spread out.

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Answer:

X=5

Explanation:

lots of math

It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer: AE=10, AD=14, x=5, BC=36, DE=52

Step-by-step explanation: finding x

4x-32=2(3x-21) || 4x-32=6x-42 || 10=2x || 5=x

Answer:3/8

Step-by-step explanation:

1/4-1/8=.125

in fraction form it’s 3/8 hope it helps

Answer:

Step-by-step explanation:

-10x+11y+11x=10 1x+11y=10

The height of the tree after 6 years can be expressed as "3 feet + 6f feet."

The correct answer is A. 3f + 6 feet.

To determine the current height of the tree in terms of "f,"

let's analyze the given information.

We know that the tree was initially 3 feet tall when it was planted 6 years ago.

Since the tree grows every year, we can assume that its growth rate is consistent.

Let's denote the current height of the tree as "h" (in feet).

After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").

Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

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Answer:

6.4

Step-by-step explanation:

c=\(\sqrt{a^{2}+b^{2} } =\sqrt{4^{2}+5^{2} } =6.4\)

The quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown value and where a, b, and c represent known values, where a 0 is a quadratic equation.

We know that the standard form of a quadratic equation is represented as: a\(x^{2}\) + bx + c = 0.

Here, we are given a = 4, b = -8 and c = -60.

On substituting these values, we get

⇒ a\(x^{2}\) + bx + c = 0

⇒ 4\(x^{2}\) - 8x - 60 = 0

On dividing both sides by 4, we get

⇒ \(x^{2}\) - 2x - 15 = 0

Hence, the quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.

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The given numbers from greatest to least are:

22, 8, 7, 2, -11

The given numbers from greatest to least starts with 22, then 8, then 7, then 2, and finally -11.

The correct question is;

Joey borrows $2400 from his grandfather and pays the money back in monthly payments of $200.

a. Write a linear function that represents the remaining money owed L(x) after x months.

b. Evaluate L(10) and interpret the meaning in the context of this problem.

A) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey still owes his

grandfather after 10 months.

B) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey has paid his

grandfather after 10 months.

C) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey has paid his

grandfather after 10 months.

D) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey still owes his

grandfather after 10 months.

Answer:

A) L(x) = 2400 - 200x

B) Option D is correct

Step-by-step explanation:

A) We are told that Joey borrowed 2400.

Now he pays back in installments of 200 every month.

Thus for x number of months he would have paid 200x.

Thus,the linear function that represents the remaining money owed is;

L(x) = 2400 - 200x

B) L(10) = 2400 - (200 * 10)

L(10) = 2400 - 2000

L(10) = 400

Thus, after 10 months, Joey is owing 400.

So, looking at the given options, the correct one is option D.

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

still a square units.

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

answer attached

Answer: 1)3.26.3

2)326.15

3)325.39

4)326.48

Step-by-step explanation: you want to start from the lowest number to get your answer

Answer:

The first option

Step-by-step explanation:

The first option:

f(x) = 4(x^2)

Each time x is squared and then multiplied by 4.

___

f(1) = 4(1^2) = 4

f(2) = 4(2^2) = 16

f(3) = 4(3^2) = 36

f(4) = 4(4^2) = 64

Answer:

The first one

Step-by-step explanation:

This is because the function of it is f(x) =  4x^2. Additionally, this can be seen as there is not a perfect difference between the values.

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The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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The work that gravity does;

W = F.S = mgΔh

In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.

W = mgΔh

g = 9.8 m/s²

Δh  = 4.6 m

m = 0.60 kg

W = 0.60 x 9.80 x 4.6

W = 2.7 J

The source of gravitational potential energy in relation to the ground is;

U = mgh

The release point therefore

Ug = mgh(0)

U0 = 0.60 x 9.8 x 6.1

U0 = 35.87 J

At the point of release

U(gf) = mgh(f)

U(gf) = 0.60 x 9.80 x 1.5

U(gf) = 8.820 J

Gravitational potential energy changes are;

ΔU(g) = U(gf) - U0

ΔU(g) =  8.820 J - 35.87 J

ΔU(g) = -27.05 J

Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.

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Answer:

x=−9. Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12. therefore a line ...

x=−9 Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12 therefore a line parallel ... More

We can write g in terms of f as: g(x) = f(x) - 3 = x² - 3

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To write g in terms of f, we can use function composition, which involves plugging the function f(x) into g(x) wherever we see x.

So, we have:

g(x) = f(x) - 3

where f(x) = x².

Substituting f(x) into g(x), we get:

g(x) = (x²) - 3

Therefore, we can write g in terms of f as:

g(x) = f(x) - 3 = x² - 3.

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