The square below has an area of 1+ 2x + x² square meters.
What expression represents the length of one side of the square?
Side length
1+2x+x²
Side length
www
meters

The ordered pairs (0,13) and (10, 0) are joined to best draw the line of best fit for the given scatter plot. So, option 4 is correct.

For the given scatter plot, to draw a line of best fit, the slope is to be calculated. The slope of the required line is calculated by

m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]

Where,

∑xy = sum of the product of x and y values

∑x = sum of x values

∑y = sum of y values

∑x² = sum of square values of x

n = total number of scatter points

And the y-intercept is calculated by

b = [∑y - m(∑x)]/n

Where m is the slope obtained above

The given scatter plot has the coordinate points:

(0,14), (1, 11), (2, 9), (3, 10),(4, 7), (5, 7), (6, 5), (7, 5), (8, 3), (9, 1), (10, 0)

Such that n = 11

Then the required components are calculated as follows:

∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

∑y = 14 + 11 + 9 + 10 + 7 + 7 + 5 + 5 + 3 + 1 + 0 = 72

∑xy = (0 × 14) + (1 × 11) + (2 × 9) + (3 × 10) + (4 × 7) + (5 × 7) + (6 × 5) + (7 × 5) + (8 × 3) + (9 × 1) + (10 × 0) = 220

∑x² = 0² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² = 385

Then the slope is calculated as follows:

slope m =  [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]

On substituting,

m = [11(220) - (55)(72)]/[11(385) - (55)²]

⇒ m = -14/11 = -1.2727273 ≅ -1.3

∴ m = -1.3

Then calculating the y-intercept:

we have b = [∑y - m(∑x)]/n

On substituting,

b = [72 - -1.3(55)]/11

∴ b = 13

Then the slope-intercept form of the required line is

y = -1.3x + 13

When x = 0,

y = -1.3(0) + 13 = 13

When y = 0,

0 = -1.3x + 13

⇒ 1.3x = 13

⇒ x = 13/1.3 = 10

Therefore, the coordinates (0, 13) and (10, 0) give the best draw for the line of best fit.

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The power series  is

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.

Its radius of convergence is 0.5

Let,

f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....

The power series expansion (geometric series),

valid for I2xI < 1 , IxI < 0.5

so, radius of convergence = 0.5

The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5

Now, g(x) = ln(1-2x)

= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]

=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

is the power series expansion for g(x).

radius of convergence =0.5

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Answer:

[tex]f(x)=-2(x-3)^2+2[/tex]

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.

x-intercept(s): (2,0),(4,0)

y-intercept(s): (0,−16)

Answer:

D     f(x) = -2(x - 3)² + 2

Step-by-step explanation:

The y-intercept occurs at x = 0.

A

f(x) = 2x(x + 14) - 64

f(0) = -64     Not -16

B

f(x) = (x + 4)² + 2x

f(0) = 16     Not -16

C

f(x) = (x - 16)² + 4

f(0) = 260      Not -16

D

f(x) = -2(x - 3)² + 2

f(0) = -18 + 2 = -16   <-------------------- this is it

The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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Samantha and Mia are 13 km apart from each other.

A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.

Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.

Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.

A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.

Hypotenuse of the triangle, which measures distance between the females

the Pythagorean theorem,

H² = P² + B²

H² = 7² + 11²

H² = 49 + 121

H = √170

H = 13.038

H = 13km

Between them, there is a 13 kilometer distance.

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the area and volume of the Pyramid of Gaza are  139, 840 m²

and 52950 m³ respectively.

The formula for volume and area of a square pyramid are given thus;

Volume, V= [tex]a^2\frac{h}{3}[/tex]

Area , [tex]A=a^2+2a \sqrt{\frac{a^2}{4}+ h^2 }[/tex]

Where

Substitute the values;

Area = [tex]230^2 + 2(230) \sqrt{\frac{230^2}{4}+ 150^2 }[/tex]

Area = [tex]52900 + 460 + \sqrt{13225 + 22500}[/tex]

Area = [tex]52900 + 460(189)[/tex]

Area = 52900 + 86, 940

Area = 139, 840 m²

Volume , v = [tex]230^2 + \frac{150}{3}[/tex]

Volume = 52900 + 50

Volume = 52950 m³

Thus, the area and volume of the Pyramid of Gaza are  139, 840 m²

and 52950 m³ respectively.

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answer is in the attachment below

goodluck!!

The volume of the tank is (70 cm)³ = 343,000 cm³.

Now,

1 mL = 1 cm³

1 L = 1000 mL

so we convert the given rate to

[tex]\dfrac{7\,\rm L}{1\,\rm min} \cdot \dfrac{1000\,\rm mL}{1\,\rm L} \cdot \dfrac{1\,\mathrm{cm}^3}{1\,\rm mL} = \dfrac{7000\,\mathrm{cm}^3}{1\,\rm min}[/tex]

Then the time it will take to fill up the tank is

[tex]343,000\,\mathrm{cm}^3 \cdot \dfrac{1\,\rm min}{7000\,\mathrm{cm}^3} = \boxed{49\,\rm min}[/tex]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's consider the shape given to us:

 ⇒ a rectangle with two semicircles cutout on the edges

     ⇒ perimeter/circumference of the two semicircles can count as one

         circle

Let's solve:

               [tex]\hookrightarrow \text{Total circumference} =\frac{1}{2} *\pi *\text{ diameter} +\frac{1}{2} *\pi * \text{diameter}\\= \pi *\text{diameter}=10\pi =10 * 3.14 = 31.4[/tex]

Answer: 59.4 square units

Hope that helps!

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Small numbers that are added to avoid unfair scoring of low-probability outcomes are called pseudocodes

From the statement, we have the following highlights:

The term for the statements in the above highlight is pseudocodes

This is because pseudocodes are false codes or small numbers

Hence, the small numbers that are added to avoid unfair scoring of low-probability outcomes are called pseudocodes

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Point E is where the statue should be placed.

At what point should the statue be:

The intersection of the doors to the arena, the spirit store, and the parking lot forms a triangle, with Point E in its center. The radius of the circumscribed circle will therefore equal the distance from the statue to each vertex, placing it at the same distance from all three landmarks.

Point E is where the statue should be placed.

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Answer: A, C, and D

Step-by-step explanation:

          A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.

✓ A. 0.032

✗ B. 0.999...

✓ C. 0.525

✓ D. 0.75

Answer:

a₁ = 5

a₂ = 8

a₃ = 13

a₄ = 20

Step-by-step explanation:

Given sequence formula

aₙ = n² + 4

Requirement of the question

Find the 4 terms in the sequence

Substitute 4 values into the sequence formula

a₁ = (1)² + 4 = 1 + 4 = [tex]\Large\boxed{5}[/tex]

a₂ = (2)² + 4 = 4 + 4 = [tex]\Large\boxed{8}[/tex]

a₃ = (3)² + 4 = 9 + 4 = [tex]\Large\boxed{13}[/tex]

a₄ = (4)² + 4 = 16 + 4 = [tex]\Large\boxed{20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a)  2x + 4

b)  2x + 5

c)  8

d)  9

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]

Function composition is an operation that takes two or more functions and combines them into a single function.

(f o g)(x) means find g(x) first and then substitute the result into f(x).

(g o f)(x) means find f(x) first and then substitute the result into g(x).

Part (a)

[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]

Part (b)

[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]

Part (d)

[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]

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(fog)(x)

(gof)(x)

(fog)(2))

(gof)(2)

The value of the polynomial difference when the value of x is 2.1 is -3.51

Polynomials are functions that has a leading degree of 3 and above. Given the following polynomial expression below;

g(x)= 2x^2+3x-9 and;

h(x)=x^2+2x-6

Take the difference

(h-g)(x) = h(x) - g(x)

Substitute

(h-g)(x) = x^2+2x-6 - (2x^2+3x-9)

(h-g)(x) = x^2+2x-6-2x^2-3x+9
(h-g)(x) = -x^2-x+3

Substitute the value of x to have;

(h-g)(2.1) = -(2.1)^2 - 2.1 + 3

(h-g)(2.1) = -4.41 + 0.9

(h-g)(2.1) = -3.51

Hence the value of the polynomial difference when the value of x is 2.1 is -3.51

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The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].

Then the plane we want has equation

[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]

Answer: 35.7 feet per second.

Step-by-step explanation: The scientist starts at -86 feet. Then she goes to -193 feet. The difference here is 193-86 =  107 feet. That means she traveled 107 ft in 3 seconds. 107/3 = 35 with a remainder of 2. 2/3 approximately equals 0.6666667. We need to round to the nearest tenth which is 0.7. So, we are left with  35.7.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Radius of smaller circle = 25 in

Radius of larger circle = 25 + 13 = 38 in

Area of ring : Area of larger circle - Area of smaller circle

[tex]\qquad❖ \: \sf \:\pi {(38)}^{2} - \pi {(25)}^{2} [/tex]

[tex]\qquad❖ \: \sf \:\pi( {38}^{2} - 25 {}^{2} )[/tex]

[tex]\qquad❖ \: \sf \:3.14(1444 - 625)[/tex]

[tex]\qquad❖ \: \sf \:3.14(819)[/tex]

[tex]\qquad❖ \: \sf \:2571.66 \: \: in {}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Volume=80cubic feet

Length×Width×Height =80cubic feet

Base area×Height =80cubic feet

25square feet×Height =80cubic feet

Height =80÷25

=3.2feet

The height of the rectangular prism is 3.2 feet.

To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,

The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.

Given:

Volume (V) = 80 cubic feet

Base area (A) = 25 square feet

We know that the base area is equal to the product of the length and width:

A = lw.

Calculate the length (l) and width (w) from the given base area:

We know that A = lw, and A = 25 square feet.

If we assume the length to be greater than the width, we can express the base area as lw = 25.

We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.

We can choose l = 5 feet and w = 5 feet.

V = lwh.

80 = 5 * 5 * h

Divide both sides of the equation by 25:

80/25 = h.

h = 16/5 = 3.2 feet.

Therefore, the height of the rectangular prism is 3.2 feet.

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Answer:

rotate 180° about origin

The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).

Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.

Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:

(x, y) → (-x, y)

A(-3, 2) → A'(3,2)

B(-1, -1) → B'(1, -1)

C(-4, -2) → C'(4,-2)

Hence, the transformation rule is (x, y) → (-x, y).

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Answer + Step-by-step explanation:

10 × 5 × 2

= 10 × (5 × 2)   (associative property)

= 10 × (10)

= 10 × 10

= 100

Correct option for solving the system of two equation is ([tex]y\times z =6[/tex])[tex]\times -8[/tex] .

What is simultaneous linear equation?

A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. Finding values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.

Simultaneous linear equations are two linear equations in two variables put together.

The ordered pair (x, y) that satisfies both linear equations is the system of simultaneous linear equations' solution.

Given,

Equation p: [tex]y+z=6[/tex]

Equation q: [tex]8y+7z=1[/tex]

To solve the above simultaneous linear equation multiply the equation p with (-8)

[tex](y+z=6)\times -8[/tex]     ...................................................... Equation (1)

Now add Equation (1) with Equation (q)

[tex]-8y-8z=-48[/tex]

+ [tex]8y+7z=1[/tex]

⇒ [tex]-z=-47[/tex]

⇒ [tex]z=47[/tex]

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Answer:

dean = 10

franco = 50

helen = 2

steps

you want to get the age of one of the people first

'is' means equal

'older than' means plus

'sum' means total by adding

d

f = 5d

d = 8 + h

d + f + h = 62

make sure there is 1 letter to solve for

d = 8 + h -> h = d - 8

f = 5d

d = d

d + f + h = 62

d + (5d) + (d-8)

7d - 8 = 62

7d = 70

d = 10

f = 50

h = 2

Answer:

[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]

Explanation:

Let the total water required water the entire ground be g

Equation:

[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]

rearranging

[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]

simplify

[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]

rewrite in mixed fraction

[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]

The water required to water the entire ground is  1 1/6 liters.

The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.

According to the given question.

We have a sequence,

[tex]a_{n} = 2^{\frac{1}{n} }[/tex]

Since, we know that

The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.

The nth root function is strictly increasing for positive real values.

Therefore,

[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex]           [tex]\forall \ n\geq 2[/tex]

Also,

[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]

[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex]   ( by squeeze theorem)

Thereofore,

[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]

So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.

Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.

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Answer:

48/80 = 6/10

Step-by-step explanation:

 48 wins

+ 32 lost

= 80 total games

Then the fraction of the games win is:

48/80

= 6/10

Answer:3/5 of the games

Step-by-step explanation: The total number of games played by the team is 48+32 = 80 games. out of hose 80, they won 48 so they won 48/80 games. We can simplify this by dividing both sides by 8 to get 6/10. Which is 60%. Finally we can simplify again by dividing the fraction by 2/2 to get 3/5.

Answer:

I don't understand the formatting after the first two equations.

Step-by-step explanation:

See attached graph.

The Distance - Time graph that represents that represents Charlie's trip is attached accordingly.

A distance-time graph can be used to illustrate the distance traveled by an item moving in a straight line.

The gradient of the line in a distance-time graph equals the speed of the item. The quicker the item moves, the higher the gradient (and the steeper the line).

Some of the uses of the distance-time graph are;

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Find inverse of given function :

[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]

[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]

[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]

Next, replace x with f-¹(x) and y with x ~

[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

[tex]\bold{Becomes,}[/tex]

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]

[tex]\bold{Then,}[/tex]

[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]

[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]

[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]

[tex]\small\bold{Square \: both \: sides }[/tex]

[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]

[tex]\sf{(x-7)^2=y}[/tex]

We now re-write in function notation. Take note however that this is the inverse:

[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]

[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]

[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]

Answer:

∠a=40°, ∠b=50°, ∠c=115°.

Step-by-step explanation:

∵The opposite vertex angles are equal,

∴∠a=40°.

∴∠b=90°-∠a=90°-40°=50°.

∠c=180°-65°=115°.