F(x) = 2x² +1
g(x) = 3x - 5
f-g

Triangle Proportionality Theorem is defined by a line parallel to one side of a triangle divides the other two sides proportionally.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We know that;

Triangular Proportionality Theorem states that:

''If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.''

Therefore, Triangle Proportionality Theorem is defined by a line parallel to one side of a triangle divides the other two sides proportionally.

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The corners of the square touch the circular plot at points W, X, Y, Z. The distance from point W to Y is equal to diameter of the circular plot, that is 14.

A square sand box is in a circular plot of grass so that the corners of the square sandbox  touch the edge of circular the plot. The vertices are W, X, Y, and Z. This situation can be depicted in the attached picture.

The distance from point W to Y is equal to the diameter of the circle.

WY = d = 2r

( d = diameter, r = radius)

The formula for the area of a circle is given by:

A = πr²

49π = πr²

49 = r²

r = ±√49 =  ± 7

Since radius is always a positive number, hence,

r = 7

Therefore,

WY = 2r = 2 x 7 = 14

Your question is incomplete, most likely your question was:

In a certain playground, a square sand box rests in a circular plot of grass so that the corners of the sandbox just touch the edge of the plot of grass at points W, X, Y and Z, as shown. What is the distance from point W to point Y. The area of the circular plot is 49π

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The largest number that divides two or more numbers evenly is greatest common divisor (GCD).

The biggest positive number that divides any non-zero integer by two or more is known as the greatest common divisor.

The greatest common divisor is the biggest number that divides two or more numbers proportionally (GCD).

Using the LCM method, the steps to calculate the GCD of (a, b) are as follows:

Find the result of a and b in step 1.

Find a and b's least common multiple (LCM) in step two.

Step 3: Dividing the results of Steps 1 and 2.

Step 4: The value that results from division is the most significant common divisor of (a, b).

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Answer:

x^3(4+5x^3)cuberoot(x)

Step-by-step explanation:

In order to add the two problems, you need to make sure the radical is the same. Since the cube root of 8x is 2 cuberoot(x) and the cube root of x^10 is x^3 cuberoot(x) this allows the radical to be the same so we can add them.

Now whenever you take out something from within the radical, you multiply it to whatever it is already next to it. So, you would get 4(x^3) cuberoot(x) + 5x^3(x^3) cuberoot(x) From here you get 4(x^3) cuberoot(x) + 5x^6 cuberoot(x).

To finally simplify it, you can put the addition (because the x exponent outside of the cube root isnt the same, you can't add the 4 and 5) so you can get (We can put the x^3 outside of the parenthesis because both numbers have x^3)  x^3(4+5x^3)cuberoot(x)

Yes, this confidence interval provides evidence that the average battery life of this ipad is not 10 hours, since the interval does not contain 10 hours.

Yes, this confidence interval provides evidence that the average battery life of this ipad is not 10 hours. The 99% confidence interval for the mean battery life of this ipad is (8.45, 10.05) hours. This means that 99% of the time, the true mean battery life of the ipad will be between 8.45 and 10.05 hours. Since the interval does not contain 10 hours, it is evidence that this ipad does not have an average battery life of 10 hours. This is because the interval suggests that there is only a 1% chance that the true mean battery life is 10 hours, which is not enough evidence to support the claim that the latest ipad has an average battery life of 10 hours.

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Answer:

y=-x+7

Step-by-step explanation:

Line l intersects y=x^2-2x+5 at the two abscissas, -1 and 2.  Lets find these points [(-1,y1) and (2,y2)] by solving the given equation for y:

f(x) = x^2-2x+5

f(-1) = (-1)^2-2*(-1)+5  for x = -1

f(-1) = 8  This is point (-1,8)

f(2) = (2)^2-2*(2)+5

f(2) = 5  This is point (2,5)

Assuming line l is a straigh line, we can now calculate the slope between points (-1,8) and (2,5).

Rise = (5 - 8) = -3

Run = (2 - (-1)) = 3

Slope = (-3/3) or -1

The slope-intercept form of a straight line is y=mx+b, where m is the slope and b the y-intercept (the value of y when x is zero).

With slope of -1, we can writre y = -x + b

To find b, enter one of the two points and solve for b:

y = -x + b

5 = -(2) + b for (2,5)

b = 7

The equation of line l is y=-x+7

See the attached graph.

The ants there are more blue whales  with the marging of 1.06 * 10^13 in  ants there are then blue whales in scientific notation.

The concept that will be used here is division. A division is the action of dividing a sum into equal pieces. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

The number of the blue whales from the figure is 4.7*10^3

The number of the blue ants from the figure is 5*10^16

Then the nuber of the more ants

= 5*10^16 / 4.7*10^3

= 1.06 * 10^13.

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Answer:

[tex]\frac{12}{25}[/tex]

Step-by-step explanation:

[tex]\frac{12}{(2+3)^{2} }[/tex]

[tex]\frac{12}{5^{2} }[/tex]

[tex]\frac{12}{25}[/tex]

The lines given, based on the picture, can be said to be skew.

Skewed lines are two lines that are not parallel to one another, neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist in various planes. Two lines in a two-dimensional space can either intersect or run parallel to one another. Skew lines can never exist in 2D space as a result.

Skew lines occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. These lines go on forever in both directions.

The picture shows lines on steps. These steps therefore exist on different planes but are not parallel. They must therefore be skew.

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There is no solution when the lines that make up a system are parallel since the two lines do not share any points.

A linear equation with two variables has the for [tex]ax + by + c = 0[/tex], where variables are belongs to R. An A system of linear equations that cannot be solved is a pair of inconsistent linear equations. We can determine whether a system of linear equations has no solution by comparing the coefficients of the equations in the system.

Take into account the pair of linear equations in x and y:

[tex]a1x + b1y + c1 = 0\\a2x + b2y + c2 = 0[/tex]

There won't be a solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex].

An inconsistent pair of linear equations is the name given to this kind of equational system. The system of equations cannot be solved if the graph's lines are parallel.

So here, both equations are called no solution line.

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Answer:

the teacher does not have enough paint and he needs 1351.5-1324.8 = 26.7 square cm more paint.

Step-by-step explanation:

The canvas each student has is 5.3 cm wide and 8.5 cm tall. The area of the canvas is (5.3 cm)(8.5 cm) = 45.05 square cm.

The art teacher has 6 bottles of paint, each bottle covers 220.8 square cm of canvas. So he has 6220.8 = 1324.8 square cm of paint.

There are 30 students in the class and each student has a canvas of 45.05 square cm. So in total the students have 30*45.05 = 1351.5 square cm of canvas.

The teacher has 1324.8 square cm of paint and the students have 1351.5 square cm of canvas.

Therefore the teacher does not have enough paint and he needs 1351.5-1324.8 = 26.7 square cm more paint.

The length of the quilt is 12 feet.

We can start solving this problem by using algebra. Let x be the quilt's length in feet. Then, the width of the quilt can be represented as (x - 4) feet. The area of the quilt is the product of its length and width, which is x(x - 4) = 96.

Expanding the left side of the equation:

x^2 - 4x = 96

Now we have a quadratic equation that we can solve by factoring or using the quadratic formula.

x^2 - 4x - 96 = 0

(x-12)(x+8) = 0

x=12 or x=-8 (length cannot be negative)

So the length of the quilt is 12 feet.

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The three consecutive integers are 137 , 138 and 139

Given that

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Consecutive Even Numbers:

Even numbers are numbers that end with 0, 2, 4, 6 or 8. The examples of consecutive even numbers are:0, 2, 4, 6, 8, 10, 12, …

Consecutive Odd Numbers:

Odd numbers are numbers that end with 1, 3, 5, 7 or 9. The examples of consecutive odd numbers are:1, 3, 5, 7, 9, 11, 13, 15, ….

there are three consecutive integers

let's assume that consecutive integers are x, x+1 and x+ 2

given that  the sum of the first and the third number is two hundred and seventy-six

x + (x+2) = 276

2x + 2 = 276

2x = 276 - 2

2x = 274

x = 137

The three consecutive integers are 137 , 138 and 139

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We must first calculate the area of a single tile in order to figure how many floor tiles are required to cover a space that is 1080 square meters.

Since the area of a parallelogram is equal to its base times its height, the tile's area is 24 x 10 cm, or 240 [tex]cm^{2}[/tex].

Since one square meter equals 10,000 square centimeters, we divide by 10,000 to convert this area to square meters: 240 [tex]cm^{2}[/tex] / 10,000 = 0.024 c[tex]m^{2}[/tex]

Thus, a single tile has a surface area of 0.024 square meters.

We divide a room's 1080 square meters by a tile's area to determine how many tiles are required to completely cover the space:

1080 [tex]m^{2}[/tex] / 0.024 [tex]m^{2}[/tex]= 45,000

 Therefore ,45,000 floor tiles would be required to cover a space that is 1080 square meters in size.

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We can use algebra to set up and solve a system of equations to determine the size of a rectangle given the given information.

Step 1: Assign the rectangle's width and length the letters "w" and "l," respectively. We can determine the rectangle's 24 cm perimeter from the problem. The formula P = 2l + 2w = 24 cm can be used to draw up an equation since the perimeter of a rectangle is equal to the total of its four sides.

 Step 2: Using the additional knowledge that the length is 3 cm longer than the width, we can construct a second equation as follows: l = w + 3 cm.

Step 3: We can change the variable "l" in the first equation to read "w + 3," making P = 2(w + 3) + 2w = 24 cm. As a result, we can calculate 2w + 2(w + 3) = 24 cm.

Step 4: Finding the value of w: 24 cm = 2w + 2w + 6.

Step 5: Condensing the formula: 4w = 18 cm.

Sixth step: multiply both sides by 4 to get w = 4.5 cm.

Step 7: Using the second equation, we can get the length now that we know the width: l = w + 3 cm = 4.5 + 3 = 7.5 cm.

  Therefore the answer is option c , width is 4.5 and length is 7.5 .

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Figure A appears to be a polygon under certain conditions.

We are given the following information in the question:

Figure A is a square

Figure B is a parallelogram

Figure C is a right triangle.

Figure D is a trapezoid

We have to find which are the regular polygons.

A regular polygon is a polygon with all the sides equal and all the interior angles equal measure.

That is a regular polygon is equiangular and equilateral.

Figure A  square appears to be a polygon because

The opposite sides are parallel. All four sides are equal, and all angles measure 90°.

Figure B can be a regular pentagon provided it is equiangular and equilateral

A regular polygon is a polygon with all the sides equal and all the interior angles equal measure.

Figure C cannot be a regular polygon because a right angle follows the Pythagoras theorem and all three sides can never be equal in a right-angled triangle.

Figure D is a trapezoid Trapezoids are four-sided polygons, so they are all quadrilaterals.

Figure A appears to be a polygon under certain conditions.

Thus square looks to be a regular.

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Step-by-step explanation:

To find the coefficient of x² in the expansion of (1+ax)⁴(a-2)³, we can use the binomial theorem. The binomial theorem states that for any two numbers a and b and any non-negative integer n, the expansion of (a+b)^n is given by the sum of the terms:

(a+b)^n = C(n,0)a^n * b^0 + C(n,1)a^(n-1) * b^1 + C(n,2)a^(n-2) * b^2 + ... + C(n,n)a^0 * b^n

where C(n,k) = n! / (k!(n-k)!) is the binomial coefficient.

We can apply the binomial theorem to find the coefficient of x² in the expansion of (1+ax)⁴(a-2)³:

(1+ax)⁴(a-2)³ = (1+4ax+6(ax)²+4(ax)³+(ax)⁴)(a-2)³ = a^3 - 6a^2 + 12a - 8 + 6(ax)² + ...

So the coefficient of x² in the expansion is 6.

Answer:

153.958 [tex]cm^{2}[/tex]

Step-by-step explanation:

a = [tex]\pi r^{2}[/tex]

a = 3.142([tex]7^{2}[/tex])     The radius is half of the diameter 14/2 = 7

a = 3.142(49)

a = 153.958

The required sum of the coordinate of T is given as 9.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate the y is called ordinate.

Here,
The coordinates of the endpoints of RS are R(4, -8) and S(25, -1).
Ratio ST / RT = 4 / 3 = n/m

Coordinates of the point are given by section formula,
x = mx₁ + nx₂ / m  + n ; y =  my₁ + ny₂ / m  + n

Substitute the values,
x = 3 × 4  + 25 × 4 / 4 + 3 ; y = 3 × -8  + 25 × -1 / 4 + 3
x = 16                               ; -7

Coordinates of T = (x ,y) = (16, -7)

Sum of the coordinate of T = 16 + {-7} = 9

Thus, the required sum of the coordinate of T is given as 9.

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The equation of the tangent line at any point on the curve is y = f'(x)x + c. For the line to be horizontal, its slope has to be zero, meaning that f'(x) = 0. Therefore, the coordinates of all points on the curve with a horizontal tangent line are those points (x, f(x)) such that f'(x) = 0.

The equation for any line tangent to a curve at a given point (x, f(x)) is given by the equation y = f'(x)x + c, where c is a constant. This equation is derived from the definition of the derivative, which is the instantaneous rate of change of a function at a given point. The slope of this line is equal to the derivative of the curve at the given point, or f'(x). A line is horizontal when its slope is equal to zero, meaning that f'(x) = 0. Therefore, the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal are all points (x, f(x)) such that f'(x) = 0. This is because a line with a slope of zero is always horizontal, regardless of the value of the constant c. So, in order to find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal, we must find all points (x, f(x)) such that f'(x) = 0.

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The system of equations that represents Elliott's situation is:

[tex]\begin{cases} 2h = 2h \\ s = 2h \\h + s = 202020 \end{cases}[/tex]

The system of equations for Elliott's situation can be represented as follows:

Let h be the number of hats Elliott makes and s be the number of scarves she makes.

We know that 2 kilograms of yarn are needed for each hat and 1 kilograms of yarn are needed for each scarf.

Therefore, the equation to represent the total amount of yarn used for hats is:

h * 2 = 2h

And the equation to represent the total amount of yarn used for scarves is:

s * 1 = s

Now, we know that Elliott wants to use twice as much yarn for scarves as for hats. This can be represented as:

s = 2h

Finally, we know that Elliott wants to make a total of 202020 items. This can be represented as:

h + s = 202020

Combining all of the equations, we get:

[tex]\begin{cases} 2h = 2h \\ s = 2h \\h + s = 202020 \end{cases}[/tex]

Therefore, the system of equations that represents Elliott's situation is:

[tex]\begin{cases} 2h = 2h \\ s = 2h \\h + s = 202020 \end{cases}[/tex]

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Using a Venn diagram we find that there are 400 people who have a TV and a pet but not a car.

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

Given, Total of 6500 people, in which,

5100 had car

5420 had a television set

4800 had a TV and a car

1500 had a TV and a pet

1250 had a car and a Pet

1100 had a TV, a car and a pet

Therefore, no of people having a TV and a pet but not car

= n(TV & Pet)-n(TV, car & pet)

= 1500 - 1100

= 400

Hence, there are 400 people who have a TV and a pet but not a car.

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Three circles of radius s are drawn in the first quadrant of the xy-plane.

[tex]$r/s$\\[/tex] =9/1 =9

Set [tex]$s$[/tex] =1 so that we only have to find [tex]$r$[/tex].

Draw the segment between the center of the third circle and the large circle; this has length [tex]$r+1$[/tex]. We then draw the radius of the large circle that is perpendicular to the x-axis, and draw the perpendicular from this radius to the center of the third circle.

This gives us a right triangle with legs [tex]$r-3,r-1$[/tex]and hypotenuse [tex]$r+1$.[/tex]

The Pythagorean Theorem yields:

[tex]$(r-3)^2 + (r-1)^2 = (r+1)^2$$r^2 - 10r + 9 = 0$$r = 1, 9$Quite obviously $r > 1$, so $r = 9 \boxed{(D)}$.[/tex]

Three circles of radius s are drawn in the first quadrant of the x y -plane.

[tex]$r/s$\\[/tex] =9/1 =9

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No, the flag pole does not form a 90° angle with the ground.

We can use the Pythagorean theorem to find the length of the flag pole, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).

Let x be the length of the flag pole. Then, we have:

x² = (20 - x)² + 28.9²

Expanding and solving for x, we get x = 30.8.

Therefore, the length of the flag pole is 30.8 feet, which is greater than the height of 21 feet. This means that the angle between the flag pole and the ground is not 90°, but rather less than 90°.

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Answer:

w = 3

v = 8

Step-by-step explanation:

v + w = 11 can be written

v = 11-w  substitute this for v

2v - w = 16

2(11 -w) - w = 16   Distribute the 2

22 - 2w = 16  Subtract 22 from both sides

22 - 22 -2w = 16 - 22

-2w = -6  Divide both sides by -2

[tex]\frac{-2w}{-2}[/tex] = [tex]\frac{-6}{-2}[/tex]

w = 3

v = 11 - w

v = 11 -3

v =8

Check:

v + w = 11

8 + 3 = 11

11 = 11   Checks

2v - w = 16

2(8) - 3 = 16

19 - 3 = 16

16 = 16  checks

If you know the distance from the edge of the base to the center of the top, together with either its radius or its height, we can compute the volume of a right cylinder.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Note that h refers to half of the total height of the cylinder. I chose to use

h instead of h/2 to simplify things later on.

To find the volume of our cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;

V = pi * (radius of cylinder)² (height of cylinder)

V = pi(r² - h²) 2h

V = 2pi h(r² - h²)

This is our volume function. Next, we take the derivative of the volume function and set it equal to zero. If we move the h inside the parenthesis, we only need to use the power rule to get the derivative.

d/dxV(h) = 2pi(r² -3 h²) = 0

The 2π divides out and we are left with;

r² − 3h²=0

After some rearranging;

h² = r²/3

Take the square root of both sides.

h = r/√3

That is how we can calculate  the volume of a right cylinder, if you know the distance from the edge of the base to the center of the top along with either its radius or its height.

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Answer:

0.81

Step-by-step explanation:

The value of the line integral ∫Cxe^{yz}ds is approximately  8.645×10⁻⁵.

Given the line integral ∫Cxe^{yz}ds, where C is the curve r(t) = (t, 2t, -4t) for 1 ≤ t ≤ 2.

To convert this line integral to an ordinary integral with respect to the parameter, we need to express the integrand xe^{yz} in terms of the parameter t. We can do this by substituting r(t) into the integrand, giving us

te^{(2t)(-4t)}

= te^{-8t²}

Next, we can use the change of variable formula: ∫Cxe^{yz}ds = ∫[1,2]xe^{yz}||r'(t)||dt

We know that r'(t) = (1, 2, -4), so

||r'(t)|| = √(1² + 2² + (-4)²)

= √(17)

So the new integral becomes ∫[1,2] √(17)te^{-8t²} dt

On calculating ∫[1,2] √(17)te^{-8t²} dt ≈ 8.645×10⁻⁵

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Answer:

H(x) = (x - 5) * (1 - 0.25) = x - 5 - 0.25x = 0.75x - 5

Answer:

The function H(x) that represents how much you would pay if you use the mall coupon followed by applying the discount from the store would be:

H(x) = (x - 5) * 0.75

Step-by-step explanation:

First, we apply the mall coupon by subtracting $5 from the original cost of the jeans represented by x. This gives us the function f(x) = x - 5.

Next, we apply the store discount of 25% by multiplying the result of f(x) by 0.75. This is because 25% expressed as a decimal is 0.25, and to apply a discount, we multiply by the decimal form of the percentage (1 - decimal form).

So, the final function H(x) represents the cost of the jeans after both the mall coupon and store discount have been applied, and is equal to (x - 5) * 0.75.