For f, g € L’[a,b], prove the Cauchy-Schwarz inequality |(f,g)| = ||$||||$||. = Hint: Define a function Q(t) = (f + tg, f + tg) for any real number t. Use the rules of inner product to expand this expression and obtain a quadratic polynomial in t; because Q(t) > 0 (why?), the quadratic polynomial can have at most one real root. Examine the discriminant of the polynomial.

To solve the first equation, f(x) = x^2 - 7x^2 + 2x + 9 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, the equation is x^2 - 7x^2 + 2x + 9 = 0, so a = 1, b = -7, and c = 2.

Plugging in these values into the quadratic formula, we have:

x = (-(-7) ± √((-7)^2 - 4(1)(2))) / (2(1))

Simplifying further:

x = (7 ± √(49 - 8)) / 2

x = (7 ± √41) / 2

Now, let's approximate the roots up to 4 significant digits:

x ≈ (7 + √41) / 2 ≈ 6.7053

x ≈ (7 - √41) / 2 ≈ 1.3259

Therefore, the roots of the equation f(x) = 0 are approximately x = 6.7053 and x = 1.3259.

For the second equation, x^2 + 2x + 4 = 0, we can also use the quadratic formula. In this case, a = 1, b = 2, and c = 4.

Applying the quadratic formula:

x = (-2 ± √(2^2 - 4(1)(4))) / (2(1))

x = (-2 ± √(4 - 16)) / 2

x = (-2 ± √(-12)) / 2

Since the term under the square root is negative, we have complex roots. Simplifying further:

x = (-2 ± √(12)i) / 2

x = -1 ± √3i

Therefore, the roots of the equation x^2 + 2x + 4 = 0 are approximately x = -1 + √3i and x = -1 - √3i.

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On solving the provided question, we cans ay that Here, 16.7 is a sample constant value.therefore it is a statistic

The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.

Statistic.        

Here, 16.7 is a sample constant value.therefore it is a statistic

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Answer:

1173

Step-by-step explanation:

Solved on delta

Answer: 6

Step-by-step explanation: R=2 and S=1, and 2/1 is 2. Then it is simple math,

hope this helps

Answer:

0

Step-by-step explanation:

625 / 25 = 25

55g + 25 = 25

55g = 25 - 25

55g = 0

g = 0/55

g = 0

Answer:

\( \sf \: g = 0\)

Step-by-step explanation:

Given equation,

→ 55g + 25 = 625 ÷ 25

Now the value of g will be,

→ 55g + 25 = 625 ÷ 25

→ 55g + 25 = 25

→ 55g = 25 - 25

→ g = 0 ÷ 55

→ [ g = 0 ]

Hence, the value of g is 0.

Answer:

4 weeks 2 days

Answer:

4 weeks 2 days

Step-by-step explanation:

First do 30 divided by 7 to get the number of weeks.

Which is 4 weeks with a remainder of 2.

7 ounces per week is 1 ounce per day.

So to get 2 more ounces that would be 2 days.

Therefore the answer is 4 weeks and 2 days.

Answer:

\(\displaystyle m = \frac{22}{9}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 3)

Point (10, 25)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

c

Step-by-step explanation:

Answer:

8+(X×0.50)=y

Step-by-step explanation:

We know it costs 0.50 for extra toppings, so X=the amount of toppings and we multiple that by the cost of the toppings. So lets pretend you're getting 3 toppings. 8+(3x0.50)=9.50

Answer:-8,4 is ur answer

The balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

Let t be the number of seconds since the balloons took off, and Hp(t) and Hg(t) be the altitude of the purple and gold balloons respectively at time t.

We know that:

Hp(t) = 0 + 2.5t (the purple balloon starts at sea level and climbs at a rate of 2.5 m/s)

Hg(t) = 1515 + 222t (the gold balloon starts 1515 m above sea level and climbs at a rate of 2*22 m/s)

We want to find the time t when the balloons are at the same altitude, so we can set Hp(t) = Hg(t) and solve for t:

0 + 2.5t = 1515 + 222t

2.5t = 1515 + 222t

2.5t - 222t = 1515

0.5t = 1515 - 1515

t = 0

So the balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

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Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.

Given monthly income of Ron is $3,142.23

Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) = 0.055/12

time period = 40 years = 480 months

Principal amount = $314.223

Future value = \(P(\frac{(1+r)^{n}-1 }{r} )\)

Substitute, we get,

= 3142.23 \(.10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }\)

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

P = (A.i/2)/(1-(1+i/12)⁻ⁿ)

Putting values, we get,

P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰

P = $3763.25

He will receive a monthly income of $3763.25.

But  given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.

So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

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Answer:

x = 5/3

Step-by-step explanation:

-3x+5

-5= -3x

-5/-3 = 5/3

Normal mean arterial pressure is typically around 90-100 mmHg.

Mean arterial pressure (MAP) is an important measure of blood pressure and is calculated as the average pressure in the arteries over one cardiac cycle.

Normal MAP is typically considered to be around 90-100 mmHg (millimeters of mercury). This measurement is important in assessing the amount of blood flow and oxygen being delivered to the body's organs and tissues.

Abnormal MAP readings, such as values below 60 mmHg or above 110 mmHg, can indicate health problems such as low blood pressure or high blood pressure, respectively.

MAP is typically measured using a blood pressure cuff and a device called a sphygmomanometer. It's important to have regular check-ups with a doctor to monitor MAP and ensure it remains within a healthy range.

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Answer: B

Step-by-step explanation

p^2+q, use p=5 and q= -3

All you have to do for this problem is fill in for p and q.

5^2+-3 = 22

Answer:

B) 22

Step-by-step explanation:

Plugging in the values we can solve the equation:

(5)^2 + (-3)

25 + (-3)  -- Evatuate exponents first

25 - 3 = 22 -- Simplify to receive answer

Answer:

let first equation be  y=x^2-14x+23

second equation be y=-3x+5

now substitute the vale of y in equation second

y=-3x+5

x^2-14x+23=-3x+5

x^2-14x+3x=5-23

x^2-11x=-18

x^2-11x+18=0

x^2-(9+2)x+18=0

x^2-9x-2x+18=0

x(x-9)-2(x-9)=0

(x-2)(x-9)=0

either x-2=0                                        Or, x-9=0

x-2=0

x=0+2

x=2

x-9=0

x=0+9

x=9

therefore x=2,9

Step-by-step explanation:

-

Answer:

(2, - 1 ) and (9, - 22 )

Step-by-step explanation:

Given the 2 equations

y = x² - 14x + 23 → (1)

y = - 3x + 5 → (2)

Substitute y = x² - 14x + 23 into (2)

x² - 14x + 23 = - 3x + 5 ( subtract - 3x + 5 from both sides )

x² - 11x + 18 = 0 ← in standard form

(x - 2)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 9 = 0 ⇒ x = 9

Substitute these values into (2) for corresponding values of y

x = 2 : y = - 3(2) + 5 = - 6 + 5 = - 1 ⇒ (2, - 1 )

x = 9 : y = - 3(9) + 5 = - 27 + 5 = - 22 ⇒ (9, - 22 )

Answer:

its B: Y= x + 6

Step-by-step explanation:

hope this helps

After the calculation of the expression (32+4×(16x)-2³) ÷ (6×4+3+2) × (28+7+6+3)×2 ÷ (20(5×2/5+3x²)4 ÷ 2×(6+2+8)-4 ÷ (21+3+(8-2+2)))

We concluded that the answer will be (80x+30) ÷ 58 × (11+33x²)

Expressions can be written in different forms such as numerical, algebraic, or geometric expressions. Examples of numerical expressions include 5 + 2, 3 × 8, and 10 ÷ 2. Algebraic expressions involve variables and algebraic operations, such as x + 3, 2y - 5, or 4a² + b. Geometric expressions involve formulas and measurements for calculating properties of shapes, such as the area or perimeter of a rectangle.

Expressions can be simplified by performing arithmetic or algebraic operations to reduce them to their simplest form. For example, the expression 3x + 2x can be simplified to 5x by combining the like terms.

Without an equal sign or any other relation, it is not possible to find the value of x. So according to my expression we can solve it as:

(32+4×(16x)-2³) ÷ (6×4+3+2) × (28+7+6+3)×2 ÷ (20(5×2/5+3x²)4 ÷ 2×(6+2+8)-4 ÷ (21+3+(8-2+2)))

We can simplify each of the terms step by step:

(32+4×(16x)-2³) ÷ (6×4+3+2) × (28+7+6+3)×2 ÷ (20(5×2/5+3x²)4 ÷ 2×(6+2+8)-4 ÷ (21+3+(8-2+2)))

= (32+4×(16x)-8) ÷ (6×4+5) × (44) ÷ (20(1+3x²) ÷ 2×16 ÷ 30)

= (32+64x-8) ÷ (29) × (44) ÷ (20+60x²) ÷ (8/15)

= (64x+24) ÷ (29) × (44) ÷ (20+60x²) × 15/8

= (16x+6) ÷ (29/2) × (11/5+33/5x²)

= (16x+6) ÷ (58/5) × (11+33x²)

= (80x+30) ÷ 58 × (11+33x²)

Therefore, the solution is:

(80x+30) ÷ 58 × (11+33x²)

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(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.

Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.

To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:

Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.

Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.

Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.

Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.

Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.

Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.

Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.

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Answer:

10x+12 is the answer in my calculation.

Option C, Fruit- Shade, is the shortest route between the pair of nodes, with a distance of 165'.

To explain why the route Fruit-Shade is the shortest, we need to consider the distances between the nodes and compare them.

Option A, Fruit - Hay, has a distance of 160'. This means that the horse would have to travel 160' to go from Fruit to Hay.

Option B, Grass - Pond, has a distance of 190'. This means the horse would have to travel 190' to go from Grass to Pond.

Option C, Fruit - Shade, has a distance of 165'. This means the horse would have to travel 165' to go from Fruit to Shade.

Option D, Barn-Pond, has a distance of 200'. This means the horse would have to travel 200' to go from Barn to Pond.

By comparing the distances, we can see that the route with the shortest distance is Fruit-Shade, with a distance of 165'. Therefore, option C is the correct answer.

It's important to note that this determination is based solely on the given distances and does not consider other factors such as terrain, obstacles, or any other constraints that may affect the actual route taken by the horse.

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The equation y + 2 = -2(x + 6) can be rewritten in the Ax + By - C form as -2x + y + 14 = 0.

To rewrite the equation in Ax + By - C form, we need to simplify and rearrange the equation. Starting with the given equation y + 2 = -2(x + 6), we distribute the -2 to the terms inside the parentheses, resulting in y + 2 = -2x - 12.

Next, we rearrange the equation so that the x and y terms are on the left side and the constant term is on the right side. Moving the y term to the left side gives us y + 2 + 2x + 12 = 0.

Finally, we combine like terms to obtain -2x + y + 14 = 0. Now the equation is in the desired Ax + By - C form, where A = -2, B = 1, and C = 14. The coefficients A, B, and C are integers, as required.

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Answer:

albert 2500:3000 mark/÷100

25÷30 /÷5

5:6

their ratio is 5:6

Answer:

20 I think I don't really know or 0a

Step-by-step explanation:

Also it might be oc and all the things begging with o because it makes more sence lol

The hole will be of a radius of 7.63 inches when its perimeter is 48 inches.

The hole is in the form of a circle.

The perimeter of the circle = perimeter of the hole = 48 inches.

Let r be the radius of the vent,

The perimeter of the circle is known as the Circumference.

Circumference of the circle is given by \(2\pi r\)

So,

\(2\pi r = 48\\\\2*\frac{22}{7} *r =48\\\\r =\frac{48*7}{22*2} =7.63\)

The hole will be of a radius of 7.63 inches.

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(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

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Answer: 210 advanced tickets were sold. 130 same day tickets were sold.

Step-by-step explanation:

x= advanced tickets y=same day tickets

2x+3y=810 this equation represents the money

x+y=340 this equation represents the total number of tickets

x+y=340

-x     -x

y=-340-x             2x+3(340-x)=810               210+y=340

                           2x+1020-3x=810               -210     -210      

                           -x+1020=810                       y=130

                               -1020  -1020

                                 -x=-210

                                 -1     -1

                                  x=210              

a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.

If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.

b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.

c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.

All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.

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The triengle ABC and XZY are proved to be congruent by SAS.

Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.

By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)

Here in he given triangle,

BC=YZ

AC=XZ

∠ACB=∠XZY

By SAS ΔABC≅ΔXYZ

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