The table represents a quadratic function C(t).


t C(t)
2 4
3 1
4 0
5 1
6 4

What is the equation of C(t)?
C(t) = −(x − 4)2
C(t) = (x − 4)2
C(t) = −x2 + 4
C(t) = x2 + 4

Answer:

work output = 40 N*m

Work input = 60 N*m

Efficiency = 66.67%

Step-by-step explanation:

I did this on a paper so Im sorry but it's to complicated to explain the work proof on the computer. I dont want to type all that equation stuff but thats the answer.

One significant change was the implementation of the New York State Tenement House Act of 1901, which required new tenement buildings to have adequate ventilation and light, indoor plumbing, and fire escapes.

During the late 19th and early 20th centuries, tenement housing in urban areas was characterized by overcrowding, poor sanitation, and inadequate ventilation.

These conditions led to high rates of disease and mortality among the working-class population that lived in them. To address these issues, the New York City Health Department instituted a series of reforms that required tenement buildings to meet certain design and construction standards.

It also mandated minimum room sizes and set limits on the number of people who could occupy a single room.

These changes helped to improve the living conditions in the worst tenements, reducing the spread of disease and improving the overall health of the city's working-class population.

While tenement housing remained a significant problem in urban areas for many years, the reforms instituted by the Health Department represented an important step towards improving the quality of life for those who lived in these buildings.

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1. Using the mathematical operations of addition and multiplication, the number of polka dots that are in Polly's room is 130.

2. An expression representing the situation and solution is x + 2y + 4z + 15.

An expression is a mathematical statement combining variables, constants, numbers, and values with mathematical operands.

The mathematical operands for performing mathematical operations include addition (+), subtraction (-), multiplication (x), and division (÷).

The number of polka dots on the bedspread, x = 25

The number of polka dots on two pillows, 2y = 10 (5 x 2)

The number of polka dots on 4 sets of curtains, 4z = 80 (4 x 20)

The number of polka dots on 3 rugs = 15

The total number of polka dots in Polly's room = 130

Let x = 25, y = 5, and z = 20

x + 2y + 4z + 15

x + 2y + 4z + 15

= 25 + 2(5) + 4(20) + 15

= 25 + 10 + 80 + 15

= 130

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The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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Answer:

7

Step-by-step explanation:

given a polynomial divide by (x - a) then the remainder is f(a)

here f(x) is divided by (x - 5) , so remainder is

f(5) = 2(5)³ - 12(5)² + 11(5) + 2

     = 2(125) - 12(25) + 55 + 2

     = 250 - 300 + 57

     = - 50 + 57

    = 7

Answer:

The y-intercept is 2 and the slope is 1/2. So the equation is y = 1/2x + 2

Step-by-step explanation:

The y-intercept is where the line starts on the y-axis. For the slope to the next point on the line you have to move 2 units to the right and 1 unit up. When writing the slope as a fraction, you always put how far you move up or down above how far you move to the right or left.

Answer:

A. Alternate Interior

Step-by-step explanation:

A. Alternate interior

Step-by-step explanation:

Angles a and b are alternate interior angles,

Alternate interior angles are equal.

Also,

a = b

Answer:

the bin 60-69 contain the most data values

Answer:

third option is the right one

Step-by-step explanation:

Answer:

i think its 6

Step-by-step explanation:

The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The dimension of the rectangular prism will be 3 units long, 5 units wide, and 1 unit high. Then the diagonal of the prism is given as,

D² = 3² + 5² + 1²

Simplify the equation, then we have

D² = 3² + 5² + 1²

D² = 9 + 25 + 1

D² = 35

D = √35 units

The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.

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4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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Answer:

= $0.90 per bottle

Step-by-step explanation:

6 bottles of different milks cost $5.40 in all. calculate the average price of a bottle (in $/ unit):

to find  $/unit:

= $/number of bottles

= 5.40/6

= $0.90 per bottle

Answer:

D. (4,4), (8,8), (-8,4)

Step-by-step explanation:

We have A (2,2), B(4,4) and C (-4,2)

Dilation by factor of 2: (x,y) => (2x,2y)

A (2,2) => A'(4,4)

B(4,4) => B'(8,4)

C (-4,2) => C'(-8,4)

given information are :- test mean () = 25.5 populace sd () = 5.3 example size (n) = 360 a).z critical value for 95% confidence level,

both followed tests be:- the 95% confidence interval for the mean load of every one of the one-year-old child young men in the US.

To get a 95% confidence interval, we should incorporate the focal 90% of the probability of the normal distribution. On the off chance that we incorporate the focal 90%, we leave out a sum of α = 10% in the two tails, or 5% in each tail, of the normal distribution.

To catch the focal 95%, we should go out 1.645 "standard deviations" on one or the other side of the determined example mean. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the middle, an area of 0.05 in the extreme left tail, and an area of 0.05 in the extreme right tail.

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The complete question is:

According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.

a. Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the United States

b. Should this confidence interval be used to estimate the mean weight of all one-year old babies in the United States? Explain.

c. Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is less than 28 pounds?

Answer:

4.10526315789

Step-by-step explanation:

Answer: 4.10526315789

Step-by-step explanation:

Answer:

1. Since the angles on the both sides are the same

5x = 100

x = 20

The mistake is that it is absolutely unnecessary to use 180.

2. It is a right angle, which means it would be 90 degrees instead of 180.

3x + 39 = 90

3x + 39 - 39 = 90 - 39

3x = 51

3x = 17

3. The process is wrong

It should be

6x + 2x + 8 = 180

8x + 8 = 180

8x = 172

x = 21.5

Answer:

1) Mistake is that vertical angles are congruent and equal meaning the product of 5x should be equal to the other side being 100. Answer is x=20

2) Mistake is that the angle's measure should've added up to 90. Answer is x=17

3) The math is done incorrectly with the first step as the coefficients can't be added with constants. Answer is x=21.5

Step-by-step explanation:

The following image is written proof

Answer:

\(\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}\)

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)

Answer:

1. x=0,y=-1

2. x=1 y=-4

3. x=2 y=-5

4. x=3 y=-4

5. x=4 y=-1

Step-by-step explanation:

\(y=x^{2} -4x-1\)

insert x

0

1

2

3

4

The value of the exponent (2/5)^3 is \(\frac{8}{125}\)

In the above question, it is given that

(2/5)^3

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2^3) signifies 2 x 2 x 2 = 8.

We need to solve it and then find the value of the exponent

(2/5)^3

= \(\frac{2}{5}\) x \(\frac{2}{5}\) x \(\frac{2}{5}\)

= \(\frac{2 . 2. 2}{5 . 5 . 5}\)

= \(\frac{8}{125}\)

Therefore the value of the exponent (2/5)^3 is \(\frac{8}{125}\)

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Answer:

The correct equation would be:

\(x=\frac{-3±\sqrt{3^{2}-4(-2)}}{2(-2)}\)

-Therefore, the correct option is D

Answer:

d

Step-by-step explanation:

Question Completion

Answer:

\((a)120^\circ\\(b)60^\circ\)

Step-by-step explanation:

In the diagram BC(Main Street) is parallel to AD(Willow Lane)

Therefore, ABCD is a Trapezoid.

Since in a trapezoid, adjacent angles are supplementary

Therefore:

\(\angle C+ \angle D=180^\circ\\\angle C+ 60^\circ=180^\circ\\\angle C=180^\circ- 60^\circ\\\angle C=120^\circ\)

Since \(AB \cong CD\), ABCD is an Isosceles Trapezoid.

In an Isosceles trapezoid, the base angles are congruent:  

Therefore:\(\angle A \cong \angle D$ and \angle B \cong \angle C\)

Therefore:

\(\angle A \cong \angle D=60^\circ\\\angle B \cong \angle C=120^\circ\)

(a)

The angle between Main Street and the west path is \(\angle CBA = 120^\circ\)

(b)

The angle between the west path and Willow Lane is \(\angle BAD =60^\circ\)

Answer:

$28.80

Step-by-step explanation:

36 * 80%

Answer:

The dilation factor of the width is 3/4

The dilation factor of the length is 10/13

The standard court and the modified court are not similar

Step-by-step explanation:

The given dimension of a tennis courts are given as follows;

The width of the standard tennis court = 36 ft.

The length of the standard tennis court = 78 ft.

The height of the  net of the standard tennis court = 3 ft.

The width of the modified tennis court = 27 ft.

The length of the modified tennis court = 60 ft.

The height of the  net of the standard tennis court = 3 ft.

The dilation factor of the width = (Modified court width)/(Standard court width)

∴ The dilation factor of the width = (27 ft.)/(36 ft.) = 3/4

Therefore, the width of the modified court = 3/4 × The width of the standard court

∴ The dilation factor of the length = (60 ft.)/(78 ft.) = 10/13

Therefore, the length of the modified court = 10/13 × The length of the standard court

The dilation factor for the width is different from the dilation factor for the length and the net of both courts are of equal dimension, therefore, based on similarity theorem, both courts are not similar.

Answer:

  at x=0 (the origin)

Step-by-step explanation:

The equation for a proportional relationship is ...

  y = kx

The equation of a straight line is ...

  y = kx +b . . . . . for some y-intercept b

Comparing the proportional relation to the relation for a general line, we see that b=0 in the proportional relation. That is, the y-intercept is at y=0, the origin of the Cartesian coordinate plane.

The graph crosses the x-axis at (0, 0), or x=0.

__

Additional comment

In y=kx, the value k is called "the constant of proportionality." It is also the slope of the line on a graph.

In the usual representation of the slope-intercept equation of a line, y=mx+b, the slope of the line is represented by 'm'. In the above, we used 'k' for that purpose, to facilitate comparing the equations.

Answer:

67 degrees

Step-by-step explanation:

Answer: 67

Step-by-step explanation: there all parallel to one another right and y and z are right beside each other therefore the same distance from M

The value of the expression is the same as the second option: !a || (b & !c).

Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.

The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:

!(a & !(b & !c)) = !a || (b & !c)

Therefore, the value of the expression is the same as the second option: !a || (b & !c).

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Answer:

Unknown, Solve for x or y?

Step-by-step explanation:

You need to elaborate on your answer... sorry.

In the meantime, here is Microsoft Math Solver, With your equations:

https://mathsolver.microsoft.com/en/solve-problem/x-y%20%3D%20%203

You can use this tool next time :)

Have a great day,

Nate

Answer:

Step-by-step explanation:

To find the total cost and revenue of your business, we can set up a system of equations based on the given information.

Let's assume the number of goats you sell is 'x.'

The cost equation can be represented as follows:

Cost = Cost per goat + Cost of disbudding and vaccines

Cost = (275 * x) + (150 * x)

The revenue equation can be represented as follows:

Revenue = Selling price per goat * Number of goats sold

Revenue = Selling price per goat * x

Now, to find the total cost and revenue, we need to know the selling price per goat. If you provide that information, I can help you calculate the total cost and revenue using the system of equations.

Answer:

Let's denote the number of goats as x. We know that you sold 15 goats, so x = 15.

The cost for each goat is made up of two parts: the initial cost of $275 and the cost for disbudding and vaccines, which is $150. So the total cost for each goat is $275 + $150 = $425.

Hence, the total cost for all the goats is $425 * x.

The revenue from selling each goat is $275, so the total revenue from selling all the goats is $275 * x.

We can write these as two equations:

1. Total Cost (C) = 425x

2. Total Revenue (R) = 275x

Now we can substitute x = 15 into these equations to find the total cost and revenue.

1. C = 425 * 15 = $6375

2. R = 275 * 15 = $4125

So, the total cost of your business is $6375, and the total revenue is $4125.

Answer:

Réponse :Explications étape par étapea) Le vecteur AC(xc-xa;yc-ya)vecteur AC(-6;-3

Step-by-step explanation:

Les coordonnées d'un vecteur dans un r.o.n. décrivent le déplacement qu'il représente. Ainsi, un déplacement de « 3 ...

Answer:

Step-by-step explanation:

44.5

Answer:

42 units²

Step-by-step explanation:

A = \(\frac{(1+6)}{2}\) (12) = 42 units²