I'm not sure what theorem to use for this question

The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

Polynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.

ax^2+bx+c and;

mx^2+nx+p

Take the sum of the polynomials

P(x) =. ax^2+bx+c

f(x) = mx^2+nx+p

Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.

Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

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19 books can fit into a bookshelf that has a width of 19/4 feet

An equation is an expression that shows the relationship between two or more number and variables.

The bookshelf is 4 3/4 feet wide = 19/4 feet

1 ft = 12 in, hence:

19/4 feet = 19/4 feet * 12 in per feet = 57 inches

Number of books = 57 inches / 3 in = 19

19 books can fit into a bookshelf that has a width of 19/4 feet

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On the train, there are a total of 125 children.

Total number of passengers = 500

Out of 500 passengers, men =7/20

So, the number of men= 500* 7/20 = 175

Out of 500 passengers, women = 40%

So, the number of women passengers = 500*40/100 = 200

Therefore, the total number of men and women passengers= 175+200 = 375.

There are also children on the train. So, the rest number should be those children.

The rest number =children= 500- 375 = 125.

So, it is concluded from the above equation that there are 125 children on the train.

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4.440 minutes of the ride is spent higher than 37 meters above the ground.

We have to find the amount of time spent by the ride 37 meters above the ground.

We know that 37 meters above the ground is actually one meter above the center.

We can find the angle above the center as shown below:

arcsin(1/34) = 0.0294 radians

Now we have to find the angle of rotation:

The angle of rotation of the Ferris wheel above 37 meters = π - (2*0.0294)

= 3.1 radians

The angular velocity of the Ferris wheel = Angle covered/Time

= 2π/9 rad/min.

Therefore time spent above 37 meters = 3.1*9/2π

= 3.1*9/6.28319

= 4.440 minutes

Therefore, we have found that 4.440 minutes of the ride is spent higher than 37 meters above the ground.

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The outcome of the product is 4 + 2/24, so the correct option is B.

Here we want to solve:

(4 + 2/3)*(7/8)

Using the distributive property of the product we get:

4*(7/8) + (2/3)*(7/8)

28/8 + 14/24

Now we can multiply the first fraction by (3/3) (it does not change the fraction).

(3/3)*28/8 + 14/24

84/24 + 14/24 = 98/24  

Now we can rewrite it as:

98/24 = (96/24) + (2/24)  =4 + 2/24

Then the correct option is B.

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The distance travelled is 10 m

The velocity gained at the end of the time is 2 m/s

From the question, we are to determine distance travelled and the velocity gained

From one of the equations of motion for linear motion, we have that

S = ut + 1/2at²

Where S is the distance

u is the initial velocity

t is the time taken

and a is the acceleration

First, we will calculate the acceleration

Using the formula,

F = ma

Where F is the force

m is the mass

and a is the acceleration

∴ a = F/m

Where F is the force

and a is the acceleration

From the given information,

F = 50 N

m = 250 kg

Putting the parameters into the equation,

a =  50/250

a = 0.2 m/s²

Thus,

From the information,

u = 0 m/s (Since the object was initially at rest)

t = 10 s

S = 0(t) + 1/2(0.2)(10)²

S = 10 m

Hence, the distance travelled is 10 m

For the velocity

Using the formula,

v = u + at

Where v is the velocity

v = 0 + 0.2×10

v = 2 m/s

Hence, the velocity gained at the end of the time is 2 m/s

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Answer:

A. The Highest Points Of The Graph

Step-by-step explanation:

A nonperiodic function is one that generates a graph without a regular recurring pattern over a fixed time interval. A repeating section of a graph is called the period.

Answer:

m = [tex]\frac{1}{2}[/tex] , m = 5

Step-by-step explanation:

assuming you mean

2m² - 11m + 5 = 0

consider the product of the factors of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × 5 = 10 and sum = - 11

the factors are - 10 and - 1

use these factors to split the m- term

2m² - 10m - m + 5 = 0 ( factor the first/second and third/fourth terms )

2m(m - 5) - 1(m - 5) = 0 ← factor out (m - 5) from each term

(m - 5)(2m - 1) = 0 ← in factored form

equate each factor to zero and solve for m

2m - 1 = 0 ⇒ 2m = 1 ⇒ m = [tex]\frac{1}{2}[/tex]

m - 5 = 0 ⇒ m = 5

The area under the curve between the two values is (d) 0.0750

From the table, we have:

P(z = -0.45) = 0.3264

P(z = -0.67) = 0.2514

The area under the curve is calculated as:

Area = P(z = -0.45) - P(z = -0.67)

So, we have:

Area = 0.3264 - 0.2514

Evaluate the difference

Area = 0.0750

Hence, the area under the curve between the two values is (d) 0.0750

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Answer:

[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]

Step-by-step explanation:

Using trigonometric ratio cos.

Here,

[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]

Answer:

[tex]\sf 2^{(n+1)}[/tex]

Step-by-step explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

  [tex]\sf \boxed{\bf t_n=ar^{(n-1)}}[/tex]

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

    a = 4

    r = 8 ÷4 = 2

[tex]\sf t_n =4*2^{(n-1)}[/tex]

    [tex]\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n[/tex]

   [tex]\sf = 2^{(n+1)}[/tex]

The skydiver is falling at a speed of 212 miles per hour.

The speed of the skydiver is 212 mph.

What are Speed and Velocity?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, whereas velocity is a vector, speed is a scalar quantity.

Given:

If a skydiver jumps out of a plane and plummets to the ground while falling at 212 mph.

To Find:

Speed and acceleration of the skydiver.

Velocity is the speed with a direction, whereas speed is only a number with a speed unit at the end.

While velocity refers to the speed and direction of an object's movement, speed refers to the time rate at which an object moves along a path.

212 miles per hour is the descending velocity of the skydiver.

At 212 miles per hour, the skydiver is moving.

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The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

According to the statement

we have to show the square root function as a equation in the graphical representation.

So,

we know that the definition of a

Graph a diagram showing the relation between variable quantities, typically of two variables and it also show the relation between more than two variables.

Now, we know that the definition of Equation is a mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

And the equation obtained from the graph is a y=√x-2 by a some calculations in the graph.

So, The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

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Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The other parameters are given as follows:

[tex]\overline{x} = 12.3, \sigma = 1.5, n = 50[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95[/tex]

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65[/tex]

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The difference between two numbers are [tex]3[/tex] and numbers are [tex]x[/tex] and [tex]y[/tex] so the equation is [tex]x-y=3[/tex]

How to find the equation and what is the equation ?

equation, statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.

if the difference of two numbers are [tex]3[/tex]

And one number is [tex]x[/tex] and another is [tex]y[/tex]

So we write the equation with operation of subtraction

[tex]x-y=3[/tex]

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The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

The graph of the two functions alongside their equations are the given parameters of this question

The functions are given as:

f(x) = 5x - x^2

g(x) = 3x - 0.5x^2

When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value

In this case, it represents

f(x) = g(x)

Substitute the known values in the above equation

5x - x^2 = 3x - 0.5x^2

So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

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Answer:

D

Step-by-step explanation:

A' represents everything outside of the circle A

B represents the space within circle B

A' intersection B is everything not in A that is in B.

Answer:

Question 1) 2/3

Question 2) -3

Step-by-step explanation:

Question 1)

The formula of a slope is (increase in y)/(increase in x), so in the graph, all we need to do is find two precise points and look at the distance difference.

1. The two points that I've found were (0,3) and (3,5). The change in y is 3 --> 5, which is 2. The change in x is 0 --> 3, which is 3.

2. The slope will be 2/3.

Question 2)

In this question, we can consider n as x and f(n) as y.

1. The two points I chose were (4, -31) and (7,-40). The change in y is -31 --> -40, which is -9. The change in x is 4 --> 7, which is 3.

2. The slope will be -9/3.

3. -9/3 can be simplified to -3 since we can divide both the numerator and the denominator by 3.

4. The final slope will be -3.

If Angle A ≅ Angle T, then the triangles would be congruent by ASA

If Angle B ≅ Angle P, then the triangles would be congruent by AAS.

We are told that;

Sides AC and TQ are congruent.

Angles BCA and  PQT are congruent.

Thus, we can say that;

Side AC and side TQ are congruent.

Angle BCA and angle PQT are congruent too.

Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.

Lastly, if angle B were to be congruent to angle P,  it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.

The missing options are;

A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.

B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.

C) If all the angles are acute, then the triangles would be congruent.

D) If AngleC and AngleQ are right angles, then triangles would be congruent.

E) If BC ≅ PQ, then the triangles would be congruent by ASA.

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Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another

Let the side of a square be x.

So,

Area of square = [tex]x^{2}[/tex]

A =[tex]x^{2}[/tex]

Differentiating with respect to time we get,

dA/dt = 2x dx/dt

When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm

At x = 3cm and dx/dt = 5 cm/s (Given)

dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]

Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]

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Step-by-step explanation:

find the slope:

[tex]\frac{y2-y1}{x2-x1}=\frac{-4+2}{1+3} =\frac{-2}{4} =-\frac{1}{2}[/tex]

Now our equation looks like:

[tex]y=-\frac{1}{2} x+b[/tex]

To solve for b, plug in one of the coordinates

[tex]-4=-\frac{1}{2} (1)+b[/tex]

[tex]-4=-\frac{1}{2} +b[/tex]

[tex]b=-3.5[/tex]

Put our equation together to get y = -1/2x-3.5

The data of the customer responses would be classified as ordinal data.

Ordinal data is a category of categorical data that has a predetermined order or scale. Ordinal data, for instance, is said to have been gathered when a respondent rates their level of financial contentment on a scale from 1 to 10. There is no established scale for measuring the variance of each score in ordinal data.

Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. On an ordinal scale, these data are available. By having a ranking, the ordinal scale differs from the nominal scale.

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The area of the triangle pqr is 111.3 square units

The complete question is added as an attachment

The area is calculated as:

[tex]A= 0.5 ab\sin(C)[/tex]

So, we have:

[tex]A= 0.5 * 12 * 20 * \sin(68)[/tex]

Evaluate the product

A= 111.3

Hence, the area of the triangle pqr is 111.3 square units

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Given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.

The ratio of the shares of business partners Mr. Jake to Mr. Sebastian given to us is 3:2.

So we assume Mr. Jake's share of profit to be 3x, and Mr. Sebastian's share of profit to be 2x.

Thus, the total profit between them is 3x + 2x = 5x.

The total profit given is 24,000.

Thus, we get an equation:

5x = 24000,

or, x = 24000/5 = 4800.

Thus, the share of profit Mr. Jake receives is 3x = 3*4800 = 14400.

Thus, given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.

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Answer:

AC = 23

Step-by-step explanation:

Discussion

AB and AC start from the same point -- A.

That means that when speaking of tangents to a circle that AB = AC

Answer

AB = 23 in          Given

AC = 23              2 tangents to a circle starting from the same point are =

1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)

2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)

3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)

4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)

Using a trigonometric identity, the cosine of the angle is given as follows:

[tex]\cos{\theta} = \frac{60}{61}[/tex]

It is given by:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem, the sine is:

[tex]\sin{\theta} = \frac{11}{61}[/tex]

Then:

[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]

[tex]\cos^2{\theta} = 1 - \left(\frac{11}{61}\right)^2[/tex]

[tex]\cos^2{\theta} = \frac{3600}{3721}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{3600}{3721}}[/tex]

On quadrant I, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{60}{61}[/tex]

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The probability that a randomly grab 2 extra large jerseys is 18.3%.

Given that a box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys.

The number of jerseys in the box is 8+6+4=18

To find the probability of picking 2-extra large jerseys by finding the probability of 1 extra large and probability of 2 extra large.

The probability of picking 1 extra large jersey is

P₁=8/18

P₁=4/9

The probability of picking 2 extra large jerseys is remaining jerseys

P₂=7/17

The total probability of getting 2 extra large jerseys is

P=P₁×P₂

P=(4/9)×(7/17)

P=28/153

P=0.183

P=18.3%

Hence, the probability that randomly grab 2 extra-large jerseys when basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys is 18.3%.

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Step-by-step explanation:

10x2(x-2)2=100x2x2 2x2