Use the given information to prove that ∠QPR ≅ ∠SPR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ∠QPR ≅ ∠SPR

The equation has one repeated rational number solution. thus Option C is correct.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given equation is the quadratic equation:

[tex]5x^2-x-3=0[/tex]

It is required to determine the number and type of solutions.

Noted that If the discriminant equals zero, the equation has one repeated rational number solution.

If the discriminant is positive, then the equation has two real solutions.

If the discriminant is negative, then the equation has two imaginary solutions.

If the discriminant is a perfect square, then then the equation has two real rational number solutions, it has two irrational number solutions.

Calculate the discriminant of the equation [tex]5x^2-x-3=0[/tex] by substituting a= 5, b=-1  and c= 3  into the discriminant formula:

Since the discriminant equals zero, it follows that the equation has one repeated rational number solution.

The equation has one repeated rational number solution.

Option C is correct.

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Answer:

The probability that all five lines will be in use when a customer calls customer service is 1/7776.

What is probability?

The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.

Step-by-step explanation:

Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.

So, for all 5 lines to be engaged is

= 1/6 * 1/6 * 1/6 * 1/6 * 1/6

= [tex]\frac{1}{6} ^{5}[/tex]

= [tex]\frac{1}{7776}[/tex]

Therefore, the probability that all five lines are engaged is 1/7776.

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Answer:

75.4cm³

Step-by-step explanation:

height(h) = 8

2radius(diameter) = 6

radius = 6/2 = 3

volume of a cone = ⅓ πr²h

= ⅓ × 3.142 × 3² × 8

= ⅓ × 3.142 × 9 × 8

= 226.224/3

= 75.408

= 75.4cm³

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Answer: around 75.4

Step-by-step explanation:

Cone volume formula

V=[tex]\pi r^{2}[/tex][tex]\frac{h}{3}[/tex]

v= volume, r = radius, h=Height

find the radius of the base

r=6/2

r=3

V=[tex]\pi 3^{2} \frac{8}{3}[/tex]

v=75.4

From the given i) and v) are discrete metric and ii), iii), iv) and vi) are continuous metric.

What distinguishes discrete from continuous data?

i)  'X' :  is discrete   because Number of automobile accidents per year is countable  (45, 78, 90) and cannot be fraction (4.5)

ii) 'Y'   : is continuous   because it could take any time to play 18 holes of golf.  (15.10 min)

iii) 'M'  :   is continuous because volume measured can be in fraction. Like 15.6 liters of milk produced by a cow

iv) 'N'  :  is  discrete  because eggs are countable . no half eggs or broken eggs are counted.  example: 30 eggs per month by a hen.

v) 'P'   : is discrete because permits issued are in countable amount and cannot go beyond or like half permit.

vi) 'Q':    is continuous because weight can be less or more and can be in fraction. 20 AND HALF OR 56,6 Kg.

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a Markov chain is the probability defined by the below transition matrix. [ 1/3 2/3 1/5 4/5] has the steady state C. (10/13 3/13]

The steady state of a Markov chain is the probability distribution of possible states of the system. In this case, the steady state from the transition matrix ( Matrix can also be used to represent relationships between different variables.It is commonly used in mathematics, science and engineering to represent a variety of data. ) can be found by solving the system of equations:

P(X0) = P(X0) * 1/3 + P(X1) * 2/3

P(X1) = P(X0) * 1/5 + P(X1) * 4/5

Solving this system of equations yields the steady state of (10/13, 3/13).

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What is a equation in math?

Image result for What is equation?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

What is a equation in math?

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

given:

y=7x-2

first, (3, 15)

15 = 7*3-2 = 21-2 = 19

So, (3, 15) is not the solution.

Second, (-1,-10)

-10 = 7* (-1) -2

-10 = -9

Also, (-1,-10) is not the solution.

Hence, there is no solution for y=7x-2

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Answer:

Step-by-step explanation:

 7 49999977/50000000 is gallons to pints. multiply that number by 6, which is 47 24999931/25000000.

Step-by-step explanation:

32 / 2 using long division

y = 3x + 5 is a linear relationship with a slope of 3.

A straight line is formed on the graph by the equation y=2x+1, which is a linear equation. The value of y eventually rises by twice the value of x + 1. This happens when the value of x grows.

A linear graph is one that displays a single straight line for each given relation. A straight line is what the word "linear" denotes. A straight line graph linking points displayed on x and y coordinates is known as a linear graph.

A linear non - proportional relationship could be written with as a slope - intercept with a non - zero intercept value. One such relationship with a slope of 3 can be expressed thus :

y = 3x + 5

Here, the linear relationship, has a slope value of 3 and an intercept value of 5. The function cannot be proportional due to the presence of a non-zero constant

Hence, Using a graphing calculator, the sketch of the linear relationship is attached.

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Answer:

9.3 × 10^7

Step-by-step explanation:

93000000 / 10000000 = 9.3

10000000 = 10^7

So scientific notation of 93000000 = 9.3 × 10^7

The ordered pair that lie on the graph as per the equation will be equal to (-2, -4). Hence, option B is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given information in the question,

The given equation is,

f(x) = 2(x + 4) - 8

Let's check as per the points given in the question,

A. (24, 1)

f(x) = 2(24 + 4) - 8

f(x) = 48

So, the supplied exponential function's graph does not contain the point (24, 1) mentioned.

B. (-2, -4)

f(x) = 2(-2 + 4) - 8

f(x) = 4 - 8

f(x) = -4

As a result, the points (-2, -4) are located on the graph of the supplied exponential function.

C. (2, 256)

f(x) = 2(2 + 4) - 8

f(x) = 4

So, the supplied exponential function's graph does not contain the point (2, 56) mentioned.

D. (8, 0)

f(x) = 2(8 + 4) - 8

f(x) = 16

So, the supplied exponential function's graph does not contain the point (8, 0) mentioned.

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Answer:

Statements:

- When (1, 2) is substituted into the second equation, the equation is true

- The ordered pain (1, 2) is a solution to the system of linear equations

- When (1, 2) is substituted into the first equation, the equation is true.

Step-by-step explanation:

Statement 1:

y= 7/2x - 3/2

2= 7/2 * 1 - 3/2

2= 7/2 -3/2

2=4/2

2=2

Statement 2:

y= -2x + 4

2= -2 ( 1 ) + 4

2= -2 + 4

2 = 2

Statement 6:

y= 7/2x - 3/2

2= 7/2 * 1 - 3/2

2= 7/2 -3/2

2=4/2

2=2

y= -2x + 4

2= -2 ( 1 ) + 4

2= -2 + 4

2 = 2

Answer:

point form (-3, -1)

equation form x=-3, y=-1

Step-by-step explanation:

Answer:

A. Yes, but only within the domain x ≥ 0

Step-by-s+tep explanation:

What you need to know to solve the question:

1. To find an inverse function (f⁻¹(x)) of f(x), rearrange the equation in terms of f(x), in other words, it should be in the form of x = ...

2. Rules of rearranging equations

3. The domain of √x is: x ≥ 0, since you cannot find the square root of a negative number (i.e. < 0)

Find the inverse function of F(x):

According to principles 1 and 2:

F(x) = √x - 6

F(x) + 6 = √x

(F(x) + 6)² = x

x = (F(x) + 6)²

So, the inverse function is:

F⁻¹(x) = (x + 6)²

And since:

G(x) = (x + 6)²

G(x) = F⁻¹(x)

Therefore, the answer is, also in light of principle 3:

A. Yes, but only within the domain x ≥ 0

Answer:

  0.8 mm

Step-by-step explanation:

You want a diameter that is half one that is 1.6 mm.

Half of 1.6 mm is ...

  0.5 × 1.6 = 0.8 . . . . mm

The cell diameter is 0.8 mm.

Answer:

15

Step-by-step explanation:

If f(x) = -3x + 4, then plugging in -5 for x gives f(-5) = -3(-5) + 4 = 15. Therefore, the correct answer is 15.

Answer:

length = 43 ft ; width = 19 ft

Step-by-step explanation:

perimeter/2 = 124/2 = 62 ft

l = 2w + 5

l + w = 62

2w+5 + w = 62

3w = 62 - 5

3w = 57

w = 57/3

w = 19 ft

l = 2 · 19 + 5

l = 38 + 5

l = 43 ft

Answer:

Graph attached below

Step-by-step explanation:

Answer:

[tex]y=x[/tex]

Step-by-step explanation:

[tex]2(-y+x)=0\\\\-y+x=0\\\\-y=-x\\\\y=x[/tex]

To solve the system of differential equations using Theorem 1, we first need to find the eigen values and eigen vectors of the matrix X'.

The characteristic equation is given by |X' - λI| = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues to be λ = -2, 0, 3, 5.

Next, we need to find the corresponding eigenvectors. For each eigenvalue, we solve the equation (X' - λI)v = 0 to find the eigenvector.

For λ = -2, the eigenvector is v = [-2 -2 -2 -2 -2 1 -2 -2 -2 -2 -2 1 -2 -2 -2 1]

For λ = 0, the eigenvector is v = [-4 1 -2 -2 4 -3 2 -2 1 -2 -5 0 1 0 4 -1]

For λ = 3, the eigenvector is v = [4 -2 -2 -2 -4 3 -2 -2 -1 -2 5 0 -1 0 -4 1]

For λ = 5, the eigenvector is v = [0 2 2 2 0 -1 2 2 2 2 0 -1 2 2 0 -1]

Using these eigen values and eigen vectors, we can use Theorem 1 to find the general solution to the system of differential equations:

X(t) = c1e^(-2t)v1 + c2e^(0t)v2 + c3e^(3t)v3 + c4e^(5t)v4

where c1, c2, c3, and c4 are constants.

To show that this solution solves the original system of differential equations, we substitute it into the given differential equation:

X'(t) = -2c1e^(-2t)v1 + 0c2e^(0t)v2 + 3c3e^(3t)v3 + 5c4e^(5t)v4

This simplifies to:

X'(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ]

which is equal to the given matrix X'(t). Therefore, the solution we have found does indeed solve the original system of differential equations.

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Answer:

The standard deviation is a measure of how much the values of a random variable tend to vary from the mean of the variable. In this case, the standard deviation of the random variable W is 3.5, which means that the values of W typically vary from the mean of 4 by about 3.5 attempted experiments. Therefore, the best interpretation of the standard deviation, in this case, is that values of W typically vary from 4 by about 3.5 attempted experiments, on average.

Therefore solution to this problem is  the given  statement is true .

The generalization of ordinary least squares and linear regression known as weighted least squares (WLS), sometimes known as weighted linear regression, incorporates knowledge of the variance of the observations into the regression. Generalized least squares is also a specialization of WLS.

Here,

the generalized least squares estimators for correcting heteroskedasticity are also called weighed least squares estimators.

Since they are also known as weighed least squares estimators, extended least squares estimators for correcting heteroskedasticity use least squares estimation.

Therefore , the above statement is true .

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Answer:

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

Step-by-step explanation:

5 up, 2 right

The  goalie saved 70% of the shots.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, a Goalie's saves (•) and goals scored against (x)

The number of save shot = 14

The number of goals scored against = 6

The total numbers of shots = 20

A goalie's safe percentage is calculated by dividing the number of saves by the total number of shots on goal = 14/20x100 = 70%

Hence, The  goalie saved 70% of the shots.

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m and n are integers such that mn is even, but m and n are both odd. This contradicts the assumption that mn is even, so we must conclude that either m is even or n is even.

Proof:

Assume m and n are integers such that mn is even and m is not even and n is not even.

However, since the product of two odd integers is always odd, this contradicts the assumption that mn is even.

Therefore, it must be true that m is even or n is even.

We assume that m and n are integers such that mn is even, but m and n are both odd. This contradicts the assumption that mn is even, so we must conclude that either m is even or n is even. This is a proof by contraposition, meaning that we have assumed the opposite of what we want to prove and showed that this is not true. This in turn implies that the original statement is true, and so we have proven that if mn is even, then m is even or n is even.

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Answer: 23

Step-by-step explanation:

-42+65

or 65-42

= 23

If the profit function is P(x) = 13x - 741 then the units that must be produced to break even is 57 units.

What is a profit function?

The difference between income and costs is referred to as profit. A relationship that depicts the difference created by subtracting the cost function from the revenue function is called a profit function. The ideal pairing of revenues and expenses to generate the greatest possible profit can be seen on the graph of a profit function.

Here, we have

Given

R(x) = 16x (The revenue function)

C(x) = 3x + 741 (The cost function)

Profit = Revenue - Cost

P(x) = 16x - 3x - 741

P(x) = 13x - 741

Hence, the profit function P(x) is  13x - 741.

For the company to break even, R(x) = C(x)

16x = 3x + 741

13x = 741

x = 57

Hence, if the profit function is P(x) = 13x - 741 then the units that must be produced to break even is 57 units.

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One glass of milk and one snacks bar have a total of 23 carbs.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two glass of milk and Three snacks bar have a total of 56 carbs.

And, Four glass of milk and two snacks bar have a total of 72 carbs.

Now,

Let the amount of milk = x

And, The amount of snacks bar = y

So, We can formulate;

Two glass of milk and Three snacks bar have a total of 56 carbs.

⇒ 2x + 3y = 56 ..(i)

And, Four glass of milk and two snacks bar have a total of 72 carbs.

⇒ 4x + 2y = 72

⇒ 2x + y = 36

⇒ y = 36 - 2x   ..(ii)

Substitute above value in equation (i),

⇒ 2x + 3y = 56

⇒ 2x + 3 (36 - 2x) = 56

⇒ 2x + 108 - 6x = 56

⇒ 108 - 56 = 4x

⇒ 4x = 52

⇒  x = 13

And, from (ii);

⇒ y = 36 - 2x  

⇒ y = 36 - 2 × 13

⇒ y = 36 - 26

⇒ y = 10

Thus, One glass of milk and one snacks bar have a total of carbs

= 13 + 10

= 23

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Answer:

Its slope-intercept form

Step-by-step explanation:

The "Y" is the output the "M" is the slope, the "X" is the unknown input and the "B" equals the Y-intercept