Rectangles have the following properties:
(pick all that apply)
Multiple select question.

A)
Diagonals are congruent

B)
Opposite angles are congruent

C)
Adjacent sides are parallel

D)
All 4 angles are 90 degrees

E)
Opposite sides are congruent

F)
Consecutive angles add to 360 degrees

G)
Cannot be a parallelogram

Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.

A system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.

A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.

In this problem, we need to define our variables and the solve the equations.

Let;

x + 2y = 31 ...eq(i)

3x + y = 38 ...eq(ii)

Solving both equations

x = 9, y = 11

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The height of the house is 48 foot and it cast a 24 foot shadow

An equation shows the relationship between numbers and variables in an expression.

Two shapes are said to be similar if the ratio of their corresponding sides are in same proportion.

The garden shadow and house shadow are similar. An 6ft tall garden shed a 3-foot shadow and a house cast a 24-foot shadow.

Let x represent the height of the house, then:

6/3 = x/24

x = 6 * 24/3 = 48 ft

The height of the house is 48 foot

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Y=-1 is parallel to the x-axis. This is because the y-intercept of a line is the point at which it crosses the y-axis, and y=-1 is the y-intercept of the line y=x. Therefore, the line y=-1 is parallel to the x-axis.

To demonstrate this mathematically, we can use the equation for a line in slope-intercept form, which is y=mx+b. Here, m is the slope of the line, and b is the y-intercept. Since the slope of the line is not given, we can assume that it is 0, since the line is parallel to the x-axis. Therefore, the equation of the line is y=0x+b, which simplifies to y=b. Substituting the given y-intercept, y=-1, into the equation, we get y=-1. Therefore, the equation of the line is y=-1, which is parallel to the x-axis.

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Answer:

yess!

Step-by-step explanation:

CORRECT

Answer:

-8/3 is the slope of these two points.

Step-by-step explanation:

Answer:

The distance between the two points can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) = (-4, 8) and (x2, y2) = (4, 5)

So, d = √((4 - (-4))² + (5 - 8)²) = √((8)² + (-3)²) = √(64 + 9) = √73

Rounding to the nearest tenth, d = √73 ≈ 8.6

Suppose  x₁, x₂, ..., xₙ are iid random variables with uniform distribution between 0 and 1. The probability that its sum is less than 1 is 1/n!

Let x₁, x₂, ..., xₙ be independent identically distributed random variables with uniform distribution in the interval [0, 1].

Let's define the sum of those random variables as

Sₙ = x₁ + x₂ + ... + xₙ

For 0 ≤ t ≤ 1, the probability that the sum is less than t is:

P(Sₙ < t) = tⁿ/n!

Where:

n! = factorial of n

In the given problem, t = 1. Therefore,

P(Sₙ < 1) = 1ⁿ/n!

For example, if n = 4,

S = x₁ + x₂ + x3 + x₄

P(S < 1) = 1/4!

P(S < 1) = 1/(4×3×2) = 1/24

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The number of times that the sequence HH appears = 9/4

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

X follows a binomial distribution with a success probability.

p=1/4 and n=9 the number of trials.

To see this let X = HH appear in a flip coin of 10 tosses.

Clearly, as you said to get HH twice in a row has a probability equal to p=1/4.

So, you look at your problem from the point of view that HH is your successful outcome and the rest {HK, KH, KK} consists of the failure outcomes.

Now possible ways you have in order to get HH in 10 tosses = 9 ways in order to figure this out you look at the positions where the first H can appear in a sequence of HH.

It can appear in any of the first 9 positions. So, we end up with that X∼Binomial (9,1/4).

E[X]=np=9/4

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The probability that the number 75 ends up in the 45th position in the resulting permutation is 0.01.

To calculate this probability, we can use the concept of permutation. In a permutation of n distinct elements, the probability of any particular element ending up in a specific position is (1/n).

In this case, we have 100 distinct elements, and we want to find the probability that the number 75 ends up in the 45th position. So, the probability is (1/100) or 0.01.

Another way to think about it is that there are 100! (100 factorial) total possible permutations of the numbers 1 to 100. In order for 75 to be in the 45th position, the other 99 numbers can be arranged in 99! ways. Therefore, the probability of 75 being in the 45th position is (1/100!) * (99!) = 1/100 = 0.01.

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Cubic monomial describes the polynomial 5x3x4x+1.

The complete question is:

Which description is correct for the polynomial −5x3−4x+1?

A) quadratic trinomial

B) cubic binomial

C) quadratic binomial

D) cubic monomial

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(a) f(4) = -1, f(-6) = 1 and f(6) = 1

(b) x = 4 and -4, x = 0 and x = -7

(c) t = -8

(d) The set x = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

(a) The values of f(x) for the given values of x can be found from the graph by looking at the y values corresponding to the given x values.

f(4) = -1

f(-6) = 1

f(6) = 1

(b) By looking to the y values as the given numbers, we can find corresponding x values.

f(x) = -1 ⇒ x = 4 and -4

f(x) = -5 ⇒ x = 0

f(x) = 2 ⇒ x = -7

(c) We have to calculate the point (t, 3) where the y value is 3.

f(x) = 3 when x = -8

So t = -8

(d) f(x) < 0 for the set of values of x {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Hence using the diagram of the graph of a function, we can compute all the values.

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Answer:

(a) f(4) = -1, f(-6) = 1 and f(6) = 1

(b) x = 4 and -4, x = 0 and x = -7

(c) t = -8

(d) The set x = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Step-by-step explanation:

x + 5 = (5 − x) − 5, which has one solution, represents the given situation.

Option A is correct.

What is the system of linear equations?

A system of linear equations is a collection of one or more linear equations that are solved simultaneously. A linear equation is an equation that can be written in the form ax + b = 0, where x is the variable, and a and b are coefficients.

A. x + 5 = (5 − x) − 5, which has one solution.

This is the correct answer because the equation represents the given situation that Jenna is x years old and in 5 years she will be as old as Jessica was 5 years ago which means Jenna's age in five years is x+5 and Jessica's age five years ago is 5 - x, by equating the age of Jenna in five years and Jessica's age five years ago we get x+5 = 5-x-5. Solving this equation we get x = 0, the age of Jenna is 0 and the age of Jessica is 5, which is a unique solution.

Hence, x + 5 = (5 − x) − 5, which has one solution, represents the given situation.

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Answer:

Step-by-step explanation:

The integral by reversing the order of integration is [tex]\frac{1}{14}\left[e^{49}-1}\right][/tex].

In the given question, we have to evaluate the integral by reversing the order of integration.

The given integration is [tex]\int_{0}^{1}\int_{7y}^{7}e^{x^2}dxdy[/tex].

The given integral is in the form of dxdy. We must create an integral of order dydx in order to shift the order of integration. This indicates that x is the outer integral's variable. Its bounds must be fixed and match the complete range of x over the area D.

The limit of y and x is;

0 ≤ y ≤ 1; 7y ≤ x ≤ 7; dA = dxdy

Now changing the order of integration

0 ≤ x ≤ 7; 0 ≤ y ≤ x/7; dA = dydx

I = [tex]\int_{0}^{7}\int_{0}^{x/7}e^{x^2}dydx[/tex]

Now integrating with respect to dy

I = [tex]\int_{0}^{7}t[y]_{0}^{x/7}e^{x^2}dydx[/tex]

I = [tex]\int_{0}^{7}t[x/7 - 0]e^{x^2}dydx[/tex]

I = [tex]\frac{1}{7}\int_{0}^{7}xe^{x^2}dx[/tex]

Now integrating again

I = [tex]\frac{1}{14}\left[e^{x^2}\right]_{0}^{7}[/tex]

I = [tex]\frac{1}{14}\left[e^{(7)^2}-e^{(0)^2}\right][/tex]

I = [tex]\frac{1}{14}\left[e^{49}-1}\right][/tex]

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The complete question is:

Evaluate the integral by reversing the order of integration.

[tex]\int_{0}^{1}\int_{7y}^{7}e^{x^2}dxdy[/tex]

One can solve basic algebraic expressions by following these steps.

In class 8, students typically learn to solve basic algebraic expressions by following these steps:

Identify the variable and the coefficient (number in front of the variable) in the expression.

Use the order of operations (PEMDAS) to simplify any arithmetic within the expression.

Use the distributive property to combine like terms.

Isolate the variable on one side of the equation by using inverse operations (such as adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same non-zero value).

Substitute in a value for the variable to find the numerical value of the expression.

It's good to practice with a lot of examples and check the solutions, and ask for help if needed.

Example:

Solve for x: 3x + 2 = 12

variable is x, coefficient is 3

nothing to simplify

nothing to combine

subtract 2 from both sides: 3x = 10

divide both sides by 3: x = 10/3 or 3.3333

x = 3.3333

It's important to note that solving algebraic expressions can become more complex as the student progresses, but the basic steps remain the same.

Thus, One can solve basic algebraic expressions by following these steps.

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Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Making a table of values for the x and y coordinates and plotting them on a set of axes are the steps involved in plotting quadratic graph.

Graphs of quadratic functions, or any function with x2 as its maximum power, are known as quadratic graphs.

A quadratic function is, for instance, y=x2+2x+5

Each x value is substituted into the quadratic function to produce the corresponding y value, completing the table of values. Each of these represents a pair of coordinates. For the function y=x2+2x+5, the table of values from x=3 to x=2 would appear as follows,

X −3  −2   −1 0 1  2

Y   8    5    4 5 8 13

and the graph would take the form of the following:

A quadratic function's graph takes the form of a parabola, which is symmetric.

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Answer:

268.08 cubic units.

Step-by-step explanation:

The volume of a sphere is given by the formula (4/3)πr^3, where r is the radius of the sphere.

Plugging in the given radius of 4, we get:

(4/3) * 3.14 * 4^3 = 268.08

So the volume of the sphere is approximately 268.08 cubic units.

Answer:

1.

2.

Step-by-step explanation:

V and Y aren't congruent bc V and Z are

When k is o doesn't satisfy the equation.

Value of [tex]$\mathrm{k}=(?)$[/tex], equation [tex]$\mathrm{kx}(\mathrm{x}-2)+6=0$[/tex] has equal roots.

[tex]& \Rightarrow \mathrm{kx}(\mathrm{x}-2)+6=0 \\[/tex]

[tex]& \mathrm{kx} x^2-2 \mathrm{kx}+6=0 \\[/tex]

two roots of quadratic equation

[tex]& \alpha, \beta= \frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\[/tex]

[tex]& \alpha, \beta= \frac{+2 \mathrm{k} \pm \sqrt{(-2 \mathrm{k})^2-4 \times 6 \times \mathrm{k}}}{2 \times \mathrm{k}} \\[/tex]

[tex]& \alpha, \beta=2 \mathrm{k} \frac{\pm \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\[/tex]

[tex]\alpha=\beta \\[/tex] The roots are qual

[tex]& \Rightarrow \frac{2 \mathrm{k}+\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}}=\frac{2 \mathrm{k}-\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\[/tex]

[tex]& \Rightarrow 2 \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}=0 \\[/tex]

[tex]& \Rightarrow 4 \mathrm{k}^2-24 \mathrm{k}=0 \\[/tex]

[tex]& \Rightarrow 4 \mathrm{k}(\mathrm{k}-6)=0 \\[/tex]

[tex]& \Rightarrow \mathrm{k}=0 \text { or } \mathrm{k}=6[/tex]

[tex]$\Rightarrow \mathrm{k}=6[\because \mathrm{k} \equiv 0]$[/tex] as[tex]$\mathrm{k}=0$[/tex]  doesn't satisfy the equation.

The complete question is,

For what value of [tex]$\mathrm{k}$[/tex], are the roots of the quadratic equation, [tex]$\mathrm{kx}(\mathrm{x}-2)+6=0$[/tex] equal?

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A system of inequalities to describe this situation are as follows;

x + y ≤ 16

20x + 12y ≥ 240.

The system of inequalities has been solved graphically and one possible solution is (6, 10).

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours tutoring purchased and number of hours clearing tables respectively, and then translate the word problem into algebraic equation as follows:

In Mathematics, the inequality symbol for "no more than" is ≤ while the inequality symbol for "at least" is ≥.

Since Morgan makes $20 per hour tutoring and $12 per hour clearing tables and can work no more than 16 total hours and must earn at least $240, the system of linear inequalities that are required to model this situation include the following:

x + y ≤ 16

20x + 12y ≥ 240

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (6, 10).

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The perimeter of the pool will be 26.85 in.

The perimeter is defined as the sum of all the sides of the given figures like squares, rectangles, etc.

The circumference of the whole circle of diameter 5 in is C = πd, which here is C = π(5 in), or approximately 5π in.  We take only half of this since the figure shows a semicircle, not a full circle.  Then the half-circumference is (5/2)π.

To find the perimeter:  add up the lengths forming the perimeter:  

7 in + (5/2)π in + 7 in + 5 in, or:

19 in +  (5/2)π ≈ 26.85 in

The perimeter will be 26.85 inches.

The image of the pool is attached with the answer below.

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Answer:

(2,2)

Step-by-step explanation:

the intersection of the two lines represents the solution

visually, you can see the lines intersect closely to (2,2)

Grace usually does 221 performances each year

last year , she does +10 perfromances

to calculate total number of performances in year Y

we will add ( 221 + 10)= 231

therefore, grace completed 231 performances last year

Answer:231

Step-by-step explanation:

just add 10

The probability that two diagonals chosen at random intersect inside the decagon is 7/45

A decagon is a 10-sided polygon, and it has 10 vertices.

In a regular decagon, there are 10C2 = 45 pairs of distinct vertices.

The total number of diagonals that can be drawn between these pairs of vertices is (10 * 9) / 2 = 45.

To find the number of diagonals that intersect inside the decagon, we need to find the number of diagonals that do not intersect at a vertex.

A diagonal that does not intersect at a vertex is called an interior diagonal, and the number of these is given by (n-3) where n is the number of sides in the polygon.

For a decagon, the number of interior diagonals is (10-3) = 7

Therefore, probability= favorable events/ total number of events = 7/45

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When a mountain is cut off at 4,000 feet, a cone is created that has a radius that is half that of the original mountain.

This is because the radius and height of cones both change in an inverse manner as height increases. As a result, volume changes as the inverse cube of rising height (represented as a proportion of the cone's overall height):

The volume of the cone above water is [tex]1/8$[/tex] the total volume of the cone (mountain). Since these cones are obviously comparable, the little cone's radius and height must equal

V1 × Height³= VN

1/8= Height³

Height=1/2

8000.1/2=4000= A

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The inverse properties of the logarithm are [tex]log_{b}bx[/tex] = x and [tex]blog_{b}x[/tex] = x where x > 0.

What is logarithm ?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

The inverse properties of the logarithm are logb bx=x and blogb x=x where x>0. The product property of the logarithm allows us to write a product as a sum: logb (xy)=logb x+logb y. The quotient property of the logarithm allows us to write a quotient as a difference: logb (xy)=logb x−logb y.

The inverse properties of the logarithm are [tex]log_{b}bx[/tex] = x and [tex]blog_{b}x[/tex] = x where x > 0.

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Answer:

Step-by-step explanation:

0.305 meters I think almost positive. Hopes this helps!!!

The equation 3x² + 10x + k = 0, the roots of the equation exist only for k ≤ 25.

Equation is a mathematical statement that uses an equal sign to show a relationship between two expressions. An equation states that one expression is equal to the other expression. Equations are used to solve problems by finding the value of unknown variables. Equations can be used to describe the relationships between physical and mathematical phenomena.

In order to solve for the values of k, we must first understand the properties of quadratic equations. A quadratic equation is a polynomial equation of degree 2, meaning that it has at most two solutions. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. In this case, the equation is 3x² + 10x + k = 0.

In order to solve for k, we must use the quadratic formula, which states that the two solutions of a quadratic equation are given by:

x = [-b ± √(b² - 4ac)]/2a

In this equation, a is equal to 3, b is equal to 10, and c is equal to k. Therefore, the two solutions of the equation 3x² + 10x + k = 0 are x = [-10 ± √(100 - 4*3*k)]/6.

The two solutions of the equation will only exist if the discriminant (√(b² - 4ac)) is greater than or equal to 0. Therefore, for the equation 3x² + 10x + k = 0, the two solutions will only exist if 100 - 4*3*k ≥ 0, or k ≤ 25.

Therefore, for the equation 3x² + 10x + k = 0, the roots of the equation exist only for k ≤ 25.

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On solving the provided question, we can say that function y=26-2x => x = 1 => y = 26-2 = 24

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

function y=26-2x

x = 1

y = 26-2 = 24

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