The length of a rectangle is 5 cm more than its breadth. If the perimeter of the rectangle is 58 cm, find its dimensions.

Answer: Unless there is a vertical shift the range for ALL radical functions will remain [0,infinity)

Step-by-step explanation:

Answer: To prove that AB is parallel to DC, we can use the following steps:

Draw a diagram of the cyclic quadrilateral ABCD with the point E where sides AD and BC are produced to meet.

Since ABCD is a cyclic quadrilateral, all its interior angles add up to 360 degrees. Therefore, angle A + angle B + angle C + angle D = 360 degrees.

Since AE = BE, we can say that angles A and B are equal (by corresponding angles). Similarly, angles C and D are also equal.

Since angles A and B are equal and angles C and D are also equal, we can say that angle A + angle B = angle C + angle D.

Substituting this into our equation from step 2, we get: angle A + angle B + angle C + angle D = angle A + angle B + angle A + angle B.

Simplifying, we get: 360 = 2(angle A + angle B). This means that angle A + angle B = 180.

Since angle A + angle B = 180, we can say that angle A = angle B and angle C = angle D.

Now we can use the fact that corresponding angles are equal, then angle A = angle C and angle B = angle D.

We know that opposite angles of a parallelogram are equal, so we have proved that AB is parallel to DC.

It's important to note that this proof uses the fact that quadrilateral ABCD is cyclic, which means that the sum of its angles is equal to 360 degrees. It also uses the fact that opposite angles are equal in a parallelogram, and corresponding angles are equal when two lines are parallel.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer would be 10

Answer:

140 members

Step-by-step explanation:

find 70% of 200

Answer:

Step-by-step explanation: The answer is $48.15 hopes this helps :)

A 72 percent is the latest estimate for the likelihood of one or more M 6.7 earthquakes in the Bay Area region before the year 2043.

To estimate the likelihood of future earthquakes, scientists rely on a variety of techniques that help us understand the velocities and magnitudes of past earthquakes. Using the Global Positioning System (GPS) and other land surveys and geological techniques,scientists have determined how much current plate movement, totaling inches per year across the San Francisco Bay region, stresses these individuals. We were able to more accurately measure how well it disperses. Small earthquakes occur more frequently than large ones. There is a 98% chance that an earthquake of magnitude 6.0 or greater will occur before 2043. There is a 72% chance that at least one earthquake of magnitude 6.7 or greater will occur in the San Francisco Bay Area, and a 51% chance that at least one magnitude earthquake will occur. Therefore they concluded that there is a 72% chance (or probability) of at least one earthquake of magnitude 6.7 or greater occurring somewhere in the San Francisco Bay Area before 2043.

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The difference between 4 x 3 and 43 is that 4 x 3 is the mathematical operation of multiplying 4 and 3, which equals 12, while 43 is just a number.

The difference between the expression "4 times 3" and the number 43 is that the former indicates the mathematical action of multiplying "4 times 3," which results in the value 12, while the latter simply represents the number itself.

To prove this, you can perform the mathematical operation of 4 x 3 = 12 and compare it to the number 43. As 12 is not equal to 43, it is clear that these are two different values.

In general, when we see a number with multiple digits, like 43, it is generally not thought of as the result of a mathematical operation. However, when we see an expression like 4 x 3, we know that it is the result of a multiplication operation and it is not just a number.

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Answer:

The statement is misleading as it does not provide any context for the comparison. It does not clarify what the 74% more calories is being compared to or what amount of calories is being burned by using the product. Additionally, the advertisement does not provide any evidence to back up the claim.

The length of AC in the line segment is 26 units.

B is the midpoint of AC.  

AB = 6x + 1

BC = 2x + 9

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

Hence,

AB = BC

6x + 1 = 2x + 9

6x - 2x = 9 - 1

4x = 8

divide both sides by 4

x = 8 / 4

x = 2

Therefore,

AC = 2AB

AC = 2(6x + 1)

AC = 2(6(2) + 1)

AC = 2(12 + 1)

AC = 26 units

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The selling price of a used book at the store where the owner buys a used book for $1.50 and resells the used book at a price of 400% the price at which buys the used book is $6.00

The selling price of an item is the price which is displayed on the item on the shelves of a store. The selling price is often different from the price at which the item is bought, or produced, which is often lesser than the price at which the item is sold.

The amount at which the owner buys each used book = $1.50

The amount at which the owner of the used book store sells the books = 400% of the amount he paid for the books

400% of an amount x is equivalent to four times the amount. (4 × x)

The price at which the owner sells a used book at his store, P, is therefore;

P = 400% × $1.50 = 400/100 × $1.50 = $6.00

The price of a used book at the store is $6.0

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A polynomial is described as a set of mathematical phrases with numerical coefficients, variables, and operations between them. The variables' degree must be a non-negative integer (addition, subtraction, multiplication and division).

A polynomial example could be-

[tex]\mathrm{p}(\mathrm{x})=2 x^{3-3(x+y)+7 / 5}[/tex]

A mathematical notion known as an equation is one in which two quantities are equal and are indicated by the symbol "=" in between.

An illustration of an equation is

[tex]3 x-5 y=(7 x+9) / 5[/tex]

In contrast to polynomials, equations have no limits on the coefficients or the powers of the variables.

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A polynomial is described as a set of mathematical phrases with numerical coefficients, variables, and operations between them.

The variables' degree must be a non-negative integer (addition, subtraction, multiplication and division).

A polynomial example could be-

p(x) =³

A mathematical notion known as an equation is one in which two quantities are equal and are indicated by the symbol "=" in between.

An illustration of an equation is

In contrast to polynomials, equations have no limits on the coefficients or the powers of the variables.

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The area of a triangle whose height is 6 cm and the base is 10 cm is 30 cm².

Area of triangle = 1/2 × b × h

= 1/2 × 10 × 6

= 1/2 × 60

= 30 cm².

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Any value of a variable that makes the equation true is a solution. The set of all variables that makes the equation true is called a solution set. Because 2(4) + 6 = 14, the solution set for 2y + 6 = 14 is 4.

Plugging each value in the domain into the equation to obtain the range values is the first step in determining the solution set for an equation with a given domain. Write these values as a set and create ordered pairs from them. Your response is that set!

An assignment of values to the unknown variables that achieves equality in the equation is called a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used in place of the unknowns, makes the equation equal.

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Full Question = How do you find the solution set of an equation?

The required domain of the vertical line is {5} and the range is all real numbers.

Given that,
Domain and range of the vertical line x = 5 is to be determined.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
We can infer that the domain of this relation can only be constrained if a vertical line at x = 5 passes through 0 locations. This function's range can only be a collection of real numbers or a constraint.

Thus, the required domain of the vertical line is {5} and the range is all real numbers.

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In order for the variables in the first equation to cancel out, we must multiply a number in the second equation to make it equal to those variables. For instance, we must multiply the second equation by two in order to make it equal four in order to cancel out x.

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Answer:

GCF = 8.

Step-by-step explanation:

First, we divide 264 by 224 and we get the identity:

264 = 1*224 + 40  ( That is 264 divided by 224 goes once and the remainder is 40)

Now we divide 224 by 40 to get:

224 = 5*40 + 24

Repeating this process, we get:

40 = 1*24 + 16

24 = 1*16 + 8

16 = 2*8 + 0   <------ we stop because the remainder is 0.

So, The GCF is 8.

Answer: The given trinomial, 24ab-16a^2-9b^2, can be written as an expression opposite to a square of a binomial.

To do this, we first factor out the greatest common factor of -4a, which gives us:

-4a(6b-4a-9b^2)

We can then factor -9b^2 as -(3b)^2, and group the remaining terms together:

-4a((3b-2a)^2-4a^2)

So the trinomial can be written as -4a( (3b-2a)^2 - 4a^2 ) which is an expression opposite to a square of a binomial (3b-2a)^2.

Step-by-step explanation:

The values of the probability from spinning the spinner and rolling the cube are;

Probability is a measure of the liklihood that an event will occur. The probability of an event = Number of times the event occurs ÷ Sum of the frequencies of all possible events.

Numbers on the spinner are; 1, 2, 3, 4, and 5

Numbers in the number cube = 1, 2, 3, 4, 5, and 6

The probability of an event = The number of required outcomes ÷ The number of possible outcomes

The possible even numbers on the spinner = 2, and 4

The number of even numbers in the spinner = 2

The number of possible numbers on the spinner = 5

The ratio of the number of even numbers to the number of possible numbers, which is the probability of spinning an even number, therefore is; P(E) = 2/5

The number of 5s on the cube = 1

The number of possible numbers on the cube = 6

The probability of rolling a 5 on the number cube is therefore, p(5) = 1/6

The probability of landing on an even number and rolling a 5, P(E) × P(5) is therefore;

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Answer:

Probability of spinner landing on an even number-2,5

Probability of rolling a 5

on number cube-1,6

Probability of spinner landing on an even number and rolling a 5-1,15

Step-by-step explanation:

bc

The roots of a function are the points at which the graph of the function crosses the x-axis.

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The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.

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Parallel lines require the terms line and plane because line and plane that are parallel cannot cross each other. Thus, they will never create a point of intersection. The characteristics of that parallel lines consist of lines and planes.

The characteristics of parallel lines are;

The shortest distance between parallel lines is the same at all points along the lines.

The lines are on the same plane.

As the plane is prolonged indefinitely, the lines do not intersect.

The characteristic of these geometric figures that create the different requirements would be how these undefined terms are situated. In the case of parallel lines, these are lines that would not intersect no matter how long the line is extended or whether it goes infinitely; thus, the lines lie on the same plane.

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The value of z from the triangle is z = 70

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔIGJ

Let the second triangle be represented as ΔHGK

Now , K is the midpoint of GJ and H is the midpoint of GI

So , IH = GH and GK = KJ

And , the triangles ΔIGJ and ΔHGK are similar

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

The measure of HK = ( 1/2 ) measure of side IJ

And , ( z - 37 ) = ( 1/2 ) x ( z - 4 )

On simplifying the equation , we get

Multiply by 2 on both sides of the equation , we get

2z - 74 = z - 4

Subtracting z on both sides of the equation , we get

z - 74 = -4

Adding 74 on both sides of the equation , we get

z = 70

Hence , the value of z is 70

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The characteristics of perpendicular lines:

1) Perpendicular lines are intersecting lines.

2) The perpendicular lines are coplanar.

3) The perpendicular intersect at a 90° angle.

4) The product of slopes of perpendicular lines is -1.

We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°

Since these lines are inclined at 90° to each other, hence they create right angles.

Perpendicular lines are intersecting lines.

Also, the perpendicular lines are coplanar.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

If two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.

The product of slopes of perpendicular lines is always -1.

Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are perpendicular to each other then m₁ × m2₂ = -1

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Answer:

a = [tex]\frac{t-sb}{s}[/tex]

Step-by-step explanation:

s(a + b) = t    Distribute the s

sa + sb = t      Subtract sb from both sides

sa + sb - sb = t - sb  Simplify

sa = t - sb    Divide both sides by s

a = [tex]\frac{t-sb}{s}[/tex]

y = -6 is a horizontal line and perpendicular to y-axis.

A horizontal line is perpendicular to the y-axis and parallel to the x-axis.

The equation for a horizontal line is y = c.

where c is constant and c constant is the y-coordinate of every point on the line.

In the equation y = -6, the constant is -6.

This means that every point on this line has an y-coordinate of -6.

Every point on the line (x, y) will have a y-coordinate of -6, while the

x-coordinate can be anything.

Therefore, y = -6 represent a horizontal straight line with perpendicular to the y-axis and parallel to the x-axis.

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The modulus of the complex number is:

|z| = 5

Now, According to the question:

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

The modulus of complex number  z=a+bi  is:

[tex]|z| = \sqrt{(a+bi)(a-bi)}[/tex]

[tex]|z| = \sqrt{a^2+b^2}[/tex]

The given complex number is :

4 + 3i.

a = 4 and b = 3

The modulus of the complex number will be:

[tex]|z|=\sqrt{4^2+3^2}[/tex]

[tex]|z|=\sqrt{16+9}\\\\|z|=\sqrt{25}[/tex]

|z| = 5

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Answer: D, 1 1/4 cups of flour and 5/4.

Step-by-step explanation:

There are four bowls, so subtract four from 5, and you have 1. Divide the remaining 1 by 4, and you have 1/4. So, 1 1/4 cups per bowl. A simpler way would be to divide 5 by 4, as you would end up with 1.25, which equals 1 1/4.

Answer: 5/4 cups of flower

5 ÷ 4= 1.25

1.25 in fraction form is 5/4, so the answer would be a.

The length of the fence must be 282.84 ft.

Area of the field =  40,000 ft²,

The length of the fence will be equal to the diagonal of the square.

For a square of side length S, the area is:

A = S²

Substituting the values in the formula -

S² = 40,000 ft

Applying the square root on both sides -

S = √(40,000 ft²)

Calculating, the diagonal of a square of side length S is:

D = S x√2,

Substituting the values -

D = √(40,000 ft²) x √2

= √(80,000 ft²)

= 282.84 ft

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There are twelve possible combinations:

At Jaylen's school, students have a variety of course offerings from which to choose. They must choose a language, an elective, and a science class. The language options are Chinese, French, German, and Spanish.

With these four language options, four elective options, and four science options, there are twelve possible combinations of courses to choose from.

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