6) Create your own word
problem using the
format in the example
on the page above.

As a result, we take the square root of the both sides since if two expressions are equal, then so are their square roots.

By multiplying the square root of a positive integer by oneself, the number is obtained. As an illustration, 5 is the square root of 25, since 5 × 5 equals 25. Since (5) (5) = 25, 5 is also the square root of 25 as you can see. The symbol, which is, is always used to indicate the square root of a number of a variable x.

Here,

In this case, we're using the square to solve a quadratic equation.

Never forget to use both the negative and positive roots of the equation and to square the values of both sides.

We can accomplish this because to the rule that states that if two expressions are comparable, then their square roots are also equivalent.

As a result, we take the square root of both sides since if two expressions are equal, then so are their square roots.

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Answer:

40%

Step-by-step explanation:

50/125×100%

=40%

Mr Smith has covered 40 percent of the journey

Answer:

40%

Step-by-step explanation:

50/125 ×100= 40%

Answer:

The answer is 10.

16 - 3 = 13

10 + 3 = 13

Answer:

10

Step-by-step explanation:

Here,10+3=13

and,16-3=13

Answer:

The answer is D (2 1/2)

Hope u helped

From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0

and solution of these equations are x = -1/2 and y= 15/2

An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.

we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.

From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a  and detect two location of point (1, 6) and (6, 1) for line b.

As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)

hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)

                                                 y-6 = 3(x-5)

                                               y-6 = 3x -15

                                             y-3x -9 = 0

In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)

                                                       y-6 = -1(x-1)

                                                     y-6 = -x+1

                                                   x+ y -7 =0

 now, we get two equations, -3x+ y -9 =0

                                                  x+ y -  7 =0

Solving these two equations by addition method, we get x= -1/2 and y = 15/2

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Answer:The combined functions W(x) and G(x) represent the amount of wood and glass required to produce a picture frame. Based on the information provided,

W(x)= 2[(f+g)(x)] and G(x) = (f-g)(x)

By looking at the values of the given table, it can be observed that the rate of change in the amount of glass required (G(x)) is not constant, it increases as x increases.

On the other hand, the rate of change in the amount of wood required (W(x)) is not constant as well, it increases as x increases too.

It's not mentioned any information about constant rate of change for f and g.

Therefore, the correct statement that describes the combined functions W(x) and G(x) is: "Neither the amount of wood required nor the amount of glass required has a constant rate of change."

It's important to mention that the problem provided does not have a unique solution, because the values for f and g are not defined so it's not possible to infer their behaviour over time.

It is only possible to infer the behaviour of the functions W(x) and G(x) given the information provided, and it is clear that the rate of change for both functions does not remain constant, but it increases as x increases.

Step-by-step explanation:

The value of the variable 'x' is 273/27. Then the measure of the angle ∠DGH will be 2.43°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Then the equation is written as,

∠EFA + ∠DGF = 180°

x - 5 + 73x - 365 = 180°

74x = 550

x = 273/27

Then the measure of the angle ∠DGF is given as,

∠DGF = 73(273/27) - 365

∠DGF = 177.57°

Then the measure of the angle ∠DGH will be calculated as,

∠DGH + ∠DGF = 180°

∠DGH + 177.57° = 180°

∠DGH = 2.43°

The value of the variable 'x' is 273/27. Then the measure of the angle ∠DGH will be 2.43°.

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The equation system is appropriately described by the formula 4x - y=6.A mathematical formula known as an equation combines two assertions .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.

given

Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

By graphing the given equations, you can easily solve a system by finding the point(s) where they all cross.

The values of the variables you are solving for will be provided by the coordinate of this point.

The equation system is appropriately described by the formula 4x - y=6.

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the true statements for 8u + 5 + 3v are:

1.) 8u+3v+5 is written as a sum of three terms.

4.)5 is a constant.

The word "constant" in mathematics has several different connotations. When used as a noun, it can have either of the following two meanings: Non-variance (i.e., not changing in relation to some other value) or Variance.

an unchanging number or other non-changing mathematical object that is fixed and well-defined. Sometimes, to distinguish between these two meanings, the terms mathematical constant or physical constant are used.

a function with a constant value (i.e., a constant function).

These constants are frequently represented by a variable that is independent of the main variable or variables in question.

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Answer:

------------------------------------------

4 1/2% of 50 is 4.5% of 50 which is same as:

or substituting % with 1/100,

The matching choices are A and B.

The expression is factorized to give (x + 7) and (x + 7)

Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.

Given the quadratic equation;

x² + 14x +49

Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7

Now, substitute the numbers in the expression

x² + 7x + 7x + 49

Make into two expressions, we have;

(x² + 7x) + (7x + 49)

factor out the common terms, we get;

x(x + 7)+ 7(x + 7)

Then, we have;

(x + 7)

(x + 7)

Hence, the factorized form is (x + 7) and (x + 7)

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Answer: 1250

Step-by-step explanation: 50 x 50 = 2,500

                 2,500 divided by 2 is 1250

The likelihood of the word "BANKRUPT" appearing on the Wheel of Fortune is 1/9 = 11.1%.

The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it. A "1" spinning is 3 out of 8 likely.

Select a direction, get a matrix, locate an eigenvector, normalize it, take its adjoint, multiply by your vector, determine the magnitude of the result, then square that. Finished, that's the likelihood.

Two Bankrupt wedges and one Lose a Turn wedge are also included on the wheel. The contestant's turn is forfeited if they land on either, and the Bankrupt wedge also gets rid of whatever money or rewards they have acquired during the round.

The likelihood of spinning "BANKRUPT" on any given spin of the Wheel of Fortune is 1/9 = 11.1%.

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The solution is Option A.

The shortest distance is given by the two hypotenuses of the triangles and the distance is X = 7.8 cm

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the shortest distance be represented as X

Let the first triangle be the first face of the rectangular box ΔABC

The length of the triangle AB = 3 cm

The height of the triangle BC = 2 cm

Now ,

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

The measure of AC = √ ( 3² + 2² )

The measure of AC = √13 cm

And , the second triangle is the second face of the rectangular box ΔDEF

The length of the triangle DE = 4 cm

The height of the triangle EF = 2 cm

The measure of DF = √ ( 4² + 2² )

The measure of DF = √18 cm

Now , the shortest distance X = The measure of AC  + measure of DF

Substituting the values in the equation , we get

The shortest distance X = √13 cm + √18 cm

The shortest distance X = 3.60 + 4.24

The shortest distance X = 7.8 cm

Therefore , the value of A is 7.8 cm

Hence , the shortest distance for the ant is 7.8 cm

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The length of UV in the circle is given as follows:

13.2.

We are given two secant segments in the circle for this problem.

For two secants, the product of the lengths of one secant segment and it's external segment equals the product of the lengths of the other secant segment and it's external segment.

Hence, from the circle given by the image presented at the end of the answer, the relation for this problem is given as follows:

(22 + 17) x 17 = (20 + UV) x 20

Hence we must simply solve the expression to obtain the length of UV, as follows:

39 x 17 = 400 + 20UV

663 = 400 + 20 UV

20 UV = 263

UV = 263/20

UV = 13.2.

The circles are given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. [Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300.

Answer: Tonya's calculation is incorrect because she mixed units of measurement. She used feet to measure one dimension of the room (10 feet) and inches to measure the other dimension (120 inches) and then calculated the area as 10 x 120 = 1200 square feet.

Area is a measure of the amount of space inside a two-dimensional shape, and it's typically measured in square units. To calculate the area of a rectangular room, you multiply the length of the room by the width of the room,

However in this case, Tonya used different units of measurement for length and width (feet and inches), and therefore the answer is incorrect.

You would need to convert inches to feet before multiplying 10 feet by 120 inches to get the area.

120 inches = 10 feet

So, the correct calculation of the area would be 10 feet * 10 feet = 100 square feet

It's worth mentioning that before calculating any area or volume, it's important to make sure that all units of measurement are consistent and the same.

Step-by-step explanation:

Answer:-4x^2-2x+46.

Step-by-step explanation:

To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:

(-3)(x+4)(x-6)-(x^2+8x-10)

Then, you can distribute the -3 to the terms inside the first set of parentheses:

(-3x-12)(x-6)-(x^2+8x-10)

Then, you can combine like terms:

-3x^2+6x+36-x^2-8x+10

This simplifies to:

-4x^2-2x+46

Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.

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17. The triangles can be proven congruent by the SSS theorem.

18. The triangles cannot be proven congruent by the HL theorem, as it is not known if the triangles are right triangles.

The side-side-side congruence theorem, abbreviated as SSS, means that if two triangles have three equal side lengths, then the triangles are congruent.

In item 17, we have that:

As the three triangles are equal, then the SSS theorem can be used to prove the congruence of the two triangles.

The HL theorem represents the hypotenuse and leg theorem, which means that if two right triangles share a hypotenuse measure along with a leg measure, then they are congruent.

Hence item 18 cannot be proven congruent by the HL theorem, as there is no information regarding whether the triangles are right triangles.

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The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.

Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.

Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.

Now we solve

first 9 multiply with 500 so we get 4500. 5140-4500=640

then 9 multiply with 70 so we get 630. 640-630=10

then 9 multiply with 1 so we get 9.   10-9=1

Hence       500+70+1=571

And our remainder is 1.

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If the measure of angle A equals pi over 6, the angle c equals 18, and the angle an equals 9, triangles may be formed.

You only need to apply the Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side. A triangle will exist if this holds true for each of the three possible added side length combinations.

From the given information, we have that:

m<B = pi/6 = 30 degres

c = 10

b = 5

This shows that we can use the cosine rule to find the third side b of the triangle. Since all the sides are complete, hence we can use the information given to find just 1 triangle

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The multiplicative rate of change for the exponential function is 0.4.

The exponential function in mathematics is represented by the symbols f(x)=exp or ex. The word, unless otherwise stated, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

In mathematics, an exponential function has the following form: f (x) = an x, where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

Given: Exponential function [tex]$f(x)=2\left(\frac{5}{2}\right)^{-x}$[/tex]

To find The multiplicative rate of change for the exponential function.

Solution :

The general form of the exponential function is [tex]$f(x)=a b^x$[/tex]

where $b$ is the rate of change of the function.

First we write the given function In proper form:

[tex]$$\begin{aligned}& f(x)=2\left(\frac{5}{2}\right)^{-x} \\& f(x)=2\left(\frac{2}{5}\right)^x\end{aligned}$$[/tex]

The rate of change is [tex]$f(x)=a b^x$[/tex]

Therefore, The multiplicative rate of change for the exponential function Is $0.4$

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Answer:

Two thousand and twenty three

Step-by-step explanation:

Answer: Two and twenty-three thousandths

Step-by-step explanation:

An equation may have more than one solution.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The variable's value for which the equation holds true is referred to as the equation's solution. If the LHS and RHS are switched, an equation doesn't change. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

Steps to solve a linear equation:

1. If necessary, remove the parentheses and use the distributive property.

2. By merging like terms, make both sides of the equation simpler.

3. The LCD (least common denominator) of all the fractions should be multiplied by both sides of the equation if there are any fractions.

4. If the equation contains decimals, multiply both sides by the lowest power of 10 to make the result a whole number.

5. Using the addition and subtraction properties of equality, move the constant terms to the other side of the equation and the variable terms to the other.

6. Using the equality properties of multiplication or division, set the variable's coefficient to 1.

7. Get the answer by isolating the variable.

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On solving the provided question, we cans ay that - here in triangles, triangle ABC is congruent to triangle A`B`C`

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

Here,

two triangles are there

triangle ABC and triangle A`B`C`

AB =A`B`

BC = B`C`

AC =A`C`

So, by sss property

both are congruent

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I believe it's A

I hope this helps and if I'm wrong I apologize

The equation of p(x) in vertex form is p(x) = 3(x - 1)² - 2.

Option C is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

From the table,

From p(x) = 10 to p(x) = -2 the value of p(x) is decreasing and from p(x) = -2 to p(x) = 46 it is increasing.

So,

The vertex is (1, -2).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(1, -2) = (h, k)

Make (0, 1) = (x, p(x))

1 = a (0 - 1)² + (-2)

1 = a - 2

a = 1 + 2

a = 3

Thus,

The vertex equation of p(x).

p(x) = 3(x - 1)² - 2

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Answer:

$22.5

Step-by-step explanation:

$27.00/3/5=45

45*1/2=$22.5