Etsuko practices origami. The square papers she used have a side length of either 7.5 cm or 25.4 cm. Etsuko says the length of the larger paper is 32.9 cm greater than the length of the smaller paper

Answer:

Step-by-step explanation:

step 1: Absolute value inequality entered

     |14c+5| > 7

step 2: Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |14c+5|

For the Negative case we'll use -(14c+5)

For the Positive case we'll use (14c+5)

step 3:  -(14c+5) > 7

    Multiply

     -14c-5 > 7

    Rearrange and Add up

     -14c > 12

    Divide both sides by 14

     -c > (6/7)

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     c < -(6/7)

    Which is the solution for the Negative Case

step 4:

(14c+5) > 7

    Rearrange and Add up

     14c > 2

    Divide both sides by 14

     c > (1/7)

    Which is the solution for the Positive Case

c < -6/7

 c > 1/7

The solution for the value of x for the Logarithmic expression 2㏑x + 3㏑2 = 5 is

4.30716.

A logarithmic equation is one that includes the logarithm of a variable-containing expression. To address exponential equations, first determine whether both sides of the equation can be written as powers of the exact number.

Some properties of ㏑ function are-

Now, as per the given expression;

2㏑x + 3㏑2 = 5

Use the Power Rule: n㏑A = ㏑Aⁿ

㏑x² + ㏑2³ = 5

Now, apply the Product Rule : ㏑A + ㏑B = ㏑(AB)

㏑(x² ×2³) = 5

㏑(x² ×8) = 5

Raise the formation to exponential form, using e as the base.

e∧㏑(x² ×8) = e⁵

Comparing the base of both sides;

x² ×8 = 5

x² = 5/8

x = ±√5/8

x = ±4.30716

Due to domain restrictions, the argument of any logarithm is always positive & greater than zero.

Therefore, the value of x is estimates as x = 4.30716.

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The slope intercept equation for a line that passes through the points (-2,4) and (3,-5) is y = -9/5x ₊ 2/5.

Given the points are:

P₁ = (-2,4) = (x₁ , y₁)

P₂ = (3,-5) = (x₂ , y₂)

Therefore, the equation of the line that passes through the above points is:

y = mx ₊ b , Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

= ( -5 - 4 ) / ( 3 - ( -2) ) = -9 / 5

∴ m = - 9/5

Using either P₁ or P₂, plug in one of their respective x- and y-values into:

y = -9/5 x + b

substitute (3,-5)

₋5 = (₋9/5)(3) ₊ b

₋5 = ₋27/5 ₊ b

₋5₊27/5 = b

₋ 25 ₊ 27/5 = b

b = 2/5

slope intercept equation:

y = mx ₊ b

y = -9/5x ₊ 2/5

Therefore, y = -9/5x ₊ 2/5 is the equation of the line that passes through both points (-2, 4) and (3, -5).

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The solution to the system of linear equations is x=3 and y= -4.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

For solving this question, you should apply the addition method. Thus, you should sum the equations 1 and 2.

6x + y = 14  (1)

−2x −y =−2 (2)

6x-2x+y-y=14-2

4x=12

x=3

From equation 2, you can find y for x=3

−2x −y =−2 (2)

-2*3-y=-2

-6-y=-2

-y=-2+6

-y=4

y= -4

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The linear equation of the table is y = 5x + 2.

when x = 20, y = 102

when y = 42, x = 8

Linear equation can be represented in slope intercept form as follows;

y = mx + b

where

Therefore,

m = 17 - 12 / 3 - 2

m = 5 / 1

m = 5

Therefore, let's find the y-intercept using (2, 12)

y = 5x + b

12 = 5(2) + b

12 = 10 + b

b = 12 - 10

b = 2

Therefore, the linear equation is y = 5x + 2.

when x = 20

y = 5(20) + 2 = 100 + 2

y = 102

when y = 42

42 = 5x + 2

42 - 2 = 5x

5x = 40

x = 40 / 5

x = 8

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The result of the given logarithmic expression log₉27-log₉9 is log₉ 3.

A logarithmic term is one that embodies a number in logarithmic form. It can also be referred to as a log term.

A quantity is also the product of two or more quantities. As a result, a term could be the product of two or even more quantities, at least one of which can be in logarithmic form. In such cases, the terms are referred to as log terms.

A quantity is also the quotient of two quantities. So, if a term is also a quotient of quantities, and at least one of the quantities can be expressed in log form, the terms are mathematically referred to as log terms.

Now, as per the given question;

=  log₉27-log₉9

So, applying the Quotient Rule in the given expression;

=  log₉ (27/9)

=  log₉ 3

Thus, the given expression simplified in the logarithmic expression as log₉ 3.

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When the company asked its customers to describe how satisfied they were with the latest product, it's a discrete data.

It should be noted that the main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.

A count involving integers is referred to as discrete data because there are a finite number of possible values. This kind of data cannot be separated into separate components. Discrete data consists of discrete variables that are non-negative, countable, and finite.

In this case, it should be noted that the measurement was taken based on their satisfaction. Therefore, it's a discrete variable.

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Logarithmic form: logₓ y = 4

A logarithmic form is a method to write equations when solving for a variable in an exponent. Any exponential equation can be written as a logarithm. The logarithmic form is used to calculate an exponent of an equation.

The logarithmic form is a rearrangement of the exponential form.

Exponential form: aᵇ = c

Logarithmic form: logₐ c = b

Comparing this with our equation, a=x, b=4, c=y

Therefore, we get the logarithmic form as logₓ y = 4

Conversion from exponential to logarithmic form gives the final answer as logₓ y = 4

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Answer:

1/3 or 1 over 3 but that is the correct answer

Answer:

261111111/100000

Step-by-step explanation:

Answer: it's A

hope this helps : D

Answer:

B (A reflection over the line y = x)

Step-by-step explanation:

I just think of it as imagining a positive diagonal line (like this --> /)

Hope this helps in some way

The evaluation of the expression given in surd form is 6.

Surds are expressions that use a root symbol, such as a square root, or another root symbol. Since the decimals of irrational numbers do not finish or recur, they cannot be expressed accurately in decimal form, hence surds are used instead.

Surds, in mathematics, are square root values that cannot be factored into a whole number or an integer. Numbers that are surds are irrational numbers.

From the given expression, the cube root of 216 can be computed as:

[tex]\sqrt[3]{216}[/tex]

Factor the number 216 as:

= [tex]\sqrt[3]{6^3}[/tex]

= 6

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Given :

B is between A and C

AB= x²-6x

BC= x²+20x

AC= 60-12x

B divide into 2 equal parts

AB and AC are equal

AC = AB +BC

60-12x = x²-6x + x²+20x

[tex]60= 2x^{2} -6x +20x +12x[/tex]

[tex]60 = 2x^{2} -6x +32x\\[/tex]

[tex]60= 2x^{2} +26x[/tex]

[tex]30 = x^{2} +13x\\\\[/tex]

[tex]x^{2} +13x -30 = 0\\x^{2} +15x-2x-30 =0[/tex]

[tex]x(x+15) -2 (x+15) =0[/tex]

[tex](x-2) (x+15) =0\\[/tex]

x=2 , x=-15

x never be negative the x is 2

BC =  x²+20x

BC = 2*2 +20*2

BC = 4 +40

BC = 44

length of BC =44

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Answer:

AB and BC are the sides of a parallelogram, ABCD. AB = 5 cm, BC = 7 cm and ABC = 60 degrees. Draw the lines AD and CD to complete the parallelogram.

Step-by-step explanation:

The equation of solution  ln (2-x)=1 is -0.718.

ln (2-x)=1

2-x = e

x = 2-e

x= -0.718

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.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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Answer:

46.5

Step-by-step explanation:

80+(10x46.5)=545 so 46.5

Using the bisection concept, it is found that the congruent angle to <GFH is given by:

d. <GFC.

A bisection of an angle is when a line splits an angle into two equal angles, that is, it splits by half the original angle.

The two resulting angles will be congruent, that is, they will have the same measure.

For this problem, we have that line CH bisects angle GFH, hence, from the explanation above, we have that:

Angles GFH and GFC are congruent, as due to the bisection, they both measure 90º.

Thus option D is correct, which is the one that lists angle GFC as congruent to angle GFH, that is, both angles having the same measure, which in this case is of 90º.

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Answer:

No, he still needs 2 yards

Step-by-step explanation:

Say Drew Breeze is at 0 on the first possession. When he is sacked, his position drops back to -4.

-4+12=8

Knowing that you need to gain 10 yards to get 1st down, Drew Breeze still needs a gain of at least 2 yards.

Hope this helps! :)

4/9 is not an Extraneous solution of the equation

Given Equation is √x+ 2√x=2.

On Squaring both the side of the equation, we get

(√x+ 2√x)² = 2²

Using the identity (a + b)² = a² + b² + 2ab on the left hand side of the equation

(√x)² + (2√x)² + 2(✓x)(2✓x) = 4

x + 4x + 4x = 4

9x = 4

x = 4/9

Check for Extraneous Solutions

Putting the value of x = 4/9 in the original equation √x+ 2√x=2, we get

✓(4/9) + 2(✓4/9) = 2

2/3 + 2(2/3) = 2

2/3 + 4/3 = 2

6/3 = 2

2 = 2

LHS = RHS

∴ 4/9 is not an Extraneous solution of the equation.

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The value of x for log (7 x+1)=log (x-2)+1 is 7.

Due of their connection to exponential functions, logarithmic functions are crucial. Exponential equations and the characteristics of exponential functions may both be investigated using logarithms. Additionally, they will be of great service in calculus, where they will be used to determine the slope of specific functions and the region enclosed by particular curves. They also have useful uses in economics.

Given,

log (7 x+1)=log (x-2)+1

log(7x + 1) - log(x - 2) = 1

using log (m/n) = log m - log n

log (7x+1 / x-2) = 1

It can be expressed as -

7x + 1 / x - 2 = 10 ¹

7x + 1 = 10x - 20

3x = 21

x = 7

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Answer:

There are 18 bananas

Step-by-step explanation:

6 x 3 = 18

18 bananas.

The figure must be true if Ray CE seems to be the angle bisector of ZACD, as stated in the supplied statement.

∠ACE = ∠DCB.

The line or line segment that divides an angle into two equal halves is known as the (interior) bisector of the an angle.

A bisector is a tool that divides an angle equally into two equal halves. Divide the number of degrees in the angle by two to determine the angle bisector.

If the angle bisector of ADC is the ray CE

then,

Angle ACD = ACE + ECD

ACE = ECD

So,

ACD = 2(ACE)

ACE = 1/2 (ACD)

This implies that ∠ACE = ∠DCB.

The figure must be true if Ray CE seems to be the angle bisector of ZACD, as stated in the supplied statement.

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It should be noted that the ratio in simplest form of 45 to 9 is 5:1.

It should be noted that a ratio and fraction are simply used in mathematics to compare one thing with something else.

In this case, it should be noted that we want to write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator 45 to 9.

Therefore, the ratio of 45 to 9 will be:

= 45 / 9

= 5:1

Therefore, it should be noted that the ratio in simplest form of 45 to 9 is 5:1.

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A school is studying Math for Data and Financial Literacy standardized test scores. A bar chart could be used to represent the data because test scores are numerical

This is further explained below.

Generally, A bar chart or bar graph is a kind of chart or graph that displays categorical data using bars of varying lengths and heights that are proportionate to the values that they represent. It is possible to lay out the bars either vertically or horizontally.

Column charts are occasionally used interchangeably with vertical bar charts.

In conclusion,Standardized exam results in Math for Data and Financial Literacy are now being analyzed at a school.

Due to the numerical nature of the test results, a bar chart could be an appropriate representation of the data.

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Solving the problem as per a linear equation, the value of b is found to be 1/10.

A linear equation is a form of algebraic equation in which the highest value of a variable is always equal to 1. Such an equation forms a straight line when carved on a graph.

As provided, the given equation is,

1/b = 4/2b - 10

or, 1/b = 2/b - 10 (as 4/2 = 2 )

or, 1/b - 2/b = - 10

or, 1/b ( 1 - 2) = - 10

or, - 1/b = - 10, ( we are using cross multiplication )

so, b = 1/ 10 ( as a negative sign on both sides will be nullified)

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Answer:

the data below are the tempretures on randomly

Step-by-step explanation:

Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Firstly, dividing by zero is undefined.

given

f(x) = [tex]\frac{x}{x-1}[/tex] , then

f(1) = [tex]\frac{1}{1-1}[/tex] = [tex]\frac{1}{0}[/tex] = undefined

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ \dfrac{7}{100} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ \sqrt{7} }{ \sqrt{100} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ \sqrt{7} }{ \sqrt{10 {}^{2} } } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ \sqrt{7} }{ 10 } [/tex]

So, the correct choice is A

The value of x will be 12 and the angle measurements of ∠A and ∠B is 45°.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

Given is a set of two lines parallel to each other intersected by a line. From the question, we can write -

∠A = 5x - 15

∠B = 2x + 21

Refer to the image attached.

From the figure it can be seen that -

∠B = ∠TRO = 2x + 21             [Vertically opposite angles are equal]

∠TRO = ∠POR = 2x + 21       [Alternate interior angles are equal]

∠A = ∠POR = 2x + 21            [Vertically opposite angles are equal]

It is given that

∠A = ∠B

5x - 15 = 2x + 21

3x = 21 + 15

3x = 36

x = 12

Then -

∠A = 2x + 21 = 24 + 21 = 45°

∠B = ∠A = 45°

Therefore, the value of x will be 12 and the angle measurements of ∠A and ∠B is 45°

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[The question is not clearly written. The complete question is along with the correct figure attached is -

The angle measurements in the diagram are represented by the following expressions.

A= 5x - 15°

B = 2x + 21°

Solve for x and then find the measure of ∠A and ∠B.]