Please explain how.....
100 points

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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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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We have been given that -

scale = 1:75000.

we have to find out

(a) scale expressed as 1 cm represents n km.

Map scale refers to the ratio between distance on a map and the corresponding distance on the ground. For example, on a 1:100000 scale map, 1cm on the map equals 1km on the ground

so 1,00,000 cm = 1 km.

(b) given -

distance between two towns on the map is 25 cm.

Find the actual distance, in kilometres, between the two towns.

Scale is given as 1:75000

for 25 cm distance = 25×75000 cm

                              = 18,75,000 cm

therefore 1875000 cm = 18.75 km.

the real distance between two points is 18.75 km.

(c) . The area of the lake in the real world is 3.5 square kilometers.

1 square kilometer is equal to 1 kilometers squared.

since 1 kilometer is equal to 100,000 centimeters, then 1 square kilometer is equal to 100,000^2 centimeters which is equal to 1 * 10^10 square centimeters.

3.5 square kilometers on the map is therefore equal to 3.5 * 10^10 square centimeters.

1 centimeter on the map is equal to 75000 centimeters in the real world.

1 square centimeter on the map is equal to 75000^2 centimeters in the real world which is equal to5625 * 10^6 square centimeters in the real world.

take 3.5 * 10^10 square centimeters in the real world and divide it by 5625 * 10^6 square centimeters and you get .0006 * 10^4 square centimeters which is equal to 6 square centimeters on the map.

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The equation of the line that passes through  ​(-3​,2​), and is perpendicular to 3x - 5y = -2 is:

y - 2 = -5/3(x + 3), or

y = -5/3x - 3

The equations of two lines that are perpendicular to each other will always have a slope (m) that are negative reciprocals to each other.

Thus, given the equation of a line as, 3x - 5y = -2, rewrite in slope-intercept form (y = mx + b) to easily determine its slope (m):

3x - 5y = -2

- 5y = -3x - 2

y = 3/5x + 2/5

The slope (m) = 3/5.

The negative reciprocal of 3/5 is -5/3.

Hence, the slope (m) of the line that is perpendicular to 3x - 5y = -2 would be -5/3.

Substitute (a, b) = (-3, 2) and m = -5/3 into y - b = m(x - a):

y - 2 = -5/3(x - (-3))

y - 2 = -5/3(x + 3) [point-slope form]

Rewrite the equation in slope-intercept form:

y - 2 = -5/3(x + 3)

y - 2 = -5/3x - 5

y = -5/3x - 5 + 2

y = -5/3x - 3 [slope-intercept form]

In summary, the equation of the line that passes through  ​(-3​,2​), and is perpendicular to 3x - 5y = -2 is:

y - 2 = -5/3(x + 3) [point-slope form], or

y = -5/3x - 3 [slope-intercept form].

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Answer:

46.5

Step-by-step explanation:

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

Answer:

The answer is 2.4lbs

Step-by-step explanation:

1.32 divided by .55 is 2.4, meaning the bag weighed 2.4lbs :)

Answer:

y equals negative one-sixth times x plus 5

This is correct, it's not plus 3, it's plus 5!

For any function, we call x the "numerator" value and y is the "denominator" value.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. Which ultimately implies that, a function is used for mapping an input variable to an output variable.

We know that fraction represents a part of a number or any number of equal parts.

The parts of a fraction are;

In Mathematics, a fraction comprises two main parts and include the following:

Numerator

Denominator

For any function in the Mathematics, we call variable x the numerator value while y is the denominator value.

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Answer:

your equation is Y = 6

Step-by-step explanation:

Use Midpoint Formula to find the slope M first

Name the coordinates of both points x1 = -2, y1 = -6, x2 = 4,  y2 = 6

Plug them in the formula

M = y2 - y1/ x2 - x1

M =( 6 - 6)/( 4 - (-2))

M = 0/6

M = 0

Then use point slope formula

Plugin the slope M = 0 in the formula and pick one of the points above. Name the coordinates of  the point X1 = 4 and y1 = 6

y - y1 = m(x - x1)

y - 6 = 0(x - 4)

y - 6 = 0

y = 6

your equation is Y = 0x  + 6 but keep in this form y = b

This is a horizontal Line

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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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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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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[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 the expression log₅62 by using the change of base theorem is 2.5644.

Given that the expression is log₅62.

We are required to find the value of the expression by using the change of base formula.

The change of base formula is basically used to find the base of the log value is different from 10. It says that [tex]log_{a}b[/tex]=log b/log a.

Expression is log₅62.

log₅62=log 62/log 5

Now we have to use the value of log 62=1.7923 and log 5=0.6989 in the above expression.

=1.7923/0.6989

=2.5644

Hence the value of the expression log₅62 is 2.5644.

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Answer: it's A

hope this helps : D

Answer:

Step-by-step explanation:

half hisage. Then subtract

Answer: 12 years old

Step-by-step explanation:

You should use variables:

Set x as tyler's age.

32 = 2x + 8

32 - 8 = 2x

24 = 2x

12 = x

Therefore, Tyler is 12 years old.

Answer:

B.

Step-by-step explanation:

The Pythagorean theorem only works with right triangles. a and b are the lengths of the legs. c is the length of the hypotenuse. The hypotenuse is the longest side of a right triangle.

Answer: B.

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

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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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

Answer:

LCD= 24

Step-by-step explanation:

[tex]\frac{5}{8}=\frac{15}{24}\\ \\\frac{11}{12}=\frac{22}{24}[/tex]

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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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.]

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! :)

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:

261111111/100000

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

[tex]\left \{ {{A=7B} \atop {A+B=144}} \right.[/tex]

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the first equation in the second one you get:

7B + B= 144

Solving:

8B= 144

B= 144÷8

B= 18 tons

Remembering that A= 7B, the value of A is calculated as:

A= 7×18

A= 126 tons

Finally, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.

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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:

The expanded form of the given logarithms ( log 4 s⁴ t) is =  2log(2) + 4log(s)  + log(t).

The features of the log are used to increase a single logarithm into numerous logarithms (or) compression multiple logarithms together into a single logarithm. A logarithm is simply another way of writing exponents. Thus, logarithm properties are obtained from exponent properties.

log (4 s⁴ t)

can be written as log (4 s⁴ t):

Property used in the solving (log b*c = log b  + log c) and (log ₐᵇ = b log a)

log (4 s⁴) + log( t)

log (4 ) + log(s⁴) + log( t)

Expand log (s⁴) by moving 4 outside the log.

log (4 ) + log(s) + log( t)

The expression also can be written as :

2log(2) + 4log(s)  + log(t)

The expanded form of the given logarithms ( log 4 s⁴ t) is =  2log(2) + 4log(s)  + log(t).

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