Evaluate each logarithm.
log₅125

What is the question?

Putting together the solutions from each of the equations, the 4 letter code is GFBA

From the question, we are to solve each of the linear equations to determine the 4 LETTER CODE

1. -2x + 1 = 3x + 16

Add 2x to both sides

-2x + 2x + 1 = 3x + 2x + 16

1 = 5x + 16

Subtract 16 from both sides

1 - 16 = 5x + 16 - 16

-15 = 5x

x = -15/5

x = -3

The letter that corresponds to this is G

2. 7 - 8x = 4x - 17

Add 8x to both sides

7 - 8x + 8x = 4x + 8x -17

7 = 12x - 17

Add 17 to both sides

7 + 17 = 12x - 17 + 17

24 = 12x

x = 24/12

x = 2

The letter that corresponds to this is F

3. 20 -2(x - 2) = 2x

Clear the parentheses

20 -2x + 4 = 2x

Simplify

24 -2x = 2x

Add 2x to both sides

24 - 2x + 2x = 2x + 2x

24 = 4x

x = 24/4

x = 6

The letter that corresponds to this is B

4. 5(x + 4) = 6x - 5

Clear the parentheses

5x + 20 = 6x - 5

Subtract 5x from both sides

5x - 5x + 20 = 6x - 5x - 5

20 = x - 5

Add 5 to both sides

20 + 5 = x - 5 + 5

25 = x

x = 25

The letter that corresponds to this is A

Hence,

The code is GFBA

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Answer:

10

Step-by-step explanation:

8 + 2 = 10

Answer:

Yes.

Step-by-step explanation:

A good test to do is the vertical line test. You draw the equation you're trying to determine is or isn't a function, and then draw a vertical line through it, if it goes through once it is a function. If twice then it is not a function. Hope this helps. :)

The height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that:
Scott is 6 feet tall and casts a shadow that is 8 feet long. a nearby tree casts a show that is x+5 feet long

By using scale factor:

Let x be the height of the tree

x/6 = = (x + 5)/8

8x = 6(x + 5)

8x = 6x + 30

2x = 30

x = 15 feet

Thus, the height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.

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Answer:

Step-by-step explanation:

the independent variable is money.

sodas are the dependent.

the amount of sodas you buy are dependent on the amount of money you have.

population at 1992 = 3590

Population after Seven years (1999) = 4500

Given two points (t1, P1) and (t2, P2), the slope of the line m can be found.

p1 = (1992, 3590) and p2 = (1999, 4500)

m= ΔP/Δt

m= ((4500-3590))/((1999-1992))

m = 910/7

m=130 is the slope

The linear population function P(t) is

P(t)=130t + P0

Find the Y-Intercept P0

The population function P(t) is measured since the year 1990, year zero. The first moose population was measured in 1992, one year later. This provides an initial condition P (1) = 4500.

P (1) =130 (1) + P0 = 4500

P0 = 4370

P(t)=20t+4630

The moose population P(t) changes linearly year after year. The population function P(t) is measured in terms of t years since 1990.

t= 1990, P (0) =4370

t =1992, P (1) =130 (1) + 4370 = 4500 matches data

t=1999, P (2) = 130(2) + 4370 = 4630

t=2006, P (3) = 130(3) + 4370 = 4760

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The directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.

In this question, the translations are defined by a line segment.

Such that in each translation, we can easily find the segment PQ (the measure and the direction).

And all the points in the Polygon P will be connected by that same segment PQ to the equivalent point in the Polygon Q. (where you only move the segment to the correct location, but the length and direction remains constant)

Thus, to find the line segment for each transformation, you need to correctly measure the length of the segment PQ, and also the direction (that can be defined by an angle).

With the above, we can find the directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.

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The five sets of integers that has a mean of -10 will be 10, -15, -2, -12, and -11.

It should be noted that mean simply means average. Therefore, the numbers that will give a mean of -10 will be:

-10, -15, -2, -12, and -11.

Therefore, the mean will be:

= ( - 10 + -15 + -2 + -12 + -11) / 5

= -50 / 5

= -10

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Answer: 20

Step-by-step explanation: She received 1/10 of the party favors, and 1/10 of 200 is 20.

Anna ordered 200 party favors, she received only 1/10 of the party favors

she ordered, i.e., Anna received 20 party favors.

Here, given that, Anna ordered 200 party favors. she received only 1/10 of the party favors she ordered.

Now, we have to find out how many party favors Anna received,

we need to calculate 1/10 of the total number of party favors she ordered.

Anna ordered 200 party favors, and she received only 1/10 of that amount.

As, we know that, 'of' indicates 'multiplication'

so, we have to find 1/10 of 200, so that, we multiply 200 by 1/10:

1/10 * 200

= 200/10

= 20

i.e. She received 1/10 of the party favors, and 1/10 of 200 is 20.    

So, Anna received 20 party favors.

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The value of each number is 52 and 39.

The ratio given is = 4 :3

Given, the sum of x + y = 91

(4n) + (3n) = 91

7n = 91

n = 13

So,

x = a*n = 4*13 = 52

y = b*n = 3 *13= 39

The ratio of 52:39 is 4:3.

The sum 52+39 = 91

Hence, the numbers are 39 and 52.

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Answer:

B) 600000

Step-by-step explanation:

First we need to answer A

13822×623/14 = 615,079

B) 615,079 = 600000

Answer:

so x=-1

Step-by-step explanation:

substitute "-1" for x

so, 2(-1)+30=28

and, -4(5(-1)-2)>>-4(-5-2)>>20+8

so, 28=28

The price of each souvenirs is 28.33 Dollars.

Let X be the same price of all the t-shirts and all the baseball caps.

Lacey purchased

4 T-shirts and 2 Baseball caps = $162

4X + 2X = $162

        6X = $162

Anna purchased

1 T-shirt and 2 Baseball caps = $93

1X + 2X = $93

        3X= $93

Now we will add the price of souvenirs purchased by Lacey and Anna to find the price each souvenir.

6X = $162              eq. 1

3X= $93                eq. 2

As we have two equations we will add both equations :

6X + 3X = $162 + $93  

Then we will determine the value of X .

         9X = $255

           X = $255 ÷ 9

          X = $28.33

Hence the price of each souvenirs is $28.33 .

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Answer:

1. no

2. 2,684,354,560 crickets

3. $9,200

4. b

5. 7.5

6.b

Answer: (-2,3) (1,4) (-1,-4) (2,-3) the answer would be -16,1

Step-by-step explanation: graphing it

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The equation to represent the relationship between the dollar amount Kiran is spending and the number of games and the number of rides is 0.25x + y = 12

The graph that represents the relationship between the quantities in this situation is graph C.

It should be noted that the equation will be:

25x + 100y = 1200 in cents

or 0.25 x + y = 12 in dollars

where

x= games

 y= rides

The graph that will connect the x axis and y axis at the points where x= 48 and y= 12,  Only graph C seems to have a line that may end at x=48. Therefore, the correct option is C.

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The answer to the given logarithm expression is   log₂ 16 = 4

A power to which a number must be increased in order to achieve another value is referred to as a logarithm. The easiest way to represent enormous numbers is in this way.

The fact that addition and subtraction logarithms can be used to multiply and divide logarithms is supported by a number of significant features of logarithms. The use of logarithmic operations is subject to a set of rules. These guidelines are known as: Division regulations apply to products. Exponential/Power Law Changes to fundamental laws Rule of Base Change Log elaboration

We need to evaluate log₂ 16

Using the property logₐ (mⁿ) = n logₐ m

16 = 2⁴log₃ 125 can be written as

log₂ 16 = 4 log₂ 2

We know that logₐ a = 14 log₂ 2= 4

Hence , we evaluated the logarithm which is log₂ 16 = 4

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Simplifying the problem by rationalizing all denominators will give result  [tex]14\sqrt[3]{3}[/tex]

Lets begin by simplifying the equation;

[tex]10\sqrt[3]{81} - 8\sqrt[3]{24}[/tex]    

The result is;

[tex]10 * 3 \sqrt[3]{3} - 8* 2*\sqrt[3]{3}[/tex]

[tex]30\sqrt[3]{3} -16\sqrt[3]{3}[/tex]

Let [tex]\sqrt[3]{3}[/tex] be a

Thus; 30a -16a= 14a

But a is [tex]\sqrt[3]{3}[/tex]

The final solution to this equation is thus;

[tex]14\sqrt[3]{3}[/tex]

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The slope of the line whose data represents a linear function is  m = -1/4.

Slope of an straight line is denoted by m and is the measure of rate of change of 'y' with respect to 'x'. Mathematically -

m = tan(θ) = Δy/Δx

Given is a table representing a linear function. From the question, we can write -

X →    6      8     13      14

Y →  -16   -24   -44    -48

We can find the slope of this line using the formula -

m =  Δy/Δx

m =  (y₂ - y₁) / (x₂ - x₁)

Take any two coordinates from the table -

(x₁,  y₁) → (6, -16)

(x₂, y₂) → (8, -24)

Substitute the values in the formula -

m = (8 - 6)/(-24 + 16)

m = - 2/8

m = -1/4

Therefore, the slope of the line whose data represents a linear function is  m = -1/4.

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 4.8170.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: - log (5x - 4)=3

We are given a logarithmic expression: log (5x - 4)=3  

We know that e^(log b) = b

Using exponential on both sides, we have

e^(log (5x - 4)) = e^3

5x - 4 = 20.085

5x = 24.085

x = 4.817

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 4.8170.

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The amount that Archie has to pay for his share of the costs is £605

What is the amount of total cost for the holiday?

The total costs of the holiday comprise of plane tickets, accommodation as well as the care hire for a week, in essence, the total costs to be shared equally among the four friends is as shown below:

total costs of holiday=£1360+£850+ £210

total costs of holiday=£2420

Archie's share of costs=£2420/4

Archie's share of costs=£605

In other words, the cost of  the holiday, in this case, is not just plane ticket, accommodation cost as well as the cost of care hire, without any of the those , the holiday experience is not complete

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Answer:

x = 16

Half of 32 is 16

Therefore, 2 × x(16) = 32

Simplifying the given expression ( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴) gives a result of 0.

Given the expression in the question;

( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴)

First, perform the operations inside the parenthesis

( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴)

( (-9(2)³ )/4 ) + ((1/2)(6)² )/( 4²÷2⁴)

Raise 2 to power 3, 6 to power 2, 4 to power 2 and 2 to power 4

( (-9(8) )/4 ) + ((1/2)36 )/( 16 ÷ 16)

Perform the operations in the parenthesis

-72/4  + 18/1

Divide -74 by 4

-72/4  + 18/1

-18 + 18

Negative 18 and positive 18 cancels out  each other.

-18 + 18

0

Therefore, simplifying the given expression ( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴) gives a result of 0.

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Answer:

-7/3 or -2.3

Step-by-step explanation:

1. y2-y1 divided by x2-x1 which would be y2-y1/x2-x1

2. plug in : -2-19/3-(-6)

4. Solution ( -7.3 or -2.3 )

Answer:

[tex]y = -\dfrac{7}{3}x +5[/tex]

Step-by-step explanation:

The general equation of a line in slope-intercept form is

y = mx + b

where m = slope and b = y-intercept is rise over run

[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]

where (x₁, y₁) and (x₂, y₂) are any two points on the line

For the line passing through (-6, 19) and (3, -2) , the slope

[tex]m = \dfrac{-2 - 19}{3 - (-6)}\\\\[/tex]

[tex]\\\\m= \dfrac{-21}{9}[/tex]

[tex]m = -\dfrac{7}{3}[/tex]

So slope-intercept form is
[tex]y = -\dfrac{7}{3}x +b\\\\[/tex]

To compute y-intercept, b,  plug in any of the two points into the above equation and solve for b

Let's choose point (3, -2)

Plugging x = 3 and y = -2 gives

[tex]-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\[/tex]

So equation of line is
[tex]y = -\dfrac{7}{3}x +5[/tex]

Answer:

[tex]b = 10\sqrt{5-4\cos 26^{\circ}}[/tex]

Step-by-step explanation:

Using the Law of Cosines,

[tex]b^2 = a^2 + c^2 - 2ac \cos B \\ \\ b^2 = 20^2 + 10^2 - 2(20)(10)\cos 26^{\circ} \\ \\ b=\sqrt{500-400\cos 26^{\circ}} \\ \\ =10\sqrt{5-4\cos 26^{\circ}}[/tex]

Answer:

y= -3x

Step-by-step explanation:

the equation is " y = (slope)x + (y-intercept) " hope this helps !!