Given this equation...

4x - 1 6
--------- = -----
3x + 7 5

What is the value of x in this
proportion?

By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].

In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:

Now, we proceed to simplify the function:

[tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex]

[tex]\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}[/tex]

[tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex]

By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].

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Answer:

one pound of chocolate chips = $2.75

one pound of walnuts = $3.75

Step-by-step explanation:

we can solve this by first making an equation

let's write the number of chocolate chips in c

and the number of walnuts in w

5c  + 3w = 25

7c + 9w = 53

let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it

(15c + 9w = 75) - (7c + 9w = 53)

8c = 22

c = $2.75

Let's now start to solve for w by inputting c into one of the equations.

(2.75)7 + 9w = 53

19.25 + 9w = 53

9w = 53 - 19.25

9w = 33.75

w = $3.75

a pound of chocolate chips  = 2.75

a pound of walnuts = 3.75

give me brainliest, please!

Hope this helps :)

Answer:

each pound of chocolate chips costs $2.75

each pound of walnuts costs $3.75

Step-by-step explanation:

let c be the cost of a pound of chocolate chips

and w be the cost of a pound of chocolate chips

For 5 pounds of chocolate chips and 3 pounds of walnuts,

the total cost is $25  means  5c + 3w = 25

For 7 pounds of chocolate chips and 9 pounds of walnuts,

the total cost is $53  means  7c + 9w = 53

Now we have to solve the system:

[tex]\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]

The value of x is 0.5

The equation is given as:

(x -2)(x + 3) = (x - 2)(4 - x)

Divide both sides by x - 2

x + 3 = 4 - x

Evaluate the like terms

2x = 1

Divide by 2

x = 0.5

Hence, the value of x is 0.5

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The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.

The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.

From the given information:

[tex]\mathbf{y=\dfrac{1}{4}(x-1)^2+5}[/tex]

The vertex of an up-down facing parabolic equation takes the form:

y = ax² + bx + c  is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

Rewriting the given equation:

[tex]\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}[/tex]

[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}[/tex]

[tex]\mathbf{x_v =1}[/tex]

Replacing the value of x into the equation, y becomes:

[tex]\mathbf{y_v = 5}[/tex]

Thus, the parabola vertex is (1,5)

From the vertex, the focus of the parabola is (1,6), and the directrix y = 4.

The graphical representation of the parabola is seen in the image attached below.

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Answer: The center of the circle will be (1,2) and the radius will be 2.5

Step-by-step explanation: Basically since its (x-1) it would become x=1 so that's ur first value same thign with y but that would be ur second value. And since in your equation it is 6.25 that would be 2.5 because 6.25 is r^2 and you are looking for r.

hi

I cannot figure the number  2.16 thousand has it does not mean anything to me.

But the only thing you need to do is to add  15 times 220

so = 3300

Answer:

5,460 people

Step-by-step explanation:

2,160 + 220x is the expression. Now, we plug in 15 for x.

2,160 + 220(15)

2,160 + 3,300 = 5,460

Brainliest, please :)

If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

An equation is an expression that shows the relationship between two or more variables and numbers.

There are 6 days from Monday to Saturday. The factory is closed on Tuesday and 15000 packets were packed on Monday. If no less than 100000 packet must be packed, hence:

4x + 15000 ≥ 100000

x ≥ 21250

If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

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Answer: H. Parallel lines may intersect.

Step-by-step explanation:

By definition, parallel lines never intersect.

Answer:

BA + BC = AC

Step-by-step explanation:

B is the midpoint of AC

Then

BA = AC/2 and BC = AC/2

Then

BA + BC = AC/2 + AC/2 = AC

Answer:a

Step-by-step explanation:

Answer:

Gievn that l=3m,b=5m,h=4m

L.S.A=2(l+b)h

=2×(3.5)×4

=2×8×4

=64sq.m

Step-by-step explanation:

The place value in the thousands for the 0 in 10,000 is three (3).

A place value refers to a numerical value which denotes a digit based on its position in a given number and it includes:

In this scenario, the place value in the thousands for the 0 in 10,000 is three (3).

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Part A

1) (5, -1)

2) (1, -3)

3) (-2, -2)

4) (-5, -4)

Part B

1) (-5, 1)

2) (-1, 3)

3) (2, 2)

4) (5, 4)

Answer:

x = 9

Step-by-step explanation:

4x + 7 = 43

4x = 36

x = 9

The value of y  / 3 in the equation is x / 4.

Therefore,

x + 4 / 4 = y + 3 / 3

then y / 3 can be found as follows,

x + 4 / 4  = x / 4 + 4 / 4 = x  / 4 + 1

y + 3 / 3  = y / 3 + 3 / 3  = y / 3 + 1

x  / 4 + 1 = y / 3 + 1

subtract 1 from both sides of the equation

x  / 4 + 1 - 1 = y / 3 + 1 - 1

x / 4 = y / 3

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Answer:

Yes because putting value of x and y as 1 and -1 in equation :

y=3x-4

-1 = 3 * 1 - 4

-1 = -1 (True)

1) This is a Two tailed Test.

2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.

3) P-value = 0.00968764 and so we reject H₀

We are given the hypothesis as;

Null Hypothesis; H₀: m₁ = m₂

Alternative Hypothesis; H₁: m₁ ≠ m₂

1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.

2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;

If the p-value is greater than 4% fail to reject H₀.

3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;

z = 2.5868

4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.

5) P-value = 0.00968764

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Answer: -x² + 4x + 6

Given:

f(x) = 4x + 1

g(x) = x² - 5

Solve:

= (f - g)(x)

= f(x) - g(x)

= 4x + 1 - (x² - 5)

= 4x + 1 - x² + 5

= -x² + 4x + 6

Answer:

(f-g) (x) = 4x+1 - x² + 5 = -x² + 4x + 6

Step-by-step explanation:

Explanation can be given if needed in the comments (ㅅ´ ˘ `)

The measure of x in the right angled triangle shown is 4.09

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

From the diagram shown:

sin(17) = x / 14

x = 4.09

The measure of x in the right angled triangle shown is 4.09

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The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let f(n) represent the total cost of shoe rentals for n games, hence:

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

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Step-by-step explanation:

We can determine whether the change represents exponential growth or exponential decay by making a table for a few values of x.

0 -> [tex]38(1.09)^0[/tex] = 38 * 1 = 38

1 -> [tex]38(1.09)^1[/tex]= 38 * 1.09 = 41.42

2 -> 38(1.09)² = 38 * 1.09 * 1.09 = 45.1478

We see that y increases as x increases, which makes this function represent exponential growth.

The percentage rate of increase is how much the value of y increases by each time x increases.

Since we are multiplying by 1.09 each time, we are taking 109% of the previous y value to get the current y value. Hence, the rate of increase is 9%.

Answer is slope of 5

Step by step

You can graph the slope as seen on the attached picture. You go up 30, you go right +6. Slope is y/x, so 30/6, equals 5

You can also use the slope formula

(y2-y1) over (x2-x1)

Using points on the graph

(6,0) and (0,-30)

(-30-0 ) over (0-6)

-30 over -6

-30/-6

= 5

The length of side PS according to the quadrilateral descriptions is; 21.

Since, it follows from the task content that the two quadrilaterals given are congruent, hence, the corresponding sides are congruent and are in proportion to each other.

On this note, we have;

x/35 = 15/25

x = (35×15)/25

x = 21.

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The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.

In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.

IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.

Therefore, the answer is: A. The data are skewed and there are outliers.

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The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²

An equation is an expression that shows the relationship between two or more variables and numbers.

Pressure = density * acceleration due to gravity (g) * depth

g = 10 m/s², hence:

Pressure = 1025 * 10 * 23000 = 2.3575 * 10⁸ N/m²

The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²

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The possible coordinates for the vertex D of the parallelogram could be (-4, 3)

It is given that A(1, –1), B (–1, 3), and C (4, –1) are the three vertices of the parallelogram.

Let us assume that the vertices are in the order A, C, B, and D where the coordinates of D are (a, b).

In this scenario, if we join AB and CD, they will become the diagonals of the parallelogram ABCD.

According to the properties of a parallelogram, diagonals bisect each other.

Hence, mid-point of AB = mid-point of CD

Now, according to the mid-point theorem, if mid-point of AB is given as (x,y), then,

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

Here, for AC,

x₁ = 1, y₁ = -1

x₂ = -1, y₂ = 3

Then, x = ( 1 - 1)/2 and y = (-1 + 3)/2

(x, y) ≡ (0, 1)  ............. (1)

Since (x, y) is also the mid-point of CD, we also have,

x₁ = 4, y₁ = -1

x₂ = a, y₂ = b

Then, x = (4 + a)/2 and y = (-1 + b)/2

(x, y) ≡ ((4 + a)/2, (-1 + b)/2) ................... (2)

From (1) and (2),

(4+a)/2 = 0 and (-1+b)/2 = 1

4+a = 0 and (-1+b) = 2

a = -4 and b = 3

Hence, the fourth vertex D of the parallelogram can be possibly located at (-4, 3)

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Answer:

Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic

Step-by-step explanation:

12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.

Para que un número sea divisible por 6 debe cumplir dos condiciones.

En este caso tenemos 12,480, que sabemos que es par.

La suma de sus digitos da:

1 + 2 + 4 + 8 + 0 = 15

15 es multiplo de 3.

Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.

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If the company sells 0 computers, they will not make a profit. They will lose $10780

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

m represents the slope

By comparison, we have:

m = 490

This means that the slope is 490

Hence, the interpretation is

Slope; 490

The company earns $490 per computer sold

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

c represents the vertical intercept

By comparison, we have:

c = -10780

This means that the vertical intercept is -10780

Hence, the interpretation is

Vertical intercept; -10780

If the company sells 0 computers, they will not make a profit. They will lose $10780

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

-c/m represents the horizontal intercept

By comparison, we have:

-c/m = 10780/490

-c/m = 22

This means that the horizontal intercept is 22

Hence, the interpretation is

Horizontal intercept; 22

If the company sells 22 computers, they will break even. They will earn  $0

We have:

P = 490n - 10780

This gives

P = 490* 46 - 10780

P = 11760

If the company sells 46 computers, they will earn $11760

We have:

P = 490n - 10780

This gives

15190 = 490n - 10780

490n = 15190+10780

490n = 25970

n = 53

The company will earn $15190, if they sell 53 computers

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