Can someone help me with this?

given the proportion :

we will find x as follows:

So, the answer is: x = 32

Answer:

Step-by-step explanation:

Let the green graph be G and the blue graph, be B:

1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive

Note: First, we should note that the blue function must therefore be a transformation of the Green function.

This means B takes the form:

y = (s)*a*|X+b|

We are required to find a, b, and s, where s is the sign.

2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).

Therefore, s = -1

3) From (2), it follows that the first transformation produces the following effect:

y = |X| transformed to y = -|X|

and B now takes the form y = -a*|X+b|

4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.

5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;

y = -a*|X+b| implies;

0= -a*|1+b|      

|1+b| = 0/-a

|1+b| = 0

1+b = 0

and y becomes:

Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;

y = -a*|X-1|

-1 = -a*|5-1|

-1 = -a*|4|

-4a = -1

Blaise M.

Yes, conditions of randomness and normality of the population met for this test.

The textbook committee made a histogram of the sample data, and it was single peaked with no outliers. The conditions of randomness and normality of the population met for this test, the reason is that it was a random sample, and the plot of the sample data has no outliers.

So, yes, conditions of randomness and normality of the population met for this test.

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Answer: (52,72) (52 adults and 72 children)

Step-by-step explanation:

1) Create 2 formulas that show the information show above, 2.5x+2y=274 showing how the x is how many adults paid for a ticket and y is how many children paid for a ticket. The second formula being x+y=124 meaning the combination of children and adults equal 124 people.

2) Take those formulas and input them into a graph as shown in the picture (Graph 1)

3) Find the common point shown on the graph (should be the middle grey dot if on Desmos as shown (Graph 2)

4) The common point is (52, 72)

And if you plug these numbers in by replacing the x's and y's i shown in step 1 they bring an output of 274 and 124

Hope this helps :)

Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

Solution

For this case we can do the following:

tan x = 35/30

And we can solve for x and we got:

And rounded to the nearest degree is:

49º

ANSWER

EXPLANATION

Given;

Recall;

Therefore, the time taken is 3.2hours.

Answer:

A

Step-by-step explanation:

ax + by = c  Subtract ax from both sides

by = -ax + c  Divide all the way through by b

[tex]\frac{by}{b}[/tex] = [tex]\frac{-a}{b}[/tex] x + [tex]\frac{c}{b}[/tex]

y = - [tex]\frac{a}{b}[/tex] x +[tex]\frac{c}{b}[/tex]

The solution of system of equation is x = 2 and y = 7. We should multiply first equation with 2 so that when we add the two equations, we csystem of equation an eliminate the variable y.

What is system of equation?

Two or more equations that share variables are said to be .

For instance, consider two equations where x and y are shared:

x + y = 6

3x + y = 2

We might be able to solve equations that have the same number of variables. Where the lines intersect in this case is the answer (1,5)

Given system of equation:

5x + 3y = 41,

3x - 6y = 9

Lets multiply the first equation with 2, we get

10x + 6y = 82

Adding these equation with second given equation we get,

10x +6y +(3x - 6y) = 82 + 9

13x = 91

x = 91/13

x = 7

putting the value of x in any one equation

3(7) -6y = 9

y = 2

Therefore, the x and y in the given system of equation are 7 and 2 respectively.

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Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation

The problem states that "three increased by a quotient", this implies that the three is separated from the quotient, therefore, we need to create the equation in the following manner:

The correct answer is "b".

The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

A) [tex]x^{-2}+15x-3[/tex]

Here, the exponent of x is -2. So, the expression is not a polynomial.

B) [tex]-x^3+5x^2+7\sqrt{x} -1[/tex]

Here, the power of one of the term is 1/2. So, the expression is not a polynomial.

C) [tex]\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex]

Here, the power of one of the term is -2. So, the expression is not a polynomial.

D) 5.3x²+3x-2

Here, the power of each term is positive integer. So, the expression is a polynomial.

E) [tex]4x^4-10[/tex]

Here, the power of each term is positive integer. So, the expression is a polynomial.

The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.

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The approximate volume of the pyramid when it's 75% full is 303.75 inches³.

The volume of a square base pyramid can be represented as follows:

volume of the square base pyramid = 1 / 3 Bh

where

Therefore, the square bas pyramid has a base side of 9 inches and height of 15 inches. Let's find the volume when it's 75% full.

B = 9² = 81 inches²

h = 15 inches

Therefore,

volume of the square base pyramid = 1 / 3 × 81 × 15

volume of the square base pyramid = 81 × 5

volume of the square base pyramid = 405 inches³

Therefore, when it's 75% full

volume  = 75% of 405

volume = 75 / 100 × 405

volume = 30375 / 100

volume = 303.75 inches³

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The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0 and the definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)".

A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x². Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Here,

f(x)=2x²-x³

g(x)=-x²

f(x)/g(x)=(2x²-x³)/-x²

=x²(2-x)/-x²

f(x)/g(x)=x-2

The definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)". The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0.

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The reasonable domain and range are 0 ≤ x ≤ 15 and 0 ≤ y ≤ 360 and the domain is continuous

From the question, we have

Gallon gas tank = 15 gallons

This means that the domain is from 0 to 15

This can be represented as 0 ≤ x ≤ 15

For the range, we have

0 * 24 ≤ y ≤ 15 * 24

Evaluate

0 ≤ y ≤ 360

This means that

Range: 0 ≤ y ≤ 360

Lastly, the domain of the situation is continuous

This is so because the gas in the tank can take decimal values

Take for instance, the gas tank can be 13.79 gallons full

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The factors of the quadratic equation 5x^2 + 44x - 9 are (5x - 1) and (x + 9)

In Mathematics, factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.

In the given question, we can factorize 5x^2 + 44x - 9 by finding two factors that when they multiply will give us the original polynomial.

The factor for this polynomial or quadratic equation are (5x - 1)(x + 9).

This can be summarized as the factorization of 5x^2 + 44x - 9 is (5x -1)((x+ 9)

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Answer:x>-11/2

search it for a better understanding of the understanding the question

Answer:

x > -11/2

Step-by-step explanation:

Given inequation,

→ 12(x + 3) > 4x - 8

Now the value of x will be,

→ 12(x + 3) > 4x - 8

→ 12x + 36 > 4x - 8

→ 12x - 4x > -8 - 36

→ 8x > -44

→ [ x > -11/2 ]

Hence, value of x is -11/2.

‘B’ had a better college entrance exam score due to the higher value of Z-Score.

The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.

[tex]Z=\frac{(observation-mean)}{standard deviation}[/tex]

By putting the values as given in the question,We get,

A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.

B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.

Thus ‘B’ had a better score.

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Answer:

32x – 72

OR

–72 + 32x

Step-by-step explanation:

To use the Distributive Property, just simply follow my steps:

Write the equation:

–8(9 – 4x)

To distribute, multiply the numbers inside the parenthesis by the number outside of the parenthesis SEPARATELY. It should look like this:

(–8 • 9)(–8 • –4x)

(–72)(32x)

Since the 32 is positive, the equation could be written either way:

–72 + 32x

OR

32x – 72

If you want the equation to be fully solved...

Set the equation equal to zero:

32x – 72 = 0

Isolate the variable. Subtract 72 from both sides:

32x – 72 + 72 = 0 + 72

32x = 0 + 72

32x = 72

Divide:

32x/32 = 72/32

x = 9/4 (Improper Fraction Form)

OR

x = 2 (and) 1/4 (Mixed Number Form)

Convert 9/4 to a decimal:

x = 9/4

x = 2.25

Hope that helps you! Have an amazing rest of your day! Please consider giving me the Brainliest for best explanation! :)

Answer:

A would be the correct answer because to find a function when you draw a line on the graph, the line cannot cross each other. Even if the line is verticle, it is still crossing each other.

Step-by-step explanation:

Answer:

1. Fact that all individuals are created equal and are endowed by their creator with certain unalienable rights is a clear statement in the Declaration of Independence.

2. Aim of having a government is to safeguard these rights,  the people have the right and the duty to alter, abolish, or over through that government.

3. The Decoration of Independence lists the grievances that the government has failed to resolve and reconcile with the colonies.

4. The decree was made to become an autonomous nation and the motives for asserting independence are listed in the grievances.

The advantage and disadvantages are sampling.

We have to find the advantages and disadvantages of sampling.

The advantage is:

It provides an opportunity to do data analysis with a lower likelihood of carrying an error.

Researchers can analyze the data that is collected with a smaller margin of error thanks to random sampling. This is permitted since the sampling procedure is governed by predetermined boundaries. The fact that the entire procedure is random ensures that the random sample accurately represents the complete population, which enables the data to offer precise insights into particular topic matters.

The disadvantage is:

No extra information is taken into account.

Although unconscious bias is eliminated by random sampling, deliberate bias remains in the process. Researchers can select areas for random sampling in which they think particular outcomes can be attained to confirm their own bias. The random sampling does not take into account any other information, however sometimes the data collector's supplementary information is retained.

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The function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is;

(5, 3+2) +2 = (5, 5) + 2

Given,

A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3).

To find the what is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2

Now,

What is the equation of the parabola?

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3).

Hence, if the function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is; (5, 3+2) +2 = (5, 5) + 2.

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Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.

A = L * B

Hence the width B may be found from

1400 = 56 * B

B = 1400/56

B = 25 feet

b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,

the total cost to fence the backyard will be

= $10 * 2(56 + 25)

= $1,620

Step-by-step explanation:

You would start off with solving inside, the parenthesis, and you would get -8/27.

Then, your would solve the 1 1/4 - 3/4 and get 1/2.

You then have to multiply -8/27*1/2, which is -4/27.

Lastly, you divide by negative 4.

-4/27 divided by -4.

You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.

Since negative times negative is positive, the answer would be 1/27.

Answer:

1/27

Hope this helped! :)

EXPLANATION

Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:

Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,

Plugging in the numbers into the expression:

Multiplying numbers:

Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169

In conclusion, Colin will have $38,169 after 4 years

SOLUTION

From the question

Cross multiplying you have that

Hence, the answer is 70

Answer:

In both cases we get the same answer: the sum of the first 100 positive even numbers is 10,100.

Step-by-step explanation:

2 + 4 + 6 + 8 + ....+ 198 + 200 =

= (2 + 200) + (4 + 1998) + ... + (100 + 102) = 50*202 = 10,100