Explain the steps you would use to solve the equation. Find the solution.

8^2x =4096

The statement that best describes the effect on the graph of y=(x-9)² if the equation is changed to y = (x + 9)² is:O C. The graph moves left 18 units.

The graph shifts horizontally when the equation is modified from y = (x - 9)2 to y = (x + 9)2. The graph's points' x-coordinates are impacted by the inclusion of 9 inside the brackets.

The graph is moved 9 units to the left by adding 9 to the x-coordinate. As a result, the phrase "The graph moves left 18 units" is the most correct way to describe the effect on the graph.

Therefore the correct option is C.

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The kWh used is the difference between the previous and present meter reading. The kWh used are :

kWh used = Present reading - Previous reading

Household A = 2288 - 2150 = 138

Household B = 7810 - 7285 = 525

Household C = 4938 - 4605 = 333

Therefore, the power consumed in kWh by the three households is 138, 525 and 333 respectively.

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In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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The function which is modeled by the graph is y=2x+4.

We have to find the function in the given graph.

The line is passing through the points (-1, 2) and (0, 4).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = 4-2/0+1

=2

Now let us find the y intercept.

4=2(0)+b

b=4

So the function is y=2x+4.

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The value of y is 48.

To find the value of y in this scenario, we need to use the fact that the angle bisector of ∠JSL splits it into two congruent angles.

Let's denote one of these congruent angles as ∠HSL and the other as ∠LSJ. Since ∠JSL is bisected, we have:

m∠JSL = m∠HSL + m∠LSJ

Given that m∠JSL = (4y - 10)° and m∠HSL = m∠LSJ = ∠HSJ = (y + 43)°, we can substitute these values into the equation:

4y - 10 = (y + 43) + (y + 43)

Simplifying the equation:

4y - 10 = 2y + 86

Subtracting 2y from both sides:

2y - 10 = 86

Adding 10 to both sides:

2y = 96

Dividing both sides by 2:

y = 48

Therefore, the value of y is 48.

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The coordinates of P' after rotating triangle PQR counterclockwise by 270 degrees about the origin are P'(-3, 1).

To rotate a point counterclockwise about the origin, you can use the following rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

In this case, we want to rotate the triangle PQR 270 degrees counterclockwise. We can calculate the coordinates of each point after the rotation.

For point P(-1, -3):

x' = (-1) * cos(270°) - (-3) * sin(270°)

y' = (-1) * sin(270°) + (-3) * cos(270°)

We can simplify these equations using the values of cosine and sine for 270 degrees:

x' = (-1) * 0 - (-3) * (-1)

y' = (-1) * (-1) + (-3) * 0

Simplifying further:

x' = 0 - 3

y' = 1 + 0

x' = -3

y' = 1

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The polygons are not similar because they do not have a constant similarity ratio

From the question, we have the following parameters that can be used in our computation:

The polygons

To check if the polygons are similar, we divide corresponding sides and check if the ratios are equal

So, we have

Scale factor = 150/100 = 151/100

Scale factor = 1.5 = 1.51 --- false

Hence, the polygons are not similar

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The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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Hello !

Answer:

[tex]\large \boxed{\sf y=3x+10}[/tex]

Step-by-step explanation:

The slope-intercept form of a line is of the form [tex]\sf y=mx+b[/tex] where m is the slope and b is the y-intercept.

Given :

Let's substitute m with its value :

[tex]\sf y=3x+b[/tex]

Moreover, we know that the line passes through the point (-4,-2).

Let's replace x and y whith -4 and -2 in the previous equation :

[tex]\sf -2=3(-4)+b\\\sf -2=-12+b[/tex]

Let's solve for b !

Add 12 to both sides :

[tex]\sf -2+12=-12+12+b\\\underline{\sf b=10}[/tex]

The slope-intercept form of the equation is [tex]\sf y=3x+10[/tex].

Have a nice day ;)

To multiply the given binomials, we use the distributive property. So, the multiplication of the given binomials (2√3x - 2) and (3√3x + 5) is 18x + 4√3x - 10.

Using the distributive property which is given as: (a+b) (c+d) = a*c + a*d + b*c + b*d.

To multiply the binomials (2√3x - 2) and (3√3x + 5), we need to apply the distributive property which will result in four different terms.

Using the distributive property: (2√3x - 2) (3√3x + 5)= (2√3x * 3√3x) + (2√3x * 5) - (2 * 3√3x) - (2 * 5)= 6√(3x*3x) + 10√3x - 6√3x - 10= 6√9x² + (10-6)√3x - 10= 6 * 3x + 4√3x - 10= 18x + 4√3x - 10.

Therefore, the multiplication of the given binomials (2√3x - 2) and (3√3x + 5) is 18x + 4√3x - 10.

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Part A of the problem asks for the mode/modes or most frequently occurring value from all the data. The most commonly occurring value is 2 bedrooms, the value that 'reaches the highest' on the bar graph.

Part B is slightly more complicated. This asks for the most common number of bedrooms for detached houses. We can answer this by looking for the frequency of the number of bedrooms for each bar.  

Examining the graph tells us that the number of detached houses with 1 bedroom is 10, the number of detached homes with 2 bedrooms is 30, the number of detached houses with 3 bedrooms is 10, and the number of detached houses with 4 bedrooms is 30. Since we have two data points with the same highest frequency, we have two modes, [tex]$\boxed{2 \text{ and } 4}$[/tex].

The probability that a randomly selected permutation of the letters A, A, B, C, S, U would spell "abacus" is:  

(A) 1/720

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

The number of permutations of 6 letters is:

6! =720

Out of these 720 permutations, only one spells "abacus" (based on the arrangement of letters).

Thus, the probability that a randomly selected permutation of the letters A, A, B, C, S, U would spell "abacus" is:  

1/720

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The midline of the graphed function is y = 3.

For a sinusoidal function, we define the midline as the value that the function takes when the sinusoidal term is equal to zero.

So, for example in:

f(x) = k*sin(x) +M

The midline is the line y = M

so this is a line that goes through the middle of the graph.

On the given graph, we can see that the maximum value is at:

y = 5

The minimum is at:

y = 1

The midline is right between these two, at:

M = (5 + 1)/2 = 3

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There are 5040 different passwords that can be created from the word "Alabama" when using all the letters.

To calculate the number of different passwords that can be created from the word "Alabama," we need to consider the total number of permutations.

The word "Alabama" contains 7 letters. To find the number of different passwords, we need to calculate the number of permutations of these 7 letters.

The formula to calculate permutations is given by:

nPr = n! / (n - r)!

Where n is the total number of items (letters in this case), and r is the number of items selected (length of the password).

For the word "Alabama," let's assume we want to create passwords of length 7, using all the letters.

n = 7 (number of letters in "Alabama")

r = 7 (length of the password)

Using the formula, we can calculate the number of permutations:

7P7 = 7! / (7 - 7)!

= 7! / 0!

= 7! / 1

= 7 × 6 × 5 × 4× 3 × 2 × 1

= 5040

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Answer:

NO

Step-by-step explanation:

No. The sample of only the 2 fastest swimmers on the swim team is not likely to be representative of the entire swim team. It may not include swimmers with different skill levels or performance abilities, which could lead to a biased representation of the team as a whole. To have a representative sample, it would be necessary to include a diverse range of swimmers from different skill levels and performance abilities.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The solution to the inequality 9x - 3 ≤ 3 is x ≤ 2/3.

To solve the inequality 9x - 3 ≤ 3, we can isolate the variable x by performing the following steps:

9x - 3 ≤ 3

First, let's add 3 to both sides of the inequality:

9x - 3 + 3 ≤ 3 + 3

9x ≤ 6

Next, divide both sides of the inequality by 9:

(9x)/9 ≤ 6/9

x ≤ 2/3

Therefore, the solution to the inequality 9x - 3 ≤ 3 is x ≤ 2/3.

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The statement is false. It is important to consider historical facts and data when making statements or assumptions about specific events or individuals.

The counterexamples to the statement "No U.S. president has been younger than 65 at the time of his inauguration" are:

B. Theodore Roosevelt

E. John F. Kennedy

C. Barack Obama

F. James Buchanan

These presidents were all younger than 65 at the time of their inauguration, which contradicts the given statement. Theodore Roosevelt was 42, John F. Kennedy was 43, Barack Obama was 47, and James Buchanan was 60 years old when they assumed the presidency.

By providing these counterexamples, we demonstrate that there have indeed been U.S. presidents who were younger than 65 at the time of their inauguration.

The statement is false. It is important to consider historical facts and data when making statements or assumptions about specific events or individuals.

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48 minutes is equivalent to 1/5 of 4 hours.

We have,

To express 48 minutes as a fraction of 4 hours, we need to convert both the minutes and hours into a common unit of time.

Since there are 60 minutes in an hour, we can convert 4 hours to minutes:

4 hours = 4 x 60 minutes = 240 minutes

Now, we can express 48 minutes as a fraction of 240 minutes:

48 minutes / 240 minutes

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 48:

= 48 minutes / 240 minutes

= 1/5

Therefore,

48 minutes is equivalent to 1/5 of 4 hours.

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Answer:

A = 153.86

Step-by-step explanation:

A = πr^2

A = 3.14 (7)^2

A = 3.14 (49)

A = 153.86

There is a unique solution (x = 0, y = 5) that satisfies both equations, the system of equations has one solution. There is a unique solution (x = 0, y = 5) that satisfies both equations, the system of equations has one solution.

To determine the number of solutions for the given system of equations:

y = -2x + 5

4y + x - 20 = 0

We can solve the system of equations using various methods such as substitution, elimination, or graphing. Let's solve it using the elimination method:

First, we'll multiply the first equation by 4 to make the coefficients of x in both equations equal:

4y = -8x + 20

4y + x - 20 = 0

Next, we'll subtract equation 1 from equation 2 to eliminate the y term:

(4y + x - 20) - (4y = -8x + 20)

This simplifies to:

x = 0

Now, we substitute this value of x back into the first equation to find the value of y:

y = -2(0) + 5

y = 5

we have found the values x = 0 and y = 5, which satisfy both equations simultaneously.

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The perimeter (P) by multiplying the side length by 4:
P = 4 * (4√2) = 16√2
The answer: b. 16√2

To find the perimeter of a square with a diagonal length of 8 feet, first, you need to determine the side length. In a square, the diagonal length (d) is related to the side length (s) through the Pythagorean theorem as follows:

d = s√2

Now, plug in the given diagonal length (8 feet) and solve for s:

8 = s√2
s = 8/√2
s = 4√2 (simplified by multiplying both numerator and denominator by √2)

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Answer:

[tex]\Huge \boxed{\text{13.66$\%$}}[/tex]

Step-by-step explanation:

To find the rate, we need to use the following formula:

[tex]\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}[/tex]

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

[tex]\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}[/tex]

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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The area of the shaded region is 61.76 square feet.

The given figure has a rectangle and circle.

Let us find the area of both rectangle and circles.

The length of rectangle is 14 ft and width is 8 ft.

Area = length × width

=14×8

=112 square feet.

The diameter of the circle is 8 feet because diameter is equal to width of rectangle.

Radius =diameter/2

= 4 ft.

Area of circle =πr²

=3.14×4²

=3.14×16

=50.24

To find the area of shaded region subtract area of circle from area of rectangle.

Shaded area = 112-50.24

=61.76 square feet.

Hence, the area of the shaded region is 61.76 square feet.

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Answer:

the dean bought more of swiss than cheddar because hee only bought  1.5 pounds of cheddar and 1.7 of swiss

Step-by-step explanation:

The value of p is -3.

To rewrite the equation 2x² + 12x = -13 in the form 2(x - p)^2 + q = 0, we need to complete the square. Let's go through the steps:

2x² + 12x = -13

First, let's move the constant term to the right side:

2x² + 12x + 13 = 0

Next, divide the equation by the leading coefficient (2) to simplify:

x² + 6x + 6.5 = 0

To complete the square, we take half of the coefficient of x (6) and square it to get 9.

Then, we add and subtract 9 to the equation:

x² + 6x + 9 - 9 + 6.5 = 0

(x + 3)² - 3² + 6.5 = 0

(x + 3)² - 9 + 6.5 = 0

(x + 3)² - 2.5 = 0

Comparing this equation with 2(x - p)² + q = 0, we can see that p = -3 and q = -2.5.

Therefore, the value of p is -3.

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Answer:

11

Step-by-step explanation:

ijj

Answer:

y= -3/2x+1

Step-by-step explanation:

slope intercept is y = mx + b form

so the answer is y= -3/2x+1

Using synthetic division, P(a)= 9.

To find P(a) using synthetic division and the remainder theorem, we will substitute the value of a into the polynomial p(x) = x^3 + 4x^2 - 5x + 6 and perform synthetic division.

First, let's set a = 2 and write the polynomial as p(x) = x^3 + 4x^2 - 5x + 6. Now, we set up the synthetic division table:

2 | 1 4 -5 6

|_____________

1 6 7 9

The numbers in the first row of the table are the coefficients of the polynomial p(x), and the second row represents the result after each step of the synthetic division. The number at the bottom right corner, 9, is the remainder.

According to the remainder theorem, P(a) is equal to the remainder when p(x) is divided by (x - a). In this case, a = 2, so P(2) is equal to the remainder, which is 9.

Therefore, P(2) = 9.

In summary, using synthetic division and the remainder theorem, we find that P(2) for the polynomial p(x) = x^3 + 4x^2 - 5x + 6 is equal to 9.

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Answer:

A=6 and B=2

Step-by-step explanation:

if my answer is correct then DM me for explanation

The meaning of the amount his classmates spend on clothes is,

If the amount spent on clothes per month by all his classmates is leveled, that amount would be $46.

We have to given that,

The amount of money everyone spends buying snacks each month has a mean of $46.

Mean = Sum of observations / Total number of observation

Hence, It means that average amount of money spend by everyone is $46.

And, If the amount spent on snacks per month by all his classmates is leveled, that amount would be $46.

So, if some one paid more amount than $38, whereas some one paid less amount than $38.

It will be nullify by leveling the amount by all his classmate while calculating the mean.

So, Option 'D' is correct.

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