Find the value of 3x + 2 when 7 + x = 5

Answer:

4

Step-by-step explanation:

If Judge is x years old and Eden is 6 years older, then Eden is x + 6 years old.

The second part tells us that Eden will be twice as old as Judge in two years.

This means that in two years: (Eden's age) = 2 * (Judge's age).

Since we know that Eden's age can be represented as x + 6 and Judge's age can be represented as x, we can write this: x + 6 = 2 * x

Simplify the equation:

x + 6 = 2x

6 = x = Judge's age (in two years)

If Judge is 6 two years later, then he must be 4 now.

To check our work, we can just look at the problem. Judge is 4 years old and Eden is 6 years older than Judge (that means Eden is 10 right now). Two years later, Eden is 12 and Judge is 6, so Eden is twice as old as Judge. The answer is correct.

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ\(\bigstar\boxed{\large\bf{\leadsto -\dfrac{28}{9}}}\)

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‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟼ \dfrac{\dfrac{14}{9}}{\dfrac{-1}{3}-\dfrac{1}{6}}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟼ \dfrac{\dfrac{14}{9}}{\dfrac{-2-1}{6}}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟼ \dfrac{\dfrac{14}{9}}{\dfrac{-3}{6}}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟼\dfrac{14}{9}\times -2}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟼\dfrac{-28}{9}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

Answer:

the amount that nearest to the paper cost with the discount but before tax is $12.83

Step-by-step explanation:

The computation of the amount that nearest to the paper cost with the discount but before tax is shown below:

= Cost of a photo paper - discount

= $13.50  - 5% of $13.50

= $13.50 - $0.675

= $12.83

Hence, the amount that nearest to the paper cost with the discount but before tax is $12.83

Answer:

inequality form: x \(\leq\) -2 or x > 3

interval notation form: (-∞,-2] ∪ (3,∞)

Step-by-step explanation:

I attached a picture that shows all the work. You begin by isolating then solving for x on both sides. Then form a solution using the information found out about x. For example, you can combine the found inequalities for x to solve that x must be GREATER than 3 while being LESS than -2. Using that you can form an line and make a line. Remember, when writing in interval notation form you always begin from the left to the right (in reference) to the number line.

Answer:

$7.85

Step-by-step explanation:

2 pizzas at 11.99=23.98

4 soft drinks at 1.85=$7.40

23.98+7.40=31.38

31.38/4=7.845

Each friend pays $7.845, or $7.85 .........

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

324

Step-by-step explanation:

- 6 × - 54 = 324

Note : -

When a negative number multiplied with another negative number, its result is a positive number.

Answer:

B: 264 cm squared

Step-by-step explanation:

got it right

We can write the volume of the cylinder as 48π cubic feet.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is to find the area of the given composite figure.

It is given to find the area of the given composite figure. We can write the area of the figure as -

Area = Area of square + Area of trapezoid + Area of rectangle

Area = {side x side} + {1/2(a + b) x h} + {L x B}

Area = {10 x 10} + {1/2(14 + 8) x 4} + {20 x 6}

Area = 100 + 44 + 120

Area = 264 square centimeter

So, it can be concluded that the area of the figure is 264 square centimeter.

Therefore, we can write the the area of the figure is 264 square centimeter.

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The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

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The total asset of Magic mirror is $515,708

Magic Mirror has $428,210 in capital and $87,498 in liabilities.

The capital is also know as the equity which means the company's net worth.

Liabilities are everything a business owes, now and in the future.

Assets are everything a business owns. Assets may be current or fixed assets

Therefore,

Total Assets - Total Liabilities = Capital

Where

Hence,

Total Assets  =  $87,498 + $428,210

Total Assets  = $515,708

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Answer: 5 3/4

Step-by-step explanation:

Answer:

\(Perimeter = 14 + 7\sqrt{2}\)

Step-by-step explanation:

Given:

Area of the square = 49 in²

Required

Determine the perimeter of the one of the congruent triangles

First, we'll determine the length of the square;

\(Area = Length * Length\)

Substitute 49 for Area

\(49 = Length * Length\)

\(49 = Length^2\)

Take Square root of both sides

\(7 = Length\)

\(Length = 7\)

When the square is divided into two equal triangles through the diameter;

2 sides of the square remains and the diagonal of the square forms the hypotenuse of the triangle;

Calculating the diagonal, we have;

\(Hypotenuse^2 = Length^2 + Length^2\) -- Pythagoras Theorem

\(Hypotenuse^2 = 7^2 + 7^2\)

\(Hypotenuse^2 = 2(7^2)\)

Take square root of both sides

\(Hypotenuse = \sqrt{2} * \sqrt{7^2}\)

\(Hypotenuse = \sqrt{2} * 7\)

\(Hypotenuse = 7\sqrt{2}\)

The perimeter of one of the triangles is the sum of the 2 Lengths and the Hypotenuse

\(Perimeter = Length + Length + Hypotenuse\)

\(Perimeter = 7 + 7 + 7\sqrt{2}\)

\(Perimeter = 14 + 7\sqrt{2}\)

The data set  0, 2, 5, 8, and 10 have a higher standard deviation but the same mean.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set is 2, 2, 5, 8, 8.

Now, The standard deviation has other uses than serving as a measurement for the normal distribution. It is more commonly used as a measure of spread.

To have a greater standard deviation the data should have more differences from each other.

Therefore, 0, 2, 5, 8, 10 have the same mean but greater standard deviation.

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Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

Given that the magnitude of x would be lesser than < -2

Then it would consisted with the values smaller than -2

x { -3,-4,-5,-6,......,-infininty} (ans)

Hope it helps

the awnser is -12,x-1{+8}

Answer: 36/12 = 3

Step-by-step explanation:

Answer:

The expression should be something like: 36/12

Answer:

\(x=\frac{28}{9}\)

Step-by-step explanation:

\(\frac{3x}{4} =\frac{7}{4}\)

\(\Longleftrightarrow \left( 3x\right) \times 3=7\times 4\)

\(\Longleftrightarrow 9x=28\)

\(\Longleftrightarrow x=\frac{28}{9}\)

Answer:

x1 = y1 - a*y2 + (a*c - b)*y3

x2 = y2 - c*y3

x3 = y3

Step-by-step explanation:

Here we have the system:

x1 + a*x2 + b*x3 = y1

x2 + c*x3 = y2

x3 = y3

Where the variables y1, y2, and y3 are known (a, b and c are also known).

The first step is to isolate one of the variables in one of the equations, we can see that in the third equation we have x3 already isolated, so now we can just replace it on the other two equations to get:

x1 + a*x2 + b*(y3) = y1

x2 + c*(y3) = y2

Now we again want to isolate one of the variables in one of the equations, i will isolate x2 in the second equation to get:

x2 = y2 - c*y3

Now we can replace this on the other equation to get:

x1 + a*(y2 - c*y3) + b*y3 = y1

Now we canw write x1 in terms of the known variables:

x1 = y1 - a*y2 + (a*c - b)*y3

And in the process we also found that:

x3 = y3

x2 = y2 - c*y3

Then the solutions are:

x1 = y1 - a*y2 + (a*c - b)*y3

x2 = y2 - c*y3

x3 = y3

The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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By completing the square, the vertex form of quadratic equation is (x - 1)² - 3.

In this question we find a quadratic equation in standard form, which must be modified into vertex form by completing the square, which consists in modifying part of the equation into a perfect square trinomial. The vertex form of the quadratic equation is:

y = C · (x - h)² + k

First, write the polynomial in standard form:

x² - 2 · x - 2

Second, use algebra properties to expand the expression:

(x² - 2 · x - 2) + 0

(x² - 2 · x - 2) + 3 - 3

(x² - 2 · x + 1) - 3

Third, use the definition of perfect square trinomial:

(x - 1)² - 3

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

5.59

Step-by-step explanation:

unit price = total price / total number of pairs

               = 33.54/6 = $ 5.59

Answer:

5.59 each pair of socks.

Step-by-step explanation:

33.54÷6=5.59

Answer:

Step-by-step explanation:

Answer:

A. is the answer

Step-by-step explanation:

A. Since there is one value of  y  for every value of  x

B. is not a function x  =  − 4  produces  y  =  4  and  y  =  3

C. is not a function x  =  6  produces  y  =  6  and  y  =  3

D. is not a function   x  =  6  produces  y  =  3  and  y  =  5

Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

A is either 45° or 135°.

To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.

Using the distance formula, we have:

AB² = x₁² + y₁²

AC² = x₂² + y₂²

According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:

(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]

Expanding and simplifying the equation, we get:

x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)

This equation can be further simplified to:

(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)

Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.

In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.

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Answer: Its high

Step-by-step explanation: It just is

The probability that Brent draws mismatched socks is 32/153.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since Brent is drawing two socks without replacement, there are 18 choices for the first sock and 17 choices for the second sock.

Therefore, there are 18 x 17 = 306 possible ways Brent could draw two socks.

For Brent to have mismatched socks, he needs to draw a white sock first and a black sock second, or a black sock first and a white sock second.

Let's consider the first case.

There are 16 white socks and 2 black socks, so there are 16 x 2 = 32 ways Brent could draw a white sock first and a black sock second.

For the second case, there are 2 black socks and 16 white socks, so there are 2 x 16 = 32 ways Brent could draw a black sock first and a white sock second.

Therefore, the probability of Brent drawing mismatched socks is:

= (32 + 32) / 306

= 64 / 306

= 32 / 153

Thus, the probability that Brent draws mismatched socks is 32/153.

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Answer:

so first we have to make it to y- intercept form

5x + 3y = 7

3y = 7 -5x since we moved to the other side of the equal sign it turns negative

now divide both sides by 3 becuase y needs to have no number in front of it

3y divided by 3

7 divided by 3

-5 divided by 3

now its y = 7/3 - 5/3x

now we need to reorder the terms so its y = mx + b

y = -5/3x + 7/3 or 2.3

mx equals slope so -5/3 is the slope

Step-by-step explanation:

Answer:

−5/3

Step-by-step explanation:

Parallel lines have the same slope. So to find the parallel line you must first find the slope of the original line. Do this by putting the equation into slope-intercept form. Once the equation is in the slope-intercept form it is, \(y=-\frac{5}{3}x+\frac{7}{3}\). Therefore, the correct answer is −5/3.