Simplify the expression by combining like terms.
n + 4n - 7n - 1

The graph displays the pre-image function f(x) being translated into the image function g. (x). A translation of 4 units to the right and 2 units up is required to change f(x) to g(x).

A function is a statement, rule, or law that specifies the connection between two variables.

Functions are common in mathematics and are required for the formulation of physical connections.

The graph shows a translation of the pre-image function f(x) to the image function g(x).

Hence,the transformation of f(x) to g(x) is a translation of 4 units to the right and 2 units up.

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answer

x=180-87-33

= 60

The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Answer:

2x = 250. x = 125

Step-by-step explanation:

RULE: (# of sides - 2 x 180)

6-2=4x180=720

720-60-65-100-120= 375

2x + x = 3x

3x = 375

x = 125

Answer:8

Step-by-step explanation:  First you times 4 x 2 like

4+4=8 here is how i got the four you have to put the four 2 times i hope this helped

Answer:

y = 36.

Step-by-step explanation:

If you think about it, the three angles in the triangle add up to be 180. The missing angle just so happens to be part of a supplementary angle, that adds to be 180. If the unlabeled angle were denoted as x, we could have...

(y + 5) + y + x = 180

y + 41 + x = 180

(y + 5) + y + x = y + 41 + x

(y + 5) + y = y + 41

2y + 5 = y + 41

y = 36

Hope this helps!

Answer:

A i. a:c=3:10

ii. a:b:c=2:5:10

B i. x:z=2:5

ii. x:y:z=2:4:5

Step-by-step explanation:

A.) If a:b = 2:5 and b:c = 3:4, find (i) a:c(ii) a:b:c

a:b=a/b=2/5

b:c=b/c=3/4

a/b*b/c=a/c

2/5*3/4=a/c

6/20=a/c

3/10=a/c

Therefore, a:c=3:10

a:b:c

a:b=2:5

b:c=3:4

b is common to both ratios

The value of b in the first ratio is 5 and b is 3 in the second ratio

Lets take the LCM of both values

LCM of 5 and 3=15

So, we will change the value of b in the first ratio and second ratio to 15

By doing this, we will multiply the whole first ratio by 3

We have, 6:15

We multiply the whole second ratio by 5

We have, 15:20

Therefore a:b:c=6:15:20

=2:5:10

B. If x:y = 1:2 and y:z = 4:5,

x:y=x/y=1:2

y:z=y/z=4:5

x/y*y/z=x/z

1/2*4/5=x/z

4/10=x/z

2/5=x/z

Therefore, x:z=2:5

x:y:z

x:y=1:2

y:z=4:5

y is common to both ratio

Take the LCM of y values in both ratio

LCM of 2 and 4 =4

So,we will change the value of y in the first and second ratio to 4

By doing this, we will multiply the whole first ratio by 2

We have, 2:4

We will also multiply the whole second ratio by 1

We have, 4:5

Therefore, x:y:z=2:4:5

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

22.5 square units

Step-by-step explanation:

added in the picture

The problem with solving 1110 - 1110 using 2's complement in 7-bit data representation is that it results in an overflow, and to overcome this, either increase the number of bits or use a larger data type for representation.

We are subtracting 1110 from 1110 using 2's complement and using 7-bit data representation. Let's go through the steps:

Step 1: Convert 1110 to its 2's complement representation in 7 bits:

  - In 7 bits, the leftmost bit is the sign bit.

  - Since the leftmost bit of 1110 is 1 (indicating a negative number), we can simply represent it as it is: 1110.

Step 2: Perform the subtraction using 2's complement:

  1  1  1  0

- 1  1  1  0

------------

  0 0 0 0

The result of the subtraction is 0000. However, this result is problematic because it is not within the range that can be represented with 7 bits using 2's complement.

To overcome this problem and prevent overflow, we can take the following steps:

1. Increase the number of bits: Increase the number of bits used for representing the numbers. Using more bits allows for a larger range of representable numbers and reduces the chance of overflow. If possible, use more bits for data representation.

2. Use a larger data type: If using a fixed number of bits is a requirement, consider using a larger data type, such as a larger integer type, that can accommodate the expected range of values without overflow.

3. Check for overflow conditions: Before performing arithmetic operations, check for potential overflow conditions. For example, when subtracting two negative numbers or adding two positive numbers, the result should have a different sign. If the signs of the operands are the same and the result has the opposite sign, it indicates overflow.

4. Handle overflow cases: If overflow occurs, take appropriate actions based on the specific requirements of your application. This could involve truncating or discarding the most significant bits of the result or applying additional logic to handle the overflow condition appropriately.

By considering these suggestions and adjusting the number of bits or data type used for data representation, you can overcome the problem of overflow when performing arithmetic operations using 2's complement.

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Given the equation:

Solve the equation for y:

So, the answer will be:

Answer:

4 hours and 10 min

Step-by-step explanation:

For this equation we will do ratios:

\(\frac{18}{30} =\frac{150}{x} \\\\18x=4500\\x=250\)

250 min =

4 hours and 10 min

4(60) = 240

240 + 10 = 250 minutes

Answer:

45

Step-by-step explanation:

angle 7 is right angle because its congruent to 4 by alt.int.angles

so if its isosceles,

180-90=90

90/2= 45

angle 5 = 45

The option that is NOT an augmented functional dependency is: Q --> P, because it removes the attribute from the left-hand side of the existing functional dependency, which is not allowed in an augmented dependency.

Functional dependency: It is a concept in database management systems that describes the relationship between two attributes or sets of attributes in a table. In a functional dependency A → B, A is the determinant or the attribute(s) that uniquely determines the value of B.

Augmented functional dependency : It is formed by adding one or more attributes to the determinant side of an existing functional dependency.

From the given options, the only one that is not an augmented functional dependency is "Q → P". This is because it does not involve adding any attributes to the determinant side of an existing functional dependency.

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Answer:

It decreased by 61.5%

Step-by-step explanation:

The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The question is incomplete.

The complete question is attached in the picture, please refer picture.

We have an expression:

\(= \rm \dfrac{\left(14x^4y^6\right)}{\left(7x^8y^2\right)}\)

\(\rm =\dfrac{7\cdot \:2x^4y^6}{7x^8y^2}\)

\(\rm =\dfrac{2x^4y^6}{x^8y^2}\)

\(\rm =\dfrac{2y^4}{x^4}\)

Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

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Answer:

A

Step-by-step explanation:

imagine explaining

The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.

To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) =  = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The value of the given definite integral after performing a series of calculations is 14, under the condition the given definite integral is \(\int\limits^2_1 (4x^{3} -3x^{2}+ 2x)dx.\)

A definite integral is  known as an integral expressed as the difference in comparison to the values of the integral at specified upper and lower limits . In short , it is a given way of evaluating the area undergoing a curve between two points on the x-axis .

The definite integral of (4x³-3x² + 2x)dx from 1 to 2 can be evaluated as

\(\int\limits^2_1 (4x^{3} -3x^{2} + 2x)dx\)

= [x⁴ - x³ + xx²]₂¹

= [(2)⁴ - (2)³ + (2)²] - [(1)⁴ - (1)³ + (1)²]

= 14

The value of the given definite integral after performing a series of calculations is 14, under the condition the given definite integral is \(\int\limits^2_1 (4x^{3} -3x^{2}+ 2x)dx.\)

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The vertices of the hyperbola are (-4, 0) and (4, 0), the foci are (-5, 0) and (5, 0), and the asymptotes are y = -x and y = x.

The equation of the given hyperbola is in the standard form\(\(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\), where \(a\) represents the distance from the center to the vertices and \(c\) represents the distance from the center to the foci. In this case, since the coefficient of \(y^2\)\)is positive, the transverse axis is along the y-axis.
Comparing the given equation with the standard form, we can determine that \(a^2 = 16\) and \(b^2 = -16\) (since \(a^2 - b^2 = 16\)). Taking the square root of both sides, we find that \(a = 4\) and \(b = \sqrt{-16}\), which simplifies to \(b = 4i\).
Since \(b\) is imaginary, the hyperbola does not have real asymptotes. Instead, it has conjugate asymptotes given by the equations y = -x and y = x.
The center of the hyperbola is at the origin (0, 0), and the vertices are located at (-4, 0) and (4, 0) on the x-axis. The foci are found by calculating \(c\) using the formula \(c = \sqrt{a^2 + b^2}\), where \(c\) represents the distance from the center to the foci. Plugging in the values, we find that \(c = \sqrt{16 + 16i^2} = \sqrt{32} = 4\sqrt{2}\). Therefore, the foci are located at (-4\sqrt{2}, 0) and (4\sqrt{2}, 0) on the x-axis.
In summary, the vertices of the hyperbola are (-4, 0) and (4, 0), the foci are (-4\sqrt{2}, 0) and (4\sqrt{2}, 0), and the asymptotes are y = -x and y = x.



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Answer: b =27

Step-by-step explanation:

24 = b -3   Just add 3 to both sides

+3         +3

b = 27

Answer:

b=27

Step-by-step explanation:

Let's solve your equation step-by-step.

24=b−3

Step 1: Flip the equation.

b−3=24

Step 2: Add 3 to both sides.

b−3+3=24+3

b=27

Answer:

b=27

Answer:

You forgot to send the question. Send the full question when you can

The statement that an example of Instructional Task Learning is the Count on Sesame Street counting to 10, is True.

Instructional task learning refers to a type of education where students gain expertise in a particular skill or concept by completing multiple tasks that have been specifically devised to aid them in mastering the subject matter.

On Sesame Street, the students are acquiring the knowledge of numerically counting up to 10 via the character of Count. The Count offers several activities aimed at imparting the same skill to learners, including object counting, singing songs that involve counting, and engaging in counting games. Through the completion of these assignments, students can proficiently acquire the ability to accurately count up to 10.

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Answer:

x = 12.48

y = 13.22

Step-by-step explanation

Im not sure if its correct

10^2 + b^2 = 16^2

100 + b^2 = 256

b^2 = √156

b = 12.48

b= 12 ( If needed to round to the nearest whole number)

a^2 + 15^2 = 20^2

a^2 + 225 = 400

a^2 = √175

a = 13.22

a = 13 ( If needed to round to nearest whole number)

Answer:

600

Step-by-step explanation:

Volume=l*b*h=5*12*10=600

The next four terms in the geometric sequence are 500, 100, 20 and 4

Sequence is a set or series of related items or events in a particular order. It can refer to a number of different things, such as a set of numbers, a set of events, or a set of objects. In mathematics, a sequence is a series of numbers or other mathematical objects that follow a particular pattern.

In the given problem, the sequence is;

312,500, 62,500, 12,500, 2,500

This is most likely a geometric sequence and we have to find the common ratio.

r = 62500 / 312500 = 0.2 or 2500 / 12500 = 0.2

The common ratio is 0.2

The next term will be the 5th term

Tₙ = arⁿ⁻¹

T₅ = ar⁴

a = first term = 312500

T₅ = 312500(0.2)⁴

T₅ = 500

The next term is 6th term

T₆ = ar⁵

T₆ = 312500(0.2)⁵

T₆ = 100

T₇ = ar⁶

T₇ = 312500(0.2)⁶

T₇ = 20

T₈ = 312500(0.2)⁷

T₈ = 4

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Answer:

the amswer is Rs. 1,25,000

Answer:

Sum = Rs. 125000

Step-by-step explanation:

Given

Amounts = Rs. 1,32,651

Time = 3/2 years

Rate = 4%

Compounded half yearly

Concept

A = P × (1 + r/100)t

When compounded half yearly

Rate become half and Time become double (As in 1 year 12 months = 6 months + 6 months)

Calculation

Time = 3 years

Rate = 2%

⇒ 132651 = P × (1 + (2/100))^3

⇒ 132651 = P × (1 + (1/50))^3

⇒ 132651 = P × (51/50)^3

⇒ P = (132651 × 50 × 50 × 50)/(51 × 51 × 51)

Note:- 51^3 = 132651

⇒ P = Rs. 125000

∴ Sum = Rs. 125000

The statement "The intersection of two planes can be a point" is sometimes true.

When two planes intersect, the resulting intersection can take different forms depending on the relationship between the planes.

If the two planes are not parallel, they will intersect in a line. This means that the intersection of two non-parallel planes cannot be a single point.

However, if the two planes are parallel, they will never intersect, and therefore the intersection cannot be a point.

Therefore, the statement is sometimes true. It is true when the two planes are not parallel and intersect in a line, but it is false when the planes are parallel and have no intersection. The nature of the intersection of two planes depends on their relationship and can vary between a line or no intersection at all.

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)