Find the sum and express it in simplest form.
(-7n² - 8n - 8) + (-n² + 9n + 9)
008
Clear all
Enter the correct answer.
+ BO
DONE

Answer:

y = 1/3x - 7

Step-by-step explanation:

start with the point-slope form:

(y-y1) = m(x-x1)

substitute the values of (x,y) into the formula:

(y-(-5)) = 1/3(x-6)

y+5 = 1/3x - 2

now write in slope-intercept form:

y = 1/3x - 2 - 5

y = 1/3x - 7

The exponential function  can be written as y = 700e^-0.094t.

We know that the term function would have to do with a mathematical rule that we can use to be able to obtain specific values. Now we have to know that there was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.

We can use;

N = Noe^-rt

N = amount at time t

No = Amount at the beginning

r = decay rate

t = time taken

Thus we have; y = 700e^-0.094t

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the width of a rectangle is measured at 6 cm, its length at 10 cm, and its area at 60 cm2.

An example of a quadrilateral is a rectangle, which has four vertices that are all 90 degrees apart and parallel sides that are equal to one another. As a result, it is sometimes referred to as an equiangular quadrilateral. The rectangle is a 2D shape with 4 sides, 4 corners, and 4 right angles. The length of each pair of the diagonal sides of a rectangle is equal, with one pair being longer than the other. If all the sides of a rectangle were the same size, the shape would be referred to as a square.

given

Consequently, the rectangle has a length of 10 cm and an area of 60 cm2.

Since,

Area of a rectangle equals length times width

=60=10*breadth

width is 60/10.

= 6 cm in breadth.

the width of a rectangle is measured at 6 cm, its length at 10 cm, and its area at 60 cm2.

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The first equation in the second system is a multiple of  second equation

is the first equation and the second equation  in the second system is a multiple of both equation in the first system

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Answer:

$2

Step-by-step explanation:

The given parametric equation represents the graph mentioned in Option A.

A parametric equation is defined as a kind of equation that inherit an independent variable called a parameter, and where dependent variables are defined as continuous functions of the parameter.

here,
For equation, x = t cos (t), y = t, z = t sin(t), t ≥ 0.
Since,

x² + y² = t²cos²(t) + t² sin²t
x² + y² = t²
x² + y² = z²

Here, the x-z cross-section of the curve is a circle. But as t accumulates, the radius of the circle also advances in the y direction, and those circular cross-sections extend as the value of the parameter t increase.
The curve will draft as circles in x-z planes while moving towards y direction and also the radius of those circular cross sections increases at the same rate as its advancement towards y direction.

Thus, the given parametric equation represents the graph mentioned in Option A.

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Answer:

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

If you buy a sweater, the second one is at 40% discount.

Divide the discount between the two to get:

You get a discount of 20% for each sweater.

Answer:

Discount percentage = 20%

Step-by-step explanation:

Discount of the sweaters,

→ first sweater = 0%

→ other sweater = 40%

The average discount percent is,

→ (first sweater + other sweater)/2

→ (0% + 40%) ÷ 2

→ (0 + 40)/2

→ 40/2

→ 20% off

Hence, the answer is 20% off.

6% of the salary is $366

The total amount that would in the retirement account in the account each month is $732.

The amount that would be in the retirement account when you retire is $345,418.50.

The amount of money that you put in the account is $162,504.

The amount of money that the employer put in the account is $162,504.

The interest that was gained over the years is $20,410.50.

3% of the salary is $183.

The total amount that would in the retirement account in the account each month is $366.

The amount that would be in the retirement account when you retire is $172,709.25.

The amount of money that you put in the account is $81,252

The amount of money that the employer put in the account is $81,252

The interest that was gained over the years is $10,205.25.

6% of the salary = salary x percentage

6% of the salary = 6% x $6,100

6% of the salary = 0.06 x $6,100 = $366

The amount in your account at the end of the month = amount the company puts + amount you deposit

= $366 + $366 = $732

Amount that would be in your retirement account = (1 + interest rate) x amount in the account

Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year

Amount in the account at retirement = $732 x 12 x (62 -25)

$732 x 12 x 37 = $325,008

Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50

Amount the employer put in the account =  $325,008 \ 2 = $162,504

Interest earned = $345,418.50 - $325,008 = $20,410.50

3% of the salary = salary x percentage

3% of the salary = 3% x $6,100

3% of the salary = 0.03 x $6,100 = $183

The amount in your account at the end of the month = amount the company puts + amount you deposit

= $183 + $183 = $366

Amount that would be in your retirement account = (1 + interest rate) x amount in the account

Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year

Amount in the account at retirement = $366 x 12 x (62 -25)

$366 x 12 x 37 = $162,504

Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25

Amount the employer put in the account =  $162,504 \ 2 = $81,252

Interest earned = $172,709.25 - $162,504 = $10,205.25

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The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

Part A

g(x) = 9.25x

g(8) = 9.25*8

g(8) = 74

He would make $74 before taxes if he worked 8 hours.

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

Part B

g(x) = 9.25x

g(14) = 9.25*14

g(14) = 129.50

He would make $129.50 before taxes if he worked 14 hours.

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

Part C

g(x) = 9.25x

g(27.5) = 9.25*27.5

g(27.5) = 254.375

g(27.5) = 254.38

He would make $254.38 before taxes if he worked 27.5 hours.

Answer:

Solution below.

Step-by-step explanation:

This question is basically asking you to substitute corresponding x values to find g(x).

Given the function from the question:

g(x) = 9.25x where x is the work hours and g(x) is the wages.

Given x = 8,

g(8) = 9.25 * 8 = $74.00

Given x = 14,

g(14) = 9.25 * 14 = $129.50

Given x = 27.5,

g(27.5) = 9.25 * 27.5 = $254.38 (rounded off to nearest cent)

Amount of pounds that Ben get back is £75.

Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.

Ben changes £800 to Euros before he goes on holiday.

Before holiday, exchange rate is, £1 = 1.25 Euro

£800 = 800 × 1.25 Euros = 1000 Euros

He spends 895 Euros.

Euros left = 1000 - 895 = 105 Euros

Now, the exchange rate is £1 = 1.40 Euro.

or 1.40 Euro = £1

⇒ 1 Euro = £ 1/1.40

⇒ 105 Euros = £ (1/1.40) × 105 = £75

Hence Ben got £75 of pounds back.

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Answer:

p = 20

Step-by-step explanation:

120 divided by 6 would = 20

Answer: p = 20

Step-by-step explanation:

120/6=20

6x20=120

The figure with equal opposite sides and all the interior angles being right angles is a rectangle.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

A rectangle is a special type of quadrilateral in which opposite sides are of equal length(not all sides are the same) and all the interior angles are right angles.

From the given diagram the opposite sides are equal and all the interior angles are right angles hence the figure is a rectangle.

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Answer:

A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. This ratio is called the common ratio of the sequence.

In this case, the common ratio is 3/2 and the first term is 6. The nth term of a geometric sequence can be found using the formula:

a_n = a_1 * r^(n-1)

where a_n is the nth term, a_1 is the first term, and r is the common ratio.

Substituting the given values, we have:

a_8 = 6 * (3/2)^(8-1) = 6 * (3/2)^7

Calculating, we find that the 8th term is:

a_8 = 6 * (3/2)^7 = 6 * (9/2) = 27

Therefore, the 8th term is 27.

Step-by-step explanation:

The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.

An equilateral triangle have all its side lengths equal so;

line AB = line BC = line AC

At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle

Line BC form the diameter of the circle which is 2 radius of the circle so;

line BC = 2 × radius of the circle

line BC = 2 × 1

line BC = 2

Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.

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To solve this we must be knowing each and every concept related to triangle. Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The denotes a triangle having vertex A, B, and C. In Euclidean geometry, every three non-collinear points define a unique triangle and, by extension, a unique plane.

In geometry, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.

Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.

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Answer:

Step-by-step explanation:

15.9 beacuse yeah thats it

So we know that we need to add 15 to the double of this number. We know we need to add 15 since it says "15 more than" and we know we need to double/multiply the number by two since it says "twice a number"! We also know that this mystery number equals 5.

Therefore, we can set up our equation and solve! The variable x is used to represent the number we're looking for!

2x + 15 = 5

2x = -10

x = -5

So, your answer should be -5!

Barrett saves by joining the art museum instead of science museum is $2.50 plus $1.25 per month.

Saving money is one of the essential aspects of building wealth and having a secure financial future. Saving money gives you a way out of the uncertainties of life and provides you with an opportunity to enjoy a quality life.Savings represents an individual's unspent earnings. It is the amount that remains after meeting the household expenses.

Member benefits are the perks, services, and access that members receive as part of their membership. In other words they are what members get in exchange for joining the organization and if applicable, paying member dues.

Now we have

Fee charged by science museum= $10.75

Fee charged by art  museum         =$8.25

Now by subtracting he saves       =$2.50

Again

he saves =amount charged by science - amount charged by arts

              = $3.50 -$2.25

              = $1.25

In the results he saves $2.50 +$1.25 per month.

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Answer:

it is not always true that 75% of a number will be greater than 50% of any other number

Step-by-step explanation:

Leila's statement is not true. It is possible for 50% of a number to be greater than 75% of another number.

For example, consider the numbers 10 and 100. 50% of 10 is 5, and 75% of 100 is 75. In this case, 50% of 10 (5) is greater than 75% of 100 (75).

Here's another example: 50% of 20 is 10, and 75% of 30 is 22.5. In this case, 50% of 20 (10) is again greater than 75% of 30 (22.5).

Therefore, it is not always true that 75% of a number will be greater than 50% of any other number.

The two scenarios that can be represented by a ratio 4:5 are

1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books

2. The ratio of marker to crayon , if there are 4 markers and 5 crayons. ( option A and D)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For a scenario that will give ratio of 4:5, it means the first entity will be 4 and the second entity will be 5.

Therefore the two statements that obey this in the option are

1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books

2. The ratio of marker to crayon , if there are 4 markers and 5 crayons.

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The equation of the line passing through the points (-2,9) and (1,3) is

y = -2x + 11 where the slope is -2 and the y-intercept is +11

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

m = (y2 - y1) / (x2 - x1)

y1 = 9

y2 = 3

x1 = -2

x2 = 1

m = (3 - 9) / (1 - (-2))

m = - 6 / 3

m = - 2

The equation of the line;

m = (y - y1) / (x - x1)

-2 = y - 9 / x - 1

y - 9 = -2(x - 1)

y - 9 = -2x + 2

y = -2x + 11

Therefore the y-intercept is +11.

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I'm sorry but I didn't get that

The correct solutions for this question are as:

(A) Bearing of B from A = 72°

(B) Bearing of B from C = 342°

(C) Bearing of A from B = 252°

(D) Bearing of A from C = 293°

Step by step solution:

(A) Bearing of B from A:

= 72° (Given in question)

(B) Bearing of B from C: = 342°

Solution:

As sum of co-interior angles is 180° , i.e.  ∠NBC +∠NCB =180°

so, 162° + ∠NCB = 180°

     ∠NCB = 180°-162°

     ∠NCB = 18°

reflexive angle NCB =360° - ∠NCB

reflexive angle NCB = 360° - 18°

reflexive angle NCB = 342°

So, bearing of B from C: = 342°

(C) Bearing of A from B: = 252°

Solution:

First extend the line AB to any point (let's say "X")

So, ∠NBX = 72°   [BY USING CORRESPONDING ANGLES]

Bearing of A from B = ∠NBX + 180°

Bearing of A from B =72° + 180°

Bearing of A from B =252°

(D) Bearing of A from C: = 293°

Solution:

Bearing of A from C= 360° - (∠BCA + ∠BCN)

Bearing of A from C= 360° - (49° + 18°)

Bearing of A from C= 360° - (67°)

Bearing of A from C= 293°

Important Points for "Bearing of Angles":

A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.

The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.

Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.

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The slope-intercept form of the equations presented on the graph are;

y = 4

y = 3

The slope-intercept form of the equation of a line is; y = m·x + c, where;

m = The slope of the graph

c = The y-intercept of the graph

The equation of the lines in the graphs (blue line, and red line) are found as follows;

The slope of the blue line is found using the points on the graph as follows;

The coordinates of points on the blue line graph are; (0, 4), (2, 4), (4, 4)

The slope is therefore; m = (4 - 4)/(4 - 2) = 0

The y-intercept, obtained from the graph is; c = 4

The value of the slope, m = 0, indicates that the graph is an horizontal line with an equation y = c

c = 4

The equation of the blue line graph in slope-intercept form is therefore;

The coordinates of points on the red line graph are; (0, 3), (2, 3), (4, 3)

The slope of the red line graph is therefore;

m = (3 - 3)/(4 - 2) = 0

The y-intercept of the red line graph is; c = 3

The value of the slope, m = 0, and the y-intercept, c = 3, indicates that the equation of the red line graph is therefore;

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