Given f(x) = − x² - 4x – 12, find f(-7)

The domain and range of the the function are -

Domain → [0, 180]

Range → [600, 1050]

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is that the owners of a recreation area filled a small pond with water in 180 minutes. The pond already had some water at the beginning. The graph {attached below} shows the amount of water (in liters) in the pond versus time (in minutes).

Domain is the set of all possible {x} values. We can write -

Domain → [0, 180]

Range is the set of all possible {y} values. We can write -

Range → [600, 1050]

Therefore, the domain and range of the the function are -

Domain → [0, 180]

Range → [600, 1050]

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On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.

What is the mid-point theorem?

According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.

The outer triangle is ABC and the inner triangle is DEF.

It can be seen that sides AB, BC and AC are equally divided such that AD=DB,

BE=EC and

CF=FA.

So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.

Now, according to the midpoint theorem -

DF = 1/2(BC)

Plugging in the values -

x = (5x-6)/2

2x = 5x-6

2x-5x = -6

-3x = -6

x = 2

Now, for side DE -

DE = 1/2(AC)

Plugging in the values -

12 = (2z+8)/2

24 = 2z+8

24-8 = 2z

16 = 2z

z = 8

Now, for side EF -

EF = 1/2(AB)

Plugging in the values -

y = 20/2

y = 10

Therefore, the values obtained are x=2, y=10 and z=8.

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The number of bracelets is 4.

The number of bracelets is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Number of bracelets = x

Number of necklaces = y

Amount of gold in each bracelet = 8 grams

Amount of gold in each necklace = 16 grams

Now,

x + y = 12 _____(1)

x = 12 - y ____(2)

8x + 16y = 160 ______(3)

Substituting (2) in (3) we get,

8(12 - y) + 16y = 160

96 - 8y + 16y = 160

96 + 8y = 160

8y = 160 - 96

8y = 64

y = 8

Now,

x = 12 - y

x = 12 - 8

x = 4

Thus,

The number of bracelets and necklaces that were made is 4 and 8.

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Answer:

Step-by-step explanation:

Answer: An increase of a population doubling every year can be modeled using repeated multiplication. The expression for the increase after five years would be:

2 * 2 * 2 * 2 * 2 = 2^5 = 32

This can also be written as an exponential expression, with 2 as the base and 5 as the exponent:

2^5 = 32

This notation expresses that 2 is multiplied by itself 5 times to get 32, which represents the population size after 5 years with the rate of doubling every year.

It's also worth mentioning that exponential notation is used to represent the quantity of growth (doubling every year) , and using exponents makes it easy to see how much the population has grown over a certain period of time.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2^5= 32

=2 x 2 x 2 x 2 x 2

= 2^5

= 32

Cory is hiking up a hill with a constant slope the double number line shows that after Cory hikes 3 km his elevation is 120 m. Select the double number line that correctly labels is option 'A'.

From brief half-day programs to extensive itineraries lasting more than 20 days, the activity's duration varies. The majority of the time, it is an activity that accepts groups of various sizes.

A long stroll, especially one undertaken for the sake of recreation or exercise; see also hike; an increase, particularly in quantity or amount. While it is entirely up to each hiker to assign whatever classification they see fit to their experience, I have found that the vast majority of hikers fall into one of the three most common categories: peak-bagging, long-distance hiking, or day hiking.

Because it is a constant slope and Cory hikes 3 km his elevation is 120 m.

slpoe = 120m/3km = 40m/1km

So, Cory's elevation after he hikes 1 km, his elevation is 40 m.

Cory's elevation after he hikes 2 km, his elevation is (2*40 m) 80 m.

Cory's elevation after he hikes 4 km, his elevation is (4*40 m) 160 m.

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The complete question is:

Cory is hiking up a hill with a constant slope. The double number line shows that after Cory hikes 3 km his elevation is 120m. Select the double number line that correctly labels Cory's elevation after he hikes 1, 2, and 4 km. Choose 1 answer:

The formula for a directed line segment is A = (x2 - x1, y2 - y1). It is a vector equation, meaning that it describes the direction and magnitude of a line segment, rather than its endpoint coordinates.  

A directed line segment is a line segment with a starting point and an ending point, where the direction of the line can be described in terms of its magnitude and direction. To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points, and then calculate the difference between the y-coordinates of the start and end points. The result is the vector A, which describes the magnitude and direction of the line segment.

For example, consider a line segment with start point (1, 2) and end point (4, 6). To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points (4 - 1 = 3). Then, calculate the difference between the y-coordinates of the start and end points (6 - 2 = 4). The result is the vector A = (3, 4). This vector describes the magnitude and direction of the line segment, with the magnitude being the length of the line segment, and the direction being the direction from the start point to the end point.

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The coordinate of 3 4 indicates a point on a cartesian plane.

In mathematics, the coordinate system refers to the method in which a location of a point is identified in the plane or space.

There are two coordinate system, one is cartesian coordinate system and the other is polar coordinate system.

Each coordinate system has some reference lines called reference axis or reference direction or point called reference direction and point.

As per the definition of a cartesian coordinate system, a location of a point is identified by a pair of numerical terms. The first one indicates the X coordinate and the second one indicates the Y coordinate.

So, the above coordinate 3 4 refers to a point on the XY coordinate system where 3 is the X coordinate and the distance from Y axis and 4 is the Y coordinate and distance from the X axis.

ordinate refers to y point in (x, y)

in (3,4)

ordinate = 4

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The 40th term of the sequence  aₙ = - 24 - 3n is - 144.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, A sequence is represented by the explicit formula aₙ = - 24 - 3n.

We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.

Therefore, To find a₄₀, we'll simply replace n with 40.

So, a₄₀ = - 24 - 3(40).

a₄₀ = - 24 - 120.

a₄₀ = - 144.

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Answer:

y = 2x+ 3

Step-by-step explanation:

A system of equations for this problem can be written as:

x + y = 10 (1) equation for the total number of herbs planted

0.50x + 0.25y = 3 (2) equation for the total cost of the herbs

Where x is the number of basil plants and y is the number of mint plants.

Using substitution, we can solve the system of equations.

Solving equation (1) for x, we get x = 10 - y

Substituting this into equation (2) we get:

0.50(10 - y) + 0.25y = 3

5 - 0.50y + 0.25y = 3

5 = 0.75y + 3

0.75y = -2

y = -2/0.75 = -8/3

So, Eden planted -8/3 mint plants, which doesn't make sense, as a fraction of plant are not possible. This implies that either the number of plants or the amount spent are incorrect or something is missing in the problem description.

The ordered pairs that defines the solutions of the system of equations f(x) = x² - 2x + 3; f(x) = -2x + 7 are

(2, 3) and (-2, 11)

Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)

As used in the cartesian coordinates

a refers to a point in the x direction b refers to a point in the y direction

Solutions of the system of equation is the points where the straight line intersect the curve or where the two graphs intersect.

the point of intersection

x² - 2x + 3 = -2x + 7

x² - 2x + 2x + 3 - 7 = 0

x² + 3 - 7 = 0

x² - 4 = 0

solving for x

x² = 4

x = √4

x = 2 OR -2

solving for y

For x = 2, y = -2 * 2 + 7 = 3

For x = -2, y = -2 * -2 + 7 = 11

hence we have the points to be (2, 3) and (-2, 11)

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Using trigonometric ratios, the value of x is as follows:

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the angle of a right angle triangle can be found using trigonometric ratios as follows:

Hence, let's find angle x

Therefore,

sin x = opposite / hypotenuse

opposite side = 7 ft

hypotenuse side = 18 ft

Hence,

sin x = 7 / 18

x = sin⁻¹ 7 / 18

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The length of the hypotenuse will be 5√2 = 7.07

The triangle specified in the question is right-angled, one angle is mentioned to be 90°. It is also an isosceles triangle since both other angles are equal. if both angles are equal, both sides will also be equal.

So the length of both equal sides = 5 cm

Pythagoras' theorem tells us about the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse of the right-angled triangle will be equal to the sum of squares of the other two sides. If a, b, and c are the sides

 c² = a²+ b²

  c = √(a²+b²)

According to Pythagoras' theorem, Hypotenuse = √base²+ alt²

                                                          Hypotenuse = √5²+5²

                                                                                = 5√2

                                                                               = 7.07 cm

So the length of the hypotenuse is 5√2 = 7.07 cm.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

here we go~

[tex]\qquad \sf  \dashrightarrow \: 4x {}^{2} - 25y {}^{2} [/tex]

[ identity : a² - b² = (a + b)(a - b) ]

[tex]\qquad \sf  \dashrightarrow \: (2x) {}^{2} - (5y) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5y)(2x - 5y)[/tex]

Answer: Breadth? Did you mean width? If so, the answer is 128cm

Step-by-step explanation:

Area = Width x Length

8x16=128

The percentage of ounce Dariu has left of his port drink is 55%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

It is given that Dariu ha a 40-ounce port drink.

He drank 18-ounce port drink.

First calculate what percentage of port drink Dariu drank.

The equation is -

= (18/40) × 100

= 45%

So, Dariu drank 45% of the port Drink.

Now, subtract the percentage Dariu drank from the 100% (40 Ounce) drink Dariu had -

100 - 45 = 55

Therefore, Dariu has 55% drink left.

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The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = 1.5 d + h0.

The height of the tent is 22. 5 feet at a horizontal distance of 15 feet.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.

This can be written as -

h = 1.5 d, where d is the distance.

So, the equations that models the situation is -

h = 1.5 d + h0

The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge.

So, when d =20, then h =30.

Plugging the values in the equation -

30 = 1.5 (20) + h0

30 = 30 + h0

h0 = 0

The height of the tent is 22. 5 feet.

So, now h = 1.5 d and h = 22.5.

Equating these two -

22.5 = 1.5 d

d = 22.5/1.5

d = 15

Therefore, the distance value is obtained as 15 feet.

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The equation of line is given by y = 25x + 80.

The equation of a line is expressed as y = mx + b where m exists the slope and b exists the y-intercept

y - y₁ = m ( x - x₁ )

Where, y be the y-coordinate of second point

y₁ be y-coordinate of point one

m be the slope

x be the x-coordinate of second point

x₁ be the x-coordinate of point one

Let the equation of slope m be

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Equation of line be represented as A

The two points are given as A ( 2 , 130 ) and B ( 8 , 280 )

The slope of the line between the two points exists given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 280 - 130 ) / ( 8 - 2 )

simplifying the above equation, we get

m = 150 / 6

m = 25

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 130 = 25 ( x - 2 )

On simplifying the equation , we get

y - 130 = 25x - 50

Adding 130 on both sides , we get

y = 25x + 80

The equation is of the form y = mx + b where b is the y intercept.

Therefore, the equation of line is given by y = 25x + 80

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The equation of line is given by y = 25x + 80, this represent the linear function between the amount of money and the saved amount.

The equation of a line is expressed as y = mx + b where m is called the slope and b is called the y-intercept

y - y₁ = m ( x - x₁ )

Where, y be the y-coordinate of second point

y₁ be y-coordinate of point one

m be the slope

x be the x-coordinate of second point

x₁ be the x-coordinate of point one

Let the equation of slope m be

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Equation of line be represented as A

The two points are given as A ( 2 , 130 ) and B ( 8 , 280 )

The slope of the line between the two points exists given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 280 - 130 ) / ( 8 - 2 )

simplifying the above equation, we get

m = 150 / 6

m = 25

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 130 = 25 ( x - 2 )

On simplifying the equation , we get

y - 130 = 25x - 50

Adding 130 on both sides , we get

y = 25x + 80

The equation is of the form y = mx + b where b is the y intercept.

Therefore, the equation of line is given by y = 25x + 80

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Answer:

the equation of the line is y = -7x - 2.

Step-by-step explanation:

To find the equation of the line with slope -7 that passes through the point (4, -30), we can use the point-slope form of a line.

The point-slope form of a line is:

y - y1 = m(x - x1)

where:

(x1, y1) is a point on the line

m is the slope of the line

Substituting the given values, we get:

y - (-30) = (-7)(x - 4)

Expanding the right side, we get:

y + 30 = -7x + 28

Combining like terms, we get:

y = -7x - 2

So the equation of the line is y = -7x - 2.

Angles x° and 157° are neighboring because they share a shared vertex and side, preventing them from overlapping,  the sum of any two angles on a straight line equals 180°.

Two lines converge at a common point to form an angle. They are expressed by the sign ° and are measured in degrees. Acute, right, obtuse, and reflex angles are four crucial types. There are 360° in a circle. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms. The vertex of an angle is the point at which all points meet .

given

If two angles' sums are same, they are said to be supplementary.

If two angles' sums are same, they are said to be complimentary.

Each set of opposite angles generated by crossing lines are referred to as vertical angles. The term "adjacent angles" refers to two angles that share a common vertex and side but do not overlap.

Angles x° and 157° are neighboring because they share a shared vertex and side, preventing them from overlapping, and they are supplementary angles because the sum of any two angles on a straight line equals 180°.

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Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.

To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.

There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.

Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.

Step-by-step explanation:

1000 yards in kilometers will be 0.9 km.

The yard is a United States customary measurement. In this form of measurement, we have yards, feet, and inches.

1 Yard = 3 feet.

1 foot = 12 inches.

Here we are given 1000 yards,

1000 yards = 3 X 1000 feet

= 3000 feet

= 36000 inches.

Now, converting this to the metric measures we know that

1 inch = 2.5 cm

Hence, 36000 inches = 90000 cm.

1 cm = 1/100 m

Hence, 90000 cm = 90000/100 m

= 900 m

1 m = 1/1000 km

Hence, 900 m = 900/1000 km

= 0.9 km

Hence, 1000 yeard = 0.9 km.

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Answer:

The Hypotenuse

Step-by-step explanation:

The Hypotenuse is the longest side of a Triangle.

The expression is t = 0.3 + 3.2p, where t is the box's overall weight and p is the number of plaques it contains.

Let's review the data given to us to properly respond to the question:

Weight of a box by itself = 0.3 kg

Weight of a plaque = 3.2 kg

The expression can be used to determine the total weight of the box :

We shall use the following phrase to respond to the query:

Total weight of the box in kg = t

Number of plaques inside the box = p

Hence, the expression t = 0.3 + 3.2p

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Reflection and rotation will not alter the perimeter of the quadrilateral

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformations has basically classifications

Non rigid transformation are the transformation where the dimension or size of the object will be different going from preimage to the image, example is dilation

In rigid transformation, the dimensions of the object is maintained or not altered through out the transformation process. instance of rigid transformations are

Because the transformation used are all rigid transformations then all the sides will remain same and the perimeter conserved

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Answer:D. 1 and 2

Step-by-step explanation:

Domain cannot repeat

On solving the provided question, we can say that - equation  at factors  x= -3 that value of a is = 33

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

4x^2 + 5x - 8

x = -3

36 + 15 -8

33

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The probability that a sequence will contain exactly one 0 as calculated from the data given is found to be 3/8.

Taking into consideration the sequences where the digit 0 occurs , we will get the possibilities of getting 0 and 1 as 2 .

The number of sample points in the  sample space will be ,

2 x 2 x 2 = 8 sample points.

These sample space are, S = {111, 110, 101, 011, 100, 010, 001, 000},

Now , the sequence having all three 0 as seen from the sample space is found to be 3.

So the  probability becomes , P(0) = no of favorable outcomes / total number of outcomes =3/8.

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The 2-point midpoint formula is a method for finding the equation of a line that passes through the midpoint of two given points.

The formula for the 2-point midpoint is:

Where (x1, y1) and (x2, y2) are the two given points, and m is the slope of the line.

The slope of line is calculated by (y2-y1)/(x2-x1)

By using the midpoint of two given points, the 2-point midpoint formula eliminates the need for calculating the y-intercept of the line, which can save time and effort. It is particularly useful when working with geometric figures or real-world applications that involve moving objects or changing data. It also helps in predicting the values of future point when we know the past point.

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