For the function h defined as h(x) = nx² + 28, n is a constant and h(3) = 1. What is the value of h(-6) ?​

The perimeter of the quadrilateral is approximately 50.47 units

Given the vertices of the quadrilateral: H(– 4,6), I(4,9), J(2,3), K(7, – 4).

Let us calculate the distances of HI , IJ , JK and KH

[tex]{\displaystyle HI={\sqrt {(4-(-4))^{2}+(9-(6))^{2}}}.}[/tex]

or, HI = 17 units

[tex]{\displaystyle IJ={\sqrt {(2-(4))^{2}+(3-(9))^{2}}}.}[/tex]

or, IJ = 10

[tex]{\displaystyle JK={\sqrt {(7-(2))^{2}+(-4-(3))^{2}}}.}[/tex]

or, JK = √74 = 8.602... ≈ 8.60

[tex]{\displaystyle KH={\sqrt {(7-(-4))^{2}+(-4-(6))^{2}}}.}[/tex]

or, KH = √221 = 14.866... ≈ 14.87

Now perimeter = HI + IJ + JK + KH

or, perimeter = 8.60 + 14.87 + 10 + 17 = 50.47 units.

Therefore the perimeter of the quadrilateral is 50.47 units.

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Answer:

39.0015

Step-by-step explanation:

36.45 x 0.07 = 2.5515

36.45 + 2.5515 = 39.0015

Answer:

y=5x

Step-by-step explanation:

He has 10 carrots every 2 square feet

We can simplify it to 5 carrots every 1 square foot and if we put it into an equation with the variables, then we get:

y = 5x

Answer: In the first graph, you plug in the numbers, so the rule would be "+9" and the term would be 9 for the first one, the second term is 18 and the rule stays the same. In the second one, the rule is that they each go up by (+7)

I hope that helps :)

Answer: It should be 3 and 5

Step-by-step explanation: I hope this helps <33

Answer: FIRST ONE IS -1/7

The second one is 1

Step-by-step explanation:

Caroline's age is 21 years which is an odd integer.

Integers are a subset of real numbers.

It is given that Caroline is the youngest of 4 siblings and all of their ages are odd consecutive integers.

Let us consider the age of Caroline's age to be x years(x is an odd integer).

She is the youngest so the sibling's age who is just older than Caroline is given by x+2 which is also another odd integer.

Ages of the other two siblings will be x + 4 , x + 6 .

Now sum of their ages is 96.

Therefore: x + (x+2) + (x+4) + (x+6) =96

or, 4x + 12 = 96

or, 4x = 84

or, x = 21 (odd integer)

Carline's age is 21 years.

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When two random variables X and Y are considered to be independent, it means that neither X's distribution nor Y's values have any bearing on the other.

A random variable is a variable used in an experiment, such as the number of coin tosses or card draws. An independent random variable is a random variable in your experiment that doesn't affect the other random variables. In other words, it has no impact on the likelihood that another event will occur. For illustration, suppose you randomly selected 50 bags of sugar from various grocery stores in order to determine the average weight of a bag of sugar. The factors are independent since you wouldn't anticipate the weight of one bag having an impact on another. A dependent random variable, on the other hand, does have an impact on the probability of other random variables.

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The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

The function definition is given as

f(n) = -4 +2n for n > 1

Start by calculating f(2), f(3) and f(4)

So, we have

f(2) = -4 +2(2)

f(2) = 0

f(3) = -4 +2(3)

f(3) = 2

f(4) = -4 +2(4)

f(4) = 4

In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2

So, we have

f(n) = f(n - 1) + 2

Also, we have

f(1) = -4 +2(1)

f(1) = -2

Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

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Answer:

25.  0 < x < 22.9

26.  0 < x ≤ 3.3

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Question 25

[tex]\begin{aligned}\sf Perimeter & < 51.3\\\implies 14.2+14.2+x & < 51.3\\28.4+x & < 51.3\\28.4+x -28.4& < 51.3-28.4\\x & < 22.9\end{aligned}[/tex]

[tex]\textsf{As length is positive: $0 < x < 22.9$}[/tex]

Question 26

[tex]\begin{aligned}\sf Perimeter & \leq 18.7\\\implies 6.4+4.9+4.1+x& \leq 18.7\\15.4+x& \leq 18.7\\15.4+x-15.4& \leq 18.7-15.4\\x& \leq 3.3\\\end{aligned}[/tex]

[tex]\textsf{As length is positive: $0 < x\leq 3.3$}[/tex]

The statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true

The statement is given as:

In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.

As a general rule;

If any two angles are congruent in a triangle, then it means that the sides that opposite the two congruent angles are congruent sides.

The above is an illustration of the base angle theorem

The base angle theorem goes hand-in-hand with the isosceles triangle theorem which is illustrated by the given statement

Hence, the statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true

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Step-by-step explanation:

2x + 3x = -25

5x = -25

x = -25 / 5

x = -5

Answer:

30J + 15S = $1,200

Step-by-step explanation:

Since Jason earns $30 per computer and Sandra earns $15 per computer therefore the equation will be written as $30J + $15S = base salary per month.

30J + 15S = $1,200

Answer: x=36

Step-by-step explanation: a straight line is 180 degrees. on one side, it is 144 degrees. 180-144 = 36.

Answer:

Step-by-step explanation:

Answer: x=64/7 Step-by-step explanation: 4x+3=64 7x=64

4x=−64

Divide both sides by 4.

x=

4

−64

​

Divide −64 by 4 to get −16.

x=−16

Answer:

The person runs 30km/h or 30000m/h

Step-by-step explanation:

First let's find speed per minute

➟ 1500/3

➟ 500

Now let's calculate speed per hour

1 hour = 60 minutes

➟ 500 × 60

➟ 30,000 meters

If you would like the meters to be in miles

then Formula divide the meter value by 1000

➟ 30000/1000

➟30

∴ The person runs 30km/h or 30000m/h

The speed of the person is 300 km/hour.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Distance covered in 3 minutes = 1500 meters.

1 hour = 60 minutes

3 minutes = 15000 meter

Multiply 20 on both sides.

60 minutes = 300,000 meter

1 km = 1000 meter

Multiply 300 on both sides.

300 km = 300,000 meter

Now,

60 minutes = 300 km

Speed = 300 km/hour

Thus,

300km/hour is the speed of the person.

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The fence is 33 feet long when measured in yards.

Here,

In order to erect a fence around a rectangular flower garden on his property, Craig has 72 feet of material.

If the fence must be 3 feet in width, then, assuming he uses the entire 72 feet of material, we must determine the fence's length in yards.

What is the rectangle's perimeter?

The rectangle's perimeter is 2 (l + b). l being the length. b=breadth (width).

Now,

A rectangular flower bed should be x feet long.

(Length + Width)2 = the perimeter of a rectangular flowerbed.

72 = 2 (x + 3)

36 = x + 3

x = 33 feet

Hence, The fence is 33 feet long when measured in yards.

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The length of rectangle is (x - 5).

We are given-

Area of rectangle = [tex]x^{3} - 5x^{2} + 3x - 15[/tex]

Width of rectangle = [tex]x^{2} + 3[/tex]

Using the formula, the length will be calculated by rewriting the formula as -

Length = Area/width

Keep the values in formula to find the length of rectangle.

Length = [tex]\frac{x^{3} - 5x^{2} + 3x - 15}{x^{2} + 3}[/tex]

In numerator, separating the common values and rewriting the equation -

Length = [tex]\frac{x^{2} (x - 5) +3 (x - 5)}{x^{2} + 3}[/tex]

Rewriting the equation to for ease of solving to find the length of rectangle -

Length = [tex]\frac{(x^{2} +3)(x - 5)}{(x^{2} +3)}[/tex]

Cancelling [tex](x^{2} + 3)[/tex] as it is common in both numerator and denominator. Now, we will get the value of length of rectangle.

Length = (x - 5)

Hence, the length of rectangle is (x - 5).

The complete question is -

The area of a rectangle is [tex]x^{3} - 5x^{2} + 3x - 15[/tex], and the width of the rectangle is [tex]x^{2} + 3[/tex]. If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5

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4 • 23 = 92 so the correct answer is a  4(20+3).

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

For example, x + y is an expression, where x and y are terms having an addition operator in between.

Expressions can be simplified to form an answer. For example, 3+6-2 is an expression that can be simplified to 7. There are two different ways to simplify arithmetic expressions and algebraic expressions. We use the bracket open division multiplication addition subtraction rule which means the operations are performed in the given manner to simplify them.

For example, 2x+5x results in 7x, whereas 7ab-b is an expression that has two unlike terms, which cannot be added.

Checking for all the options:

option a) 4 (20+3)=4 * 23 = 92

option b) 4 (2 + 13) = 4 * 15 =60

option c) 4 (20 + 30) = 4 * 50 =200

option d) 4 (2 + 3) = 4 * 5 = 20

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The given equation has one solution which is x = 6 (which is a REAL number).

Linear Equation Solutions are the values of a variables in linear equations that give all possible solutions. Linear equations represent real-world problems by involving unknown quantities with in form with one or more variables.

Some key concepts regarding the solution of linear equation are-

Now, for the given question;

The linear equation is -

4x + 9 = 33

Solving this;

4x = 33 - 9

4x = 24

x = 24/4

x = 6

Therefore, the solution of the given linear equation is (x=6), where 6 is the real number.

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The complete question is-

The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.)

4x + 9 = 33

There are 7 meters in 279 inches.

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Based on the raw score of 82, and the 70th percentile passing, we can infer that as regards 82 being a passing score, No, it might have a percentile rank less than 70.

The passing score is one that is in the 70th percentile or higher. This means that the raw score that a student gets needs to be considered higher than 70% of the rest of the scores.

There is a chance that the exam was so easy that most people got good scores. If that were the case, then a score of 82 can be below the 70th percentile which means that the candidate would not pass.

Options for this question are:

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Answer:

(x – 4)² + y² = 36

(x + 6)² + y² = 144

Step-by-step explanation:

All other questions are parabolas!

Answer:
v = 2.33 10⁷ mi / h

Explanation:

For this exercise we must observe that the velocity module is constant, so we can use the kinematic relation       v = d / tThe distance traveled in each orbit is the length of the circle      L = 2π rThe time it takes in orbit is called period (T)Let's reduce the quantities      r = 8.9 10⁷ mi      t = 24 h (3600s / 1 h) = 86400 sWe replace      v = 2π r / TLet's calculate     v = 2π 8.9 10⁷/86400     v = 6.47 10³ mi / s     v = 6.47 10³ mi / s (3600 s / 1h)     v = 2.33 10⁷ mi / h

The equation of the linear function represented by the table below in slope-intercept form is y = 5x + 4

The equation of a line in point-slope form is expressed as y = mx + b

where

m is the slope

b is the intercept

Using the coordinate points (-1,-1) and (2, 14)

Slope = 14+1/2+1

slope = 15/3

Slope = 5

For the intercept;

14 = 5(2) + b

14 = 10 + b

b = 4

The y-intercept is at the point (0,4)

Determine the equation

y = mx + b

y = 5x + 4

Hence the equation of the linear function represented by the table below in slope-intercept form is y = 5x + 4

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Answer:

b = 1

Step-by-step explanation:

they are asking what is y when x is -4.  We can look on the graph and see that when x = -4, when is 1.  It is the point (-4,1).

We can also see it algebraically.  We can replace x with -4 and solve for y

y = 1/4 x + 2

y = 1/4((-4) + 2

y = -1 + 2

y = 1