you have to try to find m

The equivalent quadratic function in vertex form is:

y = (x + 9.97)² - 19.95.

We have,

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by: x_v, y_v

In which:

x_v = -b/2a

y_v = - b² -4ac/2a

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.

If a > 0, the vertex is a minimum point.

In this problem, the function is:

f(x) = x² + bx + 118.

The coefficients are of a = 1 and c = 118. The minimum is of y_v = 37, hence we use it to solve for b.

37 =  - (b² -4ac)/2a

b² - 472 = -74

b² = 398

b = sqrt(398)

b = 19.95

The x-value of the vertex is:

x_v = -b/2a = - 9.97

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, we have that a = 1, h = - 9.97 and k = 19.95, hence:

y = (x + 9.97)² - 19.95.

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3.3^2 = 10.89, (11^(1/2))^2 = 11, (17/5)^2 = 3.4^2 = 11.56

Therefore, -10^(1/2) < 3.3 < 11^(1/2) < 17/5

Answer:

  168 bedrooms

Step-by-step explanation:

You want the number of bedrooms Greg and his partner can paint in 24 hours if they can individually paint 4 and 3 bedrooms per hour, respectively.

The total work is the product of (work per time) and (time).

  total work = Greg's work + Partner's work

  total work = (4 bdrm/h)(24 h) +(3 bdrm/h)(24 h)

  total work = 96 bdrm + 72 bdrm = 168 bdrm

Greg and his partner can paint 168 bedrooms in 24 hours.

__

Additional comment

This is a little different than the usual "working together" problem. Often the individual rates are given as "time per work", 4 hours per bedroom, for example.

If the work rates were 4 hours and 3 hours per bedroom, respectively, then in 24 hours, they could paint 6 + 8 = 14 bedrooms.

<95141404393>

Check the picture below.

let's recall that, the arc made from 0 to π is just half a circle or namely a semi-circle, so any fraction of π refers to that arc

[tex]\cfrac{11\pi }{18}\qquad \textit{really means}\qquad \cfrac{11}{18}\qquad \textit{of that semi-circle}[/tex]

The solution to all parts if given below.

1. Side opposite to angle C is AB =x.

2. Side adjacent to angle C is AC =z

3. Hypotenuse = CB=  y

4. sin <C = x/ y

5. cos <C = z/ y

6. tan <C = x/z

7. sin <B = z/y

8. cos <B= x/ y

9. tan <B  = z/x.

1. Side opposite to angle C is AB =x.

2. Side adjacent to angle C is AC =z

3. Hypotenuse = CB=  y

4. sin <C = opposite side/ Hypotenuse

sin <C = AB/ CB = x/ y

5. cos <C = Adjacent side/ Hypotenuse

cos <C = AC/ CB = z/ y

6. tan <C = opposite side/Adjacent side

tan <C = x/z

7. sin <B =  opposite side/ Hypotenuse

sin <B = z/y

8. cos <B = Adjacent side/ Hypotenuse = x/ y

9. tan <B = opposite side/Adjacent side = z/x.

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Two points that are part of the solution set for the given inequality system are (0, -3) and (4, 28).

To find two points that are part of the solution set for the given inequality system, we can select values for x and y that satisfy both inequalities. Let's choose x = 0 and x = 4 as two points:

For x = 0:

Y < 1/3(0) - 2

Y < 0 - 2

Y < -2

For x = 0:

Y > 7(0) - 1

Y > -1

Therefore, for x = 0, the values of y that satisfy the inequalities are y < -2 and y > -1. We can choose y = -3 and y = 0 as two values of y that satisfy these conditions.

For x = 4:

Y < 1/3(4) - 2

Y < 4/3 - 2

Y < 4/3 - 6/3

Y < -2/3

For x = 4:

Y > 7(4) - 1

Y > 28 - 1

Y > 27

Therefore, for x = 4, the values of y that satisfy the inequalities are y < -2/3 and y > 27. We can choose y = 0 and y = 28 as two values of y that satisfy these conditions.

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The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

We know that,

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

⇒ A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore,

⇒ a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

⇒ B(a) = a/6 - 9

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1. The distance from the center of the planet to the satellite is approximately 17658 miles.

2. Approximately 2.61% of the planet's equator is within range of the satellite's signal.

3. It takes approximately 0.1005 seconds longer for the satellite signal to reach point B compared to point E.

4. The satellite must travel at approximately 8 miles/second to complete one revolution in 36 hours.

To solve these problems, use basic geometric principles and formulas.

1. Finding the distance: From the information given, we can see that the radius of the planet is 3,500 miles, and the distance from the edge of the planet to the satellite is 18,000 miles. Use the Pythagorean theorem to find the distance from point A to point C (the center of the planet).

Consider the right triangle ABC, where AB is the radius of the planet, BC is the distance from the edge of the planet to the satellite, and AC is the distance from the center of the planet to the satellite.

Using the Pythagorean theorem:

AC² + AB² = BC²

Substituting the known values, we get:

AC² + 3500² = 18000²

AC² = 18000^2 - 3500^2

AC² = 324000000 - 12250000

AC² = 311750000

Taking the square root of both sides, we find:

AC = √311750000

AC ≈ 17658 miles (rounded to the nearest mile)

Therefore, the distance from the center of the planet to the satellite is approximately 17658 miles.

2. Finding the percentage of the planet's equator within range of the satellite's signal:

To find the percentage of the planet's equator within range of the satellite's signal, we need to calculate the angle subtended by the distance between points B and D (i.e., the arc BD) at the center of the planet.

The circumference of the circle represents the planet's equator. Since the distance between points B and D represents the greatest distance at which the signal can be received directly, it corresponds to the arc length of the signal's coverage.

Using the formula for the circumference of a circle, C = 2πr, calculate the circumference of the planet's equator:

C = 2π(3500)

C ≈ 21991 miles (rounded to the nearest mile)

Now, calculate the angle m∠BAC in degrees:

m∠BAC = 9.4°

To find the length of the arc BD, use the formula for the circumference of a circle and convert the angle to radians:

Arc length = (angle in radians) × (radius of the circle)

Arc length = (9.4° / 360°) × (21991 miles)

Arc length ≈ 573.24 miles (rounded to the nearest hundredth)

Therefore, the signal covers an arc length of approximately 573.24 miles along the planet's equator.

To find the percentage of the planet's equator within range of the satellite's signal, divide the arc length by the circumference of the equator and multiply by 100:

Percentage = (Arc length / Circumference of equator) × 100

Percentage = (573.24 / 21991) × 100

Percentage ≈ 2.61% (rounded to two decimal places)

Therefore, approximately 2.61% of the planet's equator is within range of the satellite's signal.

3. Finding the time difference between point B and point E:

To find the time difference between point B and point E, calculate the difference in distances divided by the speed of the satellite signal.

The distance from the satellite to point B is the radius of the planet plus the distance from the edge of the planet to the satellite:

Distance from A to B = 3500 + 18000 = 21500 miles

The distance from the satellite to point E is

the radius of the planet:

Distance from A to E = 3500 miles

Using the formula: Time = Distance / Speed, we can calculate the time difference:

Time difference = (Distance from A to B - Distance from A to E) / Speed

Time difference = (21500 - 3500) / 186000

Time difference ≈ 0.1005 seconds (rounded to the nearest hundredth)

Therefore, it takes approximately 0.1005 seconds longer for the satellite signal to reach point B compared to point E.

4. Finding the speed of the satellite:

The time taken for one complete revolution by the satellite is given as 36 hours. To find the speed of the satellite, we need to convert the time to seconds and calculate the distance traveled during that time.

Given:

Time for one revolution = 36 hours

Speed of light = 186,000 miles/second

First, let's convert the time to seconds:

Time = 36 hours × 60 minutes/hour × 60 seconds/minute

Time = 36 × 60 × 60 seconds

Time = 129,600 seconds

During one complete revolution, the satellite travels the circumference of the circle with a radius equal to the distance from the center of the planet to the satellite.

Circumference = 2π × (distance from the center of the planet to the satellite)

Circumference = 2π × 17658 miles

Speed = Circumference / Time

Speed = (2π × 17658 miles) / 129,600 seconds

Calculating this value:

Speed ≈ 8.134 miles/second (rounded to the nearest whole number)

Therefore, the satellite must travel at approximately 8 miles/second to complete one revolution in 36 hours.

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we have

--------> inequality A

--------> inequality B

Using a graphing tool

the solution of the inequality A is the shaded area above the dashed line  

see the attached figure N        

the solution of the inequality B is the shaded area below the dashed line  

see the attached figure N

therefore

the solution of the compound system of inequalities is the shaded area between the two dashed lines

see the attached figure N

therefore

the answer in the attached figure N

Answer:

A.) 94

Step-by-step explanation:

Division is an arithmetic operation that involves the splitting or partitioning of a quantity into equal parts or groups.

In division, the divisor represents the number by which the dividend is divided, while the quotient represents the result or the number of times the divisor can be subtracted from the dividend. The process of division involves repeated subtraction, where the divisor is subtracted from the dividend until the remainder becomes smaller than the divisor.

Division is an essential mathematical concept used in various real-life scenarios. For example, it is used to distribute items equally among a group of people, to calculate the average or rate of change, to solve ratio and proportion problems, and to convert units of measurement.

The division operation can be represented using various notations and symbols, such as the division sign ("/"), the obelus symbol ("÷"), or the fraction bar. It is important to note that division by zero is undefined in arithmetic because it leads to mathematical contradictions.

Overall, division is a fundamental mathematical operation that allows us to distribute or partition quantities and find the quotient or the number of equal parts obtained from the division process. It plays a crucial role in solving mathematical problems and has practical applications in a wide range of fields, including science, engineering, finance, and everyday life.

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Answer: 6 days 6 hours 50 minuets.

Step-by-step explanation:

Separate each unit of time and add them up:

5 days , 29 hours, 110 minuets.

since there are 24 hours in a day, you will add one to days and subtract 24 from hours.

6 days, 5 hours and 110 minuets.

60 minuets are in an hour, to simplify it, you subtract 60 from 110 mins and carry that 1 to hours.

6 days, 5 hours and 50 mins.

Hope this helps:D

The domain and range of the given function are Domain: (−∞,∞),{x|x∈R} and Range: [−2,∞),{y|y≥−2}.

A polynomial function of the form f(x) = ax² + bx + c is called a quadratic function. We already know that the x-intercepts of a quadratic function are given by the quadratic formula (or can be found by factoring). In this worksheet we learn that the graph of any quadratic function is a parabola.

From the given graph, the vertex is (0, -2).

So, the quadratic equation is f(x)=x²-2.

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

Range: [−2,∞),{y|y≥−2}

Therefore, the domain and range of the given function are Domain: (−∞,∞),{x|x∈R} and Range: [−2,∞),{y|y≥−2}.

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Answer:

-278

Step-by-step explanation:

46-{36÷(2×3)-(6)

46-{36÷2×3×6}

46-{36÷2×18}

46-{18×18}

46-{324}

46-324

-278

Answer:

x= 10

Step-by-step explanation:

If they are parallel lines, then the corresponding angles are equal.

6x+8 = 8x-12

Add 12 on both sides

6x+ 20=8x

Subtract 6x on both sides

20 = 2x

Divide 2 on both sides to get x by itself

X= 10

Answer:

D

Step-by-step explanation:

in an isosceles triangle the 2 legs are congruent , both 6[tex]\sqrt{8}[/tex]

using Pythagoras' identity in the right triangle

the square on the hypotenuse h is equal to the sum of the squares on the 2 legs, that is

h² = (6[tex]\sqrt{8}[/tex] )² + (6[tex]\sqrt{8}[/tex] )² = 288 + 288 = 576 ( take square root of both sides )

h = [tex]\sqrt{576}[/tex] = 24

the length of the hypotenuse is 24 cm

We have found the  expression X in terms of Y as X = 500 - 0.25Y.

Given the equations:

T = M + N

X = M/20

Y = N/5

T = 10,000

We need to find an expression for X in terms of Y. To do this, we can start by substituting the given equation for T into the equation for M:

T = M + N

10,000 = M + N

M = 10,000 - N

Now we can substitute these values for M and N in the equation for X:

X = M/20

X = (10,000 - N)/20

Next, we can substitute the equation for N in terms of Y into the previous equation:

Y = N/5

5Y = N

N = 5Y

Therefore, we can substitute these values for N in the equation for X:

X = (10,000 - N)/20

X = (10,000 - 5Y)/20

Simplifying this equation:

X = 500 - 0.25Y

Therefore,  This means that our value for X will depend on the value of Y. If we know what Y is, we can plug it into this equation to find the corresponding value of X.

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The type of function that models the data in the table is a linear function with a difference of 2

From the question, we have the following table of values that can be used in our computation:

The table of values

The above definitions imply that we simply add 2 to the previous term to get the current term

This means that the function is a linear function

Hence, the type of function that models the data in the table is a linear function

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Question

Which best describes the function represented by the data in the table? linear with a common ratio of 2 linear with a common second difference of 2 quadratic with a common ratio of 2 quadratic with a common second difference of 2

x    y

0    0

1     2

2    4

3    6

4    8

Answer:

x = -4

Step-by-step explanation:

The axis of symmetry is where the line at which the function is symmetrical. In the graph above, if you divide the function in half at x = -4, the function is symmetrical. Thus, that line is the axis of symmetry

Answer:

There is no real solution

Step-by-step explanation:

Square numbers are never negative

Answer:

D. This equation has no real solution

Step-by-step explanation:

Because a squared number can not be negative

If it were x^2=144 the answer could be 12 or-12

You can afford to borrow approximately $3642.54 based on a monthly payment of $250, an interest rate of 7.5%, and a loan term of 20 years.

To determine how much you can afford to borrow, we can use the formula for calculating the loan amount based on monthly payments, interest rate, and loan term.

The formula is:

Loan Amount = Monthly Payment / [(1 - (1 + Interest Rate)^(-Number of Payments))] / Interest Rate

Let's plug in the given values:

Monthly Payment = $250

Interest Rate = 7.5% per year (or 0.075 as a decimal)

Number of Payments = 20 years * 12 months/year = 240 months

Using the formula, we can calculate the loan amount:

Loan Amount = $250 / [(1 - (1 + 0.075)^(-240))] / 0.075

Calculating the exponent:

(1 + 0.075)^(-240) ≈ 0.084873

Loan Amount = $250 / [(1 - 0.084873)] / 0.075

Loan Amount = $250 / 0.915127 / 0.075

Loan Amount ≈ $3642.54

It's important to note that this calculation assumes a constant monthly payment and interest rate for the entire loan term. Additionally, the final loan amount may be subject to other factors such as fees, loan terms, and creditworthiness, which should be considered when seeking a loan.

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The simplified form of 3³ / 3⁷ is 1/81. The top and bottom of a fraction are said to be in their simplest form if they only share the number one.

Given

3³÷3⁷

Required to convert into a simplified form.

3³ / 3⁷ = 3³⁻⁷ = 3⁻⁴

3⁻⁴ = 1 / 3⁴ = 1 / (3 × 3 × 3 × 3) = 1 / 81

When the denominator and numerator have only one common factor, the fraction is said to be in its simplest form or terms. In other words, the fraction cannot be made simpler or more compact.

Even though the numerator and denominator are larger integers, a fraction can also be thought of in its simplest form if both are coprime (have just one other factor in common).

Thus, The simplified form of 3³ / 3⁷ is 1/81.

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Answer:

64:343

Step-by-step explanation:

The ratio of the volume of the small pyramid to the volume of the large pyramid is equal to the cube of the ratio of their corresponding linear dimensions.

In this case, the ratio of the heights is 4/7, so the ratio of the volumes is (4/7)^3 = 64/343.

Therefore, the ratio of the volumes of the two pyramids is 64:343.

Here is a more detailed explanation:

The volume of a pyramid is given by the formula:

V = ⅓*Bh

where V is the volume, B is the area of the base, and h is the height.

Since the two pyramids are similar, the ratio of their areas is equal to the square of the ratio of their corresponding ki linear dimensions.

In this case, the ratio of the heights is 4/7, so the ratio of the areas is (4/7)^2 = 16/49.

Therefore, the ratio of the volumes of the two pyramids is:

(1/3) * (16/49) * (4/7) = 64/343

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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Answer:

Base x hieght=square, and rectanguler Formula.

Step-by-step explanation:

If you have 5 as the base number and 3 for the hieght, you will multiply 5 by 3. that is odvi 15.

Answer:

To find the perimeter of a shape, you add up the lengths of all the sides.

Step-by-step explanation:

Answer:

Add all lengths of a shape

Step-by-step explanation:

If a rectangle were to have lengths of: 20, 10, 20, 10, then the perimeter would be 60.

Probability that a blue marble is chosen and then a black marble is 1/6 .

Given,

15 blue marbles, 7 red marbles, 3 green marbles, and 5 black

marbles.

So,

Total number of marbles: 15 + 7 + 3 + 5 = 30

The probability of taking one blue marble is: 15/30

The probability of taking a black marble is: 5/30

(Note: since we are replacing the first marble, the total is staying constant i.e. 16)

We might draw a blue marble and then a black one, or, a black one and then a blue one. This implies that the probability will be:

(15/30 x 5/30) + (5/30 x 15/30) = 1/6

Hence the probability that a blue marble is chosen and then a black marble is 1/6 .

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Answer:

  Part A:  (b) (7, 6)

  Part B:  (c) (-6, -4)

Step-by-step explanation:

You want the coordinates of points of rectangle PQRS that have been subject to rotation, reflection, and translation.

Rotation 90° CCW is accomplished by the transformation ...

  (x, y) ⇒ (-y, x)

Then point R gets rotated to ...

  R(6, -7) ⇒ R'(7, 6)

Reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y) . . . . . . reflection in the y-axis

Translation adds the translation amount to the relevant coordinate:

  (x, y) ⇒ (x, y -2) . . . . translation down 2 units

Together, the effect on point Q is ...

  (x, y) ⇒ (-x, y -2)

  Q(6, -2) ⇒ Q''(-6, -4)

__

Additional comment

You can figure the transformation related to rotation by considering "where did it come from?"

If a point ends up on the x-axis after a rotation of 90° CCW, it had to come from the -y axis.

If a point ends up on the y-axis after a rotation of 90° CCW, it had to come from the +x axis.

These observations can be written as the transformation ...

  (x, y) ⇒ (from -y, from +x) = (-y, x) . . . . . . rotation 90° CCW

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An experiment would be the most appropriate method to compare the effects of kale on blood pressure versus the lack of kale.

The best method when trying to compare the effects of kale on blood pressure versus the lack of kale would be an experiment.

In an experiment, the researcher has control over the variables and can manipulate them to observe the cause-and-effect relationship between kale consumption and blood pressure. The researcher can randomly assign participants to two groups: one group consuming kale and the other group not consuming kale (control group).

An observational study involves observing and analyzing existing data without intervening or manipulating any variables. It may not provide a definitive cause-and-effect relationship between kale consumption and blood pressure.

Therefore, an experiment would be the most appropriate method to compare the effects of kale on blood pressure versus the lack of kale.

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