- Polynomial Functions - Find the zeros of each function algrebraically. If there is no real zero, state so.

Step-by-step explanation:

Answer: 2/4, 4,8, etc.

Step-by-step explanation:

Hello!

So basically, what I think this question is asking is for an equivalent fraction to 1/2. There are countless fractions that are the same as this and I listed a couple above!

Hope this helps! :D

Answer:

Equation: \((x-2)^2=16(y-2)\)

Vertex: \((2,2)\)

Directrix: \(y=-2\)

Focus: \((2,6)\)

Step-by-step explanation:

Standard Form of Vertical Parabola:

We know that our vertex is \((h,k)\) -> \((2,2)\), therefore, we can determine the value of \(p\) by selecting a point from the parabola as \((x,y)\):

\((x-h)^2=4p(y-k)\)

\((x-2)^2=4p(y-2)\)

\((6-2)^2=4p(3-2)\)

\((4)^2=4p(1)\)

\(16=4p\)

\(4=p\)

Therefore:

Conclusion:

Review the graph for a visual

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

Answer:

n = 37/3

Step-by-step explanation:

3n = 30 +7

3n = 37

n = 37/3

Answer:500%

Step-by-step explanation:

The solution is in the file below

Answer:

HL

Step-by-step explanation:

Since both triangles are right angle triangles that means one angle is 90°. other two sides are given congruent .

that means lengths of hypotenuse and the leg of the one right angle triangle is equal to the corresponding other hypotenuse and leg of other triangle.

This fulfills the condition of HL congruency.

Answer:

7m^5 - 3m^3 - 3

Step-by-step explanation:

The first set of parentheses is unnecessary, so just remove them.

To remove the second set pf parentheses, since there is a negative sign to its left, change every sign inside the second set of parentheses. Then combine like terms.

(6m^5 + 3 - m^3 - 4m) - (-m^5 + 2m^3 - 4m + 6) =

= 6m^5 + 3 - m^3 - 4m + m^5 - 2m^3 + 4m - 6

= 7m^5 - 3m^3 - 3

Answer: \(3x^2+x-9\)

Step-by-step explanation:

f(x) + g(x)

Given: f(x) = -3 and g(x) = 3x^2+x-6

\(-3+3x^2+x-6\)

Final answer:

\(3x^2+x-9\)

Answer:

Not sure but probably 11 units

Answer:

11 units because if u count up or down from the dot it will equal up to 11

Answer:

16

Step-by-step explanation:

To find the median, we find the middle of the data set.

7, 9, 11, 14, 18, 20, 30, 35

There are 8 values

7, 9, 11,    14, 18,     20, 30, 35

The median is between the 4th and 5th numbers

We need to find the mean of the middle two numbers

(14+18)/2 =32/2= 16

Answer:

16

Step-by-step explanation:

             \(\sf (\frac{n+1}{2}\:)^ t^h \:data\)

       Here,

             n ⇒ number of terms

Let us find it now.

7, 9, 11, 14, 18, 20, 30, 35

\(\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data\)

In this case, add 4th and 5th data and divide it by 2.

\(\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16\)

Answer:

1 = 50⁰

2 = 130⁰

3 = 50⁰

4 = 85⁰

5 = 130⁰

6 = 50⁰

7 = 85⁰

8 = 45⁰

9 = 45⁰

10 = 135⁰

11 = 135⁰

12 = 45⁰

The surface area of the box is 408 in²

The surface area of the box can be calculated by using the formula for the surface of rectangular prism.

The surface area of rectangular prism is given by:

A = 2LW + 2WH + 2LH

Where L, W and H are the length, width and height of the prism respectively

L = 15 in, W = 7 in and H = 4 1/2 in

A = 2(15×7) + 2(7×4.5) + 2(15×4.5)

A = 210 + 63 + 135

A = 408 in²

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The value of angle RPQ in the circle is 115 degrees.

The intersecting chords theorem, also known as the chord theorem, is an elementary geometry statement that describes a relationship between the four line segments formed by two intersecting chords within a circle.

If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

The angle is 115°.

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The value of x in the equation -12.6x -4-9=154 is -13.25.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation is illustrated as:

-12.6x -4-9=154

Collect like terms

-12.6x - 13 = 154

-12.6x = 154 + 13

-12.6x = 167

Divide

x = 167/-12.6

x = -13.25

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Complete question

What's the answer to -12.6x -4-9=154

The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

1. The product of the numbers are:

a. √2 (√8) = √16 = 4

b. √49 (∛ 8) = 14

c. √3 (2/ √3) = 2

d. √2(4)

Option d is the correct answer.

Similarly, taking the product:

2. Option a is correct.

3. Option d is correct.

4. Option b is correct.

Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

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The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top

The function of the height where the man falls is a quadratic function, and the equation of the function is given as:

d = t^2 * 0.25

The height of the building is 500

This means that the value of d is 500.

So, we have;

d = 500

Substitute 500 for d in the equation d = t^2 * 0.25

500 = t^2 * 0.25

Divide both sides of the above equation by 0.25

500/0.25 = t^2 * 0.25/0.25

Evaluate the quotient in the above equation

t^2 = 2000

Take the square root of both sides in the above equation

√t^2 = √2000

Evaluate the exponent

t = 44.7

Hence, it takes the man 44.7 seconds to fall

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The slopes of opposite sides are equal and product of slopes of adjacent sides is -1. All the sides are of equal length. So the given parallelogram is a square.

First we have to calculate the slopes of each sides.

Equation for slope, m= (y₂-y₁)/(x₂-x₁)

Slope of JK, m₁ = (3-2)/(0-⁻4) = 1/4

Slope of KL, m₂ = (-1-3)/(1-0) = -4

Slope of LM, m₃ = (-2-⁻1)/(-3-1) = 1/4

Slope of MJ, m₄ = (-2-2)/(-3--4)= -4

m₁= m₃ and m₂= m₄. That means the slope of opposite sides are equal. So they are parallel. Now we have to check whether the slopes are perpendicular.

If two lines are perpendicular, then product of slope will be -1

Multiplying two adjacent slopes,

m₁ ×m₂= 1/4 × -4 = -1

m₂ × m₃ = -4 × 1/4 = -1

m₃ m₄ = -4 × 1/4 = -1

So opposite sides are parallel and corresponding sides are perpendicular. So it may be a square or a rectangle.

Now we have to find the length of each sides,

Distance formula = \(\sqrt{{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)

JK = \(\sqrt{(0--4)^{2}+ (3-2)^{2} }\) = √16+1 = √17

KL = √(1-0)²+(-1-3)² = √(1+16) = √17

LM = √(-3-1)²+(-2--1)² =√(16+1) =√17

MJ = √(-3--4)²+(-2-2)² =√1+16) =√17

Length of all sides are equal.

So the given parallelogram is a square.

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-3/8 - 7/12 =

First we need to get the denominators same.

(-3 x 3/8 x3) - (7 x 2/12 x 2) =

-9/24 - 14/24 =

-9 - 14/24 =

-23/24

Answer = -23/24

Answer:

5/24

Step-by-step explanation:

y-x y is 7/12 so its positive x is -3/8 so its negative the answer is 5/24

Therefore , the solution of the given problem of triangle comes out to be LJ rounded to the closest tenth, is about 7.5

A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward rectangular form. A, B, and C are the only three sides that set a triangle apart from a simple triangle. When the boundaries are not exactly collinear, Euclidean geometry results in a singular area instead of a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

The respective sides of the triangles CHI and JKL are proportional because of their similarity. Using the matching sides, we can construct a proportion:

=> JK / CI = LJ / CH

The values JK = 15 and CI = 8 are provided. Using the data shown in the picture, we must locate CH and LJ.

We can see from the picture that HI = 4 and KL = 20. By taking HI away from CI, we can discover CH:

=> HI = 8 - 4 = 4 CH = CI =

We can now solve for LJ by substituting the numbers we already know into our proportion:

=> LJ / 4 = 15 / 8

=> LJ = 4 * 15 / 8

=> LJ = 7.5

LJ, rounded to the closest tenth, is about 7.5.

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Answer:

9(4-n)

Step-by-step explanation:

Hope this helps

Tell me if I'm wrong

Answer:

pi= 56.12/12

if you know, you know

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The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.

In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.

Here we have

- 3x² + 33 = 48x

Keep 'x' terms on one side and constant terms sides on another side

=> - 3x² - 48x = - 33

Divide by - 3 on both sides

=> -3(x² + 4x)/3 = - 33/3  

=> x² + 16x = 11      

Take half of the 'x' term and square it and add on both sides

=> x² + 2(8x) (x) + (8)² = 11 + (8)²  

Which is in the form of x² + 2bx + b² = (x + b)²

=> [x + 8]² = 75

Therefore,

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

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Answer:

0.2240418 ; 0.57681

Step-by-step explanation:

Given the information above :

A) What is the probability of exactly three arrivals in a one-minute period?

Using poisson probability function :

p(x ; m) = [(m^x) * (e^-m)] / x!

Here, m = mean = 3, x = 3

P(3 ; 3) = [(3^3) * (e^-3)] / 3!

P(3;3) = [27 * 0.0497870] / 6

= 1.3442508 / 6

= 0.2240418

B) What is the probability of at least three arrivals in a one-minute period?

Atleast 3 arrivals

X >= 3 = 1 - [p(0) + p(1) + p(2)]

P(0 ; 3) = [(3^0) * (e^-3)] / 0! = (1 * 0.0497870) / 1 = 0.0497870

P(1 ; 3) = [(3^1) * (e^-3)] / 1! = (3 * 0.0497870) / 1 = 0.1493612

P(2 ; 3) = [(3^2) * (e^-3)] / 2! = (9 * 0.0497870) / 2 = 0.2240418

1 - [0.0497870 + 0.1493612 + 0.2240418]

1 - 0.42319 = 0.57681

There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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Answer:

42°

Step-by-step explanation:

According to Exterior Angle Theorem,

an exterior angle of a ∆ is equal to the sum of the opposite interior angles.

So,

h+96°=138°

h=138°-96°

h=42°