Find an nth-degree polynomial function
n= 3;
- 2 and 6 + 2 i are zeros;
f(-1)= 53

Answer:

Step-by-step explanation:

mJK + mKL= 180°

31+9x+23= 180°

54+9x=180°

x=180-54/9=126/9

x = 14°

Hope this help!

simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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Answer:

B

Step-by-step explanation:

We essentially have the sequence:

10, 13, 16, 19, 22,25...

This is an arithmetic sequence because each subsequent term differs only by a constant.

And this constant, the common difference, is +3 since each subsequent term is 3 more than the previous term.

Hence, we can write a recursive formula for our sequence.  

We will first define our first term. The first term, at x=0, is 10. Hence:

\(f(0)=10\)

Each term, x, is +3 the previous term (x-1). Therefore:

\(f(x)=f(x-1)+3\)

Hence, our answer is B.

Answer:

B

Step-by-step explanation:

f(x)=f(x-1)+3x

Answer:

Step-by-step explanation:

Given

Original number of students = 250

New number of students = 195 students

Number of students absent = 250 - 195 = 55

percentage decrease = Number absent/Original number * 100

percentage decrease = 55/250 * 100

percentage decrease = 5500/250

percentage decrease = 22%

Hence the percentage decrease is 22%

The value of the given expression is equivalent to -3

Linear equations are equation that has a linear degree of 1.

The statement three eighths times the quantity 1 plus the square root of 49 end quantity squared minus the quantity four minus one end quantity cubed is written mathematically as:

3/8(1+√49)² - (4-1)³

Expand to have:

3/8(1+7)² - 3³

3/8(8)² -27

3/8(64) - 27

3(8) - 27

24 - 27

-3

Hence the value of the given expression is equivalent to -3

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Answer:

5*2=10.

Step-by-step explanation:

So sorry if this isn't the right answer, your equation is a tad confusing. I can edit it if it's wrong, just comment on the answer and I'll respond as fast as possible. Anyways, I hope it's right. If not, please explain what the two 'x's mean.

Answer:

standard form?

Step-by-step explanation: if so its x to the power of 2 +5x-10=0

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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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

Answer:

4x25/100=1

Step-by-step explanation:

How I came up with it

4÷100=25

25÷25=1

Julie will only get a 1% discount

Hope it helps

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Answer:

Let's start by finding the volume of water in the trough as a function of its depth.

At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:

V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm

Simplifying this expression, we get:

V(h) = (13/2000) h^2 m^3

Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:

dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)

At the moment when the water is 10 cm deep, we have:

h = 10 cm

dV/dt = 0.1 m^3/min

Plugging in these values, we get:

0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)

Solving for dh/dt, we get:

dh/dt = 0.1 m^3/min / (26/2000) / 10 cm

dh/dt ≈ 0.192 m/min

Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.

Answer:

3.63 * 10^19

Step-by-step explanation:

Given that :

Number of choices to select = 12

Category available :

Blues - 14

Country - 25

Disco - 21

To select an equal number of song for each category ; then 4 songs will be selected from each :

Using combination :

(14C4 * 25C4 * 21C4)

Since the order matters for the 12 selected songs ; it thus requires 12 permutation

Thus ;

(14C4 * 25C4 * 21C4) * 12!

nCr = n! / (n-r)!r!

Using calculator;

14C4 = 1001 ;

25C4 = 12650

21C4 = 5985

12! = 479001600

Hence,

(1001 * 12650 * 5985) * 479001600

= 36301596217286400000

=3.63 * 10^19

Answer:

x = 7

Step-by-step explanation:

x + 3 < 10

x < 10 - 3

x < 7 ( this supposed to be the answer not x = 7 so please check the options again )

Answer:

C. similar by SAS

Step-by-step explanation:

Answer:

25 and 35

Step-by-step explanation:

Let the numbers be 5x and 7x

(5x+5)/(7x+5)=3/4

4(5x+5)=3(7x+5)

20x+20=21x +15

20-15=21x-20x

5=x

So,the numbers will be

5x=5*5 =25

7x=7*5=35

The expression can be completed as 4 × (4 + 3)

A mathematical expression is a combination of numbers, symbols, and operations that represent a mathematical relationship or calculation.

Mathematical expressions can be used to represent a wide range of concepts, including algebraic equations, geometric formulas, and statistical models.

Looking at the pages:

On page 2, we have 4 stickers per row while on page 3 we have 3 stickers per row. Also, both page 2 and page 3 have 4 rows each. Thus, we can complete the expression as follows:

4 × (4 + 3)

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We can use the identity sin(2θ) = 2sin(θ)cos(θ) to simplify sin 17°cos 17° as follows:

sin 17°cos 17° = (1/2)sin(2(17°)) = (1/2)sin 34°

Therefore, we can express sin 17°cos 17° in terms of p as:

sin 17°cos 17° = (1/2)sin 34° = (1/2)p

So the value of sin 17°cos 17° in terms of p is (1/2)p.

Answer:

The total number of ways to choose 2 students from a class of 16 is given by the combination formula:

C(16,2) = 16! / (2! * (16-2)!) = (1615) / (21) = 120

This means there are 120 possible pairs of students that could be drawn.

The probability of you and your best friend being chosen is the number of ways that you and your friend can be selected divided by the total number of possible pairs. There is only 1 way to select you and your best friend out of the class of 16, so the probability is:

P(you and your best friend are chosen) = 1/120

Therefore, the probability that you and your best friend will be chosen is 1/120. Option (B) is the correct answer.

Answer:

The probability of choosing one specific student out of 16 is 1/16. After one student is chosen, there are 15 students left, so the probability of choosing the second specific student out of the remaining 15 is 1/15. The probability of both events happening is the product of the probabilities: (1/16) x (1/15) = 1/240. However, there are two ways that the students can be chosen (your friend first, then you or you first, then your friend), so we need to multiply the probability by 2: 2 x (1/240) = 1/120. Therefore, the probability of you and your best friend being chosen is 1/120. Answer: 1/120.

Answersin -> 48

Step-by-step explanation:

solve for the length of the horizontal line by doing:

sin(55)=x/58

rearrange: x = sin(55) times 58 = 47.51

round UP to 48

Answer:

\(S_{1000}=500500\)

Step-by-step explanation:

\(\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500\)

Assume that an A is a 90% (getting at least 9 questions out of 10 right).

The probability that exactly 9 questions are right is 10 (choose one question to get wrong) * (1/4)^9 (1/4 chance of getting each question right) * (3/4) (chance of getting the wrong question wrong) =  10∗3∗(1/4)10 .

The probability that all 10 questions are right is  (1/4)10 (1/4 chance of getting each question right).

The total probability of getting an A is  (10∗3+1)(1/4)10=31410,  or about 0.002956%.

I hope I helped! If I misinterpreted your question, please let me know and I'll try my best to help.

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

n + 9 = 14

=> n + 9 - 9 = 14 - 9. [For isolating the variable we subtract 9 from both sides]

=> n = 5 (Ans) [ Variable isolated]

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Answer:

$ 2,890

Step-by-step explanation:

Volume of a cube = width x length height

Cubic root of 4913 = 17 feet

Area of the floor = 17 x 17 = 289

289 x 10 = $2,890

Answer:

k=3/2

Step-by-step explanation:

6=k(4) where k is constant, or

k=6/4 which is equal to k=3/2

Answer:

x =2

Step-by-step explanation:

Solve for x:

log(x + 3) = log(10) - log(x)

Hint: | Move everything to the left hand side.

Subtract log(10) - log(x) from both sides:

-log(10) + log(x) + log(x + 3) = 0

Hint: | Combine logarithms.

-log(10) + log(x) + log(x + 3) = log(1/10) + log(x) + log(x + 3) = log(1/10 x (x + 3)):

log(1/10 x (x + 3)) = 0

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

1/10 x (x + 3) = 1

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides by 10:

x (x + 3) = 10

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

x^2 + 3 x = 10

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 9/4 to both sides:

x^2 + 3 x + 9/4 = 49/4

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x + 3/2)^2 = 49/4

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x + 3/2 = 7/2 or x + 3/2 = -7/2

Hint: | Look at the first equation: Solve for x.

Subtract 3/2 from both sides:

x = 2 or x + 3/2 = -7/2

Hint: | Look at the second equation: Solve for x.

Subtract 3/2 from both sides:

x = 2 or x = -5

Hint: | Now test that these solutions are correct by substituting into the original equation.

Check the solution x = -5.

log(x + 3) ⇒ log(3 - 5) = i π + log(2) ≈ 0.693147 + 3.14159 i

log(10) - log(x) ⇒ log(10) - log(-5) = -i π + log(2) ≈ 0.693147 - 3.14159 i:

So this solution is incorrect

Hint: | Check the solution x = 2.

log(x + 3) ⇒ log(3 + 2) = log(5) ≈ 1.60944

log(10) - log(x) ⇒ log(10) - log(2) = log(5) ≈ 1.60944:

So this solution is correct

Hint: | Gather any correct solutions.

The solution is:

Answer: x = 2

Answer:

Quotient: 5x+4  Remainder: -1

Step-by-step explanation:

Hope this helps!

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