Please help ASAP, will give brainliest

The polynomial function of least degree with integral coefficients is equal to f(x) = x³ - 4x² + x + 6 with the given zeros 3, 2, -1.

As given in the question,

Given zeros of the polynomial function are :

3, 2, -1

⇒ ( x - 3 ) =0 or ( x - 2 ) = 0 or ( x + 1 ) = 0

Polynomial function of the given factors  ( x - 3 ) =0 or ( x - 2 ) = 0 or

( x + 1 ) = 0 is given by :

f (x ) = ( x - 3 )( x - 2 )( x + 1 )

⇒ f(x) = ( x² - 3x - 2x + 6 ) ( x + 1 )

⇒ f(x) = ( x² - 5x + 6 ) ( x + 1 )

⇒ f(x) = x³ + x² -5x² - 5x + 6x + 6

⇒f(x) = x³ - 4x² + x + 6

Therefore, the required polynomial function of least degree with integral coefficients using given zeros is equal to f(x) = x³ - 4x² + x + 6.

The complete question is:

Write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?

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this equation is only valid at the point (a, b) where we found the slope of the normal line. To find the equation of the normal line at a different point, we would need to repeat this process with new values of a and b.

To find the equation of the line normal (perpendicular) to the graph of y = x^3 + 3x^2 + 7x - 1 at a point (a, b), we need to determine the slope of the normal line at that point.

The slope of the tangent line to the curve at (a, b) is given by the derivative:

f'(x) = 3x^2 + 6x + 7

So the slope of the tangent line at x = a is:

m = f'(a) = 3a^2 + 6a + 7

The slope of the normal line is the negative reciprocal of the slope of the tangent line, so:

m_n = -1/m = -1/(3a^2 + 6a + 7)

Now we have the slope of the normal line at (a, b), and we just need to find the equation of the line in point-slope form, using the point (a, b):

y - b = m_n(x - a)

Substituting the expression for m_n, we get:

y - b = (-1)/(3a^2 + 6a + 7)(x - a)

Multiplying both sides by 3a^2 + 6a + 7 to eliminate the fraction, we get:

(3a^2 + 6a + 7)(y - b) = -(x - a)

Expanding and rearranging, we get the equation of the line normal to the graph of y = x^3 + 3x^2 + 7x - 1 at (a, b):

(3a^2 + 6a + 7)y = -x + (3a^2 + 6a + 7)b + a

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Answer: 80

Step-by-step explanation:

To solve this,we will use the formula for direct proportion which is:

y = kx

where k = number of cookies made = 24

x = time taken = 1.5 hours

Since y = kx

24 = 1.5k

k = 24/1.5

k = 16

Then, the amount of cookies that can she make in 5 hours will be:

y = kx

y = 16 × 5

y = 80

She can make 8 cookies in 5 hours.

Answer:

315.74

Step-by-step explanation:

=268.75−(−46.99)

=268.75+46.99

=315.74

Line 2 has a positive slope with respect to the angle made with the x-axis.

Slope refers to the tan of the angle with the x-axis. For example. if the line makes an angle β with the x-axis, then the slope is the tan β.

Now taking line 1,

The line is parallel to the x-axis, therefore the line makes 0 angles with the axis which gives slope 0.

Now taking line 2,

The line passes to the origin and has the equation x=y, thus the slope is 1

Now taking line 3,

The line is parallel to the y-axis, therefore the line makes 90°, thus the slope is 1/0 which gives infinity.

Now taking line 4,

The line is making an angle of 60°, therefore the line is having a slope:       - \(\sqrt{3}\)

Hence considering the above values, line 2 has a positive slope only.

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Answer:

a. 6  b. |-23|  c. |-72|  d. 29  g. <  h. >  q. -1, 0, |-2|, |-3|

r. -2, -1, |1|, |-2|  s. -26, -24, |-20|, 21  t. -201, 120, |-121|, 210

Step-by-step explanation:

I really don't want to explain every single one

Answer:

carolina needs to buy at least 713 paintballs to get $10 off

Step-by-step explanation:

Entrance fee = $18

Fee per ball = $0.08

The field has a promotion that says, "Get $10 off if you spend $75 or more"

Let B represent the number of paintballs that Carolina buys.

18 + 0.08B ≥ 75

Subtract 18 from both sides

0.08B ≥ 75 - 18

0.08B ≥ 57

Divide both sides by 0.08

B ≥ 57 / 0.08

B ≥ 712.5

Approximately

B ≥ 713

carolina needs to buy at least 713 paintballs to get $10 off

Answer:

The mean is 4.5

Step-by-step explanation:

u add the numbers and divide by how many numbers there are

Answer:

1 12th (1 over 12)

Step-by-step explanation:

If she had a whole cake it would be 1 6th (1 over 6) of the cake. To get the answer for this do fraction for the amount of food then multiply that by 1 as the numerator and the number of people as the denominator (1 over the # of people). Then the fraction you get as your answer from multiplying that is the fraction or answer to your question. Note this only works with these types of questions. I really hope this helps.

The equation in standard form where all coefficients are expressed relatively is -x + 0y = 12.

If the slope of a line is undefined, it means the line is vertical. A vertical line does not have a defined slope, but its equation can still be expressed in standard form.

The equation for a vertical line passing through the point (-12, 12) can be written as:

x = -12

In standard form, the equation is typically written as:

x + 0y = -12

However, to express all coefficients relatively, we can multiply the equation by any non-zero constant to make the coefficient of x equal to 1. In this case, we can multiply the equation by -1 to achieve that:

-x + 0y = 12

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In the parallelogram BCDE, the measure for ∠CBE is evaluated to be 123°.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A parallelogram BCDE is given.

A diagonal BD is drawn.

The measure of ∠BDC = 68°.

The measure of ∠BCD = (2x + 57)°.

The measure of ∠BDE = (x + 55)°.

According to the properties of a parallelogram opposite interior angle are equal which gives -

∠BDC = ∠DBE = 68°

∠BDE = ∠DBC = (x + 55)°

Another property of parallelogram states that the adjacent angles of the parallel sides of the parallelogram form an angle sum of 180°.

This can be mathematically represented as -

∠EBC + ∠BCD = 180°

(∠DBE + ∠DBC) + ∠BCD = 180°

Substitute the values into the equation -

[68° + (x + 55)°] + (2x + 57)° = 180°

Solving the equation we get -

(123° + x) + (2x + 57)° = 180°

180° + 3x = 180°

x = 1/3

Substitute the value of x in ∠DBC -

∠DBC = 1/3 + 55°

∠DBC = 55°

So, the measure of ∠CBE = ∠DBE + ∠DBC

∠CBE = 68° + 55°

∠CBE = 123°

Therefore, the value for ∠CBE is obtained as 123°.

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Answer:

9

Step-by-step explanation:

99 : 66 ( divide both parts by 11 )

= 9 : 6

In a function, there is only one value of y for a given value of x. In this case, we are told that for each radio frequency (x) there is exactly one radio station (y), then this relation of x and y is a function

The reported area, including the uncertainty, should be 6.0 ± 1.5 square units.

To report the area calculated from the recorded length and width, including the uncertainty, we need to consider the range of values obtained from the length and width measurements.

Let's assume the recorded length is L with a range of ±ΔL, and the recorded width is W with a range of ±ΔW.

The uncertainty in the area can be determined by propagating the uncertainties using the formula for the area of a rectangle:

Area = Length × Width

To find the uncertainty in the area, we can use the following formula:

ΔArea = |Width × ΔLength| + |Length × ΔWidth|

Now, let's substitute the given values:

ΔLength = (2.143 - 2) = 0.143 (using the value from part (a))

ΔWidth = (3.536 - 3) = 0.536 (using the value from part (b))

ΔArea = |3 × 0.143| + |2 × 0.536|

= 0.429 + 1.072

= 1.501

Therefore, the uncertainty in the area is approximately 1.501.

To report the area, we should round the calculated value to 1 significant figure, considering the uncertainty. Since the uncertainty is 1.501, we can round the area to the first digit containing the uncertainty:

Area = 6.0 (rounded to the first digit containing the uncertainty)

Therefore, the reported area, including the uncertainty, should be 6.0 ± 1.5 square units.

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No, to construct a confidence interval, the population should be is approximately normal.

The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.

1. The data needs to be randomly selected.

2. The sampling distribution needs to be normally distributed

3. The observations must be independent.

So one of the conditions is to ensure that the population is normally distributed.

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

n(1 - p) ≥ 10

When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.  

Therefore, the population is approximately normal before constructing a confidence interval.

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Answer:

7 sides

Step-by-step explanation:

formula for sum of interior angles

(n-2)× 180= 10 right angles

(n-2)× 180 = 900

n-2= 900÷180

n= 5+2

n= 7

120 units are needed to complete the number of equivalent units if the ending work in the process contains 300 units.

Number of units =  300 units

Percentage of units completed  = 40%

To determine the number of equivalent units for a display operation, you need to view the teams that are fully satisfied as well as the partly finished units in the cessation outcome in the process.

Equivalent units = Number of fully completed units + Equivalent units in finishing work in process

Number of equivalent units = 0 + (300 units x 40%)

Number of equivalent units = 0 + 120 units

Number of equivalent units = 120 units

Therefore, we can conclude that the number of equivalent units is 120 units.

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The complete question is-

if the ending work in the process contains 300 units that are 40% complete the number of equivalent units is?

Answer:

± 1.13432%

between 23.966% and 26.234% households in the population who tuned into the final episode of ​"When Will it End question mark​"

Step-by-step explanation:

Given that:

Sample size (n). = 5613

Proportion (p) = 25.1% = 0.251

Margin of Error can be obtained using :

MOE = z * √p * (1 - p) / √n

Zscore at 95% confidence interval = 1.96

1 - p = 1 - 0.251 = 0.749

Hence,

Margin of Error :

1.96 * √0.251 * 0.749 / √5613

1.96 * (0.4335885 / 74.919957)

= 0.0113432

= ± (0.0113432) * 100%

= ± 1.13432%

B.) between (25.1 - 1.134)% = 23.966% and 25.1 + 1.134)% = 26.234% households in the population who tuned into the final episode of ​"When Will it End question mark​"

Margin of Error (MOE) is a function of the critical value. We will choose a confidential interval of 95 %.

Solution is:

a) MOE = 0,011

b) We can affirm with 95 % of confidence that the porcentage of TV households in the population watching th final  episode of " When ...

would be between  25,1 - 0,011  and  25,1 + 0,011

In our question we got:

Sample size    n = 5613

p = 25.1 %    ( positive events expressed as porcentage )

q = 1 - p     q = 1 - 0,251    q = 0,749

According to the size of the sample, and the fact that

q×n    and   p×n   are both    q×n > 10   p×n > 10

We are in condition to apply the approximation of the binomial distribution to normal distribution and use table z scores

CI   = 95 %    then  confidence level   α = 5 %    α/2 = 0,025  and fom z-table we get the critical value

z(c) = 1,96

Now to find MOE

MOE = z(c)×√(p×q/n)  ⇒ MOE = 1,96 × √ ( 0,251×0,749)5613

MOE = 1,96 × 0,005787

MOE = 0,011

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If Confidential Interval is 95%

Answer:

Red Line

m = 1/2

b = 1

Blue Line

m = 1

b = -1

Green Line

m = 3

b = 0

Step-by-step explanation:

First off, we need to know what m and b are first.

m is the slope

b means y-intercept, or, when x is 0

And to find slope use "m = y2 - y1/x2 - x1" (remember, Rise over Run, not Run over Rise!)

Red line: if you count it, you get a point on the line each time you go up once and to the right twice. We can use Rise over run. Rise is y, or its name, go up, which is the 1. then the run which is 2. So, the slope is 1/2 or m = 1/2. and we can see that the y-intercept is 1. m = 1/2, b = 1

Blue Line: This is pretty much the same as the red line, see the slope it's rise once and run once so, the slope is 1/1 which is 1. Then the y-intecept is b which is when x is 0, we check the y-axis line and we see that the y-intercept is -1. m = 1, b = -1

Green Line: And once again, the same as Red Line and Blue Line, the slope is 3. Rise is 3 times, run is once, so, 3/1 which is 3. While the y-intercept is 0 since it is on (0,0). Meaning that it goes through the origin. m = 3, b = 0

======================================================

Explanation:

We can apply the remote interior angle theorem. Some math books or teachers may refer to this as the "exterior angle theorem". They're the same idea just with different names.

According to that theorem, the interior angles x and 53 add up to the exterior angle 158

x+53 = 158

x = 158-53

x = 105

This theorem only works if neither interior angle is adjacent to the exterior angle. Hence the "remote" part.

----------

If you wanted a slightly longer approach, then let y be the missing angle that isn't marked in the diagram. Angle y is adjacent to the 158 degree angle.

We can find y by noting how 158 and y are supplementary

158+y = 180

y = 180-158

y = 22

Then we use the fact that adding three angles of any triangle always gets us 180 degrees

x+y+53 = 180

x+22+53 = 180

x+75 = 180

x = 180-75

x = 105

Effectively, this example helps reinforce why the remote interior angle theorem is true.

Answer:

4 units

Step-by-step explanation:

Create an equation where w is the width of the rectangle

Use the area formula, A = lw.

Since the length is the sum of the width and 1, it can be represented by w + 1

Plug in this and the area into the formula, and solve for w

A = lw

20 = (w + 1)(w)

20 = w² + w

w² + w - 20

(w + 5)(w - 4)

Solve for w:

w + 5 = 0

w = -5

w - 4 = 0

w = 4

Since the width cannot be negative, the answer must be 4.

So, the width of the rectangle is 4 units.

Answer:

We know that

Area = Length × Width

Area = w + 1 × w

Area = w² + w

w² + w - 20

w² + (5w - 4w) - 20

(w + 5)(w - 4)

Either

w = -5

or w = 4

Breadth can't be negative

So,

Breadth = 4 units

Answer: d

Step-by-step explanation:

x*4=4x

5*4=20

Thus, all the new inequality is is a new, more complex version of the original.  Thus, the sign stays the same.

Hope it helps <3

Answer:

d)  ≥ .

Step-by-step explanation:

When x = 5 4x = 20.

hen x > 5  4x > 20.

Answer:

hai

Step-by-step explanation:

a. the equation for the object's velocity is v(t) = -6 cos(t) - 1. b. the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

a) To find the equation for the object's velocity, we need to integrate the acceleration function with respect to time.

The integral of a(t) = 6 sin(t) with respect to t gives us the velocity function v(t):

v(t) = ∫(6 sin(t)) dt

Integrating sin(t) gives us -6 cos(t), so the equation for the object's velocity is:

v(t) = -6 cos(t) + C

To find the constant C, we use the initial velocity v(0) = -7 m/s:

-7 = -6 cos(0) + C

-7 = -6 + C

C = -1

Therefore, the equation for the object's velocity is:

v(t) = -6 cos(t) - 1

b) To find the object's displacement from time 0 to time 3, we need to integrate the velocity function over the interval [0, 3]:

Displacement = ∫[0,3] (-6 cos(t) - 1) dt

Integrating -6 cos(t) gives us -6 sin(t), and integrating -1 gives us -t. Applying the limits of integration, we have:

Displacement = [-6 sin(t) - t] from 0 to 3

Plugging in the upper and lower limits:

Displacement = [-6 sin(3) - 3] - [-6 sin(0) - 0]

Displacement ≈ -6 sin(3) + 3

Therefore, the object's displacement from time 0 to time 3 is approximately -6 sin(3) + 3 meters.

c) To find the total distance traveled by the object from time 0 to time t, we need to integrate the absolute value of the velocity function over the interval [0, t]:

Total Distance = ∫[0,t] |(-6 cos(t) - 1)| dt

Since the absolute value function makes the negative part positive, we can rewrite the equation as:

Total Distance = ∫[0,t] (6 cos(t) + 1) dt

Integrating 6 cos(t) gives us 6 sin(t), and integrating 1 gives us t. Applying the limits of integration, we have:

Total Distance = [6 sin(t) + t] from 0 to t

Plugging in the upper and lower limits:

Total Distance = [6 sin(t) + t] - [6 sin(0) + 0]

Total Distance = 6 sin(t) + t

Therefore, the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

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When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

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Given system of linear equations is:$$ \begin{aligned} x_1 + x_2 + 8x_3 &= 20 \\ x_1 + 5x_2 - x_3 &= 10 \\ 4x_1 + 2x_2 + 6x_3 &= 12 \end{aligned} $$

To solve the system by Jacobi's iterative method, write each equation in terms of the corresponding variable (i.e., isolate each variable on the left-hand side of the equation) as follows:$$ \begin{aligned} x_1 &= 20 - x_2 - 8x_3 \\ x_2 &= 10 - x_1 + x_3 \\ x_3 &= \frac{12 - 4x_1 - 2x_2}{6} \\ \end{aligned} $$Using initial estimates of x as [0, 0, 0], start the iteration process:$$ \begin{aligned} \text{Iteration 1:} & & \\ x_1^{(1)} &= 20 - 0 - 8(0) = 20 \\ x_2^{(1)} &= 10 - 0 + 0 = 10 \\ x_3^{(1)} &= \frac{12 - 4(0) - 2(0)}{6} = 2 \\ \text{Iteration 2:} & & \\ x_1^{(2)} &= 20 - 10 - 8(2) = -6 \\ x_2^{(2)} &= 10 - (-6) + 2 = 18 \\ x_3^{(2)} &= \frac{12 - 4(-6) - 2(18)}{6} = -4 \\ \text{Iteration 3:} & & \\ x_1^{(3)} &= 20 - 18 - 8(-4) = -10 \\ x_2^{(3)} &= 10 - (-10) - 4 = 24 \\ x_3^{(3)} &= \frac{12 - 4(-10) - 2(24)}{6} = -10 \\ \text{Iteration 4:} & & \\ x_1^{(4)} &= 20 - 24 - 8(-10) = 102 \\ x_2^{(4)} &= 10 - (102) - 10 = -102 \\ x_3^{(4)} &= \frac{12 - 4(102) - 2(-102)}{6} = 34 \\ \text{Iteration 5:} & & \\ x_1^{(5)} &= 20 - (-102) - 8(34) = 302 \\ x_2^{(5)} &= 10 - (302) + 34 = -258 \\ x_3^{(5)} &= \frac{12 - 4(302) - 2(-258)}{6} = 110 \\ \end{aligned} $$The iteration stops when the error of each estimate is less than the tolerance of 10³. In this case, since the magnitude of the third estimate exceeds the tolerance, the process must continue until the tolerance is met:$$ \begin{aligned} \text{Iteration 6:} & & \\ x_1^{(6)} &= 20 - (-258) - 8(110) = 1,118 \\ x_2^{(6)} &= 10 - (1,118) + 110 = -998 \\ x_3^{(6)} &= \frac{12 - 4(1,118) - 2(-998)}{6} = 330 \\ \end{aligned} $$Therefore, the solution to the system of linear equations by Jacobi's iterative method with initial estimate [0, 0, 0] and tolerance of 10³ in the norm is:$$ \boxed{x \approx [1,118, -998, 330]} $$

The iterative method is used to solve a system of linear equations, as in the Jacobi iteration method. The method is used when the original method is not effective or too complex. Iterative techniques are popular because they can compute a large number of equations using a computer quickly and accurately.Jacobi's iterative method is a technique used to solve a set of linear equations with n variables that requires at least n iterations to converge. It works by isolating each variable on one side of the equation and then iteratively substituting the previous estimate of each variable into the corresponding equation until the estimated values converge within a certain tolerance.The iteration formula for Jacobi's method is given by$$ x_i^{(k+1)} = \frac{1}{a_{ii}} \left(b_i - \sum_{j=1, j \ne i}^{n} a_{ij} x_j^{(k)} \right) $$where k is the iteration number and x^(k) is the vector of previous estimates. In this formula, the diagonal element aii is isolated on one side of the equation, and the summation term represents the contribution of all other variables except xi. The previous estimate xi^(k) is then substituted into the equation to compute the updated estimate xi^(k+1).

Jacobi's method is a powerful tool for solving a system of linear equations with multiple variables. The method involves iterative substitution of the previous estimate of each variable into the corresponding equation until the estimated values converge within a certain tolerance. The process continues until the desired level of accuracy is reached. This method can be effectively used to solve many problems that would otherwise be too difficult or complex.

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Answer:

As we know that

\(\sf 1 \:Foot=12inches \)

\({:}\longrightarrow\)\(\sf {\dfrac {7}{12}}\:of \; 12 \)

\({:}\longrightarrow\)\(\sf {\dfrac {7}{{\cancel {12}}}}\times{\cancel { 12 }}\)

\({:}\longrightarrow\)\({\underline{\boxed{\bf 7inches}}}\)

The real causes of World War I included politics, secret alliances, imperialism, and nationalistic pride.

The nations of Europe were continually vying for dominance and forming alliances in the years preceding the conflict. In 1881, Germany formed an alliance with Italy and Austria-Hungary. All of these nations committed to defending one another in the event that France attacked them. But after that, Italy went and formed a covert alliance with France, declaring they would not support Germany.

In 1892, France and Russia formed an alliance in response to Germany's alliances. Britain and France signed a contract in 1904. France, Britain, and Russia established the Triple Entente in 1907. Germany believed that the strong alliance that surrounded them posed a serious danger to their existence and regional dominance.

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