find the remainder when f(x)=4x3-20x-50 is divided by x-3

Answer:

y = -1.5x

How to build equation?

Given points: (0, 0), (2, -3)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5[/tex]

Then find equation:

[tex]y-y_1 = m(x - x_1)[/tex]

[tex]y - 0 = -1.5(x -0)[/tex]

[tex]y = -1.5x[/tex]

Answer:

y = (-3/2)x

Step-by-step explanation:

I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:

[tex]m=\frac{-3-0}{2-0}=\frac{-3}{2}[/tex]

Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x

The value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].

Given that, (1+tanx)(1-tanx)+sec²x.

Now, (1-tan²x)+sec²x

=1-tan²x+sec²x

=1+sec²x-tan²x

=1-1=0

Now, evaluate [tex]\frac{sec^{2}-4 }{sec+2}[/tex]

[tex]=\frac{sec^{2} \theta \ -2^{2} }{sec\theta \ +2} =\frac{(sec \theta \ +2)(sec \theta \ -2)}{sec \theta \ +2}[/tex] (∵a²-b²=(a+b)(a-b))

[tex]=sec \theta \ -2[/tex]

Hence, the value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].

To learn more about trigonometric identities visit:

https://brainly.com/question/12537661.

#SPJ1

The 97% confidence interval for the proportion of adults is 0.801<P<0.851.

Given that 867 adults are randomly selected from 1050 who always wear seat belts.

A confidence interval refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Let's assume n=1050 and x=867

Find the sample proportion by dividing the given proportion with sample size as,

[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\\hat{p}&=\frac{867}{1050}\\ \hat{p}&=0.826 \end[/tex]

Find the α by subtracting the given confidence interval that is 97% from 1 as

α=1-(97÷100)

α=1-0.97

α=0.03

To find the critical value that is [tex]Z_{\frac{\alpha}{2}}[/tex] by dividing alpha with 2,

[tex]\begin{aligned}Z_{\frac{\alpha}{2}}&=Z_{\frac{0.03}{2}}\\ Z_{\frac{\alpha}{2}}&=Z_{0.015}\end[/tex]

From this table which is shown in the figure it says that the critical value is

[tex]Z_{crit}=\pm 2.17[/tex]

Use this formula to find the confidence interval [tex]P=\hat{p}\pm Z_{Crit}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Substitute the values in the formula,

[tex]\begin{aligned}P&=0.826\pm 2.17\times \sqrt{\frac{0.826(1-0.826)}{1050}}\\ P&=0.826\pm 2.17\times \sqrt{\frac{0.826\times 0.174}{1050}}\\ P&=0.826\pm 2.17\times 0.0116995\\ P&=0.826\pm 0.025\end{aligned}[/tex]

Hence, a 97% confidence interval for the proportion of adults who always wear seat belts is 0.801<P<0.851.

Learn more about confidence interval from here brainly.com/question/13929861

#SPJ4

the answer is

X=5

y=3

hope you like it

Answer:

c because have great day

Answer:

is this tye required answer

Answer:

the median is 9

Explanation

Finding the median is easy, all you need to do is put the numbers in numeric order and the one that's in the middle of the numbers is the median

9 , 9 , 9 , 4 , 9 , 1 , 10  =   1, 4, 9, (9), 9, 9, 10

                                              (median)

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Given the Ages of students: 9,9,9,4,9,1,10. State the median

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{7cm} Before finding the median, we\\ need to arrange \\ our data from least to greatest. \end{minipage}}[/tex]

Thus,

[tex]\bf{1,4,9,9,9,9,10}[/tex].

[tex]\fbox{The median is the number in the middle.}[/tex]

Thus,

[tex]\bf{9}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=9}[/tex]

[tex]\begin{tabular}{c | 1} Data Parameter & What to Do \\ \cline{1-2} \\ Mean & Add all the numbers and divide by how many there are \\ Median & Arrange the numbers from least to greatest and take the number \\ & in the middle. Take the mean of the 2 numbers in the middle \\ & if there's an even amount of numbers \\ Mode & The number that occurs the most \\ Range & The largest number minus the smallest number \\ Minimum & The smallest value \\ Maximum & The largest value \end{tabular}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Answer:

90 degrees

Step-by-step explanation:

the clock is a circle so the entire # of degrees is 360.

there are 12 sections on the clock so 360 /12 =30

so each section is 30 degrees.

if you go from 3:00 to 3:15, that is 3 sections.

so 3 times 30 is 90

ΔFGH is congruent to ΔFJH They are not congruent because only one pair of corresponding sides is congruent.

The correct option is (C)

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Given:

ΔFGH and ΔFJH share common side FH. Sides FG and GH are congruent.

As, per the information, it can be seen that the triangles are not congruent as one pair of corresponding side is not congruent.

Learn more about congruency here:

https://brainly.com/question/7888063

#SPJ1

Answer: C

Step-by-step explanation: edge

Using a piece-wise function, the representation of the graph is given as follows:

Walking uphill for 3 hours and downhill for 1 hour.

A piece-wise function is a function that has multiple definitions, depending on the input.

In this problem, we have that:

Hence the meaning of the graph is:

Walking uphill for 3 hours and downhill for 1 hour.

More can be learned about piece-wise functions at https://brainly.com/question/27262465

#SPJ1

Answer: 12

Step-by-step explanation:

For this counting question, we need to figure out the possible choices for each selection.

For main protein, there are four options, so we can make four slots

_ _ _ _

For beans, there's three options, so we can make three slots
_ _ _

Doing some casework, we know that 4*3 = 12, which is the answer.

Answer:

true

Step-by-step explanation:

Since their wise or intelligent guess

Answer: one

Step-by-step explanation:

     When a system of equations is graphed the solutions are the point of intersections. Here, we only have one point of intersection since these are both linear equations. That means there is only one solution.

Answer:

22x^2-9x+32

Step-by-step explanation:

(21x² - 6x +14) + (x²-3x+18)

To add, we need to combine like terms

21x^2+x^2     -6x-3x    +14+18

22x^2-9x+32

Answer:

22x² - 9x + 32

Step-by-step explanation:

(21x² - 6x +14) + (x²-3x+18)

Get rid of the parenthesis:

21x² - 6x + 14 + x² - 3x + 18

Group like terms:

22x² - 9x + 32

Now, ORQ is a straight angle and RS its bisector.

It means:

So, ∠ORS and ∠QRS are supplementary.

We also have ray RP, that divides the angles ORQ and QRS.

It gives us one more pair of supplementary angles:

Since ∠QRS is right angle, its parts are forming a pair of complementary angles:

Considering her change, it is found that she will donate $0.28 to the animal shelter.

The amount of change is given by the subtraction of the total paid and the price of the products.

In this problem, the price of the products bought is given by:

$15.74 + $3.98 = $19.72

She paid $20, hence the change is given by:

$20 - $19.72 = $0.28.

More can be learned about the amount of change in a purchase at https://brainly.com/question/10866253

#SPJ1

Answer:

1/4

Step-by-step explanation:

The ratio of the areas is the square of the ratio of the lengths of sides.

(1/2)² = 1/4

Answer: 1/4

A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways

The selections are given as:

3 boys from 5 boys

3 girls from 4 girls

Each selection is calculated using:

[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]

So, we have:

[tex]Ways = ^5C_3 * ^4C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]

Expand

[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]

Simplify

Ways = 5 * 2 * 4

Evaluate

Ways =40

Hence, the number of ways is 40

Read more about combination at:

https://brainly.com/question/11732255

#SPJ1

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:

y - k = C · (x - h)²

Where:

Please notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:

7 - 1 = C · (0 - 3)²

6 = 9 · C

C = 2/3

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

To learn more on parabolae: https://brainly.com/question/21685473

#SPJ1

Answer:

(2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i

Step-by-step explanation:

I'm 100% sure! ^^

Answer:

B: (2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i

Step-by-step explanation:

Took the quiz

One can determine the number of roots by seeing the degree of the given polynomial.

The number of roots can be determined by just seeing the highest power of the given equation.

1) for the equation  x-4=0

here, the highest power of the equation is one. So, it will have one root.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on,  and non-negative integer exponentiation of variables.

Let's check it by simplifying x-4=0  which implies x=4

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

10t^2-t-3=0

here, the highest power of the equation is two. So, it will have two roots.

Let's check it by simplifying using the middle term splitting method,

10t^2+5t-6t-3=0

5t(2t+1)-3(2t+1)=0

(5t-3)(2t+1)=0

t=-3/5 or t=-1/2

Thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the given polynomial.

To learn more about the polynomial visit:

https://brainly.com/question/2833285

#SPJ1

Limit of x approaches two from the left of f of x: 3. Limit of x approaches two from the right of f of x: - 1 (negative 1)

If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.

In order to find the limit as x approaches two from the left of f of x:

Lim x→2- f(x) = ?

According to the graph, when x approaches two from the left (x<2), the function approaches 3:

Lim x→2- f(x) = 3

IN order to find the limit as x approaches two from the right of f of x:

Lim x→2+ f(x) = ?

According to the graph, when x approaches two from the right (x>3), the function approaches -1:

Lim x→2+ f(x) = - 1

Learn more about one-sided limits here:

https://brainly.com/question/23625942

#SPJ1

The sum of the unknown angle and 33 degrees are supplementary. The measure of x is 147 degrees

The sum of the unknown angle and 33 degrees are supplementary to have:

x + 33 = 180

Subtract 33 from both sides

x + 33 - 33 = 180 - 33

x = 180 - 33

x = 147degrees

Hence the measure of x is 147 degrees

Learn more on supplementary angles here: https://brainly.com/question/12919120

#SPJ1

Answer:

Step-by-step explanation:

x + 33° = 180°

reason :( they are cointerior angle )

x = 180° - 33°

x = 147°

Answer:

Inversión en una circunferencia es una transformación que conserva la magnitud de los ángulos pero cada ángulo se transforma en un ángulo de signo opuesto . El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).

Step-by-step explanation:

El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).

Answer:

inversion transformations are a natural extension of Poincaré transformations to include all conformal one-to-one transformations on coordinate space-time.

In 2.44 seconds lindsey be 30 feet in the air.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

Given:

y= -16x²+33x+45

If the height is 30 feet.

30= -16x²+33x+45

-16x²+33x+45-30=0

-16x²+33x+15=0

16x²-33x-15=0

Solving the quadratic equation

x=-b±√b²-4ac/ 2a

x= 33 ± √2049/32

x= (33+ √2049)/32    and x=33-√2049/32

x=2.44 and -0.3833

Learn more quadratic equation here:

https://brainly.com/question/2263981

#SPJ1

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

An equation is an expression that shows the relationship between two or more variables and numbers.

The maximum height (H) of a projectile is given as:

H = u²/2g

Where u is the initial speed = 145 m/s, g is the acceleration due to gravity = 10 m/s²

H = 245²/ 2(10) = 3001.25 m

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: a

Step-by-step explanation:

[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x^{2}-1}}{\sqrt{x-1}}}=\sqrt{\frac{x^{2}-1}{x-1}}=\sqrt{\frac{(x-1)(x+1)}{x-1}}=\boxed{\sqrt{x+1}}[/tex]

Answer:

nth term: 0.5n² + 2.5n + 3

Explanation:

pattern 1 = 6 bowls

pattern 2 = 10 bowls

pattern 3 = 15 bowls

pattern 4 = 21 bowls

First difference:

Second difference:

This is not an arithmetic nor a geometric sequence.

Solve:

2a  = 2nd difference

2a = 1

a = 1/2 or 0.5

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

3a + b = 1st difference

3a + b = 4

b = 4 - 3(1/2)

b = 2.5

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

a + b + c = first term

1/2 + 2.5 + c = 6

c = 3

Quadratic nth term:

0.5n² + 2.5n + 3

Step-by-step explanation:

the answer is C) 8x^5y - 6x^4y^2

pls like and follow.

hope you understand as well