-4z^2 + 13z - 3 = 0 solve in quadratic form

Answer

Check Explanation

Explanation

a ≡ b (mod n)

This means a and b have the same remainder when they are divided by n

So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.

1) 67 × 73 ≡ 1 × 3 (mod 5)

4891 ≡ 3 (mod 5)

So, to check,

(4891/5) = 978 remainder 1

(3/5) = 0 remainder 3

The remainders are different.

So, this equation is wrong and does not work.

This equation is false.

2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

Noting that it is the units digit that determines the remainder

3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer

5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer

So, using these numbers,

83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

81 ≡ 625 (mod 17)

(81/17) = 4 remainder 13

(625/17) = 36 remainder 13

The remainders are the same.

So, this equation is correct and it works.

This equation is true.

Hope this Helps!!!

Answer:

Step-by-step explanation 10:

Answer:

2a

Step-by-step explanation:

8a² / 4a

8/4 a²-¹

2a

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Answer:

2a

Step-by-step explanation:

8a^2 = 4a x 2a

8a^2 ➗ 4a

= ( 4a x 2a )/4a

= 2a

Answer:

The factors are (x+9),(x−9).

Step-by-step explanation:

Base on congruency of vertical angles, the value of z is 7.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

In other words, vertically opposite angles are angles that opposed each other at one specific vertex, and are formed by two straight intersecting line.

Vertically opposite angles are congruent to each other.

Therefore,

7z + 7 = 9z - 7

subtract 9z from both sides of the equation

7z + 7 = 9z - 7

7z - 9z + 7 = 9z - 9z - 7

-2z + 7 = - 7

subtract 7 from both sides of the equation

-2z + 7 = - 7

-2z + 7  - 7 = - 7 - 7

- 2z = - 14

divide both sides by - 2

z = - 14 / -2

Therefore,

z = 7

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The parent function of the quadratic function is

∵ x is added by 7

∴ The graph of the function is translated 7 units to the left

∴ The image of the function will be

∵ The function is added by -4

∴ The graph of the function translated 4 units down

∴ The image of the function will be

The transformation is

Shift 7 units left and shift down 4

The answer is D

Answer:

x=9

y=27

Step-by-step explanation:

the scale factor is [tex]\frac{4}{3}[/tex] so 6 × [tex]\frac{4}{3}[/tex] is x - 1

x-1 is 8

so x is 9.

The given equation x²-2x=(-2)(3-x) is a quadratic equation.

A second-degree quadratic equation in algebra is one that involves x.

The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

The coefficient of x2 must be a non-zero term in order for an equation to meet the definition of a quadratic equation.

given:

x²-2x=(-2)(3-x)

on expanding,

x²-2x = -6+2x

x²-4x+6 = 0

hence above equation is in form of ax²+bx+c=0, where a=1, b=-4. c=6

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If arthur walks 3 km north, and then turns east and walks 4 km. The  distance traveled  is 7km and his displacement is 5km.

Distance traveled:

Distance traveled = Km north + East Km

Distance traveled  = 3 km + 4 km

Distance traveled  = 7 km

Displacement

Using  Pythagoras theorem to determine  or find the displacement

B² = A ²+AB²

B² = 3 ² +4 ²

B = 9+16

B = √ 25

B = 5 km

Therefore the 7km is the distance and 5km is the displacement.

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Answer:

[tex]y+2=\frac{5}{2} (x-6)[/tex]

Step-by-step explanation:

point-slope form: y-y1=m(x-x1)

x1=6

y1=-2

m=5/2

[tex]y+2=\frac{5}{2} (x-6)[/tex]

Answer:

[tex] {2x}^{2} + 7[/tex]

so hope it helps

Answer:

A

Step-by-step explanation:

ax + by = c  Subtract ax from both sides

by = -ax + c  Divide all the way through by b

[tex]\frac{by}{b}[/tex] = [tex]\frac{-a}{b}[/tex] x + [tex]\frac{c}{b}[/tex]

y = - [tex]\frac{a}{b}[/tex] x +[tex]\frac{c}{b}[/tex]

step 1

Find the slope of the line represented by the table of values

take the points

(-8,13) and (-4,5)

m=(5-13)/(-4+8)

m=-8/4

m=-2

step 2

Write the equation of the line that contains the point (-8,6) and has the same slope as the line represented by the table

y=mx+b

we have

m=-2 -----> the same slope of the given line

point (-8,6)

substitute in the equation of the line in slope intercepot form

6=-2*(-8)+b

solve for b

6=16+b

b=-10

therefore

teh equatiion of the line is

Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:

2x² + 5x + 1.

In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:

8, 26, 19 and 3.

The divisor is found as follows:

4x + 3 = 0

4x = -3

x = -3/4

x = -0.75.

The resulting coefficients of the quotient are given as follows:

8, 20, 4 and remainder of 0.

Hence the quotient is:

8x² + 20x + 4.

Which can be simplified as:

2x² + 5x + 1.

The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.

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the derivitvte of 2x^2(cotx) is −4cot2xcsc^2(2x)

A polynomial function of degree 3 with real coefficients and given zeros of -3, -1, and 4 is 4(x - 4)(x + 3)(x + 1) for which f(-2) = 24.

Any modifying value connected to a variable through multiplication is referred to as a "coefficient." Any non-imaginary number is a "real" number

How do you locate a degree 3 polynomial with real coefficients?

A polynomial of degree 3 must take the form a(xr1)(xr2)(xr3) since it has three roots. We are provided with the roots 3, 1, and 4. So, all we have to do is change these to r1, r2, and r3. We now get a(x+3)(x+1)(x4).

We must first factor the provided polynomial equation into a linear and quadratic equation in order to obtain the roots of the three-degree polynomial. The zeros of the three-degree polynomial can then be easily found.

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SOLUTION

We want to solve the equation

cross multiplying, we have

Hence the answer is x = 2, the first option

The value of the given function h(k(3)) when h(x) =√ x+3  and k(x) = 2x +7 is equal to 4.

As given in the question,

Given functions are :

h(x) =√ x+3  and k(x) = 2x +7

To find the value of the composite function h(k(3)) :

First calculate for k(3) we get,

k(x) = 2x+ 7

Substitute x =3 in k(x) we get,

k(3) = 2(3) +7

⇒ k(3) = 13

Now, Substitute the value of k(3) in the composite function h(k(3)) we get,

h(k(3))

= h(13)

= √ 13 +3

=√16

= 4

Therefore, the value of the given function h(k(3)) when h(x) =√ x+3  and k(x) = 2x +7 is equal to 4.

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The correct option regarding the ratio is given as follows:

For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.

A ratio of an amount a over a total amount a + b is given as follows:

r = a/(a + b) = a:b.

In the context of this problem, the ratio is given as follows:

r = 3:2.

Hence the number of equal parts is given by:

equal parts = 3 + 2 = 5.

The length of the segment is:

B - A = 6 - (-4) = 10 units.

Hence the length of each equal part is:

length equal part = 10/5 = 2.

The point that is 3/5 of the way from point -4 to point 6 is found as follows:

x - (-4) = 3/5(6 - (-4))

x + 4 = 30/5

x + 4 = 6

x = 2.

Meaning that the correct option is given by the last one.

The coordinates of A and B are missing, and they are given as follows:

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The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

Given that, a lighthouse is located on a small island 4 km away from the nearest point P.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

[tex]\frac{d\theta}{dt}[/tex] = 6 rev/min

= 6π rad/min

tan θ = x/6

[tex]\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )[/tex]

[tex]sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )[/tex]

[tex]\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}[/tex]

At x=1 km; tan θ= x/6 = 1/6

[tex]sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2[/tex]

[tex]sec^2 \theta = \frac{10}{9}[/tex]

[tex]\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}[/tex]

dx/dt = 6 × 10/9 × 6π

dx/dt = 125.66 km/min

Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

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By central limit theorem ,with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.

The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.

Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.

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The cost of endless chicken wings at Restaurant X is $5. So cost equation for n chicken wings at Restaurant X is,

The cost of chicken wings at Restaurant Z is 20 cents and $1.40 for sauce. So cost equation for Restaurant Z is,

So answer is,

Restaurant X: c = 5

Restaurant Z: 0.20n + 1.40

(b)

Plot the system of equation on the graph.

(c)

The lines of two restaurant X and restaurant Z intersect each other at point (18,5). This means that restaurant X and restaurant Z has same cost 5 at n = 18. So both restanurant has same cost for 18 chicken wings.

Answer: 18

The correct option regarding the scale and the origin of the graph are as follows:

D.

x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin: (0 weeks, 0 minutes)

The scale should be chosen focusing on improving the readability of the data-set by the reader, while the origin should be chosen according to the values assumed by the variables.

In the context of this problem, the values of x, in weeks, are:

2, 3, 4, 5, 6, 7, 8.

They increase by one, hence the scale of x should be of 1 unit = 1 week.

The values of y, in minutes are given as follows:

300, 450, 600, 750, 900, 1050, 1200.

They increase by 150, hence the scale of y should be of 1 unit = 150 minutes, which is the rate of change of the problem.

As the measures are both positive values, the origin should be of (0,0), hence the correct option for the scales and the origin is option D.

The table is:

Weeks Minutes

2 300

3 450

4 600

5 750

6 900

7 1,050

8 1,200

The options are:

A. x-axis scale: 1 unit = 2 weeks

y-axis scale: 1 unit = 50 minutes

origin: (0 weeks, 0 minutes)

B. x-axis scale: 1 unit = 2 weeks

y-axis scale: 1 unit = 150 minutes

origin: (2 weeks, 300 minutes)

C. x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 50 minutes

origin: (2 weeks, 300 minutes)

D. x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin: (0 weeks, 0 minutes)

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Answer:

0

Step-by-step explanation:

the domain can’t be the same

The value of XZ is 32.

What is the value of XZ?

Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.

From the figure, XY = 15 and YZ = 17

XZ is the sum of XY and YZ:

XZ = XY + YZ

XZ = 15 + 17 = 32

Therefore, XZ is 32.

This shows the concept of trigonometry.

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12

1) Considering this Data Set:

8 12 15 9 10 12 12 18 14 15 10 11 12 9 17

2) And the fact that the mode is the central tendency measure that indicates the data point that repeats itself the most, we can tell that the mode is:

Note that this is the data point that repeats itself the most.

Answer:

-4

Step-by-step explanation:

6 + 4x-y = 6 + (4x-y) = 6 + (-10) = -4

The graph of the equation -4x = -60 is shown below.

A vertical line is expressed as the equation, x = b. Here, the variable "b" is the point on the x-axis where the line intercepts the horizontal axis.

Thus, to plot the graph for a vertical line with the equation, x = b, we would simply draw a vertical line that crosses the x-axis at point b.

Given the equation, -4x = -60, rewrite the equation in the form x = b, to determine the value of b:

-4x/-4 = -60/-4 [division property of equality]

x = 15

This means that the graph of the equation, -4x = -60, would be a graph that has a vertical line that crosses the x-axis at 15.

the graph is shown below.

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The quadratic formula for a polynomial is given by:

Therefore, option (C) is correct.