Marked price of a pen is Rs 20. It is sold at a discount of 15%. Find the selling price?

By the factor theorem, we have

[tex]x^2+5x+3=(x-p)(x-q)\implies\begin{cases}3=pq\\-5=p+q\end{cases}[/tex]

[tex]x^2+bx+c=(x-p^2)(x-q^2)\implies\begin{cases}c=p^2q^2\\-b=p^2+q^2\end{cases}[/tex]

Then

[tex]c=p^2q^2=(pq)^2=3^2=9[/tex]

and

[tex]p+q=-5\implies(p+q)^2=p^2+2pq+q^2=25\implies b=-(p^2+q^2)=-19[/tex]

So we have b + c = -19 + 9 = -10.

The given roots of the equation x² + 5x + 3 = 0 as p and q, and x² + bx + c = 0 as p² and q², gives us the value of b + c = -10.

If the quadratic equation ax² + bx + c = 0, has roots as α and β, then:

In the question, we are informed that the roots of the expression x² + 5x + 3 = 0 are p and q, and the roots of the expression x² + bx + c = 0 are p² and q².

We are asked to find the value of b + c.

Since the roots of the equation x² + 5x + 3 = 0 are given as p and q.

So, we can say that:

Now, we are informed that the roots of the equation x² + bx + c = 0 are p² and q². So, we can say that:

∴ b + c = -19 + 9 = -10.

∴ The given roots of the equation x² + 5x + 3 = 0 as p and q, and x² + bx + c = 0 as p² and q², gives us the value of b + c = -10.

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Answer:

????

Step-by-step explanation:

Where is the question????

Answer:

answer Z

Step-by-step explanation:

Look for a graph that contains the following zeros: x = 1, x = 2 , x= 3, following the info derived by the binomial factors that the function contains. Also look ate the fact that the function in question has for leading term positive [tex]x^3[/tex] , then this function must go towards plus infinity when x becomes large. This is the case for the graph option Z (the last graph of the group)

Answer:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Answer:

84 km... Mark me as BRAINLIEST

Step-by-step explanation:

Refer to the pic...

Hope it helped you!

Step-by-step explanation:

Since it takes 6 trips to cover 24 km -

1 trip = 24/6

Therefore 1 trip is -

4 km

Now, the distance for 21 trips is -

21*4 = 84

Therefore, Brad has walked -

84 km

HOPE YOU FIND THIS HELPFUL

Answer:

h(x) = -15.6(x - 3.8)² + 241

Step-by-step explanation:

if you were to graph these equations, you can see that the second equation has a lower maximum than the rest of equations, including the original. therefore, that answer can be eliminated.

or simply recognize the equation is in vertex form and realize that 222 is the y-value of the vertex. and 222 < 230. (230 being the y-value of the parent function's vertex)

the a-value (-15.9 for the parent/original function) of the new equation must be less than the parent function's a-value. this is the rate at which the pumpkin is decreasing. the lower the value, the slower the pumpkin moves. this is an advantage, as the length it travels increases. therefore, the third and fourth options are eliminated, leaving the first option as the answer.

Answer:

Step-by-step explanation:

3x + 45 = 4x + 21

45 - 21 = 4x - 3x

24 = x

Answer:

Step-by-step explanation:

[tex]3x + 45 = 4x + 21 \\ collect \: like \: terms \\ 3x - 4x = 21 - 45 \\ - x = - 24[/tex]

[tex]x = 24[/tex]

Answer:

C = 314 m

Step-by-step explanation:

The circumference of a circle is given by

C = pi * d

Using 3.14 for pi

C = 3.14 * 100

C = 314 m

Answer:

The answer is option D.

Step-by-step explanation:

Circumference of a circle = πd

Where d is the diameter

From the question

d = 100m

Circumference of the circle is

100π

= 314.2

Which is 314m to the nearest whole number

Hope this helps you

Answer:

? = 57

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos ? = adj/ hyp

cos ? = 14/26

Taking the inverse cos of each side

cos ^-1 ( cos ?) = cos ^-1 ( 14/26)

? = 57.42102961

To the nearest degree

? = 57

Answer:

A.  x = 36

B.  x = 10

C.  x = 36

D.  x = 25

E.  x = 60

Step-by-step explanation:

A.  Since it is a straight line, the total degrees will be 180.  Add the two angle values and set them equal to 180.

2x + 3x = 180

5x = 180

x = 36

B.  This is right angle, meaning that the total degrees will be 90.  Add the two angle values and set them equal to 90.

4x + 5x = 90

9x = 90

x = 10

C.  The angles are around a point, meaning that the total degrees will be 360.  Add the angle values and set them equal to 360.

x + 2x + 3x + 4x = 360

10x = 360

x = 36

D.  Like part A, the straight line has 180 total degrees.  Add the angle values and set them equal to 180.

3x - 5 + x + 20 + 65 = 180

4x - 5 + 20 + 65 = 180

4x + 80 = 180

(4x + 80) - 80 = 180 - 80

4x = 100

(4x)/4 = 100/4

x = 25

E.  Like part A, the angles around the point have 360 total degrees.  Add the angles values and set them equal to 360.

x + 2x + 2x + 60 = 360

5x + 60 = 360

(5x + 60) - 60 = 360 - 60

5x = 300

(5x)/5 = 300/5

x = 60

Answer:

a = 36°

b = 20°

c = 36°

d = 25°

e = 60°

Step-by-step explanation:

A)

2x + 3x = 180° (angles on a straight line = 180°)

5x = 180°

X = 180 / 5

x = 36°

B) 4x + 5x = 90° (sum of two acute angles in a right angle triangle = 90°)

9x = 90

x = 90 / 9

x = 10°

C) 2x + x + 4x + 3x = 360° (sum of angles at a point = 360°)

10x = 360°

x = 360 / 10

x = 36°

D) (3x - 5) + (x + 20) + 65 = 180 (sum of angles on a straight line = 180)

Open brackets

3x - 5 + x + 20 + 65 = 180

4x + 80 = 180

Collect like terms

4x = 180 - 80

4x = 100

X = 100 / 4

x = 25°

E)

x° + 60° + 2x° + 2x° = 360° (angle at a point = 360°)

5x° + 60° = 360°

Collect like terms

5x° = 360° - 60°

5x° = 300°

x = 300 / 5

x = 60°

Answer:

[tex] s = 14.1 [/tex]

Step-by-step explanation:

Find s using the Law of Cosines:

m < S = 31°

SR = q = 21

SQ = r = 9

QR = s = ?

Thus,

[tex] s^2 = r^2 + q^2 - 2(r)(q)*cos(S) [/tex]

[tex] s^2 = 9^2 + 21^2 - 2(9)(21)cos(31) [/tex]

[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]

[tex] s^2 = 522 - 324.0216 [/tex]

[tex] s^2 = 197.9784 [/tex]

[tex] s = \sqrt{197.9784} [/tex]

[tex] s = 14.07 [/tex]

[tex] s = 14.1 [/tex] (to the nearest tenth)

Answer:

The correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The types of correlation coefficient are:

The correlation coefficient value between the hour of the day and the speed over the limit at which the motorist is ticketed is:

r = 0.12.

The value of r lies between:

0 < 0.12 < 0.30

Thus, the correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.

and the answer should be 18 x 27. The answers were reversed.

Step-by-step explanation:

basically you can do (6x4) + 3 = 27

and (4x4) + 2 = 18.

A ratio shows us the number of times a number contains another number. The real size of the bedroom is 2536' by 1648'.

A ratio shows us the number of times a number contains another number.

Given that architectural drawing lists the scale as 1/4" = 1'. Therefore, we can write the scale ratio as,

1/4" = 1'

1" = 4'

Now, given that the bedroom measures 634" by 412" on the drawing. Therefore, the real dimensions of the bedroom are,

634" = 634 × 4' = 2536'

412" = 412× 4' = 1648'

Hence, the real size of the bedroom is 2536' by 1648'.

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Answer:

it is C.

Step-by-step explanation:

The common difference is -7

-27 -(-20)= -27 + 20 = -7

-34 -(-27)= -34 + 27 = -7

-41 -(-34)= -41 + 34 = -7

-48 -(-41)= -48 + 41 = -7

Answer:

5x +3

Step-by-step explanation:

f(x) = 2x-6

g(x) = 3x+9

(f+g) (x) = 2x-6+ 3x+9

Combine like terms

            = 5x +3

We are given the following two equations:

[tex]f(x)=2x-6[/tex]

[tex]g(x)=3x+9[/tex]

To find (f+g)(x), we just add f(x) and g(x) and simplify:

[tex](f+g)(x)=f(x)+g(x)[/tex]

[tex]=2x-6+3x+9[/tex]

[tex]=5x+3[/tex]

Let me know if you need any clarifications, thanks!

Answer:

George must run the last half mile at a speed of 6 miles per hour in order to arrive at school just as school begins today

Step-by-step explanation:

Here, we are interested in calculating the number of hours George must walk to arrive at school the normal time he arrives given that his speed is different from what it used to be.

Let’s first start at looking at how many hours he take per day on a normal day, all things being equal.

Mathematically;

time = distance/speed

He walks 1 mile at 3 miles per hour.

Thus, the total amount of time he spend each normal day would be;

time = 1/3 hour or 20 minutes

Now, let’s look at his split journey today. What we know is that by adding the times taken for each side of the journey, he would arrive at the school the normal time he arrives given that he left home at the time he used to.

Let the unknown speed be x miles/hour

Mathematically;

We shall be using the formula for time by dividing the distance by the speed

1/3 = 1/2/(2) + 1/2/x

1/3 = 1/4 + 1/2x

1/2x = 1/3 - 1/4

1/2x = (4-3)/12

1/2x = 1/12

2x = 12

x = 12/2

x = 6 miles per hour

Answer:

The answer is D.

Step-by-step explanation:

When x=0, then y=300, so it has to be more than that.

When x=25, y=300, so it has to be less than that.

Answer:

They are not perpendicular because their slopes are not negative reciprocals.

Step-by-step explanation:

Well first we need to find slope.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

Line HJ)

(-4,-2) , (0,4)

y2 is 4 y1 is -2, so 4 - -2 = 6

0 - -4 = 4

6/4 -> 3/2

Due to the point (0,4) having no x value 4 is the y intercept.

Hence, y = 3/2x + 4 is the slope of line HJ

Line FG)

(-4,1) , (0,-2)

y2 is -2 y1 is 1, so -2 - 1 = -3

0- -4 = 4

Because (0,-2) is missing an x value -2 is the y intercept,

Equation: y = -3/4x - 2

They are not perpendicular because their slopes are not negative reciprocals.

The slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

Recall:

Given that lines HJ (blue line) and FG (red line) are on a coordinate plane as shown in the diagram attached below, let's find their slope:

Slope of line HJ:

[tex]Slope (m) = \frac{-2 - 4}{-4 -0} = \frac{-6}{-4} = \frac{3}{2}[/tex]

Slope of line FG:

[tex]Slope (m) = \frac{-2 - 1}{0-(-4)} = \frac{-3}{4} = -\frac{3}{4}[/tex]

Therefore, the slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

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Answer:

A. 2 real roots:  (2, 7) and (1, 4).

Step-by-step explanation:

y = x^2 + 3

y = 3x + 1

So equating the right sides:

x^2 + 3 = 3x + 1

x^2 - 3x  + 2 = 0

(x - 2)(x - 1) = 0

So there are 2 roots.

They are x = 2 , y = 3(2) + 1 = 7 and

x = 1, y = 3(1) +1 = 4.

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

   [tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]

Here, we have a = -21, b = -11, c = 40, so it gives:

[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]

So, we have two solutions:

[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]

We only want x > 0 so the solution is

   [tex]\dfrac{8}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

The given system is

[tex]3x+y-5=0\\2x-y-5=0[/tex]

First, you need to graph both lines. To do so, you just need to find the interceptions with both axis.

[tex]3x+y-5=0[/tex]

For [tex]x=0 \implies y=5[/tex]

For [tex]y=0 \implies x=\frac{5}{3}[/tex]

Then, you draw both points to have the straight line.

Repeat the process for the second line. The image attached shows both lines.

Remember, the solution of a linear system of equation is the common point between lines. In this case, we can observe that the solution is (2, -1).

On the other hand, to find the area of the triangle formed, we need to use the length of its base and its height.

Now, we use the area formula for triangles

[tex]A=\frac{bh}{2}=\frac{10(2)}{2}= 10 \ u^{2}[/tex]

Therefore, the area of the triangle formed is 10 square units.

Answer:

We move all terms to the left:

4t+6-(-24)=0

We add all the numbers together, and all the variables

4t+30=0

We move all terms containing t to the left, all other terms to the right

4t=-30

t=-30/4

t=4.5

Brainiest?

Answer:

[tex]\boxed{t=\frac{9}{2} }[/tex]

Step-by-step explanation:

[tex]4t+6=24[/tex]

Subtract 6 on both sides.

[tex]4t+6-6=24-6[/tex]

[tex]4t=18[/tex]

Divide 4 on both sides.

[tex]\displaystyle \frac{4t}{4} =\frac{18}{4}[/tex]

[tex]\displaystyle t=\frac{9}{2}[/tex]

Hey there! I'm happy to help!

We know that the perimeter is 2L+2W. Le'ts plug in the values 3 and 5 from our ratio and see what our perimeter would be with that.

2(3)+2(5)

6+10

16

How can we get this 16 to 64?

64/16=4

So, we need to multiply this length and width by four to get 64 as our perimeter!

3*4=12

5*4=20

We can plug this into our perimeter equation

2(12)+2(20)

24+40

64

Therefore, our length is 12 and our width is 20.

Have a wonderful day! :D

Answer:

The solutions of 2·cos(θ) - √3 = 0in the interval [0, 2pi) are;

π/6,  13/6·π

Step-by-step explanation:

The given that the equation is 2·cos(θ) - √3 = 0

The solution of the above equation in the interval [0, 2pi) are required

Therefore, the domain includes 0 ≤ θ < 2pi

2·cos(θ) - √3 = 0

2·cos(θ)  = √3

cos(θ)  = √3/2

Therefore;

θ = cos⁻¹(√3/2)

The values are;

[tex]\theta =\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6} \, or \, \theta =-\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6}[/tex]

Where the domain is 0 ≤ θ < 2pi, we have;

π/6,  13/6·π

Answer:

25

Step-by-step explanation:

a=15

2(15)-5=25

30-5=25

Answer:

25

Step-by-step explanation:

The problem substituting a for 15 would be 2(15)-5

2*15 is 30, then -5 is 25.

Answer:

13/25

Step-by-step explanation:

The total number of people is 20 + 6 + 17 + 7 = 50.

Of these, the number that have brown or green eyes is 20 + 6 = 26.

So the probability is 26/50, which reduces to 13/25.

The probability that a person chosen at random from this group has brown or green eyes is; 13/25

From the given data values, we can deduce that;

Total number of people = 20 + 6 + 17 + 7 = 50.

Now, the total number of people that have brown or green eyes is;

Total(brown or green eyes) = 20 + 6 = 26.

Thus, the probability that a person chosen at random from this group has brown or green eyes is;

P(brown or green eyes) = 26/50 =  13/25.

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Answer:

[tex]a^{\frac{1}{3} }[/tex]

Step-by-step explanation:

Apply rule:  [tex]\displaystyle \sqrt[n]{x} =x^{\frac{1}{n}[/tex]

[tex]\sqrt[3]{a} =a^{\frac{1}{3} }[/tex]

Answer:

d. will always be unbiased.

Step-by-step explanation:

When some of variables are omitted the estimator on indulge charge regressor may still be unbiased. If there is a special case where T = 2 then the FE estimator will be unbiased. Fixed effect regression model has different intercepts.

Answer:

The answer is option D

Step-by-step explanation:

32m + 56mp

First factor out the HCF out

The HCF of 32and 56 is 8

So we have

8 ( 4m + 7mp)

next factor m out

We have the final answer as

Hope this helps you