Evaluate the expression (8×6) +(8-3)

Answer:

x = (√10  -3)/2  and (-√10  -3)/2

Step-by-step explanation:

(2x+3)^2 = 10

To solve the equation, take the square root of each side

sqrt((2x+3)^2) = ±√10

2x+3 = ±√10

Subtract 3 from each side

2x+3-3 = ±√10  -3

2x = ±√10  -3

Divide each side by 2

2x/2 = (±√10  -3)/2

x = (±√10  -3)/2

There are two solutions

x = (√10  -3)/2

and (-√10  -3)/2

Answer:

[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

Step-by-step explanation:

Given: (2x + 3)² = 10

In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.

Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.

Step 1: Square both sides of the equation.

[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]

Step 2: Separate into possible cases.

[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]

Step 3: Solve for x in both cases.

[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]

[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]

Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

Learn more about quadratic equations here:
brainly.com/question/27031173

The answer for the following part is

Surface area is the amount of space covering the outside of a three-dimensional shape.

Surface Area of Cone,

= πrl + πr²

=3.14*8*15.77 + 3.14* 8*8

= 597.61804 mm²

Surface Area of triangular pyramid,

= apothem * slant height * length

= 73.6 m²

Surface Area pentagonal pyramid

= B + LA

= 247.75 + 5 ( 1/2*12*19.5)

= 247.75 + 5 ( 117)

= 832.75 in²

Surface area of square pyramid

= P*l /2

= 2400 ft²

Learn more about surface area here:

https://brainly.com/question/15643964

#SPJ1

1) [tex]OA=OB[/tex] (all radii of a circle are equal)

2) [tex]\angle OBA=52^{\circ}[/tex] (angles opposite equal sides in a triangle are equal)

3) [tex]\angle OAB+\angle OBA+\angle AOB=180^{\circ}[/tex] (angles in a triangle add to 180 degrees)

4) [tex]52^{\circ}+52^{\circ}+\angle AOB=180^{\circ}[/tex] (substitution)

5) [tex]\angle AOB=76^{\circ}[/tex] (subtraction)

6) [tex]\angle AOB+\angle BOD=180^{\circ}[/tex] (angles on a line add to 180 degrees)

7) [tex]76^{\circ}+\angle BOD=180^{\circ}[/tex] (substitution)

8) [tex]\angle BOD=104^{\circ}[/tex] (subtraction)

9) [tex]\angle ODE=\angle OBC=90^{\circ}[/tex] (tangents are perpendicular to the radius of a circle at the point of tangency)

10) [tex]\angle ODC=117^{\circ}[/tex] (angle addition postulate)

11) [tex]\angle BOD+\angle OBC+\angle ODC+\angle DCB=360^{\circ}[/tex] (angles in a quadrilateral add to 360 degrees)

12) [tex]104^{\circ}+90^{\circ}+117^{\circ}+\theta=360^{\circ}[/tex] (substitution)

13) [tex]\theta=49^{\circ}[/tex] (subtraction)

Answer:

x=20

Step-by-step explanation:

The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees

so 4x +5x =9x

9x=180

x=20

4x=80

5x=100

Answer:

5y + 3= 14

subtract 3 from each side

5y=11

divide each side by 5

5y/5=11/5

y=11/5 or 2.2 or 2 1/5

Hope This Helps!!!

Answer:

2.2

Step-by-step explanation:

Properties needed:

First we need to subtract 3 from both sides because of subtraction property of equality to make both sides equal.

5y + 3 = 14

      -3    -3

5y = 11

Then we need to divide 5 from both sides (division property of equality) to get y.

[tex]\frac{5y}{5} = \frac{11}{5}[/tex]

And we get 2.2

Please mark brainliest!

I hope this helps!

Have a great day!

Answer:

y = 2x - 1

Step-by-step explanation:

Given equation: 2x - y = 1

We're being asked to solve for y. This is also known as the Slope-Intercept Form. It is represented by the following formula:

y = mx + b

where:

Steps:

1. Subtract 2x from both sides:

[tex]\sf 2x-2x - y = 1-2x\\\\\implies-y=-2x+1[/tex]

2. Divide both sides by -1:

[tex]\sf \dfrac{-y}{-1}=\dfrac{-2x+1}{-1}\\\\\implies y=2x-1[/tex]

This equation has a slope of 2, and a y-intercept of -1.

Learn more about the Slope-Intercept Form here:

brainly.com/question/27913326

brainly.com/question/27941697

The velocity of the wind will be 50 km per hour.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.

Then the velocity of the wind will be

Let x be the speed of the wind. Then we have

x² = 50² + 50² - 2 x 50 x 50 x cos 60°

x² = 2500 + 2500 - 2500

x² = 2500

x = 50 km per hour

More about the vector link is given below.

https://brainly.com/question/13188123

#SPJ1

Answer:

A. g(x)=x^2+5x+2

Step-by-step explanation:

f(x) = x^2 + 5x - 1 Shift 3 units to the left. k=3

g(x)=x^2+5x-1+3=x^2+5x+2

g(x)=x^2+5x+2

Hope this helps!

If not, I am sorry.

Answer:

23 min 30 sec

Step-by-step explanation:

First, you add 35 + 14 + 18 + 27 which is 94.
Next, you divide 94 by the number of deliveries there were. Which is 4.
94/4 = 23.5.
So your answer would be 23 minutes and 30 seconds.

I Hope This Helped :D

Answer:

23.5 minutes or 23 minutes and 30 seconds

Step-by-step explanation:

1. add all the minutes

35 minutes + 14 minutes + 18 minutes+ 27 minutes = 94 minutes

2. Divide the total amount of minutes by the number of deliveries

94 minutes =  23.5 minutes or 23 minutes and 30 seconds

4 deliveries

Answer:

given - a rectangle ABCD

AB = 40

AC. = 90

BC = ?

in triangle ABC

using Pythagoras theorem

(AB) ² + (BC) ² = (AC) ²

(40)² + (BC) ² = (90)²

(BC) ² = (90)²- (40)²

(BC) ² = 8100 - 1600

(BC) ² = 6500

BC =

[tex]20 \sqrt{10} [/tex]

Answer:

pounds (£)

Step-by-step explanation:

pounds are used in countries such as the UK and South Georgia

Answer: 280

Step-by-step explanation:

50 cents for each banana so: 4* 50= 200

200+80

Answer is 280

The volume of the cylinder is 1692.46dm³.

It should be noted that the volume of a cylinder is calculated as:

= πr²h

r = radius = 7dm

h = height = 11dm

Volume = πr²h

Volume = 3.14 × 7² × 11

Volume = 3.14 × 49 × 11

Volume = 1692.46dm³

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

Answer:

Step-by-step explanation:

Answer:

25:28 is the simplest form

Step-by-step explanation:

This is a ratio, think of it like a fraction. You can simplfy it by dividing by common factor.

25 and 28 have no common factors except for 1.

25: 1,5,25

28: 1,2,4,7,14,28

It will stay as 25:28

Answer:

it stays the exact same or 0.893

Step-by-step explanation:

Answer:

(0.5,2) and (-3,3)

Step-by-step explanation:

Answer:

Y = 4x -2 is (0.5,2)

y = x +3 is (-3,3)

Answer:

The answer for this question is c

The value of x from the quadratic term equation is x = ( -11/2 ) ± ( 5√5 ) / 2

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 11x + 121/4 = 125/4

Subtracting ( 125/4 ) on both sides , we get

x² + 11x + ( 121 - 125 ) / 4 = 0

x² + 11x - 1 = 0   be equation (1)

On simplifying , we get

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

So , x = [ -11 ± √ ( 11 )² - 4 ( 1 ) ( -1 ) ] / 2

On further simplification , we get

x = -11 ± √ ( 121 + 4 ) / 2

x = [ -11 ± √125 ] / 2

x = ( -11/2 ) ± ( 5√5 ) / 2

Therefore , the roots of the equation are x = ( -11/2 ) ± ( 5√5 ) / 2

Hence , the quadratic equations are solved

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ5

Answer:

x = 37

Step-by-step explanation:

A straight angle is 180 degrees. That means ∠DFG & ∠EFG have to add together to be 180.

2x + 6 + 3x - 11 = 180     Combine like terms

5x - 5 = 180                   Add 5 to both sides

5x = 185                         Divide by 5

x = 37

∠DFG = 80°

∠EFG = 100°

Answer:

Step-by-step explanation:

What are the 6 types of journals?

There are various types of journals including:

academic/scholarly journals.

trade journals.

current affairs/opinion magazines.

popular magazines.

newspapers.

Answer:

What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5 EndFraction x minus 3.x – 3?

Step-by-step explanation:

The equation of line that is parallel to the given line having slope m = -1 and passes through the point ( -3 , 1 ) is y = -x - 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

The slope of the line m = -1

Now , the line is parallel to the line passing through P

So , the slopes of the lines are equal

And , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 1 = -1 ( x - ( -3 ) )

y - 1 = -1 ( x + 3 )

Adding 1 on both sides , we get

y = -x - 3 + 1

y = -x - 2

Hence , the equation of line is y - 1 = -1 ( x + 3 )

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ5

The differential equation

[tex]M(x,y) \, dx + N(x,y) \, dy = 0[/tex]

is considered exact if [tex]M_y = N_x[/tex] (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function [tex]f(x,y)=C[/tex] such that [tex]f_x=M[/tex] and [tex]f_y=N[/tex].

We have

[tex]M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)[/tex]

[tex]N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)[/tex]

and [tex]M_y=N_x[/tex], so the equation is indeed exact.

Now, the solution [tex]f[/tex] satisfies

[tex]f_x = \tan(x) - \sin(x) \sin(y)[/tex]

Integrating with respect to [tex]x[/tex], we get

[tex]\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx[/tex]

[tex]\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)[/tex]

and differentiating with respect to [tex]y[/tex], we get

[tex]f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}[/tex]

[tex]\implies \dfrac{dg}{dy} = 0 \implies g(y) = C[/tex]

Then the general solution to the exact equation is

[tex]f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}[/tex]

Step-by-step explanation:

yo thara bhai joginder tu he ek bndr

The number of adults are 2 . the number of youths are 8

Given charge $7 for adults , $2 for youth and $0.50 for children

Let the number of adults , youths and children be x , y and z

Now it is given that there is total pay of 100

Therefore the equation formed is

7x + 2y +0.50 = 100

Now it is also given that 150 people enter

Therefore

x+y+z=150

x+y+z =150

14x+4y+z=200

Using argument matrix

[tex]\left[\begin{array}{ccc}1&1&1\\14&4&1\end{array}\right] \left[\begin{array}{ccc}150\\200\end{array}\right][/tex]

Corresponding system equation is

x+y+z=150

y+(13/10)z=190

Take z = m (arbitary)

y = 190 - 1.3 m

x = 150 - y

m = 140 x = 2 and y = 8

Hence The number of adults are 2 . the number of youths are 8

Learn more about argument matrix here:

https://brainly.com/question/1821869

#SPJ10

Answer:

Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save

Average speed of the whole trip is equals to 37.5 mph.

" Average speed is defined as the ratio of the total distance travelled to the total time taken."

Formula used

Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]

According to the question,

Total distance travelled = 300miles

Speed for first 150 miles = 30 miles per hour

For,  30  miles = 1hour

    ⇒150 miles = 5 hours

Speed for remaining 150 miles = 50 miles per hour

For,  50  miles = 1hour

    ⇒150 miles = 3 hours

Substitute the value in the formula to get average speed,

Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]

                          [tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]

Hence, average speed of the whole trip is equals to 37.5 mph.

Learn more about average speed here

https://brainly.com/question/12322912

#SPJ2

Divya should not check her answers for extraneous solution as it's not required in this case.

It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.

Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.

Learn more about extraneous solution on:

brainly.com/question/2959656

#SPJ1

Answer:

No, she shouldn't.

Answer:

Using the concept of equation of line, we find that the relationship will be

C = $6.5p.

Step-by-step explanation:

If the cost per head is $6.5 and there are p persons entering the car, then the total amount would be $6.5p.

The final equation would resemble the equation of line y = mx + c.

The expression for the total cost C, would be

C = 6.5p.

Here y = C, x = p, m = 6.5 and c = 0.

So, the expression for the total cost will be the equation of line C = 6.5p.

For more explanation, refer the following link:

https://brainly.com/question/11552995

#SPJ10

Answer:

16.6

Step-by-step explanation:

Add the numbers together.

13.2+20=33.2

Now divide the number by 2.

33.2/2=16.6

Hope this helps!

If not, I am sorry.