Solve the following system of equations. What is one x-value of a solution? f(x)=x^(2)+7x-24 g(x)=-3x-40

The product  that would result in a sum of cubes if a =2x and b = y is: (2x + y)(4x² – 2xy + y²).

Given:

Product of polynomials=(a + b)(a²- ab + b²)

Sum of cubes=a³+ b³

Hence,

a³+ b³ = (a + b) (a²-ab + b²)

When:

a=2x

y=b

So,

a³+ b³= (2x + y ) [ (2)² - (2x) (y) + y²)  

a³+ b³= (2x + y ) [ 4x² - 2xy + y²]  

a³+ b³ = (2x + y)(4x² – 2xy + y²)

Therefore the product  that would result in a sum of cubes if a =2x and b = y is: (2x + y)(4x² – 2xy + y²).

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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.

The equation of the directrix of the parabola given is x = 6, Option D is the correct answer.

A parabola is a U shaped curve whose all point are at same distnace from a  point called as focus and a line called as Directrix .

The equation of the parabola given is

y² = -24x

When the standard equation of parabola is

 (y - k)² = 4p (x - h),

where the focus is (h + p, k) and the directrix is x = h - p.

here h = 0

p = -24/4 = -6

x =  0 - (-6)

x = 6

Therefore Option D is the correct answer.

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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

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Answer: 43.5

Step-by-step explanation:

[tex]A=\frac{1}{2}(8)(12)(\sin 65^{\circ}) \approx \boxed{43.5}[/tex]

Answer:

x = 3

y = 2

Step-by-step explanation:

3x + 2y = 12

-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2

2 * 3x + 2y = 12

6x + 4y = 24

3 * -2x + 3y = 5

-6x + 9y = 15  now find the sum of both equation:

6x + 4y  -6x + 9y = 24 + 15 add like terms

13y = 39 divide both sides by 13

y = 3 now that we found the value of y we can use this to calculate the value of x

3x + 2y = 12 replace y with 3

3x + 2*2 = 12

3x + 4 = 12 subtract 4 from both sides

3x = 9 divide both sides by 3

x = 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]

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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:

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 )

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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.

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It should be noted that the volume of the pyramid will be 14.8 unit³.

From the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².

The height of the pyramid is also 6 units.

Therefore, the volume of the pyramid will be

= 1/3 × Area of the base × height

= 1/3 × 7.4 × 6

= 14.8 units³

In conclusion, the volume of the pyramid is 14.8 unit³.

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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:

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.

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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

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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:

C. To plot the ordered pair (3 , 4), travel three units to the right on the x-axis and four units up on the y-axis, from the origin.

Step-by-step explanation:

Which statement is true about the ordered pair (3, 4)?

A. To plot the ordered pair (3 , 4), travel four units to the right on the y-axis and three units up on the x-axis, from the origin.

The y-axis is the vertical line you can't go left or right, you go up or down

Hence this answer is NOT correct

B. To plot the ordered pair (3 , 4), travel four units to the right on the x-axis and three units up on the y-axis, from the origin.

The coordinates of a point is (x, y) where x = 3 and y = 4 so moving right 4 units is wrong as x = 3

Hence this answer is NOT correct

C. To plot the ordered pair (3 , 4), travel three units to the right on the x-axis and four units up on the y-axis, from the origin.

three units to the right on the x-axis

four units up on the y-axis

Hence this answer is the correct

D. To plot the ordered pair (3 , 4), travel three units to the right on the y-axis and four units up on the x-axis, from the origin.

y does not equal 3 and you cant move right or left on the y-axis

Hence this answer is NOT correct

Answer:

Step-by-step explanation:

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:

C. (-2.2, -3)

An axis of symmetry passes through the vertex and is perpendicular to the base. Then the correct options are B, C, and E.

Take a rectangle. This is the base. Now take 4 triangles such that each of them are connected to one-one side of the base rectangle and when they're taken together, they form a closed object. That shape is called rectangular pyramid.

The base of the pyramid is a rectangle that is not a square.

The pyramid has two planes of symmetry.

An axis of symmetry passes through the vertex and is perpendicular to the base.

An angle that measures 90° is an angle of rotation for an axis of symmetry for the pyramid.

Then the correct options are B, C, and E.

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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

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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:

14

Step-by-step explanation:

First divide 24 and 6 to find how much 6's there are in 24.

24/6=4

Now, we take that number and multiply it by 3.5 to find how long it will take the group to walk 24km.

3.5*4=14.

It will take the group 14 hours to walk 24 km.

Hope this helps!

If not, I am sorry.

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

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Answer:

x =  -12

y = 3

Step-by-step explanation:

[tex]1/2x + 6(x+15) = 12\\1/2x + 6x + 90 = 12\\6\frac{1}{2} x + 90 = 12\\6\frac{1}{2} x= -78\\x = -12[/tex]

[tex]y = x + 15\\y = -12 + 15\\y = 3[/tex]

Answer:

∠ AEC = 49°

Step-by-step explanation:

the sum of the angles in Δ ACE = 180° , that is

∠ AEC + 90° + 41° = 180°

∠ AEC + 131° = 180° ( subtract 131° from both sides )

∠ AEC = 49°

Answer:

49°

Step-by-step explanation:

<AEC = 180°_(41°+90°)

=180°_131°

<AEC= 49°

**90° (Complementary Angles)**

[And if u add: 41°+90°+49°= 180°]

{180° is the area of all triangles}

Hope I helped :)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y=-x-1[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Taking two points : (-1 , 0) and (0 , -1)

[tex] \textsf{Calculate slope (m)} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 1)}{ - 1 - 0} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{0 + 1}{ - 1}[/tex]

[tex]\qquad \tt \rightarrow \: m = - 1[/tex]

[tex] \textsf{Y - intercept (c) of graph = -1 } [/tex]

Equation of line in slope - intercept form :

[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]

[tex]\qquad \tt \rightarrow \: y = - x - 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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.

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