A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5. What is the length of the third side of the triangle?

x + 13
2x + 13
5x − 5
12x + 3

The angle between the two vectors < 8, 3 > and < 4, −3 > is 57.43°

Given: vectors < 8, 3 > and < 4, −3 >

To find the angle between two vectors, we can use the dot product method:

First, you will compute the dot product and magnitudes of both vectors. Thus,

Let a = < 8, 3 > and b = < 4, −3 >

a · b = <8, 3> ·<4, -3> = 8(4) + (3)(-3) =  32-9 = 23

|a| = √(8² + 3²) = √(64+9) = √73

|b| = √(4² + (-3)²) = √(16 + 9) = √25 = 5

By using the angle between two vectors formula using dot product,

θ = cos⁻¹ [ (a · b) / (|a| |b|) ]

θ = cos⁻¹ (23 / √73 · 5)

θ  = cos⁻¹ (23/42.72) = 57.43°

Therefore, the angle between the following two vectors is 57.43°

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Answer:

[tex]y=-4x+29[/tex]

Step-by-step explanation:

Using point-slope form,

[tex]y-9=-4(x-5) \\ \\ y-9=-4x+20 \\ \\ y=-4x+29[/tex]

Answer:

Step-by-step explanation:

probably close to 5$

Answer: B

Kyler earns more money in one week. Kyler earns $1,150 and Xiang earns $685 in one week.

Step-by-step explanation:

Have A Good Day!

The ordered pairs representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

Given, the ordered pairs representing the vertices of the polygon.

as, the given ordered pairs are

(-11, 13) , (1, -1) , (1/4 , 2(2/1)) , (1,-3).

Now, from the given ordered pairs

the pairs which are representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

So, the ordered pairs representing the vertices of a polygon are (-11, 13) ,

(1, -1) and (1,-3).

Hence, the ordered pairs representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

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For the given triangles , developing proof is not possible due to following reasons:

First triangle : 21 + 25 < 48 not true.

Second triangle : Interior angle 130° > Exterior angle 125°

As given in the question,

For the given triangles developing proof is not possible due to following reasons:

First triangle:

Measure of three sides are given as 21, 25 , and 48.

As per the property to form a triangle : Sum of two sides is always greater than the third side.

Here, 21 + 25 < 48 .

Above mention property does not satisfied by given triangle.

Second triangle:

In a triangle, measure of exterior angle is always greater the opposite interior angles.

Here, measure of interior angle 130° > measure of exterior angle 125°

Does not satisfy the relation of exterior angles with interior angle.

Therefore, for the given triangles , developing proof is not possible due to following reasons:

First triangle : 21 + 25 < 48 not true.

Second triangle : Interior angle 130° > Exterior angle 125°.

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Answer:

A)

[tex]\sf -2x+7=-x+9[/tex]

[tex]\sf -2x+7-7=-x+9-7[/tex]

[tex]\sf -2x=-x+2[/tex]

[tex]\sf -2x+x=-x+2+x[/tex]

[tex]\sf -x=2[/tex]

[tex]\sf \cfrac{-x}{-1}=\cfrac{2}{-1}[/tex]

[tex]\boxed{\sf x=-2}[/tex]

____________________

B)

[tex]\sf 4x +15=2x+6[/tex]

[tex]\sf 4x+15-15=2x+6-15[/tex]

[tex]\sf 4x=2x-9[/tex]

[tex]\sf 4x-2x=2x-9-2x[/tex]

[tex]\sf 2x=-9[/tex]

[tex]\sf \cfrac{2x}{2}=\cfrac{-9}{2}[/tex]

[tex]\boxed{\sf x=-\cfrac{9}{2}}[/tex]

____________________

C)

[tex]\sf 8x+26=5x+14[/tex]

[tex]\sf 8x+26-26=5x+14-26[/tex]

[tex]\sf 8x=5x-12[/tex]

[tex]\sf 8x-5x=5x-12-5x[/tex]

[tex]\sf 3x=-12[/tex]

[tex]\sf \cfrac{3x}{3}=\cfrac{-12}{3}[/tex]

[tex]\boxed{\sf x=-4}[/tex]

____________________

D)

[tex]\sf 7x+31=16x+17[/tex]

[tex]\sf 7x+31-31=16x+17-31[/tex]

[tex]\sf 7x=16x-14[/tex]

[tex]\sf 7x-16x=16x-14-16x[/tex]

[tex]\sf -9x=-14[/tex]

[tex]\sf \cfrac{-9x}{-9}=\cfrac{-14}{-9}[/tex]

[tex]\boxed{\sf x=\cfrac{14}{9}}[/tex]

After multiplying the simplified expression is   [tex]\frac{-x+5}{2x + 6}[/tex] ; x  ≠ -3 , 3 , -2 , -5  , the correct option is (b) .

In the question ,

it is given that ,

the expression is (x²-25)/(2x²+10x+12) × (-x²+x+6)/(x²+2x-15)

we need to find the value of the expression after multiplication .

= (x²-25)/(2x²+10x+12) × (-x²+x+6)/(x²+2x-15)

On splitting the given quadratic equation into factors , we get  

= (x+5)(x-5)/2(x+3)(x+2) × -(x+2)(x-3)/(x-3)(x+5)

= [tex]\frac{(x+5)(x-5)}{2(x+3)(x+2)}[/tex] × [tex]\frac{-(x+2)(x-3)}{(x-3)(x+5)}[/tex]

After cancelling out the common factors , we get

= -(x - 5)/2(x + 3)

= -x+5 / 2x + 6

= [tex]\frac{-x+5}{2x + 6}[/tex]    : x  ≠ -3 , 3 , -2 , -5

Therefore  , After multiplying the simplified expression is   [tex]\frac{-x+5}{2x + 6}[/tex] ; x  ≠ -3 , 3 , -2 , -5  .

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Answer:

Step-by-step explanation:

The total compound interest obtained is $756.6.

We are given an initial amount equal to $4,800. This is the principal amount that is denoted by the variable "P". The rate of interest is 5% per annum and is denoted by "r". The interest is compounded annually and denoted by "I". The time duration is 3 years, denoted by the variable "t". Let the final amount be represented by the variable "A". We can use the given formula.

A = P(1 + r)^t

A = $4,800*(1 + 0.05)³

A = $4,800*(1.05)³

A = $4,800*1.157625

A = $5,556.6

The compound interest earned is the difference between the initial and the final amount.

I = A - P

I = $5,556.6 - $4,800

I = $756.6

Hence, the interest amount is $756.6.

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Answer:

Step-by-step explanation:

Answer:

D) Alan was farther away from Madison when he started driving

F) Alan and Andrew started the same distance from Madison

Step-by-step explanation:

Hopefully I got them all!!!

Karen spent $42.00 on movie ticket and $11.00 on popcorn.

Firstly calculating the amount spent on movie tickets

Cost of one movie ticket = $10.50

Cost of four movie tickets = 4×10.5

Performing multiplication on Right Hand Side of the equation

Cost of four movie tickets = $42.00

Now calculating the amount spent on popcorn

Cost on one bucket of popcorn = $5.50

Cost of two buckets of popcorn = 2 × 5.50

Performing multiplication on Right Hand Side of the equation

Cost of two buckets of popcorn = $11.00

Hence, the cost spent on movie tickets and popcorn is $42.00 and $11.00 respectively.

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The product of a, b, and c is -45/4.

Multiplication is the process of adding a number up to a given number.

The given expression is [tex]\frac{\sqrt{25x^5y^5}}{xy^4}[/tex].

Rewrite the expression as follows,

[tex]\frac{\sqrt{25x^5y^5}}{xy^4}[/tex]

[tex]=\frac{5x^{\frac{5}{2}}y^{\frac{5}{2}}}{xy^4}\\=5x^{\frac{5}{2}-1}y^{\frac{5}{2}-4}\\=5x^{\frac{3}{2}}y^{-\frac{3}{2}}[/tex]

The values of a, b, and c are 5, 3/2, -3/2.

The product of a, b, and c is,

5 × 3/2 × (-3/2)

= -45/4

Hence, the product of a, b, and c is -45/4.

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Answer:

  (a)  (-26, -34)

Step-by-step explanation:

You want the solution to the system of equations ...

apparently using inverse matrices.

The system can be represented by the matrix equation ...

  AX = B

where A is the 2×2 matrix of coefficients, X is the 2×1 variable vector, and B is the 2×1 matrix of constants.

The solution to this system is found by multiplying on the left by the inverse of A:

  A⁻¹·AX = A⁻¹·B

  X = A⁻¹·B

The attachment shows the result of making this calculation:

  [tex]\boxed{X=\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}-26\\-34\end{array}\right]}[/tex]

Answer:

Step-by-step explanation:

f(x)=3x

2

+9x−16

Quadratic polynomial can be factored using the transformation ax

2

+bx+c=a(x−x

1

​

)(x−x

2

​

), where x

1

​

 and x

2

​

 are the solutions of the quadratic equation ax

2

+bx+c=0.

3x

2

+9x−16=0

All equations of the form ax

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±

b

2

−4ac

​

​

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=

2×3

−9±

9

2

−4×3(−16)

​

​

Square 9.

x=

2×3

−9±

81−4×3(−16)

​

​

Multiply −4 times 3.

x=

2×3

−9±

81−12(−16)

​

​

Multiply −12 times −16.

x=

2×3

−9±

81+192

​

​

Add 81 to 192.

x=

2×3

−9±

273

​

​

Multiply 2 times 3.

x=

6

−9±

273

​

​

Now solve the equation x=

6

−9±

273

​

​

 when ± is plus. Add −9 to  

273

​

.

x=

6

273

​

−9

​

Divide −9+

273

​

 by 6.

x=

6

273

​

​

−

2

3

​

Now solve the equation x=

6

−9±

273

​

​

 when ± is minus. Subtract  

273

​

 from −9.

No It is not possible to have 220 participants in the 5k race.

Information from the question

She makes $20 for each 5K participant

$45 for each 10K participant.

x represents the number of participants in the 5K race

y represents the number of participants in the 10K race

Eve raises exactly $9,500, is it possible for there to be 220 participants in the 5K race = ?

From the question

$20 for each 5K participant and x represents the number of participants in the 5K race. = 20x

$45 for each 10K participant and y represents the number of participants in the 10K race = 45y

Eve raises exactly $9,500 means the sum of amount from 5k and 10k is 9500 =  20x + 45y = 9500

if Eve raise 220 participants in the 5k race then the equation will be

20 * 220 + 45y = 9500

4400 + 45y = 9500

45y = 9500 - 4400

45y = 5100

y = 113.333

The participants are human being and cannot be represented as fractions hence 220 is impossible for the 5k race

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Answer:

672

Step-by-step explanation:

600+ .12(600)

600 + 72 = 672

If the raft travels the distance between ports a and b after 30 hours and the motorboat travels the distance in 6 hours. After the departure the two boats will after 5 hours 4 minutes.

Given that,

After leaving the port,

Raft travels the distance between a and b ports = 30 hours

Motorboats travels the distance between a and b ports = 6 hours

The triangle formed by their tracks and the line joining their current positions in a right angled triangle.

According to the Pythagoras Theorem,

    a² + b² = c²

⇒ (30)²+ (6)² = c²

⇒ 900 + 36 = c²

⇒ 936 = c²

⇒ c = √936

⇒ c = 30.59

Rounding up 30.59 in 30.6.

Therefore, the boats will the two meet by 30 hours and 6 minutes after they leave the port.

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The horizontal position for the left edge of the image should Joelle use to center the image is  -4.46 cm .

In the question ,

it is given that ,

the length of the over sized image = 30.51 cm and

the length of the page = 21.59 cm

to find the margin , we subtract the width of the word processor page from the width of the oversized image.

that is

margin = 30.51 - 21.59 = 8.92 cm

Since , we have margin on two side ,that is  horizontal positions to the left most side and horizontal positions to the right of the left most edge of the page . we divide 8.92 by 2 .

= 8.92/2

= 4.46 cm

it is given that the horizontal positions to the right of the leftmost edge of the page are positive,

So , horizontal position for the left edge of the image which Joelle should use to center the image would the negative .

the horizontal position is -4.46 cm  .

Therefore , The horizontal position for the left edge of the image should Joelle use to center the image is  -4.46 cm .

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Answer:

y= -3/4 x + 8

Step-by-step explanation:

y-2 = -3/4 (x-8)

y-2 = -3/4 x + 6

y = -3/4 x + 6 + 2

y = -3/4 x + 8

Many solutions for a = c and b = 8.

No solution for a = c and b ≠ 8.

One solution for a ≠ c, b can be anything.

What is solution of equations?

Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is considered a solution to the problem. Finding the solution or solutions to an equation is known as solving it.

The two sides of the equation must be identical for all values of x if

ax + b = cx + 8 has an unlimited number of solutions. This suggests that

a = c and b = 8.

The two sides of the equation cannot be equal for any value of x if

ax + b = cx + 8 has no solutions. The only way this is possible is if

a = c and b ≠ 8, therefore b can be anything other than 8.

If there is exactly one solution to the equation ax + b = cx + 8, then a ≠ c, meaning that 'a' can be anything other than c. In this situation, 'b' is not constrained in any way (b can be anything).

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A line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the line passes through the points (0, 0) and (–17, –11).

The slope of the line is,

m = (5+4)/(5-0)

m= 9/5

The equation of the line passes through the point as,

(y-y₁)=m(x-x₁)

(y-0)=9/5(x-0)

5(y-0)=9(x-0)

5y=9x+0

y=9/5x+0

Thus, a line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0

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The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)

Acceleration: it is defined as rate of change of velocity with respect to time.

Unbalanced Force:  it means that the force applied in one direction is greatest than the force applied in the opposite direction.

Given that, F = 8n.

let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.

According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.

                         F = m × a

                 ⇒     a = F/ m

where,  F is Force, m is mass and a is acceleration.

Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²

         acceleration of the box of 4kg = 8÷ 4 = 2 m/m²

         acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²

         acceleration of the box of 8kg = 8÷ 8 = 1 m/s²

∴ the box with mass of 2kg experience the greatest acceleration.

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The slope is 1/6x

You have to re-arranged the problem

x - 6y = 9 --> 6y = x - 9

6y = x - 9

__   ____    ---->  y = 1/6x - 3/2

6        6

Answer:

0,1,2,3,4

Step-by-step explanation:

[tex]\frac{50}{16.68}[/tex] = 4.68 rounded to the nearest hundredths.

The function which has real zero at  x = –8 and x = 5 is x² + 3x - 40

Given the real zeroes at x = -8 and x = 5.

Factor theorem states that (x-r) is a factor of the polynomial function f(x) if and only if r is a root of the function f(x).

Since, we know that the root of the function i.e g(x) are -8 and 5 then the function has the following factor:

(x+8) = 0 and (x-5) =0

Zero product property states that if ab = 0 if and only if a =0 and b =0.

By zero product property,

(x+8)(x-5) = 0

Now, distribute each terms of the first polynomial to every term of the second polynomial we get;

x(x - 5) + 8(x - 5)

Now, when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.

x² + 8x - 5x - 40

Combine like terms;

x² + 3x - 40

therefore, the function  has real zeros at x = -8 and x =5 is x² + 3x - 40

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