What is the equation of the line?

Expanding out the equation, we get

[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]

Considering the discriminant,

[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]

This is always non-negative, meaning the roots are real.

The roots are equal if and only if the discriminant is 0, which is when a=b=c.

b+3=12

because a+5=b+3 and a+5=12 which means b+3 must be 12 as well

Answer:

[tex](x + 4)^{2}[/tex] = 36

Step-by-step explanation:

So the "sum of a number and 4" is what gets squared and that together is equal to 36.

f(t) = 80,00[tex](1+ 0.056)^{t}[/tex] is the exponential function that represents the model. The number of visits increase by 0.015% daily.

Here, we are given that a blogger found that the number of visits to her Web site increases 5.6% annually.

The exponential function is given as-

Final value = initial value [tex](1 + r)^{t}[/tex]

where r = rate of change

and t = time

here, r = 5.6%

r = 0.056

Further, the Web site had 80,000 visits this year ⇒ initial value = 80,000

Thus, we can get the following function-

f(t) = 80,00[tex](1+ 0.056)^{t}[/tex]

where f(t) represents the views after t years.

Now, since we are given that the views increase by 5.6% in 1 year

and 1 year = 365 days

⇒ daily rate = 5.6/365

= 0.015

Thus, the number of visits increase by 0.015% daily.

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The limit dimensions of the part are 3.135 inches and 3.155 inches

The given parameters are

Thickness = 3.145 inches

Tolerance = 0.010 inches

The limit dimensions of the part are calculated as

Limit = Thickness +/- Tolerance

So, we have

Limit = 3.145 inches +/- 0.010 inches

Expand the above expression

So, we have

Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)

Evaluate the sum

Limit = (3.135 inches, 3.155 inches)

Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches

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Answer: D.

hope this helps

The number of mums created every hour by each friend are:

Given data

Friend A, Friend B, and Friend C working = 6 mums per hour

Friend B and Friend C working = 5 mums per hour

Friend A and Friend B are working = 4 mums per hour

A + B + C = 6         equation 1

B + C = 5               equation 2

A + B = 4                equation 3

from equation 2, make C the subject of the formula

B + C = 5

C = 5 - B

from equation 3, make A the subject of the formula

A + B = 4

A = 4 - B

substitute A and C into equation 1 to get

A + B + C = 6

4 - B + B + 5 - B = 6

4 + 5 - B = 6

9 - B = 6

-B = 6 - 9

-B = -3

B = 3

substituting B for A we have

A = 4 - 3

A = 1

substituting B for C we have

C = 5 - 3

C = 2

Therefore , Friend A working every hour creates 1 mum, Friend B working every hour creates 3 mums, and Friend C working every hour creates 2 mums,

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The value of f(5) is 4375.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(1)= 7,

f(n) = 5f(n-1)

f(2) = 5f(1)

     =5*7

f(2)= 35

f(3) =  5f(3-1)

f(3) =  5f(2)

f(3) =  5*35

f(3) = 175

f(4) =  5f(4-1)

f(4) =  5f(3)

f(4) =  5*175

f(4) = 875

f(5) =  5f(5-1)

f(5) =  5f(4)

f(5) =  5*875

f(5) = 4375

Hence, the value of f(5) is 4375.

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Answer:

Length = 60 inches

Width = 17 inches

Step-by-step explanation:

Let width = w

Length = 3w + 9

Perimeter = 154

Perimeter = 2(length + width)

2(3w + 9 + w) = 154

8w + 18 = 154

8w = 154 - 18

8w = 136

w = 136/8

w = 17 inches

Length = 3w + 9 = 3(17) + 9 = 60 inches

The triangles ΔRST and ΔXYZ are congruent, then all the same construction make triangles congruent. All the options are correct.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If two triangles are congruent, then the ratio of the corresponding sides will be one.

The triangles ΔRST ≅ ΔXYZ. Points P and W lie on ST and YZ, respectively.

The diagram is given below.

A) If P is the midpoint of ST and W is the midpoint of YZ then ΔRSP ≅ ΔXYW is true.

B) If RP bisects ∠SRT and XW bisects ∠YXZ, then ΔRSP ≅ ΔXYW is true.

C) If RP = XW, then ΔRSP ≅ ΔXYW is true.

D) If RP ⊥ ST and XW ⊥ YZ, then ΔRSP ≅ ΔXYW is true.

All the options are correct.

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The absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.

Here, we are given that the population of a town increased from 3,250 in 2008 to 4,300 in 2010.

The absolute change can be calculate as-

Final population count - initial population count

= 4,300 - 3,250

= 1,050

Thus, absolute increase = 1,050

Now, the percentage increase can be calculated as follows-

percentage change = absolute change in population/ initial population count × 100

= 1,050/ 3,250 × 100

= 10500/ 325

= 32.3%

Thus, the absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.

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Answer:

the answer is 13,221 ...........

Answer:

13221...........

Step-by-step explanation:

9888-1111=8777

8777+4444=13221

Answer:1

Step-by-step explanation:

The expression that shows another way to write -2/5 divided by 3/2 will be -2/5 ÷ 3/2.

It should be noted that an expression simply shows the relationship between the variables.

Therefore, the expression that shows another way to write -2/5 divided by 3/2 will be:

= -2/5 ÷ 3/2

= -2/5 × 2/3

= -4/15.

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The domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

The domain of a function is the set of inputs that are accepted by the function. The range, also known as the codomain, is the set of all the output values of the function.

Here, we are given a relation with the following set of solutions-  

{(5,-3), (2,2), (0, -3), (2,1) (5,3)}

We know that all x values will form the domain and all the y values will make up the range.

Here the x values are: 5, 2, 0, 2, 5

and the y values are: -3, 2, -3, 1, 3

Thus, the domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

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Step-by-step explanation:

[tex] \frac{1}{ {x}^{ \frac{ - 1}{3} } } \times \frac{1}{3x} \\ \frac{1}{ {3x}^{ \frac{2}{3} } } \\ \frac{1}{ 3\sqrt[3]{x {}^{2} } } [/tex]

Answer:The LCM of 15 and 20 is 60.

Step-by-step explanation: I used the internet/gggle

5x-2y = -2 is the equation of line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6.

Given that, (x₁, y₁) = (-2, -4) and parallel to 5x - 2y = 6

Let's calculate the slope of 5x - 2y = 6

Rewrite the equation in y = mx + c form

5x - 2y = 6

⇒ -2y = 6 - 5x

⇒ -y = 3 - 5/2x

⇒ y = -3 + 5/2x

⇒ y = 5/2x - 3

Thus, the slope (m) = 5/2

As the line is parallel to 5x - 2y = 6 it will have a slope of 5/2.

The point-slope formula states (y - y₁) = m(x - x₁)

Now, substituting the value of m = 5/2 and (x₁, y₁) = (-2, -4), we get

(y - y₁) = m(x - x₁)

⇒ (y - (-4)) = 5/2(x - (-2))

⇒ (y+4) = 5/2(x+2)

⇒ 2(y+4) = 5(x+2)

⇒ 2y+8 = 5x+10

⇒ 5x-2y+10-8 = 0

⇒ 5x-2y+2 = 0

⇒ 5x-2y = -2

Hence, the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 is 5x-2y = -2.

Therefore, 5x-2y = -2 is the required answer.

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The probability that a can will take more than 29 minutes is approximately 0.66807

The mean time taken by the soda to move through the assembly line = 26 minutes

The standard deviation of the time it takes = 2 minutes

Required: The probability that the can takes more than 29 minutes

Solution: The Z-Score formula is presented as follows;

[tex]Z = \frac{x - \mu}{ \sigma} [/tex]

The Z-Score of a can that takes 29 minutes is given as follows;

[tex]Z = \frac{29 - 6}{ 2} = 1.5[/tex]

Which gives;

Z = 1.5

The probability P(x < Z) obtained online or from the Z-Score table gives;

Which gives;

The probability that the can will take more than 29 minutes P(x > Z) ≈ 1 - 0.93319 = 0.66807

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Answer:

see explanation

Step-by-step explanation:

the relationship between angles a and b

they are alternate interior angles

these angle pairs are on opposite ( alternate) sides of the transversal and are in between ( in the interior of )the parallel lines.

Greetings from Brasil...

It is possible to answer this question through Determinant

| X     Y     1 |

| X₁    Y₁    1 |  = 0

| X₂    Y₂   1 |

We have:

(X₁; Y₁) = (-9; 8)

(X₂; Y₂) = (-3; -1)

then

| X   Y   1 |

| -9  8   1 |  = 0

| -3  -1   1 |

Answer:

2745

jow to get this is you do this then dis

Step-by-step explanation:

this is similar to the complete approach to find the midpoint. just instead of 1/2 we are looking for 3/10 of the distance.

the general approach is

A + (B - A)×factor

factor can be 1/2 or 3/10 or 7/10 or 24/29 or ...

so, we have

(-3, -6) + ((9 - -3)×3/10, (5 - -6)×3/10) =

= (-3, -6) + (12×3/10, 11×3/10) =

= (-3, -6) + (3.6, 3.3) = (0.6, -2.7)

the point 3/10 of the way from A to B is

(0.6, -2.7)

Answer:

5

Step-by-step explanation:

4(|−2|)−|−3|

=(4)(2)−|−3|

=8−|−3|

=8−3

=5

The dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.

Leth the width of the revtangle be x.

According to the given question.

The perimeter of the rectangle is 126 inches.

The length of the rectangle is three more than double the width.

⇒ Length of the rectangle  = 3 + 2x

Now, according to the given conditions we can say that

Perimeter of the rectangle = 2( length + width)

⇒ 126 = 2(3 + 2x + x)

⇒ 126  = 2(3 + 3x)

⇒ 63  = 3 + 3x

⇒ 63 - 3 = 3x

⇒ 60 = 3x

⇒ x = 20 inches

Therefore, the length of the rectangle = 3 + 2(20) = 3 + 40 = 43

Hence, the dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.

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Answer:

v = 4.4

Step-by-step explanation:

Let's solve your equation step-by-step.

8/11 = v/6

Step 1: Cross-multiply.

8/11 = v/6

(8)*(6)=v*(11)

48=11v

Step 2: Flip the equation.

11v=48

Step 3: Divide both sides by 11.

11v/11 = 48/11

v= 48/11

v = 4.4

Answer:

  x2 = 7/6

Step-by-step explanation:

You want the second approximation using Newton's method, given that the first approximation is x1=1 and the function tangent at x=1 is y=7-6x.

Newton's method approximates the function by its tangent line at the point (x, f(x)). That is, the second approximation is the x-intercept of the tangent line y = 7 -6x. That value of x is ...

  0 = 7 -6x

  6x = 7 . . . . . add 6x

  x = 7/6 . . . . divide by 6

The second approximation is x2 = 7/6.

The volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.

The formula for the volume of a cylinder is given as:

V=π r² h

Now from the figure,

We have, for the first cylinder the height is 16 units and the radius is 7 units.

Hence,

V = 22/7 × 7² × 16

V = 22/7 × 7 × 7 × 16

V = 2424

Therefore the volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.

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