The area of a rectangle is represented by the expression 2x2 + 10x + 12. Daniel is convinced that the dimensions of this rectangle could be (2x + 4) and (x + 3) or (x + 2) and (2x + 6). Do you agree or disagree with Daniel? Use words to justify your opinion.

Given:

The equation of parallel line is:

[tex]3x-2y=5[/tex]

The required line passing through the midpoint of the line segment joining the points (-4,2) and (2,4).​

To find:

The equation of required line.

Solution:

Midpoint of  line segment joining the points (-4,2) and (2,4) is:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-4+2}{2},\dfrac{2+4}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-2}{2},\dfrac{6}{2}\right)[/tex]

[tex]Midpoint=\left(-1,3\right)[/tex]

It means the required line passes through the point (-1,3).

The slope of line [tex]Ax+By=C[/tex] is:

[tex]m=\dfrac{-A}{B}[/tex]

The given equation is:

[tex]3x-2y=5[/tex]

Here, A=3 and B=-2. So, the slope of the line is:

[tex]m=\dfrac{-3}{-2}[/tex]

[tex]m=1.5[/tex]

Slope of parallel lines are same. So, the slope of the required line is 1.5.

The required line passes through the point (-1,3) with slope 1.5. So, the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-3=1.5(x-(-1))[/tex]

[tex]y-3=1.5(x+1)[/tex]

[tex]y-3=1.5x+1.5[/tex]

Adding 3 on both sides, we get

[tex]y=1.5x+1.5+3[/tex]

[tex]y=1.5x+4.5[/tex]

Therefore, the equation of the required line is [tex]y=1.5x+4.5[/tex].

Answer:

6.25

Step-by-step explanation:

17.50/2=8.75

8.75+2.50=11.25

17.50-11.25=6.25

Answer:

Toni has $7.50

Step-by-step explanation:

Tobi = x

Sabi = x + 2.5

x + x +  2.5 = 17.5

2x + 2.5 = 17.5

2x = 15

x = 7.5

Answer:

[tex]y = 4x - 3\\Slope \ m_1 = 4[/tex]

EQUATION OF LINE PERPENDICULAR

[tex]Lines \ are \ perpendicular => m_1 \cdot m_2 = -1\\[/tex]

[tex]slope, m_2 = \frac{-1}{4}[/tex]

[tex]equation \ of \ the\ line \ passing \ through \ (-2, 2) \ slope ,m_2 :\\(y - y_2) =m_2(x - x_2)\\ (y - 2) = \frac{-1}{4} (x -(-2))\\\\y - 2 = \frac{-1}{4} (x +2)\\\\y = \frac{-1}{4}x - \frac{1}{2} + 2\\\\y = \frac{-1}{4}x + \frac{3}{2}[/tex]

EQUATION OF LINE PARALLEL

[tex]Lines \ are \ parallel => m_1 \cdot m_3 = 1\\slope, m_3 = \frac{1}{4}[/tex][tex]Equation \ of \ the \ line \ through \ (-2, 2) \ and \ slope, m_3:\\(y - y_3) =m_3(x - x_3)\\\\(y-2) = \frac{1}{4} (x - (-2))\\\\y-2 = \frac{1}{4}(x+2)\\\\y = \frac{1}{4}x + \frac{1}{2} +2\\\\y = \frac{1}{4}x + \frac{5}{2}[/tex]

9514 1404 393

9514 1404 393

Answer:

  a)  P = -28(x -112)² +7500

  b) $102.55 or $121.45

Step-by-step explanation:

a) A quadratic relation with a maximum of 7500 at x=112 can be written in vertex form as ...

  P = a(x -112)² +7500

The other given point (x, P) = (89, -7312) can be used to find the value of 'a'.

  -7312 = a(89 -112)² +7500

  -14812 = a(529)

  a = -14812/529 = -28

So, the desired quadratic relation is ...

  P = -28(x -112)² +7500

__

b) The values of x that make P = 5000 can be found from ...

  5000 = -28(x -112)² +7500

  -2500 = -28(x -112)² . . . . . . . . subtract 7500

  89.286 = (x -112)² . . . . . . . . . . . divide by -28

  ±9.45 = x -112 . . . . . . . . . . take the square root

  x = 112 ± 9.45 = {102.55, 121.45}

Setting the price at about $102.55, or $121.45, will yield a profit of $5000.

Answer:

x^2+x+3=0

Step-by-step explanation:

x=-(1+√1-12)/2

Answer:

it will decrease

Step-by-step explanation:

if theres not enough food water, ect for all 55 to survive and only enough to support 40 wolves they will die down

Answer:

It will decrease

Step-by-step explanation:

There are 55 wolves means the wolf population will decrease as the place have only sufficient resources to 40 wolves and will eventually die.

I think this is the answer.

Answer:

It's B

Step-by-step explanation:

B makes the most sense to me

Given:

The figure of a triangle.

To find:

The measure of angle 1.

Solution:

Exterior angle theorem: In a triangle, the measure of an exterior angle of a triangle is equal to the sum of two opposite interior angles.

Using Exterior angle theorem, we get

[tex]101^\circ =31^\circ +m\angle 1[/tex]

[tex]101^\circ -31^\circ =m\angle 1[/tex]

[tex]70^\circ =m\angle 1[/tex]

Therefore, the measure of angle 1 is 70 degrees.

Answer:

The point (0, 6.7) is the point where the ball was launched.

Step-by-step explanation:

The ball was launched from a point 6.7 feet from ground level.

In this scenario (ball tossed toward the goal), the constant  c  at the end of the function formula gives you the initial position (height).

Answer:

[tex]Pr = \frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6\}[/tex] --- the faces of the dice

[tex]n(S) = 6[/tex]

Required

Pr(Multiple of 8)

The multiples of 8 in the given dataset are:

[tex]Multiples = \{1.,2,4\}[/tex]

[tex]n(Multiples) = 3[/tex]

So, we have:

[tex]Pr = \frac{n(Multiples)}{n(S)}[/tex]

[tex]Pr = \frac{3}{6}[/tex]

Simplify

[tex]Pr = \frac{1}{2}[/tex]

Answer:

To determine this simply multiply the values together to determine the final distance.

Step-by-step explanation:

The product of red blood cell diameter for a single blood cell multiplied by the number of red blood cells that are found within a person would enable you to find the total distance the cells would be if it were to be lined end to end.

Answer:

Step-by-step explanation:

(7 × 10^-6)(2 × 10^-13): Original Equation

(7 × 2)(10^-6 × 10^-13): Commutative Property of Multiplication (Just switched the numbers)

(14 × 10^-19): Simplify (Since you are multiplying numbers with exponents, just add the exponents: -6 +(-13) = -19)

Answer:

a

Step-by-step explanation:

Answer:

I recommend trying this it explains it and gives you the answer

Answer:

17/12 or 1 5/12

Step-by-step explanation:

You need to make the denominators the same, the common denominator is 12. In the end, they become 9/12 and 8/12. ad those to you get 17/12 or 1 5/12. Was this helpful?

Answer:

=17/12

Step-by-step explanation:

Get a common denominator between the two fractions.

Common denominator will be 12

Multiple 2/3 by 4 (top and bottom) to get 8/12

Multiply 3/4 by 3 (top and bottom) to get  9/12

Add the numerators of both fractions (8+9=17)

final fraction is 17/12 (denominator stays the same)

Answer:

Step-by-step explanation:

980

Answer:

[tex]595.54[/tex]

Step-by-step explanation:

The formula for a sector of a circle with angle [tex]\theta[/tex] is [tex]\frac{\theta}{360}\cdot r^2\pi[/tex].

Substituting given values, we have:

[tex]\frac{141}{360}\cdot 22^2\pi\approx \boxed{595.54}[/tex]

Answer:

the answer is No

Step-by-step explanation:

he needs $800 yet he only has $650, he will need $150 more

Answer:

A) -33 is yr answer.

Answer:

A) [tex] - 33[/tex]

Step-by-step explanation:

[tex][{(−4+3) \times (4+2)−5} \times 3][/tex]

[tex]{[−1 \times (4+2)−5} \times 3][/tex]

[tex](−1 \times 6−5) \times 3[/tex]

[tex](−6−5) \times 3[/tex]

[tex]−11 \times 3[/tex]

[tex] - 33[/tex]

Answer:

last option:  y = 1/6x+3; y = 1/2x+3

Step-by-step explanation:

6y = x + 18

Solve the above for 'y' to get:

y = 1/6x + 3

2y - x = 6

Solve the above for 'y' to get:

2y = x + 6

y = 1/2x + 3

the answer is C. (x+9)(x-5)

Answer:

The answer is C :)

Step-by-step explanation:

Answer:

B: 8

Step-by-step explanation:

The area of the two smaller squares equals the area of the big square so find the area to the big square

17 * 17 = 289

289 - 225 = 64

The square root of 64 is 8 so the answer is 8.

Answer:

Leading coefficient is the coefficient of the highest power of x.

[tex]x^5[/tex] is the highest power.

Therefore, leading coefficient = [tex]\frac{1}{4}[/tex]

Option D

Answer:1/4

Step-by-step explanation:

Step-by-step explanation:

V = l.W.H

3(5)(4) = 60 units

The volume of rectangular prism is given by the product of its dimensions hence the correct option is 3(5)(4) = 60 units

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere. Different shapes have different volumes.

Given that, we need to determine the correct calculation for the volume of the prism,

We know that, the volume of a rectangular prism is the  product of its dimensions = length x width x height

Therefore, the correct formula is 3(5)(4) = 60 units

Hence, the correct option is 3(5)(4) = 60 units

Learn more about volumes, click;

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Answer:

the y-int is at the point (0,3)

Step-by-step explanation:

Answer:

(0,3)

Step-by-step explanation:

f(x)=x²+2x+3

x=0

f(0)=0²+2×0+3

f(0)=3

y=3

(0,3)

Answer:

141.3 km

Step-by-step explanation:

First crater has the radius (that is, half the diameter) of 7.5 km; the circumference of this crater is C = 2(pi)r, or 2(3.14)(7.5 km) = 47.1 km;

Second crater radius is C = 2(pi)(30 km) = 188.4 km

The circumference of the complex (larger) impact crater is

(188.4 - 47.1) km greater than the circumference of the simple (smaller) crater:

141.3 km

Step-by-step explanation:

5x+5+79+11x=180°{sum of angle of triangle}

16x+84=180°

x=96/16

x=6

now angle A=5x+5

Answer:

5x+5+11x=180-79

16x=101-5

16x=96

x=6

Measure of angle A=5x+5

=(5×6)+5

=35