Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut out 2 inch squares from both the lengths and widths. Given that the length will need to be 6 inches longer than the width create an equation for the volume of the box, find the zeroes, the dimensions of the box, and graph the function.

Answer:

[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]

Step-by-step explanation:

We are given the equation:

[tex]ax^2+bx+c=0[/tex]

Which has roots α and β.

And we want to express (α + 1)(β + 1) in terms of a, b, and c.

From the quadratic formula, we know that the two solutions to our equation are:

[tex]\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

Let x₁ = α and x₂ = β. Substitute:

[tex]\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)[/tex]

Combine fractions:

[tex]\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)[/tex]

Rewrite:

[tex]\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}[/tex]

Multiply and group:

[tex]\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}[/tex]

Difference of two squares:

[tex]\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}[/tex]

Expand and simplify:

[tex]\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}[/tex]

Distribute:

[tex]\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}[/tex]

Cancel like terms:

[tex]\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}[/tex]

Factor:

[tex]\displaystyle =\frac{4a(a+c-b)}{4a(a)}[/tex]

Cancel. Hence:

[tex]\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]

Therefore:

[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}[/tex]

Answer:

1. a) x^2 + 6x + 27

b) 4x^2 - 4x + 1

c) x^2 - 4y^2

d) x^3 + 6x^2 + 12x + 8

e) x^3 - 9x^2 + 27x - 27

Answer:

either 5 or 6

Step-by-step explanation:

I can't have a direct answer because you didn't get all of the histogram in there, but from what I can conclude from just this there's definitely either 5 or 6.

Answer:

P.=2(2x+5)+2(x-10)=80cm

6x-10=80

x=90/6=15cm

Area= L*W= 35*5=175 squared cm= 0.0175 squared m

Cost= 0.24 * 0.0175 = GHc 0.0042

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.  The cost of weeding the rectangular plot is 0.0042 GHc.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

A.) The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Therefore, we can write,

Perimeter of the rectangel = 2(L+W)

80 = 2[(2x+5)+(x-10)]

80/2 = 2x+5+x-10

40 = 3x -5

40+5 = 3x

x = 15

Hence, the value of x is 15.

B.) The length of the rectangle = (2x+5) = 2(15)+5 = 35 cm = 0.35 m

The width of the rectangle = (x-10) = 15-10 = 5 cm = 0.05 m

Now, the area of the rectangle = L×B = 0.35m × 0.05m  = 0.0175m²

C.) Given the cost of weeding 1m² is 0.24, therefore, the cost of weeding the rectangular plot is

Cost = 0.0175 × 0.24 = 0.0042 GHc

Hence, the cost of weeding the rectangular plot is 0.0042 GHc.

Learn more about Rectangle:

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Answer:

The length of each hot dog is 0.5000 inches.

Step-by-step explanation:

Total number of hot dogs eaten = 7 000 000 000

Circumference of the earth = 24 860 miles

21.5 times the circumference of the Earth = 21.5 x 24 860 miles

                                                = 534490 miles

But,

1 mile = 5280 feet

So that,

534490 miles = X

X = 5280 x 534490

   = 287707200 feet

Also,

1 feet = 12 inches

Then,

287707200 feet = Y

Y = 12 x 287707200

   = 3452486400 inches

Thus,

the length of each hot dog = [tex]\frac{3452486400}{7000000000}[/tex]

                     = 0.4932

The length of each hot dog is 0.5000 inches.

Answer:

134.1

Step-by-step explanation:

Area of the circle = 49π = 153.9 (rounded to the nearest tenth)

Segment area,

49/2(150π/360-sin(150))

= 19.8 (rounded to the nearest tenth)

Subtracting them,

153.9-19.8

= 134.1 cm²

Answered by GAUTHMATH

The area of the shaded region is 134.1 cm²

'A segment of a circle is the region that is bounded by an arc and a chord of the circle.'

According to the given problem,

Area of the circle = πr²

                              = π × 7 × 7 cm²

                              = 153.9 (rounded to the nearest tenth)

Area of the Shaded region,

= [tex]\frac{r^{2} }{2}( \frac{angle in degrees * \pi }{360 - sin(angle in degrees)} )[/tex]

=[tex]\frac{49}{2}(\frac{150\pi }{360 - sin(150)})[/tex]

= 19.8 (rounded to the nearest tenth)

Subtracting them,

= 153.9 - 19.8

= 134.1 cm²

Hence, we can conclude that the area of the shaded region is 134.1cm²

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Answer:

17

Step-by-step explanation:

8+2+(3×3-2)=8+2+(9-2)=8+2+7=17

mistake in the first step

firstly we do × and ÷

then + and -

Answer:

Step-by-step explanation:

Let

x = cost per mile

y = Total cost

Plan 1:

y = 59 + 0.15x

Plan 2:

y = 50 + 0.20x

Equate the total cost of the two plans

59 + 0.15x = 50 + 0.20x

59 - 50 = 0.20x - 0.15x

9 = 0.05x

x = 9/0.05

= 180

x = 180 miles

y = 50 + 0.20x

= 50 + 0.20(180)

= 50 + 36

= 86

y = 86

Answer:

C

Step-by-step explanation:

f is neither even nor odd

Answer:

option 3

Step-by-step explanation:

Given

3x + 5 + 7x + 2 ← collect like terms

= (3x + 7x) + (5 + 2)

= 10x + 7 → option 3

According to the question

=3x + 5+7x + 2

Combining Like terms

= (3x + 7x) +(5+2)

= 12x + 7

Therefore the correct option is third

10x + 7

Answered by Gauthmath must click thanks and mark brainliest

Answer:

4√3

Step-by-step explanation:

5√27-2√48-5√3-(√3-2√3)2

= 5√(3x9)-2√(3x16)-5√3-2√3+4√3

= 5(3)√3-2(4)√3-5√3-2√3+4√3

= 15√3-8√3-5√3-2√3+4√3

= 4√3

Answer:

I think the answer is B

Answer:

Step-by-step explanation:

We know that the thickness of the lake decreases at a rate of 0.2 meters per week, so we can write:

S(t)=-0.2t+4

we also know that after 7 weeks, the sheet is only 2.42 meters thick, which means we can write:

S(7)=2.42

S(7)=-0.2*7+X

S(7)=-1.4+X

2.42=-1.4+X

X=3.82

So, the function is: S(t)=--0.2*t+3.82

Answer:

y = 3.8 - 0.2x

Step-by-step explanation:

Khan Academy

Answer:

9

Step-by-step explanation:

We know that a^b / a^c = a^(b-c)

9^8 / 9^7

9^(8-7)

9^1

9

If two parallel lines are intersected by a transversal, then internal opposite angles are equal.

So, x° = 61°

=> x = 60

Because they are internal opposite angles.

Answer:

10/3

Step-by-step explanation:

rate of change = gradient

(17-7)/(6-3) = 10/3

basically difference of y values / difference of x values

Answer:

x^2 +2x+xy +2y

Step-by-step explanation:

(x + y) (x + 2)

FOIL

first x*x = x^2

outer  x*2 =2x

inner y*x= xy

last = y*2 =2y

Add together

x^2 +2x+xy +2y

Answer:

Step-by-step explanation:

F - First ; O - Outside ;  I - inside  ; L -last

(x + y)(x + 2) = x*x + x*2 +y*x +y*2

                    = x² + 2x + xy +2y

Answer: A x> -2

Step-by-step explanation:

Answer:

b=3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

b = 3

Step-by-step explanation:

3(9+9b)=69+136

27+27b = 205

27b = 205-27

27b = 178

b = 178/27

*slaps face*

In the comments you said the "136" is "13b" so ok...

3(9+9b)=69+13b

27+27b = 69 + 13b

27+14b = 69

14b = 69-27

14b = 42

b = 3

Answer:

Total number in favour:

Probability:

Total number in against:

Probability:

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

If you want to read more about triangle rectangles, you can see:

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Answer:

3x+ 7 =49

Step-by-step explanation:

49-7= 42

42 divided by 3 = 14

her daughter is 14 years old

I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.

have a great day!

Step-by-step explanation:

9 a = soln

3:9 = 6:n

or, 3/9 = 6/n

or, 3n = 54

or, n = 54/3

so, n = 18

b = soln

n/10 = 6/15

or, 15n = 60

or, n = 60/15

so, n= 4

10) a = 15% of 450

= 15/100 * 450

= 15/10 * 45

or, 15/2 * 9

or,  135/2

= 67.5 g

b= 125% of 60

= 125/100 * 60

= 5/4 * 60

= 5*15

= $75

Answer:

0 =-4.5X +49.5

x = 11

Step-by-step explanation:

x1 y1  x2 y2

1 45  3 36

(Y2-Y1) (36)-(45)=   -9  ΔY -9

(X2-X1) (3)-(1)=    2  ΔX 2

slope= -4  1/2    

B= 49  1/2    

Y =-4.5X +49.5    

Answer:

[tex]y = \frac{1}{4}x -2[/tex]

Step-by-step explanation:

Step 1:  Find the standard form of the equation

The equation that was given made no sense so I will recreate the entire equation using the point slope formula.

Use the point slope formula

[tex]y - y_{1} = m(x - x_{1})[/tex]

[tex]y - (-3) = m(x - (-4))[/tex]

[tex]y +3 = m(x + 4)[/tex]

Find the slope

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \frac{1-(-3)}{12-(-4)}[/tex]

[tex]m = \frac{1+3}{12+4}[/tex]

[tex]m = \frac{4}{16}[/tex]

[tex]m=\frac{1}{4}[/tex]

Combine them together

[tex]y +3 = \frac{1}{4}(x + 4)[/tex]

Convert to standard form

[tex]y +3 = \frac{1}{4}x + 1[/tex]

[tex]y +3 - 3 = \frac{1}{4}x + 1 - 3[/tex]

[tex]y = \frac{1}{4}x -2[/tex]

Answer:  [tex]y = \frac{1}{4}x -2[/tex]

Answer:

1/3

Step-by-step explanation:

Slope is rise over run

your rise is 1 (because you only go up one block each time)

your run is 3 ( because you go right three times)

so 1/3

Answer:

12

Step-by-step explanation:

Add 10l to 12l to13l to11l to 14l=60l the divide 60l by the number of houses which will be 12 and there is your correct answer

Answer:

slope: -3

y-intercept: 9

Step-by-step explanation:

To find the slope and y-intercept, we can manipulate the equation to slope-intercept form. Slope-intercept form is y=mx+b where m is slope and b is y-intercept.

[tex]3x+y-9=0[/tex]        [subtract both sides by 3x]

[tex]y-9=-3x[/tex]            [add both sides by 9]

[tex]y=-3x+9[/tex]

Now, our equation is in slope-intercept form. We can see that the slope is -3 and the y-intercept is 9.

you can go for option g cause ans is 14:5

Answer:

SOH-CAH-TOA

[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°

SOH = SIN = OPP/HYP

SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]

Step-by-step explanation: