I need help with these questions. Thanks!​

[tex]\text{Width} ~= w ~ cm \\\\ \text{Length}~,l = (20+ w) ~ cm \\\\\text{Area of rectangle} = 1000 cm^2\\\\\\\text{Now,}\\\\l \cdot w = 1000\\\\\implies (20 + w) w= 1000\\\\\implies w^2 +20w -1000=0\\\\\\\implies w = \dfrac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot (-1000)}}{2 \cdot 1}\\\\\\\implies w = \dfrac{-20 \pm \sqrt{4400}}{2}= \dfrac{-20\pm 20\sqrt{11}}2 = -10 \pm 10\sqrt{11}\\\\\text{Width cannot be negative so,} \\\\w= -10+10\sqrt{11}=10\left(\sqrt{11} - 1 \right) ~ cm\\\\[/tex]

[tex]\text{And length,}[/tex]

[tex]l= 20+ 10\left(\sqrt{11} - 1} \right) = 20 + 10\sqrt{11} - 10 = 10 + 10\sqrt{11} = 10 \left(1+ \sqrt{11} \right)~ cm[/tex]

Answer:

Smallest: 12.8 square meters

Largest: 13.5 square meters

Step-by-step explanation:

I'm not 100% sure I understand this correctly as it seems like a very strange problem, but here it goes.

The smallest number that rounds to 3.2 is 3.15, and the smallest number that rounds to 4.1 is 4.05.

[tex]3.15*4.05=12.7575[/tex]

The smallest possible area is 12.8 rounded to the nearest 10th.

The largest number that rounds to 3.2 is 3.24999... and the largest that rounds to 4.1 is 4.14999...

[tex]3.24999*4.14999=13.4875[/tex]

That rounds to 13.5.

[tex]\\ \sf\longmapsto (4x+2)(x-3)[/tex]

[tex]\\ \sf\longmapsto 4x(x-3)+2(x-3)[/tex]

[tex]\\ \sf\longmapsto 4x^2-12x+2x-6[/tex]

[tex]\\ \sf\longmapsto 4x^2-10x-6[/tex]

Answer:

Step-by-step explanation:

(4x + 2)(x - 3) =4x *(x -3) + 2*(x -3)

                    = 4x*x - 3*4x + x*2 - 3*2

                    = 4x² - 12x + 2x - 6   {Combine like terms}

                    = 4x² - 10x - 6

Answer:

The code is 8415

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

8x - 4 = 4x + 12

Add 4 to both sides:

8x = 4x + 16

Subtract 4x from both sides:

4x = 16

Divide by 4 from both sides"

x = 4

Answer:

x=5-y

Step-by-step explanation:

Answer:

-6, -5

-3, -3

0, -1

3, 1

Step-by-step explanation:

Answer: I got 60d+115f

Step-by-step explanation:

Hope this helps.

Answer:

60d+115f

Step-by-step explanation:

if you were basically asking to simplify then this is your answer

Answer:

310 miles

Step-by-step explanation:

You can set up a proportion and solve for x.

2 6.2

___ = ___

100 x

Cross multiply

2x=6.2*100

Simplify

2x=620

Divide each side by 2

x=310

Answer: 99013114

Step-by-step explanation: Due to the solution to your question. 2234x44321= 99013114. This is because we multiply each digit to its own other digit.

Answer:

C

Step-by-step explanation:

The line would be dotted since it's > not ≥. You would shade above the line since it's greater than, not less than.

You don't need to graph the line to choose the correct answer, but if you would like to:

y - 3 > 2x + 2

y > 2x + 5

Answer:

x=54

Step-by-step explanation:

2x+13=3x-41

   -13       -13

__________

2x=3x-54

-3x  -3x

__________

-1x=-54

__   __

-1      -1

X=54

I Hope this helped <3

Answer:

x = 54

Step-by-step explanation:

If m||n, these two angles will be equal in degrees

3x - 41 = 2x + 13

3x - 2x = 13 + 41

x = 54

Answer:

Yes, Yes they are. Unless they are supposed to be in the order "20 99101" then they are most definitely a pythagorean triple.

Answer:

Yes, the sides would form a right triangle.

Step-by-step explanation:

[tex]99^2 + 20^2 = 101^2\\\rule{150}{0.5}\\99^2 + 20^2 = 10201\\\\9801 + 400 = 10201\\\\\boxed{10201 = 10201}[/tex]

Hope this helps.

Answer:

$6 per cat, $10 per car

Step-by-step explanation:

I guess and checked my work.

Answer:

y = 1/3x +1

Step-by-step explanation:

y intercept is 1 and the rise is one with a run of 3

k(-3)=36(2)

hope it helps

Step-by-step explanation:

as you can see, the distance between 2 points can always be seen as the Hypotenuse or baseline of a right-angled triangle created by the differences of the x and y coordinates of both points.

the drawn triangle is nothing else than that.

to calculate the length of a side in such a triangle we need to use Pythagoras :

c² = a² + b²

c is the Hypotenuse of baseline of the triangle and is opposite of the 90 degree angle.

a and b are the legs of the triangle "enclosing" the 90 degree angle.

so, we have

AB² = AC² + BC²

AC and BC we know : the coordinate differences in x and y directions.

AC = (4, 5) to (4, 2). as the x coordinates are the same, the difference is just the difference in the y coordinates : 5-2 = 3.

BC = (1, 2) to (4, 2). as the y coordinates are the same, the difference is just the difference in the x coordinates : 5-1 = 3.

AB² = 3² + 3² = 9 + 9 = 18

AB = sqrt(18)

FYI : sqrt(18) = sqrt(9×2) = 3×sqrt(2)

The correct answers are that Earth’s North Pole is close to the magnetic south pole, magnets allowed to move freely align themselves to point north, and the north pole on a compass is attracted to Earth’s south pole. I really hope this helps you!!

Answer:

y+5=3(x-2).

Step-by-step explanation:

1) according to the condition m=3; x₁=2; y₁= -5, then

2) the required equation is y+5=3(x-2).

Answer:

Step-by-step explanation:

If the ratio of two numbers is 8 : 1, the smaller number is what fractional ... 20. 80 m to 16 m. 21. 75 g to 100 g. 22. 36 cm to 72 cm. 23. 54 g to 90 g there you go hope it helps

Answer:

90

Step-by-step explanation:

start from the beginning, then if you go 2 steps at a time, then you have 1 step left over at the end, let's assume the length of the stair case is x, so then we will be going up 2/3x steps, and have 1/3 x steps left.

2/3 x = somewhere between 80 and 90, so that means it must be divisible by 3, so 81,84,87,90

3/5 x ==> only 90

ok done. Thank to me :>

Answer:

b

Step-by-step explanation:

Answer:

B. 8

Step-by-step explanation:

Point-slope form:

[tex]y-y1=m(x-x1)[/tex]

m is the slope, and that is 8 in this equation.

Answer:

It is 0.6 miles

Step-by-step explanation:

Answer:

1-a) 78+x+16+x+24=180°

118+2x=180

2x=62

so x=31

Step-by-step explanation:

thats a

Answer:

1a) x = 31

1b) x = 12

2) angle A = 60 degrees

3) x = 40 degrees

Step-by-step explanation:

Answer:

1. GCF is 15.

2. 8 servings

Step-by-step explanation:

1. Continuous Division              

            3     15         30

            5      5          10

                     1           2

Multiply the factors in the left side (3 and 5)

= 15

Greatest Common Factor is 15

2. Continuous Division

              2      16         24

              2      8           12

              2      4            6

                      2            3

Multiply the factors in the left side (2,2 and 2)

= 8

Greatest number of servings is 8

Answer

The ratio of bananas to apples is 3 to 4

Step-by-step explanation: