A bookcase has a mass of 20 kilograms. A book in the bookcase has a mass of 500 grams.

Solve 12x+6≥9x+12 (apex)

Crazy boy [7]

Answer:

x≥2

Step-by-step explanation:

12x+6\ge \:9x+12

12x+6-6\ge \:9x+12-6

12x\ge \:9x+6

12x-9x\ge \:9x+6-9x

3x\ge \:6

8 0

2 years ago

Explain the difference between the two inequalities. how does this affect your method of solution?

AfilCa [17]

I mean they both have a factor of 3 you just take -3x > 9 and just flip it

4 0

2 years ago

Match the steps to find the equation of the parabola with focus (-1, 2) and directrix x = 5.

Archy [21]

Answer:

The matched options to the given problem is below:

Step1: Choose a point on the parabola

Step2: Find the distance from the focus to the point on the parabola.

Step3: Use (x, y).

Find the distance from the point on the parabola to the directrix.

Step4: Set the distance from focus to the point equal to the distance from directrix to the point.

Step5: Square both sides and simplify.

Step6: Write the equation of the parabola.

Step by step Explanation:

Given that the focus (-1,2) and directrix x=5

To find the equation of the parabola:

By using focus directrix property of parabola

Let S be a point and d be line

focus (-1,2) and directrix x=5 respectively

If P is any point on the parabola then p is equidistants from S and d

Focus S=(-1,2), d:x-5=0

Step1: Let P(x,y) be any point on parabola

Step2: Therefore the $d=\sqrt{(x+1)^2+(y-2)^2}\hfill (1)$

Step3: The perpendicular distance from p to d is

$\frac{|x-5|}{\sqrt{(-1)^2+2^2}}$

$=\frac{|x-5|}{\sqrt{5}}\hfill (2)$

Step4: equating (1) and (2)

$\sqrt{(x+1)^2+(y-2)^2}=\frac{|x-5|}{\sqrt{5}}$

Step5: squaring on both sides

$(x+1)^2+(y-2)^2=\frac{|x-5|^2}{5}$

$5[(x+1)^2+(y-2)^2]=(x-5)^2$

$5[x^2+2x+1+y^2-2y+4-x^2+10x-25]=0$

$12x+y^2-2y-24=0$

Step6: Equation of the parabola is

$y^2-2y+12x-24=0$

8 0

2 years ago

Find the slope-intercept form of the line that passes through given the point and has the given slope. Include your work in your

nignag [31]

Slope-intercept form is y=mx+b
we know m is 10 and we have x and y
if you plug in x, y and m and solve for b, like this
y=mx+b
1=10 (7) + b
1=70+b
-69=b
so now we know b is -69. just plug that in
the final answer is y=10x-69

6 0

2 years ago

Find the volume of the following. Please round your answer to the nearest tenth. Please do not put units. Hint: You need to use

Sophie [7]

Answer:

Step-by-step explanation:

<u>The Volume of a Square Pyramid</u>

Given a square-based pyramid of base side a and height h, the volume can be calculated with the formula:

$\displaystyle V=\frac{1}{3}a^2h$

We are given a square pyramid with a base side a=14 ft but we're missing the height. It can be calculated by using the right triangle shown in the image attached below, whose hypotenuse is 25 ft and one leg is 7 ft

We use Pythagora's theorem:

$25^2=h^2+7^2$