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2 years ago

The difference of a number and thirty-six is seven. Algebraic expression

Mathematics

1 answer:

sleet_krkn [62]2 years ago

6 0

Answer:

x-36=7

Step-by-step explanation:

x-36=7

x=36+7

x=43

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Write the equation of the circle below to complete the square. Also determine the area of the circle.

diamong [38]

Answer: $(x-7)^2+(y+2)^2=11^2$ ; $A=121\pi$

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

$(x-a)^2+(y-b)^2=r^2$

Begin by grouping the 'x' terms and 'y' terms:

$(x^2-14x)+(y^2+4y-68)=0$

Complete the square for the second polynomial:

$(\frac{b}{2} )^2=(\frac{4}{2} )^2=4$

$(x^2-14x)+(y^2+4y+4-4-68)=0$

$(x^2-14x)+(y^2+4y+4)-4-68=0$

$(x^2-14x)+(y^2+4y+4)-72=0$

$(x^2-14x)+(y+2)^2-72=0$

Do the exact same process with the other polynomial:

$(x^2-14x-72)+(y+2)^2=0$

Complete the square:

$(\frac{14}{2} )^2=49$

$(x^2-14x+49-49-72)+(y+2)^2=0$

$(x^2-14x+49)-49-72+(y+2)^2=0$

$(x^2-14x+49)-121+(y+2)^2=0$

$(x-7)^2-121+(y+2)^2=0$

Bring the 121 to the other side to get:

$(x-7)^2+(y+2)^2=121$

$(x-7)^2+(y+2)^2=11^2$

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

$A=\pi r^2=121\pi$

8 0

1 year ago

Algebra 2 please help quickly

Amiraneli [1.4K]

Answer:

$(f - g)(x) = - 5 {x}^{2} + 5x - 7$

4 0

1 year ago

Read 2 more answers

Two trains are traveling towards each other at a constant speed. The trains are currently 714 miles from each other. The speeds

shutvik [7]

55mph.

you can solve it using the equation distance=speed x time

your total distance is 714, and you have 2 trains, one traveling some speed, x, and one traveling x+8, both traveling for 7 hours.
your equation would look like this
$714 = x(7) + (x+8)(7)$
and you can then solve for x, which would be 47. this is the speed of the slower train, but 47+8=55 with give you the speed of the faster train.

6 0

2 years ago

Sammi has 2 1/3 feet of rope. If he cuts the rope into pieces that are each 1/2 foot long, there will be 1/3 foot of rope left o

Stells [14]

Answer:

Step-by-step explanation:

Sammi has 2 1/3 feet of rope.

To write this type of fraction = 2 + 1/3 - The integer 2 in the expression is the amount of feet of rope that was cut.

Thus to know the number of 1/2 foot pieces produced, let this number be x. Thus, we have 1/2 of x pieces = 2

x/2 = 2; x = 2x2 = 4.

Thus, Sanmi has 4 pieces of 1/2 foot long piece each of rope.

4 0

2 years ago

The dimensions of a right prism

kupik [55]

Answer:

v = 3/2

Step-by-step explanation:

volume = length × width × height

volume = 3/2 × 1/2 × 2

volume = 3/4 × 2

volume = 6/4 = 3/2

5 0

2 years ago