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3 years ago

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Three consecutive integers have a sum of 81 . Find the integers.

1 answer:

Yuri [45]3 years ago

3 0

The 3 consecutive integers of a sum of 81<span>X+(X+2)+(X+4)=81
3X+6=81
3X=81-6
3X=75
X=75/3</span>

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How many solutions are there to

Alika [10]

Answer:

C

Step-by-step explanation:

there are infinitely many solutions since different values of x and y will work for this simultaneous equation

8 0

3 years ago

Calculate the side lengths a and b to two decimal places.

Zinaida [17]

Answer:

$a=10.92 units$

$b=14.51 units$

Step-by-step explanation:

We are given that c=6 units

$\angle A=43^{\circ}$

$\angle B=115^{\circ}$

We have to find the side length a and b.

We know that sum of angles of a triangle =180 degrees

$\angle A+\angle B+\angle C=180$

Substitute the values then we get

$43+115+\angle C=180$

$158+\angle C=180$

$\angle C=180-158=22^{\circ}$

sine law: $\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}$

$\frac{a}{sin 43^{\circ}}=\frac{6}{sin 22^{\circ}}$

$a=\frac{6}{sin 22^{\circ}}\times sin 43^{\circ}$

$a=10.92 units$

$\frac{b}{sin 115^{\circ}}=\frac{6}{sin 22^{\circ}}$

$b=\frac{6}{sin 22^{\circ}}\times sin 115^{\circ}=14.51$

$b=14.51 units$

6 0

3 years ago

Edge: Which equation has a focus at (–6, 12) and directrix of x = –12?

Volgvan

Answer:

C) (y - 12)^2 = 12(x+9)

8 0

3 years ago

Read 2 more answers

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any meth

Lubov Fominskaja [6]

Answer:

$\frac{128\pi}{3}$ cubic units

Step-by-step explanation:

We are given that a region bounded by a curves $x=(y-7)^2$

x=4 and about y=5

We have to find the value of volume of the resulting solid

To find the volume of resulting solid we are using cylinder method

Substitute the values of x then we get

$(y-7)^2=4$

$y-7=\pm2$

y-7=2 and y-7=-2

y=7+2=9 and y=-2+7=5

Radius of cylinder =r=y-5

and height =h= $4-(y-7)^2=4-y^2-49+14 y=-y^2+14 y -45$

Using cylinder method and integrate along y -axis from y=5 to y=9

Volume = $\int_{a}^{b}2\pi r h dy=\int_{5}^{9}2\pi(y-5)(-y^2+14 y -45) dy$

volume= $2\pi\int_{5}^{9}(-y^3+19y^2-115y+225)dy$

Volume = $2\pi[-\frac{y^4}{4}+19\frac{y^3}{3}-115\frac{y^2}{2}+225y]^9_5$

Volume = $2\pi[-\frac{6561}{4}+\frac{625}{4}+19(\frac{729-125}{3})-115(\frac{81-25}{2})+225(9-5)]$

Volume= $2\pi(-1484+\frac{11476}{3}-3220+900)$

Volume = $2\pi(\frac{11476}{3}-3804)$

Volume = $2\pi(\frac{11476-11412}{3})=\frac{128\pi}{3}$

Hence, volume of resulting solid = $\frac{128\pi}{3}$ cubic units

3 0

3 years ago

Question 29 of 40<br> Find f(-2) for f(x) = 5.3*.

blsea [12.9K]

Answer:

A. $\frac{5}{9}$

Step-by-step explanation:

To find f(-2) in f(x)=5*3^x, plug in -2 into all the x values.

f(-2)=5*3^-2, you can use calculator to calculate 3^-2 which equals 0.1, forever 1's.

f(-2)=5*0.1=0.5 Forever 5's.

f(-2)=0.5 or $\frac{5}{9}$

Hope this helps!

If not, I am sorry.

4 0

2 years ago