All categories

3 years ago

PERSEVERE Find the values of x and y,

Mathematics

1 answer:

Vlad [161]3 years ago

8 0

y² = 8y - 15 (alternate angles are equal)

y² - 8y + 15 = 0

(y - 5)(y - 3) = 0

y = 5 or 3

x + 8y - 15 = 180 (angles in a straight line add up to 180)

when y = 5

x + 40 - 15 = 180

x = 155°

when y = 3

x + 24 - 15 = 180

x = 171°

You might be interested in

In this problem,y = 1/(x2 + c)is a one-parameter family of solutions of the first-order DEy' + 2xy2 = 0.Find a solution of the f

trasher [3.6K]

Differentiate the given solution:

$y=\dfrac1{x^2+C}\implies y'=-\dfrac{2x}{(x^2+C)^2}$

Substitute $y$ and $y'$ into the ODE:

$-\dfrac{2x}{(x^2+C)^2}+2x\left(\dfrac1{x^2+C}\right)^2=0$

and it's easy to see the left side indeed reduces to 0.

6 0

2 years ago

The LCD for the fractions 1/3 , 3/4 ,5/32 , and 8/9 is

TiliK225 [7]

Your LCD is 288.

Thank You,
Helpingothers

7 0

3 years ago

What is the volume of a right circular cone that has a height of 18.8 m and a base with a radius of 19.3 m

12345 [234]

Answer: 7,333.32 m3

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cone = 1/3 x π x radius^2 x height

Replacing with the values given:

V = 1/3 π (19.3)^2 (18.8) = 7,333.32 m3

The volume of the right circular cone is 7,333.32 cubic meters.

Feel free to ask for more if needed or if you did not understand something.

7 0

3 years ago

Read 2 more answers

Solve this problem please

djyliett [7]

The formula for depreciation is:

$y=x(1-r)^t$

Where x = Initial value,

y= Amount after depreciation.

r= Rate of depreciation,

t = time (in years)

According to given problem,

x = 1040, y= 944 and t = 12 months =1 year.

So, first step is to plug in these values in the above formula, So,

$944 = 1040(1-r)^1$

944 = 1040 (1 -r)

$\frac{944}{1040} =1-r$ Divide each sides by 1040.

0.907692308 =1 - r

0.907692308 - 1 = -r Subtract 1 from each sides.

-0.092307692 = -r

So, r = 0.09 or 9%.

Now plug in 0.09 in the above equation to get the depreciation equation. So,

$y = x (1- 0.09)^t$

So, $y = 0.91x^t$

b) To find the value of the bike after 5 months,

plug in t = 5 months= 5/12 = 0.41667 years in the above equation of depreciation.

So, $y= 1040 *(0.91)^{0.41667}$

y = 1040 * 0.961465659

y = 999.9242852

y = 1000 (Rounded to nearest integer).

Hence, the value of the bike after 5 months is $1000.

7 0

3 years ago

Help me pls!!!!!!!!!

Dominik [7]

Answer:

$x^2+18=-9x : x = -3, x = -6$

Step-by-step explanation:

$x^2+18=-9x$

Add 9x to both sides:

$x^2+18+9x=-9x+9x$

Simplify:

$x^2+9x+18=0$

Solve with the quadratic formula:

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are:

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For $a=1,\:b=9,\:c=18:\quad x_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \:18}}{2\cdot \:1}$

$x =\frac{-9 + \sqrt{9^2-4\cdot \:1\cdot \:18}}{2\cdot \:1} : -3$

$x =\frac{-9 - \sqrt{9^2-4\cdot \:1\cdot \:18}}{2\cdot \:1} : -6$

The solution to the quadratic equation are:

$x=-3,\:x=-6$

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day!

6 0

3 years ago