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WITCHER [35]
3 years ago
12

Write the equation of the line in fully simplified slope intercept form.

Mathematics
1 answer:
umka2103 [35]3 years ago
4 0

Answer:

y = -1/3 x - 7

Step-by-step explanation:

First, the intercept form is in y = ax + b, where b is the intercept at y-axis which is -7, then pick any point in the line, in the case I chose (3,-8), then substitute it into the equation, -8 = 3a - 7, then solve for a, get 3a = -1, so a = -1/3 which is the slope.  

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The ratio of Val's savings to Dan is 2:3 at first. After Dan spent P3000.00, Val's saving became 11/3 more of that Dan's remaini
andrew11 [14]

Answer:

P.7500.00

Step-by-step explanation:

We are told that:

The ratio of Val's savings to Dan is 2:3 at first.

Now, Dan spent P3000.00 and Val's saving became 1⅓ more of that Dan's remaining savings.

Let's say the total amount of savings they had at first was x.

Thus;

Val had: 2x/5

Dan had: 3x/5

Now, Dan spent P3000.00.

So amount Dan has left = (3x/5) - 3000

We are told Val's savings is now 1⅓ = 4/3 times that of Dan's remaining savings

Thus; 2x/5 = (4/3)((3x/5) - 3000)

2x/5 = 12x/15 - 4000

Multiply through by 15 to get;

6x = 12x - (3000 × 15)

6x = 12x - 45000

Rearranging, we have;

12x - 6x = 45000

6x = 45000

x = 45000/6

x = P.7500

4 0
3 years ago
Evaluate the integral Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is d
algol13

You want to find the volume inside the hemisphere x^2+y^2+z^2=4 (i.e. inside the sphere but above the plane z=0) and outside the cylinder x^2+y^2=1. Call this region R.

In cylindrical coordinates, we have

\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta

\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr

\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du

(where u=4-r^2)

\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du

=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi

7 0
4 years ago
4-0.25g+0.5h= when g=10, h=5
neonofarm [45]
The answer to this problem is 4
4 0
3 years ago
Read 2 more answers
I have 273 points, I ask a question that only 2 people can answer, if the question is worth 100 points, how much would each pers
Mariulka [41]
I think 171 but I’m not sure
6 0
3 years ago
Read 2 more answers
What is the solution to the equation below? Round your answer to two decimal places? (apex) 5+8*In x=15.8
Sliva [168]

Option A : $x=3.86$ is the solution of the equation.

Explanation:

The equation is $5+8 \ln x=15.8$

To determine the value of x, let us simplify the equation.

Subtracting 5 from both sides of the equation, we have,

$5+\ 8  \ ln \ x-5=15.8-5$

Simplifying, we get,

8 \ ln \ x= 10.8

Now , dividing both sides of the equation by 8, we get,

$\ ln \ x=1.35$

Using the logarithmic definition that if $\log _{a}(b)=c$ then $b=a^{c}$

Thus, rewriting the above expression $\ ln \ x=1.35$ using the logarithmic definition, we have,

$\ln \ x =1.35$ ⇒ $x=e^{1.35}$

Substituting the value of e^{1.35}$=3.85742... , we get,

$x=3.85742 \ldots$

Rounding off the answer to two decimal places, we get,

$x=3.86$

Hence, the solution of the equation is $x=3.86$

Therefore, Option A is the correct answer.

8 0
3 years ago
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