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3 years ago

Some please help i’ll give brainliest

Mathematics

1 answer:

Orlov [11]3 years ago

5 0

Answer:

Statement Reason

∠1 = ∠2 Given

AP = BP Given

∠APD = ∠BPC Vertical angles

Therefore, by ASA , ΔAPD ≅ ΔBPC

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Y varies directly with x and y = 12 when x =5 what is the value of y when x = 8

torisob [31]

Y and x are directly proportional, as stated by hypothesis. Let's use the rule of three to find y when x = 8.

x=5 --> y=12
x=8 --> y=?

? = (8*12)/5 = 96/5 = 19.2

So y directly varies with x, and y=12 when x = 5, then y=19.2 when x=8.

Hope this Helps! :D

3 0

4 years ago

(15 pts) 4. Find the solution of the following initial value problem: y"-10y'+25y = 0 with y(0) = 3 and y'(0) = 13

jolli1 [7]

Answer:

$y(x)=3e^{5x}-2xe^{5x}$

Step-by-step explanation:

The given differential equation is $y''-10y'+25y=0$

The characteristics equation is given by

$r^2-10r+25=0$

Finding the values of r

$r^2-5r-5r+25=0\\\\r(r-5)-5(r-5)=0\\\\(r-5)(r-5)=0\\\\r_{1,2}=5$

We got a repeated roots. Hence, the solution of the differential equation is given by

$y(x)=c_1e^{5x}+c_2xe^{5x}...(i)$

On differentiating, we get

$y'(x)=5c_1e^{5x}+5c_2xe^{5x}+c_2e^{5x}...(ii)$

Apply the initial condition y (0)= 3 in equation (i)

$3=c_1e^{0}+0\\\\c_1=3$

Now, apply the initial condition y' (0)= 13 in equation (ii)

$13=5(3)e^{0}+0+c_2e^{0}\\\\13=15+c_2\\\\c_2=-2$

Therefore, the solution of the differential equation is

$y(x)=3e^{5x}-2xe^{5x}$

5 0

3 years ago

Given 6(x) = (x+41, what is b(-10)?

prisoha [69]

The value of $b(-10)$ is 31

Explanation:

The given expression is $b(x)=x+41$

We need to determine the value of $b(-10)$

The value of $b(-10)$ can be determined by substituting $x=-10$ in the expression $b(x)=x+41$

Thus, we have,

$b(-10)=-10+41$

Adding the terms, we have,

$b(-10)=31$

Thus, the value is 31.

Therefore, the simplified value of the expression by substituting $x=-10$ in the expression $b(x)=x+41$ is 31.

7 0

3 years ago

Compare 2 x 10^4 and 8 x 10^3

agasfer [191]

2* 10^4 would be bigger than 8* 10^3.

10^4 = 10000*2=20000
10^3 = 1000*8=8000

8 0

3 years ago

Read 2 more answers

In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rat

monitta

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

$f(t) = 10000(0.9407)^t$

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

$f(t) = f(0)(1-r)^t$

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that $f(0) = 10000$ , thus:

$f(t) = 10000(1-r)^t$

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

$f(2) = 8850$

We use this to find 1 - r.

$f(t) = 10000(1-r)^t$

$8850 = 10000(1-r)^2$

$(1-r)^2 = \frac{8850}{10000}$

$(1-r)^2 = 0.885$

$\sqrt{(1-r)^2} = \sqrt{0.885}$

$1 - r = 0.9407$

Thus

$f(t) = 10000(1-r)^t$

$f(t) = 10000(0.9407)^t$

7 0

3 years ago