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3 years ago

What is the solution of (2X+94) = (8x+10)

Mathematics

2 answers:

egoroff_w [7]3 years ago

4 0

94=6x+10
6x=84
X=14 <---ANSWER

elena-14-01-66 [18.8K]3 years ago

3 0

2x+94=8x+10
Subtract 8x on both sides
-6x+94=10
Subtract 94 on both sides
-6x=-84
Divide by -6 on both sides
x=14

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heather has divided $6300 between two invesments, one paying 9%, the other paying 4%. If the return on her investment is $372, h

Ganezh [65]

Assuming that the two investments are X & Y
X + Y = 6300
X = 6300 - Y (1)

9/100X + 4/100 Y = 372 (2)
replacing X from (1) into (2)
9/100(6300-Y) + 4/100 Y = 372
567 - 9/100Y +4/100Y = 372
(-9+4)/100Y = 372 - 567
5/100Y = -195
Y = 100*195/5 = 3900
From (1) we can get X
X = 6300 - 3900 = 2400

I hope this is helpful

6 0

3 years ago

Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

8 0

3 years ago

Read 2 more answers

Jim had some dimes, quarters, and nickels. First, he counted only the dimes and quarters and found that he had 9 coins. Then, he

Olegator [25]

Answer:

$1.90

Step-by-step explanation:

Represent the numbers of nickels, dimes and quarters by n, d and q.

Then: d + q = 9, or q = 9 - d.

Also, n + d = 10

Lastly, n + d + q = 15.

Let's substitute 9 - d for q in the equation immediately above:

n + d + (9 - d) = 15, or n + 9 = 15. Then n must be 6.

In summary, Jim has 6 nickels, (10 - 6) dimes and (9 - 4) quarters, or:

6 nickels, 4 dimes and 5 quarters

Thus, he has 5($0.05) + 4($0.10) + 5($0.25), or

$0.25 + $0.40 + $1.25, or $1.90

7 0

3 years ago

3y-x=3 and x is four times the value of y what is the value of x-y?

Aleonysh [2.5K]

Answer:

x - y = -9

Step-by-step explanation:

from the equation

3y - x = 3

and x is four times the value of y

i.e x = 4y

put x = 4y into the first equation

we have;

3y - 4Y = 3

-Y = 3

Divide both sides by -1

we have

y = -3

so put y = -3 in the 2nd equation

i.e x = 4y

x = 4 × -3

x = -12

therefore x = -12 and y = -3

so tho find x - y

we have

-12 - (-3)

= -9

therefore x - y = -9

7 0

3 years ago

If the image of a triangle is congruent to the pre-image, what is the scale factor of the dilation

Evgen [1.6K]

Answer:

Step-by-step explanation:

Scale factor is 1 because the triangle and image are congruent ( same shape and size).

3 0

3 years ago