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2 years ago

11

2 times the sum of a number and 9 equals 4

1 answer:

ratelena [41]2 years ago

4 0

Answer

Step-by-step explanation:

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It took the carriage 2.5 hours to travel 20 miles. H ow long will it take for the carriage to travel in 12 miles

Tomtit [17]

$\bf \begin{array}{ccll}
hours&miles\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2.5&20\\
h&12
\end{array}\implies \cfrac{2.5}{h}=\cfrac{20}{12}\implies \cfrac{2.5\cdot 12}{20}=h$

6 0

2 years ago

-4x -7 - 3x + 4 = 25

zimovet [89]

Answer:

x=-4

Step-by-step explanation:

-4x -7 - 3x + 4 = 25

-7x=25-4+7

x=-28/7

x=-4

7 0

2 years ago

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What is the area of the figure?

aniked [119]

See attached picture:

7 0

3 years ago

Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was

enyata [817]

50

Step-by-step explanation:

Because at the beginning samuel score was 14 points but when he continue buiding a high-rise-apartment building then his score rose to 36 point, then we add the two together then it give us 50

8 0

2 years ago

Solve the initial value problem y'=2 cos 2x/(3+2y),y(0)=−1 and determine where the solution attains its maximum value.

zloy xaker [14]

Answer:

$y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

$x={\pi}{4}$

Step-by-step explanation:

We are given that

$y'=\frac{2cos2x}{3+2y}$

y(0)=-1

$\frac{dy}{dx}=\frac{2cos2x}{3+2y}$

$(3+2y)dy=2cos2x dx$

Taking integration on both sides then we get

$\int (3+2y)dy=2\int cos 2xdx$

$3y+y^2=sin2x+C$

Using formula

$\int x^n=\frac{x^{n+1}}{n+1}+C$

$\int cosx dx=sinx$

Substitute x=0 and y=-1

$-3+1=sin0+C$

$-2=C$

$sin0=0$

Substitute the value of C

$y^2+3y=sin2x-2$

$y^2+3y-sin 2x+2=0$

$y=\frac{-3\pm\sqrt{(3)^2-4(1)(-sin2x+2)}}{2}$

By using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$y=\frac{-3\pm\sqrt{9+4sin2x-8}}{2}=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

Hence, the solution $y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

When the solution is maximum then y'=0

$\frac{2cos2x}{3+2y}=0$

$2cos2x=0$

$cos2x=0$

$cos2x=cos\frac{\pi}{2}$

$cos\frac{\pi}{2}=0$

$2x=\frac{\pi}{2}$

$x=\frac{\pi}{4}$

3 0

3 years ago