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galina1969 [7]
3 years ago
10

____________________

Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

Answer:

top one im pretty sure

Step-by-step explanation:

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Does dose anyone know how to solve this?
solniwko [45]

Answer:

Width of rectangle = 6 m

Length of rectangle = 11 m

Step-by-step explanation:

Let width of rectangle = w

Length of rectangle = 3w-7

Area of rectangle = 66 m²

We need to find length and width of rectangle

The formula used is: Area=Length \times Width

Putting values and finding w

Area=Length \times Width\\66=(3w-7)(w)\\66=3w^2-7w\\3w^2-7w-66=0\\

Solve using quadratic formula: w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

We have a=3, b=-7, c=-66

Putting values and finding w

w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-(-7)\pm\sqrt{(7)^2-4(3)(-66)}}{2(3)}\\w=\frac{7\pm\sqrt{49+792}}{6}\\w=\frac{7\pm\sqrt{841}}{6}\\w=\frac{7\pm29}{6}\\w=\frac{7+29}{6}\:,\:w=\frac{7-29}{6}\\w=6, w=-3.6

We get values of w as w=6 and w=-3.6

As we know width cannot be negative, so considering w = 6

So, Width = 6

Length = 3w-7 = 3(6)-7 = 18-7 = 11

So, Width of rectangle = 6 m

Length of rectangle = 11 m

6 0
2 years ago
Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
Read 2 more answers
What is the solution set? ​ −5x−6.5>12
Vesna [10]

-5x-6.5>12

Add 6.5 to both sides...

-5x>18.5

Divide both sides by -5 and flip the sign...

x<-3.7

8 0
3 years ago
Read 2 more answers
Two trains started moving at the same time, train A from Boston to New York, and train B from New York to Boston. The distance b
Ede4ka [16]

Answer:

  • <u>After 1.7 hours</u>

Explanation:

<u>1. Calculate the average speed of train B</u>

  • 60mph = 3/4 (s) ⇒ s = 60 (4/3) mph = 80 mph

<u>2. Build a table</u>

When the two trains meet:

Train     Average speed     Distance       time (distance/average speed)

                 mph                            

A                 60                             x                        x/60

B                 80                        240 - x                (240 - x) / 80

<u>3. Write the equation</u>

The time, when the two trains meet, is the same for both trains:

                  \dfrac{x}{60}=\dfrac{240-x}{80}\\ \\ \\ 80x=14,400-60x\\ \\ 80x+60x=14,400\\ \\ 140x=14,400\\ \\ x=14,400/140\\ \\ x=102.85miles

<u>4. Calculate the time:</u>

  • x/60 = 102.86 / 60 = 1.7 hours

The two trains will meet after 1.7 hours

7 0
2 years ago
it was found that out of 45 girls,10 joined singing but not dancing and 24 joined singing.How many joined both. options: A: 21 B
katrin [286]

Answer:

answer is 24

out of 45,

24+10=singing

only 24=dancing

so 24 girls joined both

3 0
3 years ago
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