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3 years ago

Vie

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

Answer:

c. 2

Step-by-step explanation:

the Y- intercept is 2 because it says +2

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If the ratio of the length of a rectangle to its width is 9/4 and its length is 18 cm, what is the width of the rectangle?

Kruka [31]

Answer:

The width is 8

Step-by-step explanation:

if the ratio of length to width is 9 to 4. and we know the length is 18, 18 is 2 times as much as 9, so 4*2=8. 9*2=18,4*2=8

6 0

3 years ago

Read 2 more answers

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

4 years ago

Three times a number minus five equals two times the number.what is the equation

kirill [66]

3x - 5 = 2x is the equation

5 0

3 years ago

259 Students go on a field trip. There are 19 vehicles, some vans and some buses.

Sunny_sXe [5.5K]

Answer:

12 vans

7 Buses

Step-by-step explanation:

I tried multiple versions but I finally got it right.

Since the buses can hold 25 students at a time I multiplied it by 7.

7 x 25 = 175

Then you'll need to find the remainder.

259-175 = 84

This number would be used to find the students going in the van

84/7= 12

So in total there would be 12 vans

and 7 buses

I hope this helps

5 0

3 years ago

Find the circumference of a circle with the diameter of 10 inches. Leave your answers in form of pi

MrRa [10]

Answer:

Circumference = 10π

Step-by-step explanation:

First identify the circumference formula as such:

2πr (where r ⇒ radius, π ⇒ pi)

Knowing 2 times the radius (2r) in the formula can be rewritten as the diameter, the formula itself can be rewritten as:

πd (where d ⇒ diameter, π ⇒ pi)

If we know the diameter = 10 inches, substitute in the circumference formula πd to get:

π * 10 inches = 10 * π inches = 10π inches

4 0

4 years ago