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3 years ago

Don’t know what do -7>20+c

Mathematics

1 answer:

tankabanditka [31]3 years ago

7 0

Answer:

c < -27

Step-by-step explanation:

-7>20+c

Subtract 20 from both sides

-7 - 20 > 20 + c -20

Simplifying

-27 > c

c < -27

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Triangle ABC was dilated around the origin by a scale factor of 2. The

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8,4

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2 years ago

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Each unit on the map represents 5 miles. If you drive 20% of the way from Landview to Seaside, how many miles have you driven, a

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We use the distance formula for this problem.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The distance between point (-2,-2) and point (-2,4).
d = √[(⁻2 - ⁻2)² + (4 - ⁻2)²] = 6 units

Then, compute for 20% of 6 units:
Distance traveled = 6(0.2) = 1.2 units

Use 1.2 units as distance and the starting point (-2,-2). The x-coordinate should still be at -2 because the distance is a straight line as shown in the picture.
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y = -0.8

The point is found at (-2,-0.8). This is located at quadrant 3. As to the distance traveled, that would be: 1.2*6 = 6 miles. Thus, the answer is C.

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2 years ago

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

WARRIOR [948]

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

3 years ago

A \greenD{7\,\text{cm} \times 5\,\text{cm}}7cm×5cmstart color #1fab54, 7, start text, c, m, end text, times, 5, start text, c, m

erma4kov [3.2K]

Answer:

The area of the shaded region is 148.04 cm².

Step-by-step explanation:

It is provided that a 7 cm × 5 cm rectangle is inside a circle with radius 6 cm.

The sides of the rectangle are:

l = 7 cm

b = 6 cm.

The radius of the circle is, r = 6 cm.

Compute the area of the shaded region as follows:

Area of the shaded region = Area of rectangle - Area of circle

$=[\text{l}\times\text{b}]-[\pi\test{r}^{2}]\\\\=[7\times5]+[3.14\times 6\times 6]\\\\=35+113.04\\\\=148.04$

Thus, the area of the shaded region is 148.04 cm².

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3 years ago

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The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

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2 years ago

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