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Ket [755]
2 years ago
7

Solve the system of equations.

Mathematics
1 answer:
postnew [5]2 years ago
4 0

Step-by-step explanation:

y = x² + x + 5

y = x + 1

x² + x + 5 = x + 1

x² + 4 = 0

x² = -4

x = ±√-4 undefined

No solutions

Option → B

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6. Calculate the area of the octagon in the<br> figure below.
Kryger [21]

Answer:

41\text{ [units squared]}

Step-by-step explanation:

The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.

The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:

  • 4 triangles (corners)
  • 3 rectangles (one in the middle, two on top after you remove triangles)

<u>Formulas</u>:

  • Area of rectangle with length l and width w: A=lw
  • Area of triangle with base b and height h: A=\frac{1}{2}bh

<u>Area of triangles</u>:

All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.

Thus, the total area of one is A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}

The area of all four is then 2\cdot 4=8 units squared.

<u>Area of rectangles</u>:

The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of 3\cdot 2=6 units squared, and the both of them have a total area of 6\cdot 2=12 units squared.

The last rectangle has a width of 7 and a height of 3 for a total area of 7\cdot 3=21 units squared.

Therefore, the area of the entire octagon is 8+12+21=\boxed{41\text{ [units squared]}}

4 0
3 years ago
Find the exact value of cos(sin^-1(-5/13))
son4ous [18]

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

8 0
2 years ago
In the accompanying diagram of ABC ca is extended to D, m∠ABC = 70 and m∠BCA =50 Find m∠DAB
zvonat [6]

Answer:

<em>120 degrees</em>

Step-by-step explanation:

Find the diagram attached.

From the diagram;

Interior angles are m∠BCA and m∠ABC

Exterior angle is m∠DAB

The sum of interior angle of the triangle is equal to exterior

m∠BCA +m∠ABC =m∠DAB

Given

m∠ABC = 70

m∠BCA =50

m∠DAB = 70 + 50

m∠DAB = 120 degrees

<em>Hence the measure of m∠DAB is 120 degrees</em>

6 0
3 years ago
Work out (3.6 x 10^-5) ÷ (1.8 x 10^2) give your answer in standard form
tatuchka [14]

.000036/180=.0000002

3 0
3 years ago
If AB = 4 centimeters, which is closest to BC?
Misha Larkins [42]

Answer:

The correct answer AC = 11.52

Step-by-step explanation:

From the figure attached with this answer shows the triangle ABC.

BC=4 centimeters, m angle B=m angle c, and m angle a = 20 degrees

To find AC

From the figure we can see that D is the mid point and AD⊥BC

Then BD = CD = 4/2 = 2 cm

<BAD = 10° and <CAD = 10°

By using trigonometric ratio,

sin 10 = CD/AC = 2/AC

AC = 2/sin 10 = 2/0.1736 = 11.52

Therefore the value of AC = 11.52 cm

4 0
3 years ago
Read 2 more answers
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