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kow [346]
1 year ago
15

HELP! WILL GIVE BRAINLEST

Mathematics
2 answers:
trasher [3.6K]1 year ago
7 0

Answer:

Option C: 41

Step-by-step explanation:

<ABD+<CBD=90

<ABD=8x+1

<CBD=6x+5

(8x+1)+(6x+5)=90

Combine like terms

(8x+6x)+(1+5)=90

14x+6=90

14x=90-6

14x=84

divide both sides by 14

x=6

Now we plug that value into <DBC = 6x+5

6(6)+5=

36+5

41

Dennis_Churaev [7]1 year ago
3 0

<u>Let's take this problem step by step</u>:

<u>∠ABC is 90 degrees</u>

 ⇒ made up of two angles ⇒ <em>∠ABD and ∠DBC</em>

     ⇒<em> in mathematical equation form:</em>

<em>             </em>ABD + DBC= ABC

<u>Since </u><u><em>∠ABD = 8x + 1 </em></u><u>and </u><u><em>∠DBC = 6x+5</em></u>

<em>     </em>8x + 1+6x + 5=90\\14x+6=90\\14x=84\\x=6

<u>Let's plug it into </u><u><em>∠DBC = 6x+5</em></u>

  ∠DBC = 6x+5 = 6(6)+5=41

<u>Answer: ∠DBC = 41</u>

<u></u>

Hope that helps!

#LearnwithBrainly

   

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A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes
Alenkinab [10]

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The area to be planted with flowers is approximately <u>923.558 m²</u>

The reason the above value is correct is as follows;

The known parameters of the garden are;

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The area of an heptagon, is;

A = \dfrac{7}{4} \cdot a^2 \cdot  cot \left (\dfrac{180 ^{\circ}}{7} \right )

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The length of a side, S, is given as follows;

\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}

s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69

The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52

The area of the heptagon MNSRQPO is therefore;

A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94

MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times  21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08

By sine rule, we have

\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}

sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})

\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

Area \ of \Delta MSQ = \dfrac{1}{2}  \times  43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}

The area of the of the garden plated with flowers, A_{req}, is given as follows;

A_{req} = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

A_{req}= 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, A_{req} ≈ <u>923.558 m²</u>

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<h3>What is a quadratic function?</h3>

A function of the form f(x)=ax^{2} +bx+c with a\neq 0 is called a quadratic function means the highest exponent of polynomial should be 2.

Let us check one by one.

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The function is also of form f(x)=ax^{2} +bx+c so u(x) is a quadratic function.

The functions v(x), y(x), and z(x) are having highest exponents as 3,5, and 3 respectively so they are not quadratic functions.

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