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dem82 [27]
3 years ago
8

How to work out an angle using cosine. three sides are; 8,19,12.

Mathematics
1 answer:
Kay [80]3 years ago
7 0
To solve for cos use 
adjacent over hypotenuse 
divide the lengths of the sides 
adj. / hyp.

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Hi I need help with the question in the image. Step by step, thank you!
VashaNatasha [74]

The exponential function is f(x) = 18(12)^{-x-4} + 2

<h3>How to determine the equation?</h3>

An exponential function is represented as:

y = b^x

Where b represents the base.

The base is given as:

b = 12

So, we have:

y = (12)^x

It is vertically compressed by a factor of 1/8.

So, we have:

y = 18(12)^x

When reflected across the y-axis, we have:

y = 18(12)^{-x}

The horizontal asymptote is y = 2.

So, we have:

y = 18(12)^{-x} + 2

It passes through the point (-3, 4).

So, we shift the function to the right by 4 units

y = 18(12)^{-x-4} + 2

Express as a function

f(x) = 18(12)^{-x-4} + 2

Hence, the exponential function is f(x) = 18(12)^{-x-4} + 2

Read more about exponential functions at:

brainly.com/question/14355665

#SPJ1

6 0
2 years ago
A rectangular area of 36 f t2 is to be fenced off. Three sides will use fencing costing $1 per foot and the remaining side will
OLga [1]

Answer:

x = 8,49 ft

y  = 4,24  ft  

Step-by-step explanation:

Let  x be the longer side of rectangle   and  y  the shorter

Area of rectangle     =    36 ft²     36  =  x* y   ⇒ y =36/x

Perimeter of rectangle:

P  =  2x   +   2y    for convinience we will write it as    P  = ( 2x + y ) + y

C(x,y)   =  1 * ( 2x  +  y  )  +  3* y

The cost equation as function of x is:

C(x)  =  2x  + 36/x   + 108/x

C(x)  =  2x  + 144/x

Taking derivatives on both sides of the equation

C´(x)  = 2  - 144/x²

C´(x)  = 0         2  - 144/x² = 0       ⇒  2x²  -144 = 0    ⇒  x² =  72

x = 8,49 ft       y  = 36/8.49    y  = 4,24  ft    

How can we be sure that value will give us a minimun

We get second derivative

C´(x)  = 2  - 144/x²      ⇒C´´(x)  = 2x (144)/ x⁴

so C´´(x) > 0

condition for a minimum

7 0
3 years ago
Simplify 2x – 9y + 4x + 11y by combining like terms and then evaluate at x = -2<br> and y = 4.
Mashcka [7]

Step-by-step explanation:

= 2x - 9y + 4x + 11y

First of all combining like terms

So

= 2x + 4x - 9y + 11y

= 6x + 2y

Now putting values

= 6 (-2) + 2(4)

= - 12 + 8

= - 4

7 0
3 years ago
Instructions:Select the correct answer from each drop-down menu. ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has
Akimi4 [234]

to compare the triangles, first we will determine the distances of each side

<span>Distance = ((x2-x1)^2+(y2-y1)^2)^0.5
</span>Solving 

<span>∆ABC  A(11, 6), B(5, 6), and C(5, 17)</span>

<span>AB = 6 units   BC = 11 units AC = 12.53 units
</span><span>∆XYZ  X(-10, 5), Y(-12, -2), and Z(-4, 15)
</span><span>XY = 7.14 units   YZ = 18.79 units XZ = 11.66 units</span>

<span>∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).</span>

<span>MN = 6 units   NO = 11 units MO = 12.53 units
</span><span>∆JKL  J(17, -2), K(12, -2), and L(12, 7).
</span><span>JK = 5 units   KL = 9 units JL = 10.30 units
</span><span>∆PQR  P(12, 3), Q(12, -2), and R(3, -2)
</span><span>PQ = 5 units   QR = 9 units PR = 10.30 units</span> 
Therefore
<span>we have the <span>∆ABC   and the </span><span>∆MNO  </span><span> 
with all three sides equal</span> ---------> are congruent  
</span><span>we have the <span>∆JKL  </span>and the <span>∆PQR 
</span>with all three sides equal ---------> are congruent  </span>

 let's check

 Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).

 1)     If ∆MNO   ---- by a sequence of reflections and translation --- It can be obtained ------->∆ABC 

<span> then </span>∆MNO<span> ≅</span> <span>∆ABC  </span> 

 a)      Reflexion (x axis)

The coordinate notation for the Reflexion is (x,y)---- >(x,-y)

<span>∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).</span>

<span>M(-9, -4)----------------->  M1(-9,4)</span>

N(-3, -4)------------------ > N1(-3,4)

O(-3,-15)----------------- > O1(-3,15)

 b)      Reflexion (y axis)

The coordinate notation for the Reflexion is (x,y)---- >(-x,y)

<span>∆M1N1O1  M1(-9, 4), N1(-3, 4), and O1(-3, 15).</span>

<span>M1(-9, -4)----------------->  M2(9,4)</span>

N1(-3, -4)------------------ > N2(3,4)

O1(-3,-15)----------------- > O2(3,15)

 c)   Translation

The coordinate notation for the Translation is (x,y)---- >(x+2,y+2)

<span>∆M2N2O2  M2(9,4), N2(3,4), and O2(3, 15).</span>

<span>M2(9, 4)----------------->  M3(11,6)=A</span>

N2(3,4)------------------ > N3(5,6)=B

O2(3,15)----------------- > O3(5,17)=C

<span>∆ABC  A(11, 6), B(5, 6), and C(5, 17)</span>

 ∆MNO  reflection------- >  ∆M1N1O1  reflection---- > ∆M2N2O2  translation -- --> ∆M3N3O3 

 The ∆M3N3O3=∆ABC 

<span>Therefore ∆MNO ≅ <span>∆ABC   - > </span>check list</span>

 2)     If ∆JKL  -- by a sequence of rotation and translation--- It can be obtained ----->∆PQR 

<span> then </span>∆JKL ≅ <span>∆PQR  </span> 

 d)     Rotation 90 degree anticlockwise

The coordinate notation for the Rotation is (x,y)---- >(-y, x)

<span>∆JKL  J(17, -2), K(12, -2), and L(12, 7).</span>

<span>J(17, -2)----------------->  J1(2,17)</span>

K(12, -2)------------------ > K1(2,12)

L(12,7)----------------- > L1(-7,12)

 e)      translation

The coordinate notation for the translation is (x,y)---- >(x+10,y-14)

<span>∆J1K1L1  J1(2, 17), K1(2, 12), and L1(-7, 12).</span>

<span>J1(2, 17)----------------->  J2(12,3)=P</span>

K1(2, 12)------------------ > K2(12,-2)=Q

L1(-7, 12)----------------- > L2(3,-2)=R

 ∆PQR  P(12, 3), Q(12, -2), and R(3, -2)

 ∆JKL  rotation------- >  ∆J1K1L1  translation -- --> ∆J2K2L2=∆PQR 

<span>Therefore ∆JKL ≅ <span>∆PQR   - > </span><span>check list</span></span>
6 0
3 years ago
Ava,Carter,Luke and their dad each mow a different section of their yard.Ava mow 1 /12 of the yard, Carter mow 2 /12 of the yard
lubasha [3.4K]
His dad mowed 5/12 of the yard
4 0
3 years ago
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