Simplify -6
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8
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The given triangles ΔDOA and ΔABC are right triangles that have a

common vertex at point A.

Reasons:

The given parameters are;

The diameter of the circle with center O = AB

DO ⊥ AB (DO is perpendicular to AB)

Required:

Prove that ∠AEC = ∠ODA

A two column proof is presented as follows;

Statement [tex]{}[/tex]                                                 Reason

1. AB is the diameter of circle     [tex]{}[/tex]                 1. Given

2. DO is perpendicular to AB [tex]{}[/tex]                     2. Given

3. ∠DOA = 90° [tex]{}[/tex]                                             3. Definition of DO ⊥ AB

4. ∠BCA = 90°   [tex]{}[/tex]                                             4. Thales theorem

5. ∠BCA ≅ ∠BCA [tex]{}[/tex]                                         5. Reflexive property

6. ΔDOA ~ ΔABC   [tex]{}[/tex]                                        6. AA similarity postulate

7. ∠ABC ≅ ∠ODA   [tex]{}[/tex]                                       7. CASTC

8. ∠ABC = ∠ODA   [tex]{}[/tex]                                        8. Definition of congruency

9. ∠AEC ≅ ∠ABC   [tex]{}[/tex]                                        9. Angles in the same segment

10. ∠AEC = ∠ABC   [tex]{}[/tex]                                       10. Definition of congruency

11. ∠AEC = ∠ODA   [tex]{}[/tex]                                        11. Transitive property of equality

In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity

postulate, therefore, the three angles of ΔDOA are congruent to the three

angles of ΔABC.

Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles

are Congruent, CASTC.

Learn more about circle theorem here:

https://brainly.com/question/16879446

Answer:

24 packages

Step-by-step explanation:

One dozen is 12, so 4 x 12 = 24

Answer:

Step-by-step explanation:

Answer:

  (17.5√2 miles west, 17.5√2 miles north)

Step-by-step explanation:

The distance in the west direction will be ...

  35cos(45°) = 17.5√2 . . . . miles west

The distance in the north direction will be ...

  35sin(45°) = 17.5√2 . . . . miles north

The vector components are ...

  (17.5√2 miles west, 17.5√2 miles north)

_____

Additional comment

When a map with the usual "north is up" orientation is overlaid on an x-y coordinate grid, the (x, y) ordered pair directions correspond to (east, north). Using that coordinate meaning for the vector components here, they would be ...

  (-24.7, 24.7) miles

Answer:

151.5 cm = 1.515 m

151.5 cm = 1515/1000 m

Answer:

1125.

Step-by-step explanation:

I'm going to work out the answer is grams.

1kg = 1000g

0.225kg of butter = 225g, 225g of sugar, 225g of flour, 0.2kg of eggs = 200g, 250g of berries.

225 + 225 + 225 + 200 +250 = 1125.

Hope that helps. x

Answer:

1.125kg or 1125g

Step-by-step explanation:

1kg: 1000g

Butter: 0.225kg or 225g

Sugar: 225g or 0.225kg

Flour: 225g or 0.225kg

Eggs: 0.2kg or 200g

Berries: 250g or 0.25kg

In kg: 0.225 + 0.225 + 0.225 + 0.2 + 0.25 = 1.125

In g: 225 + 225 + 225 + 200 + 250 = 1125

Answer:

.....

Step-by-step explanation:

merry Christmas to you too

[tex](1-\sin^2 x) \tan x \\\\=\cos^2 x \cdot \dfrac{\sin x}{\cos x}\\\\=\cos x \sin x[/tex]

Answer:

Here's one possible solution

Step-by-step explanation:

Double the number and subtract the corresponding value from the sequence

0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5...

        1 + 1 - 0 = 2

      2 + 2 - 0 = 4

       4 + 4 - 1 = 7

       7 + 7 - 1 = 13

   13 + 13 - 2 = 24

 24 + 24 - 2 = 46      ←←←

 46 + 46 - 3 = 89

 89 + 89 - 3 = 175

175 + 175 - 4 = 346

[tex]\text{Given that,}\\\\\\f(x) = \ln(x^4 +e^{2x})\\\\\\f'(x) = \dfrac{1}{x^4 + e^{2x}} \left(4x^3+2e^{2x}\right) = \dfrac{2(2x^3+e^{2x})}{x^4 + e^{2x}}~~~~;[\text{Chain rule}]\\\\\\\text{Note:}\\\\\dfrac{d}{dx} \ln x = \dfrac 1x\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} e^{mx} = m e^{mx}[/tex]

After solving the given equation, the value obtained is equal to [tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex].

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given data in the question,

f(x) = ln (x⁴ + e²ˣ)

[tex]f'(x)=\frac{1}{x^4+e^2^x}(4x^3+2e^2^x)[/tex]

Now, use the chain rule,

[tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex]

Also, note some points,

d/dx ln (x) = 1/x

[tex]\frac{d}{dx}x^n=nx^n^-^1[/tex]

To know more about Expression:

https://brainly.com/question/14083225

#SPJ2

[tex]\mathfrak{ x ^ { 2 } + b x - 4 = 0} [/tex]

[tex]\mathfrak{bx-4=-x^{2} } [/tex]

[tex]\mathfrak{bx=-x^{2}+4 } [/tex]

[tex]\mathfrak{xb=4-x^{2} } [/tex]

[tex]\mathfrak{\frac{xb}{x}=\frac{4-x^{2}}{x} } [/tex]

[tex]\mathfrak{ b=\frac{4-x^{2}}{x} } [/tex]

[tex]\mathfrak{b=-x+\frac{4}{x} } [/tex]

AnSwEr

[tex]\boxed{\mathfrak{b=-x+\frac{4}{x},x\neq 0 } }[/tex]

 ღ ꪑ꠸᥅ꫀꪊ

Mathew decided to have a picnic with his 4 friends. They were each assigned to bring 10 different foods. The food were to be brought in 15 bags total. How much food are there in each bag in total?

Answer: -1 = (-3/3)

Step-by-step explanation

You go from one point to another, i started from 3,1 and went to 3,0. I got down -3 which is my rise and right 3 for the run. Tell me if this is correct

Answer:

The domain corresponds to the values of the x and the range to the values of the y. So:

D: {-3, 0, 3}

R: {-6, 0, 6}

Answer:

[tex]\huge\boxed{A.}[/tex]

Step-by-step explanation:

Domain:

"Set of values on x-axis"

Domain = {-3,0,3}

Range:

"Set of values on y-axis"

Range = {-6,0,6}

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

6x sec2 (x2+5) the number to are in the top of x a c.

Answer:

x=-1±[65]

________

8

Step-by-step explanation:

solve the equation for xby finding a,b, and come of the quadratic then applying the quadratic formula

Answer:

5.96 x 36 = 214.56.

286.08 - 214.56 = 71.52

71.52 divided by 8.94 = 8.

He worked 8 additional hours.

Answer:

The worker worked about 8 hours overtime.

Step-by-step

First we figure out how much they made without overtime.

Multiply 5.96 x 36 and you would get 214.56

Then we figure out how many hours he worked overtime

Multiply 8.94 times 8 and you would get 71.52

Then take 214.56 and add 71.52, you would get 286.08, the answer is 8 hours overtime.

Answer:

.6 miles

Step-by-step explanation:

Answer:

0.6 miles

Step-by-step explanation:

6 × t = 4 × (15 - t)

6t = 60 - 4t

6t + 4t = 60 - 4t + 4t

10t = 60

t = 6

6 × [tex]\frac{1}{10}[/tex] = 0.6

Answer:

Between 400$ and 500$

Step-by-step explanation:

Draw a straight line that follows the scatterplot - either by guesstimating (best choice) or by applying any known method to extrapolate a line. Then it's just a matter of reading the y value corresponding to that x. Hardly a perfect image, but close enough since it's a prediction

Answer:

  82/63

Step-by-step explanation:

The sum can be found using the formula ...

  [tex]\dfrac{a}{b}+\dfrac{c}{d} =\dfrac{ad+bc}{bd}[/tex]

For the given fractions, the sum is ...

  [tex]\dfrac{6}{7}+\dfrac{4}{9} =\dfrac{6\cdot9+7\cdot4}{7\cdot9}=\dfrac{54+28}{63}=\boxed{\dfrac{82}{63}}[/tex]

_____

Additional comment

When the denominators have no common factor, the least common denominator is their product, as here.

Answer:

For this question, you can make the denominators the same to get the answer.

LCM of 7 and 9 = 63

[tex]\frac{6}{7} + \frac{4}{9} = \frac{54}{63} + \frac{28}{63} \\[/tex]

         = [tex]\frac{82}{63}[/tex]

         = 1[tex]\frac{19}{63}[/tex]

Answer:

  lim = 1/6

Step-by-step explanation:

Apparently, we have ...

  [tex]g(t)=\sqrt{t+7}[/tex]

It often works well to multiply by the conjugate of a difference that approaches zero.

  [tex]\displaystyle\lim_{h\to 0}{\frac{g(2+h)-g(2)}{h}}=\lim_{h\to 0}{\frac{\sqrt{(2+h)+7}-\sqrt{2+7}}{h}}\\\\=\lim_{h\to 0}\frac{(\sqrt{9+h}-\sqrt{9})(\sqrt{9+h}+\sqrt{9})}{h(\sqrt{9+h}+\sqrt{9})}=\lim_{h\to 0}{\frac{(9+h)-9}{h(\sqrt{9+h}+\sqrt{9})}}\\\\=\lim_{h\to0}{\frac{h}{h(\sqrt{9+h}+3)}}=\left.\frac{1}{\sqrt{9+h}+3}\right|_{h=0}=\boxed{\frac{1}{6}}[/tex]

Answer:

  length: 62 ft

  width: 31 ft

Step-by-step explanation:

Let w represent the width. Then the length is 2w and the perimeter is ...

  P = 2(L+W)

  186 = 2(2w +w)

  31 = w . . . . . . . . . divide by 6

  2w = 2(31) = 62

The length of the shed is 62 feet; its width is 31 feet.

Answer:

C

Step-by-step explanation:

There isnt rly a lot of information from this question but my best guess would be C.  It says "1 drop in each eye bid every 10 days", so assuming that 1 drop equals 1 ml and knowing we have to do it in "each eye bid" we could assume 2ml of eye drops would be used every 10 days.

Sorry if im wrong but i hope this helps have a great day and happy holidays (｢•-•)｢

Answer:

48.1

Step-by-step explanation:

Seven rounds up.

Hope this helped! :)

Answer:

This is not a linear function, as it isn't any function because 3 has two outputs.

Step-by-step explanation:

Explained above

x = 27

Step-by-step explanation:

The two angles shown are called co-exterior angles and by definition, their sum is equal to 180° so we can write

[tex](3x - 3) + (4x - 6) = 180[/tex]

[tex]\Rightarrow 7x - 9 = 180[/tex]

Simplifying this further, we get

[tex]7x = 189 \Rightarrow x = 27[/tex]

Answer:

new equation : 1.09t = new price

Step-by-step explanation:

1.09(15.99) = 17.4291

it's about $17