Review the data you collected for the angles in Question 2. Notice that ∠CFB is one of four angles formed by the two intersecting chords. What relationship do you observe that could help you determine the measure of any of the four angles created by two intersecting chords? Write the relationship as an equation.

The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given the equation

[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2

We know that,

xlogb = log[tex]b^{x}[/tex]

So,

2[tex]log_{8}[/tex](x) = logx²

For the same base

logA + logB = log(AB)

So,

[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2

[tex]log_{8}[/tex](16x²) = 2

We know that

[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]

so,

[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²

x = 2 hence x = 2 will be correct answer.

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Answer:

[tex]\tan x=21/20[/tex]

Step-by-step explanation:

In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)

For angle [tex]x[/tex], its opposite side is 21 feet and its adjacent side is 20 feet. Therefore, we have:

[tex]\boxed{\tan x=21/20}[/tex]

Answer:

Step-by-step explanation:

The easiest way to do this is to complete the square on the quadratic. This allows us to see what the vertex is and answer the question without having to plug in a ton of numbers to see what the max y value is. Completing the square will naturally put the equation into vertex form:

[tex]y=-a(x-h)^2+k[/tex] where h will be the time it takes to get to a height of k.

Begin by setting the quadratic equal to 0 and then moving over the constant, like this:

[tex]-4.9t^2+19.6t=-58.8[/tex] and the rule is that the leading coefficient has to be a 1. Ours is a -4.9 so we have to factor it out:

[tex]-4.9(t^2-4t)=-58.8[/tex] Now take half the linear term, square it, and add it to both sides. Our linear term is a -4, from -4t. Half of -4 is -2, and -2 squared is 4, so we add a 4 to both sides. BUT on the left we have that -4.9 out front there as a multiplier, so we ACTUALLY added on to the left was -4.9(4) which is -19.6:

[tex]-4.9(t^2-4t+4)=-58.8-19.6[/tex] and now we have to clean this up. The right side is easy, that is -78.4. The left side...not so much.

The reason we complete the square is to create a perfect square binomial, which is the [tex](x-h)^2[/tex] part from above. Completing the square does this naturally, now it's just up to us to write the binomial created during the process:

[tex]-4.9(t-2)^2=-78.4[/tex] Now, move the constant back over and set the equation back equal to y:

[tex]-4.9(t-2)^2+78.4=s(t)[/tex] and we see that the vertex is (2, 78.4). That means that 2 seconds after launch, the object reached its max height of 78.4 meters, the third choice down.

Answer:

42.78⁹, 137.22⁹.

Step-by-step explanation:

sine Ф=0.6792

Angle Ф in the first quadrant = 42.78 degrees.

The sine is also positive in the second quadrant so the second solutio is

180 - 42.78

= 137.33 degres.

Answer:

Choice C.

[tex]y + 1 = - 2(x - 2)[/tex]

Step-by-step explanation:

When converting to

[tex]y = mx + b[/tex]

We are left with:

[tex]y = - 2x + 3[/tex]

Which fits both the x-intercept and y-intercept.

Answer:

29

Step-by-step explanation:

all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151

then 180-151=29

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]

Answer:

[tex]8\sqrt{5}[/tex]

Step-by-step explanation:

[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]

 [tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]

[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]

[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]

            [tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

Answer:

- 22.5

Step-by-step explanation:

Substitute x = 3 into f(x) and x = 16 into h(x) , then

[tex]\frac{1}{2}[/tex] g(3) - h(16)

= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)

= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)

= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)

= - 13.5 - 9

= - 22.5

Answer:

m<EFG = 72°

m<GFH = 108°

Step-by-step explanation:

m<EFG = 2n + 16

m<GFH = 3n + 24

Linear pairs are supplementary, therefore,

m<EFG + m<GFH = 180°

Substitute

2n + 16 + 3n + 24 = 180

Add like terms

5n + 40 = 180

5n + 40 - 40 = 180 - 40 (subtraction property of equality)

5n = 140

5n/5 = 140/5 (division property of equality)

n = 28

✔️m<EFG = 2n + 16

Plug in the value of n

m<EFG = 2(28) + 16 = 72°

✔️m<GFH = 3n + 24

Plug in the value of n

m<GFH = 3(28) + 24 = 108°

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

(x-h)^2 + (y-k)^2 = r^2

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

Answer:

-3/5

Step-by-step explanation:

Pythagorean formula :

x^2 + y^2 = r^2

(-8)^2 + (-6)^2 = r^2

64 + 36 = 100

r^2 = 100

r= 10

sin is the y coordinate over the radius :

-6/10

-3/5

Answer:

72√2

Step-by-step explanation:

3√2 × 2√8 × √3 × √6

The above can be simplified as follow:

3√2 × 2√8 × √3 × √6

Recall

a√c × b√d = (a×b)√(c×d)

3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)

= 6√288

Recall

288 = 144 × 2

6√288 = 6√(144 × 2)

Recall

√(a×b) = √a × √b

6√(144 × 2) = 6 × √144 × √2

= 6 × 12 × √2

= 72√2

Therefore,

3√2 × 2√8 × √3 × √6 = 72√2

Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]

Divide through by 2

[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]

Complete the square by adding the square of the half of the coefficient of x to both sides:

[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]

[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]

Take the square root of both sides

[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]

Hence the value of x is 6.58m

Answer:

write question in short form

Step-by-step explanation:

Answer:

m∠DAB+m∠ADC=180

115+ 29 + m∠ADB=180

m∠ADB=180 - 115 -29

= 36°

Answer:

a(y_2)_b(y_2) =a_b)(y_2(

Answer:

19: 5

Step-by-step explanation:

Total fruit  is 5+10+4 = 19

fruit: pears

19: 5

Answer:

19:5

Step-by-step explanation:

5+10+4= 19

Pears= 5

Answer:

c = 21

Step-by-step explanation:

**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**

If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.

PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.

With that in mind, we can apply this ratio to find WX.

We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.

c = 21

Hope this helps (●'◡'●)

For sinø = cosø, ø = 45°. Because it is right, it is also a right, isosceles  triangle

Answer:  13.46 km/h

Step-by-step explanation:

7 1/2 hr= 450 min

6057/450= 13.46

Answer:

7 slices

Step-by-step explanation:

1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.

Answer:

5, 12, 19, 26, 33

Step-by-step explanation:

Using the recursive rule and a₁ = 5 , then

a₂ = a₁ + 7 = 5 + 7 = 12

a₃ = a₂ + 7 = 12 + 7 = 19

a₄ = a₃ + 7 = 19 + 7 = 26

a₅ = a₄ + 7 = 26 + 7 = 33

The first 5 terms are 5, 12, 19, 26, 33

Answer:

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.

Step-by-step explanation:

Answer:

The line of reflection in [tex]y=mx+b[/tex] form is [tex]y=\frac{1}{3} x-2[/tex]

Step-by-step explanation:

Answer:

C) 840

C) 87

D) 3000-150n

Step-by-step explanation:

Answer:

c

c

d

Step-by-step explanation:

Answer:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

We used the information we know to give us this equation.

90°+60°+x=180°

We add 90° and 60° to give 150°

150°+x=180°