Now measure the lengths of the sides of polygon ABCD and tbe lengths of the sides of the translated images. Record the measurements in the table.

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

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.

For more about logarithm

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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:

- 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

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

Answer:

1/4

Step-by-step explanation:

a^2

Let a= 1/2

(1/2)^2

(1/4)

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{a^2}\\\\\mathsf{= \ (\dfrac{1}{2})^2}\\\\\mathsf{= \ \dfrac{1}{2}\times\dfrac{1}{2}}\\\\\mathsf{= \ \dfrac{1\times1}{2\times2}}\\\\\mathsf{= \ \bf \dfrac{1}{4}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, the ANSWER is: }\boxed{\mathsf{\bf \dfrac{1}{4}}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

x1 y1 x2 y2

-2 -2 0 3

ΔY 5

ΔX 2

slope= 2 1/2

B= 3

Y =2.5X +3

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 (●'◡'●)

Total gasoline = 10 gallons

Gasoline left after 100 miles = 5 gallons

Gasoline used in 100 miles

= Total gasoline - Gasoline left after 100 miles

= 10 gallons - 5 gallons

= 5 gallons

Gasoline used in 1 mile

= Gasoline used in 100 miles/100

= 5 gallons/100

= 0.05 gallons

Answer:

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

Step-by-step explanation:

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:

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°

Answer:

A

Step-by-step explanation:

A compressed by a factor of 1/4 in the y or vertical direction

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:

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:

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:

C) 840

C) 87

D) 3000-150n

Step-by-step explanation:

Answer:

c

c

d

Step-by-step explanation:

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:  13.46 km/h

Step-by-step explanation:

7 1/2 hr= 450 min

6057/450= 13.46

Answer:

14

Step-by-step explanation:

The a value is from the center to the maximum

We want from minimum to max so we need 2 times the amplitude

a = 7

2 *7 = 14

Answer:

8

Step-by-step explanation:

Using the chord chord theorem

10(4) = 5x

Solve for x

Simplify multiplication

40 = 5x

Divide both sides by 5

40/5 = 8

5x/5 = x

We're left with x = 8

Note:

Chord chord theorem states that if two chords intersect then the product of the measures of each part of one chord is equal to the product of the measures of the parts of the other chord.

Because the chords shown intersect the product of the parts of each chord should be equal to each other ( 4 * 10 = 5x )

Source: https://www.dummies.com/education/math/geometry/how-to-use-the-chord-chord-power-theorem

Answer:

a +73°=90°

a= 90°-73°

a =17°

d+18°=90°

d=90°-18°

d =72 °

Answer:

3

Step-by-step explanation:

Answer:

Each week = $ 1311.41

Each fortnight = $ 2622.84

Each month =  $ 5702.5

Step-by-step explanation:

Given that,

Annual salary of Kelly = $ 68,430

As we know,

There are 52.18 weeks in a year.

So,

Weekly income = Annual salary ÷ no. of weeks in the year

= $ 68,430 ÷ 52.18

= $ 1311.42

Fortnight income = 2 * weekly income

= 2 * $ 1311.42

= $ 2622.84

Each month's income = Annual income ÷ 12(no. of months)

= $ 68,430 ÷ 12

= $ 5702.5

Answer:

The 65,000 salary

Step-by-step explanation:

Because the 30,000 salary after 5 years would be 31,500.

30,000+300=30,300

30,300+300=30,600

30,600+300=30,900

30,900+300=31,200

31,200+300=31,500

The 65,000 paying company

65,000x1.05=68,250

68,250x1.05=71.662.5

71,662.5x1.05=75,245.625

75,245.625x1.05=79,007.90625

79,007.90625x1.05=82,958.3015625

her salary after 5 years would be 82,958.3015625

Answer:

9 sides

Step-by-step explanation:

Sum of the measures of the interior angle of a polygon with n sides:

(n - 2)180

Measure of 1 interior angle of a regular polygon of n sides:

(n - 2)180/n

Sum of the measures of the exterior angles of a polygon, one per vertex:

360

Measure of 1 exterior angle of a regular polygon of n sides:

360/n

(n - 2)180/n = 360/n + 100

Multiply both sides by n.

(n - 2)180 = 360 + 100n

Distribute on left side.

180n - 360 = 360 + 100n

Subtract 100n from both sides.

80n - 360 = 360

Add 360 to both sides.

80n = 720

Divide both sides by 80.

n = 9

Answer: 9 sides

Answer:

a)

b)

Answer:

a.) 12 + 5√2 - 2√6

b.) 24

Step-by-step explanation:

a) √25 + √50 - √24 + √49

Calculate the square root .

Simplify the radical expression.

Combine like terms.

b.) √2 ( 2√8 - 3√32 + 4√50 )

Simplify the radical expression.

Evaluate the power.

Calculate the products.

Combine like terms.

Multiply.

Answer:

A.

Step-by-step explanation:

85.9 > 85.31 > 85 > 84.52

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