P is a point inside a rectangle ABCD, where PA = 3, PC = 7 and PD = 6. Find PB.

Answer:

The length of the arc is [tex]\frac{5\pi}{3}[/tex] centimeters.

Step-by-step explanation:

The length of an arc ([tex]\Delta s[/tex]) with a given central angle is determined by the following expression:

[tex]\Delta s = \frac{\theta}{360^{\circ}}\cdot 2\pi\cdot r[/tex]

Where:

[tex]r[/tex] - Radius, measured in centimeters.

[tex]\theta[/tex] - Central angle, measured in sexagesimal degrees.

Given that [tex]r = 5\,cm[/tex] and [tex]\theta = 60^{\circ}[/tex], then:

[tex]\Delta s = \frac{60^{\circ}}{360^{\circ}} \times 2\pi \times 5\,cm[/tex]

[tex]\Delta s = \frac{5\pi}{3}\,cm[/tex]

The length of the arc is [tex]\frac{5\pi}{3}[/tex] centimeters.

Answer:

The answer is 3

Step-by-step explanation:

5.424 ≈ 5.420

5.424

↓4 = Tenth

   ↓2 = Hundredth

      ↓4 = Thousandth

The value of number after rounded to the nearest hundredth is, 5.42

In rounding a number into the nearest hundredth,

We look at the tenths place digit, If tenths place digit is 0, 1, 2, 3 or 4,

Then the number rounded to previous hundredth,

While, if the tenths place digit is 5, 6, 7, 8 or 9,

Then the number is rounded to next hundredth,

Here, the given number is,

⇒ 5.424

Here, Tenths place digit = 2,

Hence, it would be rounded to previous hundred,

Which is, 5.424 ≈ 5.42

Learn more about the rounding number visit:

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Answer:

$60.30

Step-by-step explanation:

0.45 x 134 = $60.30

Answer:

Interest earned in two years is approximately $1,837

Step-by-step explanation:

A= P( 1+r/n)^nt

Where,

A= principal + interest

P= principal= $10,000

r= interest rate = 8.5%

t= Time = 2years

n = periods = 4

A= P( 1+r/n)^nt

= 10,000(1+0.085/4)^4*2

= 10,000( 1 + 0.0213)^8

= 10,000(1.0213)^8

= 10,000(1.1837)

=11,837

A= $11,837

The interest earned in two years is

A = p + I

A - P = I

$11,837 - $10,000 = I

$1,837 = I

I= $1,837

Interest earned in two years is approximately $1,837

Answer:

x=4

Step-by-step explanation:

RS + ST = RT

5+ 2x-2 = 3x-1

Combine like terms

2x+3 = 3x-1

Subtract 2x from each side

2x+3-2x = 3x-1-2x

3 =x-1

Add 1 to each side

3+1 = x-1+1

4=x

Answer:25.7

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

First do whats in the parentheses

so it will look like this

3x+3=2x-2 now subract 2x from 3x you get x

x+3=-2

now minus 3 from -2 and you get -5

x= -5

Answer: $229.62

Step-by-step explanation:

mark down 11 %= (1-11%)

original price × percent left after mark down=new price

 258.00 × (1-11%)= $229.62

Hope this helps!! :)

Please let me know if you have any question

Answer:

(-3,-4)

Step-by-step explanation:

The vertex is where the parabola curves.

Answer:

(A)-3 (B)-4

Step-by-step explanation:

♥☺

Answer: v = 793.77 mph

Step-by-step explanation: Linear speed of a circular movement is calculated by using the formula:

v = ω.r

where

ω is angular velocity

r is radius of the path

Angular velocity is the rate of change of the angular position of an object with respect of time, i.e., is how fast an object changes its angular position with time:

[tex]\omega = \frac{d \theta}{dt}[/tex]

[tex]\omega = \frac{2\pi}{time}[/tex]

The Earth takes 24 hours to complete a rotation, then angular velocity:

[tex]\omega = \frac{2\pi}{24}[/tex]

[tex]\omega =[/tex] 0.262 rad/h

At a location 40° north, radius is 3033.5 miles, so:

v = 0.262*3033.5

v = 793.77

At latitude of 40°north, linear speed is 793.77mph.

Step-by-step explanation:

a unit rate is a rate that compares a quantity to exactly one of another quantity.

Answer:

Ted is 6 years old

Leon is 7 years old

Andrew is 8 years old

Step-by-step explanation:

Ted+Leon=13 ⇒T+L=13 ⇒L=13-T

Leon+Andrew=15 ⇒L+A=15 ⇒A=15-L ⇒A=15-(13-T) because Leon =13-Ted

A=2+T

Ted+Andrew=14

T+A=14  ( substitute Andrew age from A=2+T)

T+2+T=14

2T=12

check: Ted+Leon=13 ⇒ 6+7=13

Leon + Andrew=15 ⇒7+8=15

Andrew+Ted=14 ⇒ 6+8=14

Answer:

121, 64, and 16

Step-by-step explanation:

A perfect square is the product of a rational number multiplied by itself. So 11*11=121, 8*8=64, and 4*4=16

Answer:

x = 17

Step-by-step explanation:

To solve this equation, we can illustrate the algebraic concepts being employed and solve for the variable.

3(x - 4) = 2x + 5 Distribute the 3 into the parentheses.

3x - 12 = 2x + 5 Subtract 2x from both sides of the equation to combine like terms.

x - 12 = 5 Add 12 to both sides of the equation.

x = 17

Answer:

[tex] \displaystyle \rm \longmapsto \:3(x - 4) = 2x + 5[/tex]

[tex] \displaystyle \rm \longmapsto \:3x - 12 = 2x + 5[/tex]

[tex] \displaystyle \rm \longmapsto 3x - 2x - 12 = 2x - 2x + 5[/tex]

[tex]\displaystyle \rm \longmapsto x - 12 = 5[/tex]

[tex]\displaystyle \rm \longmapsto x - 12 + 12 = 5 + 12[/tex]

[tex]\displaystyle \rm \longmapsto x = 15[/tex]

Answer:

= (6×25)

= 150 - (27÷9)

= 150 - 3

= 147

Answer:

163

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The value of x in the equation -3-(-8)-(-2) = x is 7.

The correct option is 07.

When resolving expressions containing several operations, the procedure to follow is denoted by the acronym PEMDAS. "Parenthesis," "exponents," "multiplication," "division," "addition," and "subtraction" are all represented by the letters P through E.

Given information:

The given equation is described as -3-(-8)-(-2) = x.

To solve the equation as per the PEMDAS rule:

First, we need to simplify the terms within the parentheses: -(-8) is the same as +8, and -(-2) is the same as +2. Therefore, the equation becomes:

-3 + 8 + 2 = x

Next, we can simplify the addition and subtraction from left to right:

-3 + 8 = 5

5 + 2 = 7

Therefore, the value of x is 7.

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Answer:

10

Step-by-step explanation:

Since T is the midpoint of PQ, we know that PT = TQ, therefore:

3x + 1 = 5x - 5

-2x = -6

x = 3

Since PT = 3x + 1, the answer is PT = 3 * 3 + 1 = 10.

Answer:

-3x+7=-17  x=8

Step-by-step explanation:

-3*8+7=-17

Answer:

The answer should be:

[tex]=\frac{8x^3-18x}{3x+2}[/tex]

The closest answer is A, so I'll go with that.

Step-by-step explanation:

So we have the rational expression:

[tex]\frac{4x^3-9x}{2x-7}\div\frac{3x^2+2x^2}{4x^2-14x}[/tex]

First, remove the division sign. To do so, turn the division into multiplication and flip the second term:

[tex]\frac{4x^3-9x}{2x-7}\cdot \frac{4x^2-14x}{3x^2+2x}[/tex]

Now, simplify. From the first term, in the numerator, factor out a x. On the second term, factor out a 2x in the numerator and a x in the denominator:

[tex]\frac{x(4x^2-9)}{2x-7}\cdot\frac{2x(2x-7)}{x(3x+2)}[/tex]

Multiply straight across:

[tex]\frac{x(4x^2-9)(2x)(2x-7)}{(2x-7)(x)(3x+2)}[/tex]

Cancel out the (2x-7):

[tex]\frac{x(4x^2-9)(2x)}{x(3x+2)}[/tex]

Cancel out the x:

[tex]\frac{(2x)(4x^2-9)}{(3x+2)}[/tex]

At this point, we can factor the (4x^2-9) term, but we won't be able to cancel it out. Thus, this is the simplest it can get.

To get the answer, expand the numerator:

[tex]=\frac{8x^3-18x}{3x+2}[/tex]

Thus, the answer is...

A?

Answer:

The right solution is option a : [tex]\frac{8x^2 - 18}{3x+2}[/tex]

Step-by-step explanation:

We have to simplify the following rational expression,

[tex]\frac{4x^3-9x}{2x-7}[/tex] ÷ [tex]\frac{3x^3+2x^2}{4x^2-14x}[/tex]

Take into account the rule (a / b) / (c / d) = ad / bc. This simplifies the expression a bit further --- (1)

[tex]\left(4x^3-9x\right)\left(4x^2-14x\right)[/tex] ÷ [tex]\left(2x-7\right)\left(3x^3+2x^2\right)[/tex]

Let's now factor each individual expression as demonstrated below. Afterwards we can substitute back into the expression above --- (2)

Goal - Factor : (4x³ - 9x)(4x² - 14x),

4x³ - 9x ⇒ x(4x² - 9)

4x² - 14x ⇒ 2x(2x - 7)

[tex]x\left(4x^2-9\right)\cdot \:2x\left(2x-7\right) = 2x^2\left(4x^2-9\right)\left(2x-7\right)[/tex]

That leaves us with the following expression,

[tex]2x^2\left(4x^2-9\right)\left(2x-7\right)[/tex] ÷ [tex]\left(2x-7\right)\left(3x^3+2x^2\right)[/tex]

As you can see the " 2x - 7 " cancel out, and the " x² " cancel as well, leaving us with a further simplified expression,

[tex]2\left(4x^2-9\right)[/tex] ÷ [tex]3x+2[/tex]

Which can also be rewritten as [tex]8x^2 - 18[/tex] ÷ [tex]3x + 2[/tex] = [tex]\frac{8x^2 - 18}{3x+2}[/tex], in other words the first option.

Answer:

V=72 cm³

Step-by-step explanation:

V=3 cm*3 cm*8 cm

V=72 cm³

Answer:

[tex] \frac{3}{20} [/tex]

Step-by-step explanation:

[tex] \frac{3}{5} \times \frac{1}{4} [/tex]

[tex] = \frac{3 \times 1}{5 \times 4} [/tex]

Simplify

[tex] = \frac{3}{20} [/tex]

If you have any more questions please let me know.

Answer:

[tex]$\large\boxed{\frac{3}{20} = 0.15} $[/tex]

Step-by-step explanation:

[tex]$\frac{3}{5} \cdot \frac{1}{4} = \frac{3 \cdot 1}{5 \cdot 4}=\frac{3}{20} = 0.15 $[/tex]

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

l = 12m

w = 400 cm

First we must convert the length from meters to centimeters

1 m = 100 cm

12 m = 12 × 100 = 1200 cm

So l = 1200 cm

Substitute the values into the above formula

We have

Perimeter = 2(1200) + 2(400)

= 2400 + 800

We have the final answer as

Hope this helps you

Answer:

11/6 as an  improper fraction

Step-by-step explanation:

1 5/6 is 11/6 as an importer fraction and 1.86 as a decimal  

Answer:

p(1/2)= 0 , p(-1/2)= -2

Step-by-step explanation:

p(1/2)= 2(1/2)-1

= 1-1

= 0

p(-1/2) = 2(-1/2)-1

= -1-1

= -2

Answer:

integers

integers are both whole and real numbers as well as they can be negative and/or positive

Answer:

Step-by-step explanation:

18+7*2+11x+4

18+14+11x+4

32+11x+4

11x+36

Answer:

the total will be $27.31

15 percent tip is $3.56

Step-by-step explanation:

Answer:

Step-by-step explanation:

The center of dilation is at the point of intersection of the lines through an image point and the corresponding pre-image point.

Here, A and A' are both on the line x=5. C and C' are both on the line y=2, so the center of dilation is (x, y) = (5, 2).

__

The point A' is half as far from (5, 2) as the point A is, so the scale factor of the dilation is 1/2. (A' is 3 units down; A is 6 units down from the center of dilation.)

Answer:

50 Minutes

Step-by-step explanation:

For the empty tank to hold the same amount of water, we can simply take the total water of the full tank divided by the rate, divided by two to allow both tanks to be equal, aka, half.

500 L / 5 L per minute / 2

100 minutes / 2

50 minutes.

For both tanks to have the same amount of water, 250L, it would take 50 minutes with a flow rate of 5L per minutes.

Cheers.