Find the distance between the two points rounding to the nearest tenth (if necessary).
(3, 1) and (5,-2)

The height of the lighthouse to the nearest tenth of a foot is 137.8 feet.

This is a question of heights and distances.

It is given in the question that the passing boat is 310 feet from the base of a lighthouse. Also, the angle of depression from the top of the lighthouse is 24°.

We have to find the height of the lighthouse to the nearest tenth of a foot.

As you can see in the figure, using trigonometry we can write,

cot 24 = 310/Height of the lighthouse

Hence,

Height of the lighthouse = 310/cot 24

We know that,

cot 24 ≈ 2.25

Hence,

Height of the lighthouse = 310/2.25 ≈ 137.77778 ≈ 137.8 feet.

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Measure of the combined angle of 71° .

71 degrees is an acute angle .

Given, that two measure of angles 44 degrees and 27 degrees .

Classification of angles :

Acute angle : 0° ≤ Ф ≤ 90°

Right angles : Ф = 90 degrees

Obtuse angles : 90° ≤ Ф ≤ 180°

Reflex angle : 180° ≤ Ф ≤ 360°

Here the angles given are 44 degrees and 27 degrees.

Combined measure of two angles = 44 + 27

= 71 degrees.

Acute angle : 0° ≤ Ф ≤ 90°

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The jars are nor enough because the applesauce is more than 35 cups which is what 20 glass jars can contain. Since each of the cup will hold 1 3/4 cups of applesauce.

Given data

number of cups of apple sauce = 40

number of glass jars = 20

number of cups each glass jar can hold = 1 3/4

solution

if one glass jar hold 1 3/4 cups then 20 glass jars will hold

= 20 * 1 3/4

= 35 cups

Since there are 40 available cups of apple sauce and the 20 glass jars is equivalent to 35 cups, hence the glass jars will contain 35 cups and there will be 5 cups left.

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Answer: 70 days

Step-by-step explanation:

Answer:

f (x^2-4)  =  2x^2 - 5

Step-by-step explanation:

The value is 3/2 (a)

The given function is , f(x)= 2x 3 where x = value of this function .

Here , we will put the value 1/4 ( here x = 1/4 ) into the given function. if , f(1/4) = 2 . 1/4 . 3 = 3/2

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Step-by-step explanation:

[tex] = \lim \limits_{x \to0}x \cot(2x) [/tex]

[tex] = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } [/tex]

[tex] = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \times \frac{2x}{2x} [/tex]

[tex] = \lim \limits_{x \to0} \frac{2x}{ \tan(2x) } \times \lim \limits_{x \to0} \frac{x}{2x} [/tex]

[tex] = \lim \limits_{u \to0} \frac{u}{ \tan(u) } \times \frac{1}{2} [/tex]

[tex] = \frac{1}{2} [/tex]

On solving for x, we get x = -1

A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. Decimal system is the most commonly used number system with base 10.

Given is the following expression -

3 base x + 34 base x - 40 base x = 0

The given expression can be solved by converting the above expression in decimal form. Therefore -

3 base x in decimal = (3 x⁰) base 10 = 3

34 base x in decimal = (3 x¹ + 4 x⁰) base 10 = 3x + 4

40 base x = (4 x¹ + 0 x⁰) base 10 = 4x

Substituting the decimal values in the expression given -

3 + (3x + 4) + 4x = 0

7x + 7 = 0

7x = -7

x = - 1

Therefore, on solving for x, we get x = -1

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As per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.

As given in the question,

Number of elephants in zoo = 2

Sally weighs = 7,645 pounds

Joe weighs = 12, 479 pounds

Total weight of Sally and Joe is equal to

= ( 7,645 + 12,479 ) pounds

= ( 20,124 ) pounds

Therefore, as per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.

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Answer:Substitute the value of the variable into the equation and simplify.

84

Step-by-step explanation:

Answer:

the equation would be 12m+125

Step-by-step explanation:

-

Answer:

[tex] \sf \large \: m=−1[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

m/2 =m+5/10

Step 1: Simplify both sides of the equation.

1/2m=m+1/2

Step 2: Subtract m from both sides.

1/2m−m=m+1/2−m

−1/2m=1/2

Step 3: Multiply both sides by 2/(-1).

(2/−1)*(−1/2m)=(2/−1)*(1/2)

m=−1

The probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is  π/9 .

Probability of an event is defined as the Number of favorable outcomes divided by total number of outcomes.

It is denoted by P(E).

Given that

radius of circle = 3

side of the square = 9

Let E be the event that a randomly chosen point in the interior of the square will also lie in the interior of the circle

then

[tex]P(E)=\frac{AreaOfCircle}{AreaOfSquare}[/tex]   ...(i)

Area of Circle = πr² = π(3)² = 9π

Area of Square = (side)²=(9)²=81

Substituting the values in equation (i) we get

[tex]P(E)=\frac{9\pi }{81}[/tex]

[tex]=\frac{\pi }{9}[/tex]

Therefore  , the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is  π/9 .

The correct option is (C)  π/9

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The line which have a steeper slope is Line 1.

It is given in the question that the points on the line are given by:-

Line 1: (-9,-4) and (7,0)

Line 2:(0,1) and (7,4)

We have to find which line has a steeper slope.

First we will find the slope of each line.

We know that slope of a line with points (a,b) and (c,d) is given by:-

(d-b)/(c-a)

Slope of Line 1:

(0-(-4))/(7-9) = 4/(-2) = -2 (we will take the absolute value)

Slope of Line 2:

(4-1)/(7-0) = 3/7

We know that greater the slope of the line means greater the steep of the line.

As,

2 > 3/7

Hence, Line 1 is steeper than Line 2.

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A triangle is a shape whose all three angles have a sum of 180 degrees. So from the above definition, we know that:

P + Q + R = 180

Q=3P

T=P + 20

Therefore:

P + 3P + P + 20 = 180

5P + 20 = 180

5P = 160

P = 32

Q = 3(32) = 96

R = 32 + 20 = 52

To Additional Control P + Q + R = 32 + 96 + 52 = 180 °Degree

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Answer:  The claim is true

The proof is below

=====================================================

A = some nonzero rational number

B = some irrational number

Because value A is rational, this means A = p/q where p,q are nonzero integers.

Let's do a proof by contradiction. The claim is that A*B is irrational, but let's do the opposite and assume A*B is rational. We should get to a contradiction somewhere based on this assumption.

If A*B is rational, then A*B = r/s for some integers r and s

Then we can have the following steps

A*B = r/s

(p/q)*B = r/s

B = (r/s)*(q/p)

B = (rq)/(sp)

B = (some integer)/(some other nonzero integer)

B = some rational number

Recall we made B irrational. There's no way to have B rational and irrational at the same time. This is where the contradiction happens. This causes the original assumption of "A*B is rational" to be false. Therefore, the opposite must be the case and A*B has been proven to be irrational.

Therefore, the product of a rational number and an irrational number is irrational.

------------------------

Example:

5 is rational

sqrt(3) is irrational

5*sqrt(3) is irrational

[tex] \bf \implies \large{ - 2x}^{2} \\ [/tex]

[tex] \bf \longrightarrow - 4 \sqrt{16 {x}^{8} } \\ \\\bf \longrightarrow - { ({2}^{4} {x}^{8}) } ^{ \frac{1}{4} } \\ \\\bf \longrightarrow ( - 2x)^{ \frac{1}{ \cancel{4}}1 \times \cancel{ 8}2 } \\ \\\bf \longrightarrow \boxed{- 2x^{2}} \: ans.[/tex]

If linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. tanya is 20 years old.

Let Vera's age be v

Let Linda's age be 2v

Let Tanya's age be 8v- 4

Let the total age be 9v + 2

Hence,

v + 2v + 8v- 4 = 9v + 2

11v - 4 = 9v + 2

Collect like terms

2v = 6

Divide both side by 2v

v=6/3

v = 3

So,

Tanya's age = 8v - 4

Tanya's age= 8(3) - 4

Tanya's age=24-4

Tanya's age = 20 years

Therefore if linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. tanya is 20 years old.

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By combining the like terms, the simplified form of the expression -(3x-4y)+x is -2x+4y

Given,

The algebraic expression = -(3x-4y)+x

Expand the terms

-(3x-4y)+x= -3x+4y+x

Combine the like terms

-3x+4y+x= (-3+1)x+4y

=-2x+4y

Hence, by combining the like terms, the simplified form of the expression -(3x-4y)+x is -2x+4y

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Answer:

9

Step-by-step explanation:

Since one place to the right is greater than or equal to 5 you round up.

The expression at the end of the third year would be:  500x³ + 200x² + 600x

We have the rate at x = 1 + r

This is the rate of the interest that is earned per year.

In the first year.

initial deposit = $500

deposit at the end of the year = 500 * x = 500x

In the second year

The initial balance = 500x + 200

The balance at the end of the year = (500x + 200)x

= 500x² + 200x

In the third year

Initial balance = 500x² + 200x + 600

Then the year end balance would be (500x² + 200x + 600)x

= 500x³ + 200x² + 600x

Hence the expression that can be used to show the polynomial is given as 500x³ + 200x² + 600x

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This is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.

A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:

1. The initial term in the series.

2. The general rule for determining any term from its preceding term.

Recursive Arithmetic Sequence Formula

The following is the recursive formula to determine the nth term in an arithmetic series:

an = an-1 + d for n ≥ 2

where

The common difference is d, and an is the nth term of an A.P.

given that

a₁ = -2

a (n) =a (n-1) -5 so, d = -5

For example, we need to extend the sequence term by term in order to find the first five terms:

a(1) = -2

a(2) = a(1) + d = -2 + (-5) = -7

a(3) = a(2) + d = -7 + (-5) = -12

a(4) = a(3) + d = -12 + (-5) = -17

a(5) = a(4) + d = -17 + (-5) = -22

a(6) = a(5) + d = -22 + (-5) = -27

Hence,this is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.

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Answer:

11 zeros

Step-by-step explanation:

10^13 = 100 000 000 000 000

Round the two first numbers(which makes 11 zeros left), then lastly the zeros

According to the given statement The total far distance = 88.2cm

A lens equation, sometimes known as a lens formula, is an equation that connects focal length, image distance, as well as object distance. . where v is the distance between the picture and the lens, u is the object distance, and f is the focal length

A lens's power is defined as both the reciprocal of its focal length. It is symbolized by that the letter P. P=1f gives the power P of something like a lens with a focal length of f (in m). The SI unit of lens power is a 'diopter.'

P = -1.16

The expression of the focal length is represented as:

f = 1/p

p is the power.

so,

f = 1/-1.16

 = -0.862

 = -86.2 cm

the expression for the lens formula is:

1/f = 1/v - 1/u

1/(-86.2) = 1/v - 0

v = -86.2

The total distance is represent as:

d = v + s

so,

d = 86.2 + 2

  = 88.2 cm

The total far distance = 88.2cm.

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The value of variable x in the given expression 9 √2 . x=18 √2 is equal to 2

As given in the question:

Given expression

9 √2 . x=18 √2

Simplify the given expression to get the value of variable x

9 √2 . x=18 √2

Divide by √2 both the side

(9 √2 . x ) / √2= ( 18 √2 )/ √2

⇒9x = 18

⇒ x= 18 /9

⇒ x = 2

Therefore, the value of variable x in the given expression 9 √2 . x=18 √2 is equal to  2

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The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.

The given arithmetic series is 50+55+60+ . . .

The summation notion of given series is ∑50+5n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=7, [tex]a_{1}[/tex] = 50

To calculate sum of arithmetic series, we need to find [tex]a_{7}[/tex] .

[tex]a_{7} = a_{1} + (n-1)d[/tex]

d = 5 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{7}[/tex] = 50 + (7-1)(5)

[tex]a_{7}[/tex] = 50 + 30 = 80

On substituting values in sum of arithmetic series formula, we get

[tex]S_{7}[/tex] = (7(50 + (80)))/2 = 455

The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.

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A large ship lowered its anchor, The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in sec) E=-2.4t+75. The anchor drop 12 meters every 5 seconds.

Given that in the picture we can see the question that is

A large ship lowered its anchor,

The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in second).

E=-2.4t+75

According to the function E=-2.4t+75

We assume that [tex]t_{1}[/tex].

So, every 5 second [tex]t_{1}[/tex]=t+5.

So, we get

ΔE=E(t)-E(t+5)

ΔE=-2.4t+75-(-2.4(t+5)+75)

ΔE=-2.4t+75+2.4t+12-75

ΔE=12

Therefore, the anchor drop 12 meters every 5 seconds.

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