What is (a+b)(a-b) equal

Answer:

Ten minutes ago, the diver was  450  feet below sea level.

Step-by-step explanation:

Since the diver is being pulled up, measuring his movement for the past  10 minutes requires that we use  −25  for the movement over those  10  minutes. So, his depth  10 minutes ago is given by the expression

−200−25(10)

−200

−250

−450

So,  10  minutes ago, the diver was  450 feet below sea level.

Answer:

The diver 450 feet deep into sea 10 minutes ago.

Step-by-step explanation:

At present position ,depth at which diver was = 200 feet

Rate at which diver is pulled up = 25 ft/min

Let the depth of the diver 10 minutes ago be x

The depth of the diver 10 minutes ago will be sum of present position and distance covered by exploring ship by pulling diver in a 10 minutes.

x = 200 + 25ft/min × 10 = 200 ft + 250 ft = 450 ft

The diver 450 feet deep into sea 10 minutes ago.

Answer:

r = - 6

Step-by-step explanation:

Given

6r + 7 = 13 + 7r ( collect terms in r on the left and numbers on the right )

Subtract 7r from both sides

- r + 7 = 13 ( subtract 7 from both sides )

- r = 6 ( multiply both sides by - 1 )

r = - 6

6r+7=13+7r

-6r -6r

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

7=13+1r

flip the equasin to make it easier

13+1r= 7

-13 -13

---------

1r= -6

Answer:

The all polar coordinates of point P are  (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n).

Step-by-step explanation:

The polar coordinates can be written as (r,Ф)= (r,Ф+2nn) or (r,Ф) =(-r,Ф+(2n+1)n) and n is any integer value.

We are given p=(1,-pi/6)

P(r,Ф), then r = 1 and Ф = -pi/6

The polar coordinates will be

P(r,Ф)= (r,Ф+2nn)  = (1 , -pi/6 + 2nn) and n is any positive integer and the value of r is positive.

P(r,Ф) =(-r,Ф+(2n+1)n) = (-1, -pi/6+(2n+1)n) and n is any positive integer and the value of r is negative.

The all polar coordinates of point P are  (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n)

Answer:

Well, to find the area of a:

square and rectangle you multiply (Length x Width) the formula is (LxW)

triangle you multiply (Base x Height) ÷ 2 the formula is (BxH/2)

The meaning of area is: the number of unit squares that can be contained in an object.

The meaning of volume is: the number of unit cubes that completely fill up a solid figure such as an ice cube.

To find the surface area of an object you:

Multiply the length times the width. (of only one side)

But for a triangle you multiply the base times the height, then divide the answer by 2 ( of only one side)

To find the volume you multiply the length times width times height.

But for a triangle you multiply the base times height.

Hope I helped ; )

Final answer:

The surface area and volume of shapes can be found using specific formulas. Surface area is the total area of the outside surface of a three-dimensional object, while volume is the amount of space occupied by the object.

Explanation:

The surface area and volume of certain shapes can be found using specific formulas.  Surface area refers to the total area of the outside surface of a three-dimensional object. It is measured in square units. The formula for surface area depends on the shape of the object. For example, the formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

Volume, on the other hand, refers to the amount of space occupied by a three-dimensional object. It is measured in cubic units. Like surface area, the formula for volume also depends on the shape of the object. For a rectangular prism, the formula is V = lwh.

Answer:

Inverse property

Step-by-step explanation:

The definition of the inverse property is to add to get a result of zero. Since we are adding the inverse of each term to get a result of zero each time, we are using the inverse property.

Answer:

[tex]160\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to the area of its six rectangular faces of the net

so

[tex]SA=2(2*4)+2(12*2)+2(12*4)\\ \\SA=16+48+96\\ \\SA=160\ m^{2}[/tex]

Answer:

160 m2

Step-by-step explanation:

Answer:

10 and 8

Step-by-step explanation:

consecutive even numbers have a difference of 2 between them.

let the width be n then the length is n + 2

Area = n(n + 2) = 80, thus

n² + 2n = 80 ( subtract 80 from both sides )

n² + 2n - 80 = 0 ← in standard form

(n + 10)(n - 8) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 10 = 0 ⇒ n = - 10

n - 8 = 0 ⇒ n = 8

But n > 0 ⇒ n = 8

width = n = 8 and length = n + 2 = 8 + 2 = 10

The answer is 243 27×9 is 243 and area is length times width

ANSWER

243 square feet.

EXPLANATION

The rectangular flower bed has length,

l=27 ft

and width, w=9ft.

The area of a rectangle is

Area=length x width

Since the flower bed is rectangular, we use this formula to find its area.

[tex]Area = 27 \times 9 = 243 {ft}^{2} [/tex]

Therefore the area of the flower bed is 243 square feet.

Answer:

B

Step-by-step explanation:

P(A)+P(A')=1

m+n=1

B is the only answer equal this if you add m to both sides.

Answer:

I got B! n=1-m

andy has 40

david has 60

tim has 80

Answer:

Step-by-step explanation:

Alright, lets get started.

Let Andy have A stamps.

Let David have D stamps.

Let Tim have T stamps.

Andy, David and Tim altogether have 180 stamps, means

[tex]A+D+T=180....................... equation 1[/tex]

Andy has 20 fewer than David, means

[tex]A+20=D...............................equation 2[/tex]

Tim has 80% of the sum of Andy's and David's stamps, means

[tex](A+D)*0.8=T........................equation 3[/tex]

Putting the value of D as A+20 in equation 1 and 3

[tex]A+A+20+T=180[/tex]

[tex]2A+T=160[/tex]........................equation 5

[tex](A+A+20)0.8=T[/tex]

[tex](2A+20)0.8=T[/tex]

[tex]1.6A+16=T[/tex] .......   equation 6

Plugging the value of T in equation 5

[tex]2A+1.6A+16=160[/tex]

[tex]3.6A=144[/tex]

[tex]A=40[/tex]

[tex]D = 40+20 = 60[/tex]

[tex]T=1.6*40+16[/tex]

[tex]T=64+16=80[/tex]

It means Andy has 40 stamps.

It means David has 60 stamps.

It means Tim has 80 stamps.

Hope it will help :)

Answer:

Correct symbol is = .

Step-by-step explanation:

Given statement is : 13?13

Now we need to find about which of the symbols correctly relates the two numbers 13?13.

When we compare two numbers then there are only three cases possible.

First number is less than ( < ) second number.

First number is greater than ( > ) second number.

First number is equal to ( = ) the second number.

we see that both numbers 13 and 13 are equal so we will use = symbol.

Hence correct symbol is = .

Final answer:

The correct symbol to relate two identical numbers, such as 13 and 13, is the equals to (=) symbol.

Explanation:

The question asks which symbols correctly relate the two numbers 13 and 13. In mathematics, numbers can be compared using different symbols to show their relationship. These symbols include equals to (=), greater than (>), less than (<), greater than or equal to (>=), and less than or equal to (<=). When two numbers are identical, the correct symbol to relate them is the equals to (=) symbol because they have the same value.

Answer:

False

Step-by-step explanation:

To be a function each x can only go to one y

The number 5 goes to both 2 and 1, which violates the rule

Therefore, this is a relation, not a function

Answer:

-2; 16

Step-by-step explanation:

Rewrite the equation [tex]x^2-14x+31=63[/tex] as:

[tex]x^2-14x+31-63=0\\ \\x^2-14x-32=0[/tex]

Now use the quadratic formula:

[tex]D=b^2-4ac\\ \\D=(-14)^2-4\cdot 1\cdot (-32)\ \ [a=1,\ b=-14,\ c=-32]\\ \\D=196+128=324=18^2[/tex]

Now

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}\\ \\x_{1,2}=\dfrac{-(-14)\pm\sqrt{18^2}}{2\cdot 1}=\dfrac{14\pm18}{2}=\dfrac{-4}{2},\ \dfrac{32}{2}=-2,\ 16[/tex]

Answer:

x = 16 or x = -2

Step-by-step explanation:

Points to remember

Solution of a quadratic equation  ax² + bx + = 0 is given by

x = [-b ± √(b² - 4ac) ]/2a

To find the solution of equation

We have x² - 14x + 31 = 63

x² - 14x + 31 - 63 = 0

x² - 14x - 32 = 0

a = 1, b = -14 and c = 32

x = [-b ± √(b² - 4ac) ]/2a

 = x = [- -14 ± √((-14)² - 4*1 * (-32)) ]/2*1

 = [14 ± √324]/2

x = -2 or x = 16

Answer:

47.5 miles

Step-by-step explanation:

So, every morning, you travel 4.75 miles to get to school... and another 4.75 miles in the afternoon to return.

So, each day, you travel a total of 9.5 miles (4.75 + 4.75) to go school and back.

On a typical school week, you'll go to school 5 times... so you'll need to travel a total of 47.5 miles (5 * 9.5).

Answer: 40 +60+20= 120

Step-by-step explanation:

Answer:

A = 40 degrees

B = 60 degrees

C = 80 degrees

a = 13.1

b = 17.6

c = 20

Step-by-step explanation:

They give us A = 40 degrees and B = 60 degrees and in one triangle the sum of the angles should be 180, so you add 40 and 60, and then subtract that value by 180.

40 + 60 = 100

180 - 100 = 80

C = 80 degrees

From here you use the law of sines

20/sin(80) = a/sin(40)

when you cross multiply them you should get this:

20 * sin(40) = sin(80)*a

Simplify them

12.9 = sin(80) * a

Divide them to isolate the variable

12.9/sin(80) = a

a = 13.1

To find side length b you use law of sines again

20/sin(80) = b/sin(60)

Cross multiply

20 * sin(60) = sin(80) * b

Simplify

17.3 = sin(80) * b

Divide to isolate the variable

17.3/sin(80) = b

b = 17.6

Answer:

b

Step-by-step explanation:

Given K is the midpoint of JL, then

JK = KL ← substitute values

6x = 3x + 3 ( subtract 3x from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Hence

JK = 6x = 6 × 1 = 6

KL = 3x + 3 = (3 × 1) + 3 = 3 + 3 = 6

JL = 6 + 6 = 12

The measure of B is 51.06°

From pythagoras;

Substituting into the relation;

Sin(B) = 7/9

Sin(B) = 51.057

To the nearest hundredth , we have ; 51.06

Answer:

I think it shifts horizontally by 7 units to the right. Not completely sure though.

Step-by-step explanation:

Answer: i think it’s the last one

Step-by-step explanation:

Answer:

√7 ≈ 2.646

Step-by-step explanation:

The triangle apparently has two sides of length 4 and a third side of length 6. The altitude of the triangle will divide the long side in half, making that half one leg of the right triangle with hypotenuse 4.

The altitude of interest is then the length of the other leg:

√(4² -3²) = √7 ≈ 2.646

Answer:

The answer is yes , k = -2 and y = -2x ⇒ first answer

Step-by-step explanation:

* To prove the variation

- Check the constant change in the values of x and y

- Lets check that from the table

# At x = 1 ⇒ y = -2

# At x = 3 ⇒ y = -6

# At x = 5 ⇒ y = -10

* -6 - -2 = -6 + 2 = -4 ⇒ 3 -1 = 2

 -10 - -6 = -10 + 6 = -4 ⇒ 5 - 3 = 2

∴ y decreased by 4 when x increased by 2

* This is a constant change

∴ y is varies directly with x

∴ y ∝ x

∴ y = k x ⇒ where k is the constant of the variation

* Lets find the value of k

- You can use one value of x and y from the table

∵ x = 3 and y = -6

∴ -6 = k (3) ⇒ divide two sides by 3

∴ k = -2

∴ The equation of the variation is = y = -2x

* The answer is yes , k = -2 and y = -2x

Answer:

Yes, k=-2 and y=-2x

Step-by-step explanation:

Using (1,-2) and (3,-6)

[tex]k=\frac{-6--2}{3-1}=-2[/tex]

This implies that

y=-2x

check for the 3rd point;

When x=5,

y=-2(5)=-10

Hence y varies directly as x. The constant of variation is k=-2

Answer:

I believe it is 11.5 but I’m not 100% sure

Step-by-step explanation:

Answer:

x < 5

Step-by-step explanation:

- 7x + 14 > - 3x - 6

14 > 4x - 6

20 > 4x

x < 5

Answer:

x>5

Step-by-step explanation:

-7x+14>-3x-6

-4x+14>-6

-4x>-20

-x>-5

x>5

Answer:

A cube or a cuboid.

Step-by-step explanation:

A cube or a cuboid is a three dimensional shape that has

12 edges, 8 corners or vertices, and 6 faces.

The difference between a cube and cuboid is that a cube has all edges equal which makes every face a square while a cuboid has two square faces and four rectangular faces.

ANSWER

[tex]\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]

EXPLANATION

The given ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin.

The equation of an ellipse with vertices on the x-axis and center at the origin is:

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

The ellipse has vertex at (4,0) , hence a=4.

Also the co-vertex is at (0,3) , b=3

We substitute the values into the equation to get:

[tex] \frac{ {x}^{2} }{ {4}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]

The equation of the ellipse centered at the origin with a vertex at (4,0) and a co-vertex at (0,3) is (x/4)² + (y/3)² = 1.

The ellipse in question has a vertex at (4,0) and a co-vertex at (0,3), with a center at the origin. The standard form equation for an ellipse with a center at the origin is given by (x/a)² + (y/b)² = 1. In this case, 'a' represents the distance from the center to a vertex, and 'b' represents the distance from the center to a co-vertex. Since our vertex is at (4,0), 'a' equals 4, and  since our co-vertex is at (0,3), 'b' equals 3.

So in this case the standard form equation of the ellipse would be (x/4)² + (y/3)² = 1.

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Answer:

10

Step-by-step explanation:

g (3 (2)² - 4)

g (3 (4) - 4)

g (12 - 4)

g (8)

------

2 (8) - 6

16 - 6

10

To find the value of g(f(2)), we first compute f(2) and then substitute this output into the g(x) function. So, f(2)=8, and g(8)=10, which means that g(f(2))=10.

The question is related to the concept of functions in mathematics. Specifically, it asks to compute the function g(f(2)), where f(x)= 3x^2-4 and g(x)= 2x-6.

First, we need to find the value of f(2).  substitute x=2 in the function f(x). f(2)= 3*(2)^2 - 4 = 3*4 - 4 =12 - 4 = 8.

put this value into the function g(x), so  find g(8). By substituting x=8 in g(x): g(8) = 2*8 - 6 = 16 - 6 = 10.

So, g(f(2)) = g(8) = 10.

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Answer:

[tex]y=\frac{3}{2}x+\frac{7}{2}[/tex]

Step-by-step explanation:

Slope-intercept form is given by  y = mx + b

We need to re-arrange the equation given to have y to the left side of the equal sign (in other words, solve for y). Steps are shown below:

[tex]-3x+2y=7\\2y=3x+7\\y=\frac{3x+7}{2}\\y=\frac{3x}{2}+\frac{7}{2}\\y=\frac{3}{2}x+\frac{7}{2}[/tex]

the last answer is correct.

For this case we have that the line equation of the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut point with the y axis.

We have the equation:

[tex]-3x + 2y = 7[/tex]

By adding 3x to both sides of the equation we have:

[tex]-3x + 3x + 2y = 7 + 3x\\2y = 3x + 7[/tex]

Dividing between 2 on both sides of the equation:

[tex]\frac {2y} {2} = \frac {3x} {2} + \frac {7} {2}\\y = \frac {3x} {2} + \frac {7} {2}[/tex]

ANswer:

Option D

Answer:

$135.70

Step-by-step explanation:

First step is to calculate the daily consumption for this family of four.  We'll assume they're all in age to use and flush the toilet themselves (no babies).

So, one person flushes 9.1 gallons a day, a family of 4 would then flush 4 times that:

daily family flushes = 9.1 gal/person * 4 persons/family = 36.4 gal/family

That's for one day... now for a year...

yearly = 36.4 gal/day * 365 days/yr = 13 286 gal/year

Let's convert those gallons into cubic feet:

13 286 gal / 7.48 gal/ft³ = 1,776.2 ft³

Then we multiply the gallons by the price for 100 cubic feet and divide by 100:

1,776.2  ft³ * $7.64 /100 ft³ = $135.70

Answer:

About 68 or 68.03

Step-by-step explanation:

Answer:

it is 68.0388555 Kg when you convert it to Kg.

Step-by-step explanation:

1 pound is 0.45359237 Kg

Answer: 13/25

Step-by-step explanation:

The probability that a person chosen at random from this group has brown or green eyes is 0.52.

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The table of the number of people and the colour of their eyes colour is given as,

Colour of Eyes     Number of People

Brown                              20

Green                              6

Blue                                 17

Hazel                               7

According to the table, the total number of people who participated in the survey is 50. Therefore, the probability that a person chosen at random from this group has brown or green eyes can be written as,

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

[tex]\rm Probability=\dfrac{\text{Number of people with brown and green eyes}}{\text{Total number of people who participated in the survey}}[/tex]

[tex]\rm Probability=\dfrac{20+6}{50}=\dfrac{26}{50} = 0.52[/tex]

Hence, the probability that a person chosen at random from this group has brown or green eyes is 0.52.

Learn more about Probability:

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