Evaluate 3x2−9
when x=−2

Step-by-step explanation:

Given point are: P(at², 2at)

Q(a/t², 2a/t)

S(0, 0)

Now, the distance between A(x₁y₁) and B(X₂, y₂)

then AB = √{(x₂ - x₁)² + (y₂ - y₁)²} units

(i) The distance between S and P:

(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0

(x₂, y₂ ) = (at², 2at) ⇛x₂ = at², y₂ = 2at

SP = √{at² - 0)² + (2at - 0)²}

= √{(at²)² + (2at)²}

= √{a²t²*² + 4a²t²}

= √{a²t⁴ + 4a²t²}

= √{a²t²(t²+4)}

SP = at√(t² + 4)→→→Eqn(1)

(ii) The distance between S and Q :

(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0

(x₂, y₂ ) = (a/t², 2a/t) ⇛x₂ = a/t², y₂ = 2a/t

SQ = √[{(a/t²) - 0} + {(2a/t) - 0}

= √{(a/t²)² + (2a/t)²}

= √{(a²/t²*²) + (4a²/t²)}

= √{(a²/t⁴) + (4a²/t²)}

= √{(a² + 4a²t²)/t⁴}

= √[{a²(1 + 4t²)}/t⁴]

SQ = (a/t²)√(1 + 4t²) →→→ Eqn(2)

Now,

(1/SP) + (1/SQ) = [1/{at√(t² + 4)}] + [1/{(a/t²)√(1 + 4t²)}]

= (1/at)[1/{√(t² + 4)}] + (t²/a)[1/{(√1 + 4t²)}]

= (1/a)[[1/{t√(t² + 4)}] + [t²/{√(1 + 4t²)}]]

(1/SP) + (1/SQ) = 1/a is not independent of 't'

If suppose S = (a, 0) then

SP = √{(at² - a)² + (2at - 0)²}

= √{a²(t² - 1)² + (2at)²}

= a√{(t² - 1)² + 4t²}

= a√{(t² + 1)²}

SP = a(t² + 1)

1/SP = 1/{a(t² + 1)} →→→Eqn(1)

And

SQ = √[{(a/t²) - a}² + {(2a/t) - 0}²]

= √[a²{(1/t²) - 1}² + a²(2/t)²]

= a√[{(1 - t²)²/t⁴} + (4/t²)]

= a√[{(1 - t²)² + 4t²}/t⁴]

( a/t²)√(1 + t²)²

SQ = (a/t²)(1 + t²)

1/SQ = 1/{(a/t²)(1 + t²)} = t²/{a(1 + t²)} →→→Eqn(2)

Therefore, (1/SP) + (1/SQ)

= 1/{a(t² + 1)} + t²/{a(1 + t²)}

= (1 + t²)/a(1 + t²)

= 1/a

1/a is independent of 't'.

Answer:

The common denominator of 5/8 and 5/4 is 8.

4×2 is 8 and 5/8 already has a denominator of 8

The common denominator of two fractions 5/8 and 5/4 is 8.

A number system is defined as a system of writing to express numbers.

To find a common denominator for 5/8 and 5/4, we need to find the least common multiple (LCM) of the denominators 8 and 4.

The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...

We can see that the least common multiple of 8 and 4 is 8, since 8 is the smallest number that appears in both lists.

To convert 5/8 to an equivalent fraction with denominator 8, we can multiply both the numerator and the denominator by 1, which is equivalent to multiplying by 8/8

Hence, the common denominator of two fractions 5/8 and 5/4 is 8.

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Answer: $7401.22

Step-by-step explanation: it’s right just trust me

Step-by-step explanation:

let, the tulips be 'x'

According to the question,

heather=4x

& sarah=x

but heather planted 64 so,

4x=64

or, x=64/4

x=16

hence, sarah planted 16 tulips

Heather planted 4x Sarah's tulips. On the off chance that Heather has 64 tulips, Sarah has 16 tulips (64/4 = 16).

Let's utilize algebra to illuminate this issue. Let s speak to the number of tulips Sarah planted.

Concurring to the data given, Heather planted 4 times as numerous tulips as Sarah, so we will compose this as:

Heather's tulips = 4 * Sarah's tulips

64 = 4s

Presently, ready to fathom for s:

s = 64 / 4

s = 16

Sarah planted 16 tulips.

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Answer:

Step-by-step explanation:

We can think of this problem like a triangle that Tom, Blair, and Marcia live in.

This triangle is a right triangle.

the opposite is 3, the hypotenuse is 7, and the adjacent side is unknown.

Solving for the adjacent side will give us the distance that Tom and Blair live from each other

a^2 +b^2 = c^2

3^2 + b^2= 7^2

Now we solve for B

7^2 =49

3^3=9

9+b^2=49

Now we subtract

49-9=40

9+40=49

The square root of 40 is 6.3246

Now we check our work

3^2 +6.32^2=7^2

9+ 40 =49

The answer is, tom and Blair live approximately 6.3246 blocks from each other

Hope this helps!

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Answer:

Average: a calculated "central" value of a set of numbers

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How to find it in the average:

Add all of the numbers given, then divide by the number of digits.

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Example:

Question 1. ) Find the average of the digits.

10, 12, 7, 9, 14, 8, 5, 19

Step 1. Add all of the numbers - 70

Step 2. Count how many different numbers there are - 8

Step 3. Take your first answer and your second and divide them

Step 4. 70 ÷ 8 = 8.75 So 8.75 would be the average

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Answer:

see explanation

Step-by-step explanation:

look at the photo

Answer:

A=lw+l(w

2)2+h2+w(l

2)2+h2=30·20+30·(20

2)2+282+20·(30

2)2+282≈2127.25933

Your answer is 2127.259

I think it will help you

If "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.

To find the length of "s" in the rectangular pyramid, we first need to understand the terminology used to describe the different dimensions of a pyramid.

In a rectangular pyramid, "l" usually represents the length of the base, "w" represents the width of the base, and "h" represents the height of the pyramid (the perpendicular distance from the base to the apex or top vertex of the pyramid).

However, there is no standard notation for the length of the slant height (s) in a rectangular pyramid. In this context, the term "s" could represent either the slant height or some other unknown dimension of the pyramid.

If "s" represents the slant height of the pyramid, we can use the Pythagorean theorem to find its value. The slant height, "s," is the hypotenuse of a right triangle formed by one of the triangular faces of the pyramid and the height and half the width of the base.

Using the given dimensions:

l = 30 (length of the base)

w = 20 (width of the base)

h = 28 (height of the pyramid)

Let's find the value of "s" using the Pythagorean theorem:

[tex]s^2 = h^2 + (w/2)^2\\s^2 = 28^2 + (20/2)^2\\s^2 = 28^2 + 10^2\\s^2 = 784 + 100\\s^2 = 884\\[/tex]

Now, take the square root of both sides to find the value of "s":

s ≈ √884

s ≈ 29.75 (rounded to two decimal places)

So, if "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.

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Answer:

3cm

Step-by-step explanation:

V = L * W * H

V = 10 * W * 4

10 * 4 = 40

120 / 40 = 3

W = 3

Answer:

4

Step-by-step explanation:

Find the least common multiple of those two denominators, which would be 2 and 4.

Then do LCM of 2 and 4 and that should be 4.

The required point that could have been one of the points that Tom graphed is (-3,-7) lies in Quadrant III. The correct answer would be an option (A).

A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.

A point that could have been one of the points that Tom graphed is (-3,-7). This is because it lies in Quadrant III of the coordinate grid. In Quadrant III, the x-coordinate is negative and the y-coordinate is negative.

Point A has a negative x-coordinate and a negative y-coordinate, so it satisfies the requirement of being in Quadrant III.

Hence, the correct answer would be option (A).

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Answer:

19

Step-by-step explanation:

(Assuming that each cube is 1 unit), the volume is 5 + 6 + 8 which equals 19

Answer:

m = 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

To find the measure  of m we use the following Euclidian theorem:

m^2 = 5*(5+20)

m^2 = 125 find the root for both sides

m = 5[tex]\sqrt{5}[/tex]

Answer: Range: 24, interquartile range: 8

Step-by-step explanation:

The expected value for the player by participating in the game of the deck of cards is $0.50.

The expected value is the payoff that is expected less the cost of the game.

Expected value =  total benefits of the game - cost

(fraction of face cards x payoff of picking a face card) + 0 - $1

(12/52 x 7) - $1 = $0.50

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Answer:

n=1

Step-by-step explanation:

Still stuck? Get 1-on-1 help from an expert tutor now.

Right now, Scott is 5.
His Aunt Mary is 4*5 = 20

We can solve this algebraically if your teacher requires to.
In x years, Scott will be half as old as his Aunt right now (which is 20).

5+x= 20/2
5+x=10
x=5

In 5 years Scott will be half as old as his aunt was.

Answer:

Height of the triangle = 12 feet

Base of the triangle = 19 feet

Step-by-step explanation:

Let the height of the triangle be x feet

-> Base of the triangle = (x + 7) feet

[tex]A(\triangle)= 114\: ft^2[/tex]

[tex]\because A(\triangle)=\frac{1}{2}(base)(height) [/tex]

[tex]\implies 114=\frac{1}{2}(x+7)(x) [/tex]

[tex]\implies 114\times 2= x^2+7x[/tex]

[tex]\implies 228= x^2+7x[/tex]

[tex]\implies x^2+7x-228=0[/tex]

[tex]\implies x^2+19x-12x-228=0[/tex]

[tex]\implies x(x+19)-12(x+19)=0[/tex]

[tex]\implies (x+19)(x-12)=0[/tex]

[tex]\implies (x+19)=0,\:\:(x-12)=0[/tex]

[tex]\implies x =-19,\:\:x=12[/tex]

x represents the height of the triangle.

-> x can not take negative value.

[tex]\implies x\neq -19[/tex]

[tex]\implies x = 12[/tex]

[tex]\implies x +7= 12+7=19[/tex]

Thus,

Height of the triangle = 12 feet

Base of the triangle = 19 feet

Answer:

Code: AHAN

Step-by-step explanation:

Domain: 0 to 8.

Range: 0 to 18.

0 is A.

H is 8.

N is 18.

We are given the equation of circle (x - 7)² + (y - 3)² = 64² , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-7)^{2}+(y-4)^{2}=(64)^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's use distance formula :

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(x - 1) {}^{2} + (2 - 5) {}^{2} } = 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: {(x - 1) {}^{2} + ( - 3) {}^{2} } = 5 {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 1) {}^{2} + 9 = 25[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 1) {}^{2} = 16[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 1) = 16[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 1) = \pm4[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 5 \: \: or \: \: - 3[/tex]

Answer:

The probability of a correct guess on the first try is 0.024%.

Since a thief steals an atm card and must randomly guess the correct four -digit pin code from a 8 -key keypad, and repetition of digits is allowed, to determine what is the probability of a correct guess on the first try the following calculation must be performed:

8 x 8 x 8 x 8 = X

8 ^ 4 = X

4096 = X

1/4096 = X

0.000244140625 = X

0.000244140625 x 100 = 0.024%

Therefore, the probability of a correct guess on the first try is 0.024%

Step-by-step explanation:

Answer:

10 6/25

Step-by-step explanation:

"three and one fifth" symbolically is 3 1/5 or 3.2 or 16/5.

Then "three and one fifth" of 1 1/2 is:

3.2*3.2 = 10.24 or 10 24/100 or 10 6/25 or 256/25

Step-by-step explanation:

the area is the sum of the top square of 9×9 and the bottom parallelogram.

we know the length of the parallelogram is still also the square side length : 9ft.

but we don't need to bother about the lengths of the inclined sides, as the area of a parallelogram is

baseline × height

and the height we can see on the right hand side, as the height of the total shape is 14ft. given that the square side length is 9ft, that leaves us with 14-9 = 5ft as the height of the parallelogram.

so, the area of the square is

9×9 = 81 ft²

the area of the parallelogram is

9×5 = 45 ft²

the total area is then

81 + 45 = 126 ft²

Answer:

  (b)  0.3 microns or larger

Step-by-step explanation:

A particle of size 0.3 microns is judged to be the most penetrating particle size. So, a rating for the filtering of those particles will be a worst-case rating. For particles of any other size, the filter will perform better than for 0.3 micron particles. HEPA filters are rated based on their performance with particles ...

  0.3 microns or larger